HETEROGENEOUS PLASTIC DEFORMATION
 
 
By
 
Songyang Han
 
 
 
 
 
 
 
 
 
A DISSERTATION
 
 
Submitted to
 
Michigan State University
 
in partial fulfillment of the 
requirements
 
for the degree of
 
 
Materials Science and Engineering 

 
Doctor of Philosophy
 
 
2020 
 
 
 
 
ABSTRACT
 

HETEROGENEOUS PLASTIC DEF
ORMATION
 
 
By
 
 
Songyang Han
 
 

-
titanium, 
because the hexagonal crystal structure makes it more prone to polycrystalline compatibility 
issues.  At the dislocation scale, this compatibility involves the process of ho
w dislocations 
being initiated, propagating through grains, and the ability of grain boundaries accommodating 
dislocation shear in one grain with shear in its neighboring grain.  To characterize the 
development of plasticity in a polycrystalline array due 
to dislocation nucleation, and slip across 
grains and grain boundaries, electron channeling contrast imaging (ECCI) based analysis is used, 
since this special scanning electron microscopy (SEM) technique possesses variety observation 
scopes, providing a li
nkage between the macro
-
 
and the micro
-
 
world.  
 
The first study presented a robust comparison between several techniques for the very 
first time:  the digital image correlation (DIC), atomic force microscope (AFM), ECCI, and EBSD 
(cross
-
correlation).  In 
this study, a Ti7Al alloy was deformed to 3% plastic tensile strain.  The 
plasticity evolution of the sample was assessed through BESD
-
slip trace analysis, digital image 
correlation, and ECCI contrast analysis.  The comparison between different methods rev
ealed 
ECCI as a powerful technique in slip system identifications.       
 
The second project was more focused on the interactions between slip systems around 
the grain boundary area.  The geometry of slip planes and grain boundaries was assessed as a 
funct
ion of depth, allowing the analysis of slip transfer parameters, including the geometric 
 
 

slip planes.  Locally accommodation behavior at the grain boundaries w
ere revealed by ECCI.
 
The third project was the identification of the propagation direction of a slip system 
across a polycrystalline grain patch by ECCI.  Analysis indicated that slip bands would likely to 
become broader as they propagated further into th
e grain from the nucleation points, possibly 
due to cross
-
slipping.  Together with the trace analysis, a better understanding of the 
development of plasticity within polycrystals during heterogeneous deformation was achieved.
 
The highlight of this work not
 
only focusing on the infinitesimal change in the local 
lattice structure in terms of dislocation nucleation and propagation in a grain, but also involves 
the plasticity development of deformation in a macroscopic view, such as the mechanism of 
dislocation
 
across grain boundaries, and the estimation of overall deformation behavior within 
a region of grains.  More importantly, together with other powerful characterization methods, 
ECCI in this study shows a strong potential that successfully links the macros
copic deformation 
with dislocation movement during the deformation.
 
 
iv
 
 
To my wife Dongqing Tao and daughter Freya Han.  Thank you for your love and supports. 
v
 
 
ACKNOWLEDGEMENTS
 
 
First and foremost, I would like to gratefully acknowledge my advisor, Dr. Martin Crimp.  
Over the numerous conversations of research ideas, 
paper discussions, and even non
-
academic 
topics, I continuously sharpen my writing skills, being more diligent as a researcher, and 
becoming more confident and expressive as an overall person.  These improvements are mostly 
relied on his wisdom, patience, 
and the confidence in me.  It will be an honorable memory as a 
graduate student of his.
 
 
I also give my thanks to the committee members, Professor Philip Eisenlohr, Professor 
Carl Boehlert, and Professor Thomas Pence, for their enlightening discussions.
 
 
T

(Jason), Harsha Phukan, Mingming Wang for helping me in the research.  I also want to thank 
Dr. Per Askeland on training the scanning electron microscope and teaching me th
e 
maintenance of microscope.     
 
Many thanks go to Dr. Christopher Cowen, formerly at National Energy Technology 
Laboratory, Albany OR, for supplying the titanium studied in this work.  Acknowledgements also 
go to Professor Samantha Daly, and Dr. Zhe Chen
, at University of California Santa Barbara, for 
the DIC support, and Professor David Fullwood, at Brigham Young University, for the CC
-
EBSD 
support.
 
Finally, the research is supported by the United States Department of Energy, Office of 
Basic Energy Scien
ce Division, through grant number DE
-
SC0001525 and DE
-
FG02
-
09ER46637.  
 
 
vi
 
 
TABLE OF CONTENTS
 
 

 

 




x
 
1.
 

 
   
1.1.
 

 
    
1.1.1.
 

 
    
1.1.2.
 

 
    
1.1.3.
 

 
    
1.1.4.
 

 
   
1.2.
 
Int

 
    
1.2.1.
 

 
    
1.2.2.
 

 
    
1.2.3.
 
Electron 

 
    
1.2.4.
 

 
    
1.2.5.
 

 
    
1.2.6.
 
Free surfacing biasing and
 
limitation of surface
-

 
    
1.2.7.
 

 
   
1.3.
 

 
2.
 


 
37
 
   
2.1.
 

 
   
2.2.
 

 
    
2.2.1.
 
Deformation of Ti
-

 
    
2.2.2.
 
Deformation 

40
 
   
2.3.
 

 
    
2.3.1.
 

 
    
2.3.2.
 


 
    
2.3.3.
 
HR
-

 
3.
 

 
   
3.1.
 
The overall status of as deformed samples 1
-

 
   
3.2.
 
Slip system 

7
 
    
3.2.1.
 

 
    
3.2.2.
 

 
   
3.3.
 
The comparisons of 
surface
-

 
    
3.3.1.
 

 
    
3.3.2.
 

 
vii
 
 
    
3.3.3.
 
Comparison between the 

 
    
3.3.4.
 

 
   
3.4.
 

3
 
    
3.4.1.
 
Categories of slip sy

 
    
3.4.2.
 

 
    
3.4.3.
 

 
    
3.4.4.
 
Comparison of slip 

 
    
3.4.5.
 

 
    
3.4.6.
 

 
   
3.5.
 
The direction of sl

 
    
3.5.1.
 

7
 
    
3.5.2.
 
Comprehensive analysis of deformation within grain 1
-

 
    
3.5.3.
 
Conclusions 

 
4.
 

 
5.
 

 
APPENDICES 

01
 
  


. 102
 
  
APPENDIX B: Removal of polymer film and gold nanoparticles (AuNPs) for DIC patterning
.
106
 
  
APPENDIX C: Strain meas
urement after four
-

 
  
APPENDIX D: The calibration of MIAR III FEG
-
SEM with SACPs module for ECCI and CC
-
EBSD
 
                          
  

 
  
APPENDIX E: Procedures of EC

 
  

 
  

 
  
APPENDIX H: Calculation of the 

 

 
149
 
 
BIBL
I
OGRAPHY
 

 
 
viii
 
 
LIST OF TABLES
 
 
Table 1
. 
Slip systems 
identified by EBSD slip trace analysis, ECCI, and AFM/DIC
 

 
Table A1.  Electropolishing parameters
 

 
 
ix
 
 
LIST OF FIGURES
 
 
Figure 1 Top two crystals present the major slip systems activated during deformation, namel
y:  
(Top left) prism <a> slip system on {




} prismatic plane, basal <a> slip system on {0001} basal 
plane, and pyramidal <a> slip system on {




} pyramidal plane with <




> Burgers vector;  
(Top right) type I <c + a> slip system on {



} pyramidal pla
ne, and type II <c + a> on {





} 
pyramidal plane.  Bottom two crystals show the geometry of two tensile twinning (labeled in 
blue and yellow) and two compression twinning (labeled in purple and dark green), which is not 
readily observed in room temperatur
e deformation and not the interest of this study

 
 
Figure 2a) Sketch of a pure tilt boundary, indicating two crystals are rotated by angle 

tilt
 
about 
a rotation axis lying on the grain boundary plane.  b) A pure twist boundary is formed, which 
looks like a single crystal is twisted into half along a rotation axis lying perpendicular to the grain 
boundary with misorientation angle 

twist
.  c) Sket
ch of 

 
boundary, formed by a 36.9
o
 
rotation 
between two same lattices about a common [001] axis.  In this picture, the atom A and B in grain 
1 are represented by circles with no fill, while the same atom in grain 2 are pattern filled circles, 
and the gr
ain boundary lattice area is limited by the dotted square.  After carefully counting, it 
can be found that every 2 out of 10 atoms are sharing the same lattice position.  It is noticeable 
that 

 
value may different about different rotation axis. 
 
(
A
mended 
from [57, 65])
 

 
 
Figure 3a) Direct transfer of dislocation across grain boundary.  b) Direct slip transfer with 
residual dislocations at the grain boundary. 
 
 
c) Absorption of dislocation slip and dissipated 
along grain boundary.  d) indirect slip
 
transfer by absorption and re
-
emission, leaving grain 
boundary dislocations.  e) Absorption and reflection of dislocations slip with residual grain 
boundary dislocations.  f) Complicated mechanism, involving both slip transfer and reflection 
with the form
ation of grain boundary dislocations

  
 
 
Figure 4 As crystal A with known lattice orientation is continuously deformed, a known type 
dislocation slip (blue) is piling up at the grain boundary, where dislocation slip (red) will 
be 
activated in crystal B due to stress build
-
up as it deformed with crystal A.  During the slip transfer, 
tangential continuity constrain is required that requires the strain component induced by 
dislocations in crystal A be fully balanced in crystal B to
 
maintain grain boundary integrity. 
 
(Amended from [80])
 

  
 
 
Figure 5 A sketch of the geometry of slip planes intersecting at a grain boundary plane.  
b
, 
t
, 
n
, 
are the Burgers vector, the intersection line direc
tion of the slip plane in the grain boundary 
plane, and the slip plane normal that are used in the various slip transmission criterion [80, 81, 

grain, and slip 


 
 
Figure 6a) The simplified mechanism of the formation of electron backscatter patterns (EBSPs).  

x
 
 
incident beam.  b) A Kikuchi map is formed by collecting a
ll the backscatter signals coming out of 
different planes on the phosphor screen.  c) With each zone axis identified and labeled, one is 
able to know the crystal orientation of the scanned grain.  This is extremely useful in the 
predication of slip systems
 
during plastic deformation. 
 
(Amended from [107])
 

 
 
Figure 7  Sketched mechanism of 
g
 

 
b
 
= 0 and 
g
 

 
b
 
x 
u
 
= 0 invisibility criteria in the determination 
of dislocation Burgers vector.  The dislocations will go completely out of contrast or show low 
contrast when the dislocation plane lies parallel to the channeling direction, because the it is 
where almost al
l electrons diffracting between planes in the same way, leaving no intensity 
differences between distorted region and perfect lattice.  On the contrary, larger value of 
g
 

 
b 
suggests more intensity variation around the distorted region, revealing dislocat
ions in better 
contrast. 
 
(Amended from [124])
 

 
 
Figure 8a) An example of ECPs collected from a p
-
type boron doped synthetic diamond single 
crystal with close to [110] crystal orientation in low mag BSE mode (~ 20x).  
The band in the 
upper left corner with bright and dark contrast is one of the Kikuchi band formed during incident 

attached on the surface.  b) An example of EBSPs
 
collected among one of the grains from a 
commercially pure titanium sample in this research (sample 2).  The image was taken at a working 
distance of 24 mm, a 30 kV accelerating voltage and a 184 µA probe current, with sample tilted 
at 70
o
.  The edges of 
Kikuchi bands are significantly sharper than that of ECPs.  c) An example of 
SACPs collected from the same target with b) using the same voltage and current, but the 
working distance is around 9mm within 10
o
 
tilt.  SACPs provide much accurate information w
here 
the closest zone axis the crystal is orientated.  With more sharp edges on the channeling bands 
and higher special resolution, SACPs fits ECCI analysis more than the other two options

  
 
 
Figure 9 Schematic mechanism on the formation of ECPs (A
mended from [146]), with the incident 
beam sweeping angle large enough, intensity of BSE signal changes significantly around the 

 

 
 
Figure 10a
-
c) Mechanism of the formatio
n of SACPs. As beam trajectory changes or beam rocking 
around a certain point, the lattice channel become open and close with respect to the directions 
of the incoming electrons, providing different yield of backscatter electron 

.  The signal profile 
is c
ollected and create a SCAPs on the detector.  For a channeling condition that allows the most 
electrons channeling into the perfect crystal and leave an overall dark background, lattice 
distortion around a dislocation will make more backscatter electrons c
ollected by the BSE 
detector.  Dislocations will be resolved.  d) An example of dislocations (bright) from the dark 
background.
 

 
 
Figure 11 An example of the change of channeling contrast with respect to the
 
deviation 
parameter 
s
, which s = 0 indicates the optical axis is exactly at the edge of the channeling band.  
With optical axis move into or away from s = 0, signal intensity will change dramatically.  As the 
lattice is no longer aligned symmetrically tow
ards the incident beam due to dislocation distortion, 
xi
 
 
contrast will occur with bright/dark contrast around a dislocation compared to the overall grey 
background.  (Amended from [152])
 

 
 
Figure 12a) Overall mechanism of D
IC.  The surface is coated with evenly deposition of 
nanoparticles, with fiducial marks.  The reference image is the upper right square area labeled 
with four fiducial marks, with a reference point P (x,y).  During deformation, arbitrary shape 
change and r


to surface topography, the absolute height difference (Z) is recognize
d by the laser reflection on 
the position sensitive detector and recorded upon each position (X) from the starting point.  
After scanning the whole area line by line, a 3
-
D topographic map can be created by correlating 
height profile (Z) with the plane pro
file (X,Y).
 

 
 
Figure 13 The overall mechanism of the slip trace analysis.  The hexagonal cell presents the 
crystal orientation, and the red line is the intersection line between the slip plane (grey) and the 
sample surface (b
lue).  With the profile of each trace (1~12) at the surface, possible slip system 
can be identified.
 

  
 
 
Figure 14a) The dimension of the Ti
-
7Al dog
-
bone tensile sample 1.  b) The dimension of the CP 
Ti bending 
sample 2 & 3.
 

 
 
Figure 15 Sketch of the electropolishing stage.  Based on what type of electrolyte is used, the 
voltage, temperature while electropolishing, the distance between cathode (stainless steel) and 
sampl
e (anode), and the agitating speed of the stir bar will be different and recorded in 
Appendix 
A
. 

 
 
Figure 16a1) The SE image from the center of the 3% tensile strained Ti
-
7Al sample 1, with the 
tensil
e direction along A2 axis.  Almost all grains were deformed, with some grains having more 
than one type of slip traces.  Surface and grain boundary elevation could be indicated by the 
brighter contrast against the dark grains.  a2) The corresponding EBSD d
ata in the red region of 
a1, which was collected under the same coordinate system as a1.  Despite the noises due to 
higher deformation strain that disrupts the diffraction (with confident index only 0.65), color 
gradient within grains can be clearly seen, 
especially where slip bands were densely packed.  Slip 
traces appear mostly straight, while some curved traces were found near grain boundaries or in 
the grains which were heavily deformed.  b1) An example of one of the grain boundaries between 
two neighbo
ring grains in the center area of sample 2 after 1.5% deformation on four
-
point
-
bending stage.  Again, most slip traces appear straight, while the bright and dark contrast on the 
slip traces may indicate they may not share the same Burgers vector.  Despite
 
some primary slip 
traces that were fully propagated across the grains, some of the slip traces disappear as they 
propagated out of the grain boundary.  b2) The corresponding EBSD map of the red area of b1, 
indicating the formation of slip bands was not si
gnificant enough to affect the quality of the 
EBSD, with a high confident index of 0.81, and the topography developed during deformation 
was not big enough to be shown in the EBSD compared to a2.  c1) SE image of a patch of 4 
consecutive grains in the cent
er of sample 3, which was deformed in the same manner with 
xii
 
 
sample 2 to 1% plastic strain.  Slip traces in grains 2
-
4 appear straight while traces in grain 1 are 
wavy.  Some traces disappear near the grain boundary in grain 2, which is indicated by the whit
e 
arrow.  Traces in grains 1 and 2 meet at the same point on the grain boundary, so are the traces 
in grains 3 and 4, while traces in grains 2 and 3 do not meet at the same point on the grain 
boundary.  c2) EBSD map of the grain patch in c1.  The deformati
on is not large enough for EBSD 
to recognize the formation of slip bands at 1% strain level.  No crystal rotation is detected.  It 
should be noted that all the prism cells in a2, b2, and c2 indicate the crystal orientations of the 
grains they were located,
 
with the black dots indicating the optical axis.
 



 
4
4
 
 
Figure 17a) BSE image of grain 2 in sample 1.  Two straight and planar slip traces can be clearly 
observed, with their trace outlined as black lines.  The hexagonal cells on the right indi
cate the 
orientation of this grain.  The shaded plane in each cell indicates the slip plane, the blue line 
indicates the slip direction, and the red dashed line is the plane trace on the sample surface.  For 
a potential slip system active during deformatio
n, the red dashed line should match the trace on 
the surface.  b) BSE image of a patch of grains 1~3.  Some slip systems with different Burgers 
vectors or slip planes may exhibit similar slip traces at the surface, resulting in uncertainties.  The 
colored 
dashed lines in each grain represent the possible slip systems that leave similar slip 
traces.  The Burgers vectors and slip planes of all possible slip systems are listed on the right.  
The color of the slip system is using the same color with the dashed 
line.
 

 
 
 
Figure 18a) BSE image of one of the areas of interest after deformation of sample 1.  b
-
f) ECC 
images taken at different channeling conditions from the red boxed area.  The upper left circles 
are the Kikuchi patterns.  Each black ar
row across a Kikuchi band indicates the specific channeling 
band, and the arrowhead is where the optic axis is focused.  Each channeling condition is 
identified from the T. O. C. A software.  The Burgers vectors of dislocations are identified by 
g
 
.
 
b
 
= 0 
 
and 
g
 
.
 
b 
x 
u
 
= 0  contrast analysis, and the slip plane can be revealed through different tilting 
and rotating along a certain channeling band (
Appendix E
).  A total of four different slip systems 
are identified and labeled by colored arrows, namely:  (01


0)[2




0] pri
sm <a> slip system (green), 
(10


0)[1


10] prism <a> slip system (blue), (10


1)[1


10] pyramidal <a> slip system (purple), and 
(0001)[11


0] basal <a> slip system (red).  Amended from [185]
 

 
 
Figure 19a) SE image of the upper right corner o
f grain 2 in Ti
-
7Al sample 1.  b) AFM color
-
scale 
map from the black boxed area in figure a).  The black line is the AFM line profile showing the 
topography change across the line.  The black arrows indicate the edges of slip bands, and the 
dashed line ind
icates the undistorted surface plane and is the basis of the height measurement.  
c) 3
-
D Greyscale topography map around the line sectioned area, the surface normal is calculated 
based on undistorted surface, H is the step of the slip band.  d
) 
A sketch of
 
the mechanism to 
calculate the local shear distribution across the slip bands.  The Burgers vector 
b
 
and slip plane 
normal 
n
 
can be directly achieved from the EBSD data once the slip system is confirmed by ECCI 
contrast analysis.  Height difference across
 
a slip band H can be directly measured from the AFM 
line profile.  The distance across a slip band X is 0.3 µm in this study.
  
(Amended from [185]) 
.. 53
  
 
 
Figure 20a) color
-
scale AFM map from an area in grain 2.  b) The heat map of local shear 
distribution across individual slip bands.   The local shear contributed by the (01


0)[2




0] prism 
xiii
 
 
<a> slip system ranges from 0.3 to 0.7, and the shear caused by the (10


0)[1


10] prism <a> slip 
system ranges from 0.08 to 0.15.  c) The relative shear distr
ibution map of the same area 
calculated by the DIC method [185].
 

  
 
 
Figure 21a) ECC image of the same area with Figure 20.  Besides the (01


0)[2




0] (green) and 
(10


0)[1


10] (blue) two prism <a> slip systems identified 
in the slip trace analysis, (0001) [11


0] 
(red) basal <a> dislocations are revealed by the contrast analysis.  The prism <a> type dislocations 
appear to align perfectly along the slip bands, while the basal <a> dislocations are less uniformly 
distributed a
cross the observed area.  b) The GND logarithm map of the red boxed area of a).  
The GND map is consistent with ECCI observation, although individual dislocations cannot be 
resolved as good as the ECCI observation.  c) The ECC image at the grain boundary o
f grain 2, 
with (01


0)[2




0] (green) and (0001) [11


0] (red) dislocations.  Prism <a> dislocations align 
close to the slip bands and basal <a> dislocations are more randomly distributed across the 
surface.  d) The GND map from the red box area of c).  The 
GND on the other side of the grain 
boundary is not available due to misorientation angle exceeding the threshold from the reference 
point in grain 2.  The GND map is consistent with ECCI observation.
 

 
 
Figure 22a) AFM color
-
scale topograp
hy map at the upper right corner of the grain 1 in sample 
1.  Two different deformation shear system can be observed by the AFM.  b) ECC image of the 
same area, two slip systems were identified through the EBSD
-
based slip trace analysis, which 
are the (0


1
0)[2




0] prism <a> slip system (blue) and the (


100)[11


0] prism <a> slip system 
(red).  The slip trace marked in light brown cannot be identified by the slip trace analysis.  c) High 
magnification ECC image of the red box area in b).  Contrast analysis sh
ows several additional 
dislocations, including  (10


1)[1


10] and (


011)[1


10] two pyramidal <a> slip systems and a 
mixture of basal <a> dislocations with majority belong to (0001)[1


10] slip system.  The unknown 
branched slip trace is caused by the (


011)[1


10] pyramidal <a> slip system.
 

 
 
Figure 23a
-

-

same points on the grain boundary at surface in sample 2.  It appears that slip traces that area 
far from para

-

-

-

in sample 2.  The slip traces do not intersect at the same point on the grain boundary at surface, 
despite the slip system is highly activated.  h
-


The strong activation of slip systems that propagate up to the grain boundary only occurs in one 
of the grains, with the other grain undeformed.  At certain circumstances, the unresolved shear 

 
activate new slip systems that are travelling back into the 
originated grain.
 

  
 
 
Figure 24a) 3
-
D geometry of slip system interactions at a grain boundary.  The two slip systems 
are considered as well
-
correlated 
slip systems since they intersect at the same point at the grain 
boundary on the free surface.  Although slip systems intersect at the same black point at the 
surface, it can be clearly seen that they do not meet below the surface since the geometric 
orien
tations of the two slip systems are different, with 

 

o
.  b) Another 3
-
D geometry of slip 
bands interactions in the vicinity of a grain boundary.  The two slip systems are defined as non
-
correlated since they do not meet at the surface.  However, they m
ay meet at the grain boundary 
xiv
 
 
plane somewhere below the surface.  Although the slip transfer mechanism may be different 
between a) and b), current studies of slip transfer ignore this potential difference and directly 
use the slip transfer criteria to eval
uate the strain accommodating events at the grain 
boundary. 

 
 
Figure 25a) SE image showing two slip traces that are well
-
correlated at the surface.  The despite 
a large angle between the slip traces, they 
intersect at the same points on a grain boundary.  
ECCI facilitated slip trace analysis indicates the slip system in the upper grain is the (0


10)[


110] 
prismatic <a> slip system with the Schmid factor 0.48.   The slip system in the lower grain is 
(10


0)[


2


0] prismatic <a> slip system, with a lower Schmid factor of 0.36.  The white arrows 
mark one of the well
-
correlated slip traces for comparison. b) ECC image of the same region, but 
5 µm below the surface.  The observed slip bands are now due to dislocati
on contrast, rather 
than topography.  It can be clearly seen that the slip bands are misaligned in the electropolished 
area, which is indicated by the relative position change of the white arrows.  Nevertheless, the 
relative spacing and distributions of th
e slip bands remains unchanged.  c) high magnification 
ECC image of the area in the red boxed area in figure (b).   It shows the activation of (


011)[


2


0] 
pyramidal <a> secondary slip systems (M =0.45) in the lower grain from an intersection point of 
the 
slip system form the upper grain at the grain boundary. The secondary slip system propagates 
a short distance and appears to merge into the primary slip system in the lower grain.  There 
might be multiple activation of such secondary slip system, possibly 
from different sources at 
different depth in the grain boundary plane, which is indicated by the small arrows. 

 
 


slip bands in the lower grain at the grain boundary.  The 
red dashed tangent line represents the trace of the grain boundary at the intersection point with 

through el
ectropolishing.  The grain boundary orientation is significantly changed, which is 
indicated by the change of the red dashed tangent line around the same strongest activated slip 
band.  The slip band spacings and relative distributions remain the same befo
re and after surface 
removal.  c) Higher magnification ECC image of red tangent line area.  A ~50 nm misalignment 
between the two slip systems below the surface has been observed.  d) ECC image of the red 
boxed area in figure (c).  A small number of second
ary slip system is observed in the upper grain 
in this case.
 

 
 
Figure 27a) SE image of non
-
correlated slip systems on the surface.  The small white arrows 
indicate the relative positions of the selected sli
p bands on the surface.  It can be clearly seen 
that these slip bands do not intersect at the same point on the grain boundary.  b) ECC image of 
the same region below the surface.  The relative spacing and distributions of the slip lines remain 
unchanged w
ithin either grain, but the relative intersection points on the grain boundary changes, 
as indicated by the small white arrows.  c) ECC image of the grain boundary area in the red box.  
Pyramidal <a> secondary slip system is activated from the intersection
 
points of the incoming 
prism <a> slip system in the upper grain at the grain boundary.  d) ECC image of the grain 
boundary area in the blue box.  Secondary pyramidal <a> slip system is activated to accommodate 
the strain induced by the prism <a> slip syst
em in the lower grain.
 

 
xv
 
 
 
Figure 28a) SE image of the third interaction type.  The slip system appears to be blocked by the 
grain boundary and no active slip system is observed in the lower grain. b) ECC image in the red 
boxed area.  A nu
mber of dislocations within a limited zone is observed, with majority belong to 
the basal plane, and some on the pyramidal plane.
 

