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Anomalous thermal expansion at phase transitions of Ag4RbI5
~
Solid State Communications, Vol.40, pp.253-254. Pergamon Press Ltd. 1981. Printed in Great Britain.
ANOMALOUS THERMAL EXPANSION AT PHASE TRANSITIONS
Department
0038-1098/81/390253-02
$02.00/0
OF Ag4RhI5*
J. Genossar, A. Gordon, M.O. Steinitz**, and R. Well of Physics, Technion - Israel Institute of Technology, Haifa, Israel (Received 27 July 1981 by J. Tauc)
High resolution capacitance dllatometry has been used to verify the first-order nature of the 208 K phase transition in Ag Rbl and to measure the volume change at the 122 K first-order phase transition. The latter is in accord wlth prediction using the Clausius-Clapeyron equation. Problems relating to the chemical stability of the compound are discussed.
digital plotter (Houston Instruments HI-Plot). Polycrystalline samples were prepared by melting dried Agl and Rhl in stoichiometric proportions, quenching and crushing the Ag~Rhl s to form a powder. The powder was thoroughly mixed, placed in the bottom of a test-tube, remelted and quenched to room temperature. The test-tube was then broken. The cast Ag~Rbl s broke into several roughly equal pieces with edges of the order of 3 mm. The samples were then annealed in a sealed vessel under a vacuum of about 5x10 -2 Torr for 45 hours at 465 K. All operations were carried out in the dark, apart from handling, which was done under red light. Specimens consisting of several large (m,, size) monocrystalline grains were kindly supplied by M.B. Salamon of the University of Illinois. At 122 K, as shown in Figure IA, we find a clear change in volume of dV/V = 3xd~/£ = = l.Sx10-~ This varied by less than 10% among seven fresh samples. Using the value of dTc/dP = 5.65K/kbar found by Allen and Lazarus 4 and the latent heat of 190 cal/mole as determined by Johnston et al. 6 the ClausiusClapeyron equation gives a value of dV/V = --3. = 1.7x10 in very good agreement with our measurements. At 208 K, we find a first-order change in volume of dV/V = 3xd£/£ = 9x10 -~ which is reproducible to within 10% on cycling the temperature within a range of about 30 K around 208 K. Figure iB shows this phase transition in a large-grained sample. However, it is difficult to correlate this length (volume) change with other reported measurements. Allen and Lazarus ~ report a very small linear term in their T c versus P experiment for the 208 K transition (viz. AT c = 0.141xP + 0.111xP 2, where P is in kbars). This together with our measurements of volume changes implies a very large change in entropy (AS 50 cal/mole K) at the phase transition. However, no latent heat has been reported6'~ only a wide (~2 K) peak in specific heat, which when integrated gives AS ~ 0.8 cal/mole K. Also.the ~uadratic term as determined by Allen and Lazarus , is of the opposite sign from that expected from the observed jump in the modulus of compressibility (Chang and Graham 5 ). In addition, the alternative assumption, that the 208 K phase transi-
There has been m u c h interest recently in the nature of the phase transitions at 122 K and 208 K in Ag~Rbls, one of the most extensively studied of super-ionic-conductors. The transition at 122 K is known to be of first order. Although nuclear quadrupole resonance I and neutron d i f f r a c t i o ~ h o t h suggest that the transition at 208 K is of first order, a previous thermal expansivity study of single crystals 3 showed "no anomaly such as a kink, discontinuity or critical behavior at T ffi 209 K.". We report here the results of a successful search for such discontinuities at 122 and 208 K using a highly sensitive capacitance dilatometer. Previous research on this material has provided a background of relevant information. The pressure dependence of both transition temperatures had been measured by Allen and Lazarus ~, the anomalies in the elastic constants by Graham and Chang s, the latent heat at 122 K by Johnston et al. 6 and the specific heat and resistivity near 208 K by Vargas et al. 7 Salamon 8, by adding a Jahn,Teller-like interaction with the lattice to a three-dimensional Ising model, was able to explain the behavior of the optical birefringence near 208 K and predicted that this transition should be weakly first-order. We have made high-resolution measurements of the thermal expansivity of Ag~Rbl s near 122 K and 208 K using a capacitance dilatometer in conjunction with a General Radio 1688 Capacitance Bridge. Temperature was measured using a copper constantan thermocouple and a Tabor digital voltmeter. All instruments were connected via the IEEE-488 interface bus to a Commodore PET microcomputer which reduced the capacitance changes to length changes, reduced the thermocouple voltage to temperature (with a ten-term series approximation good to 0.5 K over the range 33 to 433 K), and plotted the data on a
*
**
Work supported in part by the Natural Sciences and Engineering Research Council of Canada. Permanent address: Dept. of Physics, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G ICO. 253
ANOMALOUS THERMAL EXPANSION AT PHASE TRANSITIONS OF Ag4Rbl S
254
T (K) 220
200 l
i
l
240 i
l
RbAg415
I
I
100
I
I
120
I
14(
T(K) Fig, I
Chart recorder tracing of relative sample length changes vs, temperature A) in the vicinity of 122 K, B) in the vicinity of 208 K. Both measurements made during heating at 0.5 deg/mln. Hysteresis is visible.
