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Thermal conductivity of Rochelle salt
Volume 39A, number 3
PHYSICS LETTERS
8 May 1972
THERMAL CONDUCTIVITY OF ROCHELLE SALT* H. SCHAFER, J. ALBERS, and J. HELWlG Institut ffir Experimentalphysik 11 der Universitk't des Saarlandes, Saarbriicken Received 20 March 1972 The temperature dependence of the anisotropic thermal conductivity of a Rochelle salt single crystal was investigated in different crystallographicdirections in the range from -35 to + 40°C. No anomalous behaviourwas found near the Curie points.
Because of the great interest in experimental data of materials near a continuous phase transition we decided to measure the thermal conductivity of Rochelle salt, which presents two second order transitions at about - 1 8 and +24°C. Our intention was to investigate any influence of the scattering of longitudinal or transverse thermal phonons by polarization fluctuations at the Curie points on the thermal conductivity. The measurements were performed by means of a stationary heat flow method and with an apparatus described elsewhere [ 1]. The experimental error of the absolute value of thermal conductivity was about 5%; the scattering of measuring points for repeated measurements was about +- 1%. With regard to the anisotropy of Rochelle salt the thermal conductivity was measured along the plate normals of five sample plates in different crystal directions: parallel to the axes a, b, c corresponding to the conventional system [2] and in two directions perpendicular to the a-axis with the angles a=45 ° and a=135 °. The sample plates with dimensions of about 1X 12× 12 mm 3 were cut from a Rochelle salt single crystal which was kept at a defined humidity by sulphuric acid (density p= 1.530 g/cm 3 at 20°C) during more than half a year. The thermal conductivity measurements were performed at atmospheric pressure with the above mentioned humidity. The dielectric constant (at 1.6 kHz) along the ferroelectric a-axis reached a maximum of 5.0 × 103 at the upper Curie point Tc=23. I°C, with the Curie constant C=2220°K. * This paper w a s read by title at the Second European Meeting o f Ferroelectricity, Dijon 1971.
The temperature dependence of the anisotropic thermal conductivity is shown in fig. 1. Except for the direction parallel to the b-axic all curves show a small linear increase with temperature. Within the scattering limits no deviations from linearity occur; this holds especially near the transition points, though there the temperature differences across the samples were chosen smaller than 0.2 deg. In the paraelectric state, the symmetry class of Rochelle salt is orthorhombic; therefore, the thermal conductivity tensor only consists of the three diagonal components which were determinated to k 11=0.543 Wm- 1deg- 1, k22 =0.682 Wm- 1deg- I, and k33=0.484 W m - l d e g - 1 , at 300C. Between the Curie points, in the ferroelectric phase, Rochelle salt is monoclinic, but the additional tensor component k23 , connected with this symmetry class, is zero within the limits of error, since the measuring curves k45o and k135o show no deviation from linearity. However, it should be mentioned, that in case of a single domain crystal the sign of the tensor component k23 depends on the direction of polarization in a fixed coordinate system. As the domain structure of our crystal plates was not known, our value of k23 is an undefined average value over all domains. The temperature dependence of the thermal conductivity we found is similar to that measured by Chauvin and Remoissenet [3] along the ferroelectric axis, but it differs from the measurement of Krsti~ and Blinc [4] who found a dip at the lower and a peak at the upper Curie point for the direction parallel to the c-axis. As the dimensions of their sample were much larger (lc = 37.2 mm) than ours (lc= 0.96 mm), we furthermore investigated the temperature dependence 159
Volume 39A, number 3
0.70
PHYSICS LETTERS
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Fig. 1. Thermal conductivity of Rochelle salt in different crystallographic directions. of the thermal conductivity along the c-axis of a sample with l c = 7.9 mm in order to evaluate any thickness effects. In addition, this investigation did not yield any anomaly, but it showed the same temperature dependence of thermal conductivity as given in fig. 1. The lattice theory [5] gives an expression for the thermal conductivity k: k ~ ~ Ck,sOk,slk,s; k,s here Ck, s = hOOk,s Onk,s/OT is the specific heat of the mode of the phonon brach s with wave vectgr k (nk, s is the average occupation number),ok, s = dWk,s/d Ikl is the phonon group velocity, and lk, s is the mean free path of the phonons. The main contribution to the thermal conductivity comes from the low frequency parts of the acoustic branches for which approximately holds: o k,s = v s = x/cDs /P, where c Ds is the corresponding eleastic constant at constant polarization, and p is the
160
8 May 1972
density. The density and the elastic constants cD of • ,b l Rochelle salt show no anomalies near the Curie points [6,7]. Furthermore, the specific heat due to the acoustic phonon branches is not touched by the ferroelectric phase transitions; even the total specific heat of Rochelle salt, measured by Wilson [8], scarcely exhibits anomalies at the phase transitions. As our measurements do not indicate any anomaly of the thermal conductivity, we can suggest, that the phonon mean free path near the Curie points also does not show an anomalous behavior and is not noticeably influenced by polarization fluctuations. We are grateful to Prof. Dr. H.E.MiJser for his support and continuous interest in our work. This investigation was sponsored by the Deutsche Forschungsgemeinschaft.
