School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS
In principle, lattice dynamics is an attractive route for the calculation of the thermodynamic properties of crystals with periodic symmetry. Quantum effects are readily taken into account and the method does not rely on long runs for high precision. Unstable vibrational modes provide a sensitive test for interionic potentials and interpretation of the normal modes is straightforward, revealing, for example, the mechanisms of phase transitions or thermal expansion. The kinetic barriers and critical slowing-down effects suffered by Monte Carlo and molecular dynamics techniques are avoided. The bulk of the computational effort is usually expended in the optimisation problem of finding the equilibrium geometry at a given temperature and pressure; given this, calculation of the free energy, heat capacity, thermal expansion etc. is rapid and accurate. We have recently developed a new code, SHELL [1], for three- dimensional ionic crystals and slabs which calculates the full set of free-energy first derivatives analytically and so for the first time a full minimisation of the quasiharmonic free energy with respect to all internal and external variables is possible for large unit cells. Currently short-range interactions are via two and three-body potentials. In this talk the theory [2,3] will be outlined and recent applications discussed, including (i) negative thermal expansion ceramics (ii) surface [3] and defect [4] free energies. Lattice dynamics is also the basis of a recently proposed methodology [5] for obtaining the free energy of disordered solids and solid solutions, which is quite different from standard approaches. Results for MnO/MgO and CaO/MgO will be presented.
Paul Sherwood Computational Science and Engineering Dept. CLRC, Daresbury Laboratory, Daresbury, Warrington. WA4 4AD
The talk will describe the QUASI project (Quantum Simulation in Industry), a European funded collaboration developing simulation techniques based on QM/MM (coupled Quantum Mechanical / Molecular Mechanical) schemes and application to industrial problems. The QM/MM method will be reviewed, and the software development aspects of the project described. The functionality of the MD module, currently under development based on elements of the DL_POLY package) will be discussed. Particular emphasis will be given to the use of a Tcl interpreter to control the simulation protocol, statistics collection and constraint terms in free-energy simulations. The target applications for QUASI, spanning biological, zeolitic and surface catalytic systems, will be summarised.
Lehigh University, Dept. of Mat. Sci. and Eng., #5 Whitaker Lab, 5 E Packer Avenue, Bethlehem PA 18105-3195, USA
In the last few years a number of complementary approaches have been devised to obtain free energies from simulation. In this talk I will discuss several such methods including: histogram techniques, cumulant expansions, harmonic approximation schemes and so-called "mechanical" calculations wherein the entropy of a system is determined directly from its region of motion in phase space. For the purposes of illustration, the results of the application of these methods to various model systems will also be presented. Finally, I will outline some recent progress in the application of stereological techniques to the determination of entropy.
Institut fuer Physik, WA331 (Theorie der Kondensierten Materie), Johannes Gutenberg-Universitaet, Staudingerweg 7, D55099 Mainz, Germany.
Surface free energies and interfacial tensions are important for many practical applications (e.g. wetting, coatings, adhesion). We study wetting phenomena and interfacial properties in a binary polymer blend by Monte Carlo simulation of a coarse grained polymer model (bond fluctuation model). Two methods for calculating the interfacial tension shall be discussed: reweighting techniques and the analysis of interfacial fluctuations. Employing an expanded ensemble where the monomer wall interaction is a stochastic variable we are able to accurately measure the surface free energy difference of the two species of the blend at a wall. Both free energies allow a localisation of the wetting transition via the Young equation. For our model of a binary polymer blend we find strongly first order wetting transitions. The consequences for the phase diagram of a mixture confined into a film are discussed.
Atomistic Simulation Group, School of Maths and Physics, The Queen's University, Belfast BT7 1NN
There are a number of methods for calculating changes in Free Energy in Molecular Dynamics simulations. I shall describe three recent rather different calculations which illustrate some of the methods and technical problems involved.
Lattice Switch Monte Carlo is a technique for obtaining free energy differences directly without calculating the absolute free energies. As such, it offers considerable computational advantages over methods which attempt to evaluate the exact free energy. The method requires construction of a bipartite phase space describing the two systems to be compared, and incorporating a Monte Carlo move which switches between regions of space.
A practical application of the method, involving biassed sampling techniques, will be illustrated with an example of the free energy difference between the fcc and hcp structures of hard spheres. Further applications of the method will be discussed, including switching between different models for the total energy of a system.
Materials Research Centre, Department of Physics and Astronomy, University College London, Gower St., London WC1E 6BT
Point defects in solids affect the vibrational spectrum of the crystal; producing both a general perturbation of the form of the density of states and individual, strongly localised modes ('true' local modes, gap modes and resonances). These effects are an important contribution to the entropy of defect processes and also offer a sensitive test of the model of crystal forces used.
We discuss methods for obtaining free energies of defect processes in ceramics within the quasi-harmonic approximation and the problems of comparison with the (rather limited) experimental data available.