AbstractGuided by the results and concepts of band theory and tight binding theory, a simple model of cohesion in TiCxand related compounds is proposed, in which each carbon atom claims four d electrons from its transition metal neighbours to form saturated covalent bonds; and in which any d electrons surplus to this are used to form metal–metal covalent bonds. In the non-stoichiometric alloys, the atomic heterogeneity of the structure plays a significant secondary role in allowing carbon free octahedral cells to expand slightly and therefore increase the overall lattice constant. Using cohesive parameters derived from experiment, this model is able to represent approximately the observed variation of lattice constant with composition and the range of existence of the TiCxphase.MST/1876