Correlation factor values

The correlation factor, k, is a function of the liquid drop size, liquid viscosity, liquid load, disengaging space, type of mesh weave, etc. k varies somew hat with system pressure as pressure increases the k value decreases. The manufacturers should be consulted for final design k valves for a sys-... 

Bohm-Pines" plasma model seems at first sight to be very different from the expansion methods treated here, but in Section III.E(2b) it was shown that it is rather closely connected with the method using correlation factor. Similar to Wigner s formula, it probably gives reasonable values for the correlation energy for the... 

There is not sufficient experimental evidence to continue this discussion quantitatively at the present time, but the sparse experimental data suggests that for a given compound, the D0 value is significantly lower than is the case in simple metals. This decrease may be attributed to a low value in the correlation factor which measures the probability that an atom may either move forward or return to its original site in its next diffusive jump. In simple metals this coefficient has a value around 0.8. 

The correlation factor, for any mechanism, is given by the ratio of the values of the mean square displacement of the atom (often the tracer) moving in a correlated motion to that of the atom (or vacancy) moving by a random-walk process. If the number of jumps considered is large, the correlation factor/can be written as... 

Table 5.1 lists some values of the correlation factor for a variety of diffusion mechanisms in some common crystal structure types. 

No attempt has been made to correlate the value of probability factor p with the structure and properties of the reacting molecules and it is also not possible to interpret the abnormally high rates that we sometimes observe. The value of p has been found to vary from unity to 10 9 when we move from simple atomic reaction to reactions involving complex molecules. There is no explanation in terms of collision theory for such a wide variation in the value of p. 

An important aspect of our AI application is the attention paid to including well-established Fortran programs and database search methods into the decision structure of an expert system network. Only certain AI software tools (such as TIMM) effectively handle this critical aspect for the analytical instrumentation field at this time (57-60)> The ability to combine symbolic and numeric processing appears to be a major factor in development of multilevel expert systems for practical instrumentation use. Therefore, the expert systems in the EXMAT linked network access factor values and the decisions from EXMATH, an expert system with chemometric/Fortran routines which are appropriate to the nature of the instrumental data and the information needed by the analyst. Pattern recognition and correlation methods are basic capabilities in this field. 

The electron diffraction study was complemented by an all-electron theoretical calculation of Lu, Wei, and Zunger (LWZ) (1992), using the local density approximation for the exchange and correlation terms in the Hamiltonian. They find agreement within x0.6% between the calculated and dynamic structure factor values for the lowest three reflections, (100), (110), and (111). But for (200), with sin 0/A = 0.3464 A-1, the discrepancy is as large as 1.7%. The discrepancy is attributed to insufficiently accurate knowledge of the temperature factors in this diatomic crystal, which affect the derivation of the X-ray structure factor from the electron diffraction measurement, as well as the calculation of the dynamic theoretical structure factors needed for the comparison with experiment. For the monoatomic Si crystal for which the B values are well known, the agreement is... 

Parameter Central atom Def. value Compound Individual L s Correl. factor Ref. 

Parameter Correlations Definition value Individual L s n Correl. factor Ref. 

The same measurement is repeated by assuming different values of a. The coefficient of determination or correlation factor r2 is calculated for each value of a. The best value of a is the one with its value of r2 closest to one. In a calibration done by Ren et al.71 for the Penn State flight-time-focused atom-probe, the following values were obtained ... 

For very dilute solid solutions of B in A, the basic physics of diffusional mixing is the same as for (A, A ). An encounter between VA and BA is necessary to render the B atoms mobile. But B will alter the jump frequencies of V in its surroundings and therefore numerical values of the correlation factor and cross coefficient are different from those of tracer A diffusion. Since the jump frequency changes also involve solvent A atoms, in addition to fB, the numerical value of fA must be reconsidered (see next section). 

For a random walk, f = 1 because the double sum in Eq. 7.49 is zero and Eq. 7.50 reduces to the form of Eq. 7.47. In principle, f can have a wide range of values corresponding to physical processes relating to specific diffusion mechanisms. This is readily apparent in extreme cases of perfectly correlated one-dimensional diffusion on a lattice via nearest-neighbor jumps. When each jump is identical to its predecessor, Eq. 7.49 shows that the correlation factor f equals NT.6 Another extreme is the case of f = 0, which occurs if each individual jump is exactly opposite the previous jump. However, there are many real diffusion processes that are nearly ideal random walks and have values of f 1, which are described in more detail in Chapter 8. 

In our approach [1, 2] termed the dynamic method the complex susceptibility x = x — ix" is determined by a law of undamped motion of a dipole in a given potential well and by dissipation mechanism often described as stosszahlansatz in the underlying kinetic or Boltzmann equation. In this review we shall refer to this (dynamic) method as the ACF method, since it is actually based on calculation of the spectrum of the dipolar autocorrelation function (ACF). Actually we use a one-particle approximation, in which the form of an employed potential well (being in many cases rectangular or close to it) is taken a priori. Correlation of the particles coordinates is characterized implicitly by the Kirkwood correlation factor g, its value being taken from the experimental data. The ACF method is simple and effective, because we do not employ the stochastic equations of motions. This feature distinguishes our method from other well-known approaches—for example, from those described in books [13, 14]. 

FIGURE 37. Comparison of calculated and experimental 73Ge NMR chemical shifts of some simple germanium compounds. The experimental values of GeMe4 nCln (n = 1-3) were not available. They have been estimated from the analogues silicon compounds using empirical correlation factors. Reproduced by permission of John Wiley Sons, Inc. from Reference 158... 

The availability of experimental dipole moment (Section Ill-a), dielectric constant, refractive index and density data for NMA has made possible the calculation of values of the correlation factor (g) using the following equation of Kirkwood97 and Frohlich98) ... 

These workers were not able to correlate the values of k or of settling time with any more general properties. To free the correlation from the restriction imposed by the presence of factors which could be determined only by specific experiments, the following relation was given ... 

The enthalpy trend can be examined in terms of electronic and steric contributions to the enthalpy of reaction, the relative importance of which can be quantified in terms of the respective Ai /A2 ratios obtained in a treatment first proposed by Tolman, where enthalpies of reaction are correlated with steric (6, cone angle, see Tolman s Cone Angle) and electronic (v, carbonyl stretching frequency in Ni(CO)3L, L = tertiary phosphine) factors. A correlation factor of 0.95 is obtained when enthalpic data are fitted to equation (3) and a value of 2.32 is calculated for the A1/A2 and quantitatively denotes the overwhelming influence of steric factors. Since the steric factors have such a profound influence on the enthalpy of reaction, a direct relationship between the enthalpy of reaction and the phosphine cone angle can be established as shown in Figure 1. 

If the macromolecules of the solution at saturation are of the oblate variety, the Langevin functions tend to 0 at ATz - oo and the correlation factor (323) tends to the value... 

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