The effect of compressional plastic deformation on the superconducting transition temperatures of tin alloys

Scripta

METALLURGICA

THE

Vol. 7, pp. 1011-1018, 1973 P r i n t e d in the U n i t e d States

EFFECT

Press,

Inc.

D E F O R M A T I O N ON T H E T E M P E R A T U R E S OF TIN A L L O Y S

OF C O M P R E S S I O N A L

SUPERCONDUCTING

Pergamon

PLASTIC

TRANSITION

M.L. Swanson and A.F. Q u e n n e v i l l e C h a l k River N u c l e a r L a b o r a t o r i e s A t o m i c E n e r g y of C a n a d a L i m i t e d Chalk River, Ontario, C a n a d a

(Received

June

29,

1973)

Introduction It has been

observed

of the n o n - c u b i c large

compressional

torsional ual"

plastic

electrical

small

torsion

stresses latter

(5),

the

superconducting

deformations

deformations

transition

increments

and p a r t l y

as much

temperatures

as AT

c (1-3).

at low t e m p e r a t u r e s

of In or TI, w h i c h

as m e a s u r e d

be due p a r t l y

(3),

(3).

plastic

in Tc,

could

deformations

that

In, T1 and Sn are i n c r e a s e d

resistivity

decrease

difference

and

metals

produced

to d i f f e r e n t

to d i f f e r e n t

point

defects

(4).

in d i f f e r i n g

dislocation

The p r e s e n t

experimental

results

by the

in c o m p r e s s i o n

distributions

for Sn alloys

in a

This

produced

of d e f o r m a t i o n

resulting

"resid-

resulted

or m a g n e t i c a l l y

modes

However,

comparable

of Ap 0 = 10 -7 ohm cm,

resistively

T c = 0.3°K by

and internal

support

the

explanation.

The

introduction

presumably because

of a s m e a r i n g

electron

linearly

impurity

because

concentrations

of changes

to

atoms

impurity

(6,7),

vacancies

(8) and

of the energy

concentrations solute

gap by the a d d i t i o n a l

up to %0.2

concentration

at.%

(6).

in Sn,

T

c

At h i g h e r

up to %1 at.%, of changes above

point

(9).

(impurities

superconductors d e c r e a s e s T c s l i g h t l y

increasing

Point

T of Sn d e c r e a s e s further in a nonc in the e l e c t r o n density of states (6). At

1 at.%,

in the e l e c t r o n - p h o n o n

irradiation-induced impurity

For

with

concentrations,

linear manner,

defects

out of the a n i s o t r o p y

scattering.

decreases impurity

of point

self-interstitials)

defects

an increase

interaction

in T may occur, on account c parameter. The e f f e c t of

on T

defects

appears to be larger c do not g e n e r a l l y broaden

than the

that of superconduct-

ing transition. Dislocations ways,

of the point (a)

introduced

w h i c h may be d i f f i c u l t defects

Dislocations scattering,

by plastic to separate

produced

can d e c r e a s e

deformation

can a f f e c t

from one another

T in several c and from the e f f e c t

by the deformation: Tc,

just as is u s u a l l y

because

of the a d d i t i o n a l

observed 1011

for small

electron

impurity

concentrations.

1012

C O M P R E S S I O N A L PLASTIC D E F O R M A T I O N AND THE S U P E R C O N D U C T I N G T R A N S I T I O N

Vol.

7, No.

i0

This e f f e c t h a s been o b s e r v e d for A1 p l a s t i c a l l y d e f o r m e d at 4 o or 300°K (b)

(i0), but was not o b s e r v e d for Ta

(ii).

It has been c a l c u l a t e d that the i n t e r a c t i o n of e l e c t r o n s w i t h v i b r a t i n g dislocations

can produce a small increase in T of < 0.1°K c e x p e r i m e n t a l v e r i f i c a t i o n of this has been obtained. (c)

The internal stresses caused by d i s l o c a t i o n p i l e - u p s d e f o r m e d metals cause a b r o a d e n i n g of the

(13,14).

in p l a s t i c a l l y

s u p e r c o n d u c t i n g transition,

b e c a u s e T c of a small volume under c o m p r e s s i o n volume under tension is raised

(12), but no

is lowered,

and T c of a

Since regions of higher T

c e f f e c t i v e l y short circuit the regions of lower Tc, an increase in T c is m e a s u r e d resistively. polycrystalline strains

A similar effect is o b s e r v e d in s m a l l - g r a i n e d

samples, where thermal c o n t r a c t i o n s

cause internal

(14-16).

The c o m b i n e d e f f e c t of room t e m p e r a t u r e plastic d e f o r m a t i o n and impurities in Sn has been i n v e s t i g a t e d by L a z a r e v et al.

