First-principles study of the structural and elastic properties of Ti 5 Si 3 with substitutions Zr, V, Nb, and Cr
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The formation enthalpy, electronic structures, and elastic moduli of the intermetallic compound Ti5Si3 with substitutions Zr, V, Nb, and Cr are investigated by using firstprinciples methods based on the density-functional theory. Our calculation shows that the site occupancy behaviors of alloying elements in Ti5Si3, determined by their atom radius, are consistent with the available experimental observations. Furthermore, using the Voigt–Reuss–Hill (VRH) approximation method, we obtained the bulk modulus B, shear modulus G, and the Young’s modulus E. Among these four substitutions, the V, Nb, and Cr substitutions can improve the ductility of Ti5Si3 effectively, while Zr substitution has little effect on the elastic properties of Ti5Si3. The elastic property variations of Ti5Si3 due to different substitutions are found to be correlated with the Me4d–Me4d antibonding and the strengthened Me4d–Si bonding in the solids. I. INTRODUCTION
Titanium silicide (Ti5Si3) has been extensively investigated over the past few decades as a candidate material suitable for high-temperature applications, because of its high melting point (2130 C), low density (4.32 g/cm3), relatively high hardness (11.3 GPa), and capacity to retain high strength up to 1200 C, as well as good oxidation and creep resistance at and below 850 C.1,2 However, the development and applications of Ti5Si3 has still been severely restricted in recent years because of its low fracture toughness (2.5 MPam1/2) below the ductile–brittle transition temperature.3,4 To overcome this deficiency, several toughening methodologies have been developed, including densification,3,5 refining grains,3,6 and solid-solution alloying,7,8 as well as the introduction of a second reinforcing phase to form composites,9 etc. Among these approaches, element alloying, which is achieved by doping with interstitial atoms, or by incorporation of substitutional atoms into Ti5Si3, has received considerable attention in recent years. Figure 1 gives the detailed D88 hexagonal structure of Ti5Si3 with a space group of P63/mcm. There are two titanium sites and one silicon site: Ti4d at (0.333, 0.667, 0), Ti6g at (0.240, 0, 0.250), and Si at (0.615, 0, 0.250).10 This configuration forms an ABAC stacking sequence along the c direction. Interstitial atoms are considered to occupy the center of the antiprism formed by Ti6g atoms.7,11 Williams et al.7 calculated the electronic density of states of Ti5Si3, Ti5Si3Zx (Z = B, C, N, and O) a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2010.0293 J. Mater. Res., Vol. 25, No. 12, Dec 2010
using the LMTO method and asserted that the stability of D88 structure with interstitial additions increased as a result of the bonding between the interstitial atom’s p electrons and the Ti6g atom’s d electrons.7 From an experimental viewpoint, Thom et al.12 suggested that carbon additions can reduce the anisotropy of coefficient of thermal expansion (CTE) of Ti5Si3. Compared with additions of interstitial atoms, inco
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