Differential anharmonicity and thermal expansion coefficient in3C-SiC nanowires

Surface and core are two essential but distinct structural parts of a nanowire---but their individual effects on overall thermal expansion coefficient of a nanowire have never been quantified. Here we present an average bond-length based framework to determine the effects of the surface and core regimes of $3C$-SiC nanowires on their effective volumetric thermal expansion coefficient over a wide range of temperatures. Our results suggest that the surface and core atoms exhibit differential anharmonic response at finite temperatures, which makes the surface regime exhibit disparate expansion behavior compared to the core. While at lower temperatures the differential anharmonicity is negligible, at temperatures higher than the room temperature there is a pronounced differential anharmonicity in the nanowire. Furthermore, temperature-dependent expansion coefficients of the nanowire and the surface and core regimes qualitatively follow the behavior of the bulk---but they vary substantially quantitatively, with the maximum coefficient exhibited by the surface at higher temperatures. The diameter-dependent expansion coefficients follow inverse power laws with their exponents varying from 0.95 to 2.5. In thinner nanowires the expansion coefficient is controlled by an intricate combination of mass inertia and bond stiffness at the surface and core, whereas the expansion of thicker nanowires is dominated by the anharmonic motion of the core atoms alone. The surface effects saturate with increasing diameter, but the core effects decay nonlinearly with increasing diameter and approaches the bulk value as $d\ensuremath{\rightarrow}\ensuremath{\infty}$.