First-Principles Total Energy Study of NbCr2 + V Laves Phase Ternary System
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ABSTRACT The C15 NbCr 2 + V Laves phase ternary system is studied by using a first-principles, self-consistent, full-potential total energy method. Equilibrium lattice parameters, cohesive energies, density of states and formation energies of substitutional defects are calculated. Results of all these calculations show that in the C15 NbCr 2 + V compounds, V atoms substitute Cr atoms only.
INTRODUCTION Among the intermetallic compounds studied for use as high-temperature structural materials, Laves phases have been attracting an increasing attention. Laves phase compounds are intermetallic compounds of composition AB 2 and they have highly symmetric crystal structures: cubic C15 (MgCu2), hexagonal C14 (MgZn 2) and dihexagonal C36 (MgNi:)[1]. These crystal structures are topologically closed-packed (TCP) structures; assuming hard spheres, atomic volume accounts for about 71% of the unit cell volume. A number of Laves phase compounds have properties that are quite desirable for high-temperature structural applications, such as high melting temperatures, low densities and high oxidation resistance[2]. The C15 Laves phases have so far been studied more exclusively compared to the other two, primarily because of the availability of more slip systems in the fcc-lattice-based C15 structure. A C15 compound of particular interest is NbCr 2. This compound has been subject to quite extensive experimental [3-7] and theoretical [8-12] studies. NbCr 2 has a high melting temperature (1730'C), reasonable oxidation resistance, high strength, excellent creep behaviour and intermediate density (7.7 g/cm 3)[13,141. However, as is also true for the other TCP compounds in general, poor low-temperature ductility is a major obstacle in the use of C15 NbCr 2 in practical applications. Consequently, in recent years there have been focused efforts in finding ways to improve its lowtemperature ductility without compromising much on its attractive high-temperature properties [1317]. The central idea behind these studies is adding a third metal to form a ternary alloy. The particular C15 NbCr 2-based systems that are studied are NbCr 2 + V [13-16], NbCr 2 + Ti [18], NbCr 2 + Be and NbCr 2 + Mo [19]. Another example of this approach in the context of C15 Laves phases is the HfV 2 + Nb system [15,20-23]. In this study we will confine our interest to the NbCr 2 + V system for which there exists quite an extensive body of experimental results [13-16]. By using a full-potential linear muffin-tin orbital (FP-LMTO) method based on the local density approximation (LDA) to the density functional theory [24], we carried out total energy calculations to understand the electronic structures of the C 15 Laves phase NbCr 2 + V compounds. These calculations will enable us to account for the major experimental findings; namely, (i) the lattice parameter increases linearly with the vanadium content, (ii) the C15 phase region in the ternary phase diagram of the Nb-Cr-V extends towards vanadium by up to more than 30 at.% of V, (iii) V atoms replace C
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