7
 
 
Figure 29 Comprehensive analysis of slip transfer parameters between well
-
correlated slip (top 
1
0 lines), non
-

of the angles 

 
between incoming primary and outgoing primary (black)/ secondary (red) slip 
system intersection lines at the grain boundary plane, and the g

between the incoming primary and outgoing primary (black)/ secondary (red) slip systems.  b) 
Comparison of the global Schmid factors M of the outgoing primary (black)/ secondary (red) slip 

rs vectors of incoming and outgoing slip systems, and angle 


same 
Burgers vectors.  Schmid factors for the outgoing primary slip systems are shown in italics 
in the cases where there is no correlated slip observed between the incoming primary and 

ases because only 
limited slip was observed in the outgoing grains in the vicinity of the primary incoming slip 
systems.  The fine dotted line between the non
-

indicates the similarity in the accommodating beh
avior.
 

  
 
 

slip systems, b) the angles 

 
between the various outgoing slip systems and the incoming primary 
slip system, and c) glob
al Schmid factors M of the outgoing slip systems. 

 
 
Figure 31a) SE image of grains 1
-
3 in the as
-
deformed sample 3.  The slip systems are identified 
by the ECCI facilitated slip trace analysis, which are marked by dash lines in different col
ors and 
labelled in different colored fonts.  It appears the slip lines in grain 2 and 3 are not well
-
correlated.  
The slip systems in grain 1 appear to meet the slip systems in grain 2 at the boundary, while the 
slip propagation in grain 1 is difficult. b
) General BSE image of the same grains 1
-
3 in the 
electropolished sample 3.  All the slip traces are removed by the electropolishing and no clear 
contrast is seen because the sample is not under a channeling condition.  c) One example of ECCI 
analysis on t
he electropolished surface.  At g = [1



], the slip line contrasts are distinct.  These 
contrasts come from dislocation contrasts rather than topography.  d
-
i) High Mag ECC images 
taken from the red boxed area in grain 3 for the Burgers vector identificat
ion.  The Burgers vector 
is [1


10].  With the information from the slip trace analysis, the slip system that is active in grain 
3 is (10


0)[1


10] prism <a> slip system.  ECCI identification of slip system in grain 1 and 2 can be 
found in the 
Appendix F
, fo
llowing the same approach.
 

6
 
 
Figure 32a) electropolished surface of grain 3. b
-
f) ECC images taken at the same channeling 
condition at different positions along a slip line.  Dislocations are limited in a sharp and narrow 
line 
from the nucleation point at the grain boundary with grain 2, and spreading out as going 
deeper into the grain and will finally distributed around the grain boundary with grain 4.
 

 
xvi
 
 
 
Figure 33a) Low mag ECC image of grain 3, the four arrows indicate th
e slip transfer directions of 
slip bands with strong ECC contrast.  The dashed arrow indicates the opposite transfer direction 

-
f) ECC images following 
the slip band from the boundar
y with grain 4 into grain interior.  Overall dislocation density is 
low compared with the case in Figure 31.  As the slip band broadening effect further dilutes the 
dislocation concentration, the dislocation contrast of the slip band is hardly detectable. 

 
 
Figure 34a) A wide spread of dislocations in grain 1 from where a dislocation slip in grain 2 is 
nucleated at the grain boundary.  b) Wide spread of dislocations in grain 1 interior.  c) a sharp 
slip band is nucleated from the boundary in 
grain 2.  d) The slip band is wider in grain interior 
than it is at the grain boundary.  e) Intersection of dislocation slip at the grain boundary with 
grain 3, slip systems in grain 2 and 3 are not correlated.  Dislocation density is high in grain 2.  F) 
Accommodating dislocations nucleate from the intersection point of a slip system in grain 3, and 
propagate only a short distance with significant broadening effect.
 

3
   
 
 
Figure 35 Deformation slip in the lower grain interacting with the d
eformation twin in the upper 
grain.  ECCI analysis in the red boxed area shows the dislocation propagating out of the tip of the 
deformation twin.
 

 
 
Figure A1 A scheme shows the general four stages of electropol
ishing with respect to different 
voltage and current density ratio.
 

 
 
Figure A2 Left) Below 29 V results in etching of metal with rough surface under optical & electron 
microscope.  Middle) A good polishing zone result
s in shinning & smooth surface with good 
contrast under electron microscope.  Right) Above 40 V results in a dimmer surface in optical 
microscope. Under electron microscope, pitting occurs, especially at grain boundaries, with 
slightly worse SACPs.
 


 
 
Figure A3 Calculation of the surface removal by the Vickers indent.  Several Vickers indents are 
placed at the surface before electropolishing and final result is the average of each calculated 
one.
 


 
 
Figure A4a1) Surface condition of as received sample.  a2) SE image of AuNPs taken at high 
magnification from the red box, with weak SACPs due to interference.  b1) Surface condition 
after 1 hour at 30 
o
C, showing rem
oval of majority patterning material.  b2) SE image showing 
one of the unremoved clusters of AuNPs, with sharp SACPs. Particles in these areas are the 
focused point during DIC data acquisition.  Long time exposure of beam may condense the NPs 
into the mate
rial or strengthen the bonding interaction, with detailed mechanism unknown.  The 
patterns c1) At 4
th
 
hour, all nanoparticles are consumed, including the clusters.  c2) SE image of 
the same area with b2, showing clean sample, with sharp slip traces and gra
in boundaries.  d1) 
24
-
hour reaction time of an undeformed control sample 1, showing the slightly etching of 
material.  d2) SE image of the etched area in the red box, showing line type etched marks and 
small etched cavities.  e1) Surface condition of an u
ndeformed control sample 2 after the 3
rd
 
xvii
 
 
hour in solution at 50 
o
C, also showing large areas being etched.  e2) SE image of the red box 
area, showing surface material has been etched away.
 

 
 
Figure A5a) SE image of a random area, sho
wing clear slip traces on surface after the uncoating.  
b) 2
-
D AFM map showing topographic information of the same area.  c) 3
-
D AFM map showing 
clear steps from the slip band and the grain boundary (concaved). 

 
 
Figure A6 Left) The dist
ance between triple points before deformation.  Right) The distance 
between same triple points after deformation.
 

 
 
Figure A7 Secondary electron (SE) images taken at the field of view of 3.86 µm that shows:  a) 
The particle is
 
out of focus.  b) The dirt is in focus, but astigmatic.  c) The dirt is stigmatic and in 
perfect focus.
 

 
 
Figure A8a) SE image in resolution mode (field of view 3.86 µm) that shows the optic axis (black 
cross
) is on a particle.  b) SE image in field mode (field of view 65.3 µm) that shows the deviation 
of optical axis from the resolution mode.  Although it appears blurry, this particle is already in 
focus in field mode since the resolution between modes is dif
ferent.  c) SE image in field mode 
that shows the optical axis is moved back to the same position after aperture alignment after 

 

 
 
Figure A9a) An asymmetric SACP aperture with overlapping of p
atterns from surrounding grains.  
b) A symmetric, perfect round aperture with interference signals from surrounding grains.  c) A 
perfect circular aperture within pattern only from the target grain.
 

 
 
Figure A10a) ECC image taken at s <0
, the contrast of dislocations in the lower grain is not perfect.  
b) ECC image taken at s = 0, a crisp image of sharp dislocations in perfect contrast.  c) ECC image 
taken at s > 0, the dislocations in the same area are badly resolved with poor contrast.
 

 
 
 
Figure A11a) The dislocation tails are in weak contrast, as indicated by the small black arrows 
while some other dislocation tails are in strong contrast, as indicated by the small white arrows 
when ECCI is taken close to the upper zone axis.   b
) The dislocations indicated by the small black 
arrow are in strong contrast, on the contrary, the tails marker by the small white arrows are in 
weak contrast when the optic axis moves closer to the lower zone axis.
 

 
 
Figure A12 The interface
 
of T. O. C. A. software shows 3 components in the simulation display, 
including the simulated patterns shown on the left pop
-
up window, the corresponding pole 
figure shown on the upper
-
right window, and the crystal orientation shown on the bottom
-
right 
wi
ndow.  The most useful parameters input in the control panel are listed as: 1. The Euler angle; 
2. The 90
o
 
rotation; 3. The acceleration voltage at which ECCI is taken; 4. The magnification at 
which ECCI is taken.
 

122
 
 
Figure A13 Left) Simulated channeling patterns with these bands labeled.  Right) The real patterns 
collected from channeling mode in MIRA III SEM, with the optic axis labeled as black cross.
 

 
xviii
 
 
 
Figure A14a) 
G
rain 1 as deformed.  b) 
G
rain 1 after electropolishing.  c
-
h) ECC images from the 
red box area taken at different 
g
 
vectors, dislocations are (1



)[11


0] and (1



)[11


0].
 

 
 
Figure A15a) Grain 2 as deformed.  b) Grain 2 after electropolishing.  c
-
h) ECC images from the 
red box area taken at different 
g
 
vectors.  Dislocations are (1



)[11


0].
 

 
 
Figure A16a) Grain 3 as deformed.  b) Grain 3 after electropolishing
.  c
-
h) ECC images from the 
rex boxed area at different channeling conditions.  Dislocations are (10


0)[1


10].
 

 
 
Figure A17a) Grain 4 as deformed.  b) Grain 4 after electropolishing.  c
-
h) Dislocations at the 
boxed area (grain boundary between gr
ains 3 and 4) taken at different channeling conditions.  
Dislocations are majority (10


0)[


2


0]. 
 

 
 
Figure A18 One example of dislocations identification in sample 2 after electropolishing.  a) ECC 
image of slip traces aft
er electropolishing.  The contrast is not due to topography but from the 
contrast of dislocations.  b
-
f) Dislocations taken at different 
g
 
vector.  Dislocations are (10


0) 
[


2


0].
 

 
 
Figure A19 One exampl
e of dislocations identification in sample 2 after electropolishing on the 
other side of the grain.  Dislocations are (01


0) [


110].
 

 
 
Figure A20 Neighboring grains in Sample 2.  First six ECC images) Identified dislocations are 
(1


00)[11


0].  Second six ECC images) Identified dislocations are (1


00)[11


0] and 
(1


01)[11


0].
 

 
 
Figure A21 Neighboring grains in Sample 2.  First six) Identified dislocations are (1


00)[




20] and 
(


101)[11


0
].  Second six) Identified dislocations are (1


00)[




20] and (1


01)[11


0].
 

 
  
 
Figure A22 Neighboring grains in Sample 2.  First six) Identified dislocations are (10


0)[





0] 
and (


011)[1


10].  Second six) Identified dislocations are (0


10)[2




0] 
and (01


1)[


110].
 

  
 
 
Figure A23 Neighboring grains in Sample 2.  First six) Identified dislocations are (10


0)[





0] 
and (


011)[1


10].  Second six) Identified dislocations are (0


10)[2




0].
 

 
 
 
Figure A24 Neighboring grains in Sample 2
.  First six) Identified dislocations are (10


0)[





0] 
and (


011)[1


10].  Second six) Identified dislocations are (0001)[




20]. 
 

 
 
Figure A25 Neighboring grains in Sample 2.  First six) Identified dislocations are (1


00)[




20] and 
(1


01)[11


0].  Second six) Identified dislocations are (



00)[




20].
 

 
 
Figure A26 Neighboring grains in Sample 2.  First six) Identified dislocations are (0


10)[


110].  
Second six) Identified dislocations are (



0)[





0]. 

 
xix
 
 
 
Figure A27 Neighboring grains in Sample 2.  First six) Identified dislocations are (1


00)[11


0].  
Second six) Identified dislocations are (



0)[





0]. 

 
 
Figure A28 Neighboring grains in Sample 2.  Fi
rst six) Identified dislocations are (1


00)[11


0] 
and(1


01)[11


0].  Second six) Identified dislocations are (



0)[





0].
 

 
 
Figure A29 Neighboring grains in Sample 2.  First six) Identified dislocations are (0001)[1



0] 
and(


011)[1



0].  
Second six) Identified dislocations are (



0)[





0].
 

 
 
Figure A30a) AFM color
-
scale topography map of grain 3 in sample 1.  b) Slip systems identified 
by the trace analysis are the (10


0)[


2


0] and (0



0)[2




0] prism <a> slip systems.  c) 
ECC 
image of the red box area in b).  Contrast analysis also reveals two additional slip systems, which 
are (1


00)[




20] prism <a> slip system and the (0


11)[2




0] pyramidal <a> slip system.  The 
pyramidal <a> dislocations are responsible for the curvy sli
p traces.  d) AFM color
-
scale 
topography map of grain 5 in sample 1.  e) (1


00)[11


0] prism <a> slip system is identified by 
the slip trace analysis.  f) ECC images of the red box area in e).  Contrast analysis also reveals a 
significant number of (0


10)[2




0] prism <a> dislocations within the observed area. 

 
 
 
Figure A31 3
-
D geometry of the well
-
correlated slip systems at the grain boundary by the 
correlation of surface and subsurface images. (Amended from [171])
 

 
 
Figure A32 All ca
ses slip interactions at grain boundaries with calculated results. 

 
 
 
Figure A33 Slip band broadening effect observed along two different slip bands.
 

 
 
xx
 
 
KEY TO ABBREVIATIONS AND SYMBOLS
 
 
 
 
AFM 
 
 
A
tomic 
F
orce 
M
icroscopy
 
Au
 
 
Gold
 
AuNP
 
 
G
old 
N
anoparticles
 
BSE 
 
 
B
ack
s
cattered 
E
lectron
 
CC
-
EBSD 
 
C
ross
-
C
orrelation 
E
lectron 
B
ack
s
cattered 
D
iffraction
 
CRSS 
 
 
C
ritical 
R
esolved 
S
hear 
S
tress
 
CSL 
 
 
C
oincident 
S
ite 
L
attice
 
DIC
 
 
Digital Image Correlation
 
EBSD 
 
 
E
lectron 
B
ackscattered 
D
iffraction
 
EBSPs
 
 
E
lectron 
B
ackscattering 
P
atterns
 
ECCI 
 
 
E
lectron 
C
hanneling 
C
ontrast 
I
maging
 
ECP
s
 
 
 
E
lectron 
C
hanneling 
P
attern
s
 
EDM 
 
 
E
lectronic 
D
ischarge 
M
achining
 
FEG
-
SEM 
 
F
ield 
E
mission 
G
un 
S
canning 
E
lectron 
M
icroscope
 
FIB 
 
 
F
ocused 
I
on
 
B
eam
 
FSE
 
 
F
orward
-
S
catter 
E
lectron
 
GNDs 
 
 
G
eometrically 
N
ecessary 
D
islocations
 
hcp 
 
 
hexagonal close
-
packed crystal structure
 
HR
-
EBSD 
 
High Resolution Electron
 
Backscattered Diffraction
 
LRB
 
 
Lee

Robertson

Birnbaum
 
xxi
 
 
MATLAB
 
M
atrix 
L
aboratory
 
Ni
 
 
Nickel
 
OIM 
 
 
Orientation Imaging Microscopy
 
OPS
 
 
C
olloidal 
S
ilica
 
Suspension 
 
SACP
s
 
 
 
S
elected 
A
rea 
C
hanneling 
P
attern
s
 
SE 
 
 
S
econdary 
E
lectron 
 
SiC 
 
 
S
ilicon 
C
arbide
 
TBAF
 
 
T
etra
-
n
-
B
utylammonium 
Fl
uoride
 
TEM 
 
 
T
ransmission 
E
lectron 
M
icroscopy
 
Ti
 
 
Titanium
 
Ti
-
7
-
Al
 
 
Titanium Aluminum Alloy
 
b 
 
 
Burgers vector
 
g 
 
 
vector that describes the electron imaging/channeling condition
 

 
 
 
angle between 
Burgers vectors
 
l
 
 
rotation axis between intersecting lattices
 
M
 
 
 
Schmid factor
 
m' 
 
 
predictive parameter of slip transfer using 

 

 
n 
 
 
slip plane
 
normal
 
S 
 
 
stress
 
q[
 
 
 
a
ngle between 
s
lip 
p
lane normals
 
s 
 
 
deviation factor
 

 
t
 
 
intersection line of a slip system on the grain boundary plane
 
xxii
 
 
qy
 
 
 
resolve shear 
stress
 
qy
c
 
 
 
critical resolved shear stress
 
u 
 
 
dislocation line direction
 

 
 
the reciprocal of total atoms at Coincident Site Lattice to the 
tota
l atoms
 

 
             
rotation angle between two intersecting lattices
 

 
 
strain
 
P
 
 
stress on the slip 
system
 

 
 
angle between intersection lines of slip systems at a grain boundary plane
 
Å
 
 
Angstrom, 10
-
10
 
meters
 
 
1
 
 
1.
 
Introduction
 
1.1
 
Heterogeneous deformation of commercially pure titanium
 
With the increasing demand for 

-
titanium and titanium alloys across a wide range of 
industries, due to their good corrosion resistance, high strength to density ratio, and biomedical 
compatibilities [1
-
5], the desire to manipulate and precisely predict th
e performance of such 
hexagonal materials during service also grows stronger.  However, wide replacement of cubic 
materials (i. e. steel) with such promising metals is still impossible, because the detailed 
deformation evolution mechanisms of hexagonal tit
anium are not yet well understood.  Cubic 

makes it easier to precisely model the deformation textures [6
-
8].  On the contrary, such 

 
exist in commercially pure 

-
titanium (and other hcp 
metals) [9
-
12] since the orientation change and slip
-
twin distribution are not consistent to give 
predictable textures under the same deformation mode [13, 14].  Nevertheless, such 
inconsistency challen
ges the establishment of a reliable model, and the key to elucidate this 
unpredictable deformation behavior is the full understanding of the mechanisms of 
heterogeneous deformation of hcp titanium.  
 
1.1.1
 
Plastic heterogeneity of commercially pure titanium 
 
Het
erogeneous deformation is common in all polycrystalline metals.  Plastic 
heterogeneity happens due to strain variations from grain to grain since all the grains 
experience different deformation processes due to varying crystal orientations.  In plastic 
def
ormation models, Talyor and Houttee [15, 16] suggested that strains could be equally 
distributed among all the grains under a macroscopically uniform deformation.  This worked 
2
 
 
well for materials with cubic symmetry because each grain is able to activate mu
ltiple slip 
systems with comparable critical resolved shear stress (CRSS,
 

c
) to accommodate the 
partitioned strain.  Thus, heterogeneous deformation is not a serious problem for cubic 
materials.  However, this assumption failed on materials with lower sym
metry, such as hcp 
titanium.  As shown in 
Figure 1
, there are several deformation slip systems in commercia
lly 
pure titanium, including {




} <




 
> prismatic <a> slip, {

} <




 
> basal <a> slip, 
 
Figure 1 Top two crystals present the major slip systems activated during deformation, namely:  (Top left) 
prism <a> slip system on {




} prismatic plane, basal <a> slip system on {0001} basal plane, and pyramidal 
<a> slip system o
n {




} pyramidal plane with <




> Burgers vector;  (Top right) type I <c + a> slip system 
on {



} pyramidal plane, and type II <c + a> on {





} pyramidal plane.  Bottom two crystals show the 
geometry of two tensile twinning (labeled in blue and yello
w) and two compression twinning (labeled in purple 
and dark green), which is not readily observed in room temperature deformation and not the interest of this 
study.  
 
3
 
 
{




} <




 
> pyramidal <a> slip, and {




} <





 
> pyramidal <c + a> slip ({





} 
pyramidal <c + a> is rare).  Tensile and compressive twinning does 
exist as additional 
deformation systems, but twinning activation is dependent on elemental composition [17] and 
thus not easily predictable.  Due to the anisotropic nature of the low symmetry of hexagonal 
crystal lattice, the activities of these deformatio
n systems are dramatically different, with the 
prismatic <a> slip systems being the most observed among all deformation systems [18
-
25].  
Such different activation of deformation systems is due to a large deviation in the CRSS value 
among these deformation
 
systems [26].  Although CRSS values are sensitive to elemental 
compositions [27
-
30] and dependent on testing methods [31
-
38], the CRSS of the prismatic slip 
system is more likely found to be the lowest at room temperature in commercially pure 
titanium
1
. 
 
The CRSS value of the basal slip system is the second lowest, around 1.2 ~ 2.6 times 
larger than the prism <a> slip [28, 36, 37].  Pyramidal deformation systems, including pyramidal 
<a> and pyramidal <c + a> slip systems, usually have CRSS values around 1
.3 ~ 8 times larger 
than the prism <a> slip system [25
-
28, 34
-
37].  As a result, it is much harder for other slip 
systems, especially pyramidal slip systems, to be activated.  As indicated by Von Mises [39], an 
individual grain needs at least five independ
ent slip systems to accommodate change shape.  
Thus, every titanium crystal needs to activate multiple different slip system types to maintain 
polycrystalline integrity.  In reality, this constraint is hard to achieve since slip activities in 
titanium is n
ot uniformly distributed due to the variability of CRSS of the different slip system 
types.  Thus, plasticity models of titanium often fail since heterogeneity is not able to be 
 
1
 
Basal may become lower than prism slip system at levitated temperature and in some alloys [38], that is why CRSS 
value is material dependent. 
 
4
 
 
correctly modelled to reflect the real
-
life deformation.    
 
  
In addition to 
the CRSS issue, due to the low symmetry of titanium, the deformation of 
a single crystal through one type of slip system at a certain orientation usually means the 
activation of the other slip system is not favorable.  For example, if [11



] is favorably a
ctivated 
with a high Schmid factor, then [1


10] and [2





] slip are typically not equally activated at the 
same time since their Schmid factors are usually low.  Thus, the deformation of a crystal has to 
follow a certain direction, with other slip activati
on somewhat suppressed.  However, in 
polycrystal deformation, it is not quite possible to relief all the strain by the activation of the 
primary slip system, and the suppression of other slip systems cause incomplete strain 
relaxation, thus cause strain ac
cumulation within the grain.  In a polycrystal, some grains are 


orientations on
ly allow high
-
CRSS
-
value deformation systems [40
-
42].  Based on the uneven 
distribution of plastic strain among the grains and the incomplete strain relaxation due to lack 
of slip activation, strains that are not fully relaxed may accumulate at the grain b
oundaries.      
 
1.1.2
 
Accommodation at grain boundaries
 
Micro
-
cracks will form at the grain boundaries if they fail to sufficiently accommodate 
the strain localization on both sides [43
-
46].  At the grain
-
scale level, in order to maintain grain 
boundary integri
ty, the resulting strain must be released by either transferring across the grain 
boundary into the neighboring grain, or sometimes reflecting back to the original grain.  At the 
nanoscale or atomic level, dislocations that are carrying the strain get rest
rained at a grain 
boundary, because the extensive atomic disordered grain boundary interface disrupts the 
5
 
 
propagation of dislocations within a confined plane.  The continuous piling
-
up of dislocations 
around the grain boundary can be sources for the disloc
ation activations in either grains [47
-
48],  and cause strain hardening of the grain boundary if the strain is not completely carried 

dislocation slip encourages t
he further disruption of the grain boundary atomic configuration, 
creating more defects and voids at the interface between the joining grains, and eventually 
create micro
-
cracks on the grain boundary.  This is believed as the precursor of material failure 
[45, 50, 51].  In the heterogeneous deformation of titanium, the capability of a grain boundary 
to accommodate the strain is difficult.  As discussed previously, individual grains with varying 
crystal orientations deform differently, so the grain boundarie
s have to deal with different 
amounts of strain from different directions at the same time.  As a result, it is critical to 
understand the nature of grain boundaries and how grain boundaries accommodate the 
heterogeneous strain from the grains.  
 
1.1.3
 
The geome
try of grain boundary and its effect on dislocations
 
It is important to understand how a grain boundary reacts to dislocation shear based on 
its geometric characters.  Compared with the unique atomic arrangement within a lattice, a grain 
boundary is a disordered interface between the joining crystals.  Such 
disordered structural 
defects are usually high energy sites and can be dislocation sinks and sources [52
-
55] based on 
how the lattice is misorientated at the grain boundary. 
 
By and large, there are several different ways to describe the crystallography of
 
a grain 
boundary, namely: tilt/twist boundary, symmetric/asymmetric boundary, 
and the 

 
boundary.
  
Tilt and twist boundaries are formed when two adjoining crystal lattices share a same rotation 
6
 
 
axis 
l
, as illustrated by 
Figure 2 a&b
.  For a pure tilt boun
dary, the rotation axis 
l
 
lies in the 
boundary plane.  On the contrary, the axis 
l
 
lies perpendicular to boundary plane in a pure twist 
boundary [56].  This approach defines the configuration of a grain boundary by five
-
degrees of 
freedom, including the gr
ain boundary normal 
n
, two crystallographic orientations of the 
neighboring crystals 
n
1
 
and
 
n
2
, the rotation axes 
I
, and the rotation angles 

(the 
total 
misorientation can be broken down into a combination of 

tilt
 
and 

twist
 
about the respective 
 
Figure 2a) Sketch of a pure tilt boundary, indicating two crystals are rotated by angle 

tilt
 
about a rotation axis 
lying on the grain boundary plane.  b) A pure twist boundary is formed, which looks like a single crystal is 
twisted into half along a rotation axis lying perpendicular to the grain boundary with misorientation angle 

twist
.  c)
 
Sketc
h of 

 
boundary, formed by a 36.9
o
 
rotation between two same lattices about a common [001] 
axis.  In this picture, the atom A and B in grain 1 are represented by circles with no fill, while the same atom in 
grain 2 are pattern filled circles, and the gra
in boundary lattice area is limited by the dotted square.  After 
carefully counting, it can be found that every 2 out of 10 atoms are sharing the same lattice position.  It is 
noticeable that 

 
value may different about different rotation axis. 
 
