- Email: [email protected]
Heat capacities, magnetic phase transition at 42.02 K and order-disorder phase transition at 673 K of AgCrS2
J. P/y. C/em. Solids Vol. 50, No. 2. pp. 215-220. Printed in Great Britain.
1989
0022-3697/89 $3.00 + 0.00 0 1989 Pergamon Press plc
HEAT CAPACITIES, MAGNETIC PHASE TRANSITION AT 42.02 K AND ORDER-DISORDER PHASE TRANSITION AT 673 K OF AgCrS, HITOSHI KAWAJI, TOORU ATAKE and YASUTOSHI SAITO Research Laboratory of Engineering Materials, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku,
Yokohama
227, Japan
(Receioed 12 July 1988; accepted 7 September 1988)
Abstract-Heat capacities of AgCrS, were measured by adiabatic calorimetry between 7 and 327 K and by a.c. calorimetry from room temperature up to 720 K. The antiferromagnetic-paramagnetic phase transition was detected as a diffused first-order type of anomaly at 42.02 K. The enthalpy and entropy of transition were determined as 360 J’mol- and 9.3 J.K-‘.mol-‘, respectively. Phase transition due to the order-disorder AH, = 1.9 kJ.mol-’
of Ag+ ions was observed and AS, = 3.0 J,K-‘.mol-I.
as a typical
second-order
type of anomaly
at 673 K with
Keywords: AgCrS,,
orderdisorder
heat capacity, adiabatic calorimetry, a.c. calorimetry, magnetic phase transition, phase transition.
INTRODUCTION A family of layered chalcogenide compounds of type MCrX, (M = Ag, Cu, Na, Li; X = S, Se) has become of interest in recent years. One of the important features is that some compounds of this group are superionic conductors at high temperatures [l]. As the temperature decreases, some of them exhibit phase transitions due to ordering of M+ ions and of
magnetic spins on the Cr3+ ions. Structures and magnetic properties of these crystals have been reported [2-4]. CrX, forms sandwichlayers of trigonal symmetry, between which the monovalent cations are intercalated. In the case of compounds with M = Ag and Cu, Ag+ (Cu’) ions are located on the tetrahedrally coordinated sites which form a puckered honeycomb lattice; there are two sublattices which are slightly displaced with respect to each other in the direction of the hexagonal c-axis. All the sites on one of the sublattices are occupied with Ag+ (Cu’) ions while the other sublattice is empty at low temperatures (space group R3m). As the temperature increases, however, an order-disorder phase transition occurs at 673 K in AgCrS, [5,6] and at 675 K in CuCrS, [3]. Above the phase transition temperature, Ag+ (Cu’) ions are distributed randomly in both sublattices (space group Rh). The ionic conductivity of AgCrS, is 0.3 S.cm-’ at 673 K [5]. In the case of M = Na and Li, no order-disorder phase transition has been reported [2,3]. Furthermore, an antiferromagnetic ordering takes place for the spin system on Cr3+ ions in the temperature region of 1950 K [2]. The magnetic susceptibility curve of AgCrS, shows a sharp change at 40 K (NCel temperature), above which the magnetization follows the Curie-Weiss law with a nega215
tive Weiss constant (- 55 K, i.e. antiferromagnetic) [2]. The Weiss constant generally reflects the interaction between the nearest neighbor spins. Thus, an AgCrS, crystal can be regarded as a two-dimensional antiferromagnet of triangular lattice of Cr3+ ions. Although some studies have been made on the phase transition phenomena described above [2-91, little is known about the thermodynamic properties and the mechanism of the transitions still remains open. Hence, the present authors have started thermodynamic studies of series of such compounds, and the results of the ac. calorimetry above room temperature have been preliminarily reported for AgCrS, [lo]. In the present paper, the results of heat capacity measurements by adiabatic calorimetry will be given. EXPERIMENTAL Sample preparation
Samples of AgCrS, were synthesized directly from the reactant elements. The high-purity starting materials were purchased from Rare Metallic Co. (Tokyo, Japan) as powdered sulfur of nominal purity of 99.999%, silver shots (99.999%, 1 mm in diameter) and chromium powder of 200 mesh (99.99%). The reactants were mixed in the stoichiometric ratio except for sulfur which was added in slight excess (ca 0.2%). A mixture of about 20g was put into a fused-silica tube (20 mm in diameter and 350 mm in length), which was evacuated and hermetically sealed by fusing. The tube was placed in an electric furnace which was designed to maintain a temperature of 670 K at the top end and 1270 K at the bottom end. The vaporized sulfur was able to react easily with the other reactants and the excess sulfur condensed at
216
HITOSHI KAWAJI et al.
the cooler end of the tube (670 K), avoiding breakage of the tube. A transient intermediate compound Ag,S which possibly formed during the reaction should be in liquid state at 1270 K. Thus, the synthesis was performed in the bottom part of the tube which was maintained at 1270 K for seven days. To remove the excess sulfur, the product was put into a glass tube, which was evacuated at 670 K for 6 h. The final product was identified as the expected
compound AgCrS, by powder X-ray diffractometry using CuK, radiation. No impurity was detected.
