Ab Initio Modeling of the Stress-Strain Response of Sialon (Si6 Zalzozn8 Z, Z ¼ 0:5 and 1)
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Materials Transactions, Vol. 45, No. 5 (2004) pp. 1469 to 1472 Special Issue on Advances in Computational Materials Science and Engineering III #2004 The Japan Institute of Metals Ab initio Modeling of the Stress-Strain Response of SiAlON (Si6ÀzAlzOzN8Àz, z ¼ 0:5 and 1) Cenk Kocer1;2, Naoto Hirosaki1 and Shigenobu Ogata3;4 1Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba 305-0044, Japan 2University of Sydney, School of Physics, Sydney NSW 2006, Australia 3Department of Mechanical Engineering and Systems, Graduate School of Osaka University, Suita 565-0871, Japan 4Handai Frontier Research Center, Graduate School of Osaka University, Suita 565-0871, Japan A derivative of the Si3N4 ceramic is the quaternary SiAlON solid solution. In this paper the characteristic stress-strain response of the - and c-SiAlON phases is investigated using an ab initio computational procedure, for the 11 strain component, where different substitutions of the atomic pairs, Al-O, were performed. From the modeled data the ‘ideal’ strengths and other material constants were estimated for the two polymorphs. Estimates of the elastic constants were found to be in reasonable agreement with existing data. (Received November 10, 2003; Accepted February 3, 2004) Keywords: SiAlON, mechanical properties, strength, stress-strain curve 1. Introduction z > 4 a supersaturated SiAlON system is obtained. There are two well-known polymorphs of silicon nitride Silicon nitride (Si3N4) is a non-oxide ceramic that exhibits ceramics, which are the - and -Si3N4 phases. The lattice desirable high temperature properties.1) However, the non- configuration of these two polymorphs have been outlined by oxide ceramic is inherently difficult to produce, since, in many workers,8) and various properties have been inves- general, high temperatures, high pressures and additives are tigated in detail.9–13) Both of the phases have an underlying required during the fabrication process. Nevertheless, the use atomic structure that is hexagonal and only differs along the of oxide additives does produce a variation of silicon nitride, z-axis, the stacking sequence. The -phase, (density of which is the quaternary SiAlON solid solution. The solid 3:183 gcmÀ3) is generally synthesized at ambient pressure solution can be produced using reaction sintering or hot (below 2000 K) and the -phase, the more stable of the two, pressing techniques, utilizing oxide, nitride and oxynitride (density of 3:200 gcmÀ3) is obtained from a transformation powders. The SiAlON solid solution exhibits excellent of the -to -phase at high temperatures.8) Moreover, it is properties, such as excellent resistance to wear, corrosion generally believed that both polymorphs can be synthesized and thermal shock, yet can be formed at lower temperatures concurrently over a wide temperature range. Recent studies and exhibits greater thermodynamic stability, making it a have shown that there exists a cubic spinel phase of silicon suitable alternative to silicon nitride. Furthermore, variations nitride. Zerr et al.14) reported, in 1999, the synthesis of a in additional parameters (i.e. the physico-chemical proper- cubic spinel structure, c-Si3N4, with a density of 3:93 Æ ties) in the SiAlON system could produce increased strength, 0:12 gcmÀ3 (23% higher than the -or -phases). wear resistance and chemical inertness, along with other Likewise, studies to date have reported the synthesis of -, advantageous electronic properties.2) - and c-SiAlON. Naturally, the well known single crystal - It is well-known that the mechanical properties and and -SiAlON phases exhibit a hexagonal lattice structure fracture behavior of sintered silicon nitride composite that clearly is derived from the - and -Si3N4 phases. materials, at elevated temperatures above 1200 C, are Furthermore, the existence of c-Si3N4 has led to the directly related to the intergranular glassy phase, which is hypothesis that cubic spinel SiAlON can be produced by an mostly made up of oxides, at triple junctions or between the appropriate process. Recently, the discovery of cubic spinel 3) single crystal Si3N4 grains (generally, -Si3N4 particles). SiAlON (c-Si6ÀzAlzOzN8Àz, z ¼ 1:8 and 2.8) was reported, Additionally, it is known that the thickness and properties of the cubic phase was synthesized using a shock compression the intergranular phases (including other properties4)) can be method,15) with other workers reporting the use of other altered, using various sintering additives, where in most cases methods.16) rare-earth elements are used. The addition of the elements Various studies have been reported that have employed aluminium and oxygen into sintered materials effects the computational and experimental methods to understand growth of grains and the strength of the crystalline-glass better the properties of the SiAlON system.17–22) Using interface. In particular, it has been