PROPERTIES OF TI3SIC2
A. L. Ivanovskii, N. I. Medvedeva and A. N. Enyashin
Institute of Solid State Chemistry, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
ABSTRACT
Layered ternary transition-metal carbides (so-called nano-laminates, or MAX phases) attract much attention of physicists and material scientists owing to their unique physical and chemical properties and their technological applications as high-temperature and ultrahigh-temperature structural materials. The ab initio approaches are very helpful in optimization and prediction of properties of these materials. Here, recent achievements in the theoretical studies of electronic band structure, chemical bonding and some properties of Ti3SiC2 as a basic phase of a broad family of nano-laminates are reviewed.
Besides, the peculiarities of electronic properties of non-stoichiometric and doped Ti3SiC2 - based species are described, and Ti3SiC2 surface states and hypothetical Ti3SiC2
– based nanotubes are discussed.
1. INTRODUCTION
The MAX phases (known also as nano-laminates) are a wide group of ternary layered compounds with formal stoichiometry Mn+1AXn (n=1,2,3...), where M are transition d metals,
A are p elements (such as Si, Ge, Al, S, Sn etc.) and X is carbon or nitrogen.
In recent years, the MAX phases have become materials of intense research owing to their remarkable mechanical properties, fully reversible plasticity, exceptional shock resistance, damage tolerance, negligible thermopower, high thermal conductivity and some others, which are very attractive for industrial applications of these systems as advanced ceramic materials [1-3].
Besides great efforts, which have been made in synthesis of new promising nano- laminates (in the form of both bulk materials and thin films) and in experimental characterizations of their properties, much activity was focused on the theoretical studies, which have shown powerful ability to understand and to predict the properties of these unusual materials.
Ti3SiC2 is a prototype of the M3AX2 phases (so-called 312 nano-laminates) and the most
extensively studied member of this family. The theoretical studies on the band structure of Ti3SiC2 and related materials (such as Ti3AlC2, Zr3SiC2, V3SiC2, Ti3AlN2 etc.) by means of
the ab initio calculations within the density-functional theory (DFT) approaches were started in the middle of 1990s by our group [4-9] and are continued till now, see [10-33].
In those works the following main topics were examined: (i) Detailed studies of the electronic band structure, chemical bonding and some properties (such as structural, optical properties, cohesive parameters etc.) of the basic phase Ti3SiC2 and some related compounds
such as Ti3AlC2, Zr3SiC2, V3SiC2, Ti3AlN2, Ti3GeC2 etc.; (ii) The investigation on the phase
stability of Ti3SiC2 and related phases at high pressures and polymorphism of Ti3SiC2; (iii)
The influence of lattice defects and various impurities on the properties of bulk Ti3SiC2; (iv)
The surface states for Ti3SiC2 and related compounds as well as some interfaces; (v) and
simulations of the Ti3SiC2-based solid solutions such as Ti3SiC2-x Nx; Ti3Si1-xAlxC2 or Ti3Si1- xGexC2. The results obtained are discussed below in Sec. 1.
Besides, as Ti3SiC2 is of interest mostly as advanced ceramics, we will focus also on the
mechanical properties of this material and discuss the cleavage characteristics, fracture properties under tensile stress and lattice resistance to sliding predicted from ab initio calculations, Sec. 2. Finally, the structural models and electronic properties of the recently proposed hypothetical Ti3SiC2 nanotubes are shortly discussed in Sec. 3.
1.1. Electronic Band Structure of Ti
3SiC
2and Related Phases
Ti3SiC2 adopts a hexagonal structure (space group P63/mmc, Z= 2), see reviews [1-3].
There are two non-equivalent Ti atoms (denoted as Ti1 and Ti2), which are located at the Wyckoff positions 2a= (0,;0;0) and 4f = (1/3;2/3;zTi), respectively. Here, two (per cell) Ti1
atoms have carbon atoms as nearest neighbors, while the other four (per cell) Ti2 atoms have both C and Si atoms as nearest neighbors. The silicon atoms are in 2b = (0;0;1/4) positions and carbon atoms are in positions 4f = (1/3;2/3;zC). Here zTi and zC are internal parameters.
The experimentally determined lattice parameters are a = 3.068 Å and c = 17.669 Å and the internal coordinates are zTi = 0.135 and zC = 0.567 [1-3]. The structure of Ti3SiC2 can be
described as two edge-shared Ti6C octahedron layers linked together by a two-dimensional
atomic Si layer or, in other words, as formed from the hexagonal layers …[Si-Ti2-C-Ti1-C- Ti2]… stacked in the repeated sequence as is shown in Figure 1.
