X-RAY BIFFRMUON AMLYSSS
0F
FABRECATION DEFDRMITIES 3N MENU

WESES MR NE MERE! M" I: S.
MICHIGAN STATE COLLEGE

HAWK MSEPH SKINNER
194:8

This is to certify that the
thesis entitled
X—Ray Diffraction Analysis

of
Fabrication Deformities in Metals

presented by

Martin Joseph Skinner

has been accepted towards fulfillment
of the requirements for

M

M . S 0 degree in _E.:§2_

    
     

 

I Major prééss

Date—MEHW_-

H496

X-RAY DIFFRACTION ANALYSIS

By
mew: JOSEPH SKITETER

#

A THESIS

Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Apolied Science
in partial fulfillment of the requirements

for the degree of

MA ESTER OF SC IEJCE

Department of Electrical Engineering

194a

TABLE OF CONTENTS
IntrOdUCtionOOOOoooooo00. ............. ......OQOQOO 1

Theory of Diffraction princinles....... ........ ... 3
Theory of Crystal Structure.................. 3

Theory of X-Ray Diffraction in Crystals...... '(

X-Ray Diffraction Methods......................... 11
Direct Transmission Methods.................. 11
Reflection Methods........................... 16

POWderItlethOd-S.......0........O-OCOOOOOOOIOOOO19

X-Ray Study of Grain Size and Preferred
Orientation.................................. 23

X-Ray Study of Stress and Strainr................. 32
COnCIuSionO O C O O O O o 0 O O. O 0 0 O O O O o O O O O O O 0 O 0 O O O I O O O O O O O 41
Appendix. 0 O C Q Q 0 Q}. C 0 O O O O O O O O 0 O O O I O O Q Q 0 Q 0 O O O O O O O O 0 O 0 4B

BiblicgraophyOOOOOOOOOO0.0...OOOOOOOOIOOOOOOOOOO... 52

5‘95"}..“1' , “Fifi
I‘v'fljg} l .1}

6/‘3/ 98"

l”

ACKTOWLEDGEIENT

The writer is indebted to the representatives of
several x-ray corporations for their suggestions and
descriptive material that were helpful in preparing
this thesis. The material submitted by Hr. J.
Fredrikson of Picker X-Ray Corporation was eSpecially
helpful.

My Special gratitude goes to Dr. R. B. Bowersox
whose classes initiated the subject matter, and to
Dr. J. A. Strelzoff who has given helpful suggestions

and guided this thesis to completion.

IfTsoDUcoon

 

This thesis shall attempt to describe the methods of
analysis of fabrication deformities in metals. Both the
theoretical and practical descriptions will be given, and
wherever possible sketches which show analyses of such
deformities will be included.

Discovery of diffraction and interference effects
associated with the passage of x-rays through matter very
soon led to the recognition that studies of these effects
are useful in determining the structure of matter. Work
on the diffraction of x-rays by crystals was initiated in
1912 with the discovery made by von Laue and his associates.
The result of their eXperiments will be dealt with later
in the section on methods of analysis. '

X-ray analysis provides a new tool for solving indust-
rial problems. It found its earliest application in the
study of crystalline structure, the pattern of the atomic
arrangement in the perfect crystal. The results of these
analyses have had profound influence on fundamental concepts
of the nature of chemical combination. Such work ultimately
influences technical application because it clarifies ideas
that had previously been in question.

The progress of an x-ray analysis is far from being a
direct method. Instead, the results are a series of clues
which point to some possibilities and exclude others until
finally enough evidence is accumulated to make one confident
that he has arrived at the correct solution. Instead of

logically deducing a solution, intelligent guesses have to
-1-

be made and tested against t-e observations. The sane is
true for x-ray analyses of all types. 'The clues afforded by
the more or less diffuse Spots, arcs, or lines on an x-ray
photograph of some nysterious :aterial must be combined
with a wealth of other knowledge if they are to be followed
up. Much of the fascination of X-ray analysis is due to its
taking one into so many other fielis of science. The X-ray
eXpert must not only understand the optical principles on
which his science is founded; he nust at the same tine be
a chemist, a biochemist, or a metallurgist. The Optical
principles can be logically deduced, but iaagination,
comnon-sense, and a wide general knowledge lead him to
make his intelligent guesses.

Each crystalline solid gives a characteristic diffrac-
tion pattern and can be recognized just as an elegant can
be recognized by spectrun analysis. Extrenely small samples
measured in fractions of a milligram are sufficient, and
he constituents are deternined without destruction of the
specimen. Applications are found in the structure of alloys,
identification of intermediate products during processes,
determination of crystal size and orientation, and submicro-
sc0pic changes within iniividual crystals such as occur in
age-hardening. Such structures profoundly influence physical

pronerties and hence are of great interest and importance.

THETRY 2E DIFFRACTION PRI“CIDLES

The diffraction principles are, in reality, a
combination of two theories; the theory of crystal
structure, and the theory of x-ray diffraction from such
crystal structure. A fundamental understanding of these
theories is necessary to thoroughly understand the

working principles of x-ray diffraction analysis.
THEE: QB; CRYSTAL STR’JCTETRE

Previous to the discovery of x-rays in 1897, invest-
igations had shown that all crystalline bodies could be
considered to be built up of_molecules placed at the points
of a Space-lattice, such as that shown; the smallest com-
ponent unit of this Space-lattice having a regularity of
structure being known as the unit cell. Different kinds

of crystals have different types of Space-lattice.

 

 

 

1
[l
//

 

 

 

 

2' [IV fl

M ./V

o t I V
X

Fig. l. The crystal Space-lattice.

Since, in effect, the different types of Space-lattices
are deteriined by the differences between the alial lengths
and the angles between the axes, it is necessary to know the

lengths of the axes of the unit cell upon which the Space-

fl

-3-’

lattice is founded and the angles between these axes. Thus,
in the Space-lattice shown (iig. 1.), the unit cell has

the axes, K, Y, Z, and the oricin being at O. The angles
between these axes are d,p, U, reapectively. The possible
number of combinations of axes and angles upon which a
Space-lattice can be built is limited, and although many
thousands of crystals are known, they can be classified

into only 14 types of space-lattices having these combin-
ations of axes and angles, these Space-lattices being based
upon 7 different systems of crystal symmetry.

Although crystals of all these Space-lattices are net
with, by far the greatest majority of them have structures
of the higher forms of synmetry, namely the cubic, tetragonal,
and hexagonal. Among these three, the substances with which
the metal industry most often deals, fall into the cubic and
tetragonal classifications and it is these two which will be
described more fully.

There are three forms of the cubic lattice, the simple
cubic, the body centered cubic, and the face centered cubic.
They derive their names from the location of the atoms in
the lattice. These three are shown in Fig. 2a, b, and c.
The body centered cubic has an atop at each corner and one
at the center of the cell, and the face centered cubic has
an atom at each corner and one in the Center of each of the
six faces. Because some of these atons are shared by
neighboring unit cells, the number of atoms per unit cell

is one, two, and four resnectively.

-4-

 

/ X
/ X
/
[

 

(a) Simple cubic

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/ /
f 7

(b) B. C. cubic

 

Fig. 2. Arrangement of atoms in cubic lattices.

‘v

.7“ /
/ ./

(a) Simple tetragonal (b) B. C. tetragonal

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 3. Arrangenent of atoms in tetraqonal lattices.

-1:-

./

-he tetragonal Space-lattice has two forns, the sihple
and the body centered lattice. The differences between
these and the corresnonding cubic lattices in that one of
the three axes is longer than the other two. See Fig. 3.
If this axial length is designated as "c" and the length of
the edge of the unit cell as "a", then the ratio 3 is
termed the axial ratio.

