Composite lattice

The whole system, nuclear spin and the composite lattice, is described by the equation of motion ... 

Lso is the commutator with the electron spin Zeeman Hamiltonian (assuming isotropic g tensor, Hso = gS- Bo), Lrs = Lzfs (the sub-script RS stands for coupling of the rotational and spin parts of the composite lattice) is the commutator with the ZFS Hamiltonian and Lr = —ir, where is a stationary Markov operator describing the conditional probability distribution, P(QolQ, t), of the orientational degrees of freedom through ... 

Table 10.2 Composition, lattice parameters, unit cell volume, magnetization (M), and Curie temperature (Tc) for Sm2(Fe1 J.Co )17C>22...

Simons, B. (1980) Composition-lattice parameter relationships of the magnesiowiistite solid solution series. Ann. Rept. Geophys. Lab., Yearb. 79, 376-80. 

Table 1. Superconducting properties of the samples label, nominal composition, lattice constants a and c, onset of superconducting transition as measured by susceptibility (1-3) or deduced from lattice parameters6 (4-5), isotropic shift CT so and fidl width at half maximum A...

The study of the electronic structure of impurities and defects in solids has a long tradition, both because of its own intrinsic theoretical interest and because of the technological importance in improving the performance of solid state devices. Lattice defects can be point defects (such as substitutional or interstital foreign atoms, vacancies, antisite defects in composite lattices), line defects (such as dislocations), planar defects (such as boundaries, adatom surfaces, stacking faults corresponding to misplaced planes of atoms), and so on. 

Deactivation of the Co plus Mo cathodes occurred during the first 1000 s of cathodic electrolysis, an effect that was tentatively attributed to sorption of H into the composite lattice by diffusion. However (cf. Ref 75), because H is codeposited anyway during electroforming of these composite cathode materials, this may not be the critical reason for this effect other impurity effects may be involved. 

The inverse calculation is also possible the content of the unit cell may be determined from the known chemical composition, lattice parameters and density of a material. Assume that the total mass of all atoms located in one unit cell is m. Also, assume that the unit cell volume is V. The latter is known from diffraction analysis as soon as lattice parameters have been established (see Eq. 5.41) Thus, provided the gravimetric density (p) of the crystalline material has been measured, the mass of one unit cell can be easily calculated ... 

Figure 1 The common hydrate cages and structural families, giving the unit cell compositions, lattice symmetry and parameters. The guests indicated are those typically found in natural gas hydrates of each structure. The guests in the last column usually are a minor component and may be present in any of the structures since they fit in the small D and D cavities. The actual hydrate stnictiire formed depends on the partial pressure of each gas component and the pressure and temperature.

Because the individuals building the twin or allotwin are related by point group operations, the A-B-C sequence has no influence on the composite lattice and the two or three portions can be described as juxtaposed and non-mixed for example, Zj... 

After fitting one molecular lattice to euiother, it is possible to merge the information contained in both to form a composite lattice. This lattice would then reflect the spatial and atomic requirements of both molecules simultaneously. The fitting and merging cycle can be repeated for each additional molecule, continually building up the information content of the resulting composite lattice. Thus, the composite lattice of points represents the spatial and atomic character requirements of all molecules used in its construction. 

Enzyme inhibition data is commonly expressed as 1(50) or Kl. This data can be made a part of the composite lattice. In this way, not only can the lattice act to assess FIT of novel structures, but it can also provide an estimate of Ki for the novel structures. In order to clearly focus on active site binding, the present investigation is limited to the consideration of competitive enzyme inhibitors. However, in principle, the HASL methodology would lend Itself to applications involving less definitive binding as is often encountered in studies where only 1(50) values are available, in cases of unspecified binding to a receptor, or where in vivo data, e.g. percent growth inhibition, are considered. 

The key to solving the partial pKi distribution problem is found in the body of inhibition data. The pKi of each molecule (or molecular lattice) that was used to construct the composite lattice needs to be incorporated into the lattice in such a way that refitting an inhibitor molecule to this lattice and adding the partial pKl terms at each lattice point representing that molecule would result in a predicted pKi identical to the original value for the fitted molecule. In this way, a self-consistent mathematical model of active site binding is produced. 

VasiUev VV, Barynin VA, Razin AF. Anisogrid composite lattice structures — development and aerospace applications. Compos Struct 2012 94 1117—27. 

Most of the above simulations are performed on three-dimensional simple cubic lattices with periodic boundary conditions in all directions. (Some of the early studies were based on two-dimensional square lattices but have since been updated.) Additionally, all of the works discussed in this section (except where noted otherwise) use the standard Metropolis Monte Carlo algorithm discussed in detail in Sec. III. B, but the major difference lies in the selection of which of the components contribute to the total energy of the system. Other differences include the lattice rearrangement methodology and parameters such as surfactant structure, temperature, composition, lattice size, and dimensionality. The specifics of each model are summarized below. 

Table 8.1 Base structure, composition, lattice parameter and synthesis of (1 or 2)g(13)xSi46 x compounds... 

Base structure Composition Lattice parameter, a (A) Synthesis References... 

Structure Structure Composition Lattice Maximum Ring Cross section Direction Dimension- Porm of Ref. ... 

Fig. 1. Pathways for the formation of zeolite-like composite lattices and porous lattices...

Composition, Lattice Parameters, and Thermai Expansion of Cordierites... 

Phases Composition Lattice parameter Structure Investigator... 

---