Lattice dynamic simulations

The next four chapters address several applications of MD to water and aqueous solutions. Floris and Tani describe tiie development of force fields for water-water and water-ion interactions in Chapter 10. Balbuena et al. analyze force fields for cation-water systems introducing new descriptions of short-range interactions. Li and Tomkinson assess the estimation of neutron scattering spectra of ice by MD and lattice dynamics simulations in Chapter 12. Tanaka in Chapter 13 discusses the stability and dynamics of ice and clathrate hydrate using Monte Carlo, MD, lattice dynamics simulations, and a statistical mechanical formulation. 

For lithium hydride an early (1981) lattice dynamics simulation [70] was in better agreement with the spectrum recorded on the TOSCA spectrometer than an older (1965) INS spectrum [71]. The INS spectra of the sodium, potassium, rubidium and caesium hydrides were accurately... 

Once a reliable potential has been obtained which can model the elastic constants, lattice dynamical simulations can be used to predict the phase stability as a function of pressure. The next section gives an example of the calculation of phase stability for MgSi03 pyroxenes. 

Lattice dynamics simulations provide a powerful extension of energy minimization methods by evaluating the dynamical matrix that relates forces and atomic displacements for a crystd. Originally developed by Bom and Huang (1954), this method incorporates a statistical mechanics approach to determine the vibrational modes and thermodynamic... 

The heat capacity, Cp, of an organic crystal can be subdivided into an internal part and an external part (recall Section 6.3 and the discussion around equation 6.19). The external part is the structure-sensitive part because it depends on the lattice vibrational frequencies and hence on the cry stal structure and the packing forces within the cry stal. External contributions can be estimated by lattice dynamics simulations [7], or can be derived from variable-temperature molecular dynamics simulations (recall Section 9.5 and especially equation 9.21). 

Abstract The phonon density of states for ice II has been calculated using a lattice dynamics simulation. The calculated results show that the hydrogen bonds linked to the different six-molecule rings in the structure are significantly weaker in comparison with the interactions widiin the rings, which may result fi om the distortion of the hydrogen bonding in the structure. 

Small metal clusters are also of interest because of their importance in catalysis. Despite the fact that small clusters should consist of mostly surface atoms, measurement of the photon ionization threshold for Hg clusters suggest that a transition from van der Waals to metallic properties occurs in the range of 20-70 atoms per cluster [88] and near-bulk magnetic properties are expected for Ni, Pd, and Pt clusters of only 13 atoms [89] Theoretical calculations on Sin and other semiconductors predict that the stmcture reflects the bulk lattice for 1000 atoms but the bulk electronic wave functions are not obtained [90]. Bartell and co-workers [91] study beams of molecular clusters with electron dirfraction and molecular dynamics simulations and find new phases not observed in the bulk. Bulk models appear to be valid for their clusters of several thousand atoms (see Section IX-3). 

An algorithm for performing a constant-pressure molecular dynamics simulation that resolves some unphysical observations in the extended system (Andersen s) method and Berendsen s methods was developed by Feller et al. [29]. This approach replaces the deterministic equations of motion with the piston degree of freedom added to the Langevin equations of motion. This eliminates the unphysical fluctuation of the volume associated with the piston mass. In addition, Klein and coworkers [30] present an advanced constant-pressure method to overcome an unphysical dependence of the choice of lattice in generated trajectories. 

Although the folding of short proteins has been simulated at the atomic level of detail [159,160], a simplified protein representation is often applied. Simplifications include using one or a few interaction centers per residue [161] as well as a lattice representation of a protein [162]. Some methods are hierarchical in that they begin with a simplified lattice representation and end up with an atomistic detailed molecular dynamics simulation [163]. 

At the same time, many lattice dynamics models have been constructed from force-constant models or ab-initio methods. Recently, the technique of molecular dynamics (MD) simulation has been widely used" " to study vibrations, surface melting, roughening and disordering. In particular, it has been demonstrated " " " that the presence of adatoms modifies drastically the vibrational properties of surfaces. Lately, the dynamical properties of Cu adatoms on Cu(lOO) " and Cu(lll) faces have been calculated using MD simulations and a many-body potential based on the tight-binding (TB) second-moment aproximation (SMA). " ... 

Boundary Conditions although CA are a.ssumed to live on infinitely large lattices, computer simulations must necessarily be run on finite sets. For a one dimensional lattice with N cells, it is common to use periodic boundary conditions, in which ctn + i is identified with ai. Alternatively, all cells to the left and right of a finite block of N cells may be arbitrarily defined to possess value 0 for all time, so that their dynamics remains uncoupled with that taking place within the block. Similarly, in two dimensions, it is usual to have the dynamics take place on a torus, in which o m+i = <7, 2 and = cTi,j- As we will see later it turns one... 

The point of this terse introduction is that cellular automata represent not just a formalism for describing a certain particular class of behaviors (lattice gas simulations of fluid dynamics, models of chemical reactions and diffusion processes, etc.), but a much more general template for original and heretofore untapped ways of looking at a large class of unsolved or only poorly understood fundamental problems. 

The density of states (DOS) of lattice phonons has been calculated by lattice dynamical methods [111]. The vibrational DOS of orthorhombic Ss up to about 500 cm has been determined by neutron scattering [121] and calculated by MD simulations of a flexible molecule model [118,122]. 

Due to particles extrusion, crystal lattice deformation expands to the adjacent area, though the deformation strength reduces gradually (Figs. 10(a)-10(other hand, after impacting, the particle may retain to plow the surface for a short distance to exhaust the kinetic energy of the particle. As a result, parts of the free atoms break apart from the substrate and pile up as atom clusters before the particle. The observation is consistent with results of molecular dynamics simulation of the nanometric cutting of silicon [15] and collision of the nanoparticle with the solid surface [16]. 

FIG. 23 Surface pressure vs. area/molecule isotherms at 300 K from molecular dynamics simulations of Karaborni et al. (Refs. 362-365). All are for hydrocarbon chains with carboxylate-like head groups, (a) (filled squares) A 20-carbon chain, (b) (filled circles) A 16-carbon chain with a square simulation box the curve is shifted 5 A to the right, (c) (open squares) A 16-carbon chain with a nonsquare box with dimensions in the ratio xly = (3/4) to fit a hexagonal lattice the curve is shifted 5 A to the right. (Reproduced with permission from Ref. 365. Copyright 1993 American Chemical Society.)... 

Ten Cate, A., Turbulence and particle dynamics in dense crystal slurries—a numerical study by means of lattice-Boltzmann simulations , Ph.D. Thesis, Delft University of Technology, Delft, Netherlands (2002). 

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