In Fig. 4, it can be seen that on the planes marhed
ABC and ADEF passing through the unit cell, there lie
certain atozs. These planes also bass through all the
other unit cells making up the Space-lattice of the crystal
and on them lie he correspondins_atons of each cell. The

number of such atonic planes that can be passed through

the Space-lattice in different directions is very greet.

E

 

 

 

 

 

 

 

Fig. 4. Atomic Planes

To distinruish the different sets of planes fron one
another, they are disicnated by the reciprocal of the inter-

cepts nade by each plane of each set on the axes of its
-5-

resoective unit cell. Thus, in Fig. 4, the plane ABC cuts

off a unit intercent on each of three axes and the

recinrocals of these are l, l, l. Similarily, the recinrocals
of the intercebts made by the plane ADEF are l, O, 0, since
the intercepts are 1,60,00. The bigger the intercept, the
smaller the index, and vice versa.

These reciorocals are termed Killer indices and are
enclosed in round brackets, thus (lll); (lOO).The general
form is written (hkl), h being the recinrocal of the X axis
intercent; h, the reciprocal of the Y axis intercept; and
l, the reciorocal of the Z axis intercept. The miller
indices are always the least whole numbers, never fractions.
If any of the intercents are negative, the negative sign

is shown above the indice as, (2ll).

 

THEOR QB; X-RAY DIFFRACTIoN 1:; g CRYSTAL

The sinnlest form of x-ray diffraction is that
arising from the imningenent of x-rays uoon a ruled
grating. The theory of this diffraction is the same as
von Laue oronosed for the diffraction of x-rays from a

single atomic plane. Fig. 5 is an examole of such a

 

diffraction. ,
”1 A/
C
, D ’V
M, I, ‘
I \
_. g I 62- 9' 3‘ .__
A d 8

F17. 5. X-ray diffraction from single atomic plane.

-7...

From this diagram, it nay be seen that if the two
diffracted beans are to reinforce each other at N'N, the
difference in the length of path of the two beams must be
a whole number of wavelengths of the impingina x-ray beam.
In other words, CB - Ad = nA ; where "n” is designated as
the order of reflection; "A" is the wave length in 0:11.
of the x-ray bean. From the figure, CB 3 d cosie,;

AD 3 d cos 65. Puttina these identities into the above
equation, von Laue's equation is established.
nA '-' d(cos9, - cos 92)

For the crystal von Laue really used three similiar
equations; each dealing with a directional plane of the
crystal.

W. H. and W. L. Bragg were the foremost physicists who
turned their attention to x-ray diffraction after von Laue
had published his discoveries. They soon prOposed a sinpler
method of analysis that made the three-dimensional geonetry
involved easier to visualize. Instead of dealing with just
the surface layer of atoms, or a single layer of atoms as
von Laue did in his analysis, the Braggs based their analysis
upon a number of successive parallel planes as is shown by
Fig. 6.

This nethod is simplified by the fact that 9, must
equal 6% in order that the scattered beans reinforce each
other for all wavelengths. Then again set the difference in
path length equal to a whole nunber of wavelengths. The

difference in path length is BC + CD. BC '-' d sin 6,,

-3-

 

Fig. 6. X-ray diffraction frog parallel atomic planes.

CD = d sine“ BC +CD = d( sin6,+sin62). But 9.= 52 ,
therefore, Bragg's law is established.
n)\ 3 2d sin

This expression is the fundamental equation of x-ray tech-
nique. The equation cannot be satisfied if n is greater
than 2d and though several planes can reflect the beam in
several orders, for a given wavelength and a certain lattice,
the number of possible reflections is limited.

Fig. 7 shows the action of numerous atonic planes of
a crystal upon the impinging x-ray beam. It is the basis

for later discussion of x-ray diffraction analysis methods.

 

 

 

 

 

Maze)
0 O O O
O O a o
I
M —-b: k 0 (’30)
C C O 6:
N —):
O O
+
O O 6: O
4 o o o
O I! I. O I. a
Fig. 7. Reflected x-ray beams from numerous

atomic planes in a crystal.

Impinging x-ray beam - polychromatic
Reflected x-ray bean - monochromatic

-19-

x-aaz DIFFRACTICW 2373o33

A logical division of diffraction methods is by the
three different ways in which the diffraction patterns
may be photographed. Some authors have separated the
methods into the work of various exoerimentors, but under
each of these divisions come the three basic methods of
photography; direct transmission, reflection, and powder
methods. It is this division that will be followed in
this thesis.

No matter which method of diffraction is used, each
crystal has a certain diffraction pattern and that crystal
may be identified and analysed to ascertain its nature,
whether it is perfectly formed or deforned in some manner.
Thus, it may be seen that the various methods for x-ray
diffraction lead to a study of crystal size, stress and

strain, and deformation.

U)
i)

DIRTCT 'w.—“<.A.1~I.sf:ssroT jawsoo -F x-awr Dirsaaswioy

 

 

This method of x-ray diffraction is most conionly
referred to as the Laue method for it follows the manner
in which his investigations were carried out. This is
especially true for the stationery crystal method.
Although this is the oldest method of crystal analysis by
x-rays, it is still used today by some of the foremost-
crystal analysts. It differs from other methods in that

continuous radiation, or polychromatic x-ray beam is used.

-11-

Fin. 8 illustrates a simple tyre of "

Laue camera".
The beam of x-rays, usually from a tunssten target, passes
through a slit system onto a fixed specimen wh ch consists
of a shall single crystal. From the x-ray been, the
different sets of atomic planes pick out the appropriate
wavelength accordins to Braig's law and give rise to
reflection spots on the nhotoarsohic film. The two main
features of the Laue diagram are, (l) the reflection Spots
lie on ellipses, the Spots on each ellipse being due to
reflection of the x-ray beam by the planes belonging to
one particular zone, one end of the major axis of the
ellipse being at the central spot of the filo, and (2)

all the spots produced by reflection from one wavelength

lie on a circle with its center at the central spot.

   
  

 

 

 

 

 

 

 

 

 

 

 

 

Pm Hour Ca vs TA L
X----- :3— ---
7:
Fin. 8. Simple Laue camera.

As an example of just what happens to create a Laue
photograph, Fig. 9 is included in the hOpe that the process
may be made more clear. The x-ray action is like that

shown in Fig. 7.

o," ‘-’\
.- 4 - l

{W
“LI-7

x. E".

1\
,LJ.

no

Gil

l

we Speci;

l

t?

113.,
e slit

I) <3:

_

ameter of

ii

1
I
v
.—

hoi

U .L

'I‘
.
ii

of tie

4

thictnes;

«14k

to the

cordinf

-v

"A
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(Tl

if
Va

1111 l o

to

ant,

,rt

"AW “\

lygi

‘ T

...
\
‘1

el

A
as
.I_
i,
\./

"tr'
4 I‘ K
4;- .

Q
\.,

> I”.
3..\.

-:- '2 c1; 31m

‘-.l

structure

\/

VVE-

.if‘

q -
l

‘f‘?“.'*‘

‘. I...)
.. \t ’

Ivy

\
L1

7' 'f‘ L.

U i531

 

Unless requirod for some snecicl purpose, Laue
photographs are tahen with the x-ray beam traveling in
simple crystallosraphic directions. In such circum-
stances the photograph will be syunetricsl. Several
methods can be used to obtain this condition. They are:

(1) With well-developed crystals, the positions of
the axes can be determined by measuring the angles between
the crystal faces with a goniometer.

(2) Photographs are taken with the crystal at
different settings in order to obtain those with the
hishest symmetry.

