The stresses and strain values at various indentation depths are applied to determine the Gibbs free energy at various phases. The intersections of the Gibbs free energy lines are used to determine the possible paths of phase transitions arising at various indentation depths. All the critical contact stresses corresponding to the various phase transitions predicted by the proposed model for the specimens treated at four annealing temperatures were found to be consistent with the experimental results. The proposed model is thus valid for predicting contact parameters using nanoindentations. The critical contact stresses for the phase transitions increased with increasing specimen annealing temperature.