Phase transition and anisotropy of thermal expansion in TlInS2

Sohd State Communications, Vol. 53, No. 7, pp. 6 0 1 - 6 0 2 , 1985. Printed in Great Britain

0 0 3 8 - 1 0 9 8 / 8 5 $3.00 + .00 Pergamon Press Ltd.

PHASE TRANSITION AND ANISOTROPY OF THERMAL EXPANSION IN TIInS2 N.A Abdullaev, K.R. Allakhver&ev, G L Belenkn, T.G Mamedov, R A Sulelmanov and Ya.N Shanfov (USSR, Baku 370143, Institute of Physics, Academy of Sciences of Azerbaijan SSR)

(Received 4 October 1984 by F. Bassam ) Linear expansion coefficients parallel and perpendicular to the layer plane of TIlnS2 layer crystal were measured in the temperature range 2 0 - 2 5 0 K At T ~ 200 K a strong anomaly m a± behavlour was observed - the value ofc~± increased abruptly up to the 200 x 1 0 - 6 K - 1 due to phase transition m this crystal It was shown that there is no anomaly m the behavlour of linear expansion coefficient t~ll. This fact allowed to conclude that the phase transition in TIlnS2 is caused by changes in interlayer distances. SINGLE CRYSTALS of TIlnS2 have the layer crystal structure IR measurements show [1 ] that the anomahes observed m the temperature mvestlgatlons of dielectric constant are due to phase transxtlons To clear up the nature of the phase transmon in TIInS2 crystals thermal expansion coefficients m two directions parallel and perpendicular to the layer plane were measured In the temperature range 2 0 - 2 5 0 K. Measurements were carried out by mterferometnc technique with accuracy 1 0 - 7 K - 1 . The investigated samples had the form ofacube5x 5x 5mm a In Fig. 1 temperature dependences of linear expansion coefficients c~L and Otll of TIlnS2 smgle crystals are presented The c~± (T) dependence is characterized by larger values due to weak interlayer forces determining the expansion in the d~rectlon perpendicular to the layer plane At T " 200 K a strong anomaly is observed m c~±(T) curve - - ~ ± increases up to the values "" 200 x 1 0 - 6 K -1 This value ofct± is the largest for investigated layer crystals (for example c~± ~ 30 x 10 -6 K - 1 at K m graptute). The described behaviour of a± near 200 K can be explained by phase transition which takes plase at these temperatures in TIlnS2 [ 1 ]. As it is seen from Fig. 1 there is no anomaly in the behaviour of t~tl near 200 K. This fact allows to make some, conclusions about the nature of the observed phase transition taking into account the layer structure of crystals According to [2] linear expansion coefficients o f umaxlal crystals have the form

C[ C33 °ql = V" l(Cn + C12)C33 -2C~3 " 3'11

-- (Cll

-4-

(1)

.~r

l' I i I

I I J

,

I I

// I

.y

/

; I I I I/

I I I f I

t I I I t

f I

I I

I I '

I

t k

o~ y.,c'" j.Ic.4c"~J /4 I,II

C{( C11 -[- C12 . O~.l_ : V C_ll +C12)C33 _2C12a %!.

2C13 C12)C33

]

cl3

(Cn + C12)C3a -- 2C~3 7±

,a'"

K~b

] -- 2c73 "~11

Fig. 1 Linear expansion coefficients o f layer crystal TllnS2

601

THERMAL EXPANSION IN TIlnS2

602

In (1) C - heat capacity, V - corresponding volume, C~k - elastic constants, 711 and 7± - Grunalsen parameters The layer structure of TIlnS2 allows to suggest that elastic constants CI3 and C3a which describe the interlayer forces are much smaller than "mtralayer" elastic constants C~I and C~2 In this approximation hnear expansion coefficients ctI and all take the form C

1

V" c3-$7, C all ~ - - V .

1 Cll + C12 " 711

(2)

The anomaly in C due to phase transition must lead to anomalies in c~± and all However the anomaly in a± ls much greater than In all Because the large values of a± are due to interlayer interaction one can conclude that the great increase of interlayer distances taking place at the phase transition causes the decrease of interlayer interaction In such a case the value o f " m t e r l a y e r " elastic constant C33 which determine the value of c~± will decrease At the same time the values of "mtra-

Vol 53, No. 7

layer" elastic constants Cll and C12 wdl not change significantly when phase transition of described type takes place The above made assumption allows the explanation of the existence of anomaly m temperature behavlour of a±, and its absence m behavlour of all The extremely large value o f linear expansion coefficient a± when phase transition takes plase testifies to the fact that in thas transition interlayer distances change significantly Thus, the phase transition taking place at ~ 200 k m layer crystal TIlnS2 IS probably due to changes m interlayer distances but not m interlayer ones At this phase transition only physical parameters which depend strongly on interlayer distances will change

REFERENCES A A Volkov, Yu.G. Goncharov, K R AUakhverdlev & R M Sardarly Flz Tverd. Tela 25, 3538 (1983). T H.K. Barron, J.G Collins & G K White, Adv Phys. 2 9 , 6 0 9 (1980)