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The peculiarities of thermal expansion of $bcc$ and $fcc$ zirconium filmswith (100) and (110) crystallographic orientations are studied at a constantzero pressure by the molecular dynamics (MD) method with a many-bodyinteratomic interaction potential obtained in the embedded atom model. It isshown that after relaxation the cubic lattices become tetragonal ($bct$ and$fct$), and for the metastable $fct$ films the linear coefficients of thermalexpansion in the film plane have a negative value in a wide temperature range.The total and local vibrational density of states (VDOS) polarized along the$x,y,z$ axes is calculated for the surface and interior layers of $bct$ and$fct$ Zr films as a function of the temperature. It is shown that thepeculiarities of the behavior of the vibrational density of states of surfaceatomic layers manifest themselves in the anisotropy of the changes of the filmlattice parameters with temperature variation. A decrease in the latticeparameters with increasing temperature is observed in the directions wherethere occurs a softening of the local vibrational modes.

Study of peculiarities of the thermal expansion of zirconium thin films by molecular-dynamics simulation