First-principles study of structure and properties of x-Ti 2 Zr Pinliang Zhang a , Fanchen Meng a , Zizheng Gong b,a,⇑ , Guangfu Ji c , Shouxin Cui d , Dong-qing Wei d,⇑ a Key Laboratory of Advanced Technologies of Materials of Ministry of Education, School of Material Science and Engineering, Southwest Jiaotong University, Chengdu 610031, China b National Key Laboratory of Science and Technology on Reliability and Environment Engineering, Beijing Institute of Spacecraft Environment Engineering, Beijing 100094, China c Laboratory for Shock Wave & Detonation Physics, Institute of Fluid Physics, CAEP, Mianyang 621900, China d College of Life Science and Biotechnology and Research Center Astronautics, Shanghai Jiaotong University, Shanghai 200240, China article info Article history: Received 20 November 2012 Received in revised form 13 March 2013 Accepted 14 March 2013 Keywords: x-Ti 2 Zr Structure Elastic constants Electronic properties Thermodynamic properties abstract The structural, elastic, electronic properties, and Debye temperature of x-Ti 2 Zr under compression were investigated by the first-principles pseudopotential method based on density functional theory (DFT). The calculated structural parameters at zero pressure are in consistent with experimental values. The elastic constants and their pressure dependence were obtained using the static finite strain technique. We derived the bulk modulus, Young’s modulus and Poisson’s ratio for x-Ti 2 Zr. The Debye temperature was obtained by the average sound velocity, and compared with other Ti–Zr metals and alloys. The pres- sure dependence of electron distribution, as well as the s ? d electron transfer indicates that there is a x ? b phase transition in the high pressures regime. Finally, the heat capacity at the constant pressure and the linear thermal expansion coefficient as a function of temperature had been obtained. Ó 2013 Published by Elsevier B.V. 1. Introduction Group IV metals and their alloys have attracted tremendous sci- entific and technological interests, due to its high strength-to- weight ratio, high rigidity-to-weight ratio and excellent resistance to corrosion [1]. Ti–Zr alloys, as one of the group IV alloys, have po- tential uses in aerospace, medical, nuclear industries. Many solid phases and allotropes have been observed in the phase diagrams [2,3]. At ambient condition, it possesses a hexagonal close-packed (hcp) structure (a-phase), and transforms to body-centered cubic (bcc) b-phase under high temperature and a three atoms hexagonal structure (x-phase) under high pressure [4]. Recently, there are many investigations related to the a ? x phase transitions of the Ti–Zr systems, for example, studies of pure Ti [5–10] and Zr [5,9,11–13], TiZr alloys by Bashkin [14–16] and Aksenenkov [17]. For group IV metals, which has a narrow d band in the midst of a broad s–p band [18,19], the electrons transfer from s–p band to d band induced by pressure plays an important role in the phase stability. The elastic properties are closely related to many fundamental solid-state properties, and have a critical impact on many practical applications related to the mechanical properties of a solid [20]. Therefore, investigation of their elastic properties is important for technological applications. Early investigations on Ti–Zr system (mostly on Ti [21–24], Zr [13,25–28] and TiZr [16,29]) showed that brittleness of x-phase was more predominant than that of a- and b-phase [27,29,30], due to the unique structure of x-phase which crystallizes in the AlB 2 structure, in which Al atom occupied the 1a Wychoff site (0, 0, 0) and two B atoms held the 2d Wychoff site (1/ 3, 2/3, 1/2) and (2/3, 1/3, 1/2) [9]. This structure forms a sequence of type ABAB... describes by (0 0 0 1) plane, and with graphite-like nets of B-plane which has three nearest neighbors [31,32]. Other composites with this structure [33] also show unique physical and chemical properties such as hardness, high melting point, and chemical inertness, and belong to the most promising engi- neering materials. Theoretically, the first-principles density functional theory (DFT) is very useful in studying the structure and properties of Ti–Zr metals and alloys. Hao [21,30] and Mei [22] predicted the high pressure phase transitions and elastic properties of Ti based on the Perdew–Burke–Ernzerhof (PBE) generalized-gradient approximation (GGA) [34], which is consistent with the experi- ments. Wang [25,29] used the frozen-core projector augmented wave (PAW) method [35] with the VASP code [36] to study the phase transitions, elastic modulus and superconductivity of Zr and TiZr successfully. The bulk modulus and shear modulus are calculated from the Voigt–Reuss–Hill (VRH) approximations [37]. In addition, the plane-wave pseudopotential DFT method has been successfully applied to investigate the thermodynamic properties of MgB 2 [38], AlB 2 [31], ZrB 2 [39] and HfB 2 [40]. 0927-0256/$ - see front matter Ó 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.commatsci.2013.03.025 ⇑ Corresponding authors at: National Key Laboratory of Science and Technology on Reliability and Environment Engineering, Beijing Institute of Spacecraft Envi- ronment Engineering, Beijing 100094, China (Z. Gong). Tel.: +86 10 68746609 (Z. Gong), tel.: +86 021 34204573 (D. Wei). E-mail addresses: gongzz@263.net (Z. Gong), dqwei@sjtu.edu.cn (D.-q. Wei). Computational Materials Science 74 (2013) 129–137 Contents lists available at SciVerse ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci