BASAL THERMAL CONDUCTIVITY OF TiSe2

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BASAL THERMAL CONDUCTIVITY OF TiSe2

C. Ayache, M. Nuñez-Regueiro

To cite this version:

C. Ayache, M. Nuñez-Regueiro. BASAL THERMAL CONDUCTIVITY OF TiSe2. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-338-C6-340. �10.1051/jphyscol:1981699�. �jpa-00221636�

JOURNAL DE PHYSIQUE

CoZZoque C6, supple'ment au n o 12, Tome 42, de'cembre 1981 page C6-338

B A S A L THERMAL C O N D U C T I V I T Y OF T i S e 2

C. A y a c h e and M. N u i i e z - R e g u e i r o

Service des Basses ~'e~npe'ratures - Laboratoire de Cryophysique, Centre drEtudes NucZe'aires de GrenobZe, 85 X - 38041 Grenoble Cedex, France.

A b s t r a c t - We p r e s e n t t h e f i r s t r e s u l t s on t h e thermal c o n d u c t i v i t y o f TiSe2.

F o r t h i s semimetal t h e h e a t t r a n s p o r t i s found t o o c c u r o n l y t h r o u g h phonons w i t h i n t h e i n v e s t i g a t e d temperature range (1.65

-

1 - I n t r o d u c t i o n - The semimetal TiSe2 undergoes below 200 K a phase t r a n s i t i o n essen- t i a l l y c h a r a c t e r i z e d b y a s u p e r l a t t i c e f o r m a t i o n w i t h t h e d o u b l i n g o f t h e u n i t c e l l . Several mechanisms have been proposed f o r t h i s t r a n s i t i o n 11-41 b u t no one has y e t been d e f i n i t e l y proved. As phonons a r e t h o u g h t t o p l a y a r o l e whose importance depends on t h e mechanism, t h e y deserve s p e c i a l a t t e n t i o n .

U s i n g n e u t r o n i n e l a s t i c d i f f r a c t i o n , t h e phonon d i s p e r s i o n curves have been mea- s u r e d b o t h a t room [ 5 1 and l o w temperatures [6]. They were seen t a be o f a Z-dimen- s i o n a l n a t u r e and a l s o t o e x h i b i t an anomalous b e h a v i o u r f o r a t r a n s v e r s e mode a t t h e L - p o i n t [6-71. A l s o a c e n t r a l peak was shown t o e x i s t [ 6 - 8 1 . S p e c i f i c h e a t measure- ments gave o n l y a s m a l l evidence o f t h e t r a n s i t i o n a t 200 K [ 9 ] . Zone c e n t e r o p t i c a l phonons were a l s o e x t e n s i v e l y i n v e s t i g a t e d . However t h e thermal c o n d u c t i v i t y has n o t been so f a r examined m a i n l y due t o t h e smallness and b r i t t l e n e s s o f t h e samples. Thus we have used a method s p e c i a l l y developped f o r measuring such samples f r o m h e l i u m up t o room temperatures [ l o ] .

2 - Experimental r e s u l t s - Several samples were measured. These a r e p l a t e l e t s o f a b o u t 50 um t h i c k and 0.2 x 0.5 cm f o r basal dimensions. They a r e m o n o c r y s t a l s b u t c e r t a i n l y c o n t a i n a l a r g e number o f s t a c k i n g f a u l t s . T h e i r e l e c t r i c a l r e s i s t i v i . t y a t room temperature i s t y p i c a l l y 1 . 1 x 1 0 - ~ n cmand t h e c h a r a c t e r i s t i c r e s i s t i v i t y r a t i o s a r e r e s p e c t i v e l y p (165 K)/ p (300 K) ^Q, 2.5 and p (300 K) / p (4.2 K ) ^Q, 4.

