Efficient Calculation of the Negative Thermal Expansion in ZrW₂O₈

We present a study of the origin of the negative thermal expansion (NTE) on ZrW₂O₈ by combining an efficient approach for computing the dynamical matrix with the Lanczos algorithm for generating the phonon density of states in the quasi-harmonic approximation. The simulations show that the NTE arises primarily from the motion of the O-sublattice, and in particular, from the transverse motion of the O atoms in the W-O and W-O-Zr bonds. In the low frequency range these combine to keep the WO₄ tetrahedra rigid and induce internal distortions in the ZrO₆ octahedra. The force constants associated with these distortions become stronger with expansion, resulting in negative Grüneisen parameters and NTE from the low frequency modes that dominate the positive contributions from the high frequency modes. This leads us to propose an anharmonic, two-frequency Einstein model that quantitatively captures the NTE behavior.