Symmetric Stretching Vibrations of Two-Coordinate Oxygen Bridges as a Cause for Negative Thermal Expansion in ZrV _x P _2-x O ₇ andAW ₂ O ₈ (A=Zr, Hf) at High Temperature

To examine the origin of negative thermal expansion in oxides ZrV _x P _2-x O ₇ (x=0-2) andAW ₂ O ₈ (A=Zr, Hf),ab initioself-consistent-field molecular orbital calculations were carried out for a model compound (HO) ₃ P-O-P(OH) ²⁺ ₃ . Our study suggests that symmetric stretching vibrations of two-coordinate oxygen bridges are strongly coupled with their bending vibrations and are more important for negative thermal expansion at high temperature. The oxygen bridges accomodate a large stretching of theA-O (A=Zr, Hf) andM-O (M=P,V) bonds at high temperature by decreasing the bond angles of the oxygen bridges. When the bond angles increase, the bonds are shortened due to the π-type orbital interactions associated with the oxygen lone pair orbitals.