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School of Physics and Astronomy

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Theory and modelling

Theory is an essential complement to experiment in the modern physical sciences, helping to explain existing results or guide future work, and revealing materials' behaviour under conditions that preclude experimental observation. We have an active theory and modelling programme, with current work studying

Computational studies

Quantum mechanical methods

Much progress in modern materials research relies on accurate simulation using quantum mechanical methods, where Schrodinger's equation is solved for the electrons to enable the interatomic energies and forces to be calculated. Schrodinger's equation is one of many equations in physics that cannot be solved for systems of many particles without using certain approximations, but the state of the field is such that we now have several very reliable approximation schemes for materials research that are capable of giving high-quality results.

In addition to using quantum mechanics methods in support of our modelling studies, we are also contributing to the development of new quantum mechanical methods. In particular, we are developing methods to derive interatomic forces within molecular crystals, including induced polarisation forces and dispersion interactions. 

Lattice modelling with empirical potentials

The traditional approach to modelling materials is to represent the forces between atoms using simple equations containing parameters whose values are tuned by comparison with experimental data on crystal structure and properties, or through quantum mechanical calculations. The main program we use for this work is GULP.

One of our interests in modelling materials is to understand the flexibility of their crystal structures, particularly if the structure is described as a three-dimensional framework linking rigid groups of atoms. This work requires calculations of elasticity and vibrational frequencies. One key application is to use lattice dynamics calculations to understand why some materials shrink when heated; many examples are framework materials.

Recently we developed a module for GULP for the calculation of the pair distribution function (PDF: a histogram of instantaneous interatomic distances, which reflects both the structure and fluctuations). We used this to understand the nature of the high-temperature phase of cristobalite, a polymorph of silica, and in particular to compare the measured PDF against the predicitions from different models of the high-temperature phase.

Large-scale molecular dynamics simulations

Molecular dynamics simulations give the virtual reality of materials at an atomic level. With a model for the forces between atoms, and an algorithm to represent the classical Newton equations of motion with discrete time steps, it is possible to generate the trajectories of the atoms within an ensemble over a short period of time. Typically our work involves several thousand atoms within a periodically repeating box, using parameterised equations to model the forces between atoms. Whilst this size often represents an appropriate balance between wanting larger samples but low running times, there are some studies for which we need extremely large samples of several million atoms. One example concernces our studies of the effects of radioactive decay in nuclear materials.

The main program that we use for molecular dynamics is DL_POLY, developed at the STFC Daresbury Laboratory. Through a large escience grant we collaborated in the development of the version of DL_POLY for extremely large ensembles. More recently we have received funding to extend the capabilities of DL_POLY for large ensembles.

Examples of studies with molecular dynamics include properties of amorphous silica under pressure, phase transitions in ionic materials, dynamics of metal organic framework materials, and decay of radioactive ions encapsulated with ceramic materials. 

Monte Carlo simulations of atomic order/disorder processes

Atomic site disorder is an important feature of metals and many ionic materials, particularly for materials that exist as solid solutions. The energetics of these systems can often be represented by relatively simple pair-wise interactions with coefficients whose values can be determined by fitting to a database of energies of configurations in different states of order. We use Monte Carlo simulations (with our own codes) to study the ordering processes in these materials. One recent focus of our work has been on cation ordering in clay minerals. 

Inverse modelling: Reverse Monte Carlo studies of disordered materials

Whilst atomistic modelling often starts with representations of the forces between atoms and leads to results that can be compared with experimental data, an alternative approach that is gaining popularity is to use experimental data as the guide towards generating consistent configurations of atoms. We have been developing this approach for the study of disordered crystalline materials based on the use of experimental total scattering and Bragg diffraction data within a Monte Carlo method. We have developed the leading code for this work.

Examples of the use of this approach in our group include studies of metal organic frameworks, phase transitions in silica and oxides, and negative thermal expansion materials. 

Informatics research

Modern capabilities in computing, data storage and networks are having a significant impact on research opportunities. The challenge is how to exploit these. We have been working under the UK escience and JISC's data management programmes to develop new approaches to managing simulation jobs and corresponding data management. A significant part of our solutions consists of new approaches to data representations, and exploiting this in the way we handle data. One illustrative example is that we frequently run, say, a couple of hundred jobs as part of a single study. This number of jobs presents a challenge to extract the important information from the output files.

At the core is our use of XML (eXensible Markup Language) for data representation. Specifically, we work with the Chemical Markup Language (CML), which has been designed for representing chemical data. We use a subset of CML adapted specifically for simulation studies. Since most of our simulation codes are written in Fortran, it was necessary within our project to develop a library of Fortran subroutines to make writing CML documents easy (called FoX).

The value of using CML arises from the tools we have built. These include tools to transform a CML document to an XHTML document that gives an information-centric view of the data, and to extract tables of required data from a large collection of CML files (such as generated from studies involving hundreds of simulation jobs).

Theory

Theories of liquids and amorphous materials

Paradoxical though it may seem in this age of scientific and technological advancement, we still do not understand the most basic aspects of liquid behaviour. Indeed, physics textbooks remain silent about the most basic liquid properties such as heat capacity. The combination of strong interactions with large atomic rearrangements has proved to be the ultimate obstacle to developing a theory of liquids. This was famously summarized by L. Landau as "liquids do not have a small parameter". We have recently showed how to overcome these problems in the approach from the solid phase where strong interactions are taken into account from the outset. As a result, we have been able to

  1. calculate liquid energy and heat capacity that depends on liquid relaxation time only, an important general result.

  2. extend the solid-like approach to liquids to the problem of glass transition which some regard as one of the deepest unsolved challenges in physics. One particular problem has been to explain the origin of the heat capacity jump at the glass transition temperature Tg. We have showed that if, as is the case, Tg is defined as the temperature at which the liquid stops relaxing at the experimental time scale, the jump of heat capacity at Tg follows as a necessary consequence due to the change of system's elastic, vibrational and thermal properties. This theory explains widely observed time-dependent effects of glass transition, including logarithmic increase of Tg with the quench rate.

  3. explain the origin of cooperativity of relaxation in liquids and several universal relaxation laws such as the Vogel-Fulcher-Tammann law, by introducing a new length in liquids, the length over which local relaxation events interact via induced elastic waves.

Rigid Unit Mode model of framework materials

Our interest in phase transitions led us to consider in detail materials whose structure can be described in terms of three-dimensional frameworks of linked polyhedral groups of atoms. Two examples are perovskites and phases of silica. Our approach has been to identify vibrational modes that can propagate without distortions of the polyhedral units, which will typically mean that they will have low frequency and hence be candidates for the soft modes associated with structural phase transitions. This work led to a fuller understanding of these phase transitions, but also led to a realisation that rigid unit modes have a potential role in the origin of negative thermal expansion, probably the application for which rigid unit modes are best known.

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