Heat capacity measurements Heat capacities below room temperature were measured with a laboratory-made adiabatic calorimeter. A powdered sample of 17.7059g (0.079~5 mol) was loaded into a gold-plated copper vessel equipped with a heater (KARMA wire of
Table 1. Measured molar heat capacities T (K)
CP (J.K-‘.mol-‘) Series
7.40 8.18 8.97 9.91 7.30
8.11 9.04 10.08 11.20 12.32 13.50 14.81 16.20 17.62 19.00 13.40 13.86 12.65 13.77 14.95 16.08 17.27 18.54 19.77 20.98 22.21 23.44 24.64 25.83 27.10 28.42 29.67 30.88 32.05 33.20 34.35 35.51 36.12 37.96 39.21 40.45 41.46 41.94 42.05 42.51 43.64 45.09 46.54 47.93 49.28 SO.67 52.09
1
2.63 3.29 4.15 5.16 Series 2 2.60
3.20 4.20 5.34 6.51 1.59 8.65 9.75 10.92 12.04 12.98 Series 3 8.68 9.08 Series 4 8.03 9.01 9.95 10.80 1 I .66 12.56 13.41 14.19 14.98 15.77 16.53 17.26 18.13 18.97 19.87 20.69 21.61 22.54 23.46 24.54 25.73 27.13 28.92 32.26 63.97 526.69 1233.85 83.63 36.19 31.85 31.14 31.07 31.28 31.59 31.97
T
(K) 53.49 54.89 56.32 57.78 59.29 60.91 62.58 64.19 65.78 67.36 68.97 70.62 72.25 73.85 75.45 77.05 19.75 21.29 22.93 24.47 25.99 27.54 29.02 30.51 32.06 33.63 35.17 36.70 38.18 39.57 40.84 41.69 41.98 42.06 42.41 43.26 44.35 45.48 48.10 49.41 50.81 52.29 53.76 55.23 56.73 58.27 59.81 61.41 63.06 64.68 66.32 67.97 69.61 71.28
CP
(J.K-‘,mol-‘) 32.37 32.82 33.32 33.87 34.44 35.08 35.70 36.37 37.02 37.68 38.35 39.04 39.75 40.46 41.17 41.85 Series 5 13.40 14.39 15.44 16.41 17.40 18.39 19.41 20.45 21.61 22.87 24.22 25.72 27.42 ‘9.61 35.43 116.90 880.04 1096.28 87.86 39.53 32.95 31.48 Series 6 31.16 31.28 31.62 32.00 32.46 32.95 33.48 34.05 34.64 35.28 35.90 36.57 37.26 37.94 38.60 39.34
T
of
%
AgCrSz 7
(K)
(J.K-‘.mol-I)
(K)
72.96 14.65 76.34 78.04 79.78 81.54 83.31 85.10 86.94 88.82 90.71 92.61 94.52 96.43 98.28 100.14
40.07 40.78 41.55 42.28 43.06 43.82 44.61 45.39 46.23 47.06 41.86 48.69 49.52 50.33 51.12 51.89 Series 7 52.74 53.61 54.40 55.27 56.08 56.85 57.67 58.43 Series 8 59.20 59.96 60.71 61.43 62.16 62.88 63.64 64.29 64.99 65.71 66.50 67.18 67.87 68.53 69.24 69.85 70.47 71.11 71.79 72.36 72.91 73.51 74.03 74.58 75.10 75.67 76.08 76.60 II.02 77.57
189.66 192.16 194.64 197.12 199.58 202.03 204.50 207.00 209.49 211.96 214.47 216.99 219.51 222.02 224.51 227.00 229.48 23 1.95 234.45 236.98 239.49 242.00 244.51 247.00 249.52 252.07 254.61 25-i. 15 259.67 262.20 264.71 267.22 269.72 272.2 1 274.70 277.22 279.77 282.31 284.85 287.38 289.90 292.41 294.92 297.43 299.92 302.41 304.93 307.48 310.02 312.56 315.10 317.62 320.15 322.66 325.18 327.69
102.08 104.09 106.13 108.20 110.29 1t2.35 114.41 116.47 118.53 120.61 122.70 124.78 126.88 129.01 131.18 133.38 135.62 137.96 140.36 142.76 145.18 147.63 150.11 152.57 155.04 157.52 159.99 162.47 164.96 167.45 169.91 172.36 174.79 177.25 179.72 182.19 184.66 187.15
CP
(J.K-‘.mol-‘) 77.94 78.38 78.79 79.29 79.62 80.03 80.46 80.78 81.13 81.51 81.79 82.19 82.56 82.88 83.26 83.41 83.74 84.16 84.46 84.69 84.98 85.23 85.53 85.73 86.00 86.30 86.49 86.78 86.97 87.23 87.49 87.70 87.93 88.14 88.41 88.77 88.85 89.04 89.11 89.26 89.50 89.67 89.81 90.04 90.38 90.51 90.90 90.54 90.84 91.02 91.19 91.35 91.59 91.64 91.81 91.84
Heat capacities
100 R, Driver-Harris Co.), a platinum resistance (5187 L, H. Tinsley & Co.) and a germanium resistance thermometer (GR-200A-500, Lake Shore Cryotronics). The calorimeter vessel was evacuated and sealed with Wood’s alloy after the addition of a small amount of helium gas for heat exchange within the vessel (10 kPa at room temperature). For measurements below 50 K, liquid helium was used as the refrigerant. Solid nitrogen was used between 50 and 90 K, and liquid nitrogen was used for measurements above 90 K. Heat capacities of the sample were calculated by subtracting the values corresponding to that of the empty vessel from the measured total heat capacities. The contribution of the sample was about 35% of the total heat capacity. The platinum resistance thermometer was calibrated according to the IPTS-68 at the National Physical Laboratory in England. The germanium scale was based on EPT-76. An a.c. automatic resistance bridge (5840D, H. Tinsley & Co.) was used for temperature measurements with a precision of 0.0001 K. Heat capacities of the sample were determined with a precision of 0.1%. The details of both the apparatus and the operation will be published elsewhere [I 11. Heat capacities above room temperature up to 720 K were measured by using a commercial a.c. calorimeter (ACC-I, Sinku-Riko Inc.). A powdered thermometer
Table 2. Thermodynamic
T (K) 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320
C,(T) (J,K-‘,mol-‘) 5.27 13.56 20.08 28.94 31.41 34.70 38.80 43.15 47.55 51.86 55.94 59.73 63.19 66.34 69.18 71.75 74.07 76.15 78.03 79.71 81.23 82.61 83.88 85.03 86.08 87.05 87.94 88.76 89.52 90.22 90.88 91.48
H(T)-H(0) (J.mol-‘) 14.8 112.8 280.5 523.8 1073.8 1403.0 1770.2 2179.9 2633.4 3130.6 3669.9 4248.5 4863.4 5511.3 6189.1 6894.0 7623.3 8374.6 9145.6 9934.4 10739.2 11558.6 12391.1 13235.7 14091.3 14957.0 15832.0 16715.5 17607.0 18505.8 19411.3 20323.1
217
of AgCrS,
