Theoretical study of the phase transitions and electronic structure of (Zr 0.5 , Mg 0.5 )N and (Hf 0.5 , Mg 0.5 )N

J Mater Sci CERAMICS Ceramics Theoretical study of the phase transitions and electronic structure of (Zr0.5, Mg0.5)N and (Hf0.5, Mg0.5)N M. A. Gharavi1,* 1 2 , R. Armiento2, B. Alling2, and P. Eklund1 Thin Film Physics Division, Department of Physics, Chemistry and Biology (IFM), Linköping University, 581 83 Linköping, Sweden Theoretical Physics Division, Department of Physics, Chemistry and Biology (IFM), Linköping University, 581 83 Linköping, Sweden Received: 8 July 2020 ABSTRACT Accepted: 19 September 2020 Rock-salt scandium nitride has gained interest due to its thermoelectric properties including a relatively high Seebeck coefficient. This motivates research for other semiconductor materials that exhibit similar electronic structure features as ScN. Using density functional theory calculations, we have studied disordered solid solutions of (Zr0.5, Mg0.5)N and (Hf0.5, Mg0.5)N using the special quasi-random structure model. The results show that within a mean-field approximation for the configurational entropy, the order–disorder phase transformation between the monoclinic LiUN2 prototype structure and the rocksalt cubic random alloy of these mentioned solid solutions occur at 740 K and 1005 K for (Zr0.5, Mg0.5)N and (Hf0.5, Mg0.5)N, respectively. The density-of-states for the two ternary compounds is also calculated and predicts semiconducting behavior with band gaps of 0.75 eV for (Zr0.5, Mg0.5)N and 0.92 eV for (Hf0.5, Mg0.5)N. The thermoelectric properties of both compounds are also predicted. We find that in the range of a moderate change in the Fermi level, a high Seebeck coefficient value at room temperature can be achieved. Ó The Author(s) 2020 Introduction The aim to decrease reliance on fossil fuels has led to research on energy harvesting, for example of thermal and solar energy. Thermoelectrics, the process in which thermal gradients can be transformed into an external voltage, is particularly useful when a longlasting and maintenance-free power source is needed [1–3]. In addition to a high Seebeck coefficient and electrical conductivity, features such as chemical stability, non-toxicity and ease of manufacturing are of importance when choosing an appropriate thermoelectric material. Transition metal nitrides are known for the above properties and have been studied extensively due to hardness, temperature resistance, mechanical and Handling Editor: David Cann. Address correspondence to E-mail: https://doi.org/10.1007/s10853-020-05372-1 J Mater Sci chemical stability [4]. Among the d-block nitrides, cubic chromium nitride (CrN) [5, 6] and cubic scandium nitride (ScN) exhibit interesting thermoelectric properties [7–11]. In addition to its chemical, thermal and mechanical stability, ScN has a relatively large Seebeck coefficient (reaching -180 lV/K at 800 K). When including its low electrical resistivity, large power-factors between 2.5 and 3.5 9 10–3 Wm-1 K-2 have been reported [12, 13]. Furthermore, ScN can also become p-type by Sc-site doping [14, 15]. However, ScN does have a relatively large thermal conductivity [16–19] of approximately 8–12 Wm-1 K-1 which will reduce the thermoelectric efficiency and make it an impractical thermoelectric material in pure form. Previously, Alling [20] addressed this issue by proposing a ternary nitride mimicking the features of 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 obtain 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. The study focused on TiMgN2, and it 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 [21] hybrid functional and 0.22 eV with the PBE GGA functional known to give band gaps that are smaller than the experimental values. The SQS model was also used to study (Tix, Mg1-x)N solid solutions where (Ti0.5, Mg0.5)N was shown to be a non-magnetic semiconductor with a predicted 1.33 eV band gap. These results were also supported by Irokawa and Usami [22]. An attempt to synthesize (Ti0.5, Mg0.5)N by magnetron sputtering was conducted by Wang and Gall [23, 24]. In their study, they found a negative temperature coefficient of resistivity and a vanishing density-of-states at the Fermi level measured by X-ray photoelectron spectroscopy, showing that (Ti0.5, Mg0.5)N is a semiconductor. In a separate study by the present authors, (Ti0.5, Mg0.5)N was determined to have a Seebeck coefficient value of -25 lV/K [25]. It was also shown that at approximately 800 °C, high-resolution scanning transmission electron microscopy (HR-STEM) shows that the rock-salt cubic random alloy of (Ti0.5, Mg0.5)N goes through a phase transformation at the grain boundaries, forming a quaternary (Ti0.5, Mg0.5)NxOy superstructure when oxygen is also present. Kim et al. [26] used hydrogen gas as a means to control the oxygen content in the grain boundaries of (Mg, Zr) oxynitride thin films, which in return can be used to tailor the optoelectronic properties of such films. In a previous paper, we expanded the research on this group of compounds by studying the phase stability and band structure of ZrMgN2 and HfMgN2 [27]. It was shown that the stoichiometric compositions have an almost equal tendency to crystallize in both the NaCrS2 superstructure and the LiUN2 prototype monoclinic structures. ZrMgN2 shows a 0.89 eV indirect band gap when crystallizing into the NaCrS2 structure while as crystallization into the LiUN2 structure results in a 0.46 eV direct band gap. As for HfMgN2, the band gap increases as crystallization into NaCrS2 results in a 1.19 eV indirect band gap and crystallization into LiUN2 results in a 0.77 eV direct band gap. Predicted thermoelectric properties of the semiconducting compounds showed that in the range of a moderate change in the Fermi level, high room temperature Seebeck coefficient values can be achieved. Experimental synthesis of MgxZr2-xN2 by Bauers et al. [28] showed that Zr-rich samples are more metallic, while Mg-rich samples are more insulating, which shows a degree of tunability of the electrical properties. In the present paper, we investigate the configurationally disordered solid solutions (Zr0.5, Mg0.5)N and (Hf0.5, Mg0.5)N using the special quasi-random structure (SQS) method in conjunction with DFT calculations. By comparing the formation energy of the disordered alloys of (Zr0.5, Mg0.5)N and (Hf0.5, Mg0.5)N in the rock-salt cubic structure with that of its LiUN2 ordered structure counterparts, the order/ disorder transition temperature can be calculated within a mean-field approximation. The density-ofstates of (Zr0.5, Mg0.5)N and (Hf0.5, Mg0.5)N are also studied, and these calculations are used to predict (...truncated)