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MARTENSITIC TRANSFORMATION OF Ni3Sn ALLOY

By

Soon- Nam Chang

A THESIS

Submitted to

Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Metallurgy, Mechanics
and Materials Science

1982

ABSTRACT

MARTENSITIC TRANSFORMATION OF Ni3Sn ALLOY

By

Soon- Nam Chang

The Martensite of Ni3Sn has been investigated crystallographically
by means of transmission electron diffraction as well as optical
microscopy. The crystal structure of the martensite was identified
as the B-Cu3Ti (2H)-type orthorhombic structure. It was found that
the high temperature, parent phase of Ni3Sn was impossible to retain
at room temperature. For such a case or for another case where small
amounts of parent phases were only retained, a new method was proposed
to determine the orientation of the habit plane of martensite plates
and the orientation of the specimen surface before martensitic
transformation. This method was applied to Ni3Sn martensite and
{122} plane was determined as the habit plane of Ni3Sn. The determined
habit plane was compared with the habit plane predicted by the strain

energy minimization criterion.

ACKNOWLEDGEMENTS

The author would like to express his deepest appreciation and
gratitude his major professors Dr. H—r. Pak and Dr. M. Kato for
their advice and guidence in both areas of research work and writing
of his thesis.

Dr. K. Mukherjee was also very helpful during this investigation
along with Mr. D. Chung, and I wish to extend my appreciation to them
also.

A special thanks goes to his family for their patience and

encouragement during his study.

ii

TABLE OF CONTENTS

LIST OF TABLES ..................................................

LIST OF FIGURES .................................................

CHAPTER
1 INTRODUCTION ..............................................
2 CRYSTALLOGRAPHY OF Ni3Sn ..................................
2.1 Phase Stability of Ni3Sn Phases ......................
2.2 Crystal Structure of Ni3Sn Martensites Phase .........

2.3 Crystal Structure Determination of the Ni3Sn
Martensite ...........................................
2.3.1 Experimental Procedure ........................

2.3.2 Experimental Results ..........................

3 HABIT PLANE DETERMINATION OF Ni3Sn MARTENSITE .............
3.1 Phenomenological Analysis Based on the Strain
Energy Minimization ..................................
3.1.1 Lattice Correspondence of DO3-Type Structure
and 2H-Type Structure .........................
3.1.2 Phenomenological Analysis Based on the Strain
Energy Minimization Criterion .................

m

Page

vi

11
15

24

24

24

29

TABLE OF CONTENTS -- continued

CHAPTER Page

3.2 Experimental Determination of Habit Plane by

Means of New Method .................................. 34
3.2.1 Pr0posal of New Method ........................ 34
3.2.2 Experimental Procedure ........................ 36
3.2.3 Experimental Results .......................... 37
4 DISCUSSION ................................................ 45
5 SUMMARY ................................................... 49
REFERENCES .................................................... 50
APPENDIX A Interplanar Spacings of Ni3Sn Martensite .......... 52

B Angles between Crystallographic Planes in
Ni3Sn Martensite (in degrees) ..................... 54
C Computer Program to get the CrystalIographic

Data of Ni3Sn Martensite .......................... 63

iv

TABLE

2.1

2.2

2.3

3.1

3.2

LIST OF TABLES

Page
Lattice Parameters of the Unit Cell of DO3-Type
Structure ................................................ 9
Lattice Parameters of the Unit Cell of Cu3Ti(2H)-Type
Structure ................................................ 9
Absolute Values [F]2 of Structure Factor Fg Determined
by h,k and l .................................. , ........... 12
Observed Angles between Two Traces of NiBSn Martensite
Variants on Surface A and B .............................. 39
Example of Angles ¢ Obtained for Two Surfaces by
Assuming (122) Habit Plane ............................... 42

FIGURE

LIST OF FIGURES

Ni-Sn Phase Diagram .....................................

The Detailed Phase Diagram of Ni3Sn Compound ............

The Unit Cell of DO3—type Structure .....................

The Unit Cell of B-Cu3Ti-type Structure .................

The Reciprocal Lattice Planes of B-Cu3Ti-type

Structure ...............................................

(a) Optical Micrograph of Ni3Sn Martensite.

(b) Optical Micrograph of Ni3Sn Martensite Showing
Surface Relieves ....................................

Typical Transmission Electron Micrograph Showing

Microstructures of the Acicular Ni3Sn Martensites .......

Electron Diffraction Pattern of B-Cu3Ti-type

Ni3Sn Martensite ........................................

Electron Diffraction Pattern of B-Cu3Ti-type

Ni3Sn Martensite ........................................

Electron Diffraction Pattern of B-Cu3Ti-type

Ni3Sn Martensite ........................................

(a) Transmission Electron Micrograph of 8-Cu3Ti-type

Ni3Sn Martensite ...................................

(b) Electron Diffraction Pattern Taken from the Area
of (a). .............................................

vi

Page

13

16

17

18

19

20

21

21

LIST OF FIGURES--Continued

FIGURE

2.11

(c)(d) Dark Field Images in 201 and 201T Reflection,

Respectively .....................................
The Atom Positions on (101) Plane in the DOB—type
Structure ...............................................
The Atomic Positions on (001) Plane in 2H-type
Structure ........... I ....................................
The 2H-type Structure(" .__" line) Generated from the
Tetragonal Lattice in the Unit Cell of the
DO3-type Structure ......................................
A pair of Martensite Variants having a Twin-Relationship
with Respect to the (110)D03 Plane ......................
Model for the Fundamental Ideas to Obtain the
CrystaTlographic Data between Parent and
Martensite Phases .......................................
(a)(b) The Optical Micrographs of Ni3Sn alloy

Martensite Phase on Surface A and B, Which

are Perpendicular to Each Other ..................
The Area of the Standard Triangle of Stereoprojection...
All Surface Normals 5 Selected by Computer ..............
The Surface Normals and Martensite Habit Planes on

Two Surfaces A and B on One Grain .......................

