Computer simulation terms Links

Very recently, people who engage in computer simulation of crystals that contain dislocations have begun attempts to bridge the continuum/atomistic divide, now that extremely powerful computers have become available. It is now possible to model a variety of aspects of dislocation mechanics in terms of the atomic structure of the lattice around dislocations, instead of simply treating them as lines with macroscopic properties (Schiotz et al. 1998, Gumbsch 1998). What this amounts to is linking computational methods across different length scales (Bulatov et al. 1996). We will return to this briefly in Chapter 12. 

Molecular spectra can be analyzed for spectrometric or for spectroscopic purposes. The term spectrometric usually refers to compound identification (linking a signal to a known structure) and to the determination of its concentration. The term spectroscopic stands for interpretation of the spectrum in terms of structure (chemical, electronic, nuclear, etc.). In this chapter we will look as some theoretical and practical aspects of a key spectrometric application of bioEPR, namely, the determination of the concentration of paramagnets, also known as spin counting. Subsequently, we consider the generation of anisotropic powder EPR patterns in the computer simulation of spectra, a basic technique that underlies both spectrometric and spectroscopic applications of bioEPR. 

A review of First Principles simulation of oxide surhices is presented, focussing on the interplay between atomic-scale structure and reactivity. Practical aspects of the First Principles method are outlined choice of functional, role of pseudopotential, size of basis, estimation of bulk and surface energies and inclusion of the chemical potential of an ambient. The suitability of various surface models is discussed in terms of planarity, polarity, lateral reconstruction and vertical thickness. These density functional calculations can aid in the interpretation of STM images, as the simulated images for the rutile (110) surface illustrate. Non-stoichiometric reconstructions of this titanium oxide surface are discussed, as well as those of ruthenium oxide, vanadium oxide, silver oxide and alumina (corundum). This demonstrates the link between structure and reactivity in vacuum versus an oxygen-rich atmosphere. This link is also evident for interaction with water, where a survey of relevant ab initio computational work on the reactivity of oxide surfaces is presented. 

We are now in a position to commence our simulation, but as stated earlier we must first convert the simulation to a dimensionless form. We have already taken one step in this direction by introducing the model diffusion coefficient Dm- We now have to fix suitable values for Ax and At, Clearly it would be useful if we could set these values independently, but unfortunately this is not possible. It can be shown that stable solutions to the finite difference expressions are only obtained for values of Dm less than 0.5, and since Dm is equal to D.AtlAx the values of At and Ajc are linked. Specifically, if Ax is decreased, At also has to be reduced, and for any given length of experiment the number of iterations has to be increased. In view of the Ax term this, of course, leads to a sharply increased computation time. One of the major problems in designing a simulation is to choose all the parameters so that they are physically meaningful and so that there is a useful correlation between them and the constants of the real system. 

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