(3) With good rdlecting crystals, the Specimen can
be adjusted by obs rving the Laue pattern on a fluorescent
screen.

There are various other nethods which are correlated
with the Laue x-ray diffraction. One of these is the
crystal rotation method in which the crystal is rotated at
a constant angular velocity. This creates a different
diffraction pattern that, for some study, is more adaptable
than the stationary method. Three such photographs around
the principal axes make it possible to obtain almost
complete crystal information. Usually the film is placed
differently also. It consists of a cylindrical film,
enclosing the specimen as a center. Fig. 10 is a sketch
of such a Laue camera which allows for sample rotation. For
this method a monochromatic beam of x-rays is used. Crystal

analysis by the rotation method was not used extensively

-14-

until 1922, but since ha~ been used for the analysis of

more di ferent substances than any other method.

SLITS 3 FILTER FILM

I I SAMPLE
x---- - -—-->———

 

 

 

 

 

Fig. 10. Crystal Rotation Camera.

Still another popular variation of the Laue method
of x~ray diffraction analysis is the use of a Speciien
consistinc of more than a single crystal in the form of
a powder. This is more practical for a large number of
substances since the sincle crystals are so minute. This
gives a diffraction oattern that is completely different
from that of the single crystal. As the nuiber of grains

see the soots become more nuierous and smaller, all

incr

(D

9

traces of the zone ellipses for one grain beinq obscured.

At the same time the intensity decreases, and longer tides
of exposure are required. The condition of minute size is
finally reached where on a Laue diacrao there appears an
almost continuous darkened ring. Further discussion of such
continuous rings will be found in the section on the powder

method of x-ray diffraction.
-15-

REFLEC’ICH gzcooos or X-RAY DIFFRACTIon

 

 

Reflection from the surface of samples too thick

U

for penetration by X-rays can be used, as illustrat d in

Fic..ll.

 

 

 

 

 

 

Fig. ll. Diacraa of surface reflection method.

In industrial practice it is frequently desired to
know the ultimate crystalline condition of a finished
product or of a large specimen that cannot be sampled.
For exaanle, in very large steel structures, such an
examination of a finished unit before installation would
be invaluable.

This is the method that is comxonly used in a study

tal

(1)

of surface stress and strain defornities in the m
under consideration. The reasons for its use will be
-described with the methods for stress analysis.
Photosranhs of the relections day be taken at alaost
any position with respect to the scmple, but the two most
common positions are at the pin hole as shown in Fig. ll,
or at a position where the reflections arise from grazing

incidence. The choice of positions depends entirely upon

the study that is desired.
-16-

. ...... a. o. g . O,- 96

 

Fig. 12. Diffraction pattern; Grazing incident method.

See Fig. 160 for back-reflection method.

 

 

 

 

 

 

 

l
I
L g'l: j
F ‘ \ ‘ ‘ : I, 1' 7 I
I
\ \ ‘ ‘ I l / ,’ I
\ \ \ \ ' I I
\ \ ‘ ‘ I I I I
x \ \I u ’ I I
‘ \ ‘\ I l I ’ ’ '
\\ \\ ' II, //’ D
\\ \"’l ’I \
“\"I ’/
\\\\|,’/I e
\\\\”’,/l
5 Mill/I

 

 

 

 

 

 

 

 

 

Fig. 14. Method of accurate determination of

film to Specimen distance.

-17-

Fig. 13 is alnost self exolanatory. “he primary

source of x-rays is located at X. The specimen is desianated
as S, and the filo as F. The speciien to film distance is

D, and 9 is the usual Brace, anctle of reflection. This
figure shows that the distance D must be obtained very
accurately in order that the correct values of reflection
are ascribed to the various rings on tie diffraction pattern.
There are two comaon methods for accurate measureient
of the flld to specimen distcnce. One common method is the
use of a very thin film of either sold or silver on the
surface of the specimen. This produces the diffraction
pattern of the gold or silver along with that of the
specimen and knowing the values for the standard, the
correct values of the unknown may be deternined. The
second method is one of mechanical measurement. This is
shown in Fig. 14. The pointer E is held to the slit system

by the lock-nut sleeve L and the whole unit is moved until

M just presses the feeler N to the specimen. The thickness
of N is of the order 0.0015 in. When the adjustment has
been made, the pin-hole P is exchanneflkor I and L before

the photograph is made.

-18-

'2 .

,JJ

P3WDER LEFTODS TF X-RAY DIFFRACTITH

 

 

Such diffraction methods are con only termed the
"Hull-Debye-Scherrer powder methods for it was these men
who did the initial work in estahlishing this method of
practical x-ray diffraction analysis. These men worked
independently but their work was so alike that all three
are referred to in such work. This new method, first
used successfully in about 1916, made it possible to
deduce the crystal structure of metals and other solids
of commercial importance.

To the person interested in the practical applications
of X-rays, the powder method is far more than a method of
crystal analysis, like the Brand method, the Laue method,
or the rotation method. Since the sample may be in its
ordinary natural polycrystalline condition, the x-ray
pattern is able to reveal information regarding three
characteristics of the solid that have as much practical
importance as the structure of the individual crystals
that compose it. These three mportant characteristics
are (1) the average size of the crystals, commonly callai
the "grain size"; (2) the absence or presence of any
tendency for the crystals to orient themselves in a
preferred manner; (3) actual bending, twisting, or
similar mechanical distortion of the crystals, commonly
called "grain distortion" or strain.

Figs. 15a, b, and c show various ways in which

powder-sample photographs may be taken.
-19-

 

 

 

 

 

Fig. 15a. Flat cassette powder camera.

 

pinhole system

 

x-ray beam

 

 

 

 

L, -__

Fig. 15b. Cylindrical powder camera.

p.

film
\9\\
u‘.\‘
\‘ a“ .
‘.\ N... specimen
‘ 3M '- ¢._ ~
."h, ________ \d _” ”Hm
---- ) ‘----..- ...---"" \ 1'
xoray bail: ....... ’ ----- ""' ‘ ‘ ----)-_-_._"/“.\.
‘ OOOO ,--‘- ” t
a.

 

 

‘ schemaflc diagram of back-reflecfion camera

 

 

_.# afiri‘ ._,__.__ '7

Fig. 15c. Back-reflection powder camera.

-20-

The preparation and mountinq of a powder sample is
an exacting task. metals may be reduced to a fine powder
by using light pressure on a fine, clean file. The powder
or filinas should be sieved throush a QOO-mesh screen or
cloth. Care must be used in obtaining these filings so
that no unwanted worhipg of the metal takes place to give
incorrect results in the following analysis. Having
obtained the powder, one may coat it with Canada balsam to
produce a thick paste, which is coated onto a human hair;
this is then mounted taut in a line perpendicular to the
primary beam. For this type of sample, a camera having a
vertical axis is preferable, so that one may suspend they
hair and hang a small weigh on it to keep it taut and
vertical. If the axis of the camera is not vertical, a
class tube or rod drawn down to a diameter of about 0.01 in.
may be substituted for the hair. Still another manner of
preparing the Specimen is especially useful for substances
that are hygroscopic. For this detood the powder is loaded
into a thin-walled class tube having an inside diameter of
% mm. If a comparison test is to be taken, one half of the
tube may be filled with a known substance and the remaining
half with the unknown. The tube is then rotated while the
analysis is beins carried out and from the resultant patterns,
the-properties of the unknown may be discerned.

The powder m .hod of x-ray diffraction analysis is
most useful when the analysis is a study of grain size. In

cases where the study is one of stress or distortion

analysis, this method falters for it is practically
impossible to produce a powder specimen without adding
more stress or distortion to the material, thus giving
rise to erroroneous results. For such studies, the two
previous methods of analysis are more satisfactory.
Figs. 16a, b, and c are, respectively, the type of
photograph as obtained with the three types of powder
diffraction cameras as shown in Figs. 12a, b, and 0.
Each circle is due to the diffraction of the x-ray beam

by one certain series of atomic planes.