sample was pressed into a tablet of about 0.1 mm thickness. A small piece of the specimen measuring 2 x 3 mm was used for the a.c. calorimetry a Periodic heating on the surface of the sample was made with chopped light at 1.1 Hz. The amplitude of the temperature oscillation was measured by a thermocouple (type E) attached on the other surface of the sample. The signal was detected precisely by using a lock-in amplifier. The temperature of the bath was controlled to a scanning rate of about 5.6 x 10m3K.s-‘. Detailed measurements were made near the order-disorder phase transition temperature at a rate of 5.6 x 10-4K.~-‘. RESULTS AND DISCUSSION Heat capacities and thermodynamic functions The measured molar heat capacities of AgCrS, are tabulated in Table 1 which lists all the data obtained by adiabatic calorimetry from 7 to 327 K. As the data are listed in chronological order, the temperature increment due to each energy input can be estimated from the adjacent mean temperatures. The rate of energy input was varied with temperature, i.e. depending on the values of heat capacities and thermal conductivities. Below about 20 K, the energy input for about 1 K increase in temperature was completed in a few minutes. This input time increased as the temperature increased, and it was functions
of AgCrS,
S(T)- S(0) (J.K-‘.mol-I) 1.99 8.45 15.16 22.09 34.71 40.70 46.36 51.82 57.16 62.39 67.53 72.56 77.48 82.28 86.96 91.50 95.92 100.22 104.39 108.43 112.36 116.17 119.87 123.46 126.96 130.35 133.65 136.87 140.00 143.04 146.01 148.91
-(G(T)- ff(O))IT (J.K-‘.mol-‘) 0.51 2.81 5.81 9.00 13.23 17.32 21.07 24.57 27.90 31.08 34.17 37.16 40.07 42.91 45.69 48.42 51.08 53.69 56.25 58.76 61.22 63.63 66.00 68.32 70.59 72.83 75.02 77.17 79.28 81.36 83.39 85.40
218
HITOSHIKAWAJIet al.
ldj ‘i
‘ii
$
im
200
300
400
500
600
700
1
11---:“1
lrn
50
:
_..*
..-
;.../
9 50
,/
:
25
./
I
/
Oo 1m200
0
20
40
60
fm
0
I
T/K
Fig. 1. Molar heat capacities of AgCrS, measured by adiabatic ~lor~rne~y between 7 and 327 K and a.c. calorimetry above room temperature. about 10min for a 1.5 K increment above 100 K. After the energy input, thermal equilibrium within the calorimeter vessel was attained in a few minutes below 30K, 5 min at about 50 K, and 10 min above 100 K. In the transition region close to 42.02 K, however, it took 30 min to secure thermal uniformity within the calorimeter vessel. The value of some of the thermodynamic functions calculated from the present results are given in Table 2, where a small contribution below 7K was estimated by the method of smooth extrapolation to OK. Heat capacities above room temperature were measured by a.c. calorimetry which did not provide absolute, but relative values of heat capacities. Heat capacity values for those tem~ratures were estimated by using the parameters determined by fitting the data to those obtained by adiabatic calorimetry at 327 K. Therefore, heat capacity values for temperatures above room temperature are excluded from Tables 1 and 2. Heat capacities thus obtained are shown in Fig. 1, in which the antiferromagnetic-paramagnetic phase
/ i-
o-
20
40
60
T/K Fig. 2. Enthalpy vs temperature curve near the magnetic phase transition of AgCrS,.
0 0
20
40
60
I
T/K
Fig. 3. Excess heat capacities due to the magnetic phase transition of AgCrS,.
transition is clearly seen at 42.02 K. The orderdisorder phase transition is also observed as a typical second-order type of anomaly at 673 K.
Magnetic phase tra~s~t~un The antiferromagnetic-paramagnetic phase transition predicted for the spin system on Cr3+ions by magnetic measurements [3] was detected as a sharp anomaly in the heat capacity curve of AgCrS, as shown in Fig. I. The temperature dependence of the enthalpy measured during the present expe~ments is shown, around the transition region, in Fig. 2. The transition point is determined as 42.02 K, which corresponds to the inflection point of the curve. At the transition point, the extremely large gradient of the curve can be considered as the latent heat of transition, which is regarded as first-order though no hysteresis phenomenon was observed during the experiments. Excess heat capacities due to the magnetic phase transition are obtained by subtracting the normal heat capacities from the measured heat capacities. Even though the magnetic transition is of first-order, the lattice heat capacity should scarcely be affected at the transition point, and the normal base line may be drawn as shown in Fig. 1. Excess heat capacities thus estimated are shown in Fig. 3, where the data of two independent series of measurements are given. The anomaly has a large tail extending symmetrically to both higher and lower temperatures. An attempt to estimate the critical exponents is shown in Fig. 4. The plots are not straight lines, but they consist of two parts. The data in the region of log(l T - T,//T,) < - 1.5 lead to an abnormally large value of 1.3 of the critical exponent, which also supports the first-order nature of the transition. On the other hand, the data for the region
Heat capacities of AgCrS,
219
lm
3
0
a -1
-2
-3
1.5
1.6
logf Ir-rtI/rt) Fig. 4. Properties of the excess heat capacities close to the magnetic phase transition. (0) Below the transition temperature; (0) above the transition temperature.
