Unifying the thermodynamic and electrostatic view on the pyroelectric effect

Pyroelectricity is a first rank tensor (vector) property that connects electric displacement to temperature. Like all vector properties, it is allowed only in certain point group symmetries. In related literature, a number of formulations exist that apparently treat various contributions to the pyroelectric coefficient but without strictly considering the crystal symmetry. We revisit the formulation of the pyroelectric coefficient in the presence of external fields and find that a consistent treatment of the pyroelectric coefficient, allowing one to arrive at a single convergent formula starting from either thermodynamic or electrostatic arguments, may not be straightforward. Motivated by this outcome, we develop an approach allowing both electrostatic and thermodynamic arguments for pyroelectricity to converge to one single expression with mathematical consistency of the partial derivatives. Albeit not very significant at first sight, the approach and the manner in which fields are introduced prove vital in evaluating the field contributions to the pyroelectric effect and their deconvolution in experiments. Importance of the crystal point groups is also highlighted in the context of vector properties, specifically pyroelectric coefficient. Finally, the so-called induced pyroelectricity and a correct mathematical expansion of the polarization is discussed to clarify the contributions of the pyroelectric effect.