Page

22

26

27

28

30

35

38
41
43

44

LIST OF FIGURES--continued

FIGURE Page

3.10 Two Habit Planes,(122) and Strain Energy Minimization

Criterion, and the Lattice Parameters ................... 47

viii

1» INTRODUCTION

The name martensite was originally given to the product of the
hardening reaction in rapidly cooled steels, but its use has been
extended to similar changes in other alloy systems. The definition of a
martensitic transformation is a transformation associated with a
lattice-distortive, virtually diffusionless structual change having a
dominant deviatoric (shear) component.

Any martensite formed by such diffusionless, shear-type atomic motion
is mostly embedded in an untransformed phase, so-called parent phase,
and bound on a specific plane of the parent phase.1 This specific
plane is called the habit plane and is explained phenomenologically
as a lattice invariant plane. The habit plane and orientation
relationships between the parent and martensite phases are important in
understanding the martensitic transformation from a crystallographic
aspect. Therefore, many works on martensitic transformation have been
involved in abtaining such crystallographic informations.

In some cases, however, parent phases can not be retained at
room temperature or if any, small amounts of parent phases can be
retained. Thus, it is difficult to get crystallographic relationships
between the parent and martensite phases. 1

This research is mainly aimed to determine the orientation of -
habit planes in cases where no parent phase is retained at room
. temperature. For this purpose a new method was proposed. Ni3Sn
alloy was employed to apply this method because in this alloy it
is theoretically impossible to retain the parent phase. The

1

determined orientation was compared with the orientation of the
habit plane predicted by a phenomenological theory based on the
elastic strain energy minimization criterion. The crystal structure
and internal structures of the martensite of Ni3Sn was examined

by means of transmission electron diffraction as well as microscopy

so that the phenomenological theory could be applied.

2 CRYSTALLOGRAPHY 0F Ni3Sn
2.1 Phase Stability of Ni35n Phases

Figure 2.1 is a phase diagram of Ni-Sn binary alloy [1], and
Figure 2.2 shows the detailed phase diagram of Ni3Sn compound [2].
As can be seen in these figures, Ni3Sn has a phase transition at
around 950°C. The existence of the phase transition was found
by Heumann [3] through DTA measurements and this phase transition
was attributed to a disorder-order transition from disordered
hcp to MgBCd (0019)-type ordered hcp structure. Schubert et al [4],
however, investigated a crystal structure X-ray technique, and found
that the crystal structure was not the disordered hcp but Fe3Al (003)
-type ordered bcc structure.

Recently, Pak and co-workers [5] investigated the relation
between the high-temperature phase with the 003-type structure and
the low-temperature phase with the DOlg-type strutture in detail,
and found that the Dolg-type structure being stable at room
temperature was transformed massively from the 003-type structure
when quenched slowly. It was also found that when quenched rapidly
the 003-type structure was transformed martensitically into the
B-Cu3Ti-type (2H) ordered orthorhombic structure.

Figure 2.3 shows the unit cell of 003-type structure for the
high temperature phase of Ni3Sn alloy and Table 2.1 shows the lattice

parameter of the 00 type structure.

3

 

‘Figure 2.1 Ni - Sn phase diagram.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1300
c
‘2»
'H
1200 2 Z
+
1100
Ni3Sn + (N1) N13Sn
1000 +
g 920 \
900 23.25
g l
S \ AL
54 27.25
800
Ni3Sn + (N1) Ni3Sn + Ni3Sn2
700
600 24.15 26.85
20 22 24 26 28 30

ATOMIC PER CENT TIN

Figure 2.2 The detailed phase diagram of N13Sn compound.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.3 The unit cell of DO3-type structure.

2.2 Crystal Structure of Ni3Sn Martensite Phase

As mentioned in the previous section, Pak and co-workers [5]
determined the crystal structure of the martensite phase as the
B-Cu3Ti (2H)-type structure by means of X-ray diffraction. The
unit cell of the martensite phase is drawn in Figure 2.4 and
atomic positions of Sn and Ni atoms in the unit cell are listed

below.

Sn (0 0 0) (2/3 1/2 1/2)
Ni (0 1/2 0) (1/2 1/4 0) (1/2 3/4 0)
(2/3 0 1/2) (1/6 3/4 1/2) (1/6 1/4 1/2).

Since the crystal structure of the martensite was determined
only by means of X-ray diffraction, the structural determination of
the martensite was carried out by means of transmission electron
diffraction in order to make sure whether the martensite has the
Cu3Ti-type structure or not. This will be shown in the following

section. Table 2.2 shows the lattice parameters of this structure.

2.3 Crystal Structure Determination of the Ni3Sn Martensite

For the convenience of the structure determination, the crystal
structure of the martensite was assumed to be the B-Cu3Ti-type
structure. According to the diffraction theory, the structure factor

of the crystal is expressed as,

Fg = 2 fi exp(2nig - Fi) ,
i

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.4 The unit cell of B-Cu3Ti-type structure.

