Angular bends in whiskers

ANGULAR

BENDS G.

S.

IN WHISKERS*

BAKERt

The distributions of angular bends formed during growth in zinc, cadmium, and tin whiskers were measured. It was found that for spontaneous growth whiskers from electroplated surfaces, the distributions had peaks at angles equal to the angles between low-indices directions iu the crystal lattice. Various characteristic groupings of angles could also be related to groups of low-indice directions.

FLEXIONS

ANGULAIRES

DES

BARBES

L’auteur a mesure les distributions des flexions engulaires formees pendant 1~ croissance des barbes dans le zinc, le cadmium et 1’6tein. 11 a trouvb que pour la croissance spontan& des barbes B partir de dbpBts de surface, la distribution avait des maxima B des angles Bgaux aux angles form& par les directions d’incices faibles du rbseau cristallin. Diff&ents groupements caract&istiques d’angles peuvent aussi Btre mis en relation aver des groupements de directions de foibles indices.

KNICKWINKEL

IN

FADENKRISTALLEN

An Fadenkristrtllen aus Zink, Cadmium und Zinn wurde die Verteilung der beim Wechstum ent,sandenen Knickwinkel gemessen. Dabei wurde gefunden, dass fiir Fadenkristalle, die durch spontanes Wachstum auf elektroplattierten Ober%ohen entstanden sind, die Verteilung Maxima bei Wiukeln aufw&t, die gleich den Winkeln zwischen niedrig indizierten Richtungen im Kristallgitter sind. Ausserdem konnten verschiedene charakteristische Gruppierungen von Winkeln mit Gruppen von niedrig indizierten Richtungen in Beziehung gebracht werden.

INTRODUCTION

distribution pressure

Whiskers grown from the solid phase are occasion-

a report

of some

The present of the more

communication striking

features

is of

angular bends formed in whiskers during growth. REVIEW

Since

whiskers

OF

PREVIOUS

region of Fullman(4) from

type

of bending

which

grown

spirals.

under

He found

around 30” and 60’.

Both

the angular bend. Sears, Gatti, and reported angles in iron whiskers grown

the vapour

which

had the ability

to sustain

about the large elastic strains observed.

it was seen RESULTS OF THE PRESENT INVESTIGATION

that a few of them were bent in more or less angular t,ype bends. Koonce and Arnold(l) first reported a characteristic

whiskers form

large elastic strains. They proposed a small angle boundary at the angle, the motion of which brought

WORK

were first discovered

in

bent to

Koonce and Arnold and Levy and Kammerer have hypothesized some type of twin boundary in the

the growth and is a result of the growth process. Thus its explanation is required by a complete theory growth.

angles

peaks in the distribution

ally bent, straight segments being connected by sharp angular bends. This bending takes place during

of whisker

of

multiply

could

not

be

The

distributions

of

angular

bends

formed

in

explained by just random deformation of whiskers already grown. They reported a double bend of two angles equal in size but of opposite sense which

whiskers during growth were measured for cadmium, tin, and zinc whiskers, both grown with the applica-

left the whisker in the same orientation but offset from its original position by a small amount. Fisher,

the plane of the angle was parallel to the surface from which the whisker grew, the angle was measured

Darken and CarroP) caused whiskers to grow at an accelerated rate of growth by the application of pressure. The number of whiskers showing bends in this case is much greater than for whisker growth without the application of pressure; some whiskers showing multiple bends. Levyc3) has reported the

using a filar eyepiece

tion of pressure and in the absence

l-02

METALLURGICA, PP.)

VOL.

5,

JULY

1957

on a metallurgical

If

microscope.

The lengths of the components of one of the legs of the angle parallel and perpendicular to the other leg were measured and the angle calculated from this. Depending on the size of the angle and the lengths of the legs, the error varied from 1” to 3”. The great majority of the angles, however, could not

* Received November 9, 1956. t Dept. of Physics, University of Illinois, Urbana, 111. U.S.A. ACTA

of pressure.

be measured 353

attached

to the specimens

on which

METAI,LlJHGICS,

4(“f,4

354

601”

5,

I!)57

-

1

ZN. NON SQUEEZE

55 50

V(jL.

ANGLES

I

45 40

cn :

i

3530-

z” a 25%

20-

FIG. 3. 90” angle in zinc whisker.

:

27000

x.

