Static Lattice Simulations

Redfern, S.A.T., Dove, M.T., Wood, D.R.R. (1997b) Static lattice simulation of feldspar solid solutions ferroelastic instabilities and order/disorder. Phase Trans 61 173-194 Redfern, S.A.T., Knight, K.S., Henderson, C.M.B., Wood, B.J. (1998) Fe-Mn cation ordering in fayalite-tephroite (FexMni U2Si04 olivines a neutron diffraction study. Mineral Mag 62 607-615 Redfern, S.A.T., Harrison, R.J., O Neill, H.St.C., Wood, D.R.R. (1999) Thermodynamics and kinetics of cation ordering in MgAl204 spinel up to 1600°C from in situ neutron diffraction. Am Mineral 84 299-310... 

Static lattice simulations, in which the energy of a configuration is minimized to... 

Lattice relaxation, though, affects these A static lattice simulation of the surface shows that relaxation at the corners and at ledges serves where possible to contract the ions at these sites so that they lie closer to their neighbours , Kinks, on the other hand, relax... 

We now describe two methods of static lattice simulation used to investigate the migration of a dopant. 

We have seen that the instability of a dopant vacancy in potassium-doped PAc does not allow the energy barrier to be calculated by standard static-lattice simulation methods. If however interactions between the host and dopant sublattices really are dominated by electrostatic effects, it is straightforward to calculate the energetics of the motion of a single in its channel through the charge distribution on... 

The highly doped structures referred to in the description of static lattice simulations (Section 5.3) as PAKl and PAK2 have also been investigated by MD by Sese and her colleagues. " As in the static studies the electronic charge transferred from the dopant atoms was distributed uniformly on the carbon atoms, which therefore bear net charges of -0.25e and -0.125e, respectively in the two species. 

Static lattice simulation methods predict the tendency of polymers to avoid the strict regularity of a crystal by finding several lattice structures with similar energies but that vary in their chain-setting angle and cell vectors. The readiness with which the polymer sublattice in doped systems lowers its symmetry is echoed in both the defective static lattice simulations and the molecular dynamics treatment of lattice motions. In the former we observed the wide ranging response of the chains to even a small displacement of a dopant ion as described in Sections 5.3.2, 5.3.4, 5.4.2. and 5.6.3 while the dopant s power spectrum calculated in the course of the MD lattice simulations in Section 6.1 testifies to the important host-dopant interactions in potassium-doped polyacetylene. 

Before we can discuss in detail the simulation of adsorption and diffusion in zeolites using atomistic simulation we must ensure that the methods and potentials are appropriate for modelling zeolites. The work of Jackson and Catlow reviewed in the previous section shows the success of this approach. Perhaps the most critical test is to apply lattice dynamics and model the effect of temperature as any instability will cause the calculation to fail. Thus we performed free energy minimization calculations on a range of zeolites to test the methodology and applicability to zeolites. As noted in Section 2.2, the extension of the static lattice simulation technique to include the effects of pressure and temperature leading to the calculations of thermodynamic properties of crystals and the theoretical background to this technique have been outlined by Parker and Price [21], and this forms the basis of the computer code PARAPOCS [92] used for the calculations. 

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