(
A
mended f
rom [57, 65])
 
7
 
 
rotation axes 
l
)[57].  In this approach, the 
geometry of a grain boundary cannot be simply 
defined by a fixed rotation and twist angle, since different rotation and twist combinations can 
achieve the same misorientation structure of the boundary lattice.  Specifically, to further 
describe a pure tilt
/twist boundary, the concept of symmetric and asymmetric boundary is then 
applied based on the relationship of the tilt axis direction to the grain boundary plane.  For 
example, the symmetric boundary is defined when the grain boundary plane is mirrored ab
out 
the shared axis direction.  By specifying the family of the rotation axis and the information 
discussed above (i. e. {210}<001> symmetric tilt boundary, with misorientation angle 53.1
o
), a 
more precise definition of the grain boundary is thus presented
 
to outline the grain boundary 
atomic structure [58
-
64] for molecular dynamic modeling.  Another common approach that 
describes the geometric configuration of the grain boundary is the
 

 
boundary, usually used 
together with the 
coincident site lattice (CSL
) model [65].  The grain boundary is simply viewed 
as a region of interpenetrating lattice points between the neighboring misorientated grains.  
There will be some lattice points in that region where the atoms from the adjacent grains 
overlap. Those points
 
are called coincident site lattice points.  The 

 
value is the value of the 
total number of atoms over the number of atoms that are in coincident sites.  An example of 

5 boundary is presented in 
Figure 2c,
 
since 2 out of 10 atoms on the grain boundary p
lane are 
in coincident sites.  This boundary is formed by a 36.9
o
 
rotation between two perfect cubic 
lattices about a common [001] axis.  This pure geometric model categorizes some specific grain 
boundaries out of the common boundaries and provides another way to quantify the 
misorientation.  Grain boundaries with low 
q7
 
values (more atoms share the coincident sites) 
suggest there are little mismatch and little lattice disorder between the adjacent grains.  
8
 
 
Further studies have found that low 

 
boundaries usually show unique behaviors than non
-

 
ones during deformation.  
For instance, some low
 

boundaries are found to prevent creep 
formation in a Ni alloy [66], while coherent twin 

3 boundaries are particularly good for 
inhabiting cracks [67], etc.  Nonetheless, the energy barrier of the grain boundary for 
dislocation tra
nsmission and nucleation is also found to be related to the 

value.  As indicated 
by 

 
[62], the energy barrier for dislocation transmission and nucleation at a 
q7
3 
boundary was particularly high, suggesting this boundary was an effective block 
to dislocations.  
In that study, kinetic factors including the geometry of the loading orientations of the bicrystals, 
and the Schmid factors, were also found to have strong impacts on the dislocation/grain 
boundary interactions.
  
It should be realized tha
t the grain boundary models discussed above 
are mainly developed from cubic or other higher symmetry systems [52
-
69], until recently, K. 
Glowinski et al [70] applied this concept to hexagonal systems.  In the study, they categorized 
the grain boundary geom
etry with rotation axes/planes and 
q7
 
boundaries, and specified the 
similarity and difference with the cubic systems in the atomic configuration.  That study helped 
establish a system to correctly represent the grain boundary configuration for the hcp syste
m.  
 
All in all, these lattice models indeed provide clues on plasticity transfer across grain 
boundaries in plasticity modeling, and specifically, reveal how dislocations dissociate and cross
-
slip at/within special grain boundary interfaces [58, 62, 68, 6
9].  However, for the convenience 
of modeling
-
based studies and to reduce complexities, there are some assumptions or 
simplifications in these models.  Such compromises make the modeling less effective at 
representing real
-
life heterogeneous deformation of
 
polycrystals, with the reasons listed as 
follows:
 
9
 
 

 
Although there have been a considerable amount of studies of special grain 
boundaries (i. e. 
q7
 
3, 5, 11, etc.) that show consistent behaviors of the dislocations, the 
behaviors of dislocations at non
-
q7
 
bou
ndaries with uncategorized disordered lattice 
configurations cannot be easily predicted.  The understanding of grain boundary 
accommodations with dislocation shear in heterogeneous deformation should also 
include general boundaries, and these special model
s do not work well.
 

 
In the models, the dislocation shear is usually started from an intentionally 
induced defect within a grain and then propagated to the grain boundary.  For 
convenience, the dislocation type was also given, and the shear was considered t
o be 
homogeneous among the same type slip bands within the grain.  However, the direction 
of real
-
life deformation shear as well as the activation of dislocations are not always 
predetermined since the heterogeneous deformation is not limited to only one g
rain, 
but also its surrounding grains.  The amount of shear carried by each slip band was also 
not equal during the deformation.
 

 
Modeling studies until recent usually limit the interactions between one 
incoming dislocation with one grain boundary, includin
g new dislocation initiations or 
the absorption/reflection of the incoming dislocation.  However, except in special cases, 
there will typically be activation of multiple slip systems, which make the grain boundary 
accommodation events more complicated than
 
the models.   
 
  
Collectively, a more reliable approach is thus needed to study the accommodation 
behavior by efficiently revealing the dislocation/grain boundary interactions in hexagonal 
titanium.  The active slip systems should be correctly identified,
 
the direction of shear transfer 
10
 
 
should be grasped, and the models should be also applied on common grain boundaries.  
As is discovered by Sangid et al [62], the Schmid factors, the orientation of crystals, and 
the geometry of grain boundary interfaces are
 
all important elements affecting the 
interaction between dislocations and boundaries.  Moreover, since dislocations are 
found to dissociate into dislocation partials or cross
-
slip during propagation within grain 
boundary lattices, these studies also sugge
st that residual dislocations left in the grain 
boundary will be an important factor in the dislocation/grain boundary interaction 
studies.
 
1.1.4
 
Interactions between dislocations at general grain boundaries
 
Different from studies that focused on the effect of g
rain boundary atomic 
configurations on the dislocations, numerous studies have successfully illustrated the 
interactions between dislocation slip and unspecified grain boundaries.  Bayerschen et al. and 
other researcher [71
-
75] have summarized several poss
ible accommodating mechanisms when 
an incoming dislocation meets a grain boundary.  These mechanisms are illustrated in 
Figure 3
, 
namely:  a) The direct slip transfer of an incoming dislocation into the neighboring grain without 
leaving any residual dislocations in the grain boundary.  b) The direct transfer of an incoming 
dislocation across the grain boundary by initiating a diffe
rent type of outgoing dislocation in the 
joining grain and thus leaving residual dislocations in the grain boundary.  c) The full absorption 
of an incoming dislocation into the grain boundary.  This process creates grain boundary 
dislocations that can be m
oved elsewhere under applied stress.  d) An indirect slip transfer 
process, including the absorption of an incoming dislocation, and the re
-
emission of an 
outgoing dislocation at the boundary.  Since the incoming and outgoing dislocations are not 
11
 
 
directly connected, this process usually involves the participation of grain boundary 
dislocations.  e) The absorption of an incoming dislocation and initiation of outgoing 
dislocations back to the same grain.  f) The direct slip transfer of d
islocation, creating new 
dislocations both in the adjacent grain and back into the original grain.  
 
Situations e) and f) are not as common as the other accommodating models.  Li et al 
[76] found that it was more energetically favorable for a dislocation t
o cross a grain boundary 
than being reflected back.  It should be noted that, although not common, such mechanisms 
have been both observed by the in
-
situ transmission electron microscopy (TEM) studies [35, 77, 
 
Figure 3a) Direct transfer of dislocation across grain boundary.  b) Direct slip transfer with residual dislocations 
at the grain boundary.  c) Absorption of dislocation slip and dissipated along grain boundary.  d) indirect slip 
transfer by absorption and
 
re
-
emission, leaving grain boundary dislocations.  e) Absorption and reflection of 
dislocations slip with residual grain boundary dislocations.  f) Complicated mechanism, involving both slip 
transfer and reflection with the formation of grain boundary dis
locations.  
 
12
 
 
78] and included in the plastic modeling [76, 
79].  The mechanism f) emphasizes the conditions 
for multiple activation of dislocation slip at a grain boundary during accommodation events, 
which is important in the heterogeneous deformation.   
 
Livingston and Chalmers [80] were among the first of several res
earchers studying the 
activation of multiple slip systems in plastic deformation.  In their studies, they induced a 
deformation shear that was carried to the grain boundary through a known slip system by one 

Fi
gure 4
) and studied how the shear was 

-
crystal systems 
with different orientation combinations were tested.  The strain components (


, 


, and 


 
shown in 
Figure 4
) cre


compatibility of the bi
-
crystal system.  This theory was referred as tangential continuity, and it 
 
Figure 4 As crystal A with known lattice orientation 
is continuously deformed, a known type dislocation slip 
(blue) is piling up at the grain boundary, where dislocation slip (red) will be activated in crystal B due to stress 
build
-
up as it deformed with crystal A.  During the slip transfer, tangential conti
nuity constrain is required that 
requires the strain component induced by dislocations in crystal A be fully balanced in crystal B to maintain 
grain boundary integrity. 
 
(Amended from [80])  
 
13
 
 
req
uired a total of four degrees of freedom within the two adjoining grains during the 
accommodation events.  This included the situations of one incoming slip system in the parent 
grain A being accommodated by three outgoing slip systems in the receiving gra
in B, two slip 
systems (including the incoming one that was already known) in A being accommodated by two 
slip systems in B, and three by one, respectively.  This concept considered the potential for self
-
accommodation, where the strain accommodation was n
ot limited to the neighboring grain, 
but also the grain where the strain was originated.  Nonetheless, with the combination of the 
pile
-
up stress and the geometric tangential continuity, Livingston and Chalmers outlined a 
criterion that was used to predict
 


 
P
i
 
= P N
1i 
= P [(
n
1
 

n
i
) (
b
1
 

b
i
) + (
n
1
 

b
i
) (
n
i
 

b
1

 
where P was the stress of the slip system, 
n
1
 
& 
b
1
 
was the slip plane normal and Burgers 

n
i
 
& 
b
i
 
was the corresponding parameters for any active slip 

 
This criterion is useful for predicting
 
the primary (and sometimes secondary) slip 


prediction of minor sli
p systems, due to more complicated mechanisms at the boundary.  By 
removing the stress component that needed to be calculated/measured from case to case, this 
criterion was later simplified to a pure geometric constraint.  This criterion is now well known 
as the N factor, and is widely applied in many later studies as a slip transfer criterion [81
-
87]:
 
N
in
-
out 
= (
n
in
 

n
out
) (
b
in
 

b
out
) + (
n
in
 

b
out
) (
n
out
 

b
in

 
14
 
 
Influenced by Livingston and Chalmers [80] and their collaborators [88], sequent
ial slip 
transfer criteria have been developed in order to predict the slip systems activated as a result 
of shear accommodation at grain boundaries, with the geometry of slip systems and grain 
boundary illustrated by 
Figure 5
.  Among these criteria, the M
2
 
factor was established by Shen 
et al. [81], evaluating slip transfer events from a different perspective than the N factor:
 
M = (
t
in
 

 
t
out
) (
b
in
 

 
b
out
) = cos 

 
cos 

 
This criterion considere
d the angle 

 
between the intersection of the line directions (
t
) 
of slip planes at the grain boundary plane, and the angle 
q/
 
between the Burgers vectors (
b
) of 
the slip systems on both sides of the grain boundary.  At the same time, Lee et al. [83
-
86] lai
d 
 
2
 
M is usually a symbol of the Schmid factor (SF) in many research.  To avoid the misuse of M, this factor is us
ually 
used as the LRB factor after Lee et al.
 
 
Figure 5 A sketch of the geometry of slip planes intersecting at a grain boundary plane.  
b
, 
t
, 
n
, are the Burgers 
vector, the intersection line direction of the slip plane in the grain boundary plane, and the slip plane normal 
that are used in the 
various slip transmission criterion [80, 81, 95].  Slip plane I (blue) is usually considered from 


 
 
 
15
 
 
out criteria based on the M factor.  It agreed that slip transmissions can happen when M was 
maximized, but two additional stress components should also be included:  First, the resolved 

Second, the magnitude of 
residual Burgers vector left in the grain boundary should be minimized.  This combination 
criteria, known as the LRB criteria, provided significant insights regarding the importance of 
residual Burgers vector in slip transmissions 
as well as its influence on grain boundary 
deformation [89
-
94].  
 
Another more convenient criterion was outlined by Luster and Morris [95], referred as 
the geometric compatibility factor: 
 
 
 
 
 

n
in
 

n
out
) (
b
in
 

b
out
) = cos 

cos 


 
where 
q}
 

vectors.  This simplified version of the N factor has been extensively used [96
-
100] since the 
angle 
q}
 
between plane normals is easily acquired from electron backsca
tter diffraction (EBSD), 
whereas the measurement of angle 

 
requires grain boundary orientation assessment, which is 
not available only through surface analysis.  
 
Meanwhile, a 
qp
 
function was created by Werner and Prantl [101], dealing with slip 
transfer b
etween different phases:
 
qp
 
= cos (


q}
q}

 
) cos (









 
5
 
Slip transmission was expected only when the angle 
q}
 

a limited value (
q}
c
 
= 15
o
 

c
 
= 45
o
).  The application of this 
qp
 

16
 
 
since it was mainly for intra
-
phase slip transmissions.  
 
For the most part, the application of different criteria has fulfilled different 
requirements in the study of slip transmissions [74, 
75, 102], and in particular, combined 
criteria that coupled some of the geometric parameters with accumulated shear stress 

 
[74] or 
the Schmid factor M [103] have made more statistically reliable predictions of slip activity.  
However, one may realize tha
t despite the factor PN
1i
 
outlined by Livingston and Chalmers et al. 
[80, 88] that have indicated the need for multiple activations of slip systems during slip 
accommodation, as well as Shen et al. [81] that have discussed the observation of slip 
multiplic
ity within the vicinity of grain boundaries, many follow
-
up criteria have become more 
and more simplified, assuming: 
 

 
 

one deformation system during one slip transfer activity, altho
ugh comparisons of 
parameters between different slip systems are quite common.  
 

 
Similar to the limitation of many modeling studies, the direction of 

grain. Many studies have
 
focused on the cases where a known incoming slip piled
-
up at 

 
Undoubtedly, the simplified criteria are extremely useful, especially when the target of 
interest is limited to bicrystals.  However, this is far from accurate in the study of 
heterogeneous deformation of polycrystals.  For the first assumption, based on b
oth the 

independent slip system to maintain integrity) [39], it is necessary to have more than one 
17
 
 
accommodating slip system to be activated to fully accommodate th
e strain at the grain 
boundary
3
.   Accommodation by multiple slip systems was recently reported by Su et al. [104].  


e grain boundary.  The activation of 
double accommodation was a complicated competition between many factors including the 

Burgers vectors.  Despite this res
earch, until now, how other deformation systems affect slip 
transmission is still not clear.  For the second assumption, it only worked perfectly in the bi
-
crystal system in an ideal condition but not precise in the heterogeneous deformation, where 
shear t
ransfer is not necessarily limited to one given direction.  As reviewed by Bayerschen et 


train is primarily 

in real
-

independently due to the applied stress, and the 

needs to be transferred out at the grain boundary.  Thus, it is not reasonable to say the 


accordingly.  Nevertheless, these ideal models neglect the situation 
that dislocations can be nucleated at the grain boundary and carry the accumulated shear out 
of the grain boundary by propagating into both grains.  This is also an important mechanism to
 
 
3
 
Although grain boundary dislocations can also carry away accumulated strain at the boundary, 
the 
migration of 
grain boundary dislocations may cause 
severe 
grain boundary 
movement or 
cracking.
 
18
 
 
protect the integrity of the grain boundary, since the grain boundary can be a source for 
dislocation activation.  So far, whether slip transfer criteria can be effectively applied in this 
situation is still unanswered.  
 
Thus, in order to further the und
erstanding of heterogeneous deformation of 
commercially pure titanium, it is necessary to figure out if the classic slip transfer criteria or 

initiation at a g
rain boundary and propagation into the adjoining grains).  Additionally, it may 
also be necessary to identify the direction of strain transfer within patches of grains.  If possible, 
it is insightful to identify which grain is actively deforming with respe
ct to the applied stress and 
which is deforming passively to accommodate the deformation of its neighbor.  By extension, if 
one is able to locate the grain boundaries where the flow of strain is concentrated and is not 
able to be well accommodated, such gr
ain boundaries may be vulnerable to damage nucleation 
during the deformation. 
 
1.2
 
Introduction of experimental techniques 
 
There are generally several analytical methods used to identify the deformation slip 
systems, the nature of the dislocations (in terms o
f Burgers vectors, slip directions and slip 
planes), and the relative strain distributions across the deformed material.  Rather than simply 
laying out numerical expressions that are boring and non
-
intuitive, the following sections 
provide a brief introduc
tion and a comparison of different analytical methods that are used for 
dislocation
-
level characterization.   The purpose of this section is to elucidate the advantage of 
using electron channeling contrast imaging (ECCI) in this study, since it is capable 
of both 
grasping the macroscopic deformation of the material and providing microscopic detailed 
19
 
 
information including the nature and relative distribution of the dislocations.  When carefully 
planned, ECCI is able to avoid the biasing of the free surface a
nd provide information on how 
deformation shear is accommodated within and between grains associated with other 
techniques. 
 
1.2.1
 
Electron backscatter diffraction (EBSD)
 
EBSD is used to acquire the crystal orientation distributions and the changes in 
orientatio
n  during the loading process, both of which are important information in the study of 
heterogeneous deformation.  The overall set
-
up for the EBSD technique is shown in 
Figure 6a
.  
The crystal orientation of a grain is achieved based on the electron backsc
attering patterns 
(EBSP), which appears as a map of intersecting pairs of parallel Kikuchi
-
lines on a phosphor 
screen (
Figure 6b
) [106, 107].  In order to maximize the backscattered signal collected by the 
detector, a high surface normal tilt angle of 70
o
 
is generally used.  As the incident beam 
electrons inelastically scattering in all directions within a crystal, some electrons hit the crystal 

4
 
and will be elastically scattered and form reinforced beams 
of electrons ex
iting the sample surface.  As the inelastically scattered electrons vary in 

form a surface of a cone, referred as the Kossel cone.  Since the scattering even
ts occur in a 
very small volume and therefore can be considered to occur at single planes, a lattice plane 
thus will be represented as a pair of Kossel cones, which manifest as two parallel Kikuchi lines 
 
4
 
n

 
= 2 d
hkl 
si
n
 

B
, where n is a positive integer, 

 
is the wavelength of the electron beam, d
hkl
 
is the distance of the 
Miller indexed (h k l) lattice plane, and 

B
 

constructive signals.  Based on diffe
rent lattice structure, some combination of h, k, l will result in constructive 
reflections, enhancing the signal, while in other cases results in destructive/forbidden reflections and thus give 
weak signal.
 
20
 
 
when the two cones are projected onto the  detector 
screen.  With Bragg diffraction occurring 
from all structure factor allowed planes, cone pairs will develop from all allowed set of planes, 
and diffraction patterns are formed as intersections of numerous Kikuchi bands (
Figure 6b
).  
 
Based on this mechanism diffraction  patterns provide angular information of the crystal.  For a 
known material, the identification of Kikuchi bands (
Figure 6c
) through the Hough transform 
[108] will reve
al its crystal orientation.  After the application of EBSP in the 1970s [106], 
continuous development of automatic patterning and phase identification methods [107
-
110] 
have made the EBSD a widely used scanning electron microscopy technique for near surfac
e 
characterization.  EBSD is able to provide accurate information on crystalline orientation 
 
Figure 6a) The simplified mechanism of the formation of electron backscatter patterns (EBSPs).  Each pair of 

Kikuchi map is formed by collecting a
ll the backscatter signals coming out of different planes on the phosphor 
screen.  c) With each zone axis identified and labeled, one is able to know the crystal orientation of the 
scanned grain.  This is extremely useful in the predication of slip systems
 
during plastic deformation. 
 
(Amended from [107])
 
21
 
 
distributions, grain
-
scale misorientations, size and phase variations, and elastic strain 
distribution across a bulk sample.   
 
A well
-
prepared sample is generally
 
needed, since the highly topographical surface will 
leave residual deformation at the surface that leads to local strains and blurs the Kikuchi lines 
for a precise orientation detection [111].  It should also be realized that the inelastic electron 
intera
ction volume is strongly influenced by the sample tilt.  This means, at a high tilt of 70
°
 
for 
EBSD, the spatial resolution along the tilt axis is usually better than perpendicular to this axis.  
In a large area EBSD scans, both the top and bottom part of 
a sample will be out of focus if the 
center is in well focus.  Nevertheless, modern high
-
speed EBSD provides spatial resolution from 
30 to 100 nanometers [107, 108, 111] with good angular resolutions between 0.5
o
 
and 2.0
o
, and 
orientation precision of 0.5
o
 
[107, 112].  Several factors simultaneously affect the performance 
of the EBSD.  The atomic number of material, the geometry of mounting, the probe current, the 
accelerating voltage, and clarity of the pattern can strongly affect the spatial resolution; w
hile 
the scanning speed and the calibration of the pattern center will both affect the angular 
resolution [113
-
117].  
 
With the development of the high
-
resolution EBSD technique (HR
-
EBSD) [118
-
123], the 
angular precision has increased to 0.01
o
. This 
technique can resolve as low as 10
-
4
 
elastic strain 
across a deformed area by comparing the relative distortion of the pattern collected from an 
area to the reference pattern from a presumably strain
-
free area.  However, this technique still 
needs refineme
nt to improve the resolution and the speed for data treatment [122]. 
 
1.2.2
 
Transmission electron microscopy (TEM) 
 
To understand how a crystal is deformed and to evaluate slip transfer, a method is 
22
 
 
usually needed to identify the deformation slip (and twinning) 
within and between polycrystal 
patches.  As is mentioned in section 1.1.4, transmission electron microscopy (TEM) has been 
widely used   for the  characterization of slip activity.  This technique uses high voltage electrons 
(generally 100 ~ 400 keV) that 
can penetrate through the sample.  The sample is oriented so 

diffraction patterns and Kikuchi bands that represent the lattice parameters on the back focal 
p
lane below the sample.  Thus, the lattice distortion around the defects will be resolved due to 
contrast variations from the defect
-
free background.  Based on this contrast mechanism, 
dislocations can be visualized, with their Burgers vectors identified through the
 
g
 

 
b
  
= 0  and 
g
 
 
Figure 7  Sketched mechanism of 
g
 

 
b
 
= 0 and 
g
 

 
b
 
x 
u
 
= 0 invisibility criteria in the determination of 
dislocation Burgers vector.  The dislocations will go completely out of contrast or show low contrast when the 
dislocation plane lies parallel to the channeling direction, because the it is where almost al
l electrons 
diffracting between planes in the same way, leaving no intensity differences between distorted region and 
perfect lattice.  On the contrary, larger value of 
g
 

 
b 
suggests more intensity variation around the distorted 
region, revealing dislocat
ions in better contrast.
 
 
(Amended from [124])
 
23
 
 

 
b
 
x 
u
 
= 0 invisibility criteria as shown in 
Figure 7
 
(where 
g
 
is the channeling/diffraction vector,  
b
 
is t
he Burgers vector, and 
u
 
is the line direction) [124
-
126].  The dislocation line directions, 
the dislocation types (edge or screw), and the slip planes can also be identified by tilt
-
and
-
rotate operations.  In addition to the contrast analysis for defect i
maging, with continuous 
advancement of electron sources and the special resolution, latest TEM allows the study of 
grain boundary configuration and the distortions of atomic arrangement due to dislocation 
inductions within the vicinity of the boundaries at
 
approximately atomic level [127
-
129].  
Despite the high resolution and the capability of doing in
-
situ slip transfer experiments, TEM 
also suffers a series of limitations [130
-
134], one of which is the requirement of thin foils.  Thin 
foil sample preparat
ion can be difficult  and time consuming, but may also result in artifacts 
during improper preparation.  Another limitation of TEM is the observation volume, making it 
difficult to collect appropriate levels of information for statistical analysis.  
 
1.2.3
 
Elect
ron channeling contrast imaging (ECCI)
 
With the advancement of scanning electron microscope, other surface characterization 
techniques [135
-
138] have been introduced, such as the electron channeling contrast imaging 
(ECCI) [137
-
141].  Among those technique
s, ECCI is particularly strong at the identifications of 
near surface dislocation Burgers vectors and line directions [142
-
145], and thus serves as 
competitive  approach to the TEM.  This technique can resolve dislocation image peak widths as 
small as 15 n
m (comparable to bright field TEM) and is able to capture the dislocations 
distributed within 100 nm of the surface.  ECCI is a non
-
destructive technique and a similar 
contrast analysis as TEM, but ECCI is collecting signals from backscattered electrons ra
ther than 
the electrons penetrating a TEM thin foil.
 
24
 
 
 
 
Figure 8a) An example of ECPs collected from a p
-
type boron doped synthetic diamond single crystal with close 
to [110] crystal orientation in low mag BSE mode (~ 20x). 
 
The band in the upper left co
rner with bright and 
dark contrast is one of the Kikuchi band formed during incident beam sweeping the sample.  It disappeared in 
larger mag.  

.  b) An example of EBSPs collected 
among one of the g
rains from a commercially pure titanium sample 
in
 
this research (sample 2).  
The i
mage 
wa
s 
taken at a working distance of 24
 
mm, a 30 kV accelerating voltage and a 184 µA probe current, with sample 
tilted at 70
o
.  The edges of Kikuchi bands are 
significantly sharper than that of ECPs.  c) An example of SACPs 
collected from the same target with b) using the same voltage and current, but the working distance is around 
9mm within 10
o
 
tilt.  SACPs provide much accurate information where the closest z
one axis the crystal is 
orientated.  With more sharp edges on the channeling bands and higher special resolution, SACPs fits ECCI 
analysis more than the other two options.  
 
 
25
 
 

-

 
analysis,ECCI 
requires the sample to be oriented to specific channeling conditions in order to maximize 
contrast and facilitate defect analysis.  The orientations with respect to the incoming electron 
beam can be established using crystallographic orienta
tion information from either low
-
mag 
electron channeling patterns (ECPs) or higher magnification selected area channeling patterns 
(SACPs), with example patterns shown in 
Figure 8
 
[146].  EBSD can also be used to facilitate 
ECCI by inferring the necessary 
tilts and rotations to achieve proper two
-
beam channeling 
conditions[111, 142].  ECPs (
Figure 8a
) are typically formed at low magnification in a single 
crystal or a grain with a large size.  Such patterns were often used when the ECCI technique was 
first e
stablished.  The mechanism for the ECPs formation is sketched in 
Figure 9 
[146].  While 
the electron beam will strike the sample parallel to the optic axis in the center of a scan, as the 
 
Figure 9 Schematic mechanism on the formation of ECPs (Amended from 
[146]), with the incident beam 

the diffraction contrast at the surface.
 
26
 
 
beam is scanning across a sample, the electron beam trajectory will 
vary.  At low magnifications 
this variation in trajectory angle will be maximized.   As these trajectories vary, the electron 
beam strikes the lattice planes at different angles, and the Bragg diffraction (channeling) 
behavior changes.  Subsequently, the b
ackscattered electron yield varies as the beam is 
moving, forming a pattern of lines, known as an electron channeling pattern, indicative of the 

Figure 8a
 
in

thus a strong BSE signal is achieved.  The edge of the band indicates the lattice planes are 



detected at the screen.   Comparing the qualities of the patterns in 
Figure 8a
-
c
, it appears that 
the ECPs are blurry and show worse contras
t, which is not good for a precise establishment of 
channeling condition [147] . In theory, ECPs can only provide crystal orientations up to 1
o
, thus 
are not very suitable for accurate dislocation related studies since it is hard to precisely tilt the 
samp
le to an exact channeling condition.  Additionally, ECPs are limited to large
-
grain samples 
or single crystals, which are not readily applicable for heterogeneous deformation studies due 
to the need for large numbers of grains.  
 
