Theoretical study of phase stability, crystal and electronic structure of MeMgN2 (Me = Ti, Zr, Hf) compounds

J Mater Sci (2018) 53:4294–4305 ELECTRONIC M ATERIALS Electronic materials Theoretical study of phase stability, crystal and electronic structure of MeMgN2 (Me 5 Ti, Zr, Hf) compounds M. A. Gharavi1,* , R. Armiento2 , B. Alling2,3 , and P. Eklund1 1 Thin Film Physics Division, Department of Physics, Chemistry and Biology (IFM), Linköping University, 581 83 Linköping, Sweden Theory and Modelling Division, Department of Physics, Chemistry and Biology (IFM), Linköping University, 581 83 Linköping, Sweden 3 Max-Planck-Institut für Eisenforschung GmbH, 40237 Düsseldorf, Germany 2 Received: 6 July 2017 ABSTRACT Accepted: 21 November 2017 Scandium nitride has recently gained interest as a prospective compound for thermoelectric applications due to its high Seebeck coefficient. However, ScN also has a relatively high thermal conductivity, which limits its thermoelectric efficiency and figure of merit (zT). These properties motivate a search for other semiconductor materials that share the electronic structure features of ScN, but which have a lower thermal conductivity. Thus, the focus of our study is to predict the existence and stability of such materials among inherently layered equivalent ternaries that incorporate heavier atoms for enhanced phonon scattering and to calculate their thermoelectric properties. Using density functional theory calculations, the phase stability of TiMgN2, ZrMgN2 and HfMgN2 compounds has been calculated. From the computationally predicted phase diagrams for these materials, we conclude that all three compounds are stable in these stoichiometries. The stable compounds may have one of two competing crystal structures: a monoclinic structure (LiUN2 prototype) or a trigonal  The band structure for the two superstructure (NaCrS2 prototype; R3mH). competing structures for each ternary is also calculated and predicts semiconducting behavior for all three compounds in the NaCrS2 crystal structure with an indirect band gap and semiconducting behavior for ZrMgN2 and HfMgN2 in the monoclinic crystal structure with a direct band gap. Seebeck coefficient and power factors are also predicted, showing that all three compounds in both the NaCrS2 and the LiUN2 structures have large Seebeck coefficients. The predicted stability of these compounds suggests that they can be synthesized by, e.g., physical vapor deposition. Published online: 30 November 2017 Ó The Author(s) 2017. This article is publication an open access Address correspondence to E-mail: https://doi.org/10.1007/s10853-017-1849-0 J Mater Sci (2018) 53:4294–4305 Introduction Thermoelectric materials and devices, which directly convert a thermal gradient into an external voltage, are reliable and low-maintenance power-generating materials used for niche applications such as solidstate cooling or electric power supplying units in deep-space exploration. However, the use of thermoelectrics is presently limited [1] by their low efficiency and high cost. For example, the crustal abundance and global production of tellurium is low [2, 3]. This limits widespread use of the benchmark thermoelectric materials (Bi2Te3 and PbTe). Thus, there is a need for replacement materials. The thermoelectric efficiency is directly connected to the dimensionless figure of merit:  2  S r zT ¼  T; j where S is the Seebeck coefficient, r is the electrical conductivity, j is the thermal conductivity, and T is the absolute temperature [4]. The product S2 r is known as the power factor. In the limit of zT ! 1, the Carnot engine efficiency (i.e., the maximum efficiency achievable in a heat engine) is obtained. However, designing materials with higher zT values is a difficult challenge, as all three terms are interrelated in a way that typically limits zT to below unity in commonly available materials. In order to overcome this barrier, Slack proposed the phonon glass–electron crystal (PGEC) approach for thermoelectric material design [5–7]: one should seek a material with a high Seebeck coefficient value and engineer it in such a way that it will behave like a crystal for electrons, but scatter phonons similarly to glass. As a result, added material optimization processes are required to increase the zT of any given material. As a starting point for this approach of engineering a high zT material, prior works have suggested cubic scandium nitride (ScN) [8]. The Seebeck coefficient of ScN is relatively large (reaching - 180 lV=K at 800 K) and because of its low electrical resistivity, large power factors between 2.5 and 3.5 9 10-3 Wm1 K2 have been reported [9, 10]. Doping and alloying ScN with heavy elements [11, 12] and/or creating artificial layer interfaces such as metal/semiconductor superlattices [13–16] can alter properties and decrease the thermal conductivity, resulting in an enhanced zT. 4295 Furthermore, ScN can also become p-type by Sc-site doping [17, 18]. Although the direction of research is promising, ScN does have a relatively large thermal conductivity [19–22] of approximately 8– 12 Wm1 K1 . Scandium and nitrogen are both light atoms compared to their heavier counterparts such as lead, bismuth and tellurium which effectively scatter phonons [23], and artificial interfaces seen in superlattices are synthesized at a sub micrometer scale, while thermoelectric power generation requires millimeter-sized bulk samples [24]. Also, scandium does not have phonon isotope scattering as it is an isotopically pure element. In a recent paper, Alling [25] addressed these issues by proposing an equivalent ternary based on ScN. Scandium (which is a group-3 element) can be replaced with one group-2 and one group-4 element in a 50/50 proportion to cover the same electron valence. The final compound should then have a MeAEN2 stoichiometry, with Me representing a transition metal from the group-4 elements and AE belonging to the group-2 (alkaline earth) elements, such as magnesium. TiMgN2 was predicted to be stable using density functional theory (DFT). Band structure calculations predicted stoichiometric TiMgN2 to have a 1.11 eV band gap using the HSE06 [25, 26] hybrid functional. This methodology has also been used by Tholander et al. [27] to predict zincbased group-4 transition metal nitride stability and crystal structure. While much research has been done regarding Ti–Si–N [28–30] and Ti–Al–N [31–34] which show superior hardness and/or oxidization resistance compared to TiN, there are much fewer studies reported for Ti–Mg–N [35–39]. TiMgN2 may crystallize in the B1–L11 superstructure [25], which could open a new opportunity for hard coating research by inter-layer dissipation of heat or research for hard coatings with better mechanical properties. In this paper, we continue the work in investigating ternary structures based on ScN. We also computationally study the phase stability, band structure, Seebeck coefficient and power factor of two more candidate compounds potentially useful in thermoelect (...truncated)