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Mixed conductor properties of pure and V or Ti substituted AgCrS2
Solid State-Ionics 3/4 (1981) 203-207 North-Holland Publishing C o m p a n y
M I X E D C O N D U C T O R P R O P E R T I E S OF PURE AND V OR Ti SUBSTITUTED AgCrS2 T. H I B M A Brown Boveri Research Center, CH-5405 Baden-D~ittwil, Switzerland
AgCrS2 is a two-dimensional ionic conductor, showing an order~tisorder transition at 400°C. Materials with a variable silver content were prepared by substituting Cr partly by Ti and V. Single-phase c o m p o u n d s with the AgCrS2 structure and composition Agy(Crl-xTix)S2 (y ~ 1 - x) and Agy(Crl-xVx)S2 (y ~ 1) exist for x-values up to 0.3 and 0.6 respectively. The decrease of the transition temperature with decreasing silver content is m u c h steeper than is predicted on the basis of pure substitutional disorder. It is argued that this is caused by displacements of the silver ions.
I. Introduction Although AgCrS2 and related compounds like LiCrS2, KCrS2 etc. are usually not classified as intercalation compounds, because (a) these substances are essentially stoichiometric and (b) the layered host c o m p o u n d CrS2 does not exist [1], their structure and properties are very similar to those of intercalation compounds of transition-metal dichalcogenides with general formula MxTX2. Many of these materials are good ionic as well as electronic conductors. The ionic conduction is associated with the intercalated M ÷ ions, the semiconducting or metallic behavior with the electronic structure of the TX~- units. The structure of AgCrS2 was determined by Engelsman et al. [2] and is shown in fig. 1. The silver ions occupy tetrahedral sites in the socalled "van der Waals" gap. These sites build a pseudo-two-dimensional puckered honeycomb lattice (fig. lb). Only half of these sites are occupied. At low temperatures the silver ions are ordered on one of the triangular sublattices, because of the repulsion between the silver ions, but at higher temperatures a disordering of the silver ions over both sublattices c~ and/3 leads to a second-order phase transition at 400°C [2]. In a previous paper [3] we have reported on the ionic and electronic part of the conductivity of this material. Below the phase transition the ionic conductivity increases much faster than
exponential because of the disordering process. At the transition t e m p e r a t u r e a sudden change in the slope of the log(o-T) versus 1/T curve is observed. The electronic part of the conductivity is much smaller than the ionic part, except at very high temperatures, in agreement with the observation that the valence electrons are localized at the chromium ions [2]. Because of the simplicity of the silver sublattice, AgCrS2 appears to be a simple model system to study order--disorder p h e n o m e n a and fast ionic condition. In this respect it would be of interest to be able to change the density of the silver ions. This may be accomplished by substituting some of the ions of the CrS2 units by ions having a different valency. We have a)
b]
Fig. 1. Structure of AgCrS2 [2]. (a) View of the rhombohedral structure (space group R3m) along the a axis. (b) T h e Ag ÷ ions occupy half of the tetrahedral sites between the CrS: sandwiches. These sites form a puckered honeycomb lattice.
0167-2738/81/0000-0000/$02.50 © North-Holland Publishing C o m p a n y
T. Hibma / Mixed conductor properties of pure and V or Ti substituted AgCrS~
204
found that the C r ~+ ions may be substituted by considerable amounts of V 3+, Y i 4+ o r S n 4+ ions or the S2- by CI ions, without a change of the crystal structure. In this paper we report the phase diagrams and the total conductivities of the materials in which the C r ~+ ions have partly been substituted by Ti 4+ or V 3+ ions.
isostaticaily pressed cylindrical samples. The total conductivity was measured with a HewlettPackard vector impedence meter at 1 kHz using Pt electrodes. For the four-point dc ionic conductivity measurements voltage and current probes were cut from silver iodide pellets covered with a thin layer of silver metal.