tion is of second order, cannot be reconciled either with the discontinuities in length here, or with the observed thermal expansion coefficient data using the Ehrenfest relations. Thus we still lack a consistent picture in order to interpret the conflicting measurements at the 208 K phase transition. The length changes were found to be repro-
Vol. 40, No. 3
ducible to within 20% in the first run made on each of our seven polycrystalline samples. The measurements on the large-grained samples were in agreement with these measurements. The anomalies at 208 and 122 K decrease in magnitude, however, each time the sample is cycled between temperatures below 208K and room temperature, Reannealing at 463 K partially restores the original behavior. Unanaealed polycrystalline samples showed no anomalies at all. The compound Ag~RBI s is known to be chemically unstable, as discussed recently by Valverde s. The decomposition is most rapid around 0°C, which is in accord with our observations. The length change at 208 K was also occasionally seen to change sign, (after repeated temperature cycles) suggesting that the length changes may, perhaps, be anlsotroplc, with the cubic, high-temperature phase transforming preferentially to one or another orientation of the low symmetry low temperature phase under the influence of internal stresses, temperature gradients, etc. The volume change, being the sum of anisotropic contributions, might thus be very small. The change in sign could, however, conceivably arise from cracking of the sample. Such cracking has been mentioned by other authors. The length changes at both transitions go to zero after repeated cycling to room temperature, which we presume is due to the chemical decomposition of the sample, and which may account for the null effect observed by Wu et al. 3. - O n e of the authors (M.O.S.) would like to express his gratitude to the Technion and its Physics Department for their hospitality, and to the Lady Davis Trust for appointing him as visiting professor. We are grateful to Prof. M.B. Salamon for the use of his samples.
Acknowledgements
REFERENCES
i.
2.
3. 4.
D. Brinkmann, W. Freudenheich, H. Arend, and J. Roos, Solid State Communications
5.
2_!, 133
6.
(1978).
S.M. Shapiro, D. Semmlngsen, and M. Salamo~ in Proceedings of the International Conference on Lattice Dynamics, Edited by M. Balkanski (Fl~mmarion, Paris, 1978), p. 538. A.Y. Wu, R . J . S l a d e k , and J . C . M i k k e l s e n , S o l i d S t a t e Communications, 3_~6, 51 (1980). P.C. Allen, and D. Lazarus, Physical Review BI7, 1913 (1978).
7. 8. 9.
L.J. Graham, and R. Chang, Journal of Applied Physics 46, 2433 (1975). W.V. Johnston, H. Wiedersich, and G.W. Lindberg, Journal Chemical Physics 51, 3729 (1969). R.A. Varga, M.B. Salamon, and C.P. Flynn, Physical Review BI7, 269 (1977). M.B. Salamon, Physical Review BIS, 2236 (1977). N. Valverde, Journal of Electrochemical Society 127, 2425 (1980).
