# THE THERMODYNAMIC AND PHYSICAL PROPERTIES OF MAJOR EARTH-FORMING MINERALS

**Project ID**: SC1*0046

**Funded under**:

## THE THERMODYNAMIC AND PHYSICAL PROPERTIES OF MAJOR EARTH-FORMING MINERALS

**From**1989-01-01

**to**1991-12-31

## Project details

### Total cost:

Not available### EU contribution:

Not available### Coordinated in:

United Kingdom### Topic(s):

### Funding scheme:

CSC - Cost-sharing contracts## Objective

The results from the single crystal infrared reflectivity study of pure Mg2SiO4 forsterite and Mg0.86Fe0.14)2SiO4 olivine were published in The Journal Physics and Chemistry of Minerals (19.92). Polarized infrared reflectance spectra of these compounds were measured from 5000 to 100 cm{-1}. Out of the 35 expected infrared active modes, 33 were observed (8B1U, 12B2U, 13B3U). The observed frequency shift from pure forsterite to FO86-olivine was found to be consistent with the higher mass of the substituted iron. The substitution of only 14% of iron was also found to reduce the overall far infrared reflectivity as compared to pure forsterite. Discrepancies between previous studies of forsterite were suggested to be due to effects of polarization mixing.

A single crystal infrared reflectivity study of sinhalite, MgAlBO4, the boron analogue of forsterite is being completed. Boron occupies the tetrahedral sites whereas magnesium and aluminum occupy the M2 and M1 octahedral sites, respectively. Antisymmetric stretching modes of the boron oxide tetrahedron occur between 950 and 1200 cm{-1} in the B1u, B2u and B3u spectra. Peaks at approximately 800 cm{-1} are assigned to the symmetrical stretching modes of the AlO6 octahedron. The antisymmetric bending modes of the boron oxide tetrahedron lie below 650 cm{-1}, as do complex modes involving the other cations. Work is currently in progress to analyze the spectra. A comparison of the sinhalite spectra with the infrared reflectivity spectra of forsterite is consistent with the presence of boron in the tetrahedral site (which is substantially lighter than silicon) and with the presence of aluminum as well as magnesium in the octahedral sites. Thermodynamic properties of sinhalite will be calculated from lattice vibrational models based on the measured spectra.

A series of calculations on perovskite materials is being carried out, with the aim of understanding the rheology of the lower mantle. The defects code CASCADE is being used to predict the energies of defect formation and migration in perovskites. So far excellent quantitative agreement has been found with known data for titanates. Recently, use has been made of the atomistic computer simulation techniques to investigate the site partitioning of iron in (magnesium, iron) silicon oxide perovskites. Our calculations predict that the most energetically favorable reaction for iron substitution will be a direct exchange of iron ions for magnesium ions. Substitution of iron into the octahedral site and silicon into the 8 to 12 fold coordinated site is predicted to be extremely unlikely. This conclusion has just been confirmed by magic angle spinning nuclear magnetic resonance (MASNMR).

The activation volume and free energy of formation of Schottky defects in magnesium oxide has been investigated with the code PARAPOCS. The approach used is based on the construction of a charge neutral supercell of atoms containing the defect, which is equilibrated (within the limits of the quasi harmonic approximation) at the required pressure and temperature. The results demonstrate that the supercell method works well. We predict that both the activation volume and free energy of formation of Schottky defects in magnesium oxide are highly dependent on pressure, but only weakly affected by temperature. The activation volume is predicted to decrease by more than 50%as the pressure increases to that in the lower mantle. Moreover, the assumption used by many previous workers that the activation volume has the same pressure dependence as the atomic volume has been shown to be incorrect.

Work has begun to extend the phenomenological dislocation model of melting, successfully used by Poirier to model iron, to other metallic systems. The model assumes that a melt is isostructural with the crystal saturated with dislocation cores. By considering the volumetric dilation introduced by dislocations in a metal, estimates of the entropy and volume of melting can be obtained. So far excellent agreement has been obtained for over 12 metals between the observed melting temperature and that predicted by the model. This finding underpins the validity of Poirier's work on the melting of iron and its geophysical implications. The study is to be extended to consider the melting of silicates. Molecular dynamics offers the only approach to understanding melting at an atomic level. Both constant temperature and constant pressure molecular dynamics are being used to investigate the details of melting and premelting processes in magnesium oxide and MgSiO3-perovskite. Calculations (based on empirical potentials) predict reasonable volumes of melting, but the absolute temperature of melting seems to be overestimated by 500 to 1000K. There is particular interest in investigating the effects of defects and surfaces on the predicted melting behaviour of materials, as these will destabilize the crystal and hence encourage melting at lower temperatures than predicted for the perfect bulk. The effect of pressure on the structures of the melts produced in these systems is also being studied. The premelting enhanced oxygen mobility in the perovskite lattice is again confirmed, and further investigations will be carried out into the nature of superionic conduction in perovskites. Work on fluoride perovskites is also in hand to widen the basis of the analysis of the premelting behaviour of perovskite structure phases.

