Subgrain and electrical resistivity studies of molybdenum single crystals

Subgrain and electrical resistivity studies of molybdenum single crystals

SUBGRAIN AND ELECTRICAL RESISTIVITY MOLYBDENUM K. T. SINGLE AUSTt and R. STUDIES OF CRYSTALS* MADDIN: The electrical resistivity for sing...

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SUBGRAIN

AND

ELECTRICAL

RESISTIVITY

MOLYBDENUM K.

T.

SINGLE

AUSTt

and

R.

STUDIES

OF

CRYSTALS* MADDIN:

The electrical resistivity for single crystals of molybdenum after various amounts of bending at room temperature and after annealing isothermally at several temperatures was measured and correlated with metallographic and X-ray observations. Resistivity during room-temperature bending is found to increase slightly initially and is followed by a rapid rise coincident with crossing slip bands. Etch-pit density measurements are found to be proportional to the reciprocal of the bend radius, in agreement with the Cottrell relation. &TUDES

DE SOUS-GRAINS ET DE RKSISTIVITB BLECTRIQUE LES MONOCRISTAUX DE MOLYBDKNE

DANS

La resistivite Blectrique de monocristaux de molybdene apres divers degres de flexion Q la temperature ordinaire et revenus isothermes a des temperatures differentes a 6te mesuree et mise en relation avec des observations microscopiques et de rayons X. La resistivite pendant la flexion a la temperature ordinaire augmente d’abord legerement puis d’une man&e considerable lors de l’apparition de bandes de “crossslip”. La densite de piqures de corrosion a et& trouvee proportionnelle it l’inverse du rayon de courbure, en accord avec la relation de Cottrell. UNTERSUCHUNGEN

UBER

SUBKORNER UND ELEKTRISCHEN MOLYBDAN-EINKRISTALLEN

WIDERSTAND

AN

An Molybdan-Einkristallen wurde der elektrische Widerstand gemessen, nachdem die Kristalle bei Zimmertemperatur verschieden stark gebogen und danach bei verschiedenen Temperaturen isotherm angelassen worden waren. Die Ergebnisse wurden mit metallographischen und mit Riintgen-Beobachtungen verglichen. Es zeigt sich, dass der Widerstand mit dem Biegen bei Raumtemperatur zunitchst langsam anwachst; sein darauf folgender starker Anstieg fallt mit dem Auftreten sich durchschneidender Gleitbiinder zusammen. Das Auszahlen van Atzgrtibchen ergibt, dass ihre Dichte umgekehrt proportional sum Biegeradius ist, was mit der Cottrellschen Beziehung in Einklang steht.

It is possible to obtain in deformed of

annealing

phenomenon,

called

which leads to discontinuous X-ray

patterns.

crystals a type polygonization,

asterisms

Cahno) has observed

in the Laue

polygonization

in bent single crystals of zinc, magnesium,

aluminum,

The break-up

of the asterism

into

existence

to

the

of these

active

dislocation

slip

direction.

and

Cottrellc4)

that

of vacancies

one.

the

basic

that

singularities,

have shown that’

is effected i.e.

might

by

the

vacancies.

It

that dislocations

Hence,

recovery

be expected

of

if vacancies

to dislocations. of dislocations

the migration

Since out of

of vacancies

1956

(dislocation

climb)

would

be

by a decrease in the electrical resistivity initially

to

the

presence

of

vacancies.

It has not, as yet, been possible to calculate the resistivity due to groups of piled-up dislocations

* Received July 21, 1955; revised version March 6, 1956. t The Johns Hopkins Universitv. Now at the General Electric Research -Laboratory, Schenectady, New York. z The Johns Hopkins University. Now at The University of Pennsylvania, Philadelphia 4, Pa. 4, NOVEMBER

polygonization

attributed

This process involves the migration

VOL.

resistivity

accompanied

to or from the edges of the half-planes

METALLURGICA,

point

their slip planes involves

of the dislocations. Mottc3) and Seegarc5) have also suggested that the process of recovery, as well as

ACTA

of

metals

on a dislocation

to the edges of the half planes, it should be expected

process in polygonization is the movement or climbing of edge dislocations out of their slip planes in order to change their grouping from a “horizontal” one to a “vertical”

presence

of

are annihilated by diffusing the process of the climbing

The

walls was confirmed

conclude

resistivity

electrical

by Cahno) and by Dunn and Daniels.t2) Mottt3)

e.g. Jongenburger,(Q

electrical

can act as sinks for vacancies.