(17).

They found that T

of c in a g r e e m e n t w i t h

a n n e a l e d Sn was d e c r e a s e d by Sb c o n c e n t r a t i o n s up to 0.5%, e a r l i e r results

(6).

0.18 mm diameter,

However,

after drawing the alloys at 300°K to w i r e s of

the t r a n s i t i o n t e m p e r a t u r e s of all alloys were the same,

0.020°K h i g h e r than that of pure a n n e a l e d Sn.

Thus the p l a s t i c d e f o r m a t i o n

a p p a r e n t l y e l i m i n a t e d the e f f e c t of the impurity on Tc, while small p o s i t i v e dislocations mobile.) 350°K.

AT

from the d e f o r m a t i o n - i n d u c e d defects.

introducing a

(Presumably only

c r e m a i n e d after the 300°K d e f o r m a t i o n since point defects w o u l d be

The e f f e c t of d e f o r m a t i o n was removed by p r o l o n g e d a n n e a l i n g at The t r a n s i t i o n w i d t h s and grain sizes were not reported.

results for A1 indicate that T locations

(i0).

In contrast,

is d e c r e a s e d by both impurities and dis-

c R e l a t e d r e s e a r c h indicates that in some cases the e f f e c t of

d i f f e r e n t defects may be opposed; the e f f e c t of p a r a m a g n e t i c

for example,

diamagnetic

impurities on T c of In

In the p r e s e n t experiments,

impurities

reduce

(18).

we have i n v e s t i g a t e d the e f f e c t of

c o m p r e s s i o n a l p l a s t i c d e f o r m a t i o n at 4OK on the s u p e ; c o n d u c t i n g t r a n s i t i o n t e m p e r a t u r e s of Sn-0.10 at.% Bi and Sn-l.0 at.% In alloys. Experimental Method The alloys Sn-0.10 at.% Bi and Sn-l.0 at.% In were p r e p a r e d by m e l t i n g the h i g h p u r i t y e l e m e n t s to 0.025 cm thickness,

in e v a c u a t e d p y r e x capsules.

and samples a p p r o x i m a t e l y

w e r e cut and a n n e a l e d for 20 min.

at 100°C.

The slugs w e r e r o l l e d

2 cm long by 0.050 cm wide

The grain sizes were ~0.01 cm.

The r e s i d u a l r e s i s t i v i t i e s at 4.2°K w e r e 9 x 10 -8 ohm cm for the Sn-0.10 at.% Bi alloys and 5 x 10 -7 ohm cm for the Sn-l.0 at.% In alloys. w e r e a t t a c h e d by s o l d e r i n g w i t h In. potentiometrically,

Potential

leads

The sample r e s i s t a n c e s were m e a s u r e d

u s i n g currents of 0.01 to 0.i ampere.

The r e s i s t i v i t y at

Vol.

7, No.

I0

a temperature

COMPRESSIONAL PLASTIC DEFORMATION AND THE S U P E R C O N D U C T I N G T R A N S I T I O N

T was

1013

g i v e n by PT = RT P293/R293

where

R T and R293 were

temperature Sn-0.10

at.%

alloys.

Bi alloys

The e f f e c t

ing the r e s i s t a n c e Rule was

the m e a s u r e d

resistivities

assumed

were

and

resistances

at T and at 293°K.

The room

taken as P293 = ii.i x 10 -6 o h m cm for the

P293 = 11.5 x 10 -6 ohm cm for the Sn-l.0

of changes

in sample

at 293°K before

dimensions

and after

to be a s u f f i c i e n t l y

was e l i m i n a t e d

the deformation.

accurate

at.%

In

by m e a s u r -

Matthiessen's

approximation

for the p r e s e n t

experiments. A sample was attached a brass

through chamber

an e v a c u a b l e

dewar.

carbon

pressure.

resistance

0.002°K.

Annealing

and p a s s i n g

was

the chamber.

constantan

accomplished

a current

The a n n e a l i n g

temperatures

respectively

approximate formations

%0.01°K

agreement

with

at 4.2°K w h i c h

1.0 x 10 -7 ohm cm in each at.%

Bi,

and AT c = 0.09°K

were

in a p p r o x i m a t e Apo

(3).

compressional There was

Thus

plastic

on Tc,

drawing

liquid h e l i u m

contained

was m e a s u r e d

w h i c h was c a l i b r a t e d were

c by raising

determined the

sample

200 m A through

temperatures

chamber

of a n n e a l e d 0.05°K

earlier

results

produced alloy,

T

with

of

the

heater

a copper-

as was o b s e r v e d

In

for dilute

for Sn-0.10

values

AT

removed

additive.