to the contribution of the large tail of the anomaly. Thus the magnetic phase transition is considered as a diffused first-order transition. By integrating the excess heat capacities, the enthalpy of transition is obtained as 360 J.mol-‘. The entropy of transition is also estimated from the graph of C,/T vs T as 9.3 J.K-‘.mol-‘. The results are given in Table 3 together with those of the order-disorder transition at 673 K. The value of the entropy of transition amounts to about 70% of R ln(2S + 1) = 11.526 J.K-‘.mol-‘, which is the expected value for a complete ordering of the spins, unlike the cases of typical two-dimensional triangular Heisenberg antiferromagnets such as VCl, and VBr,, in which the AS, values are less than 10% of the ideal entropy of transition [12]. Thus, the ordering of the spins is well established through the magnetic phase transition in AgCrS,, while highly frustrated or less ordered states are maintained in VCI, and VBr, at low temperatures. Although the magnetic structure of AgCrS, below the transition has not yet been determined, it is suggested that it is more complicated than those of the other members such as LiCrS, of the MCrX, family. A collinear arrangement of the spins is realized in LiCrS, below 55 K [13], which is similar to the case of VI, below 13.5 K [14]. The detailed
Table 3.Properties of the magnetic phase transition
(2) 42.02 673
and the orderdisorder transition of AgCrS, AH, (J.mol-‘) 360 1900
phase
AS, (J,K-‘.mol-‘) 9.3 3.0
1.9
.O
Fig. 5. Properties of the excess heat capacities above room temperature. discussion
log(l T - T,I/T,) > - 1.5 correspond
1.7 1.8 T-'AK-'
of
the
analysis
and
comparison
with
CuCrS, will be published shortly [15]. Order-disorder phase transition The value of the heat capacity of AgCrS, is very close to the classical limit of 4 x 3R = 99.77 J.K-‘.mol-’ at room temperature. Above room temperature, however, the heat capacity still increases. The value increases gradually, then more rapidly at high temperatures, and finally ends with a rapid drop at 673 K as seen in Fig. 1. The shape of the anomaly is of a typical second-order transition associated with little fluctuation in the order parameters at the transition point. The thermodynamic properties of this phase transition can be analyzed on the basis of the order-disorder mechanism of Ag+ ions in the two-dimensional honeycomb lattice. The excess heat capacity due to the phase transition is calculated by subtracting the normal heat capacities in the same manner as described for the magnetic phase transition. The base line is shown by a solid line in Fig. 1. The enthalpy and entropy of phase transition are thus calculated and given in Table 3. The value of the entropy of phase transition (3.0 J.K-‘.mol-‘) corresponds to about 52% of the theoretically expected value of R In 2 = 5.76 J.K-‘.mol-‘. The Ag+ ions are ordered in one of the triangular sublattices in the two-dimensional honeycomb lattice at low temperatures. As the temperature increases, the occupation probability of one of the sublattices decreases while that of the other increases. The process can be considered as a formation of some defects which cause the gradual increase of the excess heat capacities above room temperature. Assuming that the defect concentration is dilute enough to neglect any interactions among them, the plots of
HITOSHI KAWAJI et al.
r
come effective. An attempt to obtain the critical exponents has been made from the excess heat capacities near the phase transition temperature as shown in Fig. 6. The data in Fig. 6, however, do not lie on straight lines. The order-disorder mechanism of the phase transition is considered to be affected by a deficiency of Ag+ ions and/or of other chemical impurities.
. . . i # . . . .
Acknowledgements-This work was financially supported in part by Nippon Sheet Glass Foundation for Materials Science to one of the authors (Y.S.).
. . .
-3
REFERENCES
-2 log{ Ir-rtl/rtl
Fig. 6. Properties of the excess heat capacities close to the order-disorder phase transition. (0) Below the transition temperature; (0) above the transition temperature.
In(AC; From
T2) vs T-’ the slope
are drawn
of the straight
as shown line,
in Fig.
the enthalpy
5. of
defect formation is determined as 63.7 kJ.mol-‘. The defect formation is also represented in terms of a flip-flop of a pseudo-spin, and the enthalpy of defect formation corresponds to the effective exchange interaction between the adjacent pseudo-spins. It is well known that the magnitude of the exchange interaction is proportional to and of the same order as the value of transition temperature. This is the case for the order-disorder phase transition of AgCrS,. In Fig. 5, the plots deviate from the straight line above about 620 K, which means the failure of the assumption of independent defects. As the temperature increases, the concentration of the defects increases and thus the cooperative phenomena be-
1. Murphy D. W., Di Salvo F. J., Hull G. W. and Waszczak J. V., Inorg. Chem. 15, 17 (1976). 2. Bongers P. F., van Bruggen C. F., Koopstra J., Omloo W. P. F. A. M., Wiegers G. A. and Jellinek F., J. Phys. Chem. Solids 29, 977 (1968). 3. Engelsman F. M. R., Wiegers G. A.. Jellinek F. and van Laar B., J. Solid St. Chem. 6, 574 (1973). 4. Gerards A. G., Boukamp B. A. and Wiegers G. A., Solid St. lonics 9, 10, 471 (1983). 5. Hibma T., Solid St. Commun. 33, 445 (1980). 6. Hibma T., Phys. Rev. B28, 568 (1983). 7. Hibma T., Briiesch P. and Strassler S., Solid St. Ionics 5, 481 (1981). 8. Briiesch P., Hibma T. and Biihrer W., Phys. Rev. B27, 5052 (1983). 9. Antropov V. M., Pleshcher V. G., Konev V. N. and Kiskin S. M., Fiz. Tverd. Tela (Leningrad) 25, 2767 (1953). 10. Atake T., Kawaji H. and Saito Y., Proceedings of the Fall Meeting of the Elecrrochem. Sot. (Honolulu, U.S.A.. 1987) No. 997 (in press). 11. Atake T., Kawaji H., Hamano A. and Saito Y. (in preparation). 12. Takeda K.. Ubukoshi K.. Haseda T. and Hirakawa K., J. phys. Sot. Japan 53, 1480 (1984). 13. van Laar B. and Ijdo D. J. W., J. Solid St. Chem. 3,590 (1971). 14. Kuindersma S. R., Haas C., Sanchez J. P. and Al R., Solid St. Commun. 30, 403 (1979). 15. Kawaji H.. Atake T. and Saito Y. (in preparation).