The EBSPs technique (
Figur
e 8b
), with a precision accuracy around 0.5~2.0
o
, has 
replaced ECPs in most applications for the determination of crystal orientation.  By calculating 
the rotation and tilt angles needed to reach the edge of a specific channeling band, it is possible 
to es
tablish channeling condition for ECCI analysis based on the EBSP
-
determined crystal 
orientation [149].  However, this approach is not intuitive, and the precise establishment of a 
27
 
 
channeling condition is challenged by the uncertainty induced during the sta
ge movement from 
a high
-
tilt EBSD orientation to a low
-
tilt ECCI condition
5
.  This makes the fine adjustment of the 

impossible, since this fine adjustment typically ne
eds angular accuracy within 0.1
o
, which is 
beyond the capability of EBSD.  Although this problem can be partially resolved by doing ECCI 
using a forward
-
scatter electron (FSE) detector with a similar high
-
tilt setup [149, 150], this 
technique also suffers 
issues similar to EBSD, with image/diffraction contrast shadowed by the 
severe topography and variation of focus across the tilted area [140].  High tilt ECCI also suffers 
from image foreshortening. 
 
The SACPs (
Figure 8c
), acquired by electron beam rocking
 
about a point close to the 
surface rather than sweeping across the sample, overcome the limitations of ECPs and are thus 
able to be used on small grains (20
µ
m).  The advantages of SACPs are:  1. the SACPs technique 
have a smaller angular range with a bett
er spatial resolution.  2. The SACPs have angular 
accuracy with respect to the  beam trajectory within 0.1
o
, which allows the precise 
establishment of the channeling condition 
g
 
and the deviation parameter 
s
 
for the 
enhancement of dislocation contrast.  With a precise calibration of the beam shift on a 
crossbeam field emission gun (FEG) SEM equipped with a Gemini column, a high
-
resolution 
SACP can be established with a spatial resolution of 500 nm, allowing t
he capability to perform 
a quantitative ECCI analysis [147, 148].   
 
As sketched in 
Figure 10a
-
c

 
5
 
The pattern center of EBSP is a chronic proble
m in HR
-
EBSD that still needs improvement since many factors such 
as accelerating voltage, working distance, etc. can affect the position of the center.  Without knowing the exact 
pattern center, rotation & tilt angles calculated based on EBSD is unreliabl
e.
 
28
 
 
trajectory changes when rocking around the focused point.  The diffraction pattern around this 
point is thus created since the BSE yield changes with the rocking angle.  Once a ce
rtain SACP is 
achieved, it is possible to set up a channeling condition based on the lattice orientation of the 
crystal.  Any near
-
surface stacking fault and line defects can thus be resolved since the lattice 
distortion changes the diffraction interaction
 
of electrons in defect
-
free lattice, providing a 
 
Figure 10a
-
c) Mechanism of the formation of SACPs. As beam trajectory changes or beam rocki
ng around a 
certain point, the lattice channel become open and close with respect to the directions of the incoming 
electrons, providing different yield of backscatter electron 

.  The signal profile is collected and create a SCAPs 
on the detector.  For a 
channeling condition that allows the most electrons channeling into the perfect crystal 
and leave an overall dark background, lattice distortion around a dislocation will make more backscatter 
electrons collected by the BSE detector.  Dislocations will be 
resolved.  d) An example of dislocations (bright) 
from the dark background.
 
 
29
 
 
different BSE contrast.  A typical example is shown in 
Figure 10d
, where, at a specific 
channeling condition, the perfect crystal lattice allows most of the electrons to channel into the 
material, resulting
 
in an overall dark background.  Because the near
-
surface dislocations distort 
the perfect lattice, the scattering behavior between the incident electrons and the distorted 
lattice is different than that in the perfect crystal.  With more backscatter elect
rons collected by 
the BSE detector around the dislocations, dislocations appear as brighter dots or lines 
depending on their orientation with respect to the surface.  The mechanism responsible for the 
bright
-
dark dislocations contrast is shown in 
Figure 11
 
[141, 152, 153].  
Figure 11 
(left) shows 

Figure 11 
left) is exactly at one of the channeling bands on a perfect 
lattice, with the deviation parameter 
s
 
= 0.  Due to the lattice distortion from the dislocation, 
the cha
nneling planes are deviated from the exact Bragg condition, resulting in a different 
backscatter signal yield from the background yield level (
Figure 11 
right).  
 
Once a specific channeling conditions with a proper channeling contrast have been 
 
Figure 11 An example of the change of channeling contrast with respect to the deviation parameter 
s
, which s =
 
0 indicates the optical axis is exactly at the edge of the channeling band.  With optical axis move into or away 
from s = 0, signal intensity will change dramatically.  As the lattice is no longer aligned symmetrically towards 
the incident beam due to dis
location distortion, contrast will occur with bright/dark contrast around a 
dislocation compared to the overall grey background.  (Amended from [152])
 
30
 
 
established
, dislocation identification can be achieved through ECCI 
g
 

 
b
 
= 0 and 
g
 

 
b
 
x 
u
 
= 0 
contrast analysis [140, 150, 154].  It should be noted that since there is always elastic relaxation 
of dislocation core at the free surface, there are situations that di
slocations do not fully 
disappear after adjusting the deviation parameter 
s

the surface.  One should also realize that because the working distance is around 10 mm for 
ECCI analysis at 30 kV, the tilt angle 
for a larger samples is often limited to about 20
o
 
, which 
can limit the ability to carry out contrast analysis
6
.  Thus, it is not always possible to obtain all 
the channeling conditions necessary to achieve 
g
 

 
b
 
= 0 and 
g
 

 
b
 
x 
u
 
= 0, nor is it always 
p
ossible to identify line directions by traveling between major zone axes following a channeling 
band (i. e. the sample need to tilt 35.16
o
 
to travel from [110] to [111] zone axis, procedures can 
be found in 
Appendix V
).  However, it is easier to identify t
he inclination direction of dislocation 
as well as its slip plane in ECCI, since there is only one free surface for the scanned sample.  
 
1.2.4
 
Other surface plastic evolution analysis techniques
 
A number of other techniques that are capable of providing informa
tion on the 
evolution of heterogeneous deformation has been developed, such as the digital image 
correlation (DIC) and the atomic force microscopy (AFM).  DIC was first experimentally applied 
by Sutton et al. [155] to the full
-
field (2
-
d) measurement of th
e displacements during 
mechanical testing.  With continuous improvements in computing technique and imaging 
qualities [156
-
158], this technique is now capable of resolving 1 nm horizontal displacement at 
the surface.  The  mechanism is schematically descri
bed in 
Figure 12a
.  In this method, the area 
 
6
 
the mounting stage may collide with the detector, and the dramatic drop of BSE yield at higher tilt angles 
depending on the material
 
31
 
 
of interest is covered by nanoparticles and labeled by several fiducial marks.  Following 
deformation, a strain map can be created since the displacement evolution history between 
nanoparticles within the area 
by correlating sequential images captured during deformation 
with the initial reference image [159
-
163].  AFM, with a vertical precision of 0.1 Å [164, 165], is 
able to provide a relative strain map based on the height difference across the probed area 
[44
].  The simplified mechanism of AFM is shown in 
Figure 12b
.  While the probe scanned 
across the surface, height difference across the area will oscillate the cantilever, resulting in a 
deviation in laser reflection from the tip onto a photodiode.  The heig
ht variation (Z) at 
different coordinate points (X, Y) on the surface, is then used to construct a topography map.  
Both techniques have their own advantages and limitations.  For instance, DIC is good for 
measuring the in
-
plane displacements, but cannot o
bserve dislocation scale movements, while 
 
Figure 12a) Overall mechanism of DIC.  The surface is coated with evenly deposition of nanoparticles, with 
fiducial marks.  
T
he reference image is the upper right square area labeled with four fiducial marks, with a 
reference point P (x,y).  During deforma
tion, arbitrary shape change and rotation of this area is reflected by the 

 
As the probe is deviating 
from its original position due to surface topography, the absolute 
height difference (Z) is recognized by the 
laser reflection on the position sensitive detector and recorded upon each position (X) from the starting point.  
After scanning the whole area line by line, a 3
-
D topographic map can be created by correlating hei
ght profile 
(Z) with the plane profile (X,Y).
 
32
 
 
AFM offers high accuracy for tracing out
-
of
-
plane displacement, but suffers from slow probing 
speed and artifacts [166
-
168]).  Thus, they usually complement with SEM
-
EBSD [162, 163, 44] 
based crystallographic infor
mation or other techniques that can compensate for the limitations 
in the study of polycrystal deformation.  With the incorporation of different surface analytical 
techniques, one is able to perform the slip trace analysis that identifies the slip/twin sys
tems 
that may be activated during the deformation [24, 164, 169, 170] based on the morphologies of 
the slip traces developed during the deformation.
 
1.2.5
 
Problems of the classic trace analysis 
 
The
re have been a number of recent studies that have taken the advantages of surface 
analytical techniques (i.e. slip trace analysis [24]) for statistical analysis of dislocation activity 
since the identifications of slip systems can be much easier to achieve
 
with computer 
assistance.  The mechanism of slip trace analysis is shown in 
Figure 13
.  With the Euler angle 
detected by the EBSD, the crystal orientation can be visualized, the intersection line of a slip 
 
Figure 13 The overall mechanism of the slip trace analysis.  T
he hexagonal cell presents the crystal orientation, 
and the red line is the intersection line between the slip plane (grey) and the sample surface (blue).  With the 
profile of each trace (1~12) at the surface, possible slip system can be identified.  
 
 
33
 
 
plane with the sample surface can thus be drawn, 
which is referred as the slip trace.  With the 
profile of all slip traces, it can be used to identify the active slip system by comparing the 
observed trace to the  calculated ones.  Current EBSD based slip trace analysis still have some 
problems.  For exa
mple, it cannot identify the slip system on basal plane since they show the 
same trace at the surface.  Moreover, it cannot precisely differentiate slip systems that show 
similar slip traces (5 vs 9, 6 vs 12 in 
Figure 13
).  Additionally, this method only w
orks on the 
grains that exhibit straight slip traces since the identification of slip system is solely based on 
the observation.  Thus, this method is currently blind to cross
-
slip identification (and wavy 
traces, which will be discussed in this study).  T
his limitation is seldom discussed because 
researchers will always select another grain that have easier identified slip systems, or choose 
the slip system with the highest Schmid factor among possible alternatives.  Although the slip 
trace analysis is mor
e precise in the identification of slip systems with similar slip traces with 
the help of AFM [168], and DIC [162, 163], current method is still not perfect, especially for 
wavy traces.  Thus, to study the strain accommodation simply relying on the slip tr
ace analysis 
is dangerous, since different slip interactions may indicate different strain accommodation 
mechanisms during the deformation.
 
1.2.6
 
Free surfacing biasing and limitation of surface
-
based analysis
 
Despite the limitation of the current slip trace ana
lysis, the free surface may also bias 
the slip activation and slip transfer events on the surface.  For example, current surface
-
based 
analysis, such as AFM and DIC, is not sensitive to the slip systems that do not contribute to the 
topography change at th
e observed surface.  This means there may be some dislocations that 
are not correctly identified by the slip trace analysis.  This may be a severe issue near the grain 
34
 
 
boundary, because dislocations from other slip systems may actually play more important 
role 
in the slip transfer, but are not detected by the slip trace analysis [171].  This ignorance will lead 
to improper/incomplete understanding of strain accommodation during the heterogeneous 
plastic deformation.  
 
One other limitation to the surface
-
bas
ed analysis (AFM, DIC, EBSD) in the study of slip 
accommodation at grain boundary is illustrate in Figure 5.  It appears that two slip systems 
interact differently at the grain boundary at the sample surface (meet at the same point on the 
grain boundary or
 
not).  No matter which type of interaction, evaluation of slip transfer events 
is solely based on surface observations.  Because it is hard to reveal the geometry of the slip 
system and the grain boundary [172
-
174] from surface observation
7
, the geometrically 

boundary plane orientations [75, 97, 98].  Additionally, due to not knowing the local 
accommodation mechanisms at the grain boundary plane 
(especially in the area between the 
divergent slip planes below the surface), it is risky to directly use the slip transfer criteria in the 
real
-
life deformation. 
 
1.2.7
 
The advantage of ECCI over other techniques
 
To solve the problems in current surface
-
based a
nalysis, ECCI is thus needed.  One major 
advantage of ECCI over other surficial techniques (DIC, AFM) is the capability to identify slip 
planes, slip directions, and the Burgers vectors, which is critical in the plasticity study [143, 
144].  Additionally, 

-

 
7
 
Unless using destructive FIB milling on the grain boundary area [172
-
174].  However, FIB milling may lose 
informatio
n on slip interactions at the milled area.
 
35
 
 
geometry of a grain boundary plane and the slip planes by the correlation of images taken at 
different depths [96, 174].  On the other hand, although not comparable with the darkf
ield TEM 
that is able to resolve small dislocation width, ECCI is none
-
destructive and thus is suitable for 
continuous deformation study of bulk material [140, 141].  As an SEM
-
based technique, a 
broader field of view of ECCI offers the deformation informa
tion from the macroscopic level to 
the dislocation level.  This technique links the macroscopic and the microscopic world, which is 
good for both detailed mechanism study and statistical analysis. 
 
1.3
 
The objective of this research and design plan
 
This 
Ph.D. thesis aims to solve several open questions about how plastic strain is 
accommodated within grains and across grain boundaries during the plastic deformation.  The 
answers to these questions will provide better guidance for the establishment of a rel
iable 
plastic model in the future.
 
ECCI will be used to study the dislocation slip evolution during heterogeneous plastic 
deformation, with a particular focus on slip band/grain boundary interactions.  This objective 
will be carried out in a number of step
s:  First, a robust comparison of a number of approaches 
for characterizing heterogeneous deformation will be carried out.  This will include how these 
various techniques give consistent and/or complementary information.  Second, how grain 
boundary strain 
accommodation is achieved between the interacting slip systems in order to 
maintain grain boundary integrity.  These studies will examine this behavior across 3
-
D volumes 
by carrying out ECCI studies at different depth from the surface.  It will be shown t
hat this 
approach allows a more robust assessment of the parameters that affect the accommodation 
behavior than is facilitated by surface studies alone.  Finally, it will be shown that ECCI 
36
 
 
facilitates the assessment of the sequence of slip activity across
 
patches of multiple grains, 
facilitating a better understanding of the development of heterogeneous deformation.  
 
In order to address the first objective, a surface analytical experiment was performed on 
a Ti
-
7
-
Al tensile sample to
 
facilitate the comparison of ECCI with AFM, HR
-
EBSD, and DIC.  The 
highlight is to emphasize the convenience of using ECCI in the identification of slip systems.  An 
additional consequence of this study is to introduce a method of removing DIC patterning 
without damaging the surface, facilitating further EBSD and ECCI analysis.  To fulfill the second 

-
1.5% plastic 
strain by four
-
point
-
bending.  With controlled electropolishing tech
niques, comparison of 
images of slip bands at and below surface reveal how the free surface is biases the slip 

-

slip planes and grain boundary planes available from
 
the images at and below the surface, 
several slip transfer parameters have been used to evaluate slip transmission at the grain 
boundary.  After the identification of the propagation direction of dislocation following slip 
bands within series of neighbori
ng grains, it is possible to estimate the direction of deformation 
flow traveling within the grain patches, facilitating the determination of deformation 
sequences, and locate the grain boundary where the plastic strain was not sufficiently resolved.
 
 
 
 
 
 
37
 
 
2.
 
Experimental Procedures
 
2.1
 
Samples preparation 
 
Sample 1 was a Ti
-
7Al 

-

which had already been cut by electron discharge machining (EDM) into a 42 x 8.2 x 2.2 mm 
tensile bar with a 10 mm gauge length.  The dimensions of sample 1 are shown in 
Figure 14a
.  
Samples 2 
and 3 were EDM sectioned into two 25 x 3 x 2.5 mm bars, as shown in 
Figure 14b
, 
from the 

-
titanium provided by Dr. Christopher Cowen (formerly at National Energy 
Technology Laboratory).  The sectioned samples experienced several grinding steps using silic
on 
carbide (SiC) grinding paper from 400, 600, 1200, down to 4000 grit using a polishing wheel at a 
speed of 200rpm.  Final polishing of the samples was accomplished on a Struers MD
-
Chem 
polishing cloth at 300rpm with the mixture of 5:1 volumetric ratio of
 
0.05 µm colloidal silica 
suspension (Struers OP
-
S) and 30% hydrogen peroxide solution for 30 minutes.  
All three 
samples
 
were electropolished with a polishing cell, as sketched by 
Figure 15
, using different 
electrolytes and different parameters [175
-
179].
  
Samples 1 and 2 were electropolished in a 
 
Figure 14a) The dimension of the Ti
-
7Al dog
-
bone tensile sample 1.  b) The dimension of the CP Ti bending 
sample 2 & 3.
 
 
38
 
 
solution that 
contained 30 ml perchloric acid, 200 ml butanol, and 300ml methanol, using an 
applied voltage of 38 V at 
-
35 
o
C.  Sample 3 was electropolished using 24 V at 
-
30 
o
C using a 
solution containing 10 wt% magnesium perchlo
rate and 90 wt% methanol.  Detail of the 
electropolishing mechanisms, parameters, and a comparison between the two methods are 
recorded in 
Appendix A
.  
 
Before deformation, grain orientations of the samples were characterized using EBSD, 
with grain boundar
y and surface conditions (after electropolishing) checked by general 
secondary electron (SE) and backscattered electron (BSE) imaging mode using a Tescan Mira III 
FEG
-
SEM equipped with an EDAX
-
TSL orientation imaging system.  EBSD was performed using a 
30 
kV accelerating voltage with a 148 µA probe emission current, a 20.0 nm spot size, and an 18 
mm working distance with the samples tilted to 70
o
.  The instrument parameters for SE/BSE 
(and later ECCI) observations were the same as used for EBSD, but the wor
king distance was 
 
Figure 15 Sketch of the electropolishing stage.  Based on what type of electrolyte is used, the voltage, 
temperature while electropolishing, the distance between cathode (stainless steel) and sample (anode), and 
the agitating speed of the stir bar will be 
different and recorded in 
A
ppendix
 
A
. 
 
 
39
 
 
around 8
-
10 mm (with a maximum stage tilt of 20
o
 
for ECCI analysis).  If not specifically 
mentioned, all images and analysis (including AFM) during each experimental stage were taken 
at consistent conditions, with the sample placed in the
 
same orientation on stage. 
 
2.2
 
Samples deformation
 
2.2.1
 
Deformation of Ti
-
7Al sample and uncoating
 
After mapping the crystal orientation distribution of sample 1 using EBSD, it was sent 

ith densely 
deposited gold nanoparticles (AuNP) through surface condensation reactions [162, 163].  It was 
then plasticly deformed to ~3% tensile strain (the coordinate system for deformation, 
observation, and analysis remained consistent and is sketched i
n 
Figure 16a1
), with a full
-
field 
displacement of particles and strain development monitored through DIC at different strain 
levels.  
 
After receiving the sample back from the Daly group, the sample 1 was soaked for a 
total of 4 hours at 30 
o
C in a solutio
n of tetra
-
n
-
butylammonium fluoride (TBAF) [180
-
184], 
chloroform, and ethylene glycol with a weight ratio of 10: 1: 1 respectively.  During this 
uncoating process, sample 1 was taken out every 1 hour and cleaned with soap water using 
sonication for 5
-
10 mi
nutes.  Final cleaning was accomplished by dipping the sample into 
dishwashing soap, wiping off the soap with cotton, flashing with ethanol
-
water
-
ethanol, and air 
drying.  The overall uncoating approach was successful, with no AuNPs left on the surface, 
re
sulting in a smooth surface and sharp SACPs.  The detailed coating removal procedure is 
recorded in 
Appendix B
.
 
 
40
 
 
2.2.2
 
Deformation of samples 2 and 3 
 
Samples 2 and 3 were plasticly deformed in a four
-
point
-
bending stage to around 1.5% 
and 1% surface tensile str
ain, respectively, with tensile strain measured as outlined in 
Appendix 
C 
(the coordinate systems for samples 2 and 3  are shown in 
Figures 16b1&c1
).  
 
2.3
 
Samples analysis 
 
All deformed samples (1
-
3) were placed on the SEM stage for the observation of slip 
tr
aces developed during the deformation, with post
-
deformation EBSD data collected to update 
the crystal orientations from deformation.  Combined with the information from the slip traces 
and the corresponding EBSD orientation profiles, surficial slip trace 
analysis was performed 
using an in
-
house developed MATLAB code [24], where the crystal orientation, the slip plane 
that may leave the slip trace on the surface, and the potential Burgers vector were input, with 
the global Schmid factor M calculated based o
n the Euler angle of the crystal and the geometry 
of potential slip systems relative to the surface tensile direction.  Based on the geometry of slip 
planes and the crystal orientation of a grain and its neighboring grains, the alignment of slip 
systems ac

[95]. 
 
2.3.1
 
ECCI analysis on sample 1 and electropolished samples 2&3
 
ECCI analysis was carried out directly on the plasticly deformed Ti
-
7Al sample 1, both 
within grains and n
ear grain boundaries, facilitating the identification of dislocations (the 
alignment of SEM for ECCI is in 
Appendix D
).  The Burgers vectors were identified through ECCI 
g
 

 
b 
 
= 0 and 
g
 

 
b 
x 
u
 
= 0 contrast analysis [140, 150, 154], and the slip planes and line 
directions were roughly estimated by tilting along one of the Kikuchi bands, with detailed 
41
 
 
procedure presented in 
Appendix E
.  Subsequent to this characterization, samples 2 and 3 were 
fu
rther electropolished 
using the same electropolishing conditions outlined in 
Appendix A
, 
which eliminated all surface topography.  The depth of material removed was determined by 
applied current and electropolishing time and was directly measured by the Vi
ckers indent.  The 
resulting materials removal was approximately 5 
µ
m from sample 2 and
 
approximately 20 µ
m 
being from sample 3.
 
EBSD was again carried out on these samples following this surface removal.  ECCI was 
then performed on samples 2 and 3 in order to identify dislocations, dislocation propagation 
investigation behavior, and dislocation interactions at grain boundaries. 
 
2.3.2
 
AF
M analysis on sample 1
 
The topography developed due to slip band development during the deformation was 
measured using a 
VEECO Dimension 3100 AFM operating in tapping mode
 
at a speed of 10
 
µ
m/min for every 40 x 40 
µ
m
2
 
area.  The data from AFM was processed
 
using the Gwyddion 
software package
8
, with the background surface normalized (polynomial 3) and the regions 
having the lowest height were automatically assigned as zero during the analysis.  
 
2.3.3
 
HR
-
EBSD analysis on sample 1
 
HR
-
EBSD was performed on the area
s where ECCI was performed on sample 1, using a 
sample tilt of 70
o
, a working distance of 20 mm, and a 20.0 nm spot size.  Each high
-
resolution 
pattern for the cross
-
correlation was taken at an exposure time of 0.1 s with a 480 x 480
-
pixel 
resolution and t
he EBSD patterns were saved.  As indicated by Dunlap et al. [137] and Ruggles 
et al. [138],  the step size will affect the GND density distribution determinations; the GND 
 
8
 
Available free at 
http://gwyddion.net/
 
42
 
 
analysis in this research was based on 200 nm effective step size, a parameter that 
can resolve 
dislocations as best as possible [136, 137].  This facilitated a semi
-
quantitative comparison 
between the GND measurements and the ECCI and AFM data.  
 
 
 
 
 
 
 
 
 
 
 
 
 
43
 
 
3.
 
Results and Discussions
 
The results presented here are primarily in the form of a large number of ECC images 
that allow the determination of crystallographic details, primarily Burgers vectors, dislocation 
line directions, and slip band morphologies.
 
 
These are related to underly
ing crystallographically 
dependent parameters based on EBSD analysis, including global Schmid factors, the angle 
between slip plane intersections in grain boundaries, 

, and the resulting compatibility factors 

 
 
These interdependent factors vary
 
from case to case. 
 
 
Thus, rather than 
presenting the results of various experiments in isolation, the author believes the best way to 
descriptively convey the research is to combine the results and discussion, presenting 
combined results for various case
s in order to tell complete stories without leaving unanswered 
questions, rather than laying out results fragmentally.
 
 
Nevertheless, 
sections 3.1&3.2
 
will 
outline the generalized approaches and observations used for carrying out the specific studies.  
Sec
tions 3.3
-
3.5
 
will outline the advantages of ECCI technique over other technique in the 
heterogeneous plastic deformation study, especially in terms of slip accommodation activities 
within grain interior and at grain boundary area.  
 
3.1
 
The overall status of 
as deformed samples 1
-
3 
 
The deformation of samples 1
-
3 at their respective strain levels (sample 1 at 3%, sample 
2 at 1.5%, and sample 3 at 1%) was dominated
 
by heterogeneous slip systems.
  
No deformation 
twins were observed within the targeted areas, whi
ch was confirmed by the SE images and 
EBSD orientation map of these areas, as shown in 
Figure 16
.  Although comparisons before and 
after deformation are not shown, the crystal orientations were not distinguishably changed 
with deformation.
  
