Crystallite size dependence of the coefficient of thermal expansion of metals

The coefficients of thermal expansion (CTEs) of polycrystalline Ni and Cu thin films have been investigated by employing temperature-dependent x-ray diffraction measurements of lattice parameters. Great care has been taken to exclude effects of, in particular, microstructural relaxation and mechanical stresses on the dependences of the lattice parameters on temperature. The CTEs determined in the as-deposited condition, characterized by grain sizes in the range of 25–35nm, are considerably (about 10%) larger than the corresponding literature values of bulk materials. Heat treating the specimens at moderate temperatures induced grain growth and decrease of the crystalline imperfection. After the heat treatment, the CTEs determined for the thin films had reduced considerably and had become equal to (Ni) or approached (Cu) the corresponding literature data for bulk materials.