Phase stabilities of pyrite-related MTCh compounds (M ¼ Ni, Pd, Pt; T ¼ Si, Ge, Sn, Pb; Ch ¼ S, Se, Te): A systematic DFT study Frederik Bachhuber a,b , Alexander Krach a , Andrea Furtner a , Tilo Söhnel b,c , Philipp Peter a , Jan Rothballer a , Richard Weihrich a,n a University of Regensburg, Institute of Inorganic Chemistry, Universitätsstr. 31, 93040 Regensburg, Germany b School of Chemical Sciences, University of Auckland, Private Bag 92019, Auckland, New Zealand c Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Auckland, New Zealand article info Article history: Received 12 September 2014 Received in revised form 3 December 2014 Accepted 24 January 2015 Available online 2 February 2015 Keywords: Pyrite Stability diagram Density functional calculation Semiconductors Ordering abstract Pyrite-type and related systems appear for a wide range of binary and ternary combinations of transition metals and main group elements that form Zintl type dumbbell anion units. Those representatives with 20 valence electrons exhibit an extraordinary structural flexibility and interesting properties as low-gap semiconductors or thermoelectric and electrode materials. This work is devoted to the systematic exploration of novel compounds within the class of MTCh compounds (M¼Ni, Pd, Pt; T ¼Si, Ge, Sn, Pb; Ch ¼S, Se, Te) by means of density functional calculations. Their preferred structures are predicted from an extended scheme of colored pyrites and marcasites. To determine their stabilities, competing binary MT 2 and MCh 2 boundary phases are taken into account as well as ternary M 3 T 2 Ch 2 and M 2 T 3 Ch 3 systems. Recently established stability diagrams are presented to account for MTCh ordering phenomena with a focus on a not-yet-reported ordering variant of the NiAs 2 type. Due to the good agreement with experimental data available for several PtTCh systems, the predictions for the residual systems are considered sufficiently accurate. & 2015 Elsevier Inc. All rights reserved. 1. Introduction Ternary inorganic compounds offer unique ways to combine exceptional structures and functions by the composition of different elements. The design of these materials is often based on substitution and coloring in parent structures, for instance in perovskite-related systems. Ways of preparation and possible applications are, however, limited by structural, compositional, and metastability or polymorph- ism, respectively. As recently shown for the allotropes of phosphorus, these problems can be treated by modern first principles calculations [1–4]. They are very effective for the prediction of competing stru- ctures with equal composition but challenging if they are unequal. Related questions are subsequently addressed by a systematical study on known and new ternary colored pyrites MTCh and their stabilities with respect to competing structures, compositions and decompositions from first principles. Experimentally, the concerned MTCh compounds are found in the M–T–Ch phase diagram with M as a late transition metal (group 8–10), T as a main group metal (group 14) and Ch as a chalcogen (S, Se, Te) (cf. [2]). Competing compositions are ordered half antiperovskites (HAP) M 3 T 2 Ch 2 ¼ M 3/2 TCh (e.g. Ni 3 Pb 2 S 2 , Co 3 Sn 2 S 2 ) and colored skutterudites M 2 T 3 Ch 3 ¼ M 2/3 TCh like Co 2 Sn 3 Se 3 . A range of competing structures of MTCh compounds were studied for PtSnCh [2] as low-gap semiconductors and isoelectronic to FeS 2 . Their low-dimensional structures are understood from coloring and orienta- tions of T–Ch dumbbells. The present study is extended to isoelectronic compositions with M¼ Ni, Pd, Pt and larger variety of partly unsolved structures, polymorphs, novel compositions, and their stability. In two recent contributions, we presented a graphical representa- tion that allows for the straightforward estimation of phase stabilities of a given chemical system [3,4]. Based on previous investigations on dumbbell-like pyrite-type systems MPn 2 and MPnCh (Pn ¼ N, P, As, Sb, Bi; Ch¼ S, Se, Te) [2,5–9], associations between related binary struc- ture types were worked out and a full set of ordering variants for the corresponding mixed occupied ternary derivatives was elaborated. It turned out that the largest flexibility of known structures is given for systems with 20 valence electrons such as NiAs 2 (that occurs as minerals rammelsbergite and pararammelsbergite as well as a high- pressure pyrite-type variant) or CoSbS (costibite, paracostibite, and pyrite-related phases). In order to extend the range of structurally diverse ternary dumbbell-like compounds with 20 valence electrons (ve), isoelectronic MTCh (M¼ Ni, Pd, Pt; T ¼ Si, Ge, Sn, Pb; Ch¼ S, Se, Te) compounds are taken into account now. Hitherto reported MTCh compounds with M¼ Pt reveal several unanswered questions. Early investigations by Schubert described PtGeCh, PtSnCh, and PtPbTe with disordered pyrite-related structures M(T,Ch) 2 , i.e. without ordering on the dumbbell sites. Deviations from Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jssc Journal of Solid State Chemistry http://dx.doi.org/10.1016/j.jssc.2015.01.028 0022-4596/& 2015 Elsevier Inc. All rights reserved. n Corresponding author. E-mail address: richard.weihrich@chemie.uni-r.de (R. Weihrich). Journal of Solid State Chemistry 226 (2015) 29–35