THEORETICAL INVESTIGATION OF a--b TRANSFORMATION OF QUARTZ

Artem R.Oganov, Vadim S. Urusov, Nickolai N. Eremin.

Dept. of Crystallography and Crystal Chemistry, Moscow State University, 119899, Moscow, Russia.
E-mail : oganov@openmail.irex.ru

Keywords: quartz, computer simulation, phase transition, atomization energy.

The atomization energy minimization method [1,2] has been applied for calculation (METAPOCS code) of dependencies of crystal structure, elastic properties and atomization energy of quartz (SiO₂) on the ionicity degree of Si-O bonds - f(Si-O) (for details see [1]).

Our interatomic potential includes Coulombic interactions, Born-Mayer repulsion, van der Waals attraction, O-Si-O and Si-O-Si three-body bond-bending terms; covalent terms in the interaction energy were imitated by Morse potentials. Ionic and covalent contributions were weighted in accordance to f(Si-O). The atomization energy is obtained from the lattice energy, corresponding to variable atomic charges (bond ionicities), via its correction to the charge-transfer energy; the latter being a work, required for a partial ionization of an atom. Some potential parameters were taken from the literature, others were chosen using atomic and molecular constants; the others being obtained from fitting of the minimum-energy crystal structure, atomization energy and elastic properties to the experimental ones.

With the parameters chosen the atomization energy has a minimum at f(Si-O)=48% (Figure 1); its value at this ionicity degree (-18,96 eV) closely corresponds to the experimental one (-19,47 eV). Description of the crystal structure (see Table) and elastic properties at this ionicity degree is very good.

Table. Crystal structure of -quartz : theory and experiment.

Our calculations show very strong dependence of the structure (Figures 2 and 3) and elastic constants (Figure 4) on f(Si-O). The most interesting feature is that at higher ionicity degrees b-quartz (space group P3₁21) is not stable anymore, but transforms to a-quartz (space group P6₂22). It is likely that the real phase transition can be to some extent simulated by the transition with the ionicity degree change. The transformation is accompanied (Figure 2) by a volume gap (therefore it's the 1-order transition), though there is not any energy gap (Figure 1). The volume gap (+2,6%) is due to Si-O-Si angle gap without any abrupt change in bond lengths (Figure 3) and tetrahedral angles. Thus, in this transition SiO₄-tetrahedra behave as rigid units. In accord with experiment our calculations predict b-quartz to be much more rigid (less compressible) than a-quartz (Figure 4).

In summary, a-b transition of quartz seems to be of the 1-st order, what is in agreement with the recent experimental evidences. This transition can be adequately represented by the rigid-unit mode model [4].

We acknowledge the financial support of RFFI (96-05-64567) and ISSEP (s97-2849, p97-349).

1. V.S.Urusov, N.N.Eremin, A.R.Oganov (1998). Crystallography Reports, 1998, v.43, N 5.
2. V.S.Urusov, N.N.Eremin (1997). Phys. Chem. Miner., 1997, v.24, p.374-383.
3. G.Will, M.Bellotto,W.Parrish, M.Hart (1988). J.Appl. Crystallogr., 1988, v.21, p.182-191.
4. M.T.Dove. Amer. Miner., 1997, v.82, Iss 3-4, p. 213-244.

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Fig. 4