1989
0022-3697/89 $3.00 + 0.00 0 1989 Pergamon Press plc
HEAT CAPACITIES, MAGNETIC PHASE TRANSITION AT 42.02 K AND ORDER-DISORDER PHASE TRANSITION AT 673 K OF AgCrS, HITOSHI KAWAJI, TOORU ATAKE and YASUTOSHI SAITO Research Laboratory of Engineering Materials, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku,
Yokohama
227, Japan
(Receioed 12 July 1988; accepted 7 September 1988)
Abstract-Heat capacities of AgCrS, were measured by adiabatic calorimetry between 7 and 327 K and by a.c. calorimetry from room temperature up to 720 K. The antiferromagnetic-paramagnetic phase transition was detected as a diffused first-order type of anomaly at 42.02 K. The enthalpy and entropy of transition were determined as 360 J’mol- and 9.3 J.K-‘.mol-‘, respectively. Phase transition due to the order-disorder AH, = 1.9 kJ.mol-’
of Ag+ ions was observed and AS, = 3.0 J,K-‘.mol-I.
as a typical
second-order
type of anomaly
at 673 K with
Keywords: AgCrS,,
orderdisorder
heat capacity, adiabatic calorimetry, a.c. calorimetry, magnetic phase transition, phase transition.
INTRODUCTION A family of layered chalcogenide compounds of type MCrX, (M = Ag, Cu, Na, Li; X = S, Se) has become of interest in recent years. One of the important features is that some compounds of this group are superionic conductors at high temperatures [l]. As the temperature decreases, some of them exhibit phase transitions due to ordering of M+ ions and of
magnetic spins on the Cr3+ ions. Structures and magnetic properties of these crystals have been reported [2-4]. CrX, forms sandwichlayers of trigonal symmetry, between which the monovalent cations are intercalated. In the case of compounds with M = Ag and Cu, Ag+ (Cu’) ions are located on the tetrahedrally coordinated sites which form a puckered honeycomb lattice; there are two sublattices which are slightly displaced with respect to each other in the direction of the hexagonal c-axis. All the sites on one of the sublattices are occupied with Ag+ (Cu’) ions while the other sublattice is empty at low temperatures (space group R3m). As the temperature increases, however, an order-disorder phase transition occurs at 673 K in AgCrS, [5,6] and at 675 K in CuCrS, [3]. Above the phase transition temperature, Ag+ (Cu’) ions are distributed randomly in both sublattices (space group Rh). The ionic conductivity of AgCrS, is 0.3 S.cm-’ at 673 K [5]. In the case of M = Na and Li, no order-disorder phase transition has been reported [2,3]. Furthermore, an antiferromagnetic ordering takes place for the spin system on Cr3+ ions in the temperature region of 1950 K [2]. The magnetic susceptibility curve of AgCrS, shows a sharp change at 40 K (NCel temperature), above which the magnetization follows the Curie-Weiss law with a nega215
tive Weiss constant (- 55 K, i.e. antiferromagnetic) [2]. The Weiss constant generally reflects the interaction between the nearest neighbor spins. Thus, an AgCrS, crystal can be regarded as a two-dimensional antiferromagnet of triangular lattice of Cr3+ ions. Although some studies have been made on the phase transition phenomena described above [2-91, little is known about the thermodynamic properties and the mechanism of the transitions still remains open. Hence, the present authors have started thermodynamic studies of series of such compounds, and the results of the ac. calorimetry above room temperature have been preliminarily reported for AgCrS, [lo]. In the present paper, the results of heat capacity measurements by adiabatic calorimetry will be given. EXPERIMENTAL Sample preparation
Samples of AgCrS, were synthesized directly from the reactant elements. The high-purity starting materials were purchased from Rare Metallic Co. (Tokyo, Japan) as powdered sulfur of nominal purity of 99.999%, silver shots (99.999%, 1 mm in diameter) and chromium powder of 200 mesh (99.99%). The reactants were mixed in the stoichiometric ratio except for sulfur which was added in slight excess (ca 0.2%). A mixture of about 20g was put into a fused-silica tube (20 mm in diameter and 350 mm in length), which was evacuated and hermetically sealed by fusing. The tube was placed in an electric furnace which was designed to maintain a temperature of 670 K at the top end and 1270 K at the bottom end. The vaporized sulfur was able to react easily with the other reactants and the excess sulfur condensed at
216
HITOSHI KAWAJI et al.
the cooler end of the tube (670 K), avoiding breakage of the tube. A transient intermediate compound Ag,S which possibly formed during the reaction should be in liquid state at 1270 K. Thus, the synthesis was performed in the bottom part of the tube which was maintained at 1270 K for seven days. To remove the excess sulfur, the product was put into a glass tube, which was evacuated at 670 K for 6 h. The final product was identified as the expected
compound AgCrS, by powder X-ray diffractometry using CuK, radiation. No impurity was detected.