Solid State Communications, Vol.40, pp.253-254. Pergamon Press Ltd. 1981. Printed in Great Britain.
ANOMALOUS THERMAL EXPANSION AT PHASE TRANSITIONS
Department
0038-1098/81/390253-02
$02.00/0
OF Ag4RhI5*
J. Genossar, A. Gordon, M.O. Steinitz**, and R. Well of Physics, Technion - Israel Institute of Technology, Haifa, Israel (Received 27 July 1981 by J. Tauc)
High resolution capacitance dllatometry has been used to verify the first-order nature of the 208 K phase transition in Ag Rbl and to measure the volume change at the 122 K first-order phase transition. The latter is in accord wlth prediction using the Clausius-Clapeyron equation. Problems relating to the chemical stability of the compound are discussed.
digital plotter (Houston Instruments HI-Plot). Polycrystalline samples were prepared by melting dried Agl and Rhl in stoichiometric proportions, quenching and crushing the Ag~Rhl s to form a powder. The powder was thoroughly mixed, placed in the bottom of a test-tube, remelted and quenched to room temperature. The test-tube was then broken. The cast Ag~Rbl s broke into several roughly equal pieces with edges of the order of 3 mm. The samples were then annealed in a sealed vessel under a vacuum of about 5x10 -2 Torr for 45 hours at 465 K. All operations were carried out in the dark, apart from handling, which was done under red light. Specimens consisting of several large (m,, size) monocrystalline grains were kindly supplied by M.B. Salamon of the University of Illinois. At 122 K, as shown in Figure IA, we find a clear change in volume of dV/V = 3xd~/£ = = l.Sx10-~ This varied by less than 10% among seven fresh samples. Using the value of dTc/dP = 5.65K/kbar found by Allen and Lazarus 4 and the latent heat of 190 cal/mole as determined by Johnston et al. 6 the ClausiusClapeyron equation gives a value of dV/V = --3. = 1.7x10 in very good agreement with our measurements. At 208 K, we find a first-order change in volume of dV/V = 3xd£/£ = 9x10 -~ which is reproducible to within 10% on cycling the temperature within a range of about 30 K around 208 K. Figure iB shows this phase transition in a large-grained sample. However, it is difficult to correlate this length (volume) change with other reported measurements. Allen and Lazarus ~ report a very small linear term in their T c versus P experiment for the 208 K transition (viz. AT c = 0.141xP + 0.111xP 2, where P is in kbars). This together with our measurements of volume changes implies a very large change in entropy (AS 50 cal/mole K) at the phase transition. However, no latent heat has been reported6'~ only a wide (~2 K) peak in specific heat, which when integrated gives AS ~ 0.8 cal/mole K. Also.the ~uadratic term as determined by Allen and Lazarus , is of the opposite sign from that expected from the observed jump in the modulus of compressibility (Chang and Graham 5 ). In addition, the alternative assumption, that the 208 K phase transi-
There has been m u c h interest recently in the nature of the phase transitions at 122 K and 208 K in Ag~Rbls, one of the most extensively studied of super-ionic-conductors. The transition at 122 K is known to be of first order. Although nuclear quadrupole resonance I and neutron d i f f r a c t i o ~ h o t h suggest that the transition at 208 K is of first order, a previous thermal expansivity study of single crystals 3 showed "no anomaly such as a kink, discontinuity or critical behavior at T ffi 209 K.". We report here the results of a successful search for such discontinuities at 122 and 208 K using a highly sensitive capacitance dilatometer. Previous research on this material has provided a background of relevant information. The pressure dependence of both transition temperatures had been measured by Allen and Lazarus ~, the anomalies in the elastic constants by Graham and Chang s, the latent heat at 122 K by Johnston et al. 6 and the specific heat and resistivity near 208 K by Vargas et al. 7 Salamon 8, by adding a Jahn,Teller-like interaction with the lattice to a three-dimensional Ising model, was able to explain the behavior of the optical birefringence near 208 K and predicted that this transition should be weakly first-order. We have made high-resolution measurements of the thermal expansivity of Ag~Rbl s near 122 K and 208 K using a capacitance dilatometer in conjunction with a General Radio 1688 Capacitance Bridge. Temperature was measured using a copper constantan thermocouple and a Tabor digital voltmeter. All instruments were connected via the IEEE-488 interface bus to a Commodore PET microcomputer which reduced the capacitance changes to length changes, reduced the thermocouple voltage to temperature (with a ten-term series approximation good to 0.5 K over the range 33 to 433 K), and plotted the data on a
*
**
Work supported in part by the Natural Sciences and Engineering Research Council of Canada. Permanent address: Dept. of Physics, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G ICO. 253
ANOMALOUS THERMAL EXPANSION AT PHASE TRANSITIONS OF Ag4Rbl S
254
T (K) 220
200 l
i
l
240 i
l
RbAg415
I
I
100
I
I
120
I
14(
T(K) Fig, I
Chart recorder tracing of relative sample length changes vs, temperature A) in the vicinity of 122 K, B) in the vicinity of 208 K. Both measurements made during heating at 0.5 deg/mln. Hysteresis is visible.
