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Submitted on 1 Jan 1981
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LOW TEMPERATURE THERMAL CONDUCTIVITY OF HgI2 SINGLE CRYSTALS
A. de Goër, M. Locatelli, I. Nicolau
To cite this version:
A. de Goër, M. Locatelli, I. Nicolau. LOW TEMPERATURE THERMAL CONDUCTIVITY OF HgI2 SINGLE CRYSTALS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-265-C6-267.
�10.1051/jphyscol:1981677�. �jpa-00221613�
JOURNAL
DE PHYSIQUECoZZoque C6, suppZSment au n012, Tome 42, ddcembre 1981 page c 6 - 2 6 5
LOW TEMPERATURE THERMAL C O N D U C T I V I T Y OF H g 1 2 S I N G L E CRYSTALS
A.M. D e Gogr,
M.
L o c a t e l l i and I . F . ~ i c o l a u *Service des Basses TempSratures, Laboratoire de &yophysique, Centre dlEtudes NucZSaires de GrenobZe, 85 X, 38041 GrenobZe Cedex, France
* .Laboratoire dlEZectronique e t de TechmZogie de ZIInfomatique, .kboratoire de CristaZZogenBse e t Recherche sur Zes M a t S r i m , Centre dlEtudes NucZSaires de GrenobZe, 85 X, 38041 GrenobZe Cedex, France
A b s t r a c t - The thermal c o n d u c t i v i t y o f a-HgI2 s i n g l e c r y s t a l s has been mea- sured f r o m 50 mK t o 200 K, and t h e r e s u l t s d i s c u s s e d q u a l i t a t i v e l y and quan- t i t a t i v e l y . I t i s concluded t h a t phonons a r e s c a t t e r e d m a i n l y b y c l u s t e r s o f i n t e r s t i t i a l d e f e c t s due t o t h e l a c k o f s t o i c h i o m e t r y o f t h e c r y s t a l s .
Experimental - Several c r y s t a l s have been s t u d i e d , which were grown e i t h e r f r o m s o l u - t i o n (LETI c r y s t a l s ) [I] o r f r o m t h e vapor phase (EGG-crystals) [21. The samples a r e p a r a l l e l e p i p e d s o f t y p i c a l c r o s s - s e c t i o n 3 mm
x3 mm, g e n e r a l l y c u t a l o n g a - a x i s e x c e p t one which i s p a r a l l e l t o c - a x i s . The d e v i a t i o n f r o m s t o i c h i o m e t r y o f t h e L E T I - c r y s t a l s has been a l r e a d y s t u d i e d C31.
R e s u l t s and q u a l i t a t i v e d i s c u s s i o n - The r e s u l t s o f t h e thermal c o n d u c t i v i t y measu- rements f r o m 50 mK t o 200 K a r e shown i n f i g . 1 . The main f e a t u r e s o f these r e s u l t s a r e
:( i ) t h e a n i s o t r o p y o f t h e thermal c o n d u c t i v i t y K i n t h e whole t e m p e r a t u r e range ( i i ) t h e sample dependence o f K below 10 K, ( i i i ) t h e d e p a r t u r e o f t h e expec- t e d ~ 3 v a r i a t i o n down t o t h e l o w e s t temperatures, which i s i l l u s t r a t e d i n t h e K / T ~ p l o t s ( i n s e r t o f f i g . 1 ) . The c a l c u l a t e d v a l u e s o f K / T ~ i n t h e boundary s c a t t e r i n g l i m i t a r e a b o u t 1 W cm-1 K-1 and a r e n o t reached even i n t h e case o f t h e c r y s t a l LETI 14, i n d i c a t i n g t h a t phonons a r e s c a t t e r e d by s t r u c t u r a l d e f e c t s . The shape o f t h e K / T ~ curves suggest t h e p o s s i b i l i t y o f a r e s o n a n t s c a t t e r i n g a t v e r y l o w tempe- r a t u r e s (T
<5 10-2 K), g i v i n g some evidence o f t h e presence o f l a r g e c l u s t e r s o f d e f e c t s , w i t h t y p i c a l dimensions equal o r l a r g e r t h a n 0.3 um 141.
Q u a n t i t a t i v e a n a l y s i s - The thermal c o n d u c t i v i t y has been c a l c u l a t e d w i t h i n t h e sim- p l e i s o t r o p i c Debye model [ 5 1 :
w i t h a t o t a l phonon r e l a x a t i o n r a t e
: .-I=
- 1+ Au4 +
T - 1=B P-P ( 1 )
I n a f i r s t s t e p , t h e c l a s s i c a l c o n t r i b u t i o n s from boundary s c a t t e r i n g
( r g - l )and i s o t o p e s c a t t e r i n g (Ao w4) have been c a l c u l a t e d , and t h e phonon-phonon i n t e r a c t i o n t e r m a d j u s t e d t o d e s c r i b e t h e r e s u l t s i n t h e i n t r i n s i c t e m p e r a t u r e range T
>15 K
=
BU
u2T exp (-9/aT), w i t h d i f f e r e n t values o f BU and
af o r samples / / a - a x i s and // c - a x i s ) . The t h e o r e t i c a l c u r v e such c a l c u l a t e d f o r t h e sample LETI 14 suppo-
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981677
C6-266 JOURNAL
DE PHYSIQUE
K(W.cm!K!)
Hg.12
.16-1
.
13-3.s3-7 Uaxc
c
. '
A t f. . . .
. . .. .
.. . -. .
.. . ..-
. .
.. .:
.. .
-. .. - .--.-- ...
. .
. . . .
lo?
lo1 1d
r 1 1 1 1 1 1 1 1,
1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1.
, 1 1 1 1 1 1 1 , 1 IW2 lo-' 1 10 102 T(K)
F i g u r e 2 - Experimental p o i n t s
: 0,LETI 14
;1, LETI-16 ( a ) ; A, LETI-16 ( b ) . S o l i d l i n e s a r e c a l c u l a t e d .
F i g u r e 1.
sed t o be p e r f e c t i s shown i n f i g . 1 . The e x p e r i m e n t a l r e s u l t s o f a l l samples 1 a- a x i s have been f i t t e d by a d j u s t i n g t h e f r e q u e n c y independent t e r m
r g - land t h e p o i n t d e f e c t c o e f f i c i e n t A. T h e r e f o r e phonon s c a t t e r i n g by s t r u c t u r a l d e f e c t s i s d e s c r i - bed by t h e parameters
T ~ = -( r B - ')exp.
~- ('B-' I c a l c . and A - A,. I n t h e case o f h e a t f l o w // c - a x i s , i t was n o t p o s s i b l e t o a c h i e v e a f i t i n t h i s s i m p l e way and
i twas necessary t o add a t e r m Gw2 i n t h e t o t a l r e l a x a t i o n r a t e ( 1 )
;t h i s t e r m des- c r i b e s phonon s c a t t e r i n g b y p l a n e d e f e c t s 161. The parameters used a r e g i v e n i n t a b l e 1 a n d e x a m p l e s o f f i t s a r e i l l u s t r a t e d i n f i g . 2.
TABLE 1
Sample
LET1 14 LETI 13 EGG-S3-7 LETI 16 ( a ) LETI 16 (b)
b r i e n t a t i o n ( s )
0
o
0 5.8 1 0 - l 8 2.3 10-17 ( ~ m - ~ ) Nc
9.2 l o 9
1.9 1o1O 5.4 1 0 l 0 1.1 1011 1.7 l o 1 '
T ~ - '