Strain parameter, reduced

Reduced dimensional parameters (strain parameters and near-neighbours diagrams) By comparing the space-filling theoretical curves and the actual values of intermetallic phases it has been observed that an incompressible sphere model of the atom gives only a rough description when discussing metallic structures. 

A reduced strain parameter is then defined with reference to an arbitrarily selected set of contacts. With reference to the dx distances the strain parameter may be defined as . S = (Dx — dx)/DY. This parameter gives an indication of the atomic dimension compression. It is computed, as a function of the ratio e = DX/DY = Rx/Ry, for the different kinds of interatomic contact. 

Considering that the reduced free energy s4 = Ajk T) is stationary with respect to all the strain parameters 3 (q), the configurational, or elastic, force is given by [see also Eqn. (2.1.44)]... 

A number of molecular structural parameters for trivinylborane, B(CH=CH2)3, are shown in Table 2. The most acceptable molecular model is a planar dynamic one, in which steric strain is reduced by distortion of the vinyl groups. Since the molecule is probably planar, some C B 7r-electron delocalization was postulated this was corroborated by the value for the C=C bond length. 

As an example, consider the gas-phase enthalpy of formation of cycl-opentene oxide (CsHgO) at 298.15 K. The fastest calculations are the empirical methods. Unfortunately, the GA estimate is frustrated by missing ring-strain parameters. Molecular mechanics (MM3) yields f 298.15 2 kJ mol As a check, the PM3 prediction is—71 kJ mol. The PM3 result is probably more reliable, but the severe disagreement with the empirical estimate reduces confidence. Both these calculations were done using commercial software [19,20]. 

The geometry of any particular structure adopted by a binary phase A B(, can be represented as a diagram composed of straight lines, one for every independent interatomic distance in the structure. The diagram is drawn with a reduced strain parameter (Da — dp)/D as ordinate and the diameter ratio DJD of the two component atoms as abscissa. Here Da and are the diameters of the... 

The values for actual phases that take the structure can be calculated from the unit-cell (and atomic) parameters of the phases. Each phase can therefore be represented by a point on the diagram since its reduced strain parameter and radius ratio can be determined from d, D, and From the positions of the points representing a number of phases with the structure it is possible to determine whether chemical bond or geometric factors control the stability of the structure, as explained on pp. 139-146. 

The modeling of steady-state problems in combustion and heat and mass transfer can often be reduced to the solution of a system of ordinary or partial differential equations. In many of these systems the governing equations are highly nonlinear and one must employ numerical methods to obtain approximate solutions. The solutions of these problems can also depend upon one or more physical/chemical parameters. For example, the parameters may include the strain rate or the equivalence ratio in a counterflow premixed laminar flame (1-2). In some cases the combustion scientist is interested in knowing how the system mil behave if one or more of these parameters is varied. This information can be obtained by applying a first-order sensitivity analysis to the physical system (3). In other cases, the researcher may want to know how the system actually behaves as the parameters are adjusted. As an example, in the counterflow premixed laminar flame problem, a solution could be obtained for a specified value of the strain... 

The recent synthesis of (—)-tetracycline by Myers and co-workers incorporates a biocatalytic step in the first stage which oxidizes benzoic acid aerobically to an a,f)-dihydroxy derivative in the presence of a whole-cell mutant strain of Alcaligenes eutrophus. Figure 4.61 shows a reduced tree diagram for the synthesis and Table 4.28 summarizes the metrics parameters. 

The storage modulus (G ) was recorded at a frequency of IHz under 0.015 strain amplitude until stabilization of the protein network. In order to reduce stress in the sample, G recording started just before the gelation time which corresponds to the time at which G deviated from the baseline. Data were collected and rheological parameters were calculated using Carri-Med 50 software. For each system, the experiments were performed in triplicate. 

If the distributions in D and E would be fully positively correlated, then no broadening of the EPR spectrum whatsoever would ensue, because their ratio (i.e., the rhombicity q = E/D) would remain constant, and so the effective -values would not be distributed. On the other hand, a maximal broadening effect would occur in case of full negative correlation oD = -aE. This definition reduces the description of /7-strain to the fitting of a single parameter. 

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