tion is of second order, cannot be reconciled either with the discontinuities in length here, or with the observed thermal expansion coefficient data using the Ehrenfest relations. Thus we still lack a consistent picture in order to interpret the conflicting measurements at the 208 K phase transition. The length changes were found to be repro-
Vol. 40, No. 3
ducible to within 20% in the first run made on each of our seven polycrystalline samples. The measurements on the large-grained samples were in agreement with these measurements. The anomalies at 208 and 122 K decrease in magnitude, however, each time the sample is cycled between temperatures below 208K and room temperature, Reannealing at 463 K partially restores the original behavior. Unanaealed polycrystalline samples showed no anomalies at all. The compound Ag~RBI s is known to be chemically unstable, as discussed recently by Valverde s. The decomposition is most rapid around 0°C, which is in accord with our observations. The length change at 208 K was also occasionally seen to change sign, (after repeated temperature cycles) suggesting that the length changes may, perhaps, be anlsotroplc, with the cubic, high-temperature phase transforming preferentially to one or another orientation of the low symmetry low temperature phase under the influence of internal stresses, temperature gradients, etc. The volume change, being the sum of anisotropic contributions, might thus be very small. The change in sign could, however, conceivably arise from cracking of the sample. Such cracking has been mentioned by other authors. The length changes at both transitions go to zero after repeated cycling to room temperature, which we presume is due to the chemical decomposition of the sample, and which may account for the null effect observed by Wu et al. 3. - O n e of the authors (M.O.S.) would like to express his gratitude to the Technion and its Physics Department for their hospitality, and to the Lady Davis Trust for appointing him as visiting professor. We are grateful to Prof. M.B. Salamon for the use of his samples.
Acknowledgements
REFERENCES
i.
2.
3. 4.
D. Brinkmann, W. Freudenheich, H. Arend, and J. Roos, Solid State Communications
5.
2_!, 133
6.
(1978).
S.M. Shapiro, D. Semmlngsen, and M. Salamo~ in Proceedings of the International Conference on Lattice Dynamics, Edited by M. Balkanski (Fl~mmarion, Paris, 1978), p. 538. A.Y. Wu, R . J . S l a d e k , and J . C . M i k k e l s e n , S o l i d S t a t e Communications, 3_~6, 51 (1980). P.C. Allen, and D. Lazarus, Physical Review BI7, 1913 (1978).
7. 8. 9.
L.J. Graham, and R. Chang, Journal of Applied Physics 46, 2433 (1975). W.V. Johnston, H. Wiedersich, and G.W. Lindberg, Journal Chemical Physics 51, 3729 (1969). R.A. Varga, M.B. Salamon, and C.P. Flynn, Physical Review BI7, 269 (1977). M.B. Salamon, Physical Review BIS, 2236 (1977). N. Valverde, Journal of Electrochemical Society 127, 2425 (1980).