The code PARAPOCS performs free energy minimization using interatomic potentials, and so enables the thermodynamic properties of a silicate to be calculated from their predicted lattice dynamical characteristics. The approach depends upon the validity of the quasi harmonic approximation. which is known only to hold at temperatures below the Debye temperature of the crystal. Above this temperature, phonon phonon interactions become significant, and in the past quantitative simulations in this regime have required the use of molecular dynamics (MD) techniques. MD, however, cannot usually be used with the more sophisticated potentials used in lattice dynamical calculations. A series of parallel calculations is being produced using both methods to establish firmly the point at which the quasi harmonic approximation collapses for mantle materials. There is particular interest in the effect of pressure on this, since it is known that pressure suppresses intrinsic anharmonic processes, and so at depth in the mantle, the quasi harmonic approximation may become valid over a wide temperature range. Preliminary conclusions, from calculations at simulated geothermal temperatures, are that for geophysical systems the quasi harmonic approximation will only become valid at pressures greater than 100 GPa. An alternative to using molecular dynamic simulations to model anharmonic systems is to use a self consistent phonons lattice dynamics code. This approach transcends the quasi harmonic approximation, and allows the effect of phonon phonon interactions to evaluated. Recent work by R D Ball outlines the theoretical basis for a self consistent phonons description of a system based on a shell model potential. This analysis has been implemented in the code PARAPOCS. The self consistent phonons calculation consists of 3 stages; the calculation of the Green's function from the dynamical matric of he system, the calculation of the dependence of the dynamical matrix on volume and atomic di splacement, and the averaging over all configurations of the dynamical matrices after weighing by the calculated Green's function. This new average dynamical matrix is used to recalculate a Green's function, the process is iterated until a self consistent Green's function and average dynamical matrix pair is obtained. The development of the self consistent phonons code involves a considerable amount of work, and to date the routines for stages 1 and 2 have been written.

Modelling of atomic interactions requires an accurate description of interatomic forces. It is now possible to perform quantum mechanical calculations on complex phases, from which insights into bonding, and hence accurate interatomic potential models, can be derived. The suitability of the code CRYSTAL (C Pisani et al, Lecture Notes in Chemistry, vol 48, Springer-Verlag) as a way of performing such quantum mechanical calculations is being investigated. CRYSTAL enables calculations (with periodic boundary conditions) to be carried out, within the limits of the Hartree-fock (HF) approximation. Using CRYSTAL, it is possible to perform a comprehensive study of bonding of silicon oxide in both the quartz and stishovite phases silicon core it is possible to reproduce accurately the structures of both phases using standard molecular basis sets (6-21G) provided that they are supplemented by d-functions on the silicon atom. The d-functions play a more important role in quartz than in the 6-fold coordinated stishovite; their inclusion is essential if the relative stabilities of the 2 phases are to be correctly calculated. The role of the d-orbital is, however, indirect. In effect they promote redistribution of electron density from the nonbonding lone pair O(2p) orbitals in to the bonding region between the silicon core and oxygen core. Calculations confirm that the character of the silicon oxygen bond is intermediate between covalent and ionic, with an effective charge of about +2 for silicon (according to Mulliken population analysis). The ionicity is significantly higher in stishovite than in quartz. Excellent agreement is obtained for quartz between the calculated and experimental photoemission spectra. This comprehensive set of calculations has firmly established the viability of periodic HF techniques in the study of silicates. Results on magnesium oxide, aluminum oxide, quartz, stishovite, MgSiO3-ilmenite and perovskite suggest that the calculated energy surfaces, ela stic moduli, and densities are sufficiently accurate to enable them to be used as the basis of more firmly established potential models. These calculations are also being used to reveal the physical origins of the Cauchy violations in magnesium oxide, calcium oxide etc, and to investigate the relative stabilities of the ilmenite and LiNbO3 polymorphs of various ABO3 compounds.

The PARAPOCS code has been used to model the vibrational properties of crystal lattices, which are subsequently used to interpret infrared and Raman data obtainedon perovskites, MgSiO3 and Mg2SiO4 polymorphs, etc. The use of such microscopic models is the only way to fully assign the spectra of such complex structures. This free energy code has also been used to predict the phase diagram for a number of ABO3 systems, and to calculate oxygen isotope equilibria. This lattice dynamical code is just starting to be used to establish the microscopic basis for many of the approximations used in the variety of definitions of the Gruneisen parameter.

Modelling disorder is much more difficult than modelling an ordered system, and modelling an incommensurate phase is much more difficult than modelling a normal material. Hence simulating mullite, which involves both disorder and an incommensurate structure represents a major challenge. A methodology has just been established for modelling disorder, the problem of simulating what are considered to be the key defects in the mullite structure (namely the so-called T-T-T* cluster) is being approached. The work is being extended to involve modelling aluminum silicon disorder in other silicates, and particularly in feldspars.

The aim of the project is to determine the elastic and thermodynamic properties of major, lower crustal and mantle-forming minerals from the response of their lattice dynamics and structures to changes in pressure (P) and temperature (T). These data on the atomistic or microscopic behaviour of minerals will be used critically to test hypothetical compositional models of the mantle, and to establish whether the Earth's mantle is chemically layered, by comparing calculated seismic profiles with those observed. In addition data on the behaviour of crustal minerals will enable the P-T-time histories of deep crustal rocks to be, inferred and hence will enable the rate of regional-uplift to be quantified.

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### Open Access

### Open Access

## Coordinator

WC1E 7HX London

United Kingdom

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**Administrative contact:**Geoffrey David PRICE

## Participants

**Last updated on**: 1990-10-02

**Record Number**: 533

**Last updated on**1990-10-02

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