Negative thermal expansion behavior in orthorhombic Sc2(MoO4)3 and Sc2(WO4)3

In contrast to cubic ZrW2O8 and ZrMo2O8, which have isotropic negative thermal expansion, the compounds Sc-2(WO4)(3) and Sc-2(MoO4)(3) with the orthorhombic structure show anisotropic thermal expansion that is negative along the b and c axes. Using ab initio density functional theory calculations of lattice dynamics, we identify that the anisotropic expansion is not due to anisotropic elasticity or negative linear compressibility, which is the case in several compounds; instead, it is due to anisotropic Gruneisen parameters of specific phonons, mostly of energy around 6 meV. Such a behavior not involving anomalous elasticity is unusual. The phonon eigenvectors show that these phonons have a rather complex vibrational character of MoO4/WO4 and ScO6 polyhedral units that involve translational, librational, and internal distortion dynamics.