An analytical expression for Eg and Ag modes of pyrochlores

A general analytical expression has been derived for E_g and A_1g modes in terms of stretching and bending force constant for cubic pyrochlore structure compounds. The expression has been applied to different pyrochlore oxides accounting six stretching and four bending force constants. The calculation of E_g and A_1g mode has been carried out by using the earlier reported values of force constants for titanates, hafnates and stannates. The analytical expression can be applied to any pyrochlore structure compounds for evaluating and assigning E_g and A_1g mode if the interatomic force constants are already known.