  The peculiarities of thermal expansion of $bcc$ and $fcc$ zirconium films
with (100) and (110) crystallographic orientations are studied at a constant
zero pressure by the molecular dynamics (MD) method with a many-body
interatomic interaction potential obtained in the embedded atom model. It is
shown that after relaxation the cubic lattices become tetragonal ($bct$ and
$fct$), and for the metastable $fct$ films the linear coefficients of thermal
expansion 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 the
peculiarities of the behavior of the vibrational density of states of surface
atomic layers manifest themselves in the anisotropy of the changes of the film
lattice parameters with temperature variation. A decrease in the lattice
parameters with increasing temperature is observed in the directions where
there occurs a softening of the local vibrational modes.