Table 2.1 Lattice parameters of DO -type structure.

 

 

3
lattice parameter
(A) remarks author
6.091 Ni-Sn at 950 C Schubert
5.9580 Cu-Al Tarora
5.80.: .05 Cu-Al-Ni Duggin & Rachinger
5.836 Cu-Al—Ni Otsuka & Shimizu
5.8412 1 .0004 Cu-Al-Ni at 21 C Duggin

 

 

 

 

 

Table 2.2 Lattice parameters of B-Cu3Ti type martensite.

 

 

 

 

a(A) b(A) C(A) alloy author
4.41 5.31 4.22 Cu-Al-Ni Duggin & Rachinger
4.40(i0.52) 5.33(10.SZ) 4.24(i0.5%) Cu-Al-Ni Duggin
4.6011 5.3050 4.3052 Cu-Al Geninger
4.382 5.356 4.222 Cu-Al-Ni Otsuka & Shimizu
4.504 5.304 4.277 Ni-Sn Pak et al

 

 

 

10

where fi is the atomic scattering factor of the i-th atom and in

the real lattice unit cell. The vector Fi is expressed by
F1 = uia + v16 + wiE

where ui, vi, wi are fractional coordinates of the i-th atom, and
a, 6 and E are the translations of the real lattice unit cell.
*

.. .* _*
If a , b and c are the translations of the reciprocal lattice

unit cell, every reciprocal lattice point can be expressed by the form
- -* * _*
g = ha + k6 + lc

where h,k and l are intrgers. a is normal to the crystal plane with

Miller indices hkl. Thus, a - Fi is abtained as
5 . F1 = hui + kvi + lwi .

The structure factor for layered structures such as 2H-type structure
can be obtained by the simple sum of the structure factor related
with each layer. There are one A-atom and three B-atoms on the (001)
of the B-Cu3Ti lattice, the coordinates are 0 O O , and 0 1/2 0 ,
1/2 1/4 0 , 1/2 3/4 0 , respectively. The cooresponding atoms

on the next (001) are all displaced by [2/3 1/2 1/2]. Thus,

'11
ll

9 F1 + F2 ’

fA -2wi(h/2 + k/4) + e-2m‘(h/2 + 3k/4)

7:
II

+ fB {e
+ e-2n1(k/2)}

3

11

and F2 = Fle-Zni(2h/3 + k/2 + 1/2) .

Here, F1 is the structure factor on the first (001) plane in unit
cell(shown Figures 2.4 and 3.3), F2 the structure factor on the
second (001) plane in unit cell(shown Figures 2.4 and 3.3), fA the
atomic scattering factor for A atom and fB the atomic scattering
factor for 8 atom. Multiplication by the complex conjugate of F9
will give us the square of the absolute value of the resultant wave
amplitute F ; that is,

2

[Fl = 4 {fA + fB(2 COth cos«k/2 + COSWk)}2

x coszn(2/3h + 1/2k + 1/21).

According to diffraction theory, |F|2 is proportional to the intensity

19 of reciprocal lattice points ; that is,

2
(X .
19 IFgl
|F|2 obtained from the above equation are summarized in Table 2.3 and

the resulting reciprocal lattice planes are illustracted in Figure 2.5.

2.3.1 Experimental Procedures

The NiBSn alloy of 24.6 at % Sn was prepared by melting 99.9%

pure nickle(supplied by the International Nickle Co.), and 99.999%

tin(supplied by K & K Laboratories,INC.), at 1,190°C in 18mm-diameter

5

quartz capsules which was evacuated up to about 1 x 10' torr and

Table 2.3 Absolute values IFI2
determined by h,k and l.

 

 

 

 

 

 

 

 

 

 

 

 

h k 1 IFIZ

6n , 4m 2q 4(fA + 3fB)2
6n:l:3 (om-1:2 2q

m1 m2 2cm 3<fA + 3:3)2
611:},2 4m 2qj;1

6nil 4mi2 2q (fA + 3fB)2
6n12 4m 2q

6n 4m Zqil 4(fA - fB)2
6n 4&2 2q

6nd:3 4nd:1 thl

616:3 4m 2q

6&1 4m 2q:i:1 3(fA - fB)2
6nil 4m¢1 2q

6nd:2 loud-1 24

6n12 4mi2 thl

6111-1 4m Zq (fA - fB)2
6nd:1 4&1 291*}

6n12 4mi1 th1

61112 4mi2 2q

6n(or.13) 4m Zqil

6n(or 1:3) 4mi1 2‘! 0

6n(or i3) 411:1:2 Zqfl

 

 

( m.n.q are integers )

13

 

 

 

 

 

 

r’x
VI

 

[x
\I

‘ (r
‘J.F J" \J " éd!
000 200 I100

a
(001) passing through 000 point

rm
\1
rx
\/

 

 

 

 

 

 

 

 

.1 = Li . 5014
b = S . 3014
c = 4.277

 

 

 

 

 

 

 

 

 

 

 

 

€‘ 1‘? {‘
C. v I} {P
+ i . (t
121 Jr 21
<\_ r\ 9
y 4&1
a L 4 13,—...
001 201 401
(001)* passing through 001 point
Fundamental Super-lattice
. 2(f3n+3fNi)=2F O 2(fSn’fNi)
1'. /BF C) /38
" F. c) S

Figure 2.5 The reciprocal lattice planes of 8-CU3Ti
type structure

14

then sealed. The pure nickle rod was cut into small piece after

cold rolling and then chemically polished in a 25% HNO - 25% H250 -

3 4
37% CH3C00H- 13% H202 solution at 60-7oPc . Agitation was carried
out several times in the molton state in order to mix alloy elements
well. The weight losses of the alloy ingot was about 0.03 wt%. The
ingot was sealed and evacuated quartz capsule at 1,1OOPC for 20 hrs
to homogenize well.

