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1/98 a/CIRC/DateDuepes-p. 14

Ihterninntion of Magnetic Anisotropy of Single Crystals
01‘ Iron and Iiiukel \ i'eens 01‘ the

Torque Marnetometer

BY

Joseph Mudar

A Thesis
Submitted to the School cf Graduate Studies of Michigan
State Collere of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Physics

xwea
/ '

I“

ACKNOHLEIflMEKT

I wish to express my sincere thanks to Er. R. D. Spence for
suggesting this problem and for his limitless help and patience
during the course of the problem; and to Jerry A Cowen for his many
helpful suggestions.

I would also like to extend my appreciation to Dr. Smith and
the Metallurgical Engineering EEpsrtmont for the use of their X-rsy
unit and to Mr. C. Kingston for the construction of the technical

erqcretus.

 

317522

II.

III.

IV.

TABLE OF CONTthS

Introduction and Theory

Experimental Apparatus and Procedure
Preparation of Samples

Results

Bibliography

INIPCIWCTION AYD TFECRY

It has heen known for some time that the energy required to magnetize
single crystals of ferromagnetic materials depends on the angle hetween
the magnetization vector and the crystalographic axes} This energy must

have the same symmetry as the crystalographic lattice. Thus for a

. . 2 12 2 12 2
cubic lattice: E 3 KO + K. (£02 + 02 03 + 03 al ) (I)
+ Kztafaia: + )+---

where the K58 are called the anisotropy constants and the 0:3 are
the directional cosines of the magnetization vector with reapect to
the crystallographic axes. The terms containing K1 and K2 are the only
terms of the series which are normally required to represent experimental
results. In certair situations the term containing K2 is often neglected.

This thesis reports the results of measurements of the temperature
dependence of K1 in single crystals of nickel and iron. The theory
cf the experiment has been discussed by Morriscnjand therefore, only
a brief summary of the theory will be given here.

If the magnetization vector lies in certain planes in the crystal
the expression for the anisotropy energy is greatly simplified. In the
(100) plane 0|: COS 6 ’ 02 : sin 9’ as: 0 ’ where 9 is the angle
between the magnetization vector and an easy direction of magnetization.
If the magnetic field is of sufficient strength to align the magnet-

ization vector parallel to the magnetic field in a sample in which the

magnetic field lies in the (100) plane, the torque which arises from the

I'\
m
s l

anisotropy energy is given by:

L= -' 1;. = ---a_(_|_(_l sinZQ c0529) =5. sin 48 (2)
69 69 2 -

This torque can be obtained by measuring the twisting of a fiber attached
to the sample. The torque can therefore be expresselzn377qb where 77 is
a constant characteristic of the fiber and 45 is the angle through which

the fiber is twisted. Evaluating the derivative of the torque at 6:0
we get: al- 2: QJQSIN40) = ZK' .
a0(9="-Ol 00 2 (0:0)

6774; = 77 fl; (4)
09 (9=O) 69(9=O) 09 (9=O)

therefore K] = fl 02- (5)
2 69 (6=o)
where qb

____. is the slope of the torque curve. ii'é; arm! qb are expressed

a

in the same units the slope of the curve can_be measured directly from an

(3)

m
l—J
9
0
C12
r
ll

 

experimental torque curve on which qb is plotted as a function of £9 .
The experimental torque curves for nickel are shown ianigures (6} and
(7} and the curve for iron in Figure {6}. If the expression contain-

ing K“ is neglected, K1 in a (110) plane has the same expression as given
C.

in equation five.

bXFERIHFKTAL AEPARATUS AND PROCEEIRE

The apparatus for obtaining the torque curves is essentially the same
as used by Morrison. In oruer to improve the accuracy of the torque curves,
a torque magnetaneter was designed and built which utiliz«d a rotating radar
magnet. Although this magnet had a field of 2,0t0 oersteds, this was in-
sufficient to insure the parallelism of the magnetization vector and the
external magnetic field in the samples of the shape used in this experiment.
This was shown by a shift in the maxima and minima of the torque curves of
the (100) plane, causing the positive and negative slopes at ¢so to
differ by an amount in excess of the experimental error. Since it would
be somewhat cumbersome to construct a rotating magnet capable of producing
sufficiently large fields, the rotating sample method of obtaining the
torque curves was adopted. The field used in this case was 8,000 oersteds
and was supplied by a large electromagnet.

Owing to the various sizes, materials and crystallographic planes
of the samples, it was necéssary to use various diameters of fibers to
obtain satisfactory torque curves. It was found that guitar strings served
the purpose very well.

Although the method of heating was the same as described by Morrison,
the technique of measuring the temperature of the sample differed. The
copper-constantin thermocouple w~s placed in direct contact with the sample
and rctated with it as shown in the section drawing in Figure (5}. The
e. m. f. was read, before and after the slope ¢ 9 0 was plotted, by
attaching two clips from the potentiometer to the free ends of the thermo-

couple.

(b)

 

 

 

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GLASS BEARING

     
 
   

COOLING FINS
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SAMPLE

KYREX FLASK

GLASS BEARING

FIGURE 3

FREFAhATION OF SAMPLES

Crystals of erco iron which has a purity of y9.yh per-cent were ob-
tained from Virginia Institute for Scientific Research in the form of rods
three-eighths of an inch in diameter and about h inches long. When the
rods were etched in a ten per-cent solution of nitric acid in water it was
found that the rods contained many crystals, the largest of which was about
two inches long. The crystals of nickel wore obtained from Horizons In-
corporated; Princeton, New Jersey, and were reported y9,50 per-cent pure
by the supplier. They were in the form of rods one-half inch in diameter
and about five inches long, the single crystal running the entire length
of the rod.