the e f f e c t

alloys

after

transition

of Sn-l.0

at.%

In w h i c h

had been

compressionally

for pure

Sn,

broadened

(defined

the t r a n s i t i o n

to a half w i d t h P/P4.2

F =

changed

reduced

was c o n s i d e r a b l y

0.i060K

from 0.25

as the t e m p e r a t u r e annealing

of

deformation

(17).

observed

which

of AT

c = 0.13°K for c by i m p u r i t i e s and by Sn,

in Fig.

formation,

de-

= 0.15°K

approximately

Sn-Sb

in

of Ap o =

These

in T c of Sn c a u s e d

deformation

at.% Sn,

increments c

i).

for pure

at 4.2°K were

annealed

compressional

by AT

(Fig.

Bi and Sn-l.0

of pure

resistivity

the r e s u l t

that p l a s t i c

c After

had i n c r e a s e d at.%

at.%

than T

(6).

residual

c for Sn-l.0

deformation

Sn-0.10

lower

to Ap ° = 1.0 x 10 -7 ohm cm is shown

Isochronal

above

with

at 4.2°K

Tc

by h e l i u m

a constantan

deformed

between

in

by a

to an a c c u r a c y

were m e a s u r e d

in

and D i s c u s s i o n

the changes

at 293°K

The r e s i s t i v e

and

agreement

no i n d i c a t i o n

impurities by wire

by a p l u n g e r

sample was c o n t a i n e d

thermocouple.

The t r a n s i t i o n

the same

with

in T

of about

The

temperature

thermometer

changes

fiber discs

press.

in c o n t a c t

Results

In were

two p h e n o l i c

The t r a n s i t i o n

In this way,

He level, around

between

to a h y d r a u l i c

and was d i r e c t l y

glass

Bradley-Allen vapor

compressed a bellows

where

both

2.

As was by the de-

(defined

as the t e m p e r a t u r e

to 0.75).

The t r a n s i t i o n

P/P4.2

T c and

= 0.50)

was

increased

F, and the r e c o v e r y

interval

temperature by 0.090°K.

was c o m p l e t e

1014

C O M P R E S S I O N A L PLASTIC D E F O R M A T I O N AND THE S U P E R C O N D U C T I N G T R A N S I T I O N

after a n n e a l i n g at 164°K. anneal

(3.663°K),

Vol.

i0

The reason for a s o m e w h a t lower T c after this

as c o m p a r e d w i t h the initial value,

after the 300OK anneal,

7, No.

3.672°K,

3.674°K and the value

is not known.

0.16 I i ZITc o Sn (°K) O . 1 2 - e S n - O . l O % 8i

I

I

el "

f

Z

-

0.08

0.04

I 20

0,00~

0

I

I

40 APo

I

I

60 80 100 ( 1 0 - 9 o h m cm)

120

FIG. l The change in transition temperature ATc versus the r e s i s t i v i t y increment aPo caused by compressional plastic deformation of pure Sn (3) and Sn alloys at 4.2°K. The applied pressure was relaxed for a l l measurements. The measuring current was 0.01 A. Tc was the temperature where P/P4.2 = 0.5. 1,00

I

I

P/P4.z O.80

0.60

/ f /

0

/ / ~

~

> // /

0.40

9 • • Q

.60

3.64

3.68

3.72

Z ~ K ANNEAL

X 40~ ANNEAL

0.20

O.OC

ANNEALED

I 3.76 T

I 3.80 (=K)

I 3.84

-

60*K ANNEAL 80eK ANNEAL IOOeK ANNEAL 164°K ANNEAL 300~K ANNEAL

I 3.88

I 3.92

t 3.96

4.00

FIG. 2 Superconducting transitions of Sn-l.0 at.% In before deformation, after compressional deformation at 4.2°K, and after successive isochronal 5 min. pulse anneals. The measuring current was 0.01A. p is the electrical r e s i s t i v i t y at a temperature T and P4.2 is the r e s i s t i v i t y at 4.2°K.

Vol.

7, No.

i0

C O M P R E S S I O N A L PLASTIC D E F O R M A T I O N AND THE S U P E R C O N D U C T I N G T R A N S I T I O N

1015

The r e c o v e r y data for Sn-l% In is c o m p a r e d w i t h that for pure Sn Fig.

(3) in

3.

Oi

O~ W > O 40 ~9 W I.-

6

_

Sn

L,I LD

80

~F

•

I00 0

I

I

20

40

I 60

i 80

i

I00

120

T (°K) FIG. 3

Isochronal recovery of the changes in transition temperature ~Tc., electrical resistivity Ap and transition half width A? for compressionally deformed Sn (3) and Sn-l% In (from Fig. 2). The a d d i t i o n of 1% In s u p p r e s s e d the r e c o v e r y of Ap from 40-i00°K.