2. Experimental
3. Results
The materials were prepared by heating the elements in silicon tubes at 1000°C for two days and cooling down slowly. Whether the materials were single phase and had the AgCrS2 structure was checked by powder X-ray analysis. The critical temperature of the order-disorder transition was determined from specific-heat measurements with a Perkin-Elmer differential scanning calorimeter. These measurements were also used to detect small amounts of sulphur or silver sulphide. If necessary, excess sulphur was removed by treating the materials with CS2. Conductivity measurements were performed on
3. I. Agy(Cr,-xTiO~ The Ti-substituted samples are single phase for y close to l - x. Up to x = 0.3 the rhombohedral AgCrS2 structure is stable; for larger xvalues the structure switches to a hexagonal one, most probably the AgyTiS2 structure. The phase limits with respect to Ag (for a fixed Ti content) are determined by the equilibrium with metallic silver at the high-density limit and by the equilibrium with elemental sulphur and a compound which could not be identified unambiguously but is probably a mixed sulphide of
,
Rg l_xCr I_xTt xS 2
a)
b)
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=
+
=
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1
== ++
".~
++
, S
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'%=
X-O.
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I (x)
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x x ÷÷+
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-1
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8=
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=
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,
Rg I_xCr I_xTI xS 2 +Rg
=
=/<-a 3
1OOO/T Fig. 2. The total conductivity for materials with composition Agv(Crl ~Tit)S2. (a) For y = 1 - x the conductivity is domi na t e d by the ionic contribution, except at very high temperatures. (b) For samples in contact with silver metal the electronic part becomes dominant for large x-values.
T. Hibma I Mixed conductor properties of pure and V or Ti substituted AgCrS2 ,
,
i
v
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o
oX.O.
.
b)
Rg l_xCr I_xVxS 2
4 + 4.+ X x x x + Xx % xxx x
3
%+++
+++++
== L~ 0 d
==
Ix
xx xx X-e.x2
I
x~
I=
÷
+
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+++
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+ X-O. I
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+ I II
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ss
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ss
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++++++
++
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205
2
'
3
)
II
X-O
a
1000/T Fig. 3. The total conductivity for materials with composition Agy(Crl-xV~)S:. (a) For y = 1 the electronic part of the conductivity becomes dominant for large x-values. (b) The electronic contribution increases for silver deficient samples. Note that these samples have the nominal composition y = 1 - x and are not single phase. C r a n d Ti, at t h e l o w - d e n s i t y limit. T h e specific h e a t a n o m a l y b e c o m e s b r o a d e r a n d t h e transition t e m p e r a t u r e d e c r e a s e s with i n c r e a s i n g x (fig. 4). W i t h i n e x p e r i m e n t a l e r r o r t h e s a m e results a r e o b t a i n e d for s a m p l e s in e q u i l i b r i u m with silver m e t a l o r for silver-deficient s a m p l e s . T h e c o n d u c t i v i t y of s a m p l e s with t h e c e n t r a l c o m p o s i t i o n y = 1 - x is p r e d o m i n a n t l y ionic, as was c h e c k e d by dc ionic c o n d u c t i v i t y m e a s u r e m e n t s (fig. 2a). F o r x / > 0.1 a s i m p l e e x p o n e n t i a l b e h a v i o r is o b s e r v e d (Ea = 0.25 eV), suggesting that t h e s y s t e m is a l r e a d y d i s o r d e r e d at r o o m t e m p e r a t u r e . If t h e s a m e s a m p l e s a r e b r o u g h t in c o n t a c t with silver m e t a l , t h e e l e c t r o n i c p a r t of the c o n d u c t i v i t y i n c r e a s e s s e v e r a l o r d e r s of magnitude and becomes the major contribution for large x - v a l u e s (fig. 2b).
r e s p e c t to A g for a given V - c o n t e n t i n c r e a s e s m u c h m o r e s t r o n g l y with i n c r e a s i n g x t h a n in the case of T i - s u b s t i t u t e d s a m p l e s . This m u c h w i d e r s t o i c h i o m e t r y r a n g e allows us to m e a s u r e the t r a n s i t i o n t e m p e r a t u r e for different silver c o n t e n t s , k e e p i n g t h e c o m p o s i t i o n of the trans i t i o n - m e t a l d i c h a l c o g e n i d e f r a m e w o r k fixed. T h e results a r e s h o w n in fig. 4 for x = 0.05, 0.1 a n d 0.2. N o t e that the t r a n s i t i o n t e m p e r a t u r e s h a v e b e e n n o r m a l i z e d to t h e v a l u e s for y = 1, a n d fall a p p r o x i m a t e l y on the s a m e curve, including the results for Ag]-x(Crl-xTix)S2. A t l a r g e r x - v a l u e s t h e t o t a l c o n d u c t i v i t y of t h e s a m p l e s with y = 1 is d o m i n a t e d by the e l e c t r o n i c c o n t r i b u t i o n (fig. 3a). T h e e l e c t r o n i c c o n d u c t i v i t y i n c r e a s e s still c o n s i d e r a b l y , if the silver c o n t e n t of t h e s e s a m p l e s is r e d u c e d (fig. 3b).