From these rods it was necessary to cut out slices in the (100) or
(110) plane. To do this it was necessary to find the orientation of the
cubic lattice in the rod. It was relatively easy to find a rough orien-
tation in the case of iron by observing the light reflected from the (100)
planes. A more precise determination of the crystallographic orientation
was made by the back reflection Laue X—ray technique. The crystal was
clamped in a rod holder, the base of which was roughly normal to a coll-
imated X-ray beam. A colliuator was used which had an and diameter of
one-fourth inch. A one-fourth inch hole was cut in the film holder and
this slipped over the collimator. The Laue patterns obtained are in the
form of intersecting hyperbolas as shown in Figures (b-al and (S-a}.

The rod was then adjusted until the point of intersection coincided with

the hole in the film. The reflecting plane, in this position, was then

BACK REFLECTION

CUBE SHOWS LATTICE POSITION
IN RELATION TO PATTERNS

FIG 4b T RANSMISSION

LAUE PATTERNS OF IRON WITH THE (III) PLANE
PARALLEL AND X-RAY BEAM NORMAL TO THE PAPER

 

__ BACK REFLECTION *
D CUBE snows LATTICE POSITION

IN RELATION TO PATTERNS

FIG. 5b TRANSMISSION

LAUE PATTERNS OF IRON WITH THE (IOOI PLANE
PARALLEL AND X-RAY BEAM NORMAL TO THE PAPER

 

(10)

. also normal to the X-ray Team. The rod holder was now clamped in a Di-
Met cutting saw and a slice of about .030 inch was cut out. A .020 inch
abrasive wheel was used.

The orientation of the nickel crystal was somewhat more difficult
due to the fact that no etching solution could be found which produced
etch pits with any clarity. Therefore the X-ray back reflection orien-
tation was basically by trial and error. The rod was adjusted until a
point of intersection was coincident with the hole in the film; with the
hope that the symmetry of spot patterns would be four, two, or three fold
indicating a (100), (110), or (111) plane, respectively. Considering there
are eight (111) planes, six (100) planes, and six (110) planes in a cubic
lattice, the author was amazed at the number of planes which gave centered,
intersecting patterns with no recognizable symmetry.

when a spot pattern nas obtained which appeared to give tne preper
symmetry, the orientation was checked by rotating the crystal in a plane
parallel to tne lines of symmttry the proper number of degrees to bring
other known planes normal to the beam. If these also gave the correct
symmetry the crystal was uniquely oriented.

Since the rod holder was not accurately oriented with respect to the
beam and since the process of transferring the rod from the X-ray unit
to the saw introduced errors, a final orientation was made by Laue trans-
mission patterns. To accurately position the sample holder normal to the
X-ray beam, transmission pictures of cleaved rock salt were taken with

the rock salt occupying the samples position. The sample holder was

\11)

adjusted until the Spot patterns from twe rock salt were symmetric about
the centre 1 dot .

The samples were sanded with consecutively finer sandpaper and etched
with nitric acid solutions to a depth of .009 inch. This removed any strains
introducei eY Sawing. A sample was then placed in the holder, X-rayed,
and the resultin' pattern observed. If the spot pattern did not have all
correSponding ”pots equidistant from the central dot, and in the (100)
and (111) planes, equidistant from each other, as shown in Figures {h-b;
and (S—bf, the orientation was corrected by preferential sanding of one
surface. Therefore, when the oriented side of the sample became parallel
with the desired crystallographic plane the sample was wedge-shaped. This
was corrected by sanding the other surface and checking with a micrometer
until the two surfaces were parallel. The samples of iron were then about
.010 inch thick and the nickel about .020 inch thick. In this manner sam-
ples were oriented which were accurate to within one degree.

The next task was to form the samples into approximate oblate Spheroids.
The first step was to solder the samples to the end of a brass rod. Woods
metal, which has a low melting point, was used to eliminate any strains
induced by eXCessive localized heating. The samples were then machined
circular using a very sharp tool. An oblate spheroid was approximated by
filing the corners with a fine toothed file and sending with fine sand-
Paper while the sample was turning in a lathe. A final etch was given to

remove the strained material introduced by the sanding.

R hi5 UL'i :5

The results 01' the experiment are Slmlfllfll‘izgd in the two graphs

in Figures {a} and ;10?. The temperature dependence of K1 in iron

2%

entained in this experiment agreed very well with the values given by Hond
v ‘1 . g 2 m! ‘+_ 0 \ 4:9 _ .4 I
Kaye, and Maswnceo. ine resuies for HICkCL, however, eiifer conSiuerauiy
. . . . i . 2
from the values obtaihei by honda, Masumoto, and shirakawa. They have
indicated a positive value for K1 in the temperature range from 100 to
jOO degrees Centegrafie whereas our results show Kl approaching zero asymp-
totically and ever taking on positive values.

Measurements of K2 from samples in the (111) plane was attempted.
In the iron the torque in this plane was so small that it was considered
negligible. The nickel sample produced a torque curve of roughly the pro-

per shape, (sinse ), but the curve was erratic so that no quantitative

results could be obtained.

 

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TEMPERATURE DEPENDENCE OF KI IN IRON

SAMPLE IN "loo" PLANE

 

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BIBLIOGRAPHY

Books

 

Bitter, Francis, Introduction to Ferromagnetism, McGraw—Hill

 

Book Company, Inc., New York, 1937.

Bozorth, Richard M., Ferromagnetism, D. Van Nostrand Company
Inc., New York, 1951.

 

(Thesis)

Morrison, Clyde A., Temperature Dependence of Anisotrory Constanrs

 

of an Oriented Fe-Si Alloy, Thesis for M. S.

Michigan State College, 1951

 

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