U o ‘
fx‘ . o

a
F

lflcuP-v«

'4' 1 ti? To
..z'.:."'.'1
o"

1'3?

E

o
- in

0' '9
I'.‘
0"...
10'

 

Fig. 16a. Diffraction rings Fig. 16c. Diffraction rings

of transmission photo- of back reflection photo-
graph. graph.

   

Fig. 16b. Diffraction rinqs of cylindrical photograph.

-22-

X-RAY STUDY OF GRiIY SIZT AND ”REFERRED ORIENTETIDN

 

The objective of this thesis, diffraction analysis
of fabrication deformities, splits itself into two
natural groupings. They are; a study of grain size and
preferred orientation, and a study of stress and strain.
Since these often take different methods of x-ray
diffraction for analysis and the techniques developed at
different times, they will be dealt with separately.

The matter of x-ray diffraction studies of grain size
has little significance until the size of the crystal falls
into the region of 10-4 cm. All arain or crystcl sizes
larger than this figure are measured more conveniently and
more accurately with standard microsconic methods of etching
and magnifying. However, at this point the x-ray method ,
becomes an important factor in such measurements for as the
crystal size becomes smaller, the diffraction pattern rings
become procressively broadened, especially at 10'5 cm. or
smaller. A measurement of this broadeninq is a moderate
indication of the grain size. (See Fig. 17)

In the x-ray examination of these particles, the
powder method is usually adOpted. As well as being
dependent upon the article size, the width of the
diffraction lines is also influenced by the following
factors.

(1) The diameter of the camera and of the Specimen.

(2

“/

The size and shape of the slit system of the
camera.

-23-

 

 

’ \
/, 1
\ lb
.1
\\ " /

 

 

Very large grain size

 

 

I " ‘ \
a’ \‘\\
’ I
I I \ \
I i \ \
I I - \ \
I I ’ -.\ \
o ’ I - ‘\
I o, ' I'. .. \\ \ \
l \
I" I ’ ‘ \ \ “
I. . § ‘ ‘
0' . i 0| I.
° . " I'
| ‘ o .5 .
“ .\ 0.! "
\s .\‘ o I 'l
\ \ ‘ °°°° I. I I
Q
\ o
‘ ...... '0' l
\ \ /
‘ \ I ’
I
\ “~~ ’1’ I
‘ ~.-’ ’

 

 

Grain size 0
of 10’

Fig. 17.

the order
cm.

of a metal.

-24-

 

 

<L' - :r “
4’, '\
’1 i‘ \
I] ./4' \§ \
l I \‘ 1‘
it c ‘D 3,
\ \\. l I)
\ \3~.. 4' I
\\ - d' “I
./
\\ ~ ’ /
all

 

Grain size approximately
002 "" 005 mm.

 

 

 

 

 

Grain sifi
of 10’

in th
Etc 10‘

-§

range
cm.

Diffraction patterns of various grain sizes

(3) The absorbsion of x-rsys by the sneci en.

(4) The size of the focal snot'of the x-ray tube.

In view of the variation in these factors from one
camera.to another, it might appear to be extreme ly
difficult to deter ine the particle size. However, some
Isuccess has been achieved in this direction, although in
sole cases, the values obtained are to be re arded sore as
relative than absolute.

For crystals of cubic shape belonaine to the cubic
systei, Scherrer, dra~g, and SeljaFew éive tte following
exnression connecting the line hr adth and the particle

size:

 

K.A
fl = a COS

where 3 is the breadth in radians of the intensity peak

my.

measured at the point where the intensity falls to half its

maximum value (see Fig. 18), Asthe wavelength of the

x-radiation, _X_ : 6 , the Bragg reflection angle of the
2

line that is being measured, and a i8 the cube length of

the crystal.

 

 

 

 

Fig. 18. The "half-value
maximum.

Th: values of V ranse between 0.? and 1.) so that for
most problecs the value of unity is used in the previous
equation. The value of P is easily calculated when a

e the subtended

0']

CS

11']

cylindrical camera is used, for in thi
angle of no is equal to _EE_ , where r_is the radius of

r
the cylinder. The half-valne points of intensity are f und
by use of an ionization chamber or by densitouetry of the
photographed pattern.

In using the previous foriula to calculate frain size
from a pattern, there is some doubt whether fi should be
called "breadth" or "broar‘enins", for 6 refers only to
the extra breadth of the lines due to the grain size being
less than 2 X 11)“!+ am. When the grain size is of the order
of 13'5 or 10-6 mm., this point is not important, but if
the size is of the order of 10-4 mn., So that the line
broadenins is only just detectable, allowance must be made
for the breadth of the line due to causes other than shall
partical size. This can be accoiplished'eXperimentally by
photographing on the same film the pattern of a substance
having a grain size known to be of the order of 10"3 mm.
For accurate work, a simple subtraction of the brehdth of
one of these reference lines from the observed breadth of
one of the lines of the unknown is not persissible. For

2 2 ‘
a fair estimate, one may use the relation @ = @m- 60
where finis the measured breadth and $0 is the breadth of
the reference line.

The accuracy to be expected in the measurement of the

-96-

size by the abov: exnrescion is in the order of 2) oer cent.
As well as oar icle size, strfiin that may be “recent
in a metal will nrofuce brosdenins of the diffraction lines.
For this reason, the strain must be renovtd from the
snecinen either by annealino or other deans. Any of the
above methods, on the other hand, can aooarently be apolied
to samo‘es in which some decree of nreferred orientation
is oresent.
Another nanner in which the line broadenins day be
attributed to grain size instead of deformation or strain

he effects of Aand 9 upon

rt-

is acconnlished by studyins
this line broadening. Since a broadening due to grain

size is oronortional to A and sec 9 , and, due to strain

is rrooortional to only tan 9 , the true source of the
broadening can be deternined.

The aggreement between the aboarent particle size as
given by the different lines is as good as can be exnected,
considering that generally the narticles will not all be
of the same size. It has been suqsested that the discreo-
ancy between the oarticle size as given by the different
diffraction lines is tied uo with the non-uniform shape of
the narticles. Because of the effect of this factor on the
shaoe of the intensity curves, th: ontical dimensions nust
be variable. For exannle, if the narticle size is large,
x-rays of long wavelength should be enoloyed and the ratio
of the soecinen dlianeter to that of the camera should

be small.

In processes involvips the plastic defornation of a
metal, such as drawing a rod down to a wire, rolling a

" a sheet to form

billet down to a sheet, or "deep drawing
a cup, the petal crystals cleave and slide or slip along
certain crystallographic planes parallel to certain
crystallographic axes in those planes. Such planes of

slip are usually anong the most densely pOpulated sets,
that is, sets of planes havins more 6‘338 per square
angstrom unit than other crystallographic planes.

