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Computational Methods for Mineral Sciences Research

Computer simulation and computational data analysis methods are becoming increasingly important in the work of the Mineral Sciences group in Cambridge. This work is carried out using our own workstation facilities, and by participation in the Cambridge High-Performance Computing Facility.

Modeling with Empirical Potentials

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The mineral leucite: experimental studies of the phase transitions carried out by the Cambridge Mineral Sciences group have been supported by empirical modeling calculations in order to determine the transition mechanism and the energetics of Al/Si ordering.

The mineral leucite: experimental studies of the phase transitions carried out by the Cambridge Mineral Sciences group have been

supported by empirical modeling calculations in order to determine the transition mechanism and the energetics of Al/Si ordering.

The mineral leucite: experimental studies of the phase transitions carried out by the Cambridge Mineral Sciences group have been supported by empirical modeling calculations in order to determine the transition mechanism and the energetics of Al/Si ordering.
Empirical potentials provide us with the "workhorse" techniques in our computational work. For silicates we have well-tested and reasonably accurate models that can be applied to most crystalline silicates and used to predict and interpret behaviour - that is, for the step b

eyond merely reproducing observed behaviour.

The empirical models are mostly used in lattice energy and lattice dynamics calculations, and we mostly use the GULP code written by Julian Gale. From these calculations we can obtain information about crystal structure, physical properties (e.g. elastic constants), thermodynamic functions, and infrared spectra. These calculations can be performed in a reasonably short time on a workstation.

Contact: Martin Dove

Quantum Mechanical Calculations

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Calculated electron density of the atoms in lead iodide, showing the covalent bonding as shared electrons.
Calculated electron density of the atoms in lead iodide, showing the covalent bonding as shared electrons.

Calculated electron density of the atoms in lead iodide, showing the covalent bonding as shared electrons.
Empirical models are limited in ways that we understand, and to overcome these limitations we use quantum mechanical calculations of the electronic structures of minerals. These give reasonable results for crystal structures and energies, and can be used for studies of minerals under high-pressure and where the chemical environment of atoms changes.

We use two methods. Both are based in Density Functional theory, and both represent the electrons in the atom cores by pseudopotentials. The first method uses plane waves as the basis representation of the valence electrons. Calculations with this method are performed using the CASTEP program originally developed in the Cavendish Laboratory in Cambridge. The second method uses atomic orbitals as the basis functions. In this case, the calculations are performed using the siesta code.

Contact: Martin Dove

Molecular Dynamics Simulations

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The low-temperature phase of tridymite – we are using molecular dynamics simulations to understand the mechanisms of the phase transition and the nature of the high-temperature phases.
The low-temperature phase of tridymite - we are using molecular dynamics simulations to understand the mechanisms of the phase transition and the nature of the high-temperature phases.

The low-temperature phase of tridymite - we are using molecular dynamics simulations to understand the mechanisms of the phase transition and the nature of the high-temperature phases.
The heart of the MDS method is the simulation of a collection of atoms that resembles part of a solid or fluid using models for the interatomic potentials and solving Newton's equation of motion. Thus the MDS method generates the trajectories of several thousands of atoms over a time scale of some ten's of picoseconds, from which one can calculate almost any quantity of interest, particularly those that cannot be extracted from experiment.

We use the MDS method to study phase transitions and the properties of high-temperature phases, which are not normally accessible with more simple modeling methods.

Our simulations are performed on the computers of the HPCF, using the code DLPOLY that was developed by staff of the Daresbury Laboratory particularly for parallel computers. 

Contact: Kostya Trachenko or Martin Dove

Monte Carlo Simulations

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Calculated entropy of the garnet–grossular solid solution computed using the technique of thermodynamic integration in Monte Carlo simulations.
Calculated entropy of the garnet-grossular solid solution computed using the technique of thermodynamic integration in Monte Carlo simulations.

Calculated entropy of the garnet-grossular solid solution computed using the technique of thermodynamic integration in Monte Carlo simulations.
The MC method generates a large number of atomic configurations with their correct thermodynamic probability, and from these it is possible to calculate some of the thermodynamic functions.

One common application is to study order/disorder phase transitions. We use the MC method to simulate ordering of cations on cooling, particularly to determine the temperature-dependence of the ordering process and the development of short-range order above the ordering temperature.

We have developed our own MC code, which is called OSSIA, and this runs on the parallel computer of the Cambridge HPCF. This code can simulate both order/disorder phase transitions and solid solutions for many temperatures, and by using thermodynamic integration it will generate thermodynamic functions such as entropy.

Contact: Martin Dove

Reverse Monte Carlo Methods

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Diffuse scattering in the [100] section of reciprocal space of b-cristobalite calculated in an RMC simulation. The structure of diffuse scattering exactly matches electron diffraction maps, and is consistent with the predictions of the Rigid Unit Mode model.

Diffuse scattering in the [100] section of reciprocal space of b-cristobalite calculated in an RMC simulation. The structure of diffuse scattering exactly matches electron diffraction maps, and is consistent with the predictions of the Rigid Unit Mode model.

Diffuse scattering in the [100] section of reciprocal space of b-cristobalite calculated in an RMC simulation. The structure of diffuse scattering exactly matches electron diffraction maps, and is consistent with the predictions of the Rigid Unit Mode model.
Inverse methods, of which the RMC method is an example, use experimental data to guide the development of a simulation. If the atoms in an ensemble are moved in order to give specific quantities that are in agreement with experiment, the configurations of atomic positions generated can be analysed to calculate additional quantities that are not given directly by experiment.

RMC is the most popular technique of this sort in analysing the structures of disordered solids and fluids. We have been using constrained-RMC methods to analyse the total neutron scattering data for disordered phases of silicates.

We have also developed inverse methods to generate atomic configuration

s consistent with NMR data. For example, we can use this approach to calculate the number of Al-O-Al linkages in aluminosilicates with some degree of Al/Si disorder from Si-29 NMR data. 

Contact: Martin Dove

Rigid Unit Modes

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The split-atom representation of a linkage between two rigid tetrahedra. This representation provides an algorithm for calculating the complete set of RUMs of any network structure.
The split-atom representation of a linkage between two rigid tetrahedra. This representation provides an algorithm for calculating the complete set of RUMs of any network structure.

The split-atom representation of a linkage between two rigid tetrahedra. This representation provides an algorithm for calculating the complete set of RUMs of any network structure.
The RUM approach is an example of the family of one-parameter techniques, in which only the minimum essential detail is incorporated into the simulation. In the RUM model the SiO4 tetrahedra (and other atomic polyhedra) are treated as rigid units with a single parameter used to represent their finite stiffness, and the linkages are treated as perfectly flexible. The RUMs are the phonon modes that can propagate without the polyhedra distorting, so in this approach they are calculated to have zero frequency.

The RUM model has been developed using the split-atom method within the formalism of molecular lattice dynamics. The CRUSH code and associated programs have been developed within our group.

The RUM analysis has been used to study phase transitions, the structure of high-temperature phases, negative thermal expansion, and zeolite catalysis. 

Contact: Martin Dove

 

Visualisation methods

The Mineral Sciences group has a number of visualisation techniques for crystal structures and data analysis.

One of our tools is the commercial Cerius package, which allows us to draw and manipulate crystal structures, which allows us to also views the configurations generated from molecular dynamics simulations. 

Contact: Martin Dove


Mineral Sciences

Last updated on 21-Nov-08 16:18