Comparison between the lattice dynamics and molecular dynamics methods: calculation results for MgSiO3 perovskite

The lattice dynamics (LD) and molecular In the LD method the crystal potential is usually estimated dynamics (MD) methods have been used to calculate the in the harmonic or quasi-harmonic approximation. LD structure, bulk modulus, and volume thermal expansivity of calculations are very useful and powerful for predicting MgSiO3 perovskite, in order to investigate the reliability of vibrational frequencies and thermodynamic properties of the two simulation techniques over a wide range of crystals over a wide temperature range, but break down at temperature and pressure conditions. At an intermediate very high temperatures [Price et at., 1987; Parker and temperature of 500 K and zero pressure, the LD and MD Price, 1989]. For such high temperatures, where values are in exellent agreement for both the structure and anharmonicity is important and quantum effects are small, bulk modulus of MgSiO 3 perovskite. At high temperatures it is generally more practicable to use the MD method. and zero pressure, however, the LD method, which is In this method the average structural parameters are based on the quasi-harmonic approximation, increasingly simulated by using Newton's classical equations of motion overestimates the molar volume of MgSiO 3 perovskite for atoms in crystals, as a function of time. The MD because of the neglect of higher-order artharmonic terms. method can be applied to predict not only equilibrium At the high temperatures and high pressures prevailing in properties [e.g. Matsui, 1988; Matsui and Price, 1992] but the lower mantle, the errors in the LD values for both the also time-dependent phenomena, such as first-order phase molar volume and bulk modulus, relative to the MD transitions [Tsuneyuki et at., 1989] and transport properties values, are generally small or negligible. However, since [Wall and Price, 1989]. anharmonicity decreases ubstantially with pressure but MgSiO3 perovskite isthought to be the major component increases rapidly with temperature, the error in the LD of the lower mantle. The LD and MD methods have simulated volume thermal expansivity is serious, especially therefore been extensively applied to simulating the in the lower pressure region. structural and physical properties of this phase. Examples of the application of the LD method to the simulations of Introduction MgSiO3 perovskite nclude the calculation f the equation of state [Hemtey et at., 1987], and the establishment of The detailed description of the chemical and physical constraint on mineral composition models of the lower properties of the Earth's interior requires an accurate mantle from simulated structural and elastic properties of knowledge of the elastic and thermal properties of the MgSiO 3 perovskite [Cohen, 1987; Bukowinski and Wolf, constitutive minerals at high temperatures and high 1988]. The MD technique has been used to predict the pressures. However, it is still extremely difficult to carry possible existence of a high temperature and/or high out experiments to measure accurately such properties at pressure phase transition in MgSiO3 perovskite [Matsui and the combined temperature and pressure conditions to be Price, 1991; Kapusta nd Guillopd, 1993]. found in the Earth's deep interior. As an alternative to The aim of the present investigation is to compare the direct experimental study, therefore, atomistic computer values computed using the LD and MD techniques for the simulations have recently been extensively applied to structure, molar volume, V, volume thermal expansivity, c•, predict the properties of various minerals thought o exist and isothermal bulk modulus, K T, of MgSiO3 perovskite, in the interior of the Earth [e.g. Wolf and Bukowinski, and to assess the reliability and applicability of the two 1985; Cohen, 1987; Price et at., 1987; Matsui, 1988; methods over a wide temperature and pressure range, with Matsui and Price, 1992]. special reference to the simulation of lower mantle Given a set of interatomic potentials, there are two conditions. major types of simulation techniques that can be used to calculate static and dynamic properties of crystals at a Calculation methods specified temperature T and pressure P, namely the lattice dynamics (LD) and molecular dynamics (MD) methods. All the LD and MD calculations were made using the pair potential 1MAMOK [Matsui, 1988], which has been Copyright 1994 by the American Geophysical Union. shown toreproduce th observed structural and physical properties of MgSiO 3 perovskite quite accurately [Matsui Paper number 94GL01370 and Price, 1992]. The LD calculations were carried out 0094-8534/94/94GL-01370503.00 using the PARAPOCS computer code, which obtains the