3.2. Agy(Crl-xVx)S2 4. Discussion
T h e c e n t r a l c o m p o s i t i o n for t h e V - s u b s t i t u t e d c o m p o u n d s is y = 1. S i n g l e - p h a s e samples a r e o b t a i n e d u p to x - v a l u e s of at least 0.6. T h e e n d m e m b e r , AgyVS2, h o w e v e r , d o e s not s e e m to exist. T h e s t o i c h i o m e t r y r a n g e with
4.1. T h e c o n d u c t i v i t y d a t a
If t h e c o n d u c t i v i t y d a t a of figs. 2 a n d 3 a r e c o m p a r e d with t h e results for p u r e AgCrS2, the
206
7". Hibma / Mixed conductor properties of pure and V or Ti substituted AgCrS2
most striking change is a drastic increase of the electronic part of the conductivity and the decrease of the activation energy with increasing x. In conjunction with the increase of the stoichiometry range with respect to Ag at fixed V or Ti content, these observations indicate that the substitution leads to a decrease of the effective bandgap between conduction and valence band, i.e. either to a broadening of the bands or to the appearance of "impurity levels" in the bandgap. In pure AgCrS2 the activation energy for O'e~ (~1 eV) is partly caused by the thermally activated behavior of the mobility [3]. The decrease of the activation energy upon doping with Ti or V is therefore not only due to a decrease of the bandgap, but also to a decrease of the barrier for electron transport. Nevertheless the localized nature of the d electrons seems to persist for the compositions studied, because no insulator-metal transition is observed.
effective nearest-neighbor (nn) interaction between particles, i.e.
E°°/kTc = a.
For a half-filled honeycomb lattice a can be calculated exactly [4] and is equal to 0.385. In the quasi-chemical approximation [5] Tc may be calculated as a function of the fractional occupation (p) of the honeycomb lattice from ~nn/kTc = ln[9p(1 - p)l(3p - 1)(2 - 3p)l-
In the nearest-neighbor approximation the transition t e m p e r a t u r e is proportional to the
I
I
I
I
I
I
I
|!
T~ / T~ (x=O)
!
,t
.95
o
t
Agl_x (Crt_&Vs)S z
.90 I
.85
I
8
Q.C.A.
t.00
I
i 55=.t : .2 8 :.05
Agt_ x (Crl_xTi x)s z
I .06
I .04
(2)
The above dependence of Tc on p is compared with experimental data for Agy(Crl xTix)S2 and for Agy(Crl-xVx)S2 (fixed x) in fig. 4. The experimentally observed decrease of Tc with decreasing silver ion density is seen to be much steeper. Moreover, the slope of the experimental phase diagrams at y = 1 deviates markedly from zero, which means that the phase diagram is not symmetric with respect to particles and vacancies, in contrast to eq. (2). There may be two reasons for these large deviations: (a) the changes in the electronic structure of
4.2. The phase diagram
I
(])
I
I I .02 "~--
I x
0
I -.02
-.04
Fig. 4. T h e phase diagram of the silver subsystem for Ag~ x(Crl xTix)S2 and Agl x(Crl •V,5)$2 (fixed ,5).