As shown in 
Fig
ure 16a1
, the collections of lines lying at the surface of 
 
44
 
 
 
 
 
Figure 16a1) The SE image from the center of the 3% tensile strained Ti
-
7Al sample 1, with the tensile 
direction along A2 axis.  Almost all grains were deformed, with some grains having more than one 
type of slip traces.  Surface and grain boundary elevati
on could be indicated by the brighter contrast 
against the dark grains.  a2) The corresponding EBSD data in the red region of a1, which was 
collected under the same coordinate system as a1.  Despite the noises due to higher deformation 
strain that disrupts
 
the diffraction (with confident index only 0.65), color gradient within grains can 
be clearly seen, especially where slip bands were densely packed.  Slip traces appear mostly straight, 
while some curved traces were found near grain boundaries or in the g
rains which were heavily 
deformed.  
b1) An example of one of the grain boundaries between two neighboring grains in the 
center area of sample 2 after 1.5% deformation on four
-
point
-
bending stage.  Again, most slip traces 
appear straight, while the bright a
nd dark contrast on the slip traces may indicate they may not share 
the same Burgers vector.  Despite some primary slip traces that were fully propagated across the 
grains, some of the slip traces disappear as they propagated out of the grain boundary.  b2
) The 
corresponding EBSD map of the red area of b1, indicating the formation of slip bands was not 
significant enough to affect the quality of the EBSD, with a high confident index of 0.81, and the 
topography developed during deformation was not big enough
 
to be shown in the EBSD compared to 
a2.  
 
 
 
45
 
 
 
Figure 16
 
(cont

d) 
c1) SE image of a patch of 4 consecutive grains in the center of sample 3, which 
was deformed in the same manner with sample 2 to 1% plastic strain.  Slip traces in grains 2
-
4 appear 
s
traight while traces in grain 1 are wavy.  Some traces disappear near the grain boundary in grain 2, 
which is indicated by the white arrow.  Traces in grains 1 and 2 meet at the same point on the grain 
boundary, so are the traces in grains 3 and 4, while t
races in grains 2 and 3 do not meet at the same 
point on the grain boundary.  c2) EBSD map of the grain patch in c1.  The deformation is not large 
enough for EBSD to recognize the formation of slip bands at 1% strain level.  No crystal rotation is 
detected
.  It should be noted that all the prism cells in a2, b2, and c2 indicate the crystal orientations 
of the grains they were located, with the black dots indicating the optical axis.
 
 
 
 
46
 
 
sample 1 indicate the traces of the slip systems [185].  It can be s
een that the slip traces have 
varying directions, suggesting the grains were deformed in different directions due to shear in 
different directions.  
With the exception of a few grains, almost all grains in the red region show 
apparent slip traces, with hal
f of the grains showing more than one type of slip traces.
 
 
The 
overall grain size in sample 1 was somewhat smaller than that in samples 2&3, and it appears 
that the distance between slip traces in sample 1 were smaller
.  It is also noticeable that some 
gr
ains and grain boundaries show a significant contrast difference than their surrounding 
environment as a result of local lattice rotation due to deformation leading to different electron 
channeling contrast.  For example, the upper grain boundary and the r
ight region of grain 3 
show a much brighter contrast than the rest area in this grain, which indicates there is a large 
variation of lattice orientation in that area due to the deformation.  The orientation change due 
to plastic deformation was also captur
ed by the EBSD orientation map (
Figure 16a2)
.  For 
example, the densely packed slip traces are seen as fine purple lines in contrast to the overall 
pink background in grain 4, suggesting a large local orientation change in those areas.  In 
contrast, the or
ientation variations of samples 2&3 appeared much straightforward since they 
experienced a much lower plastic strain.  At 1~1.5% plastic strain, only ~30% of grains in the 
observed areas show clear slip traces on the surface.  In addition, at this low plas
tic strain, all of 
the traces within a deformed grain (
Figure 16b1&c1
) had the same orientation, suggesting that 
no other slip systems were activated.  It is noticeable that some grains are not fully 
recrystallized and have shown interesting diffraction features (grain 5 in 
Figure 16c1
), such 
grains are rarely observed and 
not the focus of this research.    
 
 
47
 
 
3.2
 
Slip system identifications
 
3.2.1
 
EBSD based slip trace analysis
 
In order to understand the heterogeneous deformation of a p
olycrystal, it is critical to 
correctly identify the slip systems that are active during the plastic deformation.  Based on the 
slip traces developed during the plastic deformation and crystal orientation information from 
the EBSD, the active slip systems 
can be readily identified with the EBSD based slip trace 
analysis [24].  An example of slip trace analysis is shown in 
Figure 17
.  
Figure 17a
 
shows grain 2 
in sample 1 after 3% plastic deformation [185].  Two types of straight slip traces are observed in 
g
rain 2, with one lying from the upper left to the bottom right (#1) and the other from the 
upper right to the bottom left (#2).  The hexagonal cells on the right represent the lattice 
 
Figure 17a) BSE image of grain 2 in sample 1.  Two straight and planar slip traces can be clearly observed, with 
their trace outlined as black lines.  The hexagonal cells on the right indicate the orientation of this grain.  The 
shaded plane in each cell i
ndicates the slip plane, the blue line indicates the slip direction, and the red dashed 
line is the plane trace on the sample surface.  For a potential slip system active during deformation, the red 
dashed line should match the trace on the surface.  b) BS
E image of a patch of grains 1~3.  Some slip systems 
with different Burgers vectors or slip planes may exhibit similar slip traces at the surface, resulting in 
uncertainties.  The colored dashed lines in each grain represent the possible slip systems that 
leave similar slip 
traces.  The Burgers vectors and slip planes of all possible slip systems are listed on the right.  The color of the 
slip system is using the same color with the dashed line. 
 
 
 
48
 
 
orientation of grain 2.  The grey shaded planes in the cell represent th
e slip plane, and the blue 
lines are the slip directions.  The red dashed lines in the cells, referred as the slip (plane) traces, 
show the intersection line of the slip plane with the sample surface.  If the red dash line is 
parallel to the observed trace
s on the sample, then the slip plane that leaves this slip trace on 
the surface is identified as the deformation plane (similarly, the colored dashed lines are the 
slip traces from the corresponding slip systems in 
Figure 17b
).  Because there is generally 
only 
one Burgers vector on each specific plane due to lower symmetry of 

-
titanium (with the 
exception of the (0001) basal plane, which can have three Burgers vector [11


0], [1


10], and 
[


110]), the slip system can thus be identified.  
 
In some cases, slip systems with different Burgers vectors or slip planes may show 
similar slip traces, adding some uncertainty in the slip system identifications.  In 
Figure 17a
, 
particularly, (0


10) [2




0] prism <a> slip system and (10


1) [




23] pyramida
l <c + a> slip 
  
system both show similar traces with the observed trace #1.  Similarly, (01


1) [





3] pyramidal 
<c + a> slip system and (10


0) [1


10] prism <a> slip system show similar traces that match the 
observed trace #2.  Slip trace analysis is also 
not capable if identifying a specific plane for wavy 
traces, since it is difficult to match curvy surface traces with the calculated ones.  An example of 
this can be found in grain 1 of sample 3 (
Figure 17b 
[96]), due to the curved traces, four 
possible sl
ip systems may be active according to the EBSD
-
based slip trace analysis.  
Additionally, grain 2 and grain 3 may deform differently and might have different slip 
interactions based on how the slip systems are identified.  In general, previous studies [43, 
74,75, 97, 98] using this EBSD
-
based slip trace analysis have overcome this difficulty by 
selecting the slip system with the highest global Schmid factor (in this study this was calculated 
49
 
 
using an in
-
house MATLAB code), by choosing the slip system with th
e lower CRSS value
9
, or a 
combination of these approaches.  
 
The latter approach is statistically reasonable because such 
 
slip systems are more likely to be active.  However, this statistical hypothesis is not safe to use 
in the study of slip interaction
s at grain boundaries, and it is not viable in extreme conditions (i. 
e. slip systems having similar Schmid factor/CRSS ratio).  In 
Figure 17b
, there are a total of 6 
possible slip systems within grains 1
-
3 (uncertainties cannot be eliminated), resulting i
n a more 
complicated situation in the evaluation of slip transfer events.  Thus, a more reliable method is 
needed to facilitate the identification of slip systems.  In this thesis, the difficulty is overcome 
by identifying the Burgers vector using ECCI. 
 
3.2.2
 
I
dentification of slip systems using ECCI
 
To eliminate the uncertainties from surface trace analysis, ECCI was either directly 
carried out on the as
-
deformed sample surfaces or after electropolishing to remove some of 
the near
-
surface material.  The Burgers
 
vectors of the slip systems can be identified by ECCI 
based 
g

b
 
= 0 and 
g

b
 
x 
u
 
= 0 invisibility criteria [140, 150, 154], where 
g
 
is the channeling 
vector, 
b
 
is the Burgers vector, and 
u
 
is the dislocation line direction.  Once the Burgers vector 
b
 
is id
entified, the slip system that forms a certain slip trace can be identified
10
 
based on the 
combined knowledge of the Burgers vector and the subset of possible slip planes from the slip 
trace analysis. 
 
One example of the ECCI identification of dislocation Burgers vectors is given for grain 1 
 
9
 

-
titanium, prism <a> slip system is more likely to be activated than the pyramidal <c + a>
 
due to a lower CRSS 
value
.  Thus, it is more likely to consider prism <a> s
lip system is the active one
 
than other candidates, unless the 
Schmid factor of prism <a> slip is extremely low and is not possible to be activated.  
 
10
 
Dislocation line direction 
u
 
can be used to
 
reveal the inclination of the slip plane, and 
thus 
eliminate the 
situation when a pyramidal <a> and a prism <a> slip system shows a similar trace with the same Burgers vector
.
 
50
 
 
 
 
Figure 18a) BSE image of one of the areas of interest after deformation of sample 1.  b
-
f) ECC images taken at 
different channeling conditions from the red boxed area.  The upper left circles are the Kikuchi patterns.  Each 
black arrow across a Kikuchi ban
d indicates the specific channeling band, and the arrowhead is where the optic 
axis is focused.  Each channeling condition is identified from the T. O. C. A software.  The Burgers vectors of 
dislocations are identified by 
g
 
.
 
b
 
= 0  and 
g
 
.
 
b 
x 
u
 
= 0  cont
rast analysis, and the slip plane can be revealed 
through different tilting and rotating along a certain channeling band (
Appendix 
E
).  A total of four different 
slip systems are identified and labeled by colored arrows, namely:  (01


0)[2




0] prism <a> sli
p system (green), 
(10


0)[1


10] prism <a> slip system (blue), (10


1)[1


10] pyramidal <a> slip system (purple), and (0001)[11


0] 
basal <a> slip system (red).  Amended from [185]
 
51
 
 
of sample 1 in 
Figure 18
 
[185].  A series of ECC images of the same area have b
een taken at 
different channeling conditions (at different 
g
).  If the dislocation shows little or no contrast at a 
certain 
g
, then the Burgers vector can be identified through the ECCI 
g
 

 
b
 
= 0  and 
g
 

 
b
 
x 
u
 
= 0  
contrast analysis.  For example, 
dislocations with the Burgers vector of [2




0] should show 
good contrast at 
g
 
= [



], [





2], [1


00], [11


0] (
Figure 18b
-
e
), and show weak contrast at  
g
 
=  [01


1] (
Figure 18f
).  In this particular example, a total of three different Burgers vector 
were 
identified.  After combining the Burgers vector and the slip plane traces, four different slip 
systems were finally identified, namely:   the (01


0)[2




0] prism <a> slip system  (green), the 
(10


0)[1


10] prism <a> slip system (blue), the (0001)[11


0] basal
 
<a> slip system   (red),  and a 
small number of (10


1)[1


10] pyramidal <a> slip system (purple).  The majority of dislocations 
that contributed to the formation of slip bands in grain 1 were the (01


0)[2




0] prism <a> slip 
system (green) and the (10


0)[1


10] prism <a> slip system (blue).  Additionally, with the Euler 
angle acquired from the EBSD software, the global Schmid factor can be calculated based on 
the global stress state.  Based on the experimental observation, it is clear that the (01


0)[2




0] 
pr
ism <a> slip system (#1 slip system in 
Figure 17a
, green in 
Figure 18
) is more active since the 
global Schmid factor (M) is 0.49, while the other prism <a> slip system, (10


0)[1


10] (#2 slip 
system in 
Figure 17a
, blue in 
Figure 18
) is less active because i
t has a much smaller M, 0.23.  
The <a> type dislocations on pyramidal and basal planes do not contribute to the deformation 
due to the low Schmid factor (0.19 and 0.09 respectively) and higher CRSS value. 
 
Similar approaches were also applied on the electr
opolished samples 2 & 3 (
Appendix 
F
), and perfectly confirmed the slip systems active during the plastic deformation.  For example, 
in sample 3 (
Figure 17b
), the active slip system in grain 1 was dominated by the (1



)[11


0] 
52
 
 
prism <a> slip system (M= 
0.15), with dislocation cross
-
slip on (1



) pyramidal plane 
(M=0.23).  The active slip system in grain 2 was also identified to be (1



)[11


0] prism <a> slip 
system (M=0.41), and the slip system in grain 3 was the (10


0)[1


10] prism <a> slip system 
(M=0.
48).  With precise identification of slip systems, the study of shear associated with each 
slip band during heterogeneous deformation and the investigation of slip/grain boundary 
activities is thus reliable. 
 
3.3
 
The comparisons of surface
-
based techniques 
 
Th
e main purpose for analysis of the deformation of sample 1 was to compare different 
surface
-
based technologies in the evaluation of plastic deformation.  Relative techniques 
involved in this study were ECCI, atomic force microscopy (AFM), and EBSD cross
-
co
rrelation.  
Meanwhile, digital image correlation (DIC) data was provided by Dr. Zhe Chen in Professor 

data [185, 186].  
 
3.3.1
 
Local shear distribution across the surfac
e
 
AFM was used to monitor the topography change due to deformation slip activation 
during the plastic deformation of sample 1.  Each AFM grid covered a maximum area of 40 x 40 
µ
m
2
 
to maintain considerable accuracy (large area scan will sacrifice accuracy)
11
.  An example of 
AFM topography map is shown in 
Figure 19
.  
Figure 19b
 
is a color
-
scale topography map from 
the black boxed area in grain 2 (SE image) as shown in 
Figure 19a. 
 
The topography change due 
to two different slip systems can be detected from th
e AFM (no research has used AFM to 
 
11
 
Higher scanning speed will sacrifice the preciseness, so the tiny surface change will not be recorded by the 
system.
 
53
 
 
 
 
Figure 19a) SE image of the upper right corner of grain 2 in Ti
-
7Al sample 1.  b) AFM color
-
scale map from the 
black boxed area in figure a).  The black line is the AFM line profile showing the topography change acro
ss the 
line.  The black arrows indicate the edges of slip bands, and the dashed line indicates the undistorted surface 
plane and is the basis of the height measurement.  c) 3
-
D Greyscale topography map around the line sectioned 
area, the surface normal is 
calculated based on undistorted surface, H is the step of the slip band.  d) A sketch 
of the mechanism to calculate the local shear distribution across the slip bands.  The Burgers vector 
b
 
and slip 
plane normal 
n
 
can be directly achieved from the EBSD data once the slip system is confirmed by ECCI contrast 
analysis.  Height difference across a slip band H can be directly measured from the AFM line profile.  The 
distance across a slip band X is 0.3 
µ
m in this study
.  
(Amended from [185])
 
54
 
 
identify slip systems), which is consistent with the SEM observation (
Figure 18a
).  In the AFM 
data analysis, the background is subtracted and the lowest point in the map is set to zero 
height, so it is easier to find the undistort
ed surface plane that has not experienced  
deformation (surface plane normal 
e
).  Based on the line section profile across the area (
Figure 
19b&c
), the height change H (nm) across a certain distance (X 
µ
m) due to the activation of each 
slip system can be a
cquired.  With the crystal orientation achieved from the EBSD, the Burgers 
vector 
b
 
and slip plane normal 
n
 
of each identified slip system (by ECCI) can also be calculated 
from the in
-
house MATLAB code [24], as outlined earlier.  The method for local shear
 
distribution was established by Yang et al. [44], with the mechanism shown in 
Figure 19d 
[185].  
For a certain slip system that contributes to the formation of a slip band, the number of relative 
slip planes N can be calculated from the height change acro
ss the slip band H and the projection 
of the Burgers vector 
b
 
[b
x
 
b
y
 
b
z
] onto the surface plane normal 
e 
[e
x 
e
y 
e
z
]:
 
N = 






 

 
The calculation of shear is tile based.  With equation (6), the averaged shear contributed 
by each slip band 

 
along a certain distance X in each tile can be estimated as
: 
 

 
=












  
= 
















 

 
Where 
n
 
[n
x 
n
y
 
n
z
] is
 
the slip plane normal of the certain slip system.  The map of relative 
local shear distribution across one area in grain 2 is shown in 
Figure 20b
, which reveals the 
topography change of this area according to the AFM map (
Figure 20a
).  The deformation she
ar 
contributed by the 
(01


0)[2




0] prism <a> slip system 
is from 0.3 to 0.7, and the shear from 
the 
(10


0)[1


10] prism <a> slip system ranges from 0.08 to 0.15.  This is also consistent with 
55
 
 
the argument that (01


0)[2




0] prism <a> slip system (M = 0.49) i
s more active than the 
(10


0)[1


10] prism <a> slip system (M = 0.23) in slip trace analysis and the SEM observation.  
 
Based on a similar mechanism shown in 
Figure 19d
, the local shear distribution of slip 
systems can also be calculated by 
measuring the difference of in
-
plane displacement [185, 186]:
 

 
= 







 

 
Where S 

x
 

y 

z]
 
is the relative displacement that can be calculated from the Burgers 
vector and in
-
plane displacement across a slip band:
 

 
= 

 

x/b
x
 

 
or
 
 

 
= 

 

y/b
y
 


 
The resulting shear distribution map calculated by the DIC is shown in 
Figure 20c
 
[185].  
The deformation shear across each slip band calculated by the DIC method is similar with the 
AFM result.  For example, the shear contributed by s
lip band #1 is ranging from 0.26 to 0.48 and 
the shear caused by slip band #2 is ~0.16 calculated by the AFM method.  Similarly, the DIC 
method shows a similar shear amount from slip band #1 (0.25~0.45) and #2 (~0.14).  The 
difference might come from diffe
rences in the accuracy of AFM and DIC data collection (DIC is 
Figure 20a) color
-
scale AFM map from an area in grain 2.  b) The heat map of local shear distribution across 
individual slip bands.   The local shear contributed by the (01


0)[2




0] prism <a> 
slip system ranges from 0.3 
to 0.7, and the shear caused by the (10


0)[1


10] prism <a> slip system ranges from 0.08 to 0.15.  c) The 
relative shear distribution map of the same area calculated by the DIC method [185].  
 
56
 
 
more sensitive to in
-
plane displacement, while AFM is more focused on out
-
of
-
plane 
measurements) or the position variance used in the calculation (the two points at a distance of 
X µm across the
 
slip band are different in AFM and DIC calculation), etc.  Nevertheless, the 
overall results from the two methods are consistent with each other.  Besides this typical 
example, comparisons between both methods have been made across several other slip band
s, 
all giving reasonable results.  This suggests the two methods are reliable and consistent in 
revealing the local shear distribution in the plastic deformation.  
 
3.3.2
 
 
Dislocation based characterizations of plastic deformation 
 
Different from the AFM and DIC
 
approaches that directly reveal the shear that cause 
deformation, the EBSD cross
-
correlation method is able to estimate the residual elastic shear 
after slip band formations by investigating the distribution of geometrically necessary 
dislocations (GNDs).
  
Since the methodology study of parameter selection of GNDs is not the 
focus of this study and has been well illustrated by Fullwood et al.[117, 136
-
138], the specific 
parameter selection for this approach will not be discussed.  In this study a 990 nm st
ep size 
was used for the cross
-
correlation calculation in the open source OPEN
-
XY software
12
 
[187], 
which gives a relatively stable GNDs density (990 nm is where GND does not significantly 
change with step size) and eliminates potential noises from data co
llection.  Since the 
dislocations are visible by ECCI, it is possible to compare the reliability of the GNDs to ECCI [137, 

titanium is currently unavailable) and
 
ECCI is shown in 
Figure 21
.  
Figure 21a
 
shows ECCI 
 
12
 
The latest
 
OPEN
-
XY has added the GNDs calculation of 

 
titanium, however, the split GNDs for 

 
titanium is 
currently unavailable.  This is the reason for showing only total GNDs, rather than GNDs for each types of 
dislocations in this study.
 
57
 
 
 
 
Figure 21a) ECC image of the same area with Figure 20.  Besides the (01


0)[2




0] (green) and (10


0)[1


10] 
(blue) two prism <a> slip systems identified in the slip trace analysis, (0001) [11


0] 
(red) basal <a> dislocations 
are revealed by the contrast analysis.  The prism <a> type dislocations appear to align perfectly along the slip 
bands, while the basal <a> dislocations are less uniformly distributed across the observed area.  b) The GND 
logar
ithm map of the red boxed area of a).  The GND map is consistent with ECCI observation, although 
individual dislocations cannot be resolved as good as the ECCI observation.  c) The ECC image at the grain 
boundary of grain 2, with (01


0)[2




0] (green) and (
0001) [11


0] (red) dislocations.  Prism <a> dislocations 
align close to the slip bands and basal <a> dislocations are more randomly distributed across the surface.  d) 
The GND map from the red box area of c).  The GND on the other side of the grain boundar
y is not available 
due to misorientation angle exceeding the threshold from the reference point in grain 2.  The GND map is 
consistent with ECCI observation.
 
58
 
 
observation of the same area with 
Figure 20
, where the shear is calculated by the AFM and DIC.  
E
CCI correctly reveals the two prism <a> slip systems, (01


0)[2




0] (green) and (10


0)[1


10] 
(blue), that have been identified in the slip trace analysis.  The dislocations of the two types are 
uniformly aligned on the slip bands.   More importantly, ECCI c
ontrast analysis also reveals a 
number of (0001) [11


0] basal <a>  dislocations (red) that are less uniformly distributed within 
the vicinity of the slip bands.  
Figure 21b
 
shows the logarithm map of total GNDs from the red 
boxed area in 
Figure 21a
.  It ap
pears the dislocation density along the slip band (10
14.5~15
) is 
more than one magnitude larger than the overall background (10
13~13.5
), with some dislocations 
(10
14~14.5
) distributed randomly near between slip  bands.  The total GND density is consistent 
with the ECCI observation (10
14
 
corresponds to 50 nm between dislocations) that dislocations 
are more localized around the slip bands.  Similarly, ECCI and GND map at one of the grain 
boundary in grain 2 also consistent dislocation distributions on the lef
t side of the grain 
boundary (
Figure 21c&d
), although only (01


0)[2




0] (green) prism <a> dislocations and (0001) 
[11


0] basal <a> dislocations (red) are detected.  Again, the prism <a> dislocations are found 
confined in the slip bands, whereas the basal <a> dislocations are less uniformly distributed 
between slip bands.  
 
3.3.3
 
Comparison between the classic EBSD based slip tr
ace analysis and ECCI
 
It may be noticeable in the discussion of 
Figure 21
 
that EBSD based slip trace analysis is 
not able to identify all the slip systems developed during the plastic deformation.  Some slip 
systems may not develop well defined slip bands 
for a number of reasons:  if cross slip is easy, 
dislocations may not form well defined slip traces or if the slip plane is aligned close to parallel 
to the observed surface.   Additionally, if an experimentally observed slip trace does not match 
59
 
 
the theoretical trace,  the slip system for that trace cannot be identified.  Slip system 
identification in grain 1 of sample 1 is an example showing these limitations of current slip trace 
a
nalysis (
Figure 22
).  Both AFM topography map and the SEM image show two different slip 
traces.  EBSD
-
based slip trace analysis indicates the slip traces are caused by (


100)[11


0] (red) 
and (0


10)[2




0] (blue) prism <a> slip systems (
Figure 22a&b
).  
But there is another type of 
slip trace observed close to the upper grain boundary of grain 1 (brown), which cannot be 
identified,  since the slip trace does not match any of the theoretical traces.  ECCI contrast 
analysis reveals this unidentified slip sy
stem to be (


011)[1


10] pyramidal <a> slip system (light 
brown in 
Figure 22c
).  The slip trace might be distorted by local lattice rotation or the 
topography development during the plastic deformation, and thus deviate from the theoretical 
traces.  Additio
nally, a large number of basal <a> dislocations are detected by ECCI, with the 
majority belonging to (0001)[1


10] slip system.  Based on the MATLAB code calculation, at this 
 
Figu
re 22a) AFM color
-
scale topography map at the upper right corner of the grain 1 in sample 1.  Two 
different deformation shear system can be observed by the AFM.  b) ECC image of the same area, two slip 
systems were identified through the EBSD
-
based slip tr
ace analysis, which are the (0


10)[2




0] prism <a> slip 
system (blue) and the (


100)[11


0] prism <a> slip system (red).  The slip trace marked in light brown cannot be 
identified by the slip trace analysis.  c) High magnification ECC image of the red box a
rea in b).  Contrast 
analysis shows several additional dislocations, including  (10


1)[1


10] and (


011)[1


10] two pyramidal <a> slip 
systems and a mixture of basal <a> dislocations with majority belong to (0001)[1


10] slip system.  The 
unknown branched sli
p trace is caused by the (


011)[1


10] pyramidal <a> slip system.
 
60
 
 
crystal orientation, the basal plane is close to parallel to the sample surface, t
hus no slip band 
can be easily developed that can be identified in the slip trace analysis.  Furthermore, the basal 
<a> and (10


1)[1


10] pyramidal <a> dislocations are also observed (brown), but the density is 
small compared to other dislocation types.  Th
us, these dislocations have not developed slip 
bands on the surface.  Similar situations where more dislocation types can be identified by ECCI 
than the slip trace analysis were also observed in other grains of sample 1 (
Appendix G
).  
 
3.3.4
 
Advantages and disad
vantages of EBSD, DIC/AFM, and ECCI
 
A summary of slip system identification using EBSD based slip 
trace analysis, ECCI, and 
AFM/DIC [185] is shown in Table 1.  Classic EBSD
-
based slip trace analysis is not good at  
differentiating slip systems that have similar slip traces
13
.  With the help of the Schmid f
 
 
actor/CRSS ratio, some pyramidal <c + a> slip
 
systems can be eliminated (i.e. (2




2)[


113] in 
 
 
13
 
This is partially reso
lved by the EBSD cross
-
correlation that use lattice rotation across a slip band to determine 
the possible slip system [189].  This method is not the classic slip trace analysis.
 
