Revealing unusual rigid diamond net analogues in superhard titanium carbides

Transition metal carbides (TMCs) are considered to be potential superhard materials and have attracted much attention. With respect to titanium and carbon atoms, we confirm the pressure-composition phase diagram of the Ti-C system using structure searches and first-principles calculations. We firstly discovered stable TiC₄ which was expected to be synthesized at high pressure, as well as metastable TiC₂ and TiC₃. These layered titanium carbides are diamond net analogues due to the unusual C-layers in the form of puckered graphene-like, diamond-like and double diamond-like C-layers. The existence of diamond-like C-layers might help to understand the formation of diamond. All the studied titanium carbides could be recoverable at ambient pressure and exhibited great mechanical properties (strong ability to resist volume and shear deformations, small anisotropy, and high hardness). Moreover, we crystallized the structure of TiC₄ in other transition metal carbides and obtained five superhard TMC₄s (TM = V, Zr, Nb, Hf and Ta). Interactions between layers were revealed to be the source of the great mechanical properties and high hardness through combining detailed analyses of electronic structure and chemical bonding, namely, weak ionic interactions of neighboring Ti- and C-layers and the strong covalent interactions of C- and C-layers.