T. Hibma / Mixed conductor properties of pure and V or Ti substituted AgCrS2
the f r a m e w o r k due to substitution of the C r ~+ ions leads to an increased screening of the interaction potential of the silver ions, or (b) the displacements of the silver ions are so large that they must be taken into account to describe the state of order. From fig. 4 it is seen that the normalized transition temperatures for both the V- and Tisubstituted samples fall on the same curve if plotted against the silver content of the samples. This observation is not in agreement with explanation (a). In the Ti case the Ag- and Ti-content are changed simultaneously, so that the band structure changes, but the n u m b e r of charge carriers stays small. In the V case, however, the band structure stays essentially unchanged, whereas the variation of the silver content introduces a corresponding n u m b e r of electrons or holes. The nature of the changes in the electronic structure therefore are fundamentally different in both cases, which is not reflected in the behavior of the critical temperature. The asymmetry of the phase diagram rather seems to be a property of the silver subsystem, independent of the changes in the transition-metal dichalcogenide sheets. Eq. (2) is based on the assumption that the disorder is of a purely substitutional nature and the result is consequently symmetrical with respect to particles and vacancies. This symmetry is disturbed if the conduction ions are easily displaced from their equilibrium positions. Then the ions surrounding an excess ion or vacancy will adjust their positions so that the effective repulsion between nearest-neighbor particles or vacancies is reduced. However, if the framework defining the sublattice for the conduction ions is rigid the
207
effective repulsion between neighboring vacancies cannot be reduced as effectively as the repulsion between nearest-neighbor ions, because the positions of the vacancies are fixed in contrast to the positions of the ions. Thus, if the above condition is satisfied, the probability to find large clusters of vacancies is reduced as c o m p a r e d to large clusters of ions and the ordered state is more stable in the case of excess ions. This is qualitatively what is observed experimentally. There are several independent indications that the displacements are indeed large in the disordered phase of AgCrS2 and related compounds. In AgCrSe2 the mean square displacement of the Ag + ions is 0.50 ~ in the hexagonal plane as c o m p a r e d to 0.19 ]k perpendicular to these planes [2]. An electron density projection calculated from single-crystal X-ray data of AgCrS2 in the disordered phase shows that the silver ion density is indeed smeared out considerably in the plane of the ions [3]. Unpublished diffuse X-ray data, finally, are also inconsistent with a pure substitutional disorder.
References [1] J. Rouxel, in: Physics and chemistry of materials with layered structures, Vol. 6, ed. F. Lrvy (Reidel, Dordrecht, 1979), p. 201. [2] F.M.R. Engelsman, G.A. Wiegers, F. Jellinek and B. van Laar, J. Solid State Chem. 6 (1973) 574. [3] T. Hihma, Solid State Commun. 33 (1980) 445. [4] I. Syozi, in: Phase transitions and critical phenomena, Vol. 1, eds. C. Domb and M.S. Green (Academic Press, New York, 1972) p. 269. [5] R.H. Fowler and E.A. Guggenheim, Statistical thermodynamics (Cambridge Univ. Press, London, 1965).
M I X E D C O N D U C T O R P R O P E R T I E S OF PURE AND V OR Ti SUBSTITUTED AgCrS2 T. H I B M A Brown Boveri Research Center, CH-5405 Baden-D~ittwil, Switzerland
AgCrS2 is a two-dimensional ionic conductor, showing an order~tisorder transition at 400°C. Materials with a variable silver content were prepared by substituting Cr partly by Ti and V. Single-phase c o m p o u n d s with the AgCrS2 structure and composition Agy(Crl-xTix)S2 (y ~ 1 - x) and Agy(Crl-xVx)S2 (y ~ 1) exist for x-values up to 0.3 and 0.6 respectively. The decrease of the transition temperature with decreasing silver content is m u c h steeper than is predicted on the basis of pure substitutional disorder. It is argued that this is caused by displacements of the silver ions.
I. Introduction Although AgCrS2 and related compounds like LiCrS2, KCrS2 etc. are usually not classified as intercalation compounds, because (a) these substances are essentially stoichiometric and (b) the layered host c o m p o u n d CrS2 does not exist [1], their structure and properties are very similar to those of intercalation compounds of transition-metal dichalcogenides with general formula MxTX2. Many of these materials are good ionic as well as electronic conductors. The ionic conduction is associated with the intercalated M ÷ ions, the semiconducting or metallic behavior with the electronic structure of the TX~- units. The structure of AgCrS2 was determined by Engelsman et al. [2] and is shown in fig. 1. The silver ions occupy tetrahedral sites in the socalled "van der Waals" gap. These sites build a pseudo-two-dimensional puckered honeycomb lattice (fig. lb). Only half of these sites are occupied. At low temperatures the silver ions are ordered on one of the triangular sublattices, because of the repulsion between the silver ions, but at higher temperatures a disordering of the silver ions over both sublattices c~ and/3 leads to a second-order phase transition at 400°C [2]. In a previous paper [3] we have reported on the ionic and electronic part of the conductivity of this material. Below the phase transition the ionic conductivity increases much faster than
exponential because of the disordering process. At the transition t e m p e r a t u r e a sudden change in the slope of the log(o-T) versus 1/T curve is observed. The electronic part of the conductivity is much smaller than the ionic part, except at very high temperatures, in agreement with the observation that the valence electrons are localized at the chromium ions [2]. Because of the simplicity of the silver sublattice, AgCrS2 appears to be a simple model system to study order--disorder p h e n o m e n a and fast ionic condition. In this respect it would be of interest to be able to change the density of the silver ions. This may be accomplished by substituting some of the ions of the CrS2 units by ions having a different valency. We have a)
b]
Fig. 1. Structure of AgCrS2 [2]. (a) View of the rhombohedral structure (space group R3m) along the a axis. (b) T h e Ag ÷ ions occupy half of the tetrahedral sites between the CrS: sandwiches. These sites form a puckered honeycomb lattice.