Heat capacity measurements Heat capacities below room temperature were measured with a laboratory-made adiabatic calorimeter. A powdered sample of 17.7059g (0.079~5 mol) was loaded into a gold-plated copper vessel equipped with a heater (KARMA wire of
Table 1. Measured molar heat capacities T (K)
CP (J.K-‘.mol-‘) Series
7.40 8.18 8.97 9.91 7.30
8.11 9.04 10.08 11.20 12.32 13.50 14.81 16.20 17.62 19.00 13.40 13.86 12.65 13.77 14.95 16.08 17.27 18.54 19.77 20.98 22.21 23.44 24.64 25.83 27.10 28.42 29.67 30.88 32.05 33.20 34.35 35.51 36.12 37.96 39.21 40.45 41.46 41.94 42.05 42.51 43.64 45.09 46.54 47.93 49.28 SO.67 52.09
1
2.63 3.29 4.15 5.16 Series 2 2.60
3.20 4.20 5.34 6.51 1.59 8.65 9.75 10.92 12.04 12.98 Series 3 8.68 9.08 Series 4 8.03 9.01 9.95 10.80 1 I .66 12.56 13.41 14.19 14.98 15.77 16.53 17.26 18.13 18.97 19.87 20.69 21.61 22.54 23.46 24.54 25.73 27.13 28.92 32.26 63.97 526.69 1233.85 83.63 36.19 31.85 31.14 31.07 31.28 31.59 31.97
T
(K) 53.49 54.89 56.32 57.78 59.29 60.91 62.58 64.19 65.78 67.36 68.97 70.62 72.25 73.85 75.45 77.05 19.75 21.29 22.93 24.47 25.99 27.54 29.02 30.51 32.06 33.63 35.17 36.70 38.18 39.57 40.84 41.69 41.98 42.06 42.41 43.26 44.35 45.48 48.10 49.41 50.81 52.29 53.76 55.23 56.73 58.27 59.81 61.41 63.06 64.68 66.32 67.97 69.61 71.28
CP
(J.K-‘,mol-‘) 32.37 32.82 33.32 33.87 34.44 35.08 35.70 36.37 37.02 37.68 38.35 39.04 39.75 40.46 41.17 41.85 Series 5 13.40 14.39 15.44 16.41 17.40 18.39 19.41 20.45 21.61 22.87 24.22 25.72 27.42 ‘9.61 35.43 116.90 880.04 1096.28 87.86 39.53 32.95 31.48 Series 6 31.16 31.28 31.62 32.00 32.46 32.95 33.48 34.05 34.64 35.28 35.90 36.57 37.26 37.94 38.60 39.34
T
of
%
AgCrSz 7
(K)
(J.K-‘.mol-I)
(K)
72.96 14.65 76.34 78.04 79.78 81.54 83.31 85.10 86.94 88.82 90.71 92.61 94.52 96.43 98.28 100.14
40.07 40.78 41.55 42.28 43.06 43.82 44.61 45.39 46.23 47.06 41.86 48.69 49.52 50.33 51.12 51.89 Series 7 52.74 53.61 54.40 55.27 56.08 56.85 57.67 58.43 Series 8 59.20 59.96 60.71 61.43 62.16 62.88 63.64 64.29 64.99 65.71 66.50 67.18 67.87 68.53 69.24 69.85 70.47 71.11 71.79 72.36 72.91 73.51 74.03 74.58 75.10 75.67 76.08 76.60 II.02 77.57
189.66 192.16 194.64 197.12 199.58 202.03 204.50 207.00 209.49 211.96 214.47 216.99 219.51 222.02 224.51 227.00 229.48 23 1.95 234.45 236.98 239.49 242.00 244.51 247.00 249.52 252.07 254.61 25-i. 15 259.67 262.20 264.71 267.22 269.72 272.2 1 274.70 277.22 279.77 282.31 284.85 287.38 289.90 292.41 294.92 297.43 299.92 302.41 304.93 307.48 310.02 312.56 315.10 317.62 320.15 322.66 325.18 327.69
102.08 104.09 106.13 108.20 110.29 1t2.35 114.41 116.47 118.53 120.61 122.70 124.78 126.88 129.01 131.18 133.38 135.62 137.96 140.36 142.76 145.18 147.63 150.11 152.57 155.04 157.52 159.99 162.47 164.96 167.45 169.91 172.36 174.79 177.25 179.72 182.19 184.66 187.15
CP
(J.K-‘.mol-‘) 77.94 78.38 78.79 79.29 79.62 80.03 80.46 80.78 81.13 81.51 81.79 82.19 82.56 82.88 83.26 83.41 83.74 84.16 84.46 84.69 84.98 85.23 85.53 85.73 86.00 86.30 86.49 86.78 86.97 87.23 87.49 87.70 87.93 88.14 88.41 88.77 88.85 89.04 89.11 89.26 89.50 89.67 89.81 90.04 90.38 90.51 90.90 90.54 90.84 91.02 91.19 91.35 91.59 91.64 91.81 91.84
Heat capacities
100 R, Driver-Harris Co.), a platinum resistance (5187 L, H. Tinsley & Co.) and a germanium resistance thermometer (GR-200A-500, Lake Shore Cryotronics). The calorimeter vessel was evacuated and sealed with Wood’s alloy after the addition of a small amount of helium gas for heat exchange within the vessel (10 kPa at room temperature). For measurements below 50 K, liquid helium was used as the refrigerant. Solid nitrogen was used between 50 and 90 K, and liquid nitrogen was used for measurements above 90 K. Heat capacities of the sample were calculated by subtracting the values corresponding to that of the empty vessel from the measured total heat capacities. The contribution of the sample was about 35% of the total heat capacity. The platinum resistance thermometer was calibrated according to the IPTS-68 at the National Physical Laboratory in England. The germanium scale was based on EPT-76. An a.c. automatic resistance bridge (5840D, H. Tinsley & Co.) was used for temperature measurements with a precision of 0.0001 K. Heat capacities of the sample were determined with a precision of 0.1%. The details of both the apparatus and the operation will be published elsewhere [I 11. Heat capacities above room temperature up to 720 K were measured by using a commercial a.c. calorimeter (ACC-I, Sinku-Riko Inc.). A powdered thermometer
Table 2. Thermodynamic
T (K) 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320
C,(T) (J,K-‘,mol-‘) 5.27 13.56 20.08 28.94 31.41 34.70 38.80 43.15 47.55 51.86 55.94 59.73 63.19 66.34 69.18 71.75 74.07 76.15 78.03 79.71 81.23 82.61 83.88 85.03 86.08 87.05 87.94 88.76 89.52 90.22 90.88 91.48
H(T)-H(0) (J.mol-‘) 14.8 112.8 280.5 523.8 1073.8 1403.0 1770.2 2179.9 2633.4 3130.6 3669.9 4248.5 4863.4 5511.3 6189.1 6894.0 7623.3 8374.6 9145.6 9934.4 10739.2 11558.6 12391.1 13235.7 14091.3 14957.0 15832.0 16715.5 17607.0 18505.8 19411.3 20323.1
217
of AgCrS,