discrete

spots is believed to be due to the alignment of the edge dislocations introduced by bending into the walls, perpendicular

may be dependent

climb process. Calculations,

has also been suggested by Nabarro”)

and sodium chloride, after annealing near the meltingpoint.

polygonization,

which are considered to be present in cold-worked metals.(s) If groups of piled-up dislocations contribute substantially to the resistivity, as is quite likely, it is to be expected that a decrease in resistivity may be accompanying an alteration of the piled-up arrays into configurations containing less strain-energy. The present investigation was initiated to determine under what conditions polygonization or subgrain

632

AUST

formation

may

occur

MADDIN:

AND

in bent

molybdenum

crystals.

Electrical

resistance

conducted

in order to obtain a quantitative

ment of the changes polygonization.

SUBGRAIN

single

measurements

occurring

were

measure-

during recovery

and

STRUCTURE

annealing holding

OF

treatments. a bent

A

crystal

each resistance

MO

633

jig

was

constructed

in an identical

measurement,

so that

for

position

for

the distance

between the potential leads was constant.

A correction was made to take account of the increase in specimen length between the potential leads due to the bending.

EXPERIMENTAL

Single-crystal grown

from

purity,

specimens

sintered

using

DETAILS

the

of

molybdenum

molybdenum

method

rods

described

were

of

99.9%

elsewhere.(9)

A current of 5 amp was passed through the specimen for a period of less than 10 sec. All resistance measurements were made at atmospheric temperature (21”

to

The specimens were about 3 mm in diameter and 18 cm long, with single crystals approximately 2 cm

sensitivity

to 5 cm in length occupying

The

of each specimen.

the entire center sections

The specimens were electrolytically

polished and then bent at room temperature, the

same techniques

described

The bent

argon atmosphere temperatures X-ray

crystals

from

were annealed

300°C to approximately Laue

in an 1600°C.

photograms

were

obtained from the crystals in the grown and bent conditions and after the various annealing treatments. The

longitudinal

specimen

axis

orientations

for

the initially unstrained crystals are shown in Fig. 1 in a unit stereographic triangle. Microscopic examination was conducted after etching the crystals in a sodium hydroxide

and potassium ferricyanide

and also after electroetching

solution,

in 5% oxalic acid at 4 V.

The electroetch method was found to be more sensitive for

revealing

Several

subgrains

crystals

deformation Electrical

were

in also

at an elevated

molybdenum examined temperature

resistance measurements

were

the

resistance

corrected

21°C.

The

measurements

to

was

1OW ohms and the accuracy was fl

x

resistivity

1OW ohm-cm,

The

for periods of 1 hour to 25 hours at

back-reflection

and

of

values

were

x 10e6 ohms.

accurate

to

-&0.02 x

or &0.30/.

applying

previously.oO)

radius of bend of the crystals was varied from 8 cm to 1.5 cm.

1

26°C)

crystals. after

slight

(2000°C).

were made with

a Leeds and Northrup Kelvin double bridge, after increasing amounts of bend and after the various

-

EXPERIMENTAL 1.

RESULTS

High-temperabe Subgrains

AND

DISCUSSION

Deformation

were detected

microscopically

and

the split-up of Laue reflections in molybdenum crystals

subjected

to a slight external

by

single

stress during

high-temperature annealing. Typical examples are shown in Figs. 2a and 2b, which were obtained from a crystal

(M-l)

deformed

about

1 o/o in tension

at

2OOO”C, and from another crystal (M-2) deformed by bending to a l&cm radius at the same temperature. The average size of the subgrains depicted is about 10 microns.

in Fig. 2a

Etch pits which are spaced in a

nearly regular manner are visible at the sub-boundaries. It is also evident,

particularly

in the lower part of

Fig. 270,that the density of etch pits changes markedly when

the

direction

of the

The etch pits are believed

sub-boundary to occur

changes.

at dislocations

which are found at regularly spaced distances aligned in the sub-boundary. The average spacing of the etch pits in the sub-boundaries was 1 x lo-* cm to 2 x lo-* where

cm.

From the dislocation

8 = orientation

spacing,

difference,

and h = etch pit spacing,

0, of 0.01” to 0.02” were calculated deformed

relation

0 = A/h,

;1 = interatomic misorientations, for the crystals

slightly at 2000°C.

