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The secondary pyroelectric effect is the change of polarization density produced when thermal strain acts through piezoelectricity. It is additional to the primary change at fixed strain. A linear constitutive description along the polar axis iswhere $e_{3j}$ are piezoelectric stress coefficients and ${\alpha }_j$ the freely developing thermal strains per kelvin. Thermal-expansion mismatch with a support or a deliberately chosen compliant structure can change the secondary contribution. It enhances the total response only if its sign reinforces the primary response; mechanical boundary conditions and thermal cycling must be characterized rather than assuming every restraint is beneficial.

Preventing axial expansion removes the free axial-strain contribution, but does not automatically eliminate every secondary contribution. In a one-dimensional idealization with only ${\epsilon }_3$ coupling and perfect axial clamping, that strain-mediated term vanishes. A real rod may still expand transversely, and nonzero $e_{31}$ or $e_{32}$ can change $P_3$ through those strains. In a stress-based constitutive equation, the same restraint appears as thermal stress and a piezoelectric term; do not add it a second time to a coefficient already specified for the constrained condition. Full suppression of all relevant thermal strains leaves the primary coefficient at fixed strain. The answer therefore depends on which degrees of freedom are constrained, not simply on the word “nanorod”.

A pyroelectric material has a spontaneous electric polarization that changes with temperature. electrodes collect the resulting change in compensating charge. For a uniform element,Consequently temperature variation in time, rather than a steady temperature difference alone, drives a pyroelectric generator. A cyclic thermal input and a suitable electrical circuit are needed for repeated energy extraction.

The primary pyroelectric effect is the change of electric polarization at fixed strain. The secondary pyroelectric effect arises because thermal expansion strains a piezoelectric crystal and thereby changes its electric polarization. In component notation its contribution iswith piezoelectric coefficients $e_{ij}$ and thermal-expansion coefficients ${\alpha }_j$. Choosing orientation, mechanical constraint and substrate expansion so that the secondary contribution reinforces the primary one can increase the response; the signs can instead oppose one another.

An array of slender nanowires can expand more freely than a film clamped to a substrate and can exchange heat rapidly because of its high surface-to-volume ratio. Reduced clamping can recover a secondary response suppressed in the film. Faster thermal cycling can also increase electric current through $dT/dt$. This is a geometrical opportunity rather than a universal increase of the intrinsic coefficient: screening, leakage, orientation and the actual thermal excursion must be compared. ZnO nanowire generators provide an experimental realization of pyroelectric energy conversion.^[ref]