Bond Relaxation Insight into Secondary Pyroelectric Coefficient from One- to Three-Dimensional Materials: Temperature-, Size-, and Shape Effects

The physical origins of the secondary pyroelectric coefficient in response to temperature, size, and shape have long been a puzzle. Based on the local bond average approach, an analytical equation for the temperature effect of the secondary pyroelectric coefficient of bulk GaN, ZnO, ZrO₂, and HfO₂, and Janus monolayer MoSSe and CrSeBr is established. It is found that the secondary pyroelectric coefficient is inversely proportional to both cohesive energy and the cube of the Debye temperature. Combining the bond-order-length-strength theory and core–shell structural model, the analytical expressions for the size- and shape-dependent secondary pyroelectric coefficients for GaN nanostructures are derived. The results unveil that the crystal size-induced secondary pyroelectric coefficient rising results from the synergetic effect of the increase in piezoelectric coefficient and the decrease in both Debye temperature and cohesive energy caused by bond order deficiency at the surface layer. The secondary pyroelectric coefficient increases with the decrease in the number of sides for polyhedral nanoparticles and polygonal nanowires or nanotubes due to the rise in surface-to-volume ratio. The size effect of the secondary pyroelectric coefficient for nanotubes is characterized by the wall thickness and does not depend on the radius. The secondary pyroelectric coefficient for nanotubes is always higher than their nanowire counterparts because of their larger surface-to-volume ratios. The current study is anticipated to have implications in the field of nanoscale thermal energy harvesting.