observed that at high various methods the atomic and electronic structure, bulk temperatures the addition of these additives produces a modulus, various mechanical properties and the lattice material, SiAlON, which is easier to densify and exhibits parameters of crystalline -, - and c-SiAlON have been greater ductility. Thus, the SiAlON system could offer further studied. The mechanical response of the SiAlON lattice advances, as a significant material in high strength, high structures to applied strains has not so far been reported. In temperature applications.5,6) The chemical formula that is this paper, an ab initio numerical scheme is employed to used to define the system is given as Si6ÀzAlzOzN8Àz, where z determine the stress-strain response of the - and c-SiAlON is any value between the limits 0 to approximately 4,7) and for phases. The -phase has not been modeled, at this time, due 1470 C. Kocer, N. Hirosaki and S. Ogata to inherent difficulties in the complex lattice structure. The (a) determination in this case of the equilibrium structure with the stacking appropriate Al and O pair substitutions is of ongoing work. In sequence the following sections the method of calculation is outlined in Si N Al O detail, including an outline of the crystal structures employed A for the two -, -phases. Following this, the results obtained B from the simulation procedure are presented, and finally, these results are briefly discussed. (b) (c) 2. Calculation Method & Results The equilibrium structure, elastic constants and other properties of the SiAlON polymorphs were determined using the Vienna Ab-initio Simulation Package (VASP).23–25) The VASP package provides for the core region and valence electrons of the atoms in the supercell to be described by the (d) Vanderbilt ultrasoft pseudopotential.26) In addition, the electron-electron exchange interaction was described using Silicon (tetrahedral bond) the generalized gradient approximation (GGA) and the local Silicon (octahedral bond) density approximation (LDA). The GGA employs a Perdew- Nitrogen 27) 28) 91 (PW91) functional form, and a Ceperley-Alder form Atom substitution site is employed in the LDA. In many cases, the two potential functions provide comparable results.29,30) Therefore, in this study, as a matter of convenience, only the LDA results of the x stress-strain data are presented. The numerical integration of the Brillouin zone was performed using a discrete 4 Â 4 Â 4 z y and 6 Â 6 Â 6, for - and c-SiAlON, respectively, Mon- 31) Fig. 1 An illustration of the - and c-Si6ÀzAlzOzN8Àz single crystal lattice khorst-Pack k-point sampling, and the plane wave cutoff structure. Figures a, b, and c, are the -single crystal lattice for the z ¼ 0:5 À17 was chosen as 7:9 Â 10 J. (case 1 and 2) and z ¼ 1 (case 3), respectively. Figure d, is the c-single During the simulation procedure at each step, the applied crystal lattice for z ¼ 1. The pair substitution positions, of Al-O, are strain was increased by a uniform 1%. The strain definition highlighted. used in this study is equivalent to the ‘engineering strain’ definition used by Morris et al.32) The relaxation process, using the conjugate gradient method, was performed for a orthorhombic lattice, made up of two unit cells stacked along peak force at each atomic site of 1:6 Â 10À11 J/m, and a peak the c-axis, consisting of a total of 28 atoms. The initial lattice 8 2 À10 stress in the supercell of 1 Â 10 kg/m.s . At each subsequent parameters, ao and co, were defined as 7:595 Â 10 and step, the supercell configuration of the previous step was 2:902 Â 10À10 m, respectively, from experimental data.35) employed after relaxation of the supercell.33) It is important For the -phase the modeling was restricted to three simple to note that at each step the conjugate gradient method was cases of atom substitution in Si6ÀzAlzOzN8Àz, where z would performed only after a finite temperature of 1 K was applied be 0.5 and 1. In the first case, z ¼ 0:5, where the first and last to the supercell structure for 1 Â 10À13 s. In this case, the atomic positions in the 14 atom Wyckoff unit cell are favored predefined temperature value was selected to provide a for the pair substitution,17) and thus, the substitution is made sufficient amount of energy to the supercell to displace the such that in position 1, N ! O, and in position 14, Si ! Al, À10 atomic configuration by a small amount. All subsequent data see Fig. 1(a), (with an optimized lattice, ao ¼ 7:590 Â 10 À10 were calculated for a temperature of 0 K. and co ¼ 5:805 Â 10 m). In the second case z ¼ 0:5 as Clearly, the -SiAlON lattice structure is obtained from well, where the last and fourth atomic positions in the the -Si3N4 lattice structure. As a matter of convenience, in Wyckoff unit cell are favored for the pair substitution, and the following a detailed discussion of the - and c-Si3N4 thus, the substitution is made such that in position 4, N ! O, lattice structures are not presented, the reader is directed to and in position 14, Si ! Al, see Fig.