Table 1
.  
Slip systems identified by EBSD slip trace analysis, ECCI, and AFM/DIC
 
 
Grain 1
 
Grain 2
 
Grain 3
 
Grain 5
 
EBSD
-
slip trace 
analysis
 
(0


10)[2




0]
 
(0


11)[






]
 
(


100)[11


0]
 
(2




2)[


113]
 
(0


10)[2




0]
 
(10


1)[




23]
 
(01


1)[





3]
 
(10


0)[1


10]
 
(0


10)[2




0]
 
(
01


1)[




23] 
(10


0)[





0]
 
(10


1)[




23]
 
(1


00)[11


0]
 
(2




2)[


113]
 
 
ECCI
 
(0


10)[2




0]
 
(


100)[11


0]
 
(


011)[1


10]
 
(0001)[1


10]
 
(10


1)[1


10]
 
(01


0)[2




0] 
(10


0)[1


10]
 
(10


1)[1


10] 
(0001)[11


0]
 
(0


10)[2




0]
 
(10


0)[





0]
 
(0


11)[2




0]
 
(


100)[11


0]
 
 
(1


00)[11


0]
 
(01


0)[2




0]
 
AFM
 
and 
DIC [18
5
]
 
 
(0


10)[2




0] 
(


100)[11


0]
 
 
(01


0)[2




0] 
(10


0)[1


10]
 
N. A.
 
N. A.
 
Note:  Colored fonts 
indicate different slip traces, black fonts are dislocations that are only observed in ECCI.  
Shadowed slip systems are not likely to be activated because of the lower Schmid factor/CRSS ratio.
 
61
 
 
grain 1&5), however, this estimation is not always safe (such as grain 2&3).  On the other hand, 
AFM and DIC [185, 186] are more precise in the slip system identification, since the physical 
displacement
14
 
across a slip band indicates shear direction (i.e. Burgers vector), which 
supplements the trace analysis.   Unfortunately, these methods are not good for traces that do 
not match the theoretical generated traces (grain 1 in 
Figure 22
) or the slip systems t
hat do not 
show apparent slip traces (i.e. (0001) dislocations in grain 1&2).  On the contrary, ECCI is 
especially good for the identification for slip systems since this identification is based on 
dislocation contrast rather than topography/displacement c
hange.  Compared to the classic slip 

 
factor (a factor defines the deviation of an observed trace from a theorical one.  Zero deviation 
means a perfect match), 
 
of an observed trace to the theoretical one dislocation contrast 
  

different channeling conditions 
g
 
are taken, there is almost no uncertainty in the identification 
of 
dislocations regardless of the morphology of the slip traces.  Thus, ECCI is able to identify 
every dislocation slip activation during the deformation that is ignored by the classic slip trace 
analysis (ECCI row in 
Table 1
).  This is 
particularly 
important
 
when studying the strain 

roles in these events.
 
Slip system identification techniques, no matter ECCI or DIC/AFM, need the crystal 
orientation information achieved from the EBSD.  Although not shown in this study, most 
 
14
 
Currently, this method is only available on DIC, however, since the mechanis
m are similar, it is possible to 
develop a program for AFM
.
 
 
62
 
 
recent EBSD cross
-
correlation is able to more precisely identify slip systems by rela
ting the 
 
GND
-
induced rotation gradient across the slip bands to the slip system identifications [185,
 
188].  Yet EBSD cross
-
correlation is time consuming and needs extremely large data volume (30 
Gb for an area shown in 
Figure 21 
at a step size of 200 nm,
 
5 hours per scan).  
 
DIC and AFM are generally useful tools for studying plasticity.  DIC is more accurate in 
monitoring the in
-
plane displacement, while AFM is good for determining out
-
of
-
plane 
topography change.  With the crystal orientation information
, both methods give reliable 
information of the local shear distribution across slip bands.  Particularly, by correlating the 
relative displacement across a slip band to a theoretical slip system, DIC is more precise in the 
identification of the slip plane
, thus improve the reliability of the slip trace analysis.  However, 
this improved slip trace analysis is still blind to the curvy traces that will develop from cross
-
slip, 
traces that deviate from theoretical traces, and slip systems that do not form a sl
ip trace.  This 
is a chronic issue that all the slip trace analysis techniques suffer from.  Although this issue may 
not be significant in the study of overall plasticity development in the bulk sample, this issue 
may lead to severe problems in slip transf
er studies, since such irregular or hidden slip traces 
usually exist near the grain boundary.  Incorrect identification of these slip systems may bias 
the understanding of slip interactions at the grain boundary.
 
Compared to the techniques discussed above,
 
ECCI is extremely strong in the slip system 
identification since it is able to identify the Burgers vector of a slip system by contrast analysis.  
This means ECCI is not affected by the morphologies of slip traces at the free surface.  By 
revealing all ty
pes of dislocations, it is possible to investigate the accommodating events at the 
grain boundaries at dislocation level, which is generally ignored in the studies that heavily rely 
63
 
 
on the slip trace analysis.  Thus, ECCI is a perfect solution to the estab
lishment of a precise slip 
trace analysis.  The only drawback for ECCI is the time
-
consuming issue, since it generally need 
at least 6 different 
g 
vectors (must include at least one 
g
 

 
b
 
x 
u
 
= 0 or 
g
 

 
b
 
= 0) to identify 
Burgers vector and several more ti
lt & rotate operation to reveal slip planes.  Additionally, too 
much topography change after the high strain deformation will add difficulty for the 
establishment of channeling condition and resolving individual dislocations.
 
3.4
 
The reveal of the geometry of 
slip systems at grain boundaries 
 
As discussed in the previous section, one of the benefits of using ECCI in the study of slip 
accommodation is the capability to precisely identify all active slip systems at grain boundaries.  
This is particularly importan
t in the understanding of slip transfer events between grains in hcp 
titanium.  The stress state at the grain boundary may not be the same as it is within the grain, 
thus slip activation may be completely different at the grain boundary.  Such local activa
tion of 
unexpected slip systems may not be correctly revealed by the slip trace analysis due to lack of 
slip traces
15
.  This leads to a bias in the evaluation of slip transfer events during heterogeneous 
deformation due to the ignorance of local slip accommodation mechanisms at the grain 
boundary.  
 
3.4.1
 
Categories of slip system interaction at surface 
 
Different slip transfe
r mechanism may be revealed by varied interactions between an 

grain boundary were generally categorized into three types in early studies of slip transfer 
ev
ents based on the TEM observations [25, 77
-
 
87].  These classifications are still widely used in 
 
15
 
If the slip plane of a slip system is close to parallel to the surface, slip band is hard to be revealed at the surface.  
 
64
 
 
 
 
 
Figure 23a
-

-


-

-
g) SE images 

-

same point on the grain boundary at surface, despite the slip system is highly activated.  h
-
i) SE images of 

f slip systems that propagate up to the grain 
boundary only occurs in one of the grains, with the other grain undeformed.  At certain circumstances, the 

into the 
originated grain.  
 
65
 
 
the studies of heterogeneous deformation to describe how slip systems interact at the free 
surface.   The first type describes the situation that two slip systems in their respective grains 
meet at the same point at the grain 
boundary.  It appears the dislocation slip coming from a 

intersection point with the grain boundary.  The interaction between the two slip systems is 

ll
-

Figure 23a
-
d
, such well
-
correlated slip interaction 
can happen not only between slip traces that are close to parallel to each other (Figure 23a
-
c), 
but also between those that are far from parallel (Figure 23d).  The second t
ype of slip 
interaction is shown in Figure 23e
-
g.  Despite the strongly activation of slip bands in both grains, 
the slip bands do not meet at the same point  at the grain boundary, regardless of whether or 
not their slip traces appear to be parallel align

-


directly transferred into
 

Figure 23h&i
.  The slip system is highly activated only in one of the grains.  It appears the slip 

ry in 
between, and no shear is transferred across the grain boundary.  This slip interaction is then 

 
3.4.2
 
Limitations of the current category system and free surface biasing effects
 
It seems convenient to directly apply the concepts that wer
e used in TEM thin film 
studies (in
-
situ slip transfer studies) of slip transfer in polycrystal heterogeneous deformation.  

-

66
 
 
 
 
Figure 24a) 3
-
D geometry of slip system i
nteractions at a grain boundary.  The two slip systems are considered 
as well
-
correlated slip systems since they intersect at the same point at the grain boundary on the free surface.  
Although slip systems intersect at the same black point at the surface,
 
it can be clearly seen that they do not 
meet below the surface since the geometric orientations of the two slip systems are different, with 

 

 
0
o
. 
 
b) 
Another 3
-
D geometry of slip bands interactions in the vicinity of a grain boundary.  The two slip systems are 
defined as non
-
correlated since they do not meet at the surface.  However, they may meet at the grain 
boundary plane somewhere below the surfa
ce.  Although the slip transfer mechanism may be different 
between a) and b), current studies of slip transfer ignore this potential difference and directly use the slip 
transfer criteria to evaluate the strain accommodating events at the grain boundary. 
 
 
67
 
 
interactions at the surface, nor TEM thin
-
film [79
-
86] observations are able to fully represent 

-

Figure 24a&b
 
show the 
ideal 3
-

-

-

 
slip systems on opposite 
sides of a grain boundary plane.  The two slip bands from the two neighboring grains will only 
meet at one point at the grain boundary plane, since generally 

 

o
, except in very limited 
cases.  If this is true, then it is hard 
to rationalize that slip transfer only occurs at the common 
points.  Thus, the deformation shear transfer in the regions away from the common point is 
currently unclear.  In addition to this, not only in this study, but also others [45, 74, 75], have 
found
 

-

-

slip systems.  This may suggest the free surface is biasing the observations by creating more 

-

sm.  Nonetheless, the 
alignment of slip bands and the slip transfer among slip systems (

 

o
) below the surface will 
be revealed by ECCI after removing approximately five microns of material through 
electropolishing [171, 175].
 
3.4.3
 
Comparison of slip system 
alignment at and below surface
 

-

 
Figure 25a
.
 
 
Despite the large angle between the slip traces, slip traces from the two slip systems 
consistently meet at the same points on the grain boundary.  ECCI facilitated slip trace analysis 
reveals the slip system in the upper grain is the (0


10)[


110] prism <
a> slip system with a 
higher Schmid factor of 0.48, and its well
-
correlated counterpart in the lower grain is the 
(10


0)[


2


0] prism <a> slip system (lower M=0.36).  It seems dislocation slip is more easily 
activated in the upper grain than in the lower gr
ain due to a higher Schmid factor M with the 
68
 
 
 
 
Figure 25a) SE image showing two slip traces that are well
-
correlated at the surface.  The despite a large 
angle between the slip traces, they intersect at the same points on a grain boundary.  ECCI facilit
ated slip 
trace analysis indicates the slip system in the upper grain is the (0


10)[


110] prismatic <a> slip system with 
the Schmid factor 0.48.   The slip system in the lower grain is (10


0)[


2


0] prismatic <a> slip system, with a 
lower Schmid factor of 0
.36.  The white arrows mark one of the well
-
correlated slip traces for comparison. b) 
ECC image of the same region, but 5 µm below the surface.  The observed slip bands are now due to 
dislocation contrast, rather than topography.  It can be clearly seen th
at the slip bands are misaligned in the 
electropolished area, which is indicated by the relative position change of the white arrows.  Nevertheless, 
the relative spacing and distributions of the slip bands remains unchanged.  c) high magnification ECC imag
e 
of the area in the red boxed area in figure (b).   It shows the activation of (


011)[


2


0] pyramidal <a> 
secondary slip systems (M =0.45) in the lower grain from an intersection point of the slip system form the 
upper grain at the grain boundary. The sec
ondary slip system propagates a short distance and appears to 
merge into the primary slip system in the lower grain.  There might be multiple activation of such secondary 
slip system, possibly from different sources at different depth in the grain boundary
 
plane, which is indicated 
by the small arrows. 
 
 
69
 
 
same CRSS value, which is also consistent with the observation that deformation slip only 
propagates a short distance in the lower grain.  It also appears the slip system in the lower grain 
is nucleated fr
om the  intersection points between the slip system in the upper grain at the 
grain boundary to accommodate the induced deformation shear, although it is not clear where 
the slip system in the upper grain is originated.   Despite the correlation of these s
lip bands (i.e. 
two big arrows), the two slip systems do not align perfectly as they might appear to.  The 

the Burgers vectors is 15.4
o
), suggesting the two 
slip systems are still misaligned.  Since the slip 

normal is 50.4
o
), as shown in  
Figure 24a
, it can be imagined that unless 

 
= 0, there will be 
significant mi
salignment of the slip planes below the surface.     
 
Figure 25b 
is an ECC image of the same area after electropolishing.  Different from 
Figure 25a,
 
where the slip bands are observed due to topographical contrast, the observation 
of the slip bands come fr
om the contrast of dislocations at certain channeling condition (in this 
case 
g
 
= [







]).  By comparing 
Figure 25a&b
, it appears that the spatial distribution of the slip 
bands remains the same (i.e. the spacings and distributions of the slip bands on eit
her side of 
the boundary are the same at and below the surface).  It also appears that the propagation of 
all slip bands in each grain are consistent in the two images (slip bands move to the right in the 
upper grain, while the slip bands move to the left 
in the lower grain).  But critically, despite the 
spatial distribution of the slip bands remaining the same between surface and subsurface 
observation,  the intersection points of the slip bands at the grain boundary are now offset by 
approximately 7 

m (i
ndicated by big arrows).  This is consistent with the expectation that the 
70
 
 
slip systems will  no longer be well
-
correlated below surface.  Detailed ECCI analysis of the red 
boxed area is shown in 
Figure 25c
.  A number of secondary slip systems in the lower
 
grain are 
found to be well
-
correlated with the primary slip system in the upper grain (indicated by small 
arrows).  These secondary slip systems appear to nucleate from where the slip system in the 
upper grain intersects the grain boundary.  The secondary
 
slip systems then propagate a short 
distance and merge into the primary slip system in the lower grain.  ECCI contrast analysis 
reveals the Burgers vectors of the dislocations associated with the secondary slip system are 
the same as those in the primary 
slip system, [


2


0].  However, these secondary slip bands are 
on the (


011) pyramidal plane, different from the (10


0) plane of the primary slip system.  
Nevertheless, the shear accommodation at grain boundary appears to be facilitated by the 
activation of
 

primary slip system in the upper grain is still achieved by the secondary slip system in the lower 
grain.  By correlating the surface and subsurface images,  the approximate 3
-
D geometry of the 
slip systems and the grain boundary can be reconstructed (
Appendix H
), and the angle 

 
between the intersection lines of slip systems at the grain boundary (and the grain boundary 
inclination angle 

) can be calculated.  This allows the i
nteractions between slip systems at grain 
boundaries to be assessed in a more comprehensive way.  In this particular case (
Figure 25
), 
based on the seven 
microns
 
offset between the intersections points of the slip systems at the 
grain boundary at five micr
ons below the surface, the grain boundary plane inclination angle 

 
is around 20
o
.  The angle 

p
-
p
 


o
, while the 

p
-
s 

71
 
 
around 17
o


the two 


activity of this secondary pyramidal <a> slip system is supp
ressed due to a much larger CRSS 
value to the prism <a> slip system (1.3~8:1 [25
-
28,24
-
37]).  It is reasonable to conclude that the 
local activation of secondary slip system facilities strain accommodation at the grain boundary.  
The much stronger alignmen

system helps to compensate the incompatibility between the primary slip systems within the 
grain boundary below the surface.  Since dislocation propagation on the pyramidal plane is not 
favora
ble, these dislocations begin to cross
-
slip and glide onto the prism plane at a short 
distance away from the boundary, where the propagation is much easier under global stress 
state.  In conclusion, different from the overall deformation of grain interior,
 
which is strongly 
controlled by the primary slip systems with high Schmid factor/CRSS, local accommodation at 
the grain boundary generally requires the activation of secondary slip systems that are better 

 
The local
 
accommodation at the grain boundary below surface can also be found 

-

boundary.  One example is shown in 
Figure 26
.  The prism <a> slip system (M = 0.49) in the 
upper
 
grain appears to be well
-
correlated with the basal <a> slip system (M = 0.40) at the grain 
boundary in the as
-
deformed sample.  Comparison of 
Figures 26a&b
 
reveals that the relative 
spacing and distribution of the slip lines remain the same before and aft
er electropolishing, 
72
 
 
 
 


represents the trace of the grain boun
dary at the intersection point with the strongest band in the upper grain.  
b) ECC image of the same area after removing 5 

electropolishing.  The grain boundary orientation 
is significantly changed, which is indicated by the change of the red da
shed tangent line around the same 
strongest activated slip band.  The slip band spacings and relative distributions remain the same before and 
after surface removal.  c) Higher magnification ECC image of red tangent line area.  A ~50 nm misalignment 
betwee
n the two slip systems below the surface has been observed.  d) ECC image of the red boxed area in 
figure (c).  A small number of secondary slip system is observed in the upper grain in this case.
 
 
73
 
 
although the grain boundary orientation has changed signi
ficantly, as is reflected by the change 

-

grain boundary reveals an approximately 50 nm offset between the intersection points at the 
grain boundary after elec
tropolishing (
Figure 26c
).  This very small deviation between the 
primary slip systems across the grain boundary is consistent with the relative high geometric 

diffi

limited number of pyramidal <a> dislocations in the lower grain, as well as one pyramidal <a> 
secondary slip system in the upper grain.  Particularly, as shown in 
F
igure 26d
, despite the 
Burgers vector of the secondary slip system being the same with the primary slip system in the 
upper grain, ECCI contrast analysis  shows the dislocations are in different contrast.  This 
indicates the dislocations have different lin
e directions and different edge and screw 
components.  Although not shown specifically, the dislocations associated with the secondary 
slip system also have the same Burgers vector with the primary slip system in the lower grain.  
The angle 

p
-
p
 
between th
e two primary slip system is relatively small, ~15
o
, which is consistent 

exist in both grains, it is necessary to calculate the 

p
-
s 
separately
16
.  The 

p
-
s
 
betwe
en 

pyramidal <a> slip system in the upper grain is ~ 37
o
, while the 

p
-
s 


 
16
 



 
to 
complete the other half of the analysis.
 
74
 
 
slip in the lower grain is ~22
o
.  Other secondary slip systems combinations have also been 
studied, including 

p
-
s
 
between primary and secondary 
slip systems in the upper grain (~ 25
o
),  

p
-
s
 
limited to the lower grain (~36
o
), and 

s
-
s 
(~60
o
).  These suggest the secondary slip system is 
primarily accommodating the shear from the primary slip system across the boundary, rather 
than the shear within 
the own grain.  Additionally, it might not be necessary for the secondary 
slip systems to be well
-
correlated with each other.  Although the detailed mechanism of this 

t
hat local accommodation can still occur by the activation of secondary slip systems despite the 
two primary slip systems being well
-
aligned.  Atomic studies of such slip well correlated surface 
slip transfer with varying 

 
would be insightful for understan
ding the details of the dislocation 
mechanisms at these boundaries, but are beyond the scope of the present study.  
 

-

 
is shown in
 
Figure 27
.  At the 
surface, the (0


10)[


110] prism <a> slip bands (M= 0
.30) in the upper grain and the 
(10


0)[


2


0] prism <a> slip bands (M= 0.28) in the lower grain do not meet at the same points 
on the grain boundary (
Figure 27a
).  The lack of correlation between the two primary slip 
system is also consistent with the low m


p
-
p
 
=58
o
), despite the slip systems being readily 
active within their respective grains.  Following electropolishing, it can be clearly seen that the 
relative spacing and distribution of the slip bands remain the same in each grain below the 
surfa
ce, suggesting the slip bands are confined in their own slip planes (
Figure 27b
).  However, 
as indicated by the small white arrows, the relative positions of the intersection points at the 
grain boundary are significant deviated, by ~20 
µ
m.  This suggests 
the observed slip traces 
across the grain are not associated with each other and the slip transfer between them is 
75
 
 
 
 
Figure 27a) SE image of non
-
correlated slip systems on the surface.  The small white arrows indicate the 
relative positions of the selec
ted slip bands on the surface.  It can be clearly seen that these slip bands do not 
intersect at the same point on the grain boundary. 
 
b) ECC image of the same region below the surface.  The 
relative spacing and distributions of the slip lines remain unchanged within either grain, but the relative 
intersection points on the grain boundary changes, as indicated by the small white arrows. 
 
c) ECC image of 
the grain boundary area in the red box.  Pyramidal <a> secondary slip system is activated from the intersection 
points of the incoming prism <a> slip system in the upper grain at the grain boundary. 
 
d) ECC image of the 
grain boundary area 
in the blue box.  Secondary pyramidal <a> slip system is activated to accommodate the 
strain induced by the prism <a> slip system in the lower grain.
 
76
 
 
limited.  The closer examination at the grain boundary area within the lower grain (red) and the 
upper gr
ain (blue) is shown in  
Figures 27c&d
, in order to further investigate the local 



10)[


110] prism <a> slip system in the 



011)[1


10] secondary slip system
 
(M = 0.32) 


p
-
s
= 46
o
).  Similarly,  



0)[


2


0] prism <a> slip system is also accommodated by a limited number 



11) [


110] secondary slip system (M= 0.31) in 


p
-
s 
= 38
o
).  Compared to the poor compatibility between the two 


p
-
p
 
= 58
o
), the induced shear from each 
primary slip system is resolved by the activation of better aligned secondary slip systems.  
These secondary slip systems also have the  same Burgers vector as the primary slip systems 
within the respective grains, but on dif
ferent slip planes.  But due to a larger CRSS value of the 
secondary slip systems, the activity of the dislocation slip is found localized around the grain 
boundary.  It is speculated that if the sample were to be strained further, these regions might 
be s
ources for easier primary slip system activation, due to dislocation cross
-
slip.    
 

Figure 
28



0)[


2


0] prism <a> slip system (M=0.45) in the uppe
r grain 
is efficiently 
p!

other side of the grain boundary (
Figure 28a
).  However, close examination on the other side of 
the  grain boundary has found the local activation of mult
iple dislocation slip systems in the 
lower grain (limited to a small zone), with the majority of the dislocations being associated with 
the (0001)[1




p
-
s 
= 38
o
).  A number of 
 
77
 
 
dislocations on the pyramidal sl

=0.67.  These dislocations appear to be activated to accommodate the strain at the grain 

not able to 
propagate out of the grain boundary area due to a low Schmid factor.  This 
observation is  consistent with a latest work by Gioacchino et al. [189] that strain can
 
be 
partially transferred out in a more compatible way through the localized crystal lattice rotation.  

and there will always be some strain relaxation at the gra
in boundary area through dislocation 
activations, or alternatively fracture at the grain boundary. 
 
3.4.4
 
Comparison of slip transfer parameters among slip system interaction types
 
With all the crystal orientation information from EBSD and the geometry of slip s
ystems 
at grain boundaries, it is able to assess the slip accommodation events at the grain boundary, as 
 
 
Figure 28a) SE image of the third interaction type.  The slip system appears to be blocked by the grain 
boundary and no active slip system is observed in the lower grain. b) 
ECC image in the red boxed area.  A 
number of dislocations within a limited zone is observed, with majority belong to the basal plane, and some on 
the pyramidal plane.
 
78
 
 
outlined 
Section 3.4.3
.  This geometric analysis is shown in 
Figures 29a&b
, which involves 
numeric factors, namely:  the angle 

 
between intersection lines of different slip planes on a 
grain boundary plane (a key factor in the LRB criteria [83
-
86]), the geometric compatibility 
 
Figure 29 Comprehensive analysis of slip trans
fer parameters between well
-
correlated slip (top 10 lines), non
-
correlated slip (middle 9 lines), and 

blocked

 
slip (bottom 3 lines).  a) comparison of the angles 

 
between 
incoming primary and outgoing primary (black)/ secondary (red) slip system interse
ction lines at the grain 
boundary plane, and the geometric compatibility factor m

 
between the incoming primary and outgoing 
primary (black)/ secondary (red) slip systems.  b) Comparison of the global Schmid factors M of the outgoing 
primary (black)/ secon
dary (red) slip systems, angle 

 
between the Burgers vectors of incoming and outgoing 
slip systems, and angle 

 
between the incoming primary and outgoing primary (black)/ secondary (red) slip 
plane normal.  Only one value of 

 
is given because the outgoing
 
primary and secondary slip systems have the 
same Burgers vectors.  Schmid factors for the outgoing primary slip systems are shown in italics in the cases 
where there is no correlated slip observed between the incoming primary and outgoing slip systems.  O
nly one 
Schmid factor is given for the 

blocked

 
cases because only limited slip was observed in the outgoing grains in 
the vicinity of the primary incoming slip systems.  The fine dotted line between the non
-
correlated and 

blocked

 
slip band interactions
 
indicates the similarity in the accommodating behavior. 
 
 
79
 
 

the angle 
q}
 
between slip plane normals, and the global Schmid factors M [45, 46, 74].  Overall, 
 
despi

systems in all cases are mostly prism <a> slip systems, with some basal <a> slip systems.  

ed with the 
pyramidal <a> slip systems, with a limited number of basal <a> slip systems.  It should be noted 
that there are indeed  other types of dislocations observed during the ECCI analysis, however, 

sults.  
 
Cumulative distribution plots of 


, and M are provided in 
Figure 30
 
in order to  
discover the influences of these parameters on the accommodation behavior.  The cumulative 

Figure 30a
) shows the importance of alignment
 
of slip systems in the 

primary slip system when they are well
-

when the slip systems are not correlated.  Similarly,
 
it also appears to have a good correlation 


-
to
-
primary and primary
-
to
-
sec
ondary slip systems.  In general, it is expected that significant slip 
transfer will occur between well
-
correlated slip bands, with relatively good alignment between 
slip systems.  As the primary slip systems become more poorly aligned, it is possible that
 
secondary slip systems  will be more active to compensate the lack of slip from the primary 
systems.  
 

-

80
 
 
 
 
Figure 30 Cumulative distribution plots of the a) the compatibility factors m

 
between the various slip systems, 
b) the angles 

 
between the various outgoing slip systems and the incoming primary slip system, and c) global 
Schmid factors M of the outgoing 
slip systems. 
 
81
 
 
which is consistent with the lack of interactions between the primary slip systems.  Meanwhile, 

-

primary slip system to accommodate the accumulat
ed strain at grain boundaries.  This trend is 
clearly shown in 
Figure 29a
 

-


 

-
co

 




-



-

can also be interpret

primary slip system across the grain boundary being accommodated by the limited activation of 
secondary slip systems in the opposite grain.
 