Microscopic examination at x 1300 of the singlecrystal section adjacent to a polycrystalline end revealed boundary

no apparent where

it

change of direction meets

of a grain

a sub-boundary.

This

indicates that the “pull” of a sub-boundary at the junction is very much smaller than that of a grain boundary. Back-reflection Laue photograms revealed

FIG. 1. Initial orientations of molybdenum crystals investigated.

a breakup of each Laue reflection into discrete spots, similar to that observed by Chen and Maddin for a single crystal of molybdenum bent at about 2400°C. The orientation-spread between the individual spots of a Laue reflection

was less than 0.1’.

ACTlZ

634

METALLURGICA,

VOL.

suggests

4,

1956

that it is unlikely

molybdenum

crystals

form

that

sub-boundaries

by an athermal

in

process

on plastic deformation. Another

crystal

(M-7),

at room temperature at temperatures

which was bent to 2.3 cm

and then annealed for one hour

from 300°C to lOOO”C, also showed

no structural changes. This same crystal was then bent from 2.3 cm to 1.8 cm during an anneal at’ 1200°C. Microscopic

examination

revealed

sub-boundaries,

as

shown in Fig. 3a, similar to those observed in an early stage of formation

by Dunn and Danielsc2) in bent

FIG. 2. Sub-boundaries in molybdenum single crystalselectrolytically polished and electroetched 15 see in 5% oxalic acid solution. (a) Top: Crystal M-l deformed in tension at 2000°C; x 400. (b) Bottom: Crystal M-2 deformed in bending at 2000°C; x 500.

2. Bending at Room Temperature followed by Annealing In a previous investigation,(lO) of molybdenum ture revealed

X-ray Laue patterns

single crystals bent at room temperaa breakup

of Laue

spots

into

high-

intensity regions connected by diffuse areas. This phenomenon was interpreted in terms of crystallite fragmentation

where the individual

crystallites

are

connected by high-strain regions. In the present study, four single crystals (M-3, M-4, M-5, M-6) were bent from 8 cm to 1.5 cm at room temperature and annealed in an argon atmosphere

for periods up to ten hours

at temperatures from 300°C to 1400°C. No significant change was noted either in orientation or in the appearance

of the Laue reflections

after the above

treatments. Microscopic examination after chemical and electroetching showed no evidence of subgrain formation or polygonization. It is possible, of course, that subgrains were present, but still too small in size and misorientation to be detected by conventional However, the failure to detect any techniques. structural

changes

even after ten hours at 14OO”C,

* ., Fm. 3. (a) top: Sub-boundaries in molybdenum single crystal (M-7) after 1-hr anneal at 1500°C. Crystal was previously bent to 2.3 cm at room temperature, and then bent to 1.8 cm at 1200°C. Electrolytically polished and electroetched 15 set in 5% oxalic acid solution. x 300. (b) Centre: Enlarged Lam spot of M-7 after bending to 2.3 cm at room temperature. (c) Bottom: Enlarged Laue spot of M-7 after an additional bending to 1.8 cm at 1200°C and annealed 1 hr at 1500°C.

AUST

annealed and examination at boundary

in

silicon-iron x 1000

Fig.

3a

MADDIN:

AND

crystals.

indicated

consists

Microscopic

that

of

SURGRAIN

each

sub-

a discontinuous

su~eession of etch pits similar to the walls of edge dislocations revealed in aluminum crystals by Cahn.o) crystal

The M-7

average

spacing

of the etch

was 0.5 x lo-* cm, which

to a misorientation the dislocation

pits in

corresponds

t3 of 0.04O when calculated

relation

from

8 = A/h. From the relation-

w x 57.3

STRUCTURE

OF

MO

635

3. Etch-pit Densities Microscopic

measurements

of

etch-pit

densities

were conducted on several crystals after eleetroetching in 5% oxalic acid solution. The excess density of edge dislocations of the same sign to produoe a certain’ amount of strain in bending was calculated from

the

relation

given

where p is the number

by

Cottrell:(4)

of dislocations

p = I/&,

per unit area

parallel to the bend axis, r is the bend-radius

at the

neutral

of the

axis,

and

b is the

Burgers

vector

where W is the average width %eos (6) of the subgrains, i is the radius of bend, and # the

dislocation. For molybdenum, b is the interatomic distance in the (111) direction. The results are

boundary

summarized

ship,(2)