0167-2738/81/0000-0000/$02.50 © North-Holland Publishing C o m p a n y
T. Hibma / Mixed conductor properties of pure and V or Ti substituted AgCrS~
204
found that the C r ~+ ions may be substituted by considerable amounts of V 3+, Y i 4+ o r S n 4+ ions or the S2- by CI ions, without a change of the crystal structure. In this paper we report the phase diagrams and the total conductivities of the materials in which the C r ~+ ions have partly been substituted by Ti 4+ or V 3+ ions.
isostaticaily pressed cylindrical samples. The total conductivity was measured with a HewlettPackard vector impedence meter at 1 kHz using Pt electrodes. For the four-point dc ionic conductivity measurements voltage and current probes were cut from silver iodide pellets covered with a thin layer of silver metal.
2. Experimental
3. Results
The materials were prepared by heating the elements in silicon tubes at 1000°C for two days and cooling down slowly. Whether the materials were single phase and had the AgCrS2 structure was checked by powder X-ray analysis. The critical temperature of the order-disorder transition was determined from specific-heat measurements with a Perkin-Elmer differential scanning calorimeter. These measurements were also used to detect small amounts of sulphur or silver sulphide. If necessary, excess sulphur was removed by treating the materials with CS2. Conductivity measurements were performed on
3. I. Agy(Cr,-xTiO~ The Ti-substituted samples are single phase for y close to l - x. Up to x = 0.3 the rhombohedral AgCrS2 structure is stable; for larger xvalues the structure switches to a hexagonal one, most probably the AgyTiS2 structure. The phase limits with respect to Ag (for a fixed Ti content) are determined by the equilibrium with metallic silver at the high-density limit and by the equilibrium with elemental sulphur and a compound which could not be identified unambiguously but is probably a mixed sulphide of
,
Rg l_xCr I_xTt xS 2
a)
b)
2
=
+
=
J
1
== ++
".~
++
, S
X-0.2 (o)
'%=
X-O.
÷ S
I (x)
~
÷÷+
=
÷÷+÷
**
°= X-0.2 o o o
Xx x
+%+
°°oo
x x X='R" l
e÷+ 8
x x ÷÷+
Z
D
O *
-1
=
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=*= =
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8=
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-2
|
Xx
=
I l ÷
,
Rg I_xCr I_xTI xS 2 +Rg
=
=/<-a 3
1OOO/T Fig. 2. The total conductivity for materials with composition Agv(Crl ~Tit)S2. (a) For y = 1 - x the conductivity is domi na t e d by the ionic contribution, except at very high temperatures. (b) For samples in contact with silver metal the electronic part becomes dominant for large x-values.
T. Hibma I Mixed conductor properties of pure and V or Ti substituted AgCrS2 ,
,
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o
oX.O.
.
