Temperature dependence of the capacitance of a ferroelectric material

We present an alternate version of the undergraduate laboratory experiment developed by Dixon [Am. J. Phys. 75, 1038-1046 (2007)] that is suitable for second-year students. We study the temperature variation of the capacitance of a ferroelectric ceramic derived from barium titanate, the Ba(Ti _0.9Sn_0.1)O₃ solid solution. The ratio of tin to titanium is chosen to provide a convenient Curie temperature near 50 °C. Using careful temperature control and real-time capacitance measurements, we track the time evolution of the capacitance in response to temperature changes at 5 Hz for runs that last up to a day. At temperatures well above the Curie temperature, T_c, the capacitance relaxation is well-described by a single exponential decay. Near T_c, the relaxation is linear in the logarithm of time over more than three decades. For T> T_c, the permittivity deviates from the Curie-Weiss law and follows another phenomenological form commonly used to describe relaxor perovskite-ceramic capacitors.