The temperature dependence of nanocrystal heat capacity

The temperature dependence of the specific (per atom) entropy and heat capacity of a nanocrystal is studied using a nanocrystal model in the form of a rectangular parallelepiped with variable surface shape. Accounting for the temperature dependence of the surface energy showed that the temperature dependence of the surface contribution to specific entropy is described by the same function that determines the temperature dependence of the isochoric heat capacity of a macrocrystal. Thus, at T → 0 K at T/Θ > 2 the surface contribution to the specific heat is zero. The maximal surface contribution to specific heat is reached at T/Θ = 0.2026 and is equal to cst/kB = 1.0115 (where kB is the Boltzmann constant, Θ is the characteristic temperature depending both on the size and the shape of the nanocrystal). The applicability of the Grüneisen rule for a nanocrystal both at low and high temperatures is studied. It has been found that a case when the surface contribution to specific heat would be negative c(N) < c(∞), i.e. cst(N) < 0 can occur for nanocrystals with a noncubic habitus.