Then, the ingot was cut by Diamond wafering Blade to the
thickness of 1mm, and polished done with 600 grit silicon carbide
strip to the thickness, of a 0.7mm to abtain the smooth flat surface.
The sheet specimens obtained were then annealed at 1,100’C for 1 hr in
evacuated quartz capsules which were crashed when quenched in order
that the martensitic transformation took place. ‘

Optical microscope observation was carried out for the confirmation
of theoccurence of the martensitic transformation in Ni3Sn and also for
the measurement of possible crystallographical data. Sheet specimens
were prepared for this observation by hand-polishing, and etching in
a 1Hcl + 2HN03 + 6CH30H solution.

Most of the specimens were thinned down again for tranémission
electron microscope observation. Jet electropolishing was carried
out by using a 25% HClO4 and 75% CH3CH20H solution and then final
electrothinning was done at 18 volts at about -65’C by using the
same solution. The stainless steel plate was employed as a cathode.

Transmission electron microscope observation was carried out by

using an electron microsc0pe of Hitachi HV-11A, operated at 100KV.

15

2.3.2 Experimental Results

Figure 2.6(a) is an optical micrograph of Ni3Sn, showing fine
structures obtained by quenching from 1,190’C. Figure 2.6(b) is an
another optical micrograph of NiBSn prepolished before quenching,
showing surface relieves. These surface relieves clearly demonstrate
that the fine "acicular" structures were formed martensitically.
Similar surface relieves of Ni3Sn were reported by Pak et al [5].

Figure 2.7 is a typical electron micrograph, showing microstructures
of the Ni3Sn martensites, electron diffraction patterns taken
from the martensites were analyzed. Some of examples are shown
in Figures 2.8.2.9 and 2.10. The crystal structure of the martensite
was able to be determined as an ordered orthorhombic structure using
the reciprocal lattice constracted. In other words, the structure
determined was the same as reported in reference [5]. By using
the lattice parameters of the martensite determined by X-ray [5],

a = 4.504 A,‘b = 5.304 A and c = 4.277 A, Figures 2.8 to 2.10 were
indexed. Interplanar spacings and interplanar angles calculated
using the above mentioned lattice parameter were listed in Appendices
A and 8.

Figure 2.11(a) is another electron micrograph showing internal
structures of the martensite. These internal structures were identified
as (121)2H twins from Figure 2.11(b-d),(which were refered from
reference (5)). Figure 2.11(b) is an electron diffraction pattern
taken from the area of Figure 2.11(a), which obviousely shows the
twin relation. Figure 2.11(c) and (d) show dark field images in 201

reflection and 201T reflection, respectively. It is clear from

16

 

Figure 2.6 (a) Optical micrograph of Ni3Sn martensite.
(b) Optical micrograph of Ni3Sn martensite
showing surface relieves.

 

Figure 2.7 Typical transmission electron micrograph
showing microstructures of the acicular
Ni3Sn martensite.

 

 

 

 

 

Figure 2.8 Electron diffraction pattern of

B-Cu3Ti—type Ni3Sn martensite.

.19

 

 

 

 

 

Electron diffraction of B—Cu3Ti—type Ni3Sn
martensite.

6 - 53.l°

6'= 74°

Figure 2.9

20

 

 

22
102 T.
o
e
102
10 I
22~\ 20 22

 

 

Figure 2.10 Electron diffraction pattern of B-Cu3Ti-type

Ni3Sn martensite.
0 = 20°

21

 

Figure 2.11 (a) Transmission electron microgaph of Ni3Sn
martensite. (b) Electron diffraction pattern
taken from the area of (a).

22

 

Figure 2.11 (c) (d) Dark field images in 201 and 201T
reflection, respectively.

23

Figure 2.11(b),(c) and (d) that 201 and 201T reflections are twin-
related to each other. Most of internal bands are (121)2H twins,
indicated by arrowi, while small amounts of bands are parallel to

(101)2H , which was considered to be another twin plane.

3 HABIT PLANE DETERMINATION OF NiBSn MARTENSITE
3.1 Phenomenological Analysis Based on the Strain Energy Minimization
The martensitic transformations have been discussed by seversl
authors from a viewpoint of the minimization of the elastic strain
energy [6-9]. As pointed out by Kato and coworkers [10] recently,
the phenomenological analysis based on the elastic strain energy
minimization criterion is essentially identical to the phenomenological
theories proposed by Wechsler et al [11] and Bowles and Mackenzie [12].
Recently, Mukherjee and Kato [13] applied the elastic strain energy
minimization criterion to the crystallography of martensites in Ti
alloys and showed that habit planes predicted were in good
agreement with those obtained experimentally.
There are some crystallographic similarities of martensites
between Ti alloys and Ni3Sn alloy, such as lattice invariant
shear being a twinning shear. Thus, a similar procedure to one
employed by Mukherjee and Kato [13] was used in the study to

determine the habit plane of the Ni3Sn martensite.

3.1.1 Lattice Correspondence of 003-type Structure and 2H-type
Structure
Figure 2.3 illustrates a unit cell of the DOB-type ordered bcc
structure of the parent phase. The atomic positions on (101) plane
in the 003-type structure are shown in Figure 3.1. As can be

seen in Figure 3.1, the 003-type structure consists of the AB'AB'

24

25

stacking. It is well known that the 2H-type crystal structure
(deformed hcp) can be produced from bcc structure by Burgers'
mechanism, where the operation of the {112} <1lI> DO3 shear
systems followed by a small volume change results in the (001)2H
(0001)hcp plane from the (101)003 plane. In addition to this
operation, a a/12[IOI]Do suffling on every other (101)Do plane
3 3

is necessary to create the 2H structure as shown in Figure 2.4.
To understand this suffling assiciated with the martensitic
transformation, atomic positions of the 2H-type structure
are illustrated in Figure 3.2. Considering the shearing and
suffling operation mentioned above, it can be easily understood
that the 2H-type structure is generated from the tetragonal lattice
in the 003 structure, drawn as a heavy-lined lattice in Figure 3.3.

By using existing lattice parameters of the parent 003-phase
and martensite phase, the lattice variant strain(Bain strain) can
be calculated. The existing lattice parameter of the parent phase
is a = 6.006 A at zé’c [4] and a

= 4.504 A , b = 5.304 A ,

Bl 2H 2H
c2H = 4.277 A [5]. From this values, the Bain strains based on the

x'-y-z' coordinate system in Figure 3.3 are obtained as

51 = /232H / 381 - 1 = 0.0605

32 b2H / 681 - 1 = -0.1169

63 = “ZCZH / a31 - 0.0071 (3.1)

H
II

and the volume change is -5.68%.

—-—--- [010]

 

 

 

 

 

 

 

 

——.... [10‘1’]

Figure 3.1 The atom positions on (101) plane in the DO3—type
structure.

 

.Ni

26

OSn

 

 

 

 

27

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1L0

 

(1

.Ni OSn

Figure 3.2 The atomic positions on (001) plane in
2H-type structure.

28

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
 
  
 
 

 

 

    
 
 

 

 

 

 

.Ni

 

-. - l
m‘
I .

\

‘.

 

‘i.

   

 

 

 

   
 

I
-‘- -- -

I
I

 

5.

 

 

 

 

OSn

Figure 3.3 The 2H-type structure ("-—" line)

generated from the tetragonal lattice

in the unit cell of the DO3-type

structure.

29

As shown in previous section, the 2H-type martensites contain
(121)2H twins. Thus, this twinning is considered to be the lattice
invariant shear. From the lattice correspondence of the parent and
martensite, the (121)2H twinning plane is found to be parallel to the
(110)DO3 plane. In Figure 3.4 a pair of martensite variants having a

twin-relationship with respect to the (110)DO3 plane were drawn.

3.1.2 Phenomenological Analysis Based on the Strain Energy
Minimization Criterion
According to Mura et al [14] and Kato et al's [10] analysis based
on the strain energy minimization criterion, if the transformation
strain e§j(8ain strain plus lattice invariants strain) in an

xl-xz-x3 cartesian coordinate system satisfies the condition of
= 0 , (3.2)

the strain energy becomes minimum(zer0) and the condition in equation
(3.2), with the x3-axis as an invariant plane(habit plane) normal,

is equivalent to the invariant plane condition in the phenomenological
theory. As shown in equation(3.1), the Bain strain in the martensite

becomes

(3.3)

 

 

30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.4 A pair of martensite variants having a twin-
relationship with respect to the (110)D03 plane.

31

where the coordinate system is taken along the principle axes of the
003 lattice. As can be seen in equation(3.1), €1.52 > 0 (expansion)
62 < 0 (contraction). Equation(3.3) can be changed by similarity
transformation based on the x'-y-z' system in the parent phase as
Tel + £3) / 2 0 (-.1 + .3) / é-
eij = 0 s3 0 (3.4)
(-81 + 63) / 2 0 (£1 + 83) / 2_( B

B

 

 

where Eij is the Bain strain of variant 1. As shown in Figure 2.11
and 3.6, the lattice variant shear for the martensite domonantly
occurs by (121)2H twinning. Thus, the twinned variant should have

the Bain strain as

 

F.2 0 0 "
ETj = 0 (61 + £3) / 2 (£1 - e3) / 2 (3'5)
_9 (51 ‘ 53) / 2 (51 + 53) / %_ B

 

by using the x'I —x -2" system in the parent phase where egj is the
Bain strain of variant. If the volume fraction of the variant is
defined as f(0 < f < 1), which is to be determined, then the total

transformation strain in the Bl-system, Eij’ can be written as

T _ 1 _ 2
Eij - feij + (1 f)eij (3.6)

From equation (3.3) and (3.4), egj can be obtained :

32

 

 

 

 

 

 

 

‘Tf(e + e ) -s + e
1 3 1 3
2 + (1-f)e2 0 -*—§—-—-
ET = 0 f8 + (1-f)(€1 + a?) (1-f)(el-63)
Ti 2 2 2
f(-e1 + £3) (1-f)(el-s3) (81+E3)
_. 2 2 2 .1
F'T 0 T'T
E11 613
- T T
ET ET ET
__31 32 33_

 

 