b)
Rg l_xCr I_xVxS 2
4 + 4.+ X x x x + Xx % xxx x
3
%+++
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==
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xx xx X-e.x2
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ss
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2
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3
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X-O
a
1000/T Fig. 3. The total conductivity for materials with composition Agy(Crl-xV~)S:. (a) For y = 1 the electronic part of the conductivity becomes dominant for large x-values. (b) The electronic contribution increases for silver deficient samples. Note that these samples have the nominal composition y = 1 - x and are not single phase. C r a n d Ti, at t h e l o w - d e n s i t y limit. T h e specific h e a t a n o m a l y b e c o m e s b r o a d e r a n d t h e transition t e m p e r a t u r e d e c r e a s e s with i n c r e a s i n g x (fig. 4). W i t h i n e x p e r i m e n t a l e r r o r t h e s a m e results a r e o b t a i n e d for s a m p l e s in e q u i l i b r i u m with silver m e t a l o r for silver-deficient s a m p l e s . T h e c o n d u c t i v i t y of s a m p l e s with t h e c e n t r a l c o m p o s i t i o n y = 1 - x is p r e d o m i n a n t l y ionic, as was c h e c k e d by dc ionic c o n d u c t i v i t y m e a s u r e m e n t s (fig. 2a). F o r x / > 0.1 a s i m p l e e x p o n e n t i a l b e h a v i o r is o b s e r v e d (Ea = 0.25 eV), suggesting that t h e s y s t e m is a l r e a d y d i s o r d e r e d at r o o m t e m p e r a t u r e . If t h e s a m e s a m p l e s a r e b r o u g h t in c o n t a c t with silver m e t a l , t h e e l e c t r o n i c p a r t of the c o n d u c t i v i t y i n c r e a s e s s e v e r a l o r d e r s of magnitude and becomes the major contribution for large x - v a l u e s (fig. 2b).
r e s p e c t to A g for a given V - c o n t e n t i n c r e a s e s m u c h m o r e s t r o n g l y with i n c r e a s i n g x t h a n in the case of T i - s u b s t i t u t e d s a m p l e s . This m u c h w i d e r s t o i c h i o m e t r y r a n g e allows us to m e a s u r e the t r a n s i t i o n t e m p e r a t u r e for different silver c o n t e n t s , k e e p i n g t h e c o m p o s i t i o n of the trans i t i o n - m e t a l d i c h a l c o g e n i d e f r a m e w o r k fixed. T h e results a r e s h o w n in fig. 4 for x = 0.05, 0.1 a n d 0.2. N o t e that the t r a n s i t i o n t e m p e r a t u r e s h a v e b e e n n o r m a l i z e d to t h e v a l u e s for y = 1, a n d fall a p p r o x i m a t e l y on the s a m e curve, including the results for Ag]-x(Crl-xTix)S2. A t l a r g e r x - v a l u e s t h e t o t a l c o n d u c t i v i t y of t h e s a m p l e s with y = 1 is d o m i n a t e d by the e l e c t r o n i c c o n t r i b u t i o n (fig. 3a). T h e e l e c t r o n i c c o n d u c t i v i t y i n c r e a s e s still c o n s i d e r a b l y , if the silver c o n t e n t of t h e s e s a m p l e s is r e d u c e d (fig. 3b).
3.2. Agy(Crl-xVx)S2 4. Discussion
T h e c e n t r a l c o m p o s i t i o n for t h e V - s u b s t i t u t e d c o m p o u n d s is y = 1. S i n g l e - p h a s e samples a r e o b t a i n e d u p to x - v a l u e s of at least 0.6. T h e e n d m e m b e r , AgyVS2, h o w e v e r , d o e s not s e e m to exist. T h e s t o i c h i o m e t r y r a n g e with
4.1. T h e c o n d u c t i v i t y d a t a
If t h e c o n d u c t i v i t y d a t a of figs. 2 a n d 3 a r e c o m p a r e d with t h e results for p u r e AgCrS2, the
206
7". Hibma / Mixed conductor properties of pure and V or Ti substituted AgCrS2
most striking change is a drastic increase of the electronic part of the conductivity and the decrease of the activation energy with increasing x. In conjunction with the increase of the stoichiometry range with respect to Ag at fixed V or Ti content, these observations indicate that the substitution leads to a decrease of the effective bandgap between conduction and valence band, i.e. either to a broadening of the bands or to the appearance of "impurity levels" in the bandgap. In pure AgCrS2 the activation energy for O'e~ (~1 eV) is partly caused by the thermally activated behavior of the mobility [3]. The decrease of the activation energy upon doping with Ti or V is therefore not only due to a decrease of the bandgap, but also to a decrease of the barrier for electron transport. Nevertheless the localized nature of the d electrons seems to persist for the compositions studied, because no insulator-metal transition is observed.
effective nearest-neighbor (nn) interaction between particles, i.e.
E°°/kTc = a.
For a half-filled honeycomb lattice a can be calculated exactly [4] and is equal to 0.385. In the quasi-chemical approximation [5] Tc may be calculated as a function of the fractional occupation (p) of the honeycomb lattice from ~nn/kTc = ln[9p(1 - p)l(3p - 1)(2 - 3p)l-
In the nearest-neighbor approximation the transition t e m p e r a t u r e is proportional to the
I
I
I
I
I
I
I
|!
