AMPLITUDE-DEPENDENT SOUND ATTENUATION IN bcc 3He CRYSTALS WITH 4He IMPURITIES

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AMPLITUDE-DEPENDENT SOUND ATTENUATION IN bcc 3He CRYSTALS WITH 4He IMPURITIES

I. Iwasa, N. Saito, H. Suzuki

To cite this version:

I. Iwasa, N. Saito, H. Suzuki. AMPLITUDE-DEPENDENT SOUND ATTENUATION IN bcc 3He

CRYSTALS WITH 4He IMPURITIES. Journal de Physique Colloques, 1981, 42 (C5), pp.C5-37-C5-

41. �10.1051/jphyscol:1981504�. �jpa-00220960�

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JOURNAL DE PHYSIQUE

CoZZoque C5, suppZQment au nO1O, Tome 4 2 , octobre 1981 page C5-37

3 4

AMPLITUDE-DEPENDENT SOUND ATTENUATION I N bcc He CRYSTALS WITH He IMPURITIES

I. I w a s a , N. S a i t o and H. Suzuki

Department o f Physics, University o f Tokyo, Bunkyo-ku, Tokyo 113, Japan

Abstract.- The attenuation of longitudinal sound wave at 10

KEz

bas investiqated in bcc 3 ~ e crystals with 4 ~ e inpurities at a molar v o l u ~ e of 24.4 cm3/mole. The attenuation became amplitude- dependent after the crystals were cooled below the phase sepa- ration te~perature. Kamely, the amplitude dependence appeared at 86 mK and 98 mK for 4 ~ e concentrations

xq = 480

ppm and 1600 ppm, respectively, and disappearedat 350

mK

irrespective of

xq.

The critical amplitude above which the attenuation increased was independent of

x4

and

T.

It is proposed that screw dislocations which were multiplied in the course of the phase separation were responsible for the effect. The critical resolved shear stress is estimated to be

T~ =

5x10-5p from the critical amplitude, where

p

is the shear rrodulus. The value of

T,

is considerably lower than the Peierls stress so that the dislocations possibly tunnel the Peierls barrier.

It is well known that a solid solution of 3bie and 4 ~ e undergoes a phase separation at a temperature TPSs1) The phase separation curve is well described by the regular solution theory, but it is slightly asymmerical due to the difference between 3 ~ e and 4 ~ e atoms in the amplitude of the zero-point vibration. 2 r 3 ) We report here the first ultrasonic measurements on bcc 3 ~ e crystals with 4he impurities which are cooled below the phase separation temperature.

The concentration of 4 ~ e in the sample gas, x4, was determined by a mass-spectrometer-type leak detector (Shimadzu Model

MS-E)

with an accuracy of 5%. All the crystals were grown at a constant pressure of

33

atm. The corresponding solidification temperature was

0.7

K and the molar volume was 24.4 cm /mole. After the solidification the

3

filling capillary was blocked and the attenuation and velocity of the longitudinal sound at 10 HBz were measured at the constant volume.

Amplitude dependence of the attenuation was found when the

crystals were cooled below a temperature TA ( 2 100 mK). Figure 1

shows the attenuation in crystal No.% with 480 ppm 4he at two tempera-

tures above and below TA on a cooling run at input amplitudes, I,

between 10 and 60 dB. The input amplitude of RF-pulses was varied

by a step attenuator and the amplitude of the sound signal was read

on the oscilloscope.

A

20-dB attenuator was inserted between the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981504

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C5-38 JOURNAL DE PHYSIQUE

receiver transducer and the ampli-

S T R E S S A M P L I T U D E i d y n l c m 2 )

fier to avoid distorsion of large

I o3 1 o4

I I I , , , , . . . . . . , . I 05

signals, if necessary. The rela- 4 t

^{NO. 8} x 4 = 4 8 0 p p m

$ 1

tive attenuation in Fig. 1 was

:/.

^*eoe**s* e6e**ae-o*

calculated by assuming a

=

0 dB at

T = 1 1 4 O~OOO.O.OOO rnK

.

T

=

114

mK

and I

=

20 dB.

o O O ~ O O o V 6

The attenuation at 114

mK

is

;

^, ^, ^, ^, ^, ^,

1

-

" 4

essentially independent of the

2

input amplitude. At

7 7 mK,

on the

77 m ~ ^a*

0

.*..

^D...

...

