Silylated carbodiimides in molecular and extended structures

Abstract

This work studies the ternary Si-C-N phases ${\mathrm{SiC}}_2{\mathrm{N}}_4$ and ${\mathrm{Si}}_2{\mathrm{CN}}_4,$exploiting an analogy between the NCN and O groups. Starting from the molecular model of ${N,N}^{\prime }-\mathrm{bis}\left(\mathrm{trimethylsilyl}\right)-\mathrm{carbodiimide}$ and proceeding to extended models, we calculate that the energy hypersurface associated with the Si-N=C bond angle ${\phi }_{\mathrm{N}}$ is very shallow, for both molecular and extended structures. We propose a crystal structure for the low-temperature modification $\alpha -{\mathrm{SiC}}_2{\mathrm{N}}_4$ in space group ${P4\mathrm{}}_{3}22$ (95), which is $40\mathrm{meV}(\sim 4\mathrm{}\mathrm{k}\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l})$ lower in energy than an ideal cubic arrangement in space group $\mathrm{Pn}3\mathrm{}¯m.\mathrm{}$A second structure, $\beta -{\mathrm{SiC}}_2{\mathrm{N}}_4$ [space group $P4\mathrm{}¯n2\mathrm{}$ (118)], is slightly higher in energy than $\alpha -{\mathrm{SiC}}_2{\mathrm{N}}_4,$but still more stable than the cubic structure, and may be the high-temperature structure of ${\mathrm{SiC}}_2{\mathrm{N}}_4.$Both variants of ${\mathrm{SiC}}_2{\mathrm{N}}_4$ show a small bulk modulus of about $8\mathrm{GPa}\left(\sim 0.13\mathrm{Mbar}\right),$suggesting a high compressibility of these nonoxide covalently bonded materials. For ${\mathrm{Si}}_2{\mathrm{CN}}_4$ we refined the crystal structure of the compound within the experimentally determined space group $\mathrm{Aba}2\mathrm{}$ (41). We also found a second candidate nearly equal in energy, with space group ${\mathrm{Cmc}2\mathrm{}}_1,$differing only in the connection pattern of the ${\mathrm{SiN}}_2$ layered sheets. Both ternary compounds appear to be thermodynamically unstable with respect to decomposition into ${\mathrm{Si}}_3{\mathrm{N}}_4,$C, and molecular ${\mathrm{N}}_2.$