Previous work has shown that thermodynamics properties calculated by phonon model with quasi-harmonic approximation (QHA) may differ badly from experiment in some cases. The inaccuracy was examined in the present work by comparing the results of QHA for argon and copper crystal with the ones of molecular dynamics simulations, partition functions obtained by a new method or experiment. It is shown that QHA works well for the systems of atomic volume smaller than 22 Å3/atom and the accuracy gets lower and lower gradually with increasing of the atomic volume. Based on this fact, the disagreement (or agreement) between the thermodynamics properties of MgO, Si, CaO, ZrO2 calculated in previous work by QHA and the experiments can be well understood.