Crystal potential model

Recently, Orlov (1985, 1986) suggested a crystal potential model for the interpretation of crystalline electric field effects in intermetallics and used it for a discussion of these effects in PrAlj or of the sign and magnitude of the magnetic crystal anisotropy for RXj and R2X15 compounds. This effective crystal potential V(r) has the crystal symmetry and is constructed from experimental data or calculated from first principles it oscillates and decreases rapidly with distance. 

FIGURE 3.21 Model or periodical well in a Kionig-Penney crystal potential model after Putz (2006). 

There have been several simulations of discotic liquid crystals based on hard ellipsoids [41], infinitely thin platelets [59, 60] and cut-spheres [40]. The Gay-Berne potential model was then used to simulate the behaviour of discotic systems by Emerson et al. [16] in order to introduce anisotropic attractive forces. In this model the scaled and shifted separation R (see Eq. 5) was given by... 

Stelzer et al. [109] have studied the case of a nematic phase in the vicinity of a smooth solid wall. A distance-dependent potential was applied to favour alignment along the surface normal near the interface that is, a homeotropic anchoring force was applied. The liquid crystal was modelled with the GB(3.0, 5.0, 2, 1) potential and the simulations were run at temperatures and densities corresponding to the nematic phase. Away from the walls the molecules behave just as in the bulk. However, as the wall is approached, oscillations appear in the density profile indicating that a layered structure is induced by the interface, as we can see from the snapshot in Fig. 19. These layers are... 

Quantum Free-Electron Theory Constant-Potential Model, The simple quantum free-electron theory (1) is based on the electron-in-a-box model, where the box is the size of the crystal. This model assumes that (1) the positively charged ions and all other electrons (nonvalence electrons) are smeared out to give a constant background potential (a potential box having a constant interior potential), and (2) the electron cannot escape from the box boundary conditions are such that the wavefunction if/ is... 

Figure 3.7. (a) Potential energy of an electron in a one-dimensional crystal (b) Kronig-Penney model of the potential energy of an electron in a one-dimensional crystal (square-well periodic potential model). 

It is also planned to continue crystal density modeling studies in collaboration with Prof. Ammon with the expectation that comparison of predicted with experimental (X-ray derived) crystal density values will permit further refinement of the MOLPAK/WMIN computational approach. In this way, the predictive value of this computational method is likely to be enhanced, thereby rendering it of greater value for preliminary screening of proposed new candidate fuel systems as potential synthetic targets. 

Vanadium(n) Complexes.—Dehydration of VSO. THjO has been shown to proceed via the formation of VS04,mH20 (where n = 6, 4, or 1) and V(OH)-(SO4), which were characterized by X-ray studies. The polarographic behaviour and the oxidation potential of the V -l,2-cyclohexanediamine-tetra-acetic acid complex, at pH 6—12, have been determined.Formation constants and electronic spectra have been reported for the [Vlphen),] " and [V20(phen)] complexes. The absorption spectrum of V ions doped in cadmium telluride has been presented and interpreted on a crystal-field model. The unpaired spin density in fluorine 2pit-orbitals of [VF ] , arising from covalent transfer and overlap with vanadium orbitals, has been determined by ENDOR spectroscopy and interpreted using a covalent model. " ... 

The crystal potential for L-alanine calculated with Eq. (8.34) is shown in Fig. 8.1(a). The term Ospherical.atom(r) can be evaluated in direct space by the methods described in the following section. The term 0(0) for the independent-atom model [not exactly equal to the true 0(0)] was evaluated by a summation of the IAM potential over the unit cell. 

I have not described the calculation of the eigenvalues, which requires the solution of the equations of motion and therefore a knowledge of the force constants. The shell model for ionic crystals, introduced by Dick and Overhauser (1958), has proved to be extremely useful in the development of empirical crystal potentials for the calculation of phonon dispersion and other physical properties of perfect and imperfect ionic crystals. There is now a considerable literature in this field, and the following references will provide an introduction Catlow etal. (1977), Gale (1997), Grimes etal. (1996), Jackson et al. (1995), Sangster and Attwood (1978). The shell model can also be used for polar and covalent crystals and has been applied to silicon and germanium (Cochran (1965)). 

The potential of IR ellipsometric spectroscopy (IRES) for investigating surface processes and reactions relevant to gas-solid heterogeneous catalysis is examined, both for single crystal and model dispersed catalytic systems. With it, structural and chemical changes can be followed over a wide range of temperature and gas pressure, allowing one to thermally stabilize intermediates for investigation, and study surface species under conditions close to those in practical catalytic reactions. 

The screening term describes the screening of Coulomb potential due to the overlap of electronic densities of ions. Parameters of the pair potential model are listed in Table 1. The many-particle JT contribution to the crystal energy is approximated by the sum of expressions for the lower brunches of adiabatic potentials of the Mn06 clusters... 

A final set of tests of this series of investigations focused on the analysis of hydrostatic compression of some representative energetic materials. Sorescu et al. [117] have considered the case of nitramine RDX (a-phase), HMX ((3-phase), and HNIW (e-phase) and the non-nitramine PETN crystal. These studies have been performed based on NPT-MD simulations at room temperature over the pressure ranges 0-4 GPa for RDX, 0-7.5 GPa for HMX, 0-3.5 GPa for HNIW, and 0-9 GPa for PETN. In the case of the RDX, HMX, and HNIW crystals, the results indicate that the proposed potential model is able to reproduce accurately the changes in the... 

A perfect crystal structure model is very helpful for theoretical calculations, reaction mechanism analysis, and some physical property analysis such as conductivity, magnetic susceptibility, chemical potential, etc. Powder XRD (or neutron diffraction) Rietveld refinement is one of the most popular methods used to characterize crystal structure. 

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