It is well established that carbon nitride (CN) is a potential superhard material as its bond in network structures is slightly shorter than the C–C bond in diamond. However, the structure of superhard CN materials is yet to be determined experimentally. We have performed an extensive structural search for the high pressure crystalline phases of CN using the particle swarm optimization technique; seven low-energy polymorphic structures of sp³-hybridized CN have been found in an unbiased search. Density-functional theory calculations indicate that, among the seven low-energy crystalline structures, Pnnm structure (8 atoms/cell) is energetically more favorable than the previously reported most stable crystalline structure with 1:1 stoichiometry. Furthermore, Pnnm possesses the highest hardness (62.3 GPa). Formation enthalpies demonstrate that this material can be synthesized at pressure 10.9 GPa, lower than needed by β-C₃N₄ (14.1 GPa).

The piezoelectric properties of tetragonal perovskites $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$, $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, and $\mathrm{K}\mathrm{Nb}{\mathrm{O}}_3$ under uniaxial strain along the [001] direction are calculated from first principles. In order to study the piezoelectric response of individual atomic sublattices, the total polarization $P$ and piezoelectric constant $d_{33}$ are decomposed into the contributions of $A$-site and $B$-site atoms. These three materials show different behaviors at the atomic scale. In $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$, the Pb and Ti contribute almost equally to the polarization and $d_{33}$. In $\mathrm{K}\mathrm{Nb}{\mathrm{O}}_3$, most of the polarization and $d_{33}$ are contributed by the ferroelectrically active Nb. But in $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, as the $c$ axis increases, the contribution of Ba to $d_{33}$ rises rapidly, reaching 50% of the total $d_{33}$ at $c$ = 4.30 Å. This means that the covalent bonding between Ba and O is significant and has an important impact on the piezoelectric response of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$.

Enthalpies of formation of P1̄-ScN₃ and C2/m-ScN₅ are predicted relative to ScN and N₂ with CALYPSO structural search.

A structural search leads to the prediction of a novel alkaline earth nitride BeN₄ containing a square planar N₄²⁻ ring. This compound has a particular chemical bonding pattern giving it potential as a high-energy-density material. The P4/nmm phase of BeN₄ may be stable under ambient conditions, with a bandgap of 3.72 eV. It is predicted to have high thermodynamic and kinetic stability due to transfer of the outer-shell s electrons of the Be atom to the N₄ cluster, with the outer-shell 2p orbital accommodating the lone-pair electrons of N₄²⁻. The total of six π electrons is the most striking feature, indicating that the square planar N₄²⁻ exhibits aromaticity. Under ambient conditions, BeN₄ has a high energy density (3.924 kJ/g relative to Be₃N₂ and N₂ gas), and its synthesis might be possible at pressures above 31.6 GPa.