On t h e f i g u r e i s shown a l o g a r i t h m i c diagram o f t h e basal thermal c o n d u c t i v i t y data o b t a i n e d i n t h e range 1.65 - 150 K. A b s o l u t e v a l u e s a r e n o t d e f i n e d b e t t e r t h a n 30-40 % because o f a bad g e o m e t r i c a l d e f i n i t i o n e s p e c i a l l y f o r t h e thermocouple c o n t a c t s . R e l a t i v e p r e c i s i o n , however, i s w i t h i n a few p e r c e n t .

From t h e l o w e s t t e m p e r a t u r e up t o a b o u t 25 K, K i n c r e a s e s w i t h T, f o l l o w i n g a t f i r s t an a p p r o x i m a t e l y T2 l a w . The K / T ~ diagram (see f i g u r e i n s e r t ) shows t h a t above 5 K a r a p i d d e v i a t i o n from t h i s t e m p e r a t u r e dependence o c c u r s . The maximum v a l u e a t about 25 K i s 0.3 W c m - ' ~ - l , much l o w e r t h a n t h e maximum values f o r any o t h e r semi- metal o f t h e Group V [Ill. Above 30 K and up t o 100-110 K a ~-O-"aw i s observed

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981699

F i g u r e - Basal thermal c o n d u c t i - v i t y o f TiSe2. K / T ~ below 20 K i s i n s e r t e d : e x p e r i m e n t a l p o i n t s a r e f i t t e d by t h e t h e o r e t i c a l c u r v e below 5 K.

A t h i g h e r t e m p e r a t u r e K(T) d e p a r t s f r o m t h i s b e h a v i o u r and appears t o i n c r e a s e w i t h temperature. Thermal r a d i a t i o n however can have some e f f e c t even w i t h t h e method c u r r e n t l y used and need more d e t a i l e d e x a m i n a t i o n which w i l l be p u b l i s h e d l a t e r . 3 - D i s c u s s i o n - From t h e e l e c t r i c a l r e s i s t i v i t y d a t a and t h e Wiedemann-Franz l a w i t i s e v i d e n t t h a t t h r o u g h o u t t h e s t u d i e d t e m p e r a t u r e range, h e a t t r a n s p o r t i s essen- t i a l l y due t o t h e l a t t i c e c o n t r i b u t i o n . A t l o w e r temperatures t h i s i s c o n s i s t e n t w i t h t h e absence o f any T-law b e h a v i o u r . A T 2 - i n s t e a d o f a ~ ~ - 1 a w f o r t h e l a t t i c e conduc- t i v i t y i s n o t unusual i n a metal o r a semi-metal [ l l - 1 2 1 . Such a b e h a v i o u r i s gene- r a l l y a s c r i b e d e i t h e r t o ( i n t r a v a l l e y ) e l e c t r o n - p h o n o n i n t e r a c t i o n o r t o s c a t t e r i n g b y s t a t i c d i s l o c a t i o n s [121. These e x p l a n a t i o n s seem n o t t o h o l d i n t h e p r e s e n t case : t h e former because no c o r r e l a t i v e T~ b e h a v i o u r i s observed f o r t h e i d e a l e l e c t r i c a l r e s i s t i v i t y whereas t h e l a t t e r i n v o l v e s t o o l a r g e a number o f d i s l o c a t i o n s ( Z 4 1011

~ m - ~ ) For l a y e r s t r u c t u r e s , however, one a l s o has t o t a k e i n t o account t h e a n i s o t r o - py o f t h e phonon branches. Such an approach was c a r r i e d o u t f o r g r a p h i t e by Dreyfus and Maynard (DM) [13]. I n t h e i r e x t e n s i o n o f C a s i m i r ' s t h e o r y , a l s o c o n s i d e r i n g t h e a n i s o t r o p y o f c r y s t a l dimensions, t h e y showed t h e basal thermal c o n d u c t i v i t y t o m a i n l y r e s u l t from t h e s o - c a l l e d " i n p l a n e " modes which have t h e i r p o l a r i z a t i o n p a r a l l e l t o t h e basal p l a n e . A c o n t i n u o u s passage f r o m T 3 t o T2 i s p r e d i c t e d which i s c o n t r o l l e d b y o n l y one parameter connected w i t h t n e v a l u e o f t h e C4, e l a s t i c cons- t a n t . Then t h e phonon mean f r e e p a t h can be determined and i s expected t o be c o n s i s - t e n t w i t h t h e s m a l l e r b a s a l dimension. Q u a l i t a t i v e l y and t o some e x t e n t q u a n t i t a t i - v e l y , a n a l y s i s shows many s i m i l a r f e a t u r e s i n t h e s t r u c t u r a l p r o p e r t i e s o f g r a p h i t e and TiSe2. We t h u s have f i t t e d o u r r e s u l t s t o DM t h e o r y a d j u s t i n g C 4 4 and t h e phonon