References [1] J. Helwig and J. Albers, Phys, Stat. Sol. (a) 7 (1971) 151. [2] F. Jona and G. Shirane, Ferroelectric crystals, (Pergamon Press, Exford 1962). [3] D. Chauvin and M. Remoissenet, C.R. Acad. Sci. 267 (1968) 215. [4] Dj. Krsti6 and R. Blinc, Phys. Lett. 30A (1969) 387. [5] G. Leibfried, Gittertheorie der mechanischen und thermischen Eigenschaften der Kristalle, in Handbuch der Physik, Bd VII, Tell 1, ed. S. Flilgge, (Springer, Berlin 1955). [6] F. Jona, Helv. Phys. Acta 23 (1950) 795. [7] D.A. Berlincourt, D.R. Curran and H. Jaffe, Piezoelectric and piezomagnetic materials and their function in transducers, in Physical Acoustics, Vol. I, Part A, ed. W.P. Mason, (Academic Press, New York 1964). [8] A.J.C. Wilson, Phys. Res. 54 (1938) 1103.
PHYSICS LETTERS
8 May 1972
THERMAL CONDUCTIVITY OF ROCHELLE SALT* H. SCHAFER, J. ALBERS, and J. HELWlG Institut ffir Experimentalphysik 11 der Universitk't des Saarlandes, Saarbriicken Received 20 March 1972 The temperature dependence of the anisotropic thermal conductivity of a Rochelle salt single crystal was investigated in different crystallographicdirections in the range from -35 to + 40°C. No anomalous behaviourwas found near the Curie points.
Because of the great interest in experimental data of materials near a continuous phase transition we decided to measure the thermal conductivity of Rochelle salt, which presents two second order transitions at about - 1 8 and +24°C. Our intention was to investigate any influence of the scattering of longitudinal or transverse thermal phonons by polarization fluctuations at the Curie points on the thermal conductivity. The measurements were performed by means of a stationary heat flow method and with an apparatus described elsewhere [ 1]. The experimental error of the absolute value of thermal conductivity was about 5%; the scattering of measuring points for repeated measurements was about +- 1%. With regard to the anisotropy of Rochelle salt the thermal conductivity was measured along the plate normals of five sample plates in different crystal directions: parallel to the axes a, b, c corresponding to the conventional system [2] and in two directions perpendicular to the a-axis with the angles a=45 ° and a=135 °. The sample plates with dimensions of about 1X 12× 12 mm 3 were cut from a Rochelle salt single crystal which was kept at a defined humidity by sulphuric acid (density p= 1.530 g/cm 3 at 20°C) during more than half a year. The thermal conductivity measurements were performed at atmospheric pressure with the above mentioned humidity. The dielectric constant (at 1.6 kHz) along the ferroelectric a-axis reached a maximum of 5.0 × 103 at the upper Curie point Tc=23. I°C, with the Curie constant C=2220°K. * This paper w a s read by title at the Second European Meeting o f Ferroelectricity, Dijon 1971.