^.o*-*-eo

other hand, a distinct amplitude

dependence is observed: the

10 2 0 3 0 4 0 5 0 6 0 I N P U T A M P L I T U D E ( d B )

attenuation below 30 dB is con-

stant and its value is the same Fig. 1

:

Attenuation in crystal as at 114 mK (low-amplitude No.8 at two temperatures on a

cooling run.

plateau), a increases with

I

We define a critical amplitude I as the amplitude at which the

C

between 30 and 50 dB (transition

transition region begins. We find

go O ~ D ~

region) and a is constant above

50 dB (high-amplitude plateau) .

^{N O .}¹ X 4 = 5 9 0 p p m

0 ~ ~ 0 * ~ ~

oo

observe the amplitude dependence

Ic

=

32 dB from the data at

7 7

mK

^z 2

in Fig. 1.

I-

-l

Figure 2 shows how the ampli-

_Z³

tude dependence varies on a

w I-

I-

warming run. At 190 mK we still

u

and it disappears at 350 mK. The / O ~ ~ ~ ~ , , , , , I

1 0 2 0 3 0 4 0 5 0

critical amplitude does not change

A M P L I T U D E ( d B )

T=67mK ⁰

- 0 . 0 0 0 0 . 0 0 0 0 ~ ~ ~ ~ . . 0 e ~ * ~ ~ eD O

190mK ooe

-

O e O O ~ o e ~ ~ ~ ~ e O O . O O O O ~ ~ ~ o O

with temperature from

6 7

to 190

mK.

The variation of Ic from Fig. 2

:

Attenuation in crystal crystal to crystal is also neg- No.1 at three temperatures on

a warmina run.

ligible (Table

I).

We may there- fore take a's at I

=

20 dB and 50

dB as representatives for the low- and high-amplitude plateaus, res- pectively. The attenuation increment is defined as

Figure 3 shows a(20dB) and a(50dB) for crystal No.9. On the

first cooling (run

1)

a(5OdB) rose at TA

=

86

mK

and reached

6

dB at

78

nK.

Then the crystal was warmed up to 600

mK

(run 2). a(50dB) at

first remained constant, decreased gradually above 200

rnK

and

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diminished a t T B

=

350 mK. On the second cooling (run

3)

the

variation of cu (50 dB) was

_Z x r u n 3

similar to the first coolina.

_1:

50dB

In this run the temperature was

:2

bx

x

lowered down to 72 mK but no

appreciable chanae was observed below

78

mK. The attenuation

I

;, * ,

^e ^l

i:O$Bi\

, ,

"0 9 k i f

'It

at 20 dB was independent of

tem~erature within fl dB durina 0 100 200 300 400 the measurement.

T E M P . ( m K )

Figure 4 shows a similar

F i u .

3

: cu

(50 dB) and a (20 dB) in plot for crystal No.14 with crystal No.9 with x4

=

480 ppm.

x4

=

1600 ppm. At first the crystal was cooled to 60 mK (run

occurred between 90 and 110 mK and 5 i

1). Then it was warmed to 150

mK

(run

2)

and cooled to 60 mK

₂₀

(run

3).

The second warming was

up to 460 mK (run 4) , followed by

_{1 5 .}

the cooling down to 62.5 mK (run 5).

Finally the temperature was care- -

_{m 1 0}

fully raised to 140 mK (run 6). -

o

It was found that TA

=

98 mK fron

_z

a (50

dB)

on the cooling runs. On

!? 5 -

b

warming there were two stages of

_4.₃

z

^{O -}

recovery in a(50 dB). The first

the second was between 200 and 350 I * I

I

NO. 14 X 4 = 1 6 0 0 p p r n

- .

^{r u n 1}

*A rev ^{r u n 2}

? O

x r u n 3

A r u n 4

:

A A A

.

^{r u n 5}

x

rho

^{r u n 6}

-

xX

A

* . ' _.... _. _.

_• ^t A ^A^A_._._'_A_. _rr

I = 5 0 d B

mK. The first stage of recovery

2 0 dB

was never observed in crystals with

0 100 2 0 0 3 0 0 400

x4

=

480 ppm. The hysteresis of

T E M P . ( r n K )

a (50 dB) was reproducible when the

crystal was warmed above TB

=

Fig. 4

:

a(50 dB) and a(20 dB) in crystal No.14 with x4

=

1600 ppm.

350 mK.

In Fig. 4

u

(20 dB) also shows

a hysteresis which is, however, amplitude-independent.

The observed values of Ic, Aa,

T

and TB and the sound vecocity

A

vO are summarized in Table

I.

