Low compressible BP$_3$N$_6$

Using first principles calculation, the structural and mechanical properties of BP$_3$N$_6$ which adopts an orthorhombic structure with space group Pna2$_1$ (no. 33), were determined at three different pressure values (0, 20 and 42.4~GPa). The nine independent elastic constants meet all necessary and sufficient conditions for mechanical stability criteria for an orthorhombic crystal. BP$_3$N$_6$ show strong resistance to volume change hence a potential low compressible material. The Vicker's hardness of BP$_3$N$_6$ was found to range between 49-51~GPa for different external pressures imposed on the crystal. These high values of Vicker's hardness implies that BP$_3$N$_6$ is a potential superhard material.