The analysis of 

 
in 
Figure 30b
 
shows a sim


-


p
-
p
 
(and 

p
-
s
) than those that 

-


p
-
s 
is generally smaller than 

p
-
p
, but in some cases larger.  
It appears the 
strong correlation is related to the strong alignment of the slip plane 
intersections at the grain boundary and may directly affect the ease of slip transfer.  In one case 
(the third row in 
Figure 29a
), 





















One hypothesis is the 
82
 
 
angle 











































 
Figure 30c
 
is the cumulative distribution plot of the global Schmid factor M.  The global 

-


-

ses.  This 

-

primary (majority prism <a>) and secondary (majority pyramidal <a>) 
slip systems are not so 
significant, it is generally believed these secondary slip systems are more difficult to be 
activated due to much higher CRSS values [25
-
28,24
-
37].  This indicates the global Schmid 
factor is not an important element in the local ac
tivation of secondary slip systems, although it 
controls the activation and propagation of the primary slip systems.
 
3.4.5
 
C
onclusions on grain boundary local accommodation activities
 
The correlation of (ECCI) images on and below the surface reveals the 3
-
D geom
etry of 
the slip systems at the grain boundaries, allowing the comprehensive assessment of slip 
accommodation behavior between slip systems at the grain boundaries.  In general, the slip 
bands are confined within their respective slip planes on and below s
urface, with the relative 
83
 
 
spacing and distributions remaining the same.  Despite the detailed mechanism unknown, the 
free surface is indeed biasing the behavior of slip systems at the grain boundary region.  The 

-

he surface lose the well
-
correlation, and the 
resulting offsets between slip systems locally activate the secondary slip system to 
accommodate the divergency, trying to restore the integrity between the slip systems.  The 
Burgers vectors of these secondary
 
slip systems are generally the same as the primary slip 
systems in the same grain, however, are associated with different slip planes.  Due to higher 
CRSS values, the secondary slip systems are not readily activated, and cross
-
slipping into the 
primary sl
ip systems at a short distance from the grain boundaries.  Nevertheless, the apparent 

-


lip plane/grain 
boundary intersection lines (small 

).  
Consequently, as the slip systems become less and less 
correlated, local activation of these secondary slip systems become more prominent.  Overall, 
the local shear accommodation at the grain boundary
 
in the heterogeneous deformation are 
more complicated than it appears.  Thus extra care should be taken in the study of slip transfer 
due to free surface biasing effect.  
 
3.4.6
 
Short discussion on the tangential continuity theory
 
The frequent observations of t
he local activation of secondary slip systems at grain 

Livingston and Chalmers [71, 80].  The observation in this study agree with the tangential 
continuity that the accu
mulated strain at the grain boundary cannot be fully accommodated 
between two (primary) slip systems.  Although ECCI analyses in this study have found some 
84
 
 
other types of dislocations that are not associated with the primary or secondary slip systems 
aroun
d the grain boundary, it is not known if they have contributed to the strain 
accommodation activities and their densities are usually very low.  Nevertheless, the constraint 
(
Section 1.1.4
) cannot be fully fulfilled since it requires four slip systems to f
ully accommodate 
the strain at the grain boundary.  These observations reveal the fact that current understanding 
of the grain boundary accommodation activities in polycrystal deformation is still incomplete
17
 
[104].  The slip transfer studies that only in
volve the interactions between two primary slip 
systems are far from realistic to fully represent the plasticity behavior at the grain boundaries.
 
3.5
 
The direction of slip propagation within polycrystals 
 
The direction of slip transferring within a grain and across a grain boundary is always 
ignored by plastic models and majority slip transfer studies.  Most studies are insensitive to the 
direction of slip transfer, and assume the shear is always following 
one direction [75
-
77, 87
-
89].  
This may be reasonable in ideal experiments such as bicrystals since slip transfer parameters 


 
do not have a direction vector [83
-
86, 95].  However, deformation is not always in 
one direction in real
-
life deforma
tion of polycrystals.  There might be multiple nucleation 
sources, either within a grain, or at a grain boundary [190].  For example, one may expect two 
primary slip systems nucleated from a left grain boundary and a right boundary will propagate 
in a diff
erent direction.  Yet no research has been done on the propagation direction of a 
dislocation slip.  This long
-
ignored element help capture the overall flow of deformation shear 
 
17
 
The author carried out analysis based on tangential continuity model, trying to find the number of active slip 
syste


most of the accommodating systems were typically predicted to be in the 

 
grain
.   
Furthermore, the primary observed accomm
odating systems were typically not consistent with these 
predictions
.  It seems the model prefers self
-
accommodation if no external shear is applied as a driving force.  
 
85
 
 
travelling within polycrystals, and may further improve the plasticity model i
n the deformation 
prediction.  Luckily, during the throughout ECCI analysis across several neighboring grain 
patches in sample 3 after the electropolishing, it is found that ECCI is able to reveal the 
potential travelling direction of individual slip syste
m.     
 
After the EBSD
-
based slip trace analysis on the as
-
deformed sample (
Figure 17b
), ECCI 
was applied on the electropolished sample for the identification of Burgers vectors (
Figure 31
).  
Despite the change in the overall grain shape during the electro
polishing (
Figure 31b
), crystal 
orientation before and after electropolishing is not changed [96].  Dislocations on the slip 
bands
18
  
can be identified through the contrast analysis as outlined in 
section 3.2.2
 
(shown in 
Figure 31d
-
i
).  With the informatio
n from the slip trace analysis, the primary slip system in grain 
1 is identified to be (1



)[11


0] prism <a> slip system (M= 0.15), with additional cross
-
slip 
dislocations on (1



) pyramidal plane (M=0.23).  Likewise, the primary slip system in grain 2 
a
nd 3 is (1



)[11


0] prism <a> slip system (M=0.41) and (10


0)[1


10] prism <a> slip system 
(M=0.48), respectively.  Based on the observation on the as
-
deformed sample (
Figure 31a
), the 
deformation slip propagation within these grains is linked by the slip 
bands that propagate 
through three grains.  Some of the slip bands are quite distinct in grain interior (grain 2&3), 
while some slip bands in grain 2 become less distinct as they approach the grain boundary with 
grain 3.  Additionally, despite the distinct
 
slip bands in grains 2&3, they do not appear to meet 
at the same points on the grain boundary in between.  Meanwhile, it appears the slip bands in 
grains 1 and 2 meet at the grain boundary, however, the slip propagation in grain 1 is not easy, 
 
18
 
The correlation of the slip bands at and below surface is possible since the relati
ve spacing and distributions of 
the slip bands remain the same, as outlined in 
Section 3.4.3
.  Thus it is able to find the specific slip system after 
electropolishing.
 
86
 
 
 
Figure
 
31a) SE image of grains 1
-
3 in the as
-
deformed sample 3.  The slip systems are identified by the ECCI 
facilitated slip trace analysis, which are marked by dash lines in different colors and labelled in different 
colored fonts.  It appears the slip lines i
n grain 2 and 3 are not well
-
correlated.  The slip systems in grain 1 
appear to meet the slip systems in grain 2 at the boundary, while the slip propagation in grain 1 is difficult. b) 
General BSE image of the same grains 1
-
3 in the electropolished sample 
3.  All the slip traces are removed by 
the electropolishing and no clear contrast is seen because the sample is not under a channeling condition.  c) 
One example of ECCI analysis on the electropolished surface.  At g = [1



], the slip line contrasts are d
istinct.  
These contrasts come from dislocation contrasts rather than topography.  d
-
i) High Mag ECC images taken 
from the red boxed area in grain 3 for the Burgers vector identification.  The Burgers vector is [1


10].  With the 
information from the slip t
race analysis, the slip system that is active in grain 3 is 
(10


0)[1


10]
 
prism <a> slip 
system.  ECCI identification of slip system in grain 1 and 2 can be found in the 
Appendix 
F
, following the same 
approach.
 
87
 
 
as reflected by the wavy slip bands.  Overall, the deformation evolution within the grain patch is 
quite complicated. 
 

by the neighboring grain to maintain the overall integrity.  It will be easy to study the 
accommodation behavior if the direction of deformation flow within the patch is known.
 
 
3.5.1
 
Slip transfer direction identified by ECCI contrast analysis
 
The ECCI analysis reveals that dislocation morphologies appear differently when 
following a certain direction.  One example can be found in 
Figure 32
.  After electropolishing, at 
a certain channe
ling condition, the contrast of slip bands is a direct consequence of the 
channeling contrast of the individual dislocation in the slip band.  Slip bands that show strong 
contrast reflect a large number of dislocations in the slip band, suggesting this sli
p band is 
carrying a large shear (
Figure 32a
).  It appears that dislocations are nucleated from the grain 
boundary between grain  2 and grain 3, based on the following argument.  The slip
 
band width 
is very small near the grain boundary (~0.02 
µ
m in 
Figure
 
32b
), but the slip line broadens 

 
and become even 

cross
-
slip, although the mechanism is not 
clear.  Once the dislocation slip band reaches the 
grain boundary with grain 4, dislocations become widely distributed along the grain boundary 

 
Despite the change in slip band width, it is interesting to note that the contra
st of 
dislocations appears different at different positions along the slip line.  When the dislocations 
are nucleated from the grain boundary with grain 2 (
Figure 32a
), they appear as dots, 
suggesting the dislocations are close to perpendicular to the surf
ace at this channeling 
88
 
 
 
Figure 3
2
a) electropolished surface of grain 3. b
-
f) ECC images taken at the same channeling condition at 
different positions along a slip line.  Dislocations are limited in a sharp and narrow line from the nucleation 
point at 
the grain boundary with grain 2, and spreading out as going deeper into the grain and will finally 
distributed around the grain boundary with grain 4.
 
89
 
 
condition.  Based on the sense of black/white contrast of the dislocations, almost all of the 
dislocation
s along the slip band at the grain boundary area have the same Burgers vector sign.  
As the dislocations propagate into the grain interior, more dislocations show opposite contrast, 
suggesting they have the opposite sign of Burgers vectors (10% at position
 
c, ~30% at position 
 
d, ~ 50% at position e, and ~65% at position f at the grain boundary with grain 4).  Additionally, 
in the center of grain 3 at positions c and d, ECCI also reveals more dislocations appear as lines, 

This indicates the dislocations are aligned more parallel (or 

elastic relaxation [140
-
144].  The observation of more dislocations with opposite sign Burgers 
ve

-

dislocations cross
-
slip become more prevalent.  
 
Based on the change of slip band width, and the observations of more cross
-
slip activity, 
it is reasonable to beli
eve that once a slip system is nucleated from a source, the slip band is 
sharp and all the dislocations are limited strictly in one plane.  As the dislocation slip propagates 
forward into the grain interior, the slip band becomes broader due to dislocation
 
cross
-
slip.   
Once the slip system reaches the grain boundary with grain 4, more cross
-
slip event is expected 
to happen
 
a
s the dislocations pile up at the boundary, resulting in a wider spread of dislocations 
in the grain boundary region.  This indicates 
the overall slip transfer direction within grain 3 is 
from the upper left boundary with grain 2 to the bottom right boundary with grain 4.  Similar 
analysis has been done on other primary slip bands showing strong contrast (
Appendix I
), all 
the slip transf
er direction in grain 3 is from the upper left to the bottom right.  
 
However, there are indeed some slip bands with weak contrast propagating in the 
90
 
 
 
Figure 3
3
a) Low mag ECC image of grain 3,
 
the four
 
arrows indicate the slip transfer directions of sl
ip bands 
with strong ECC contrast.  The dashed arrow indicates the opposite transfer direction of a slip band with weak 

-
f) ECC images following the slip band from the boundary with 
grain 4 into grain interi
or.  Overall dislocation density is low compared with the case in Figure 31.  As the slip 
band broadening effect further dilutes the dislocation concentration, the dislocation contrast of the slip band is 
hardly detectable. 
 
91
 
 
opposite direction.  One typica
l example is shown in 
Figure 33
.  A low mag ECC image (
Figure 
33a
) reveals this apparent weak slip band nucleate from the boundary with grain 4 and 
propagate towards the upper left.  The contrast of the slip band becomes even weaker during 
its propagation,
 
and finally fades around position f,
 
 

 
magnification ECC image at the grain boundary confirms the observation that dislocation 
nucleated from the grain boundary as a narrow band (
Figure 33b
).  Additionally, the contrast 
ana
lysis also reveals these dislocations are dot
-
like, with the majority showing opposite 
contrast with those in 
Figure 32b
.  This indicates these dislocations have Burgers vectors of 
opposite sign (and opposite propagating direction) than those in the primar
y, high contrast slip 
bands.  Consequentially, dislocation cross
-
slip occurs during the propagation towards the upper 
left of the grain.  As the dislocation have not propagated as far, the slip band finally become 

nciteful reminder that a slip band that shows weak 
SEM topography contrast does  not always mean the slip band is less activated.  The apparent 

reaching the grain boun
dary, it might be a result of broadening effects that dissipates the 
dislocations in a wider region along the grain boundary.  
 
3.5.2
 
Comprehensive analysis of deformation within grain 1
-
3 patch
 
By and large, the complete ECCI analysis provides an understanding 
of
 
 
the deformation 
evolution of the grain patch.
 
 
The analysis suggests the majority deformation shear is carried 
away from the upper left boundary with grain 2 to the lower right boundary with grain 4 
through dislocation slip.
 
 
However, deformation also 
occurs from the lower right boundary and 
moves in an opposite direction, although the shear is not significant.
 
 
This might be a result of 
92
 
 
accommodation to the shear from the grain 4.
 
 
By the application of similar analyses along most 
of the slip bands in 
grains 1&2, it is possible to outline the potential deformation evolution 
history within the grains of the
 
 
polycrystal patch.
 
As indicated by the wavy slip band at the surface (
Figure 17b&31a
), the deformation 
 
shear in grain 1 
 
appears difficult, as indi
cated by the low Schmid factor (M=0.15).  This is 
consistent with the observation of wide spread of dislocations along the slip band after 
electropolishing (
Figure 34a
), as the slip band propagates to the upper left into the grain 
interior.  
However, due to the highly active slip system in grain 2 (M=0.41) nucleated from the 
grain boundary, grain 1 needs to accommodate the shear by the activation of dislocation slip 
that is better aligned
19
 


 
= 32
o
)(
Figure 34b
), although 
the further propagation of the accommodated slip system is difficult in grain 1.  It is worthy to 
point out that none of the high Schmid factor deformation systems (<c + a> slip systems and 
twinning) are observed.  This suggests grain
 
1 is passively activated in the heterogeneous 
deformation.
 

accumulation at the grain boundary, shear can be carried away through dislocations to the 
lower right into grain
 
2 by the easy activated slip system (M =0.41).  Again, the initial slip band 
in grain 2 nucleated from the boundary with grain 1 is sharp and has a small band  width (
Figure 
34c
).  Due to slip band  broadening effect, the slip band width is increasing as 
it is propagating 
inside grain 2 (
Figure 34d
).  Once the slip band in grain 2 reaches the lower right grain boundary 
 
19
 
The slip transfer parameters can also be calculated in the situation that a grain boun
dary kicks out two 

direction of slip transfer.
 
93
 
 
 
Figure 3
4
a) A wide spread of dislocations in grain 1 from where a dislocation slip in grain 2 is nucleated at the 
grain boundary.  b) Wide spread of dislocations in grain 1 interior.  c) a sharp slip band is nucleated from the 
boundary in grain 2.  d) The slip band
 
is wider in grain interior than it is at the grain boundary.  e) Intersection 
of dislocation slip at the grain boundary with grain 3, slip systems in grain 2 and 3 are not correlated.  
Dislocation density is high in grain 2.  F) Accommodating dislocations
 
nucleate from the intersection point of a 
slip system in grain 3, and propagate only a short distance with significant broadening effect.   
 
94
 
 
with grain 3, dislocations are diffused along the grain boundary area in grain 2 (left side of the 
boundary in 
Fig
ure 34e
) to partially relief strain accumulation [75].  
 
Despite the strong activity of the slip system in grain 3 (M =0.48), the two primary slip 


 
= 40
o
), as reflected by the offset 
between intersecti
on points of the two slip bands at the grain boundary (
Figure 34e
).
 
 
This 
suggests the shear from grain 2 is not efficiently transferred to grain 3, thus the grain boundary 
needs extra efforts to accommodate the accumulated shear to maintain its integrity.
  

-
 


 
=28
o
) with the highly active slip system in grain 3 (
Figure 34f
).  This 
observation indicates that slip systems can be nucleated from the same point at the grain 
boundary and propagated in an opposite direction into their respective grains.  This can be 
interpreted as slip systems in both grains are activated to accom
modate the shear at the grain 
boundary.  
 
3.5.3
 
Conclusions of polycrystal deformation identification
 
As would be expected, the detailed deformation evolution of polycrystal patch is 
complicated.  Nonetheless, slip bands are found to spread out during their prop
agation, which 
gives a key to understanding the deformation evolution.  With additional information of the 
change of dislocation contrasts and morphologies at different positions following the slip band, 
it is possible to identify the slip transfer directi
on within a certain grain.  Based on the 
observations of the nucleation of different slip systems, it is very interesting to point out that in 
this very study, it appears most dislocation slip systems are nucleated from the grain boundary, 
rather than some
where within grain interiors.  This agrees well with arguments that grain 
95
 
 
boundary can be dislocation sinks and sources [52
-
55, 190].  As there might be more defects on 
the grain boundary plane due to irregular atomic arrangement in that region, the grain 

deformation.  This might be insightful to the plasticity modeling that both grain boundary and 
grain interior can be sources for slip activations.  It is also interesting to
 
find out that the slip 
systems of the same type within one grain may not propagating towards the same direction, 
this depends on where the dislocation is nucleated (i.e. slip systems nucleated from the left 
grain boundary will propagate in a opposite dire
ction with those nucleated from the right 
boundary within the same grain).  Additionally, grain boundary accommodation can happen 


the same boundary and propagate into their respective 
grains.  Although the slip transfer parameter is not affected by the direction to slip transfer, 
understanding the transfer direction and the deformation sequences within polycrystal is 
critical for the
 
comprehensive understanding of polycrystal engineering material (i.e. local work 
hardening, crack nucleation, etc.).  
 
 
96
 
 
4.
 
Summary
 
In order to correctly understand the heterogeneous deformation of hcp titanium, post
-
deformation analysis need to be precise an
d comprehensive.  The preciseness refers to the 
correct identification of slip systems activated during the deformation, and the collectiveness 
requires the analytical method to identify all the slip systems activated in the accommodation.  
This comprehens
ive analysis cannot be simply achieved through one approach and needs 
assistance from other analytical techniques.  Slip system identification is mostly based on the 
crystal orientation data from EBSD and the SEM observation of traces at the surface.  With
 
the 
improvement of EBSD and cross
-
correlation techniques that detect local lattice rotations [185, 
188], and the AFM and DIC [162
-
165] that measure the displacements
 
resulting from 
dislocation slip, slip system identification and quantification is becomin
g more precise.  
Nevertheless, the current analyses are not able to identify the slip systems that do not 
contribute to the slip traces.  On the other hand, ECCI can precisely identify the Burgers vector 
of the slip systems based on dislocation contrast an
alysis [144
-

determinant analysis and avoids the calculation of potential deviation factor in DIC and cc
-
EBSD 
[185, 186, 188].  Implementation of the ECCI technique in concert with the current approaches 
moves the characterizati
on of local slip
 
behavior in heterogeneous deformation substantially 
forward.
 
Slip accommodation at grain boundary regions in polycrystal deformation is quite 
complicated.  By correlating SEM images at the surface with subsurface ECCI images, the 3
-
D 
geome
try of the slip systems at the grain boundary area is revealed, allowing the assessments 


.  Additionally, subsurface 
97
 
 

-

 
surface, and reveals the 
locally activation of secondary slip systems that help compensate the incompatibility between 
the primary slip systems at the grain boundary area in the subsurface.  This observation agrees 
well with the long
-
forgotten tangential 
continuity theory [71, 80], that indicates that the 
interactions between two primary slip systems are not enough to accommodate the strain at 
the grain boundary.  Although this study only finds the local activation of secondary slip 
systems, this does not 
mean there cannot be more dislocations involved in the accommodation, 
especially at higher strain levels.  Nevertheless, the current research extends the understanding 
of the complete nature of the accommodating mechanisms at the grain boundary, and again,
 
suggests the slip transfer mechanisms developed based on the slip trace analysis may be 
limited.  
 
In addition, the slip band broadening effect is clearly revealed through ECCI analysis in 
electropolished hcp titanium samples.
 
 
The comparison of dislocati
on morphologies, dislocation 
contrast, and dislocation density at different positions in slip bands suggests that the vast 
majority of dislocations are nucleated from the grain boundary, rather than sources within the 
grains, at least in the early stages o
f deformation.
 
 
However, this does not suggest dislocation 
sources cannot be found in grain interiors, as evidence shows that as the slip bands propagates, 
more dislocations with opposite sign are observed in the slip bands.
 
 
It should be noted, 
however, i
t is not known if this broadening effect is unique to hcp metals due to the lower 
crystal symmetry, or is a universal phenomenon in all metals.
 
 
Regardless, this discovery does 
help to establish an understanding of the deformation evolution in polycrystals
.
 
 
 
 
98
 
 
5.
 
Outlook and Future Direction of ECCI
 
In the latest future, one of the easiest things that can be achieved is whether slip band 
broadening effect is present in cubic materials or other hcp metals.
 
 
This effect will be valuable 
if it can be widely appli
ed on different materials. 
 
It will also be interesting to investigate the slip/twin interactions by ECCI in hcp titanium 
since deformation twin are also common in the plastic deformation in some other titanium 
materials.  One example is shown in 
Figure 35
.  In this figure, deformati
on twin is observed in 
the upper grain, whereas two types of dislocation slip systems are observed in the lower grain.  
It is interesting to investigate how the slip/twin interactions are at the grain boundary.  
Additionally, it is interesting to find <c+ 
a> dislocations kicking out of the tip of the deformation 
twin and propagate into grain interior.  It is also interesting to investigate the relationship 
between dislocation slip and the twin, and how dislocations become a part of twinning during 
the defor
mation (in
-
situ if necessary).  Sequential electropolishing of the sample may also 
 
Figure 35
 
Deformation slip in the lower grain interacting with the deformation twin in the upper grain.  ECCI 
analysis in the red boxed area shows the dislocation propagating out of the tip of the deformation twin.
 
99
 
 
reveal the geometry of the twin in the subsurface, which may also bring more insights in the 
twin evolution.
 
Since 3
-
D printing of titanium gears or other 
consumables are becoming more and more 
important in the aerospace industries, it will be an interesting and short project to correlate the 
mechanical behaviors of 3
-
D printed titanium samples (using different methods, such as 
powders or wires) during diffe
rent stages of processing with the dislocation densities, phase 
changes, etc.  This may help guide the industry to improve the overall quality of 3
-
D printed 
titanium materials.
 
By and large, ECCI is a strong SEM near
-
surface
-
based analysis technique that 
is 
complementary to many other techniques.
 
 
This non
-
destructive technique is especially useful 
for the in
-
situ study of continuous polycrystal deformation without destructively damaging the 
sample.
 
 
Thus far, this study only reveals that post
-
deformation 
analysis is able to provide some 
clues to deformation history.
 
 
With careful design in future, one may be able to observe the 
deformation evolution from the initiation to the final structure of a slip band.
 
 
This may be 
useful for understanding how the dis
location density, morphology, and contrast changes with 
increasing strain, and thus provide the opportunity to link the macroscopic deformation with 
the dislocation
-
scale activities simultaneously on the same target area.
 
 
This approach is very 
advantageou
s over the other destructive studies, such as FIB
-
lift
-
out TEM, since it is extremely 
hard to find two same grains with even similar grain and boundary orientation characteristics in 
assessable polycrystalline groups.
 
 
Unfortunately,
 
 
the electropolishing 
in this study is hard to control precisely.
 
 
Removing 
the surface topography typically requires about 2 µm removal, and establishing precise uniform 
100
 
 
removal rates can be difficult.
 
 
As a result, the surface removal in this study are typically around 
5 µm o
r more.
 
 
It is anticipated that it will not be possible to remove material with enough 
precision to track individual dislocations with electropolishing.
 
 
 
 
An alternative approach may 
be the Xe
+
 
plasma FIB technique [191, 192], which is able to precisely c
ontrol the surface 
removal.
 
 
This approach has the potential to allow high resolution real 3
-
D reconstruction of a 
full dislocation structures below the surface (One should note the potential artifact induction 
and titanium hydride precipitation during pla
sma FIB).
 
 
With proper coding facilitation, in future 
ECCI may be extended to automated identification of
 
 
Burgers vectors, slip line directions, slip 
planes and the edge/screw component of a dislocation.
 
 
Currently, as ECCI is effectively a 
manual techniq
ue, the identification of all of these parameters is done tediously by collecting 
five or more ECC images at different channeling conditions and long scan times (10 minutes per 
scan). 
 
 
 
101
 
 
APPENDICES
102
 
 
APPENDIX A  
 
Electropolishi
ng mechanisms and parameters used in this study
 
 
 
 
 
 
 
 
 
 
 
 
103
 
 
The sample was electropolished in a proper setup, consisting a power supply (can switch 
between 0 ~ 120 V and 0 ~ 30V), a cathode  (6 x 6 x 2 mm stainless steel plate) and anode 
(sample with the polished area facing the plate), a magnetic stir (50 mm in le
ngth) with a 
magnetic stir plate, electrolyte (in a 1000 ml baker) and cold bath (200 ~ 300 ml methanol 
cooled by liquid nitrogen/dry ice or a more stable control of temperature during 
electropolishing).  Two different electrolyte compositions were used in
 
the study with 
correlated electropolishing parameters, as listed in 
Table A1
.  It is worthwhile to mention that 
the experimental parameters and composition of electrolytes may be different if the minor 
element components of titanium are different.  Nevert
heless, the parameters in the table are 
based on freshly made electrolyte, which can be safely used for cumulative 10 ~ 20 times 
without changing the electropolishing result.  
 
Table A1
.
 
 
Electropolishing parameters
 
 
 
104
 
 
 
 
Figure A1 A scheme shows the general four stages of electropolishing with respect to different voltage and 
current density ratio.
 
 
Figure A2
 
Left) Below 29 V results in etching of metal with rough surface 
under optical & electron microscope.  
Middle) A good polishing zone results in shinning & smooth surface with good contrast under electron 
microscope.  Right) Above 40 V results in a dimmer surface in optical microscope. Under electron microscope, 
pitting 
occurs, especially at grain boundaries, with slightly worse SACPs.
 
