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Br0.3·3H2
Volume 51 A, number 2
PHYSICS LETTERS
10
February 1975
CALORIMETRIC STUDY OF THE PHONON INDUCED PHASE TRANSITION IN K,Pt/CN/Br0g3H20 K. FRANULNIC
and D. DJUREK
Institute of Physics, Universi~ of Zagreb, Zagreb, Yugoslavia
Received15 January 1975 The quasi-onediiensional conductor K2Pt/C!N/4Bro.3 *3H20 (KCP)exhibitsa specificheat anomalyin the temperature rangearound 123 K. KCP is one of the quasi-one-dimensional conductors which, by its interesting conducting properties, deserves a wide interest. It was already investigated by numerous [l] experimental methods. The most appropriate methods to the type of the involved phenomena ap peared to be the X-ray [2] and neutron [3] scattering. The results showed that by cooling the specimen to the temperatures of the order of 100 K the group of phonons in the vicinity of the [n/U, n/a, 2kF] point of the BriIlouin zone (BZ) is appreciably softened. We wish to report here the first observation of the specific heat anomaly related to this effect. The method used in this measurement is similar to that described previously [4]. The small glass container filled with polycrystalline KCP is thermally connected to the large heat sink by the thermal resistance R,. The specific heat information is obtained from the exponential temperature response of the sample to the applied Joule power. The total heat capacity Cp of the sample is determined from the time constant R, of the exponential temperature decay. The specific heat is avereged in the intervals of about 0.2-l K. During the exponential temperature recordings the sink was maintained at a constant temperature stabilised to 0.01 K and temperature was monitored with copperconstantan thermocouple. The maximal resolution of the specific heat measurement is about 0.3%. Because of strong corosive activity of KCP the copper constantan thermocouple used for temperature recordings was protected by thin glass cover. As pointed out previously [ 1J , the physical properties of KCP are strongly affected by the water content. Therefore, care was taken to avoid the water losses, during mounting of the specimen and the measurement run. The heat capacity of the glass container, heater wires and
bonding agent is determined in a separate blank experiment . After careful removing of the silicone rubber seal, KCP was dissolved by water and replaced by equivalent volume of fine copper powder in order to simulate the conditions of the measurement. The known heat capacity of copper powder was than subtracted from the total heat capacity obtained by blank experiment procedure. As expected, the specific heat anomaly is present in the temperature range around 100 K. The peak represents about 7% of the already large total specific heat. The background specific heat exceeds considerably the value of 3R0, the maximum specific heat of the acoustic modes. In the relatively small temperature range examined the background term seems to increase linearly with temperature [S] . The singular part of the specific heat, shown in the insert of fig. 1, is obtained by subtracting this “linear” background. The large relative value of the peak should be compared to
loo
110
120
130
x0
T(K) (
pig. 1. Specificheat of KCP.In the insert the linearbackground is substmctedin order to showthe sing&u part of the specific heat anomaly. 91
Volume 51A, number 2
PHYSICS LETTERS
the weaker effect observed in TTF-TCNQ [6] , and to corresponding anomalies in V$i [7] and Nb,Sn [8], which occur at considerably lower temperatures, in the T3 regime. The observation of the rather well defined peak is perhaps somewhat surprising in view of the neutron scattering data [3] which seem to indicate that the full long-range-order (LRO) is not attained in KCP. According to this work, the dominant softening does occur in the isolated point of the BZ [9] . The overall effect is therefore three-dimensional in the sense that deformations on adjecent Pt chains are strongly correlated. The degree of correlation between the deformations of remote chains is described by the correlation length &. Together with 5,,, .$ describes the wave vector dependence of the scattering cross section in the vicinity of the point [n/u, n/u, 2kP], i.e. the crossover from one-dimensional to three-dimensional behaviour. Due to limited experimental resolution only the distances smaller than roughly 50 A, could have been measured. This prevented the measurement of .$,,, while E1was shown to increase steeply from 5 R to 35A on cooling from 130 K to 100 K. Below this temperature .!l seems to saturate instead of diverging. This absence of LRO should probably be related to imperfection of the three-dimensional chain lattice. The soft phonons can be considered as the fluctuations of the complex (n = 2) order parameter, in which the phase only is spatially dependent [lo] . It is usually believed [ 111 that the pinning effects arising from commensurability or imperfections reduce n to n = 1. Thecrossoverinthen=1,d=3+d=1casewasrecently investigated by Dietrich [ 121, who obtained an ap roximate expression for the correlation function ! where $(p) is the scalar order parameter. The inWk), tegral of (@ over the reciprocial space, with appropriate cut-offs. ‘ves [13] the singular part of the entropy. Since ($,)? is simple Lorentzian [ 121 characterized by .$ and G, this integration can be carried out exactly [ 141. The resulting expression describes how the threedimensional singularity raises from the onedimensional non-singular [ 131 back-ground as the temperature is lowered towards the critical temperature. Close to this temperature the specific heat C, is proportional to [,, . In the Dieterich theory [ 121 this
92
10 February 1975
latter diverges with the mean-field indice v = 4, i.e. Q =L 2. Such or similar divergence is not observed, either because of the insufficient experimental resolution or because of the mentioned possibility that LRO is not complete. After going through a finite maximum Cp exhibits a “triangular” decrease. This latter is usually attributed to the temperature dependence of the static order parameter. Although probably qualitatively correct, this interpretation should be taken with some caution, again since the full LRO seems to be absent in KCP. In conclusion, our specific heat data are consistent with neutron scattering results, which in turn agree qualitatively with the theoretical crossover calculations. The authors are indebted to Dr. S. Bar-i&cfor ilhtmi. nating discussions, to Dr. I-I.Launois for a gift of the samples and to Ing. K. Uzelac for carrying out relevant calculation. This work was supported by the Scientific Research Council of the SR Croatia.