These processes obviously will reduce the grain size
by fragmentation; in addition, the special direction of
the fragmentftion and slip results in the fragnents
acquiring preferred orientations with respect to the
drawing or rolling axis. In a few instances such a
preferred orientation is desirable or beneficial. For
example, it has been found that the electrical properties
of silicon sheet steel for transformer laiinations are
improved by allowins it to retain its preferential
orientation. Such steel has a considerably higher magnetic
permeability in the direction of roll than in other
directions. Also, it has been found that the resistance
of niche steel to corrosion improves when the orientation
is preferential. In general, however, preferential
orientation is objectionable because it weakens a hetal
and reduces its ability to Withstand further deformation.
The forming operations that cause preferential orientation

are usually performed in several stages. Each foruing step

-28..

increases the preferential orientation, thus reducing the
capacity of the oetal to undergo additional forming steps.
Therefore it is often necessary to anneal the metal between
some of the stages to relieve the preferential orientation
by pernitting the grains to "recrystallize" before proceeding
to the next stage. In most cases, annealing causes a
recrystallization in which new crystals form of a size
comparable with the size of those originally present, and
these new crystals should have a nearly random orientation.
The most usual effect of preferred orientation on the
diffraction pattern is the lumping of spots in symmetrically
located positions instead of the ordinary distributation

about the ring. Fig. 19a and b show such an effect.

‘.‘o,' 3’"? .' ”I n; s _
1-.°’.’:~9':.' '6 \"'%c*‘. 2;! 0‘
..." "a .M s ’ .3
J'Afi'gf , c‘ f ‘0'. "a :3 ‘
a" 9': ‘ fl ' . "xvii. ".2 .-
." .3" a." ..‘m'u‘ "‘u “‘32. ‘4 1°;
:5 a .9 3‘. ' ','o".'.'c:o~ 3. . :5: 3. '1‘
:5 .3" .' .3" :‘r-‘r-fls. "2. E1"?
\ ’- .- ,." " .1. " 2 a. '3
a} a : '3' 13 3 1 .t3
-, .2 t? .. I: ;.' t ’ t. 12":
'.' '1 i ' '5. ‘. . .’ " 3: e :; .3
'J .' ’I .- ‘0 3: ~ 3 ' ' ...:
... '1': "a a ~t 3 3.. - ..2' 'f o.‘ I; ’5
g :3 a. s, 2-"; - ---",,.-" ,1 .-, "
.3. u. x. - ya'r‘ ... a; " -‘
...." i‘ 'J . 1- |. ' “3 :I" r:
_, ’; ‘0. " .-'.:'.--' ”5' I? ’1’
. 0’, .1" .1 .
‘3'.» :21. _ ‘4 " u. :97»?! ’ ,a' f t
" u ..“h "I" .:
49,” ’3 :., ’- f”... I "
0.... ' s s ,5" - ' -. 3
9.1.}. s h. ‘3' - p‘"
Fig. 19a. Transmission Fig. 19b. Pattern of same
pattern of aluminum wire after stretching
wire. beyond elastic limit.

The broadenine of the rings in Fig. 19b point to the
fact that the grain size has been greatly reduced by this
plastic deformation, and the "lumpiness" of the rings
indicates that the crystals have acquired a preferential
orientation as.a result of the stretching.

A method of analyzing such a preferential orientation
diffraction pattern may be accomplished with use of Fig. 20.
This figure is similar to that showing how a transmission
photograph is made. The difference is that a preferential
orientation of crystals is considered instead of the previous

random orientation. VJ

 

 

 

F I

 

Fig. 20. Analysis of lumped pattern due to preferred
orientation.

In Fig. 20, AS represents the primary x-ray beam
striking the wire WS perpendicularly at S, the undiffracted
beam then strikine the film F at O. The diffracted ray
SP strikes the film at a point P on the circumference of
one of the rings R in the resulting pattern like Fig. 19b.
Suppose, now, that P is one of the abnormally intense
lumps on the ring R. CO is a line drawn on the film
parallel to the wire W5. From the analogy with the case

of a single crystal rotation pattern, such Spots P will

-30-

occur in groups of four, symmetrically located on Opposite
sides of CO and on Opposite sides of a line on the film
through 0 perpendicular to CO. This may be seen, also, by
imasining the reflecting plane H to rotate about W8,
maintaining its fixed inclination 9 to it (NS is the normal
to plane H). If 8 is the angle between OP and OC and 69

is the usual Bragg angle for the set of planes H from which

ray SP is "reflected",

Cos‘e
Cosea

Cosés 3
The angle 8 is an indication of the shift associated with
I the preferential orientation of the crystals when deformed.
Fig. 21 shows the effect of preferred orientation upon

deep-drawn brass.

 

i\ /

 

 

 

 

\ 9/ \ /

 

Correctly treated brass Brass still showing a
shows no preferred orient- tendency for preferred

ation. orientation.

Fig. 21. The effect of preferential orientation in
deep-drawn brass cups. '

i—QAY STUDY 0‘ erases AVD STRAIN

. .A

Earlier it has been stated that a broadening of
diffraction pattern rings may be attributed to grain
distortion as well as to a reduction of grain size.

This distortion is associated with strains, designated by
the letter EC, which may be introduced by such processes

as cold working. Strains of this type have been called
"nicrostrains" by x-ray diffraction workers. Iicrostrains
may be defined as strains that vary widely and erratically
in magnitude and direction between neighboring graios, or
within the individual grains, in a crystalline solid. They
occur when the elastic limit or yield point is exceeded, as
in cold workinq. On the other hand, the strains resulting
from elastic distortion of a solid, such as a spring, when
the elastic limit is not exceeded, may be called "macrostrains."
Such distortion effects he crystals in such a way that the
strains introduced vary from crystal to crystal and from
point to point within each crystal in a systematic manner.

The fact that x-ray diffraction is capable of measuring
strains in the surface layers of any solid crystalline object,
having such a graip'size that it will yield sharp rings or
lines (shoot 2 x 10"4 to 10'2 mm. grain size), was pointed
out by G. Sachs and J. Weerts in 1930.

‘ In some respects, x-ray diffraction is inferior to
other methods of analysis; in others, superior. Its most

important advantases, perhaps, are that (1) it can measure

-32-

the strain without any necessity for codparips the strained
specimen with a supposedly unstreined speciien and (9) it
can measure the strain at a spot 1 am. in diameter or less
without any interpolation or evtrapolation obtained from
measurements outside thot soot. Its disadvantaqes are that
it is capable of measuripv the macrostrain only when micro-
strains are not unduly seVere and over the limited wrain
size range qiv;n above. In ferrous specimens, for exaiple,
this limits one to material having a hardness below

40 Rockwell C. The method is slow and reqwires an experi-
enced onerotor and rather expensive equipment. It is
useless for measurina rapidly changinw strains, as in the
parts of an enaine while it is Operatinq.

The strains introduced in a bar when it is stretched,
compressed,'bent, or twisted without exceeding the elastic
limit are macrostrains, whereas quenching and cold work
introduce both macrostrains and microstrains. A process
like shot peening also introduces both macrostrains
associated with the compressive stress set up in the surface
layer, alanced by forces of tension underneath, and micro-
strains in the aurface layer, which is stressed beyonJ the
elastic linit by the peeping. As a result of plastic
distortion, the grains are broken, compressed, stretched,
bent, and twisted sliwhtly, and the frawments slip along
the cleavaee planes of the crystaL

Both macrostrains and dicrostrains cause variation in

the interplaner d spacincs in t he crystals composing the
solid. The wrain fracture resulting from plactic deform-
ation soon reduces the rrain size below 5 x l)"3 hm., so
that a continuous rind pattern is obtained. The variation
in d snacinc associate. with the nicrostrain then causes a
broadeninv due to ultrafine drain, as mentioned previously,
and it will be indipendent of the direction of the x-ray
bean in the saiple. The broadening follows directly from
the ?raeq equation; slicht variations of d'correspond to
sli-crht variations in 9 for a given /\ in a powder sample
where all possible crystal orientations exist.

