  We study the dependence of the formation energies of oxygen and metal induced
defects in Ta2O5, TaO2, TaO, TiO2 and Ti4O7 on the chemical potential of
electron and atomic constitutes. In the study of single defect, metal induced
defects are found to be preferable to oxygen induced defects. This is against
the experimental fact of the dominant role of oxygen induced defects in the RS
process. A simple multiple defects picture without correlated atomic
rearrangement does not cure this problem. The problem is resolved under the
correlated multiple defect picture where the multiple defects result in
correlated atomic rearrangement and the final products show certain atomic
ordering.