To calculate the ground-state electronic properties of Ti3SiC2, it is necessary to obtain the
stable atomic configuration of crystal. In numerous theoretical papers the equilibrium structure was determined by relaxation with respect to lattice parameters and internal parameters. In Table 1, the calculated lattice constants and internal parameters, as well as the bulk moduli B for Ti3SiC2 (and for some related materials) are listed, and the theoretical
Figure 1. The crystal structures of Tin+1SiCn (n=1,2,3 and 4) [31]. The Wyckoff positions of various
atoms and non-equivalent Ti atoms (Ti1 and Ti2, see text) are labeled for α-Ti3SiC2.
Table 1. Calculated lattice parameters (a and c, in Å), internal coordinates (zTi,C) and
bulk modulus (B, in GPa) for Ti3SiC2 and some related materials in comparison with
experiment
phase a c c/a zTi zC B References
Ti3SiC2 3.0563 17.6604 5.78 0.1366 0.5728 195 [23] 3.0615 17.6094 5.75 - - 184 [19] - - 5.77 0.135 0.572 225 [11] 3.0603 17.6707 5.77 0.1342 0.5720 - [25] 3.0705 17.6707 5.77 0.1370 0.5741 202 [14] 3.076 17.713 5.76 - - - [21] 3.0665 17.671 5.78 - - - [1] Ti3AlC2 3.082 18.6523 6.05 0.1274 0.5693 - [25] 3.0634 18.5066 6.04 0.1286 0.5699 187 [23] 3.0720 18.732 6.10 0.1290 0.5701 190 [15] 3.0753 18.578 6.04 0.1280 0.5640 - [24] Ti3GeC2 3.0992 17.8948 5.77 0.1325 0.5718 - [25] 3.0823 17.7109 5.75 0.1361 0.5737 198 [14] 3.07 17.76 5.79 - - - [1]
* As calculated by CASTEP [14,15,19,23], FLMTO [11], VASP [21] and FLAPW-GGA [25] codes in comparison with experiments [1,24].
The calculated elastic constants (Cij) for Ti3SiC2 [19] are positive and satisfy the well-
known generalized criteria for mechanically stable hexagonal crystals: C11 > 0; C44 > 0; C11 -
C12 > 0; (C11 + 2C12)C33 - 2C132 > 0. The shear anisotropy ratio A = C44/C66, bulk modulus,
shear modulus (G) and Young‘s modulus (Y) for Ti3SiC2 calculated from the elastic constants
are presented in Table 2. It is seen that B > G; this implies that the parameter limiting the mechanical stability of this material is the shear modulus. According to the semi-empirical
Pugh‘s criteria (see, for example [49]) the material should behave in a ductile manner if G/B
< 0.5, otherwise it should be brittle. For Ti3SiC2 G/B = 0.76, thus this phase is expected to
behave as a brittle material, see also below.
Table 2. Calculated elastic constants (Cij, in GPa) and shear anisotropy ratio A, bulk
modulus, (B, in GPa), shear modulus (G, in GPa) and Young’s modulus (Y, in GPa) for
the α- and β- polymorphs of Ti3SiC2 [19]
polymorph C11 C12 C13 C33 C44 C66 A B G
α 355 96 103 347 160 130 1.26 184 140
β 375 85 74 361 121 145 0.83 175 136
Let us discuss the electronic properties of Ti3SiC2. Figure 2(a) shows the calculated [7]
band structure of Ti3SiC2 along the high-symmetry lines in the Brillouin zone (BZ) of the
hexagonal lattice.
Figure 2. (a) Electronic band structure of Ti3SiC2 according to FLMTO calculations[7] and (b) the near-
Fermi bands according to FLAPW calculations [25].
It is seen that the valence bands of Ti3SiC2 may be divided into two basic groups: a low-
energy group composed of C, Si states mainly of s-symmetry (there is also a little contribution from Ti 3d states), and the next occupied bands containing predominantly valence Si 3p, C 2p and Ti 3d states. There is no direct overlap of C and Si s-bands (the four lower and the next two bands, Figure 2(a)). The energy dispersion of the Si bands is larger than that for the C bands owing to a more diffuse character of the 3s and 3p orbitals of silicon. The top valence bands are derived from the strongly hybridized Ti 3d, Si 3p, and C 2p states, see Figure 3, where the total and partial densities of states (DOSs) are depicted.