When a force of 23,930 pounds is applied to a steel
bar 1 in. square and 1 ft. long, tendina to stretch it,
the bar becomes more than 1 ft. lone and less than 1 in.
square. This elongates the grains in a direction parallel
to the bar and causss then to shrink in directions per-
pendicular to it. This elongation in one direction and
shrinkave in another appears in the x—ray pattern as a
slight shift in the lines or rings correSpondinw to the
increase or decrease in the various crystal lattice Spacings
<1 and depending upon the direction of the primary and
diffracted x-ray beams in the sasple. This dependence of
the line shift on tho eam direction readily distinguishes
such line shifts due to strain from the otherwise sidilar
line shifts resulting from thermal eXpansion ( which increases

(1 uniformly in all directions), or from the shifts caused

-3)-

by change in conposition. Composition chances also produce
a creater anount of line shift.

To sunnarize these theories, then, ordinary macro-
strains manifest themselves in the x-ray pattern as a line
shift, whereas iicrostrains manifest themselves as a line
broadeninc which iay be difficult to distinguish from the
similar broadenins due to ultrafine grain. In spite ot this
possible anbiruity in some cases, x-ray diffraction yields
more information on microstrain than any other known method.
It is obvious that severe microstrains will subtract from
the ability of a structural med er to Withstand the macro-
stresses for which it was desisned. When a large casting
is heat-treated to "relieve stress", the thermal stresses
due to unequal rates of coolins in thick and thin portions
(which are sacrostresses) are relieved, but the relief of
the microstresses in such an operation may be equally
important.

doth the slinht line shift due to macrostrain and the
sliqht line broadening due to nicrostrains are much easier
to detect and neasure in a back-reflection pattern than in
a transmission pattern. In the first instance, the reason

may be seen from the relation

Ci€9==-€g!ten.€9 *

This shows that the sliwht shift d6 resultine from a strain
do! , . . . . _ , ,
73- varies as tan 6?, tne minus siwn indicatin~ merely tna

* See appendix for derivation.

d decreases for oositive strains (tensions), and increases
for negative strains (cognrsssions). Sincen" fiecoues larfe
as e annreaches 903, the line shift due to s-;:all chances in
d becomes erect—er, and hence easier to detect and measure,
when 9 Rnnroaches 9339. This occurs only in back-reflection
natterns.

“he reason why a slisht line broadening due to micro-
strains is easier to detect by back-reflection is also
nartly exnlainable from he above equation when 0-3-4- is
regarded as a continuous rancre of strain and dethe corre-
snondinq continous ranre. of 6 causing: the broadening.

Another reason annears noon differentiation Brage's equation

where d is regarded as a constant and A as a variable.

dA: chos QdQ

de to
an" 2‘3””

These equations show that a wavelength doublet will be
resolved much sore readily in the Brave reflection from any
friven set of planes with snacing d for large values of '
than for small ones because the ansular' senarat ion d9 for
any given wavelenrrth senaration CM and interolanar snacing
d varies as sec 9 . "flhen 6 beco-1es large enough so

that sec 6 equals 5 or 10 or more, as in a back-reflection
nattern, thende becomes a degree or two and the doublet
reflections are senarated by an angle larqer than the usual

line breadth, that is, they are resolved. 3bviously, if the

usual line Width is 33 in a doublet seoarated by 1°, the
line annears double; but as this line breadth increases to
l0 owinw to microstrainc or extremely fine grains, or both,
the * ublet nerves into a sinale line in the nattern.
Therefore doublet resolution in a back-reflection nattern
may be conveniently used as a quick'and easy index of the
rresence and oaenitude of nicrostrRins when the grain size
is known to be above 2 X lO’AL an. or as an index of srain
size below 9 X 10"4 nu. when licrostrains are absent.

Fig. 2? illustrates this noint.

 

Fig. 22. Back-reflection natterns of mild steel bar, taken
nernendicular to side. (1) and (3) before, (2) and (4)
after snot neeninz.

It has been seen that back-reflection is the best
technique for neasurins strain, and the choice of the
nrooer radiation now requires consideration. For back-
reflection, sine is nearly 1, so try t Grave's equation

becomes ”A = 2d anoro iiiately. In Finn 23 this .xeans

-37..

that ”A: .2 ’+ CD (exactly) : 2d or 2CF(annroYinately)

(

In accordents with usual nrectice in calculatins Brag?

\

reflections, fictitious olanes ner.it one to set n = l,
and on this basis it is seen that the selection of the
nrooer radiation involves a choice of A.slightly less than

gci

0

 

 

. Showinv w4y the wavelenoth should be slightly
as than 2d for back-reflection work.
For the sake of discussion, sunoose that iron, coooer,
and aluninum and their alloys are regarded as the host
innortant and the condonest materials in which one usually
tries to inef‘ sure stress. Table 1 lists the d values and
corresnondins intensities for the ADSt nroiinent reflections
from thes; net“ls, tosether with the indices of the
reflections. Table 2 lists the nean wavelennth of the-Kq

doublet for the common target elements for di1fraction wort.

J)

 

 

 

 

 

 

 

 

 

 

Aluninun, Iron,
face-cantered body-centered
cubic cubic
indices 0! 2d nercent I indices 0‘ 2d percent I
(111) 2.333 4.330 100 (110) 2.010 4.020 100
( 930) 2.020 «.140. 40 (213) 1 428 2.8: 15
(220) 1.430 2.860 30 (211) 1.166 .332 38
$311) 1.212 2.438 30 (22c) 1.010 2.020 10
.222) 1.16? 2.336 7 (310) 0.904 1.3‘3 8
(400) 1.0 L 2.322 2 (222) 0 825 1.650 3
(331 ao.921 1.856 4 (321) o 764 1.528 10
(423 0.905 ‘1.313 4
Conner,
face-centered
cubic
indices d 20!. percent I

 

(111) +2.0s0 4.160 100
(200) 1.810 3.620 53
(220) 1.277 2.554 33

 

 

 

(311) 1.089 2.178 33
(222) 1.043 2.086 2
(400) 0.905 1.810 3

 

 

Table 2
tarset atomic nean wavelength
number of K“ doublet , A3
Cr 24 2.290
Fe 26 1.932
Co 27 1.795
Ni 2% 1.655
Cu 29 1.540
Zn 30 1.435
ho 42 { 0.710

 

 

It is evident from these tables that the most pron-
inent reflections, like (111) for aluminum, have a value of
2d which would make A much too sreat for practical work.
Even iron K.(radiation (1.932 A.) is so soft that it is
absorbed to a serious degree by the air in a large camera.
Thus it is seen that, in general, back-reflection work
requires a soft radiation. The radiation chosen should,
however, be hard enough to eliminate the need for vacuum
cameras for general industrial application.' Iron Ka'is
about the softest radiation suitable for ordinary cameras;
in case of necessity, chromium Ka¢can be used in saall
precision cameras, although with this radiation it is
advisable to find some means other than black paper to
protect the film from the light.

Considering the 1.755 A0 cobalt K¢(it is seen that
this radiation is suitable for the (331) and (420) alum-
inum, the (400) cooper, and the (310) iron reflections.
Since this radiation is hard enoush to penetrate a thin
piece of paper and a few inches of air, it is now clear why
cobalt is the most widely used target material for strain 1
measurement by back-reflection. This radiation, however,
is so soft that it is easily absorbed by the metal under
investigation and so the reflected pattern is characteristic
of only the surface of he material, perhaps to a depth of
0.002 or 0.003 in. into the metal. Thus the back-reflection
method is limited to a study of a thin surface layer as

previously mentioned.

-40-

QQTLQLUSDN

From the previous discussions it may now be noticed
that x-ray diffraction methods play an important role in
the analysis of fabrication defornities in metals. These
analyses are not only of detrimental deformities but also
of structural changes that are beneficial. One may also
use such diffraction analysis to study the rate of change
of deformities in order that the most economical method of
fabrication is used to prepare a product that will be
satisfactory.

