Size-dependent heat capacity in nano-oxide crystals

Abstract

Recent developments suggest that heat capacity of nano-oxides is size-dependent, since the product of bulk modulus (B) and thermal expansion coefficient (α) scales directly with isometric heat capacity Cv. Dependence of heat capacity on crystal-size Cv(d) is explored by examining Bαao where ao is the lattice parameter. Here Bαao(d)'s show maxima at 33 nm for ceria and at 14 nm for MgO and decrease with decreasing crystal-size (d) implying similar size-dependence for Cv if the Grüneisen parameter is size insensitive. Hence, the Cv (d) contradicts with metal's heat capacities which are larger in nano-grains. Contributions from grain boundaries and surfaces were posited for the difference. Besides phonons, free electrons in metals contribute to heat capacity. The absence of electronic carriers in oxides likely explains the difference.