M o s t of the

r e c o v e r y of Ap in this t e m p e r a t u r e range is due to point d e f e c t m i g r a t i o n 20), a l t h o u g h some d i s l o c a t i o n m o t i o n p r o b a b l y also occurs suppression indicates

d e f e c t a n n e a l i n g does not s i g n i f i c a n t l y affect T

it follows that point

(Note that c the r e c o v e r y of AT c for the alloy was 11%, as c o m p a r e d w i t h 3-6%

b e l o w 20°K,

for the pure m e t a l

(3,19).

This d i f f e r e n c e

in a d i r e c t way.

lies just outside e x p e r i m e n t a l

The r e c o v e r y of changes in the t r a n s i t i o n half width AF for the alloy,

also shown in Fig.

3, is p a r a l l e l to the r e c o v e r y of AT . C

These a n n e a l i n g results, t e m p e r a t u r e curves of Fig. e f f e c t of i n t e r n a l stresses deformation, constraints

experiments,

t o g e t h e r with the form of the r e s i s t i v i t y -

2 for Sn-l% In can be e x p l a i n e d largely by the from d i s l o c a t i o n pile-ups.

a large h y d r o s t a t i c on the sample.

10 -5 d e g . / a t m

observed;

(19,

Thus this

that p o i n t defects were trapped by the i m p u r i t y atoms,

and since there was little change in the r e c o v e r y of ATc,

error).

(20).

During compressional

stress c o m p o n e n t is p r e s e n t because of the

Hydrostatic pressure

lowers T of Sn by -4.95 x c (21), so that the m a x i m u m c o m p r e s s i o n a l p r e s s u r e used in these

2000 atm., w o u l d lower T c by 0.1°K.

before

the a p p l i e d stress was relaxed,

This change was in fact the d e f o r m e d curve of Fig.

2

1016

COMPRESSIONAL PLASTIC DEFORMATION AND THE SUPERCONDUCTING TRANSITION

was displaced ~0.1°K downwards.

Vol.

7, No.

10

Thus the internal stresses in the alloy

caused by dislocation pile-ups must be of the order of 2000 atm. relaxation of the applied stress,

After

it is expected that both tensile and

compressive stresses of the order of 2000 atm. exist in the alloys because retreating dislocations will pile up against barriers. have transition temperatures higher than normal, have T c lower than normal curves of Fig.

(13,14).

Regions under tension

and regions under compression

The form of the resistivity-temperature

2 is thus attributed to the existence of a spectrum of transi-

tion temperatures,

which exist in macroscopically

long range forces between dislocations.

sized regions because of the

All the resistivity curves meet at

the normal T c since the regions under compression do not completely block the superconducting paths through regions of zero or positive tension. Following this model,

and AF occurs by relaxation of c the internal stresses as dislocations overcome barriers by thermally activated motion.

the recovery of AT

There is considerable evidence that such dislocation rearrange-

ment does occur at low temperatures

in f.c.c, metals

motion may be assisted by point defect migration

(20).

This dislocation

in the low temperature

recovery stages. In the case of In and T1 samples which had been torsionally deformed to resistively increments comparable to those of the present experiments

(AP0 =

10 -7 ohm cm), it appears that the residual stresses were much smaller

(4).

Consequently,

a small negative AT

was observed, which was probably mainly due

c to the combination of point defect and dislocation scattering centers.

During

annealing of these metals below 70°K, it was found that T c decreased further (reverse recovery),

which could be due to relaxation of internal stresses,

in the present results. ments is essential

The measurement of transition widths

as

in such experi-

for the separation of effects from point defects and from

internal stresses. References (i)

V.I. Khotkevich,

V.R. Golik,

Zh. eksp. teor. Fiz.,

(2)

G. von Minnegerode,

(3)

M.L. Swanson, A.F. Quenneville,

(4)

J. Hasse, W. Seifritz,

(5)

P.J. Sherwood, (1967).

(6)

E.A. Lynton,

B. Serin, M. Zucker, J. Phys. Chem. Solids, ~, 165

(7)

E.A. Lynton,

Superconductivity,

Z. Physik,

154, 442

2_.20, 427

(1959).

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Z. Physik 193, 52

(1950).

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Methuen

(1969).

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Vol.

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i0

COMPRESSIONAL PLASTIC DEFORMATION AND THE SUPERCONDUCTING TRANSITION

(8)

W. DeSorbo,

(9)

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J. Phys.

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Chem.

L. van Poucke,

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A.F.

(20) M.L.

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D.P.

Lab. Univ.

Seraphim,

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phys.

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stat.

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Materials

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