0 =

~~---.-.-,

direction,

the misorientation

0 is calculated

in Table 1.

to be 0.08”. The latter value of misorientation is in reasonable agreement with the 0.04” value derived

The reasonable agreement between the measured etch-pit density and the dislocation density calculated

from the etch-pit spacing. Enlarged Laue reflections

from

shown

in Figs.

bending

from

The high-intensity

bending

in a preferential

crystallographic

order to the formation

to 1.8 cm

The X-ray photo~ams

manner

suggesting of the sub-

from crystal M-7 also

revealed partial Debye rings of a textured after bending

are

regions of Fig. 3e appear

to be arranged grains.

M-7

3b and 3c, after room-temperature

and after the additional

at 1200°C.

crystal

aggregate

at 1200°C and after further

one-hour

anneals at 1400°C and 1500%. The Debye arcs consisted of very small spots, reminiscent of polygonization, which became better developed and increased from

in size as the temperature

1200°C to 1500%

interpreted

in terms

of

was increased

Tb.is phenomenon

may be

subgrain

as was

growth,

observed in bent silicon-iron crystals when annealed from 950°C to 1300”C.(2) The orientation difference between

the individual

spots in the X-ray

patterns

of crystal M-7 was less than O.l”, which is consistent with

the

19 values

observations. Crystal M-7

calculated

was next

bent

from

microscopic

a slight additional

amount at room temperature in order to reveal slip traces. It was observed on microscopic examination

the Cottrell

the etch pits locations

supports

with the surface.

measured

and

also found and

relation

are locations calculated

annealed

silicon-iron

silver

who

of sub-boundaries

found in crystal M-7 (Fig. 3a) from the irregular network

observed

in crystals

after

between

described as polygonization. However, as the structure coarsens, it loses t,he characteristics of a polygonized one, not because the lamellar structure disappears, but possibly because larger units no longer have simple orientation relationships.(2)

densities

was

and Machlin(i2) for bent

crystals,

controlled

and

by

Dunn

the geometry

crystals such that (112)-edge

and

of their

dislocations

were measured after electroetching. 4. Increase of Electrical Resistivity due to Bending. The electrical resistivity at 21°C (p 21’) of molybdenum single crystals in the “as-grown” condition cm.

or unstrained

was found to be 5.95 (*0.05)

X [email protected]

ohm-

The effect of amount of bending at room tempera-

ture on the electrical resistivity crystals was measured.

(p 21°) of molybdenum

Increases of resistivity

up to

15% were observed after bending to a radius of 2 cm. Fig. 4 shows the relationship increase

of resistivity

and

between angle

of

the per cent bend

over

a

1.25-cm length for two molybdenum crystals (M-9 and M-10). A very rapid increase of resistivity is evident

after

examination

about

a

12’

bend.

~etallo~aphic

of the slip traces as a result of bending

revealed one system of fairly straight slip bands after

Crystal No.

, / I

M-7

ilf-10 M-2

Condition

Measured etch-pit density

of crystal

1 (cm-*)

slight

bending or tension at 2000°C (Figs. 2a and 2b). The nearly parallel or lamellar sub-boundaries may be

that

Good agreement ~slo~ation

that the sub-boundaries were approximately at right angles to the slip traces, as predicted by the dislocation mechanism of polygonization.(*J The nearly straight, parallel sub-boundaries differ in appearance

belief

of dis-

by Hendrickson

Hibbard,03)

the

of intersections

i I

bentfrom 2.3cmt,o 1.8 cm 1.4 at 1200°C and annealed 1 1hr at 1500% j bent to 2.1cm at room, 1.5 temperature and annealed 12 hr at 1550°C I bent to 18cm at 2OOO”Ci 1.8

/ Cdzyd // I

’ location density (em-e)

I

x

107

x

107 j 1.7 x 10’

x

lo6

12.0 x 107 / /

2.1 x lo6

ACTA

636

METALLURGECA,

VOL.

4,

1956

. cl

Mo CRYSTAL

M - 9

l

MO CRYSTAL

M-IO

/

ANNEALING

TIME

(khs.)

AT

1550’C

J 20

ANGLE

OF

BEND

OVER

1.25

BEPiT ATi ROOM TEUPERATURE

Cu. LENGTH

Recovery data for moly~denuul single crystals bent at room temperature.

