From the phonon density of states (PDOS) of r-BN, h-BN, c-BN and w-BN in (Fig. ), it is seen that their phonon frequencies are all positive, thus confirming the dynamical stabilities of all polytypes. It is also worth mentioning that our derived PDOS is found to well match those previously reported by Yu et al. and Kern et al. in terms of both phonon frequencies and features of corresponding density of states. This strengthens the reliability of our theoretical prediction. The optimized lattice parameters of r-BN, h-BN and c-BN as a function of temperature were derived from the quasiharmonic approximation (Fig. ). At T = 300 K, the lattice parameters a and c of r-BN are 2.509 Å and 10.089 Å, respectively, and the lattice parameter a of c-BN is 3.623 Å. As can be seen from Table , our theoretical values derived in the present work are found to differ from the experimental ones, measured at room temperature, by less than 1 % . Thus, our theoretical calculations are in good agreement with the experimental data. It is worth noting that as the temperature increases from 300 K to 2400 K the isotropic c-BN lattice expands 0.05 Å, (1.3 %) while the anisotropic r-BN and h-BN lattices expands 0.4 Å (4 %) and 0.03 Å (0.4 %), respectively in the c-direction, but only 0.004 Å (0.16 %) and 0.001 Å (0.04 %), respectively, in the a-direction. This is a signature of strong B-N bonds within the sp 2hybridized basal planes. From Fig. an anomalous feature in the lattice parameters of h-BN can be noted at about 600 K, where the lattice parameter a contracts and then barely expands at higher temperature. The contraction may be interpreted as the negative thermal expansion coefficient in the a-axis, previously reported for h-BN. Table Lattice parameters of r-BN and c-BN at T = 300 K, calculated in the present work. Comparison is made with the existing experimental data, reported in the literature.