In the case of whiskers grown with the application

b 60

DEGREES FIG. 1. Distribution

of pressure there was no pronounced preference of one angle over another. However, in the case of whiskers grown without

70

8

90

whiskers and

of angles found in zinc whiskers.

they grew. These whiskers were removed from the specimen and placed flat on a microscope slide, taking care not to stress the whisker while doing so. The whisker was then examined under a magnification of 1000~

on a metallograph

the

of rotation

angle

with a rotating

readable

to

of

1

of the stage and the angles read OR as the

difference

between

measuring there

the

the two

angle

was always

settings.

was less than

the possibility

had been placed on the microscope

The error in 1 degree,

that

the

the angles that predominate

90”.

Fig.

1 gives

found in zinc nonsqueeze for cadmium is similar. typical

examples

of pressure

For cadmium the

and zinc

are 30”, GO”,

distribution

of

angles

whiskers. The distribution Figs. 2 and 3 show two

of the angles,

Compton,

Mendizza,

and Arnold’5) have reported that the whisker axis for zinc and cadmium whiskers is along one of the

stage,

one-tenth

degree. The legs of the angle were successively lined up with a hair-line in the eyepiece by means of rotation

the application

a few angles predominate.

TIN

60

NON SQUEEZE

WHISKERS

55 50 i

but

whisker

slide in a stressed

state.

0

0

IO

20

30

40

50

60

70

00

DEGREES Fm. 2. 60” angle in zinc whisker.

1850 x .

Pm. 4. Distribution

of angles found in tin whiskers.

RAKER: TABLE

1.

Angles between directions

ANGULAR

of typo HKL

RENDS

IN

WHISKERS

355

and hkl

in white tin HKL

lrkl

Angles i

001

I 100

~ 101

110 111

100 101 110 111 100 101 110 111 101 110 111 110 111 111

$123’

~ 90” 90” 2s0 37’ 90” 45”

/ “iI cl4

76” 44’ 51”38’ 410 17’ 66” 1’

~ 4i:47’ , ~

57” 15’

0” Zl”6’ 0”

9:” 40’ 48’

82” 33’

~~-

orthohexagonal axes. The three major angles found in whiskers of Zn and Cd are just the angles between the

various

orthohexagonal

tin, the distribution

axes.

In

t,he case

of

If, however, one considered the angles between the lowest index direction (those having ones and zeros as Miller indices), one gets all the angles which appear with any frequency.

Fig. 4 gives the distribution

of angles in nonsqueeze

tin whiskers.

Table

the angles between low index directions tin lattice. Many

of the whiskers

the angles forming

FIG. 6. A 38’ and a 62” angle combining in one plane to give a 90” change in direction tin whisker. 2100 x .

of angles is more complicated.

1 gives

in the white-

are bent more than once,

characteristic

groups.

In the tin

forms

acute

angles with the other two.

given in Table

2.

90”, and only these have been observed 5 shows

an example

and

angles

to Fig.

combining

cadmium

the

pair

of angles

30”

and

60”

observed. Fig. 7 shows a second type of characteristic tion, first reported

two of the directions

two

and the third

of two 45”

in tin.

to give a 90” change in direction. Fig. 6 shows a 28” and a 62” angle giving a sum of 90”. For zinc

lattice, there are four groups of three of the lowindex directions given in Table 1 in a plane, in which are perpendicular

These are

These pairs of angles adding

angles

by Koonce

of equal

forma-

and Arnold.(l)

magnitude

is

Here

in the same plane

cancel each other to leave the whisker going in the same direction usually

but offset from the previous

a small amount.

This type

line by

of a formation

has been observed for cadmium, tin, and zinc whiskers with all their characteristic angles except 90”. One often

observes

two

90”

angle

bends

following

one

close after the other. These, however, are always in perpendicular planes. Occasionally there occurs repeated bending of the whisker through equal angles which alternate in sense. If the distance between angles is small and varies, the whisker may seem to take on a curved shape. TABLE

2. Angles

between three directions white-tin lattice

Directions

FTG. 5. Two 45” angles combining in one plane to give a 90” change in direction tin whisker. 400 x .

100 110 010 100 101 001 110 111 001 101 111 010

This is seen in Fig. 8.