By rotating the coordinate system, we can find a new xl-xz-x3
system in which the total transformation strain(3.7) satisfies the
habit plane condition of equation(3.2). Since R becomes parallel

to the x3-axis in this new system, i.e.
H = [sine coso , sine sino , cose]8 (3.8)

We have three unknown parameters 6 , o , f which can be solved easily

and the results become

. tanzo — -e;2 / all (3.9)
tane = sin¢(eI1 - €22) / EIBta"¢'€;3 ' (3.10)

1/2 1 /A2+16Ac / 2A (3.11)

—h
II

15283

where A = 3:2(e1—e3)2 - 2(sl-ez)(62-63)(e3+el). From equation(3.9),
(3.10) and (3.11) the habit plane normal and the volume fraction of

the variant 1 were calculated by using the eigen strain as following

70.329
-56.17
0.8565

F0.2796'

-0.7822

 

 

_0.5567J

33

-70.329
-59.27
0.8159
(Lo.289i

0.8094

 

 

_0. 51104

34

3.2 Experimental Determination of Habit Plane by Means of New Method

3.2.1 Proposal of New Method

As mentioned in the introductory part, it is impossible to
retain the high temperature parent phase of Ni3Sn to room temperature.
Thus, it would be difficult to get the crystallographic data between
parent and martensite phases, unless some special techniques were
employed. Here, a new method is proposed to determine not only
crystal orientation of parent phase before transformation but also
the habit plane of martensites, only by measuring several angles
between paired variants.

Figure 3.5 shows the fundamental ideas of the method. 6[HKL] is
the normal to the specimen surface,i.e.,the normal to the parent
phase. Here, habit plane normals are expressed by i and 3, which
are assumed to have the same type of indeces. This assumption can
be acceptable generally. All vectors 6,3 and 3 are to be determined
as follows.

If 5 , i and 3 are all unit vectors, a and F can be obtain from

vector products of 5 and i , 6 and 3 such as

.0!
ll
'0!
X
-‘-I
\
"C
X
.1

”SI
II
Ul
><
L14
\
”C
X
L4

Vectors q and F express trace of martensite variants. The angle ¢ij
between the two traces of variants(i,j) can be obtained from a dot

product of the two vectors a and F as

35

p er13

 

 

 

I-th variant

Figure 3.5 Mbdel for the fundamental ideas to obtain the
crystallographic data between parent and
martensite phases.

36

The angle ¢ij is experimentally measurable from optical micrographs of
martensites. Since any vector can be expressed by two independent
variables and since it was already assumed that i and 3 have
equivalent indices, total independent variables are four. Thus, at
least five martensite variants are necessary to determine four
independent variables.

In other words, knowing independent angles between paired
variants, we can determine not only the surface normal of the parent
phase 6 before the martensitic transformation but also the habit
plane normal 3 or 3 . To find out the desired combination of i and
3 , computer calculation was employed. The following experiments were
carried out to obtain independent angles necessary for the computer

calculation.

3.2.2 Experimental Procedures

A rectangular parallel piped specimen was prepared from the
Ni3Sn ingot in order that two surface trace analysis can be done.
By the similar processes mentioned in the previous section, acicular
martensites were formed. To make surface observation easily, large
grains were made by annealing for 40hrs at 10506C. Surface observation
was carried out on two surfaces(A and B) in one grain, perpendicular
to each other. Angles between paired traces of martensite variants

on both surface A and B were measured.

37

3.2.3 Experimental Results

Figure 3.6(a) and (b) show the optical micrographs of Ni Sn

3
martensites surface A and B. Angles between two traces of these
martensite variants measured, ¢ij’ are shown in Table 3.1. Using
values of ¢ij measured, the vectors 5 and i could be determined.

In the present research, vector i will be assumed first as the

first step in determing vector 5. Three different vectors were chosen
as vector i from the following reasons.

Recently, the habit plane of the martensite in Cu-Al-Ni alloy
was determined by means of transmission microsc0py [15]. The habit
plane reported was between {122} and {133}. Since Ni3Sn alloy and
Cu-Al-Ni alloy has the same crystal structure for both parent and
martensite phases, the habit plane 3 was assumed to be {122} and
{133}. {112} was also chosen as a habit plane for extra example of
the computer calculation in determing vector 5. The determination of
the vector was carried out in a following way. i

As mentioned above, firstly the habit plane i was assumed and
then actually i was chosen as one of the family of the habit plane.
Then 5 was chosen to calculate all angles ¢ij for the other eleven
variants of the family. Then, values of angles ¢ij measured
experimentally were compared with those of angles ¢ij calculated.

If all of measured angles ¢ij are well explained within an allowance
of a given angle with reapect to the calculated angles ¢ij’ the
computer tells us that this vector 6 might be reasenable as the

plane normal of the parent phase. Choice of 6 was carried out

systematically in the whole area of the standard triangle of

38

    

 
 
  

H 4‘ '5‘
a" ‘3'!-
JN ‘ .gd.
._, 4. ‘l ,:

Figure 3.6 (a)(b) The optical micrographs of Ni Sn alloy
martensite phase on surface A and B, which are
perpendicular to each other.