As seen from this table,

TA

increases

with x4 and Aa is also an increasinu function of x4, so that we may

suppose that the appearance of the amplitude dependence is related to

the phase separation. The curve in Fig. 5 represents the phase

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C5-40 JOURNAL DE PHYSIQUE

s e p a r a t i o n t e m p e r a t u r e TpS a s a

n

f u n c t i o n o f x 4 , which i s o b t a i n e d from t h e s p e c i f i c h e a t d a t a w i t h t h e a i d o f t h e r e g u l a r s o l u t i o n t h e o r y

and i s g i v e n by ^-100 -

1-2x4 TpS = 0.76

I n (1-x4) / x 4 ]

IK1 .

We f i n d TpS = 99 and 1 1 7 mK f o r x4 =

480 and 1600 ppm, r e s p e c t i v e l y , which o r 1 I I I

10-5 10-4 I 0-3 10-2

a r e h i g h e r t h a n TA a t c o r r e s p o n d i n g

X L

c o n c e n t r a t i o n s . T h i s r e s u l t seems

t o be r e a s o n a b l e because o f t h e F i g . 5 : TpS c a l c u l a t e d from e q . ( 2 ) v s . xq: C i r c l e s r e - f o l l o w i n g r e a s o n s : (1) T,, i s d e t e r - p r e s e n t experimental v a l u e s o f

L U

mined by warming t h e specimen w h i l e T ~ ' TA i s determined by c o o l i n g ; ( 2 ) seve-

r a l m i n u t e s a r e r e q u i r e d f o r phase s e p a r a t i o n ; ( 3 ) some s u p e r c o o l i n g may be p o s s i b l e ; and ( 4 ) phase s e p a r a t i o n s h o u l d proceed t o some e x t e n t b e f o r e t h e a m p l i t u d e dependence a p p e a r s .

I t seems a t f i r s t s i g h t t h a t t h e a m p l i t u d e dependence o f t h e a t t e n u a t i o n i s caused by t h e c l u s t e r s of 4 ~ e atoms formed a s a r e s u l t o f phase s e p a r a t i o n . However, i t i s n o t t h e c a s e b e c a u s e t h e ampli- t u d e dependence i s s t a b l e a t much h i g h e r t e m p e r a t u r e s t h a n TA and TpS, where t h e p h a s e - s e p a r a t e d s t a t e c a n n o t e x i s t .

Amplitude-dependent a t t e n u a t i o n i s u s u a l l y c a u s e d by d i s l o c a - t i o n ~ . ~ ) A l a r g e number o f d i s l o c a t i o n s a r e p o s s i b l y i n t r o d u c e d i n t h e c r y s t a l s by t h e phase s e p a r a t i o n because o f a s i z a b l e l o c a l d e f o r - mation accompanied. The molar volume o f a p u r e b c c 3 ~ e c r y s t a l a t

33 atm i s 24.4 cm /mole w h i l e t h a t o f a p u r e hcp 4 ~ e 3 c r y s t a l i s 20.4 cm /mole a t t h e same p r e s s u r e . 3 S t r a i n f i e l d around t h e c l u s t e r s of

T a b l e I . P a r a m e t e r s f o r t h e c r y s t a l s .

C r y s t a l Tm

'm

v~

X4

o

T~ T~ T~~ I c

(mK) (atm) (cm3/mole) (ppm) ( m / s ) ( m K ) ( m ~ ) ( m K ) ( d ~ ) ( d ~ )

No.1 744 33.6 24.29 590 494

-

350 102 32 12.4

No.8 703 32.8 24.39 480 490

-

350 99 32 6.7

No.9 703 32.8 24.39 480 475 86 350 9 9 30 6.4

No.11 697 32.7 24.40 1600 472 96 350 1 1 7 31 11.4

No.14 709 32.9 24.38 1600 501 98 340 117 31 15.5

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a l m o s t p u r e hcp 4 ~ e , which a r e formed by t h e p h a s e s e p a r a t i o n , s h o u l d be r e l a x e d by p l a s t i c d e f o r m a t i o n i n t h e m a t r i x o f b c c

3 ~ e .

