Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Lattice methods

Two possible space-based schemes are the random structure approach and the lattice method. In the first, the atoms are placed in random positions to form an initial structure containing no chemical information. The configuration of the atoms is then altered in such a way as to better match a pre-selected set of chemical or physical constraints. In the second approach the cations and anions are separately arranged on lattices that minimize the electrostatic repulsions between the (like) ions. The lattices are then merged by placing the anion lattice in the cavities of the cation lattice and vice versa. [Pg.137]

Indexing rotation photographs by reciprocal lattice methods. Orthorhombic crystals. First of all, the coordinates and for each reflection on the photograph (Fig. 86) are found in one of the ways just described these coordinates may be plotted as in Fig. 87 a to form the reciprocal lattice rotation diagram. The problem now is to decide which point of the reciprocal lattice itself corresponds to each spot on the rotation diagram. [Pg.162]

If the crystal is rotated round its b axis (Fig. 89) the equatorial spots are reflections from hOl planes. The values for these spots are found as before by measuring the distance from the origin to each point of the (non-rectangular) hOl net plane (Fig. 88). Note that the indexing of equatorial reflections in this case cannot be done by a log d chart, since there are three variables, a, c, and / the reciprocal lattice method is essential. Once the indices for the equatorial reflections have been found, those of the reflections on upper and lower layer lines follow at once, since all reciprocal lattice points having the same h and l indices (such a set as 201, 211, 221, 231, and so on) are at the same distance from the axis of rotation and thus form row lines. [Pg.165]

Indexing rotation photographs by reciprocal lattice methods. Orthorhoml jc crystals 162... [Pg.518]

For triclinic crystals the expression is so unwieldy that it is not worth while attempting to use it a graphical method based on the conception of the reciprocal lattice should be used (see pp. 154 ff). The reciprocal lattice method is also more rapid than calculation for monoclinic crystals. [Pg.528]

The problem is best treated by reciprocal lattice methods. Fig. 100 gives a general view of the zero layer of the reciprocal lattice of a crystal tilted in an arbitrary direction. Fig. 101 is a plan the axis of rotation is normal to the plane of the paper the normal to the zero... [Pg.530]

Adequacy of a regression equation derived by the simplex-centroid design is tested and the confidence intervals of property values, predicted by the equation, are assigned in much the same way as in the case of the simplex-lattice method. [Pg.505]

The adequacy test and the assignment of confidence intervals using a D-optimal design (Table 3.38) are accomplished along the same lines, as in the simplex-lattice method. The variation of with composition, are given in the reference literature [12], In constructing the fourth-order polynomial for the ternary system, the design will be D-optimal at ... [Pg.522]

The study of glass transition is an important subject in current research, and simulations may well be suited to help our understanding of the phenomenon. An example is the application of Monte Carlo techniques by Wittman, Kremer, and Binder.The authors employed a lattice method in two dimensions to model the system. The glass transition was determined by monitoring the free volume changes as well as isothermal compressibility. The glasslike behavior was determined by evaluating the bond autocorrelation function. The authors found that both the dynamic polymer structure factor and the orienta-... [Pg.197]

Grand Canonical Monte Carlo simulation is used to investigate the properties of water (fluid of most importance) confined in mesoporous Controled Porous Glass (Vycor-like) numerically obtained by the off-lattice method developed by P. Levitz [Adv. Coll. Int. Sci. 76-77 (1998), 71]. We first outline the interaction model and give the adsorption isotherm obtained at 300 K. Good agreement is found with available experimental results. [Pg.371]

Using atomistic (static lattice) methods, Sayle et first modeled the (110), (310) and (111) surfaces of <7e02- The (110) and (310) surfaces are known as type I surfaces i.e. they are charge neutral with stoichiometric proportions of anions and cations in each plane (parallel to the surface). The potential for each plane is exactly zero due to the cancellation of the effects of the positive and negative charges and therefore there is no dipole moment perpendicular to the surface. The (111) surface of ceria is a type II surface, i.e. the surface terminates with a single anion plane and consists of a neutral Chree-plane repeat unit. [Pg.285]

In addition to atomistic (static lattice) methods, MD techniques have been used by Baudin et to study 20- 30/1 thick Ce02 slabs with 2-D periodicity of the three low index surfaces (111), (011) and (001). The simulations were performed within a... [Pg.285]

Lattice methods are well suited to treatment of the intermolecular, or steric , part of the configuration partition function for a system comprising particles or molecules in which volume exclusion plays its usual, dominant role. In principle, these well established methods are no less applicable to systems consisting of species of asymmetric shape, although certain modifications of the conventional procedures are required in order to accommodate highly asymmetric molecules on a lattice when they maintain a degree of orientational disorder. Lattice theory has been adapted to this purpose and the practicability of this approach has been demonstrated... [Pg.3]

Lattice methods suffer the disadvantage of apparent lack of rigor that is an inevitable consequence of adoption of an artificial model, in this instance a regular array of sites, for the representation of a disordered liquid. Owing to the marked periodicity of the radial distribution function of the liquid over short ranges, unrealities of the model in this regard are not as serious as may at first appear. [Pg.3]

