A theoretical model for describing effective thermal conductivity (ETC) of nanocrystalline materials has been proposed, so that the ETC can be easily obtained from its grain size, single crystal thermal conductivity, single crystal phonon mean free path (PMFP), and the Kaptiza thermal resistance. In addition, the relative importance between grain boundaries (GBs) and size effects on the ETC of nanocrystalline diamond at 300 K has been studied. It has been demonstrated that with increasing grain size, both GBs and size effects become weaker, while size effects become stronger on thermal conductivity than GBs effects.

Based on first-principles calculations and effective model analysis, a Dirac nodal-net semimetal state is recognized in ${\mathrm{AlB}}_2$-type ${\mathrm{TiB}}_2$ and ${\mathrm{ZrB}}_2$ when spin-orbit coupling (SOC) is ignored. Taking ${\mathrm{TiB}}_2$ as an example, several topological novel states have been found in this nodal-net structure including triple point, nexus, and nodal link, which are protected by the coexistence of spatial-inversion symmetry and time-reversal symmetry. In addition, linearly and quadratically dispersed two-dimensional surface Dirac points have been identified as getting on the B-terminated and Ti-terminated (001) surfaces of ${\mathrm{TiB}}_2$, respectively, which are analogous to those of monolayer and bilayer graphene.

A novel polymorph of boron nitride (BN) with a body-centered tetragonal structure (bct-BN) has been predicted using first-principles calculations. The structural, vibrational, and mechanical calculations indicated that bct-BN is mechanically stable at zero pressure. When pressure is above 6 GPa, bct-BN becomes energetically more stable than h-BN. The bct-BN appears to be an intermediate phase between h-BN and w-BN due to a low energy barrier from h-BN to w-BNvia bct-BN. Our results also indicated that the structure of unknown E-BN phase might be bct-BN.