Theoretical Investigation of Phase Stability in Ti-V and Ti-Cr Substitutional Alloys
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THEORETICAL INVESTIGATION OF PHASE STABILITY INTi-V AND Ti-Cr SUBSTITUTIONAL ALLOYS M. SLUITER AND P.E.A. TURCHI Lawrence Livermore National Laboratory, Condensed Matter Division, L-268, Livermore, CA 94550 Abstract
The phase stability of Ti-V and Ti-Cr alloys is examined within the context of an electronic structure description. Energies of mixing, effective pair interactions, and phase diagrams are computed and compared to available experimental data. A metastable distorted B2 type of structure is predicted in near equiatomic Ti-Cr. Introduction Many properties of Titanium-3d transition metal (TM) alloys show a similar dependence on electron per atom ratio (e/a). Such diverse properties as, elastic constants, magnetic susceptibility, electronic specific heat coefficient and critical temperature for superconductivity show virtually identical behavior when plotted as a function of e/a ratio, independent of the 3d-TM alloying species [1]. In addition, Ti-3d-TM phase diagrams exhibit striking trends in the 3d-TM sequence [2]. The importance of the e/a ratio indicates that electronic effects are the main driving forces for the physical properties and the phase stability in Ti-TM alloys. Many trends concerning the stability of ordered structures can be explained with a simple rectangular bands model [3]. However, with such a model it is not possible to predict which type of ordering will occur, and the question which electronic feature is responsible for the preference for a particular ordered structure can not be addressed. In this work, a realistic tight-binding formalism is used to give specific information concerning phase stability on the bcc lattice in the Ti-V and Ti-Cr systems. These systems provide an excellent contrast: the Ti-V system exhibits a miscibility gap and features no intermetallic phases, whereas the Ti-Cr system has stable intermetallic Laves phases (C14, C15, and C36). In this paper, the energies of mixing, effective pair interactions, and ultimately the phase diagrams will be studied in detail, and the origin of phase segregation and phase formation in Ti-V and Ti-Cr will be discussed. Moreover, the prospects of forming metastable phases based on the bcc lattice in Ti-Cr, which might be hidden by the Laves phases, is studied from a formal point of view. A brief description of the tight-binding formalism used in this study is given in [4], and will be discussed in more detail elsewhere [2]. The electronic Slater-Koster (SK) parameters are obtained from a fit to LAPW results [5]. A shift of the onsite-energies of one element is required in order to bring both elements in an alloy on a common energy scale. This shift was determined by matching the Fermi-levels of the alloying elements, which is expected to be accurate since i) the charge transfer in Ti-V and Ti-Cr is small and ii) the densities of states (DOS) at the Fermi-level of the pure elements is high. The onsite energy shift selected is -0.218191 Ry In Ti-Cr for Cr, and - 0.12673 Ry in Ti-V for V.
Results In order to gain a clear insight i
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