References [l] H.R. tiller, Festkorperproblems, 13 (1973) 31. [2] R. Comes, M. Lambert and H.R. Zeller, Phye. Stat. Sol. (b), 58 (1973) 587. [3] B. Renker et al. Phys. Rev. Lett. 32 (1974) 836. [4] D. Djurek, J. Baturic-Rubcic and K. Franulovic, Phys. Rev. L&t. 33 (1974) 1126. [ 51 The linear specific heat was also observed at very low temperatures by A. Niedoba and H. Launois, unpublished. [6] R.A. Craven et al., Phys. Rev. Lett. 32 (1974) 769. [7] J.E. Kunzler, P. Maita, H.J. Leestein, E.J. Ryder, Phys. Rev. 143 (1966) 390. [S] L.J. Vieland and A.W. Wicklund, Phys. Rev. 166 (1968) 424. [9] S. Barisic, K. Saub, J. Phys. C 6 (1973) 2367; A. Bjelis, K. Saub and S. Barisic, N. Cimento 23B (1974) 102. [lo] S. Barisic, Proc. Saarbruken Meeting on Onedimensional conductors (Springer Ver. 1974); S. Barisic and K. Uzelac, J. Phys. (Paris), to be published. [ 11 J G. Toulouse, N. Chnento, 23B (1974) 234. [ 121 W. Dieterich, Z&t&rift fur Physik, 270 (1974) 239. [ 13 j R.A. Ferrell and D.J. Scalapino, Phys. Rev. A9 (1974) 846. [ 141 K. Uzelac, unpublished.
PHYSICS LETTERS
10
February 1975
CALORIMETRIC STUDY OF THE PHONON INDUCED PHASE TRANSITION IN K,Pt/CN/Br0g3H20 K. FRANULNIC
and D. DJUREK
Institute of Physics, Universi~ of Zagreb, Zagreb, Yugoslavia
Received15 January 1975 The quasi-onediiensional conductor K2Pt/C!N/4Bro.3 *3H20 (KCP)exhibitsa specificheat anomalyin the temperature rangearound 123 K. KCP is one of the quasi-one-dimensional conductors which, by its interesting conducting properties, deserves a wide interest. It was already investigated by numerous [l] experimental methods. The most appropriate methods to the type of the involved phenomena ap peared to be the X-ray [2] and neutron [3] scattering. The results showed that by cooling the specimen to the temperatures of the order of 100 K the group of phonons in the vicinity of the [n/U, n/a, 2kF] point of the BriIlouin zone (BZ) is appreciably softened. We wish to report here the first observation of the specific heat anomaly related to this effect. The method used in this measurement is similar to that described previously [4]. The small glass container filled with polycrystalline KCP is thermally connected to the large heat sink by the thermal resistance R,. The specific heat information is obtained from the exponential temperature response of the sample to the applied Joule power. The total heat capacity Cp of the sample is determined from the time constant R, of the exponential temperature decay. The specific heat is avereged in the intervals of about 0.2-l K. During the exponential temperature recordings the sink was maintained at a constant temperature stabilised to 0.01 K and temperature was monitored with copperconstantan thermocouple. The maximal resolution of the specific heat measurement is about 0.3%. Because of strong corosive activity of KCP the copper constantan thermocouple used for temperature recordings was protected by thin glass cover. As pointed out previously [ 1J , the physical properties of KCP are strongly affected by the water content. Therefore, care was taken to avoid the water losses, during mounting of the specimen and the measurement run. The heat capacity of the glass container, heater wires and
bonding agent is determined in a separate blank experiment . After careful removing of the silicone rubber seal, KCP was dissolved by water and replaced by equivalent volume of fine copper powder in order to simulate the conditions of the measurement. The known heat capacity of copper powder was than subtracted from the total heat capacity obtained by blank experiment procedure. As expected, the specific heat anomaly is present in the temperature range around 100 K. The peak represents about 7% of the already large total specific heat. The background specific heat exceeds considerably the value of 3R0, the maximum specific heat of the acoustic modes. In the relatively small temperature range examined the background term seems to increase linearly with temperature [S] . The singular part of the specific heat, shown in the insert of fig. 1, is obtained by subtracting this “linear” background. The large relative value of the peak should be compared to
loo
110
120
130
x0
T(K) (
pig. 1. Specificheat of KCP.In the insert the linearbackground is substmctedin order to showthe sing&u part of the specific heat anomaly. 91
Volume 51A, number 2
PHYSICS LETTERS
the weaker effect observed in TTF-TCNQ [6] , and to corresponding anomalies in V$i [7] and Nb,Sn [8], which occur at considerably lower temperatures, in the T3 regime. The observation of the rather well defined peak is perhaps somewhat surprising in view of the neutron scattering data [3] which seem to indicate that the full long-range-order (LRO) is not attained in KCP. According to this work, the dominant softening does occur in the isolated point of the BZ [9] . The overall effect is therefore three-dimensional in the sense that deformations on adjecent Pt chains are strongly correlated. The degree of correlation between the deformations of remote chains is described by the correlation length &. Together with 5,,, .$ describes the wave vector dependence of the scattering cross section in the vicinity of the point [n/u, n/u, 2kP], i.e. the crossover from one-dimensional to three-dimensional behaviour. Due to limited experimental resolution only the distances smaller than roughly 50 A, could have been measured. This prevented the measurement of .$,,, while E1was shown to increase steeply from 5 R to 35A on cooling from 130 K to 100 K. Below this temperature .!l seems to saturate instead of diverging. This absence of LRO should probably be related to imperfection of the three-dimensional chain lattice. The soft phonons can be considered as the fluctuations of the complex (n = 2) order parameter, in which the phase only is spatially dependent [lo] . It is usually believed [ 111 that the pinning effects arising from commensurability or imperfections reduce n to n = 1. Thecrossoverinthen=1,d=3+d=1casewasrecently investigated by Dietrich [ 121, who obtained an ap roximate expression for the correlation function ! where $(p) is the scalar order parameter. The inWk), tegral of (@ over the reciprocial space, with appropriate cut-offs. ‘ves [13] the singular part of the entropy. Since ($,)? is simple Lorentzian [ 121 characterized by .$ and G, this integration can be carried out exactly [ 141. The resulting expression describes how the threedimensional singularity raises from the onedimensional non-singular [ 131 back-ground as the temperature is lowered towards the critical temperature. Close to this temperature the specific heat C, is proportional to [,, . In the Dieterich theory [ 121 this
92
10 February 1975
latter diverges with the mean-field indice v = 4, i.e. Q =L 2. Such or similar divergence is not observed, either because of the insufficient experimental resolution or because of the mentioned possibility that LRO is not complete. After going through a finite maximum Cp exhibits a “triangular” decrease. This latter is usually attributed to the temperature dependence of the static order parameter. Although probably qualitatively correct, this interpretation should be taken with some caution, again since the full LRO seems to be absent in KCP. In conclusion, our specific heat data are consistent with neutron scattering results, which in turn agree qualitatively with the theoretical crossover calculations. The authors are indebted to Dr. S. Bar-i&cfor ilhtmi. nating discussions, to Dr. I-I.Launois for a gift of the samples and to Ing. K. Uzelac for carrying out relevant calculation. This work was supported by the Scientific Research Council of the SR Croatia.
References [l] H.R. tiller, Festkorperproblems, 13 (1973) 31. [2] R. Comes, M. Lambert and H.R. Zeller, Phye. Stat. Sol. (b), 58 (1973) 587. [3] B. Renker et al. Phys. Rev. Lett. 32 (1974) 836. [4] D. Djurek, J. Baturic-Rubcic and K. Franulovic, Phys. Rev. L&t. 33 (1974) 1126. [ 51 The linear specific heat was also observed at very low temperatures by A. Niedoba and H. Launois, unpublished. [6] R.A. Craven et al., Phys. Rev. Lett. 32 (1974) 769. [7] J.E. Kunzler, P. Maita, H.J. Leestein, E.J. Ryder, Phys. Rev. 143 (1966) 390. [S] L.J. Vieland and A.W. Wicklund, Phys. Rev. 166 (1968) 424. [9] S. Barisic, K. Saub, J. Phys. C 6 (1973) 2367; A. Bjelis, K. Saub and S. Barisic, N. Cimento 23B (1974) 102. [lo] S. Barisic, Proc. Saarbruken Meeting on Onedimensional conductors (Springer Ver. 1974); S. Barisic and K. Uzelac, J. Phys. (Paris), to be published. [ 11 J G. Toulouse, N. Chnento, 23B (1974) 234. [ 121 W. Dieterich, Z&t&rift fur Physik, 270 (1974) 239. [ 13 j R.A. Ferrell and D.J. Scalapino, Phys. Rev. A9 (1974) 846. [ 141 K. Uzelac, unpublished.