Topology of charge density and elastic anisotropy of Ti 3 SiC 2 polymorphs
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L.L. He and H.Q. Ye Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China (Received 2 November 2004; accepted 19 January 2005)
Using an all-electron, full potential first-principles method, we have investigated the topology of charge density and elastic anisotropy of Ti3SiC2 polymorphs comparatively. By analyzing the charge density topology, it was found that the Ti–Si bonds are weaker in  than in ␣, resulting in a destabilizing effect and lower Young’s modulus in directions between a and c axes for . On the other hand, the Si–C bonds (absent in ␣) are formed in  in the c direction. The formation of the Si–C bonds not only mitigates the destabilizing effect of the weaker Ti–Si bonds, but also results in larger Young’s modulus in the c direction. In contrast to the high elastic anisotrophy, the elastic anisotropy of Ti3SiC2 is very low. I. INTRODUCTION
The layered ternary carbides and nitrides, e.g., Ti3SiC2, Ti2AlC, Ti3AlC2, and Ti4AlN3 etc., have been the subject of numerous studies in recent years due to their unique combination of mechanical, electrical, and thermal properties.1–9 Among the compounds, Ti3SiC2 has the best comprehensive properties and thus has been investigated most extensively. It has high elastic moduli and easy machinability, and good thermal and electrical conductivities, together with excellent oxidation properties and fatigue resistance.1 In fact, Ti3SiC2 has become the model material of the layered ternary compounds. There are two polymorphs10–12 for Ti3SiC2, ␣ and  phases. The structures for both ␣ and  polymorphs are hexagonal in symmetry with a space group of P63/mmc (No. 194). However, Si occupies the 2b Wyckoff position in ␣, but 2d in . Note that the 2b and 2d sites are the largest holes in ␣ and , respectively. This facilitates the transition between the two polymorphs. The possibility of the presence of the  polymorph was first proposed by Farber et al.10 In the early high-resolution transmission electron microscopy (HRTEM) investigations of Ti3SiC2, however, there was misinterpretation for the HRTEM images: the ␣ polymorph was regarded as the  polymorph.10 Using image simulations, Yu et al.11,12 clarified the relationship between HRTEM images and the underlying crystal structure for Ti3SiC2 and pointed
out that the bright spots in HRTEM images do not necessarily correspond to the atomic columns. In the same work, they identified the existence of the  polymorph. Because  is less frequently observed than ␣,11 it was proposed to be a metastable phase, which was confirmed by the first-principles calculations of the heats of formation.12 The different atomic configurations of the two polymorphs are expected to influence their bonding and mechanical properties. In this paper, the bonding properties were calculated based on Bader’s quantum theory of “atoms in molecules” (AIM).13–15 The AIM theory is a theory about atoms, bonds, structure, and structural stability. Analyzing t
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