An approach based on the virial expansion suffers from the difficulty of evaluating higher coefficients for highly asymmetric particles and from the non-convergence of the virial series at the concentrations required for formation of a stable nematic phase Lattice methods therefore take precedence over the virial expansion as a basis for quantitative treatment of the liquid crystalline state. [Pg.3]

Conventional lattice methods can be adapted to treatment of a system of rigid, rodlike particles, or molecules, by the device illustrated in Fig. 1 The particle shown in Fig. la is oriented at an angle t with respect to the preferred axis of the surrounding domain. One of the principal axes of the cubic lattice is aligned with this axis. The particle comprises x isodiametric segments, each of a size that will occupy one cell of the lattice it follows that x so defined is also the axial ratio of the particle. In order to accommodate the particle on the lattice when it is oriented as in Fig. 1 a, we imagine it to be subdivided into y sequences of segments as represented in Fig. 1 b, with each sequence oriented parallel to the preferred axis. The parameter y serves as a measure of disorientation of the particle with respect to the domain axis see Fig. lb. [Pg.4]

First, atomistic (static lattice) methods determine the lowest energy configuration of the crystal structure by employing efficient energy minimization procedures. The simulations rest upon the specification of an interatomic potential model which ex-... [Pg.282]

D. A. Stewart, T. R. Gowrishankar., K. C. Smith and J. C. Weaver, Cylindrical cell membranes in uniform applied electric field validation of a transport lattice method, IEEE Trans. Biomed. Eng, 52, 1643-1653 (2005). [Pg.525]

Most lattice methods rely on an extremely simple potential function, either a two state interresidue contact energy corresponding to native/nonnative contacts, or a three state model, corresponding to hydrophobic-hydrophobic, hydrophilic-hydrophilic, and hydrophobic-hydrophilic interactions. The interaction of the twenty naturally-occurring amino acids in real proteins are obviously more complex. [Pg.70]

G. Ganti, J. A. McCammon, and S. A. Allison, J. Phys. Chem., 89, 3899 (1985). Brownian Dynamics of Diffusion-Controlled Reactions The Lattice Method. [Pg.265]

In the cluster-Bethe-lattice method, a central cluster is treated exactly and the surrounding medium is replaced by a successively branching network containing no closed paths. [Pg.152]

We choose here instead an analytic formulation based upon the simple molecular lattice, which will immediately be generalized. This will bring the most important concepts to light and provide an interpretation of the spectrum. It can also provide the starting point for a quantitative application of the cluster-Bethe-lattice method use of the Bethe lattice should improve accuracy and reduce the computation required in comparison to the direct cluster technique. [Pg.459]

Figure 8.04. Comparison of densities of states for amorphous (solid line) and crystalline rhombohedral (dashed line) As. Experimental data are from XPS of Ley et al. (1973), and theoretical curves are from Kelly (1980) (recursion method) and from Pollard and Joannopoulos (1978) (cluster-Bethe-lattice method, CBLM) (Combined Figure from Elliott, 1984). Figure 8.04. Comparison of densities of states for amorphous (solid line) and crystalline rhombohedral (dashed line) As. Experimental data are from XPS of Ley et al. (1973), and theoretical curves are from Kelly (1980) (recursion method) and from Pollard and Joannopoulos (1978) (cluster-Bethe-lattice method, CBLM) (Combined Figure from Elliott, 1984).
In addition to the direct solution of PDEs corresponding to reaction-diffusion equations, in recent years attention has begun to be focused on the use of coupled lattice methods. In this approach, diffusion is not treated explicitly, but, rather, a lattice of elements in which the kinetic processes occur are coupled together in a variety of ways. The simulation of excitable media by cellular automata techniques has grown in popularity because they offer much greater computational efficiency for the two- and three-dimensional configurations required to study complex wave activity such as spirals and scroll waves. [Pg.230]


See other pages where Lattice methods is mentioned: [Pg.171]    [Pg.118]    [Pg.279]    [Pg.287]    [Pg.22]    [Pg.207]    [Pg.494]    [Pg.311]    [Pg.360]    [Pg.459]    [Pg.463]    [Pg.501]    [Pg.311]    [Pg.144]    [Pg.230]    [Pg.415]    [Pg.549]    [Pg.457]   
See also in sourсe #XX -- [ Pg.4 ]




SEARCH



Calculation of Internal Stresses by the Lattice Cell Method

Cluster-Bethe-lattice method

Computational methods lattice Boltzmann simulation

Coupled lattice methods

Defective lattice method

Diamond lattice methods

Finite lattice method

Hypothetical active site lattice HASL) method

Lattice Boltzmann method

Lattice Boltzmann method (LBM)

Lattice Poisson-Boltzmann Method, Analysis

Lattice Poisson-Boltzmann Method, Analysis Electroosmotic Microfludics

Lattice Poisson-Boltzmann Method, Analysis Electroosmotic Microfluidics

Lattice diagram method

Lattice dynamical method

Lattice energy calculation Monte Carlo methods

Lattice summation methods

Lattice-Boltzmann method/models

Lattices integration method

Material characterization methods lattice parameter determination

Papers Dealing with Methods for Computing Lattice Energies

Spin-lattice relaxation method

Statistical methods lattice design

© 2024 chempedia.info