39

Table 3.1 The observed angles between two traces of Ni Sn

 

 

 

 

 

 

 

 

 

 

 

martensite variants. 3
from surface A
(1) (2) (3) (4) (5)
(1) - 46.5 86 85.5 53
(2) 46.5 - 40 47.5 80
(3) 86 40 - 8.5 40
(4) 85.5 47.5 8.5 - 32.5
(5) 53 80 40 32.5 -
from surface B
(1) (2) (3) (4) (5) (6)
‘ (1) - 47 63.3 87 66.5 70
(2) 47 - 16.5 45 66 23
(3) 63.3 16.5 - 28.5 49.5 7.0
(4) 87 45 28.5 - 20.5 22.7
(5) 66.5 66 49.5 20.5 - 43
(6) 70.0 23.0 7.0 22.5 43 -

 

 

 

 

 

 

 

 

 

 

40

stereoprojection, [001]-[011]-[Ill], shown in Figure 3.7. If no
vector 6 is informed, the first assumption of vector i is considered
to be wrong under a given allowance condition. Apendix C shows an
example of the computer programs employed. In this program, vector
i was assumed to be (122) and an angle allowance was within :1.5°.
In this case, reasonable surface normals 5 were obtained, which will
be shown later. On the other hand, when {133} and {112} were assumed
to be as the habit plane normals, and when the same angle allowance
of 10.50 was permitted, no surface normal 6 was obtained. Thus, in
present research it can be conclude that (122) plane is a most
probable habit plane.

Table 3.2 shows some examples of angles ¢ij obtained for two
surfaces by assuming {122} habit plane. As it can be seen from this
table, all of the observed angles are in good agreement with the
calculated angles.

For these two surfaces, all surface normals 5 selected by
computer were plotted in Figure 3.8. These two surfaces A and B
were from one grain and were perpendicular to each other. Although
these two surface normals 6 were independently determined, the angle
between these two calculated normals is abdut 90°, which is in good
agreement with the directly measured angle. In Figure 3.9 , the
surface normals([3 13 17] for A and [952] for B) and habit planes

determined were shown.

41

T22
T33

 

001 011

Figure 3.7 The area of the standard triangle of
stereoprojection.

42

Table 3.2 Examples of angles 9 obtained for
two surfaces by assuming (122)
habit plane

audaceA
¢cal :ange beMeen(122)and0ther (1221

 

11221 (122) (221) (212) (122) (122) (221)

Foal” 8477 6397 5867 5633 4704 4513
11221 (2127 (221) (212) (221) (2'12)

¢oai<°> 3229 3196 2559 831 1.07

p”. : measued angles
85. 5. 47. 5.32.5. 8.5

 

 

 

 

 

 

 

 

 

 

 

 

 

m
56031: angle between (221) and other (221)

 

{221) (221) (221) (122) (212) (122) (221)
¢ca1(°) 8559 8518 7634 6732 0546 4558
1221) (212) (212) (122) (212) (122)
gale) 29.71 23.77 21.041959 1.23

51'1” : measured angles
87, 45. 28.5, 22.7, 205

 

 

 

 

 

 

 

 

 

 

 

 

 

43

A surface normal .1.“

 

 

001 011

B surface normal

 

Figure 3.8 All surface normals 5 selected by
computer.

44

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28
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2va .

mmmmu
momtsmi

 

.aamuw one do
a oommusm 6:9

m.m ouamfim

    

4 DISCUSSION

It was observed that the high temperature 003-structure
martensitically when quenched rapidly and to the Mg3Cd(0019)-type
structure massively when cooled slowly. Thus, it is obvious that no
high temperature phase can be retained in this binary alloy regardless
cooling rate. Recently, Kachi and Murakami [16] investigated the
phase stability of Ni3Sn high temperature phase by substituting Ni
with Cu. They reported that both the parent and martensite phases
coexisted at room temperature in a range where Cu composition was
between 18 and 21 at%. Since the best way experimentally to determine
the orientation of the habit plane of martensites is obviously to
retain the parent phase with the martensite phase, trials of getting
the retained parent phase were extensively done according to Kachi
and Murakami's reports. However, no coexistance of the martensite and
parent phases was obtained. Although the DOB-parent phases were
able to be retained in a range of Cu of 18 to 24 at%. those 003-
phases were found not to transform even if temperature was lowered
up to the liquid nitrogen temperature. Instead, it was found that
when the 003-phases were cooled slowly(actually furnace-cooled),
Nidmannstatten structures were found to be very stable up to around
400°C. The crystal structure of the Nidmannstatten was not determined
yet.

The new method was proposed to determine the habit plane of

martensites by measuring only angles between paired martensite

45

46

variants, without knowing the surface orientation of the parent
phase. This method may be called "computer-aided trace analysis
method", because without computer it would be almost impossible to
determine the habit plane of the martensite. This method is
applicable under the following two conditions : (1) all martensite
variants in one alloy system have the same type of indeces, and (2)
at least five different variants should be observed on a surface
within a grain.

Using this method, we can also obtain the surface orientation
5 of the parent phase at a same time. By comparing the actual
angle between two surfaces( A and B ) with the corresponding angle
calculated from the two surface orientations 5 obtained, the
validity of the method proposed was examined. As shown in Figure 3.10,
the angle calculated from the obtained vectors 6 was about 90° and
the angle measured directly from the specimen was also 90°. The
results were in very good agreement. In order to make sure of the
validity of this method more, however it is necessary to examine
whether this method is applicable to other systems, whose habit
planes have been known already. This will be carried out in the
near future.

The phenomenological theory based on the strain energy
minimization criterion [13] was employed to predict the habit plane
of Ni3Sn martensite. Using this theory, two habit planes and
volume fraction of twinning variants were able to be obtained. In

Figure 3.10 one of the two habit plane normals obtained was plotted.