F’rG.

FIG. 4. Per cent increase in resistivity as a function of amount of bending at room temperature.

5.

inclusive)

were bent

at room

temperature

to radii

a 5” bend, and a slight forked nature of the bands after about 12”. After a 15” bend over 1.25 cm,

of 1.5 cm to 5 cm with resulting increases of resistivity of 15 to 7%. These crystals were given various annea-

the slip bands

ling treatments,

were very

forked,

i.e. intersecting,

and the electrical resistivity measured

at room temperature

and similar to the slip bands previously observed in bent molybdenum crystals (Fig. 10 of reference IO).

of resistivity,

Load-deflection

at room temperature

curves obtained for bent molybdenum

crystalsoO) also gave some indication of a behavior similar to that shown in the resistivity-angle of bend-curves of Fig. 4. It is interesting to note, Masima

and

resistivity

SaehsQ4)

found

that

the

electrical

of single crystals of alpha brass increased

No recovery

was found after 90 hours

and after annealing for periods

up to 10 hours at 1400°C.

Also, no structural changes

were evident after mioroscopic Isothermal

in this ~ol~ne~tion, that

after each anneal.

within +0.3%,

annealing

and X-my examination.

at 1550 -j: 30°C resulted

in

partial recovery of the total increase of resi&ivity due to bending, as shown for crystals H-6 and B-10 in Fig. 5.

It

should

be noted

Jf-6

M-10 received no prior anneals (M-10 was bent to a smaller radius of curvature than M-6). This might

increase in resistivity

was observed

a marked

as a second-slip

at temperatures

was

was confined

However,

periods

crystal

annealed

to one system.

for one-hour

that

by only about 1% as slip began and then remained constant during almost the whole period when slip

300 to 14OO”C, prior to the 1550°C treatment;

from crystal

explain the differences observed in the curves of Fig. 5.

system became operative in alpha brass crystals. The rapid increase in resistivity coincident with

Microscopic and X-ray back-reflection

intersection

that the recovery of resistivity could not be attributed

of slip bands

denum crystals may

be

observed

in bent molyb-

here, and in alpha-brass

understood

if

resistivity

is

orystals,on appreciably

affected by the presence of vacancies and piled-up groups of dislocations formed by crossing dislocations. Mott,(*)

in

specifically

considering

vacancies,

has

given diagrammatic stress-strain curves which are very similar to the resistivity-strain curves found for polycryst~lline

nickel

by Broom.(r5)

The relatively

to a reduction in dislocation tion.

However,

obtained

from

crystal

scopic examination

of cross-

section,(l6) may be the result of a high concentration of frozen-in vacancies as well as piled-up groups of dislocations which can remain in the lattice when the deformation

is carried out at room temperature.

5. Recovery of Electrical Resistivity Several

single-crystal

specimens

(M-5

to

M-10

M-6

after room-temperature

bending and after 1 hour, 8 hours, and 20 hours annealing at 1550°C. A gradual alignment, of the high-intensity regions in crystallographic manner is

enum and tungsten

reduction

photo~~~~phs did reveal

distinct structural changes occurring during recovery of resistivity. The Laue reflections of Fig. 6 were

evident

>99%

density, i.e. recrystalliza-

the X-ray

high per cent increase in resistivity for bent molybdenum crystals (Fig. 4) and poIycrystalline molybafter

studies indicated

in Fig.

suggesting

6 with

increasing

the occurrence

time

of anneal,

of polygonizat.ion.

also indicated

Micro-

a partial alignment

of etch pits into sub-boundaries, which is depicted in Pig. 7. A calculation of the activation energy for recovery of electrical resistivity from the data at 14OO’C and at 1550°C during the first 5 hours yields a value of between 3.5 and 7 eV. This can be compared with the activation

energy

of approximately

2.6 eV for

AUST

AND

MADDIN:

SUBGRAIN

STRUCTURE

OF

637

MO

energy for the partial recovery

of electrical resistivity

produces

3.5 and 7 eV.

a value

of between

results are interpreted

These

in terms of the suggestions

of

Mott and Seegar that the phenomena of recovery of electrical resistivity and polygonization are dependent

on a dislocation

climb

process.