I n a p r e v i o u s p a p e r 5 ) we r e p o r t e d a m p l i t u d e dependences f o r hcp 4 ~ e c r y s t a l s c o n t a i n i n g 30 and 300 pprn 3 ~ e . I t was a t t r i b u t e d t o un- p i n n i n g of t h e e d g e d i s l o c a t i o n s i n t h e b a s a l p l a n e from 3 ~ e i m p u r i t i e s b e c a u s e t h e c r i t i c a l a m p l i t u d e I~ depended upon t e m p e r a t u r e and 3 ~ e c o n c e n t r a t i o n . I n t h e p r e s e n t c a s e , on t h e o t h e r h a n d , Ic depends n e i t h e r on t e m p e r a t u r e n o r on 4 ~ e c o n c e n t r a t i o n . T h e r e f o r e t h e d i s - l o c a t i o n s i n t h e b c c 3 ~ e c r y s t a l s a r e of screw t y p e and t h e i r o b s t a c l e s a r e n o t 4 ~ e i m p u r i t i e s b u t t h e P e i e r l s p o t e n t i a l .

The s t r e s s a m p l i t u d e a, which c o r r e s p o n d s t o I c = 30dB i s e s t i -

3 2

mated t o b e 3x10 dyn/cm

.

The r e s o l v e d s h e a r stress i s g i v e n by T = Ro, where R i s t h e Schmid f a c t o r and R

2

1 / 2 . W e t h e n o b t a i n t h e n o r - m a l i z e d c r i t i c a l r e s o l v e d s h e a r s t r e s s i C / p

5

5 x 1 0 ~ ~ u s i n g

u

⁼^3x10⁷

dyn/cm2 a s t h e a p p r o p r i a t e s h e a r modulus.

The d e p t h of t h e P e i e r l s p o t e n t i a l AV o r e q u i v a l e n t l y t h e P e i e r l s s t r e s s T c a n b e e s t i m a t e d by s e v e r a l ways. The n o r m a l i z e d P e i e r l s

P

stress i s T / p = ( 3 ~ 6 ) x ~ o - ~ i n most b c c m e t a l s . I n t h e c a s e of b c c 3 ~ e t h e z e r o - p o i n t e n e r g y of a s t r a i g h t d i s l o c a t i o n P i s much l o w e r on t h e

h i l l o f t h e P e i e r l s p o t e n t i a l t h a n i n t h e v a l l e y o f t h e p o t e n t i a l s o t h a t AV i s r e d u c e d a t l e a s t by a f a c t o r of 1 5 i n a c r u d e e s t i m a t e . 6)

Hence

r

/p < 4 ~ 1 0 - ~ . E x p e r i m e n t s on t h e p l a s t i c d e f o r m a t i o n i n b c c 3 ~ e P

a t 54 a t m 7 ) - s u g g e s t s t h a t T

/u

i s of t h e o r d e r of 5 ~ 1 0 - ~ , which g i v e s P

a n u p p e r bound t o T / p a t 33 atm. I f t h e e s t i m a t i o n s a r e c o r r e c t , T

P C

i s an o r d e r o f magnitude s m a l l e r t h a n T A s Ic i s i n d e p e n d e n t of tem- p '

p e r a t u r e , t h e p o s s i b i l i t y o f t h e r m a l a c t i v a t i o n i s e x c l u d e d . T h e r e f o r e , w e may c o n c l u d e t h a t a d i s l o c a t i o n p e n e t r a t e s t h e P e i e r l s p o t e n t i a l b a r r i e r by t u n n e l i n g u n d e r an a p p l i e d stress which i s h i g h e r t h a n T ~ .

We a r e p r e p a r i n g a new equipment f o r t h e p l a s t i c - d e f o r m a t i o n measurement a t t e m p e r a t u r e s down t o 0.3 K i n o r d e r t o g e t a more r e l i a b l e v a l u e o f T

P ' R e f e r e n c e s

1) D.O. Edwards, A.S. McWilliams and J . G . Daunt: Phys. L e t t . - 1, 218 ( 1 9 6 2 ) .

2) W . J . M u l l i n : Phys. Rev. L e t t .

20,

254 ( 1 9 6 8 ) .

3) M.F. Panczyk, R.A. S c r i b n e r , J . R . Gonano and E.D. Adams: Phys.

Rev. L e t t .

21,

594 ( 1 9 6 8 ) .

4) A.V. G r a n a t o and K . ~ u c k e : J . Appl. Phys. - 27, 583 ( 1 9 5 6 ) . 5 ) I . Iwasa and H . Suzuki: J . Phys. Soc. J p n .

49,

1722 ( 1 9 8 0 ) . 6) H . S u z u k i : t o b e p u b l i s h e d .

7 ) A . S a k a i , Y . N i s h i o k a and H. S u z u k i : J . Phys. S o c . J p n .

46,

¹¹¹⁹

( 1 9 7 9 ) .