T~ / T~ (x=O)
!
,t
.95
o
t
Agl_x (Crt_&Vs)S z
.90 I
.85
I
8
Q.C.A.
t.00
I
i 55=.t : .2 8 :.05
Agt_ x (Crl_xTi x)s z
I .06
I .04
(2)
The above dependence of Tc on p is compared with experimental data for Agy(Crl xTix)S2 and for Agy(Crl-xVx)S2 (fixed x) in fig. 4. The experimentally observed decrease of Tc with decreasing silver ion density is seen to be much steeper. Moreover, the slope of the experimental phase diagrams at y = 1 deviates markedly from zero, which means that the phase diagram is not symmetric with respect to particles and vacancies, in contrast to eq. (2). There may be two reasons for these large deviations: (a) the changes in the electronic structure of
4.2. The phase diagram
I
(])
I
I I .02 "~--
I x
0
I -.02
-.04
Fig. 4. T h e phase diagram of the silver subsystem for Ag~ x(Crl xTix)S2 and Agl x(Crl •V,5)$2 (fixed ,5).
T. Hibma / Mixed conductor properties of pure and V or Ti substituted AgCrS2
the f r a m e w o r k due to substitution of the C r ~+ ions leads to an increased screening of the interaction potential of the silver ions, or (b) the displacements of the silver ions are so large that they must be taken into account to describe the state of order. From fig. 4 it is seen that the normalized transition temperatures for both the V- and Tisubstituted samples fall on the same curve if plotted against the silver content of the samples. This observation is not in agreement with explanation (a). In the Ti case the Ag- and Ti-content are changed simultaneously, so that the band structure changes, but the n u m b e r of charge carriers stays small. In the V case, however, the band structure stays essentially unchanged, whereas the variation of the silver content introduces a corresponding n u m b e r of electrons or holes. The nature of the changes in the electronic structure therefore are fundamentally different in both cases, which is not reflected in the behavior of the critical temperature. The asymmetry of the phase diagram rather seems to be a property of the silver subsystem, independent of the changes in the transition-metal dichalcogenide sheets. Eq. (2) is based on the assumption that the disorder is of a purely substitutional nature and the result is consequently symmetrical with respect to particles and vacancies. This symmetry is disturbed if the conduction ions are easily displaced from their equilibrium positions. Then the ions surrounding an excess ion or vacancy will adjust their positions so that the effective repulsion between nearest-neighbor particles or vacancies is reduced. However, if the framework defining the sublattice for the conduction ions is rigid the
207
effective repulsion between neighboring vacancies cannot be reduced as effectively as the repulsion between nearest-neighbor ions, because the positions of the vacancies are fixed in contrast to the positions of the ions. Thus, if the above condition is satisfied, the probability to find large clusters of vacancies is reduced as c o m p a r e d to large clusters of ions and the ordered state is more stable in the case of excess ions. This is qualitatively what is observed experimentally. There are several independent indications that the displacements are indeed large in the disordered phase of AgCrS2 and related compounds. In AgCrSe2 the mean square displacement of the Ag + ions is 0.50 ~ in the hexagonal plane as c o m p a r e d to 0.19 ]k perpendicular to these planes [2]. An electron density projection calculated from single-crystal X-ray data of AgCrS2 in the disordered phase shows that the silver ion density is indeed smeared out considerably in the plane of the ions [3]. Unpublished diffuse X-ray data, finally, are also inconsistent with a pure substitutional disorder.
References [1] J. Rouxel, in: Physics and chemistry of materials with layered structures, Vol. 6, ed. F. Lrvy (Reidel, Dordrecht, 1979), p. 201. [2] F.M.R. Engelsman, G.A. Wiegers, F. Jellinek and B. van Laar, J. Solid State Chem. 6 (1973) 574. [3] T. Hihma, Solid State Commun. 33 (1980) 445. [4] I. Syozi, in: Phase transitions and critical phenomena, Vol. 1, eds. C. Domb and M.S. Green (Academic Press, New York, 1972) p. 269. [5] R.H. Fowler and E.A. Guggenheim, Statistical thermodynamics (Cambridge Univ. Press, London, 1965).