sample was pressed into a tablet of about 0.1 mm thickness. A small piece of the specimen measuring 2 x 3 mm was used for the a.c. calorimetry a Periodic heating on the surface of the sample was made with chopped light at 1.1 Hz. The amplitude of the temperature oscillation was measured by a thermocouple (type E) attached on the other surface of the sample. The signal was detected precisely by using a lock-in amplifier. The temperature of the bath was controlled to a scanning rate of about 5.6 x 10m3K.s-‘. Detailed measurements were made near the order-disorder phase transition temperature at a rate of 5.6 x 10-4K.~-‘. RESULTS AND DISCUSSION Heat capacities and thermodynamic functions The measured molar heat capacities of AgCrS, are tabulated in Table 1 which lists all the data obtained by adiabatic calorimetry from 7 to 327 K. As the data are listed in chronological order, the temperature increment due to each energy input can be estimated from the adjacent mean temperatures. The rate of energy input was varied with temperature, i.e. depending on the values of heat capacities and thermal conductivities. Below about 20 K, the energy input for about 1 K increase in temperature was completed in a few minutes. This input time increased as the temperature increased, and it was functions
of AgCrS,
S(T)- S(0) (J.K-‘.mol-I) 1.99 8.45 15.16 22.09 34.71 40.70 46.36 51.82 57.16 62.39 67.53 72.56 77.48 82.28 86.96 91.50 95.92 100.22 104.39 108.43 112.36 116.17 119.87 123.46 126.96 130.35 133.65 136.87 140.00 143.04 146.01 148.91
-(G(T)- ff(O))IT (J.K-‘.mol-‘) 0.51 2.81 5.81 9.00 13.23 17.32 21.07 24.57 27.90 31.08 34.17 37.16 40.07 42.91 45.69 48.42 51.08 53.69 56.25 58.76 61.22 63.63 66.00 68.32 70.59 72.83 75.02 77.17 79.28 81.36 83.39 85.40
218
HITOSHIKAWAJIet al.
ldj ‘i
‘ii
$
im
200
300
400
500
600
700
1
11---:“1
lrn
50
:
_..*
..-
;.../
9 50
,/
:
25
./
I
/
Oo 1m200
0
20
40
60
fm
0
I
T/K
Fig. 1. Molar heat capacities of AgCrS, measured by adiabatic ~lor~rne~y between 7 and 327 K and a.c. calorimetry above room temperature. about 10min for a 1.5 K increment above 100 K. After the energy input, thermal equilibrium within the calorimeter vessel was attained in a few minutes below 30K, 5 min at about 50 K, and 10 min above 100 K. In the transition region close to 42.02 K, however, it took 30 min to secure thermal uniformity within the calorimeter vessel. The value of some of the thermodynamic functions calculated from the present results are given in Table 2, where a small contribution below 7K was estimated by the method of smooth extrapolation to OK. Heat capacities above room temperature were measured by a.c. calorimetry which did not provide absolute, but relative values of heat capacities. Heat capacity values for those tem~ratures were estimated by using the parameters determined by fitting the data to those obtained by adiabatic calorimetry at 327 K. Therefore, heat capacity values for temperatures above room temperature are excluded from Tables 1 and 2. Heat capacities thus obtained are shown in Fig. 1, in which the antiferromagnetic-paramagnetic phase
/ i-
o-
20
40
60
T/K Fig. 2. Enthalpy vs temperature curve near the magnetic phase transition of AgCrS,.
0 0
20
40
60
I
T/K
Fig. 3. Excess heat capacities due to the magnetic phase transition of AgCrS,.
transition is clearly seen at 42.02 K. The orderdisorder phase transition is also observed as a typical second-order type of anomaly at 673 K.
Magnetic phase tra~s~t~un The antiferromagnetic-paramagnetic phase transition predicted for the spin system on Cr3+ions by magnetic measurements [3] was detected as a sharp anomaly in the heat capacity curve of AgCrS, as shown in Fig. I. The temperature dependence of the enthalpy measured during the present expe~ments is shown, around the transition region, in Fig. 2. The transition point is determined as 42.02 K, which corresponds to the inflection point of the curve. At the transition point, the extremely large gradient of the curve can be considered as the latent heat of transition, which is regarded as first-order though no hysteresis phenomenon was observed during the experiments. Excess heat capacities due to the magnetic phase transition are obtained by subtracting the normal heat capacities from the measured heat capacities. Even though the magnetic transition is of first-order, the lattice heat capacity should scarcely be affected at the transition point, and the normal base line may be drawn as shown in Fig. 1. Excess heat capacities thus estimated are shown in Fig. 3, where the data of two independent series of measurements are given. The anomaly has a large tail extending symmetrically to both higher and lower temperatures. An attempt to estimate the critical exponents is shown in Fig. 4. The plots are not straight lines, but they consist of two parts. The data in the region of log(l T - T,//T,) < - 1.5 lead to an abnormally large value of 1.3 of the critical exponent, which also supports the first-order nature of the transition. On the other hand, the data for the region
Heat capacities of AgCrS,
219
lm
3
0
a -1
-2
-3
1.5
1.6
logf Ir-rtI/rt) Fig. 4. Properties of the excess heat capacities close to the magnetic phase transition. (0) Below the transition temperature; (0) above the transition temperature.
