Ideality, deviation from INDEX

It is essential that the solution be sufficiently dilute to behave ideally, a condition which is difficult to meet in practice. Ordinarily the dilutions required are beyond those at which the concentration gradient measurement by the refractive index method may be applied with accuracy. Corrections for nonideality are particularly difficult to introduce in a satisfactory manner owing to the fact that nonideality terms depend on the molecular weight distribution, and the molecular weight distribution (as well as the concentration) varies over the length of the cell. Largely as a consequence of this circumstance, the sedimentation equilibrium method has been far less successful in application to random-coil polymers than to the comparatively compact proteins, for which deviations from ideality are much less severe. 

Body mass index (BMI) defined as weight/height2 (kg/m2) a useful index to determine one s deviation from ideal body weight. 

If either a or fi is known for a given structure, eqs. (1)—(4) in Table 6.2.1 can be used to evaluate the remaining angle. Another possible use of these equations is in assessing the extent to which the cores of related compounds deviate from idealized Id symmetry. For this purpose we assume that there is no systematic variation in the observed M-Y bond distances and define a goodness-of-fit index S by the equation ... 

Almost all these analyses are accompanied only by X-ray powder patterns (sometimes indexed using only the sulphide unit cells) or by insufficient single-crystal X-ray data While most authors assiune that deviations from ideal ratios hydroxide/sulphide are due to various inter-bedded impurities (hydroxides or layer silicates), Dshi et al. from their synthetic work (Mg + A1 and Mg + Cr valleriites powder data only), suggest that the ratios of 2.0 to 2.3 are characteristic of the obtained valleriites and that materials vnth the ideal hydroxide/sulphide ratio contain excess chalcopyiite. 

Analyzing the dissolution kinetics of alloys in a more general way, Heusler attributed deviations from the ideal behavior in simultaneous alloy dissolution (that is, a composition dependence of the phenomenological rate constants of individual alloy components) to a dissolution mechanism that proceeds from kinks in the steps of low-index planes, the concentration of these... 

Derivation of the dependence n=f(i ) from it true character at various points of r proves the deviation from the ideal focusing distribution of the refractive index (RID). It must be noted that to estimate of selfocs quality in practice it is usual to use the numerical aperture, the values of longitudinal spherical aberration, etc. [49]. 

So far we have been neglecting deviations from ideal low-index orientations. Atomic steps, however, are omnipresent on real crystal surfaces and are the smallest building blocks for all manifestations of surface morphology. Steps on surfaces are indispensable for many processes ... 

Table 4.1 Geometric properties of some periodic minimal surfaces. The "genus" of each three-periodic minimal surface (IPMS) is the genus of a unit cell of the IPMS (with symmetrically distinct sides). The "symmetry" refers to the crystallographic space group for the surface (assuming equivalent sidesl.liie surfaces are tabulated in order of deviation of the homogeneity index from the "ideal" value of 3/4. ...

A better correlation has been demonstrated for the same restricted group of phosphates between the CSA and the distortion index (DI) describing the mean deviation of the PO4 bond angles from ideal tetrahedral symmetry ... 

In general, frequencies can be measured more accurately than wavelengths because of the deviation of light waves from the ideal plane wave caused by diffraction and local inhomogenities of the refractive index. This leads to local deviations of the phase fronts from ideal planes and therefore to uncertainties in measurements of the wavelength k, which is defined as the distance between two phase fronts differing by 2n. While the wavelength A, = c/v = co/(nv) of an EM wave depends on the refractive index n, the frequency v is independent of n. 

We can conclude that the dimensions of a macromolecular coil exhibiting ex-cluded-volume effect are larger than those of the ideal coil, so that u > 1/2. However, it is necessary to fulfil a number of special and sophisticated calculations to find a specific value of power 2u in expression (19) [20]. The first estimates of the index [18, 21] were done by simple self-consistent methods. Then the mean end-to-end distance was calculated by a perturbation method, while the chain in a imaginable 4-dimensional space is considered to be non-perturbed. The deviation of dimensionality of the imaginable space from the real physical space c, is believed to be the small parameter of expansion. The first-order term gives [22] the following value of index... 

On the other hand, the value, which represents the highest bandwidth, shifted to around 2.4 because of profile dispersion, as discussed above. The dopant used in all the GI POFs shown in Figure 3.2 was diphenyl sulfide, and all the GI POFs had NAs of 0.20. This result indicates that the bandwidth characteristics are strongly influenced by the profile dispersion even if the refractive index profile deviates greatly from the ideal one. 

We have included the orthorhombic Fddd stmcture in Table 1 as having a fixed peak position ratio in order to facilitate its identification by this simple lookup table. While, in principle, an orthorhombic unit cell has three adjustable lattice constants a, b, and c, in practice for the Fddd block copolymer morphology, we usually find lattice constant ratios very close to a b c = 1 2 2- /3. For this ideal lattice constant ratio, three individual peaks with Miller indices (004), (022), (111), and a total multiplicity of 14 exactly coincide into a single peak, which is the first observed peak of the Fddd structure, having a peak position ratio of = V3 V2a 1.225 with the second peak indexed as (113). A slight deviation of the orthorhombic lattice constants from this ideal ratio leads to a split up of the first peak (and also the higher order peaks) into two or three separate peaks. However, in practice, this split up is usually so small... 

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