C6-340 JOURNAL DE PHYSIQUE

basal mean f r e e p a t h . R e s u l t s a r e shown i n t h e f i g u r e i n s e r t and a r e seen t o r e p r o - duce q u a l i t a t i v e l y t h e t r e n d below 5 K. However t h e ^{C 4 4} v a l u e o b t a i n e d ( 0 . 1 10 l o dynes i s much l o w e r t h a n t h e measured one f r o m r e f . 153 (14.3 10 l o dynes c w 2 ) . On t h e o t h e r hand, i f t h e l a t t e r v a l u e i s used t h e T2 regime would be expected a t h i g h e r temperatures (20-30 K) and i n f a c t would h a r d l y be v i s i b l e . Also t h e

mean f r e e p a t h o b t a i n e d (1.6 um) i s much s m a l l e r t h a n expected. These d i s c r e p a n c i e s c o u l d be e x p l a i n e d b y moving d i s l o c a t i o n s a b l e t o decrease t h e phonon v e l o c i t y [14].

The v e l o c i t y f o r t h e t r a n s v e r s e u l t r a s o n i c wave p r o p a g a t i n g a l o n g t h e c - a x i s s h o u l d be e s p e c i a l l y reduced. We have v e r i f i e d t h i s p r e d i c t i o n and measured a b o u t 350 m/s t o be compared w i t h 140 m/s deduced f r o m o u r f i t t e d C 4 4 . However such a t r e a t m e n t i s n o t c o n s i s t e n t because t h e c o r r e l a t i v e change i n t h e phonon mean f r e e p a t h must be t a k e n i n t o account, and so DM t h e o r y has t o be extended.

The range 5-25 K seems d i f f i c u l t t o e x p l a i n i n an usual way b u t i t c o u l d perhaps be connected w i t h observed anomalies i n o t h e r t r a n s p o r t p r o p e r t i e s . Above 25 K, t h e b e h a v i o u r o f K(T) does n o t p r e s e n t t h e usual f e a t u r e s o f umklapp processes r e s i s - tance [121. On t h e o t h e r hand, i f one c o n s i d e r s t h e a b s o r p t i o n o f phonons i n i n t e r - p o c k e t t r a n s i t i o n s t o be an i m p o r t a n t mechanism one can p r e d i c t from t h e dominant phonon scheme 1121 an e f f e c t i v e t e m p e r a t u r e range s t a r t i n g a b o u t 30-40 K u p t o 100- 130 K ; t h i s g r o s s l y corresponds t o t h e e x t e n t o f t h e T-Oslaw.Twootherargumentsalso f a v o u r such an assumption : f i r s t l y , t h e l o w v a l u e o f t h e Fermi energy i n t h i s semi- metal makes t r a n s i t i o n s p o s s i b l e o v e r t h e whole volume o f t h e pockets and, secondly, t h e thermal c o n d u c t i v i t y i s m a i n l y by t r a n v e r s e i n - p l a n e phonons w h i c h a r e seen t o be most s t r o n g l y a f f e c t e d by t h e t r a n s i t i o n [61. However more datir and development o f c a l c u l a t i o n a r e needed i n t h e range 100-300 K i n o r d e r t o make t h i s p o i n t c l e a r e r . References

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