to the contribution of the large tail of the anomaly. Thus the magnetic phase transition is considered as a diffused first-order transition. By integrating the excess heat capacities, the enthalpy of transition is obtained as 360 J.mol-‘. The entropy of transition is also estimated from the graph of C,/T vs T as 9.3 J.K-‘.mol-‘. The results are given in Table 3 together with those of the order-disorder transition at 673 K. The value of the entropy of transition amounts to about 70% of R ln(2S + 1) = 11.526 J.K-‘.mol-‘, which is the expected value for a complete ordering of the spins, unlike the cases of typical two-dimensional triangular Heisenberg antiferromagnets such as VCl, and VBr,, in which the AS, values are less than 10% of the ideal entropy of transition [12]. Thus, the ordering of the spins is well established through the magnetic phase transition in AgCrS,, while highly frustrated or less ordered states are maintained in VCI, and VBr, at low temperatures. Although the magnetic structure of AgCrS, below the transition has not yet been determined, it is suggested that it is more complicated than those of the other members such as LiCrS, of the MCrX, family. A collinear arrangement of the spins is realized in LiCrS, below 55 K [13], which is similar to the case of VI, below 13.5 K [14]. The detailed
Table 3.Properties of the magnetic phase transition
(2) 42.02 673
and the orderdisorder transition of AgCrS, AH, (J.mol-‘) 360 1900
phase
AS, (J,K-‘.mol-‘) 9.3 3.0
1.9
.O
Fig. 5. Properties of the excess heat capacities above room temperature. discussion
log(l T - T,I/T,) > - 1.5 correspond
1.7 1.8 T-'AK-'
of
the
analysis
and
comparison
with
CuCrS, will be published shortly [15]. Order-disorder phase transition The value of the heat capacity of AgCrS, is very close to the classical limit of 4 x 3R = 99.77 J.K-‘.mol-’ at room temperature. Above room temperature, however, the heat capacity still increases. The value increases gradually, then more rapidly at high temperatures, and finally ends with a rapid drop at 673 K as seen in Fig. 1. The shape of the anomaly is of a typical second-order transition associated with little fluctuation in the order parameters at the transition point. The thermodynamic properties of this phase transition can be analyzed on the basis of the order-disorder mechanism of Ag+ ions in the two-dimensional honeycomb lattice. The excess heat capacity due to the phase transition is calculated by subtracting the normal heat capacities in the same manner as described for the magnetic phase transition. The base line is shown by a solid line in Fig. 1. The enthalpy and entropy of phase transition are thus calculated and given in Table 3. The value of the entropy of phase transition (3.0 J.K-‘.mol-‘) corresponds to about 52% of the theoretically expected value of R In 2 = 5.76 J.K-‘.mol-‘. The Ag+ ions are ordered in one of the triangular sublattices in the two-dimensional honeycomb lattice at low temperatures. As the temperature increases, the occupation probability of one of the sublattices decreases while that of the other increases. The process can be considered as a formation of some defects which cause the gradual increase of the excess heat capacities above room temperature. Assuming that the defect concentration is dilute enough to neglect any interactions among them, the plots of
HITOSHI KAWAJI et al.
r
come effective. An attempt to obtain the critical exponents has been made from the excess heat capacities near the phase transition temperature as shown in Fig. 6. The data in Fig. 6, however, do not lie on straight lines. The order-disorder mechanism of the phase transition is considered to be affected by a deficiency of Ag+ ions and/or of other chemical impurities.
. . . i # . . . .
Acknowledgements-This work was financially supported in part by Nippon Sheet Glass Foundation for Materials Science to one of the authors (Y.S.).
. . .
-3
REFERENCES
-2 log{ Ir-rtl/rtl
Fig. 6. Properties of the excess heat capacities close to the order-disorder phase transition. (0) Below the transition temperature; (0) above the transition temperature.
In(AC; From
T2) vs T-’ the slope
are drawn
of the straight
as shown line,
in Fig.
the enthalpy
5. of
defect formation is determined as 63.7 kJ.mol-‘. The defect formation is also represented in terms of a flip-flop of a pseudo-spin, and the enthalpy of defect formation corresponds to the effective exchange interaction between the adjacent pseudo-spins. It is well known that the magnitude of the exchange interaction is proportional to and of the same order as the value of transition temperature. This is the case for the order-disorder phase transition of AgCrS,. In Fig. 5, the plots deviate from the straight line above about 620 K, which means the failure of the assumption of independent defects. As the temperature increases, the concentration of the defects increases and thus the cooperative phenomena be-
1. Murphy D. W., Di Salvo F. J., Hull G. W. and Waszczak J. V., Inorg. Chem. 15, 17 (1976). 2. Bongers P. F., van Bruggen C. F., Koopstra J., Omloo W. P. F. A. M., Wiegers G. A. and Jellinek F., J. Phys. Chem. Solids 29, 977 (1968). 3. Engelsman F. M. R., Wiegers G. A.. Jellinek F. and van Laar B., J. Solid St. Chem. 6, 574 (1973). 4. Gerards A. G., Boukamp B. A. and Wiegers G. A., Solid St. lonics 9, 10, 471 (1983). 5. Hibma T., Solid St. Commun. 33, 445 (1980). 6. Hibma T., Phys. Rev. B28, 568 (1983). 7. Hibma T., Briiesch P. and Strassler S., Solid St. Ionics 5, 481 (1981). 8. Briiesch P., Hibma T. and Biihrer W., Phys. Rev. B27, 5052 (1983). 9. Antropov V. M., Pleshcher V. G., Konev V. N. and Kiskin S. M., Fiz. Tverd. Tela (Leningrad) 25, 2767 (1953). 10. Atake T., Kawaji H. and Saito Y., Proceedings of the Fall Meeting of the Elecrrochem. Sot. (Honolulu, U.S.A.. 1987) No. 997 (in press). 11. Atake T., Kawaji H., Hamano A. and Saito Y. (in preparation). 12. Takeda K.. Ubukoshi K.. Haseda T. and Hirakawa K., J. phys. Sot. Japan 53, 1480 (1984). 13. van Laar B. and Ijdo D. J. W., J. Solid St. Chem. 3,590 (1971). 14. Kuindersma S. R., Haas C., Sanchez J. P. and Al R., Solid St. Commun. 30, 403 (1979). 15. Kawaji H.. Atake T. and Saito Y. (in preparation).