The temperature dependence of the pyroelectric coefficient pЈ of polyvinylidene fluoride (PVF 2) was measured from 307 K to the previously unexplored region of 3 K. The measurements were performed on a film of oriented (-phase͒ PVF 2 by monitoring its surface charge response to quasistatic heating and cooling transients. The data exhibit a pure cubic temperature dependence from 3 to 6 K with no evidence of a linear term. This is consistent with the prediction by Szigeti and the Debye limit, respectively, for the primary ͑i.e., strain-free͒ and secondary contributions to pyroelectricity. The data from ϳ20 to ϳ150 K, which include the region of largest change, are well fit by an exponential function ͑i.e., a 0 e Ϫ/T), corresponding to a thermal activation energy of ϭ(25.9Ϯ0.06) K. Our data for pЈ, from 100 to 250 K, are approximately proportional to the thermal expansion coefficient, recently published by Hartwig, which indicates that the observed pyroelectricity is dominated by piezoelectric ͑i.e., secondary͒ contributions in that temperature regime. ͓S0163-1829͑97͒08211-8͔ I. INTRODUCTION A. Overview
A rudimentary calorimeter was constructed to measure the temperature dependence of the specific heat of a 10 thick ͑0.62 mg͒ copolymer film of vinylidene fluoride and trifluoroethylene in the previously unexplored vicinity of 6 K. The data were processed with the algorithm developed by Hwang et al. ͓Rev. Sci. Instrum. 68, 94 ͑1997͔͒ as modified for our configuration in which a Cernox thermometer also served as a heater. The measurements extended from 3.75 to 8.5 K, with a temperature resolution of 0.2 K, and the ratios of the statistical uncertainties to the mean values deduced for c p are Ϯ 3% over most of this temperature range. The data taken with the intermediate resolution of this calorimeter provides evidence for the absence of any slowly varying anomaly in the temperature dependence of c p. Such rudimentary systems provide a useful option to gather exploratory information at a comparatively low cost for components.
The specific heat of a highly crystallized ferroelectric copolymer film of vinylidene fluoride (ϳ80 mol%) and trifluoroethylene (ϳ20 mol%) was measured over the previously unexplored temperature range from 3.7 to 8.5 K. The data show a dominant cubic temperature dependence, with only marginal evidence for a T 3/2 or a T 2 component. There is also no evidence for the discontinuity in slope that was observed in previous measurements of the pyroelectric coefficient of this material in the vicinity of 6 K. This difference is consistent with the supposition that thermal expansion is the dominant contributor to the pyroelectric coefficient in this temperature range. The specific heat data also show a rapid transition from the three-dimensional to onedimensional Debye limits.
The specific heat capacity c p of a 110 m thick and partially crystallized ͑ϳ77% ͒ ferroelectric copolymer film of vinylidene fluoride ͑PVDF͒ ͑ϳ75 mol % ͒ and trifluoroethylene ͑ϳ25 mol % ͒ was measured from 2 to 20 K. The temperature dependence of c p / T 3 reveals a shallow hump, centered at ϳ5 K, consistent with non-Debye behavior of semicrystalline materials. These c p data were used, in conjunction with previous measurements of the pyroelectric coefficient ͉pЈ͉, to infer the temperature profile of the macroscopic Grüneisen parameter based on ratios of ͉pЈ͉ / c p . Comparisons with similar data for PVDF are consistent with a correlation between anharmonicity of the interaction potential and excess specific heat capacity.
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