Recovery

of

electrical resistivity may also be considered in terms of a realignment of piled-up groups of dislocations into

configurations

A relatively room-temperature

FIG. 6. Laue reflections from crystal M-6 after (1) (2) (3) (4)

containing

large

increase

bending

less

strain-energy.

of resistivity

of

due to

molybdenum

single

crystals was observed. The begimring of a rapid increase in resistivity was found to coincide with the

room-temperature bending, 1 hour at 1550°C. 8 hours at 155O”C, 20 hours at 1550°C.

initiation

of intersecting

be explained

in terms

slip bands. of a high

This result may concentration

of

“frozen-in” vacancies and piled-up groups of dislocaGood agreement tions formed by crossing dislocations. was obtained

between

the experimentally

area density of dislocations

measured

and that calculated

using

the Cottrell formula for the excess density as a function of the radius of curvature experimental in

bent

consistent

and

observations annealed

of the bent crystal. of

molybdenum

with the dislocation

of sub-boundaries,

subgrain

The

formation crystals

are

model of the structure

and with the dislocation

mechanism

of polygonization. ACKNOWLEDGMENTS

The authors would like to acknowledge FIG. i. Sub-boundaries revealed by alignment of etch pits in crystal M-10 after 12.hr anneal at 1550°C. Electrolytically x 700. polished and electroetched 15 see in 5% oxalic acid.

the

climbing

silicon-iron A higher

of dislocations

in bent

and annealed

crystals obtained by Dunn and Hibbard.(lT) activation

molybdenum

energy

might

be expected

for

in view of its much greater temperature

of melting as compared

with silicon-iron.

SUMMARY

Sub-boundaries

which

separate

regions

of

mis-

orientation molybdenum

of 0.01” single

to 0.02” were observed in crystals subjected to slight

deformation

by bending or tension at approximately

2000°C. No experimental evidence of polygonization, recovery of electrical resistivity, or recrystallization was found in crystals bent only at room temperature to radii from 8 cm to 1.5 cm and annealed for periods up to 10 hours at 1400°C. However, evidence of polygonization was observed in bent molybdenum crystals after isothermal annealing at approximately 1550% for periods of 1 to 20 hours. A partial recovery of the total increase of resistivity due to bending was also found to occur during the annealing An approximate calculation of the

at 1550%. activation

the helpful

discussions

of Drs. N. K. Chen, R. IV. Cahn, and F. C. Miller. The research was sponsored at The Johns Hopkins University by the Office of Naval Research. REFERENCES

1. R. W. CAHN J. Inst. Metds 76, 121 (1949). 2. C. G. DUNN and F. W. DANIELS l’mns. Amer. Inst. Min. Met. Eng. 191,147 (1951). 3. N. F. MOTT Proc. Phys. 8oc. BS4, 129 (1951); Report of 9th Solvuu Conference (1952). Dislo&tio&s cmtl Plastic Flow in C’rystala 4. A. H. C&R& Oxford, Clarendon Press, 182 (1953). Conference on Defects in Crystal 5. A. SEEGARInternational line SoEids Univ. Bristol, July, 1954. 6. P. JONGENBURGER Phys. Rev. 90, 710 (1953). 7. F. R. N. NABARRO Report of the Co$erence on Strength of Solids (London: Physical Sot.) 75 (1948). 8. N. F. hIOTT Phil. Mag. 43, 1151 (1952). 9. N. K. CHEN, R. MADDIN, and R.B. PONI) Trans. AmeT. Inst. Min. Met. Eng. 191, 461 (1951). 10. K. T. AUST, R. MADDIN, and N. K. CHEN Trans. Amer. Inst. Min. Met. Eng. 197, 1477 (1953). 11. N. K. CHEN and R. MADDIN Tmns Amer. Inst. Min. Met. Eng. 191, 531 (1951). 12. A. A. HENDHICKSON and E. S. MACHLIN Actcc Met. 3, 64 (1955). 13. C. G. DUNN and W. R. HIBBAR~ JR. Amer. Inst. Min. Met. Eng. Research in Progress. Chicago, Feb. 1955. 50, 161 (1928); 14. M. MASID~ and 0. SACHS Zeit. Physik 51, 321. 15. T. B~oo_nl PTOC. Phys. Sot. Bf35, 871 (1952). 16. W. GEISS and J. A. M. VAN LIEMPT Z&t Physik 41, 867 (1927). 17. C. G. DUNN and W. R. HIBB~RD JR. Private Communication.