The temperature dependence of the anisotropic thermal conductivity is shown in fig. 1. Except for the direction parallel to the b-axic all curves show a small linear increase with temperature. Within the scattering limits no deviations from linearity occur; this holds especially near the transition points, though there the temperature differences across the samples were chosen smaller than 0.2 deg. In the paraelectric state, the symmetry class of Rochelle salt is orthorhombic; therefore, the thermal conductivity tensor only consists of the three diagonal components which were determinated to k 11=0.543 Wm- 1deg- 1, k22 =0.682 Wm- 1deg- I, and k33=0.484 W m - l d e g - 1 , at 300C. Between the Curie points, in the ferroelectric phase, Rochelle salt is monoclinic, but the additional tensor component k23 , connected with this symmetry class, is zero within the limits of error, since the measuring curves k45o and k135o show no deviation from linearity. However, it should be mentioned, that in case of a single domain crystal the sign of the tensor component k23 depends on the direction of polarization in a fixed coordinate system. As the domain structure of our crystal plates was not known, our value of k23 is an undefined average value over all domains. The temperature dependence of the thermal conductivity we found is similar to that measured by Chauvin and Remoissenet [3] along the ferroelectric axis, but it differs from the measurement of Krsti~ and Blinc [4] who found a dip at the lower and a peak at the upper Curie point for the direction parallel to the c-axis. As the dimensions of their sample were much larger (lc = 37.2 mm) than ours (lc= 0.96 mm), we furthermore investigated the temperature dependence 159
Volume 39A, number 3
0.70
PHYSICS LETTERS
-
b w
w-
i
.~ 0.65 .45°
";E060
|
•
T
a . l ~
T o
o..~ a . _ _ m ~ •
r
im
O.SO • JL
-40
•
-30
•
-~
.c.
I|
[
:
-20
0
20
~
T(*C)
40
Fig. 1. Thermal conductivity of Rochelle salt in different crystallographic directions. of the thermal conductivity along the c-axis of a sample with l c = 7.9 mm in order to evaluate any thickness effects. In addition, this investigation did not yield any anomaly, but it showed the same temperature dependence of thermal conductivity as given in fig. 1. The lattice theory [5] gives an expression for the thermal conductivity k: k ~ ~ Ck,sOk,slk,s; k,s here Ck, s = hOOk,s Onk,s/OT is the specific heat of the mode of the phonon brach s with wave vectgr k (nk, s is the average occupation number),ok, s = dWk,s/d Ikl is the phonon group velocity, and lk, s is the mean free path of the phonons. The main contribution to the thermal conductivity comes from the low frequency parts of the acoustic branches for which approximately holds: o k,s = v s = x/cDs /P, where c Ds is the corresponding eleastic constant at constant polarization, and p is the
160
8 May 1972
density. The density and the elastic constants cD of • ,b l Rochelle salt show no anomalies near the Curie points [6,7]. Furthermore, the specific heat due to the acoustic phonon branches is not touched by the ferroelectric phase transitions; even the total specific heat of Rochelle salt, measured by Wilson [8], scarcely exhibits anomalies at the phase transitions. As our measurements do not indicate any anomaly of the thermal conductivity, we can suggest, that the phonon mean free path near the Curie points also does not show an anomalous behavior and is not noticeably influenced by polarization fluctuations. We are grateful to Prof. Dr. H.E.MiJser for his support and continuous interest in our work. This investigation was sponsored by the Deutsche Forschungsgemeinschaft.
References [1] J. Helwig and J. Albers, Phys, Stat. Sol. (a) 7 (1971) 151. [2] F. Jona and G. Shirane, Ferroelectric crystals, (Pergamon Press, Exford 1962). [3] D. Chauvin and M. Remoissenet, C.R. Acad. Sci. 267 (1968) 215. [4] Dj. Krsti6 and R. Blinc, Phys. Lett. 30A (1969) 387. [5] G. Leibfried, Gittertheorie der mechanischen und thermischen Eigenschaften der Kristalle, in Handbuch der Physik, Bd VII, Tell 1, ed. S. Flilgge, (Springer, Berlin 1955). [6] F. Jona, Helv. Phys. Acta 23 (1950) 795. [7] D.A. Berlincourt, D.R. Curran and H. Jaffe, Piezoelectric and piezomagnetic materials and their function in transducers, in Physical Acoustics, Vol. I, Part A, ed. W.P. Mason, (Academic Press, New York 1964). [8] A.J.C. Wilson, Phys. Res. 54 (1938) 1103.