For an example of a fabrication process, let us take
the case of structual changes due to successive reductions
of a low-carbon steel by cold working. The following data.
was obtained during the process, to a final point of
97 percent reduction. The accompanying reproductions in
Fig. 24 show the change of diffraction pattern throughout

the progressive reduction.

 

 

fFig. pass gage, inches perCent pattern
reduction
0 0.1580 0
(orginal)

Fragmentation below 35/4
a 1 0.1475 7 and appearance of rings.

Appearance of four-point
b 14 0.0460 71 fiber pattern character-
istic of drawing.

Typical rolling pattern.
0 21 0.0165 90 . (81X point)

Perfected orientation.
d 30 0.005 97 (six point)

 

 

 

 

-41-

      

n . u n. u. n c ‘ a .. . v i ‘ 3....
p . . a 1. a. true. » .....05 s . . . ,
79 x». .w‘.‘ 0." . \

. $ t “ hi 1‘

3....

       
  

   

  

.... . 00

.t. . .
3.:

    

n...
v‘

 

. .. c
8.31.9210...

 

 

(d)

)

C

(

structure with steps in rolling of

Changes in

24.

..z

One pass, 7 percent

Fig.

(a)

14 passes, 71 percent reduction

low-carbon sheet steel.

30 passes,

(10)

21 passes, 93 percent reduction;

reduction;

(C)

(d)

97 percent reduction.

From a whole series of steel samples the following

average results were obtained:-

percent

Appearance of reduction
Continuous rings (fragmentation) --------------- 2!
Sharp rings ------------------------------------ 30
Six-point fiber pattern ------------------------ 54
Four-point fiber pattern ----------------------- Y6

Such values are greatly dependent upon the type of mills,
chemical composition, hickness, grain size, and orientation
in the original material. ’
The x~ray diffraction patterns of Fig. 24 were obtained
with the x-ray beam perpendicular to both the plane of the
surface of the metal and the rolling direction. If, however,
similar patterns were taken perpendicular to the rolling
direction, but parallel to the rolling plane the preferential
orientation of the grains would be noticeable after 15 to
30 percent reduction, depending again upon the above-
mentioned variables. The diffraction pattern continues to
be a six-pointed figure upon further reduction instead of
changing to a four-point at approximately 76 percent.
An interesting study is that of the effect of annealing
upon the grain structure of deformed or strained materials.
A variation in annealing temperatures can produce grains
that are recrystallized with either a preferred orientation
or a random orientation. Fig. 25 shows the change in grain
orientation obtained with two different annealing processes.
The material is cast steel.

-43-

4

,f

x

f y

,I»

 

(C)
st steel annealing.

)

b

Diffraction

ca
showino

udies of

at
Orininal struct.

a

Fig. 25.

nternal strain;

1

re,

1
4

(a)

DC
hi.
i o
n l
.l e
a e
3. t
e 8
r
e
e m
n. a
3 B
s
f
Om... O
n
.1 e
W P
Oo’u
wflet
SPC
uu
’tr
let
ans
er
Uta
nse
a 1
13
183
atn
.1th
093
Fr.”
eai1.
Mara
mte
08d
CdI
b C

-44-

 

(Cl).

 

(b)

Fig. 26. Effects of annealing an 80 percent reduced
sample ofolow-carbon steel at different temperatures.
(a) 1200 F.; (b) 1500 F.

-45-

Fig. 26 shows a similar effect upon a strained low-
carbon steel when annealed at different temperatures, the
same process being used for both samples.

Although comprehensive work in combining x-ray research
with fatigue tests has not yet been completed, progress has
been made, and more should be eXpected. The chief difficulty
has been in providing specimens sufficiently thin for x-ray
analysis. An example of such research is the study of
duraluminum airplane prOpellers. After detailed study of
all portions of the blade it was found that the surface near
the hub was the focus of all component stresses, and diffract-
ion patterns were made at different times. The results of
these studies are shown with diffraction patterns in Fig. 2{.
Through this study, improvements in prOpeller design, and
in the composition and properties of the alloy have been

made in the past few years.

 

 

 

6—: ./;’..

/ /
///”,f’////’ 1”, ////’ . c.4-

 

 

 

 

 

 

 

 

 

 

(a) (b) (0)

Fig. 2(. Patterns for aluminum-alloy airplane prepellers.
(a) Unused prOpeller, (b) after 900 flying hours,
(c) same prOpeller after 1,400 flying hours. Grain
groth and distortion with increasing use are indicated.

-46-

The three examples of x-ray diffraction studies were
chosen for they were representative of such studies as
reviewed in most published literature. More examples might
have been given but I felt that they would be extraneous.
However, it can be observed from these examples and the
text of the thesis that x-ray diffraction can and will play
an even more important role in the study of fabrication
processes than it does at the present time. Such studies
will assure a finished product that will be the finest that
can be manufactured and, at the same time, be produced most

economically.

-47-

A§3§NDLX

Characteristics and interpretation of x-ray diffraction

photographs.

 

Characteristic appear-
ance of photographs

Interpretation

 

 

Remarks

 

Sharp spots, circular
of nearly circular,
falling on the circum-
ference of two rings.
Large in number but
each of small size.

Sharp spots as above,
but large in size
and few in number.

Large spots on the
circumference of a
ring surrounded by
many others of feeble
intensity not situated
on a ring but irregul-
arly distributed over
the film.

Diffuse soots, broad-
ened chiefly in a
radial direction.

Spots broadened cir-
cumferentially or
tailed Spots.

Sharp continuous
doubled ring, back-
ground clear.

Absence of strain.
Gra n size about
10' cm.

Absence of strain.
Gra n size about
10' cm.

Large Spots indic-
ate grains about
10"2 cm. or larger.
The feeble non-ring
Spots indicate pre-
sence of much
larger grains.

Lattice distortion
denoting a state
of strain.

Fracture of grains
into smaller comp-
onents, each having
a slight tilt with
reapect to its
neighbor.

Absence of strain,
gragn Size between
10'/ and 10‘” cm.

-43-

When a small aper-
ture (0.5 mm) is
used in the x-ray
cassette and the
spots are very sharp,
each of them may be
seen to be doubled,
which is due to a
record being obtain-
ed on both sides of
a duplitised film.

The spots from large
grains are very
seldom as sharp as
those from small
grains._

The use of small
apertures would prob-
ably not enable the
feeble spots to be
observable With the
usual short eXposure
times.

Increase of the
strain causes in-
crease of the diff-
usion of the spots.

These Spots are

usually few in num-
ber, and spots rad-
ially broadened are
invariably present.

 

Characteristic appear-
ance of photographs

 

Interpretation

 

Remarks

 

Diffuse continuous,
background more dense
than above.

Very broad band of
feeble intensity
whose limits merge
into the dark back-
ground.

The doubled ring
broken into symmet-
rically dispersed
arcs, or a contin-
uous ring with sym-
metrical locations
of increased inten-
sity and increased
width.

Changes of ring
diameter. ‘

Considerable lat-

tice distortion or
grain sige of less
than 10' cm.

Grain size less
than 10-4 cm. or a
highly strained
condition.

Preferred orient-
ation. Absence of
large strains when
arcs are sharp and
clearly defined.
Large strains in-
dicated by contin-
uous non-uniform
rings.

Change of lattice
dimensions of the
unit cell as the
result of either
small changes of
composition or
large elastic
strains.

-49-

Use of a small aper-
ture usually increases
the contrast of the
diffuse rings to the
background, but may
reduce this contrast
with some complex
steels.