47

.soppm F<-_zm=u for m_ .N.
.xoppm cm *2 com ma =H= .mcmumsocma mu_uump on» use
.cowcmu_cu :o_um~_s_:ws amcmcm :_mcum use ANNHV .mmcmpa u_no: o~.m mczm_m

05 :0 50

8:35 csE_c_E
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_o A

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was News... 1N6
8mm .32? IE
83 «8.3... IN...

was 2.123 .... mono
212-8 . cmmz

0F

48

This was because the plotted habit plane was corresponding to the
large volume fraction of twinning variants. The volume fraction
calculated was 82%, which was in pretty 900d agreement with that
(about 75%) measured from Figure 3.4 and 2.11. In Figure 3.10
another habit plane normal calculated for Cu-Ni-Al alloy [15] was
also plotted. As can be seen, this habit plane normal is very
close to {122} compared with that of the present alloy. This
diffrence between the two alloys may result from the accuracy of
lattice parameters for the 003-parent phases ; the lattice
parameter of Cu-Ni-Al was measured at room temperature [15], while
that of Ni3Sn was measured at 960°C [4] and extrapolated to room
temperature by considering thermal expansion. From the habit plane
observations on Ni3Sn and Cu-Ni-Al alloys it can be concluded that
the habit plane of 2H-type martensites transformed from 003 structure

is {122} or close to {122}.

5 SUMMARY

Martensites of NiBSn alloy produced by quenching from 1050°C
were investigated crystallographically. The results obtained can be

summarized as follows :

1. The crystal structure of the martensite Ni3Sn alloy was determined
as an ordered orthorhombic structure, B-Cu3Ti-type(2H), by means
of electron diffraction. This structure is identical to that
determined by means of X—ray diffraction.

2. A new method was proposed to determine the habit plane of the
martensite for cases where none or a small amount of parent
phase can be retained. This method can be applicable if at
least five variants are observed on a surface of one grain.

3. The habit plane of the Ni3Sn martensite was determined as {122}
plane using the new method pr0posed. Phenomenological theory
based on the strain energy minimization criterion was also
employed to determine the habit plane. The angle difference
between these two habit plane normals determined is considered

to be pretty small.

49

10.

11.

12.

13.

14.

REFERENCES

Hansen, M. and Anderko, K., Constitution of Binary Alloys,
McGraw-Hill, New York, Toronto, London, (1958), 1042.

Shunk,F.A., Constitution of Binary Alloys, McGraw-Hill,
New York, Toronto, London, (1969), 555.

Heumann, T., Zeitschrift Metallkunde, 35 (1943), 248.

Schubert, K., Burkhardt, M., Esslinger, P., Gunzel,E.,
Meissner, H.G., Schutt, H., Wegst, J. and Wilkens, M.,

" Eigige Strukturelle Ergebnisse an Metallischen Phasen ",
Naturwissenschaften, 43 (1956), 248.

Pak, H., Saburi, T. and Nenno, 5., " Martensitic and
Massive Transformation in NiBSn Alloy ", J. of Japan Institute
Metals, 37 (1973), 1128.

Shibata, M. and Ono, K., Acta Metallurgica, 23 (1975), 587.
Clarke, D.R., Metallurgical Transactions, 7A (1976), 723.

Easterling, K.E. and Tholen, A.R., " Acta Metallurgica ",
24 (1976), 333.

Shibata, M. and Ono, K. Acta Metallurgica, 25 (1977), 35.

Kato, M., Miyazaki, T. and Sunaga, Y., " Re-Examination of the
Elastic Energy and the Phenomenological Crystallography Theory
in a Martensitic Transformation ",tScripta Metallurgica,

11 (1977), 915.

Wechsler, M.S., Lieberman, 0.5. and Read, T.A., " On the Theory
of the Formation of Martensite ", Transactions AIME , 197 (1953),
1503.

Bowles, J.S. and Mackenzie, J.K., " The Crystallography of
Martensite Transactions ", Acta Metallurgica, 2 (1954),
129, 224, 138.

Mukherjee, K. and Kato, M., " Lattice Correspondence and
Crystallography of Martensites ", ICOMAT-82, Leuven, Belgium,
(1982).

Mura, T., Mori, T. and Kato, M. " The Elastic Field Caused by a

General Ellipsodal Inclusion and the Application to Martensite
Formation ", J. Mech. Physics of Solids, 24 (1976), 305.

50

51

REFERENCE

15.

16.

Otsuka, K. and Shimizu, K., " Morphology and Crystallofraphy of
Thermoelastic y' Cu-Al-Ni Martensite ", Japanese J.
Applied Physics.

Kachi, S. and Murakami, Y., " Martensitic Transformation and

Phase Relation in Ni Cu Sn and Ni Mn Sn Alloys ", Sci. Report
RITU A29. Suppl. 1 (i981)§ 73. 3'X x

APPENDIX A

spacing(A-1)

b=5.304 A, c=4.277 A
hkl

Orthorhombic

a=4.504 A,

rystal Structure

hkl

Unit Cell

Interplanar Spacings of Ni3Sn Martensite
P

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52

53

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APPENDIX B

Angles between Crystallographic Planes in Ni3Sn Martensite

Orthorhombic

Crystal Structure

a=4.504 A , b=5.304 A , c=4.277 A

Unit Cell

010

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APPENDIX C

Computer Program to get the Crystallographic Data of Ni3Sn

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