1 1 i ~

in a plane of the

Angle l-2

Angle 2-3

Angle l-3

45” 28” 37’ 21” 6’ 41” 17’

%23’ 680 64’ 48” 47’

90” 90° 90” 90”

ACTA

356

METALLURGICA,

FIG. 7. Double 30” angles in tin whisker. 2700 x . There are many in a common

other groupings

of angles,

some

less frequently. Fig. 9 shows a characteristic group for zinc. These groupings of angles all can be represented as the angles between the low-index and groups

lattice.

of angles appear

among

here the background

of random

the characteristic

the distribution show

of angles. the

bends

on

However, is so large

angles are overshadowed

whiskers and nonsqueeze angles

angles

the bends

whiskers grown by the squeeze technique. that

directions

All the characteristic

in

In general, for both squeeze whiskers the characteristic

high-whisker

strength,

while

the

other angles do not.

the angles formed

in whiskers

1957

as among

nonsqueeze

latter, however,

whiskers.

In the case of the

there are at least an order of magni-

tude more bends which are relatively randomly

distributed

probably

.

accidental

in

magnitude.

weak and are These are

bends due to changes in condi-

tions in the highly inhomogeneously

stressed region

from which the whiskers are growing,

either causing

the bends or leaving weak sections of the whisker highly susceptible to mechanical deformation. The

theories

of whisker

growth

phase which have been proposed the whisker was a continuation of the base material.(6t7)

from

the

solid

have assumed that

of the crystal structure

It is further assumed that

there is in the base layer a volume of relatively perfect crystal of dimensions comparable to the

DISCUSSION

That

5,

FIG. 9. Characteristic group of angles for zinc whisker. 926 x

plane, some not, which occur more or

in the crystal

VOL.

grown

with

the application of pressure do not show any angles predominating is most likely not significant. There are as many or more characteristic angles and groups of angles which are strong among squeeze whiskers

whisker diameter a dislocation

The results compatible are two

from which the whiskers grow by

mechanism. of the present

investigation

with such a mechanism possible

explanations

of

are not

of growth. the

There

presence

of

angles assuming such growth mechanisms. One is that they are formed by the mechanical bending of a part

of the whisker

which

has already

This would not give the distribution

formed.

of angles found

and usually results in the angles so formed being weak, while those found are usually strong. The second mode of angle formation is for the whisker axes of those parts of the whisker grown to maintain their orientation the direction

FIG. 8. Tin whisker with repeated angles. 1380 x . Whisker had characteristic whisker strength.

relative

to the base material,

of growth in the base to change.

but This

could not possibly be the case for whiskers of the type shown in Fig. 9, where different segments of the whisker grew in directions 189’ from each other. In addition, the whiskers in the present investigation were grown from electroplates less than a micron thick with submicron grain size. An exaggerated case of this is seen in Fig. 10, where a whisker of

BAKER:

ANGULAR

BENDS

IN

WHISKERS

The conclusion

357

from this is that the whiskers

do

not grow with a root coherent with the base material, but are separated

by an incoherent

interface

from

the base material. change whisker,

The bend is then formed by a in direction of growth at the base of the the parts

of the whisker

already

formed

reorientating in space to give a constant orientation of the growing face. This would mean that the crystal structure is continuous through the bend, the lattice orientation of the whisker axis changing. X-ray

analysis

of

iron

whiskers

grown

from

the

vapour shows that this is true for those whiskers.(s) The similarity

of the whiskers in the two cases would

lead one to expect

that it is true also for whiskers

grown from the solid. REFERENCES

FIU. 10. Cadmium whisker much larger than grain size a.nd thickness of cadmium plate from which it grew. 925 x . large

diameter

is growing

order of magnitude

on an electroplate

of an

smaller thickness and grain size.

Thus there was no naturally whisker to grow from.

occurring

base for the

1. H. E. KOONCE and S. A. ARNOLD J. Appl. Phys. 25, 134 (1954). A. It. M. FISHER, L. S. DARKEN, and K. G. CARROI. A& iMet. 2, 368 (1954). 3. P. W. LEVY and 0. F. KAMMERER J. Appl. Phyhys. 26,1182 (1955). 4. G. W. SEARS, A. GATTI, and R. L. FULLM~~N Acta Met. 2, 728 (1954). Corrosion ‘. K. G. COMPTON, A. MINDIZZA, and S. M. ARNOLI) 7, 327 (1950). 6. F. C. FRANK Phil. Msg. 44, 854 (1953). 7. J. D. ESHELBY Phys. Rev. 91, 775 (1953). 8. G. Y. BAKEX J. Appl. Phys. 27, 1561 (1956).