Not possible to dis-
tinguish between a
small particle size
and a highly
strained condition,
but highly strained
condition implies a
fine particle size.
The converse is not
necessarily true.

On occasions the
preferred orient-
ation effect can be
confused with a pat-
tern composed of
very large spots
circumferentially
broadened.

Derivation of Equation

on Page 35

Bragg's Equation

l7.A ==.Z<d’ égfrté9

Allowing rlto be equal to unity
. A
3'" ‘9 =zd

Differentiation with Gand d variables
C05 6 d6="‘z)‘— al’zdd :: -- L’dLedd

_ -912! ___.....srne
d6- 0! C039

dd
CIE9== -'?§- 7}1r7 69

QED

-50-

 

 

By
HERBERT R. ISENBURGER
St. John X—Ray.Laboratory
Califon, N. J.

E X-ray back-reflection
method is the only means
available of accurately

analyzing existing stresses in a
structure without measuring the
unstressed structure. With it,
the actual stress can be calcu-
lated from the diffraction nega-
tive. Parts subject to strain in
service can be checked to deter-
mine if a change in the crystal-
line structure of the material has
taken place. Once such an anal-
ysis has been made, the infor-
mation obtained can be used to
predict the changes that may
occur in similar structures. The
successful use of this method
depends on the availability of
precision-built equipment; on
care in etching the specimen
and in setting the exposure; and on painstaking
evaluation of the results.

The X—ray equipment in use at the St. John
X-Ray Laboratory is shown in Fig. 1. One unit
(right) contains the high-voltage transformer
and controls; the water pump (center), which
circulates cooling water to the X—ray tube, is
mounted in a cabinet. The self-rectifying X-ray
tube, supported on a flexible tube stand, is of the
ray-proof and shock-proof type.

The back-reflection instrument is mounted di-

Fig. l.

 

X—ray Equipment for Back-Reflection Method of Stress Analysis

rectly against the X-ray tube window. It consists
of a camera and a motor to oscillate the camera
during the exposure. The X-ray beam is directed
through anextremely fine collimating bore on
the specimen being investigated, the crystals of
which reflect it back onto the X-ray film, form-
ing a circular pattern. Superimposed over this
pattern is one of a standard material, usually
gold. Since the pattern of this standard always
appears the same, it is measured for comparison
in the evaluation of the results.

 
  
 
 
 
 

Fig. 2. An Exposure Set—up for
Determining the Stress due to Weld-
ing in a l-inch Steel Plate. The Pin
in the Middle of the Disk is Used to
Obtain the Proper Distance between
the Object and Film, and is Re-
moved when Making the Negative.
A Protractor Helps to Align the
Equipment at the Correct Angle,
Usually 45 Degrees

 

MACHINERY, July, 1947—167

       
   
 

Fig. 3. Radiograph is Divided
into Four Segments, Two of
which have been Treated to in—
tensity the Lines. Pattern No. 1
Shows the Exposure of Normal-
ized Steel, while Pattern No. 2
Shows the Same Part under a
Load of 40,000 Pounds per

Square Inch. The Broadening
of the Lines is Due to Plastic
Deformation

The actual exposure set-up is depicted in Fig. 2.
In order to obtain reliable results, it is of utmost
importance that all dimensions be accurately
maintained. Thus alignment pins keep the proper
object-to-film distance, and a protractor helps in
aligning the camera at the desired angle, which
usually is set at 45 degrees to the surface of the
specimen. The angle of reflection varies, how-
ever, depending on the crystallographic plane
that reflects the rays.

Fig. 3 shows a typical back-reflection radio-
graph. The circular film is divided into four
segments, opposite segments registering an ex-
posure. In the illustration, one half of the print
appears darker. In the lighter portion the X—ray
patterns stand out more clearly. This half of the
film has been treated with a special intensifying
agent in order to strengthen the lines, which
must be measured with extreme care. Pattern
No. 1 shows the exposure of normalized steel.

The outer circle in both segments is the gold'

reference line. Pattern No. 2 is obtained from
the same test bar as pattern No. 1, but under a
40,000 pounds per square inch load. The broad-

 

 

 

 

168—-MACHINERY, July,

 

ening of the iron lines is
due to plastic deformation.
In order to determine the
stress caused by this load,
the distance between the
gold reference line and the
iron line is measured.

This is accomplished by
means of a vernier scale
mounted on an optical
stage, as seen in Fig. 4.
These measurements can-
not be made too exactly.
The lattice parameter of
the iron crystal is, of
course, extremely small,
and any variations due to
stress are of the order of
a billionth of an inch. For this reason, the work
must be carried out with extreme care, and the
results—the X-ray pattern on the film—should
be clearly defined for exact measurement to
within 0.001 inch.

The applications of this method in the machin-
ery field are too numerous to recount here. It is
particularly suited for determining changes in
residual stresses. The importance lies in the fact
that the examination can be carried out on an
object in the field without removing or destroy-
ing it. In addition, the X-ray back-reflection
method has been used successfully to determine
the stress in bridges, ships, rails, car wheels,
airplanes, etc.

While the method described is satisfactory and
in general use at present, new and improved
techniques now being studied may simplify the
procedure considerably. It is possible to elimin-
ate the use of a reference material and to employ
a special projection apparatus with low mag-
nification to evaluate the results. The film can
be projected directly on a stress scale, avoiding
mathematics in the final stress analysis.

Fig. 4. A Vernier
Mounted on an Optical
Stage is Used to Meas-
ure the Distance between
the Line of a Standard
Reference Material and
the Material being In-
vestigated. From These
1 Measurements, the Stress
in Any Particular Spot
in a Structure can be

Calculated

 
 

 

 

 
 
  
 
 
  
 
  
  
  
  
 
  
    
     
   
   
   
   
   
   
   
   
   
   
  
 

BIBLIOGRAPHY

 

Introduction to Modern Physics (book), F. K. Richtmeyer,
E. H. Kennard. McGraw-Hill Book Company, New York,

N. Y.,.1947.

Stress Analysis by X-Ray Diffraction, H. R. Isenburger.
Machinery, volume 54, July 1947, r ges 167-8.

X-Rays in Practice (book), W. T. Sproull. McGraw-Hill
Book Company, New York,.N. Y., 1946.

X-Ray Diffraction Techniques in the Industrial Laboratory,
H. P. Rooksby. Reports on Proaress in Physics,
volume 10,1944-45, pag es “83-117.

EXperimental Stress Analysis, Society for Experimental
Stress Analysis, Cambridge, Mass., volume 1, number

2, 1943: page 73‘

New X-Ray Evidence on the Nature of the Structual Changes
in Cold-Worked Metals, W. A. Wood. Nature, volume

151. 1943. page 585.

A Tension-Compression Device for Quantitative X-Ray
Diffraction Evaluation of Strain in Metals and a
Calibrated Series of Aluminum Alloys, G. L. Clark,
G. Pish, R. Seabury. Journal of Applied Physics,
volume 14,1943, page 284.

X-Rays in Retsearch and Industry (book), Henry Hirst.
Chemical Publishing Company, Inc., Brooklyn, N. Y.,
1943.

X-Ray Analysis in Industry. Nature, volume 149, 1942,
pages 503-4.

X-Ray Analysis in Industry. Cavendish Laboratory,
Cambridge, England, W. L. Bragg, President.
Journal of Scientific instruments, volume 18,
1941, part I, pages 69-102; part II, pages 126- 155.

Applied X-Rays (book), G. L. Clark. McCraw-Hill Book
Company, New York, N. Y., 1940. _

For Further Bibliographical References, see

Welding dourna1,-(Supp1ement), volume 23, Nov. 1944,
page 571-5.

-52-

 

 

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