•Complete overview of ternary ordering variants of the pyrite and the marcasite type.•Stability diagrams of MPnS (M = Fe, Co, Ni; Pn = As, Sb) systems.•Good agreement of theory and experiment allows for reliable predictions.There is a solid history of theoretical and experimental studies of pyrite- and marcasite-like systems that primarily occur for dipnictide and disulfide systems of late transition metals. Ordered mixed occupation of the anionic sites of these compounds results in a multitude of different ternary structures. A full set of possible combinations is presented here including all experimentally known structure prototypes. They are part of a series MPnS (M = Fe, Co, Ni; Pn = As, Sb) that is investigated in terms of recently established stability diagrams with decomposition lines. In contrast to the respective binary systems, significantly lower differences in cohesive energies and cell volumes have to be dealt with particularly for related ordering variants. Due to sufficient experimental data on hand, the accuracy of the GGA-based density functional theory calculations can be estimated within the marginal ranges in order to allow for reliable predictions of new phases of these and many other related systems.

In a model study the crystal structures of shandite (Pb2Ni3S2), parkerite (Bi2Ni3S2) and their Pd homologues are investigated in terms of ordered half antiperovskites AM3/2S (A = Pb, Bi; M = Ni, Pd). This addresses fundamental questions on the structural relations, ordering and chemical bonding. From crystal structure investigations a new cubic parkerite variant is presented for Bi2Pd3S2 that fits in an ordering model equivalently to shandite and parkerite. Type–antitype relations to ordered oxygen deficit perovskites are presented. With the relation to the superconductor Ni3MgC a model is deduced that provides the complete crystal structure and symmetry in terms of the Ni and Pd ordering in antiperovskite superstructures. Therein a systematic ab initio investigation on the relative stability of shandite and parkerite structures is carried out for the first time. From the DFT modelling results the preferences of the ordering variants and the distinct differences in the atomic coordination spheres are discussed. The bonding in the systems is investigated by site projected density of states and covalent bond energy calculations.