105
 
 
The electropolishing outcome is quite complicated based on the applied voltage and 
current (
Figure A1
).  
The general process usually falls into several stages [175, 176, 177], which 
include: I. The etching of metal through a direct dissolution at low voltage; II. The passivation of 
the metal surface by creating an oxidized layer at slightly elevated voltage; 
III. The polishing of 
the metal by the consistent dissolution & diffusion of anions through the stabilized passivated 
layer; IV. Pitting and gas evolution that induces imperfections on the surface beyond the 
polishing voltage.  The comparisons of optical, 
microstructures under scanning electron 
microscopy, and electron channeling patterns are shown in 
Figure A2
, indicating the perfect 
surface finish after optimization of electropolishing parameters.  As it is shown in the 
Table A1
, 
electrolyte A is speciall
y used for the controlled removal of surface material during 
electropolishing with 2 µm/min (the surface removal is calculated in 
Figure A3
) and the 
electropolishing can be finished within 2 minutes (it needs 10 ~ 20 s to reach a steady
-
state that 
the poli
sh process is homogeneous throughout the sample), however, some grains are suffered 
with hydride precipitation (around 1 out of 100 grains).  On the contrary, electrolyte B is free 
from hydride
 
formation [174], but it is almost impossible to control the el
ectropolishing rate (~ 
8 µm/min).  
 
 
Figure A3 Calculation of the surface removal by 
the Vickers indent.  Several Vickers indents are placed at the 
surface before electropolishing and final result is the average of each calculated one.
 
106
 
 
APPENDIX B
 
 
 
Removal of polymer film and gold nanoparticles (AuNPs) for DIC patterning
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
107
 
 
Introduction:
 
As indicated from recent papers [161, 162], with the addition of gold (III) chloride 

2
O) and trisodium citrate dihydrate (C
6
H
5
Na
3
O
7

2
O) to produce AuNPs 
as the patterning material, organosilanes such as (3
-
aminopropyl) trimethoxysilane (APTMS) or 
(3
-
mercaptopropyl)methyl) dimethoxysilane (MPMDMS) was added as to cova
lently bonding to 
the dangling hydroxyl group on the metal surface to form a monolayer that was able to 
immobilize AuNPs through coupling reactions.  Although the patterned DIC technique offers 
precise strain measurement during deformation without relying 
on complicated and much 
expensive experimental set
-
ups, the only limitation of this technique is the coating itself.  Due 
to overshadowing of the organic coating and nanoparticle which disturb electron interactions 
with the sample, and because of artifacts
 
created on the sample surface, no other studies have 
been accomplished after DIC patterning, such as CC
-
EBSD and AFM that are also capable of 
monitoring strain development, or perform surficial analysis such as ECCI.  The general 
approach is to mechanical
ly polish off the surface polymer within a short time, however in 
reality, this approach is nearly impossible to peel off the layers without damaging the surface of 
the sample.  As a result, using a chemical reaction which is selectively targeting only the
 
nanoparticles and polymer without touching the metal is the ultimate way to perfectly address 
this issue.  This short paragraph is provided, describing how the patterning layer is removed 
through chemical reactions.
 
Based on many synthetic papers [178
-
182
], the best way of removing AuNP as well as 
cleaving off the polymeric silyl ether layer was to use strong halogen reagents, such as F
-
.  A 
general concern is to use hydrofluoric acid (HF), however upon consideration, the reagent has 
108
 
 
to be able to penetrat
e the polymer layer and react with the AuNPs but blind to the titanium, 
which is also vulnerable in the acid, a mild organic fluorine source should be selected.  In this 
research, tetra
-
n
-
butylammonium fluoride (TBAF





O and 1mol/L TBAF in THF) is used (
from 
Sigma
-
Aldrich) since this is also considered as a phase transfer catalyst which can bring water 
and immiscible organic solvents together.  Although TBAF is not the only reagent or the best 
among all alternatives (fluorotrimethylsilane, referred as the
 
TMS
-
F, may also work but much 
expensive), picking the best reagent is not the main purpose of this paper.  
 
Experimental procedures:
 
The as
-
deformed Ti
-
7Al (
Figure 13 a
) dog
-
bone tensile sample was provided by 

terns coated on surface and strain map collected.   
The final ingredients used in this experiment were 10: 1: 1 weight ratio of TBAF, chloroform, 
and ethylene glycol.  The detailed procedure of uncoating is as follows:
 
1.
 
Merge the sample completely in the so
lution at around 30 ~ 35
o
C for 1 hour.
 
2.
 
Take the sample out, clean by 5 
-
 
10 mins sonication (20 
-
 
40 kHz) in a baker of soap 
water (pH ~ 8), flash with ethanol
-
 
DI water
-
 
ethanol, air dry and track the progress.
 
3.
 
Repeat 1 and 2 until the surface is cleaned 
enough.
 
4.
 
Place hand soap on the surface, which is then swept off by cotton stick, go through final 
ethanol
-
DI water
-
 
ethanol washing and air dry. 
 
Results and discussion:
 

-
free, with 
little residual AuNP remained.  Nonetheless, the detailed uncoating progress with time was 
109
 
 
 
Figure A4a1) Surface condition of as received sample.  a2) SE image of AuNPs taken at high magnification from 
the red box, with weak SACPs due to interference. 
 
b1) Surface condition after 1 hour at 30 
o
C, showing 
removal of majority patterning material.  b2) SE image showing one of the unremoved clusters of AuNPs, with 
sharp SACPs. Particles in these areas are the focused point during DIC data 
acquisition.  Long time exposure of 
beam may condense the NPs into the material or strengthen the bonding interaction, with detailed mechanism 
unknown.  The patterns c1) At 4
th
 
hour, all nanoparticles are consumed, including the clusters.  c2) SE image of 
the same area with b2, showing clean sample, with sharp slip traces and grain boundaries.  d1) 24
-
hour 
reaction time of an undeformed control sample 1, showing the slightly etching of material.  d2) SE image of the 
etched area in the red box, showing line 
type etched marks and small etched cavities.  e1) Surface condition of 
an undeformed control sample 2 after the 3
rd
 
hour in solution at 50 
o
C, also showing large areas being etched.  
e2) SE image of the red box area, showing surface material has been etche
d away
.
 
110
 
 
shown in 
Figure A4
, with extra uncoating information (i. e. uncoating at elevated temperature, 
longer reaction time, etc.) acquired from control samples.  In 
Figure A4 b1&2
, after one hour, it 
can be seen that major particles have been washed away,
 
with clusters of AuNPs (and some 
fiducial marks, although not shown in the image) left on the surface. Those were possibly 
segregated due to long exposure to the high energy electron beam during DIC data acquisition.  
The reagents are hard to get access t
o the clusters as the surface to ratio was diminished after 
segregation.  Meanwhile, dramatic improvement of SACPs before and after uncoating (
Figure 
A4
 
a2
&
b2
) suggests the removal of particles as well as the polymer layer.  With longer reaction 
time up to
 
the 4
th
 
hour, all particles have disappeared, even the robust clusters, suggesting the 
completion of the uncoating process, which is shown in 
Figure A4 c1&2
.  It should be noted 
that although F
-
 
anions are mostly locked in the organic environment so that 
they are only 

-
 
are still considered to 
be aggressive to Ti metal.  This has been proved that longer reaction time (i. e. 24 hours as 
shown in 
Figure A4 d1&2
) and higher temperature (i.
 
e. 50 
o
C as shown in 
Figure A4 e1&2
).  
Although not shown specifically in this manuscript, similar progress can be achieved by simply 
 
Figure A5a) SE image of a random area, showing clear slip traces on surface after the uncoating.  b) 2
-
D AFM 
map showing topographic information of the same area.  c) 3
-
D AFM map showing clear steps from the sli
p 
band and the grain boundary (concaved). 
 
111
 
 
using 1 mol/L TBAF in Tetrahydrofuran (THF), with little residual AuNPs clusters left on the 
surface (7 hours), thus t
his can serve as alternative reagent if not asking for complete extinction 
of AuNPs.  Neither approach harms the surface within the reaction time and the surface is able 
to perform ECCI and AFM analysis on the sample with little interference, as shown in 
F
igure A5
.    
 
Conclusion:
 
A weight ratio of TBAF: CHCl
3 

proved to be efficient in removing the pattern after DIC with almost no harm to the surface if 
using properly.  
 
 
 
 
 
 
 
 
 
 
 
 
 
112
 
 
APPENDIX C
 
 
Strain measurement after four
-
point bending
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
113
 
 
As the sample surface between supporting pins is 
experiencing uniaxial tensile stress, at 
low strain level that the sample does not have too much bend curvature, the tensile strain is 
approximately measured from the distance change between triple points of different grains 
along/close to the tensile dire
ction before and after deformation using Image J
TM
 
or other 
image processing software, as shown in 
Figure A6
.
 
 
 
 
 
Figure A6 
L
eft) The distance between triple points before deformation.  
R
ight) The distance between same 
triple points after deformation.
 
 
114
 
 
APPENDIX D
 
 
The calibration of MIAR III FEG
-
SEM with SACPs module for ECCI and CC
-
EBSD analysis
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
115
 
 
As it is of critical importance to ensure the calibrated status of the SEM for the accuracy 
of ECCI and CC
-
EBSD analysis, this section provides a detailed procedure on the calibration of 
MIRA III FEG
-
SEM.  Before proceeding, it is highly recommended to rea
d the manual from MIRA 
III and understand the terms that are frequently used in electron microscopes:  focus, 
magnification, stigmation, wobble, etc. 
 
Proper alignment of column and gun:
 
 
There are several modes provided in MIRA III FEG
-
SEM in the CMSC center of MSU, 
namely:   resolution mode, depth mode, field mode, wide filed mode, and channeling mode.  
ECCI images are taken in the resolution mode, while the SACPs are collected in field m
ode with 
beam rocking and shown in the channeling mode for the establishment of a diffraction vector 
g
.  
Thus, it is critical to ensure the beam alignment in each mode.  The general alignment usually 


to the conditions for ECCI analysis.  First, in resolution mode, repeat focusing and increasing 
image magnification until an out
-
of
-
focus target (
Figure A7a
) is in focus (
Figure A7b
) at the field 
of view 2 ~ 3 
µ
m.  Ast
igmatism at high magnification is corrected during focusing using the 
 
Figure A
7
 
Secondary electron (SE) images taken at the field of 
view of 3.86 
µ
m that shows:  a) The particle is 
out of focus.  b) The dirt is in focus, but astigmatic.  c) The dirt is stigmatic and in perfect focus.
 
116
 
 

Figure A7c
).  During this adjustment, the 

swinging 
when the electron beam is moving back and forth across the focus.  
 
Aft
er the beam alignment in the resolution mode is finished, the second alignment is 
done in the field mode.  Additional focusing operation in this mode is not necessary since this 
operation is already done in the resolution mode, but the aperture should be w
ell aligned using 

 
Figure A
8
a) SE image in resolution mode (field of view 3.86 
µ
m) that shows the opti
c axis (black cross) is on a 
particle.  b) SE image in field mode (field of view 65.3 
µ
m) that shows the deviation of optical axis from the 
resolution mode.  Although it appears blurry, this particle is already in focus in field mode since the resolution 
b
etween modes is different.  c) SE image in field mode that shows the optical axis is moved back to the same 

 
 
Figure A
9
a) An asymmetric SACP aperture with overlapping of patterns from surrounding grains.  b) A 
symmetric, perfect round aperture with interference signals from surrounding grains.  c) A perfect circular 
aperture within pattern only from the target grain.  
 
117
 
 
targeting the same position both in the resolution mode and field mode, so that the pattern is 
collected from the target area (
Figure A8c
).  This ste
p is critical when the ECCI analysis is 
performed near grain boundaries, at high tilt conditions (> 10
o
),
 
or in small grains (grain size 
larger than 20 
µm for a perfect SACP in this MIRA SEM
) for the diffraction condition set
-
up.  The 
final SACP 

After the aperture alignment, the aperture should appear to be a perfect circle, with an un
-
overlapped pattern (
Figure A9c
).  Crisp ECC images with precise pattern informati
on can be 
achieved after all these alignments were done properly.
 
 
 
118
 
 
APPENDIX E
 
 
Procedures of ECC image acquisition and data analysis
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
119
 
 
This section provides detailed information on the establishment of channeling 
condition, obtain 
dislocation contrast by following a Kikuchi band, and the identification of 
channeling bands using T. O. C. A. software.
 
Establishing a channeling condition:
 
The fundamental mechanism for setting
-
up of an ECCI channeling condition is analogous 
to the estab
lishing of two
-
beam diffraction condition to transmission electron microscopy 
 
(TEM),  by moving the optic axis/un
-
tilted electron beam (indicated by the black cross in 
Figure 
A10
) approaching the edge of the channeling band through proper tilt and rotation [141, 147].  
It is noticeable that the deviation from the Bragg condition 
s
 
= 0 is the imaging condition to get 
maximum contrast in ECCI analysis [140] (as illustrate in 
Figure 
A10b
).  It is more challenging to 
correctly set up 
s
 
= 0 channeling condition if the target area is highly textured or having an 
orientation gradient due to higher strain level deformation, one have to manually adjust the 
relevant position of the optic axi
s and the band edge for a best ECC image, which may need 
several attempts.  It should be mentioned that the orientation deviation after plastic 
deformation can be solved by using a higher resolution SACP module that can collect the 
 
Figure A
10
a) ECC image taken at s <0, the contrast of dislocations in the lower grain is not perfect.  b) ECC 
image taken at s = 0, a crisp image of sharp dislocations in pe
rfect contrast.  c) ECC image taken at s > 0, the 
dislocations in the same area are badly resolved with poor contrast.
 
120
 
 
accurate from smaller ar
eas (currently SACP module in MIRA III requires at least a 10 µm 
diameter area in order to set up a channeling condition, and ~ 20 µm to get a perfect, un
-
overlapped pattern).   
 
To get a crisp ECC image on a proper channeling condition, it is necessary to
 
take 
multiple ECC images as the optic axis is traveling following the same channeling band as shown 
in 
Figure A11
.  Some dislocations appear as dots with strong black contrast on one side and 
white contrast on the other side, suggesting the dislocations are more inclined near the surface, 
while some 
dislocations appear as lines, indicating these dislocations are more parallel close to 
the surface.  It can be easily recognized that the dislocations labeled by small white arrows have 
opposite black & white contrast with those marked by small black arrow
s, a reflection of the 
opposite Burgers vectors.  By comparing the same dislocations taken near different zone axis, it 
Figure A1
1
a) The dislocation tails are in weak contrast, as
 
indicated by the small black arrows while some other 
dislocation tails are in strong contrast, as indicated by the small white arrows when ECCI is taken close to the 
upper zone axis.   b) The dislocations indicated by the small black arrow are in strong c
ontrast, on the contrary, 
the tails marker by the small white arrows are in weak contrast when the optic axis moves closer to the lower 
zone axis.
 
121
 
 
is easy to find that dislocations labeled by the small black arrows have shorter tails with weaker 
contrast in 
Figure A11 a)
 
than in 
b)
,
 
while the ones with opposite black & white contrast, 
indicated by the white arrows, show slightly longer tails and better contrast in 
a)
.  This suggests 
the dislocations with opposite Burgers vector also have opposite line directions or, dislocation 
incli
nations, near the free surface.  Nevertheless, the difference in length of the dislocation tails 
with respect to the position on the channeling band also provides a clue to identify the near
-
surface dislocation line directions of these dislocations.
 
Identi
fication of the channeling band: 
 


version No. 2.2, developed by Dr. Stefa
n Zaefferer in the year 2010.  T. O. C. A. is specifically 
used for the identification of channeling bands in both TEM with the interface shown in 
Figure 
A12
.  The channeling band identification is done in the SEM mode, although the difference 
between simu
lated patterns in TEM and SEM mode is minimal.  The procedure for getting the 
simulated pattern of a target crystal after loading the 

-
Ti crystal dataset is as followed: 
 
I. Input the Euler angle, which is acquired from the EBSD
-

-
a

module.  
 
II.  Manually rotate the crystal 90
o
 
along the Z
-

 


 
122
 
 
 
 
Figure A1
2
 
The interface of T. O. C. A. software shows 3 components in the simulation display, including the 
simulated patterns shown on the left pop
-
up window, the corresponding pole figure shown on the upper
-
right 
window, and the crystal orientation shown on the b
ottom
-
right window.  The most useful parameters input in 
the control panel are listed as: 1. The Euler angle; 2. The 90
o
 
rotation; 3. The acceleration voltage at which ECCI 
is taken; 4. The magnification at which ECCI is taken.
 
123
 
 
IV.  Input the magnificatio

 
 
V. (Optional) Adjust the width of the channeling band by changing the number in the 

 
The simulated pattern should look similar to the real patterns collec
ted from the 
channeling mode in MIRA III SEM, which is shown in 
Figure A13
.  
The dislocation Burgers vector 
b
 
can be determined through 
g

b
 
= 0 invisibility analyses as 
g
 
is correctly labeled by T. O. C. A.
 
 
 
 
 
 
 
 
 
 
Figure A1
3
 
Left) Simulated channeling patterns with these bands labeled.  Right) The real patterns collected 
from channeling mode in MIRA III SEM, with the optic axis labeled as black cross.
 
124
 
 
APPENDIX F
 
 
 
Dislocation identifications
125
 
 
This section
 
only includes high quality ECC images that were not shown in the 
manuscript, some rough (poor quality) ECC images that were used to quickly identify 

 
 
Figure A14a) Grain 1 as deformed.  b) 
grain 1 after electropolishing.  c
-
h) ECC images from the red box area taken 
at different 
g
 
vectors, dislocations are (1



)[11


0] and (1



)[11


0].
 
 
 
126
 
 
 
Figure A15a) Grain 2 as deformed.  b) Grain 2 after electropolishing.  c
-
h) ECC images from the red box
 
area taken 
at different 
g
 
vectors.  Dislocations are 
(1



)[11


0].
 
 
 
 
 
 
127
 
 
 
Figure A16a) Grain 3 as deformed.  b) Grain 3 after electropolishing.  c
-
h) ECC images from the rex boxed area at 
different channeling conditions.  Dislocations are 
(10


0)[1


10].
 
 
 
 
 
 
128
 
 
 
Figure A17a) Grain 4 as deformed.  b) Grain 4 after electropolishing. 
 
c
-
h) Dislocations at the boxed area (grain 
boundary between grains 3 and 4) taken at different channeling conditions.  Dislocations are majority 
(10


0)[


2


0].  
 
 
 
 
 
 
129
 
 
 
Figure A18 One example of dislocations identification in sample 2 after electropolishing.  a) ECC image of slip traces 
after electropolishing.  The contrast is not due to topography but from the contrast of dislocations.  b
-
f) 
Dislocations taken at differe
nt 
g
 
vector.  Dislocations are (10


0) [


2


0].
 
 
 
 
130
 
 
 
Figure A19 One example of dislocations identification in sample 2 after electropolishing on the other side of the 
grain.  Dislocations are (01


0) [


110].
 
 
 
131
 
 
 
Figure A20 Neighboring grains in Sample 2.  Fir
st six ECC images) Identified dislocations are (1


00)[11


0].  Second 
six ECC images) Identified dislocations are (1


00)[11


0] and (1


01)[11


0].
 
 
132
 
 
 
 
Figure A21 Neighboring grains in Sample 2.  First six) Identified dislocations are (1


00)[




20] and (


101)[
11


0].  
Second six) Identified dislocations are (1


00)[




20] and (1


01)[11


0].  
 
133
 
 
 
Figure A22 Neighboring grains in Sample 2.  First six) Identified dislocations are (10


0)[





0] and (


011)[1


10].  
Second six) Identified dislocations are (0


10)[2




0] 
and (01


1)[


110].  
 
 
134
 
 
 
Figure A23 Neighboring grains in Sample 2.  First six) Identified dislocations are (10


0)[





0] and (


011)[1


10].  
Second six) Identified dislocations are (0


10)[2




0]. 
 
 
135
 
 
 
Figure A24 Neighboring grains in Sample 2.  First six) Ident
ified dislocations are (10


0)[





0] and (


011)[1


10].  
Second six) Identified dislocations are (0001)[




20]. 
 
 
136
 
 
 
Figure A25 Neighboring grains in Sample 2.  First six) Identified dislocations are (1


00)[




20] and (1


01)[11


0].  
Second six) 
Identified dislocations are (



00)[




20].
 
 
137
 
 
 
Figure 
A26 Neighboring grains in Sample 2.  First six) Identified dislocations are (0


10)[


110].  Second six) 
Identified dislocations are (



0)[





0]. 
 
 
 
138
 
 
 
Figure 
A27 Neighboring grains in Sample 2.  First six)
 
Identified dislocations are (1


00)[11


0].  Second six) 
Identified dislocations are (



0)[





0]. 
 
139
 
 
 
Figure 
A28 Neighboring grains in Sample 2.  First six) Identified dislocations are (1


00)[11


0] and(1


01)[11


0].  
Second six) Identified dislocations are 
(



0)[





0]. 
140
 
 
 
Figure 
A29 Neighboring grains in Sample 2.  First six) Identified dislocations are (0001)[1



0] and(


011)[1



0].  
Second six) Identified dislocations are (



0)[





0].
 
141
 
 
APPENDIX G
 
 
AFM, slip trace 
analysis and ECCI of grains 3&5 in sample 1
142
 
 
 
Figure A30a) AFM color
-
scale topography map of grain 3 in sample 1.  b) Slip systems identified by the trace 
analysis are the (10


0)[


2


0] and (0



0)[2




0] prism <a> slip systems.  c) ECC image of the red box a
rea in b).  
Contrast analysis also reveals two additional slip systems, which are (1


00)[




20] prism <a> slip system and the 
(0


11)[2




0] pyramidal <a> slip system.  The pyramidal <a> dislocations are responsible for the curvy slip traces.  
d) AFM color
-
sc
ale topography map of grain 5 in sample 1.  e) (1


00)[11


0] prism <a> slip system is identified by 
the slip trace analysis.  f) ECC images of the red box area in e).  Contrast analysis also reveals a significant number 
of (0


10)[2




0] prism <a> dislocation
s within the observed area.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
143
 
 
APPENDIX H 
 
 
 
 
Calculation of the geometry of slip systems at a grain boundary
144
 
 
The correlation of 
Figures 25 a and b
 
is used in this section as a particular example to 
show how 3
-
D geometry of the slip systems at the grain boundary is revealed.  With the 3
-
D 
geometry, it is able to characterize the angle 

 
between the intersection lines of slip planes on 
both sides of t
he grain boundary with the grain boundary plane.  
Figure A31
 
(left) is a sketch of 
the geometry of the grain boundary plane and slip planes of the two interacting primary slip 
systems.  The upper right figure is the surface image which is associated with t
he upper plane in 
the left sketch, and the lower right figure is corresponding to the subsurface image, which is 
sketched as the bottom plane to the left figure.  In order to correctly correlate the two images, 
an arbitrary coordinate system is established
, with the z direction perpendicular to the surface, 
x direction pointing down, and y direction pointing right on the surface.  The origin O (0, 0, 0) is 
set to the intersection between the two slip bands at the grain boundary, as shown in the upper 
right 
figure.  The depth of material removal, d, is the vertical distance between the surface and 
subsurface.  It can be calculated from the electropolishing current and time, and this value can 
be verified using microindentation removal measurements [96].  The 
overall electropolished 
surface is flat and smooth, with d varied between 4.8 and 5.2 µm across the examined area.  
Thus, values of 4.8, 5.0, and 5.2 µm were used in the calculations to determine the variability of 
the results.  
 
On the subsurface, the gra

-



boundary traces in the subsurface since all the parameters can be calculated during the 
145
 
 
construction of 3
-
D geometry.  However, in this calculation, it is a
ssumed that the each of the 
 
slip band is confined within its own slip plane, and there is no he
ight variation on the 
subsurface at a given d.  The calculation of the inclination of the grain boundary plane 

 
and 
more importantly, 

, is carried out as follows:  
 
The grain boundary trace on the electropolished surface can be expressed as a straight 
li
ne:
 
 
 
 
 
y = k*x 

 

 
Figure A3
1
 
3
-
D geometry of the well
-
correlated slip systems at the grain boundary by the correlation of surface 
and subsurface images. (Amended from [171])
 
146
 
 
where k is the slope of the grain boundary trace (assume the trace is close to a straight 
line).  In some cases, the grain boundary line orientation may vary between the as
-
deformed 
surface and 
the electropolished surface.  Thus, k is the averaged value between the k
surface
 
and 
k
sub
-
surface
 
that are measured on each image.  
 

-
b, 
-



, 0, 
-
d), are the intersection points of the grain boundary 

 

1
, k*x
1
 

 
b, 
-

2
, k*x
2
 

 
b, 
-
d) 


 
L =
 
|













|=
















  

 
The directions of











 
and 











 
are the respective intersections of the incoming (red) 
and outgoing (yellow) slip planes with the grain boundary plane (
Figure A31
 
left).  These will be 
perpendicular to
 
the respective slip plane normal, 
N
1
 
and 
N
2
, which are readily available from 
the MATLAB codes based on the crystal orientation information from the EBSD software:
 
N
1












 

 
N
2
 












 


 
Simultaneous solution of equations 1
-
4 allows determination of 










 
and 











.  The 
angle 

 
between slip plane intersections on the grain boundary plane is then simply expressed 
as: 
 

 
= cos
-
1
 
(










 













 
Once 















, and the corresponding grain boundary inclination angle, 

, is given by:
 
147
 
 

 
= tan
-
1
 
(
















) 

 
The value of 

 
reported in this study is 

avg
, which is calculated on the basis of d = 5 µm 
and k
average
.  The true value of 

 
has a variation range of ~3
o
 
to ~5
o
 
since different values of d = 
4.8, 5.2 µm and k = k
surface
, k
subsurface
 
have been used.  The uncertainty can be calculated by:  
 

uncertain 
=
 

max
 

 

min
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
148
 
 
 
Figure A32 All cases slip interactions at grain boundaries with calculated results.  
 
 
 
 
149
 
 
APPENDIX I 
 
 
 
 
Slip band broadening in grain 3 of sample 3
150
 
 
 
Figure A33 Slip band broadening effect observed along two different slip 
bands.
 
 
 
 
151
 
 
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152
 
 
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