Relative size factor

Fig. 8.17 The fractional change in volume ACl/Ci with respect to the CsCI lattice versus the relative size factor, 91. The upper and lower NiAs curves correspond to cja = 1-39 and (8/3)1/2 respectively. (From Pettiforand Podloucky (1984).)...

Van der Waals interactions 0.4-4.0 0.2 Strength depends on the relative size of the atoms or molecules and the distance between them. The size factor determines the area of contact between two molecules The greater the area, the stronger the interaction. 

Many of the spinel-type compounds mentioned above do not have the normal structure in which A are in tetrahedral sites (t) and B are in octahedral sites (o) instead they adopt the inverse spinel structure in which half the B cations occupy the tetrahedral sites whilst the other half of the B cations and all the A cations are distributed on the octahedral sites, i.e. (B)t[AB]o04. The occupancy of the octahedral sites may be random or ordered. Several factors influence whether a given spinel will adopt the normal or inverse structure, including (a) the relative sizes of A and B, (b) the Madelung constants for the normal and inverse structures, (c) ligand-field stabilization energies (p. 1131) of cations on tetrahedral and octahedral sites, and (d) polarization or covalency effects. ... 

Figure 1-17 [2] can be used as a guide in establishing relative sizes of equipment as represented on a flowsheet. This chart is based on approximate relative proportions pictured by the mind s eye [2]. For example, the 10-foot diameter x 33-foot high tank would scale to 1.5 inches high. By using the height-developed scale factor, the diameter would be (1.5"/33 ) (10 ) = 0.45" or say 0.5" diameter on the flowsheet. 

In addition to the grid density, the quality of a grid depends on a number of other factors such as the aspect ratio of the cells and the relative size of neighboring cells. A comprehensive listing of the quality criteria for computational grids is given elsewhere [83]. Some of the important points to be remembered are ... 

The relative sizes of batch equipment are specified by means of size factors Shj for a hypothetical product. The production requirements and characteristics of each product are converted to the equivalent data for the hypothetical product and the equipment sized to achieve the required production of the hypothetical product. The method proceeds in three steps (I) calculation of exact equipment sizes for a fixed number of units of the same size mj, (2) conversion of exact equipment sizes to standard sizes, and (3) choice of mj. 

On the other hand, the crystal structures of ionic compounds with small molecular ions depend mainly on how space can be filled most efficiently by the ions, following the principle of cations around anions and anions around cations. Geometric factors such as the relative size of the ions and the shape of molecular ions are of prime importance. More details are given in Chapter 7. 

When three different kinds of spherical ions are present, their relative sizes are also an important factor that controls the stability of a structure. The PbFCl type is an example having anions packed with different densities according to their sizes. As shown in Fig. 7.5, the Cl- ions form a layer with a square pattern. On top of that there is a layer of F ions, also with a square pattern, but rotated through 45°. The F ions are situated above the edges of the squares of the Cl- layer (dotted line in Fig. 7.5). With this arrangement the F -F distances are smaller by a factor of 0.707 (= /2) than the CP-CP distances this matches the ionic radius ratio of rF-/rcl- = 0.73. An F layer contains twice as many ions as a CP layer. Every Pb2+ ion is located in an antiprism having as vertices four F and four... 

Further ternary compounds for which the relative sizes of the ions are an important factor for their stability are the perovskites and the spinels, which are discussed in Sections 17.4 and 17.6. 

The tendency to form solid solutions depends mainly on two factors, namely the chemical relationship between the elements and the relative size of their atoms. 

It is the tertiary amides that tend to be the most problematic in terms of proton NMR. They usually exhibit two rotametric forms, the relative proportion of each being determined by both electronic factors and by the relative sizes of the two groups, R1 and R2. Note this in no way implies that the rotameric forms of a tertiary amide could ever be physically separated as the inter-conversion rate between the two forms is generally in the order of seconds. A 50/50 ratio of rotamers is only guaranteed where R =R2 (as in the case of a primary amide where R1=R2=H). Consider the two compounds in Structures 6.14 and 6.15. 

This book consists of a series of works that evaluate various aspects related to the public financing of pharmaceuticals. In all health systems with majority public funding, the financing of pharmaceuticals constitutes one of the key factors in reform policies and health cost containment measures. This importance of pharmaceutical spending can be explained by both its relative size (its share within health expenditure as a whole), and its rapid growth, which is closely related to the constant incorporation of therapeutic innovations. 

It was recently reported that the application of a protective polarization may be avoided by using corrosion-resistant activated electrodes [32], The polarization protection of the electrodes represents approximately 1-2% of the nominal electrolyzer power. Assuming the capacity factor of the electrolyzer cannot exceed the one of the wind turbine, the polarization protection should be applied during 60% of the electrolyzer s lifetime or higher depending on the relative sizes of the electrolyzer and wind turbine. 

Calculating the minimum size for the cation that can be in contact with the six anions as the anions are just touching each other is a simple problem. The critical factor is the relative sizes of the ions,... 

The diffusion of an impurity atom in a crystal, say K in NaCl, involves other considerations that influence diffusion. In such cases, the probability that the impurity will exchange with the vacancy will depend on factors such as the relative sizes of the impurity compared to the host atoms. In the case of ionic movement, the charge on the diffusing species will also play a part. These factors can also be included in a random-walk analysis by including jump probabilities of the host and impurity atoms and vacancies, all of which are likely to vary from one impurity to another and from one crystal structure to another. All of these alterations can be... 

The ratio MMD/SMD is generally recognized as a good measure of droplet size range. In addition, various indices and factors have been defined to describe the spread of droplet sizes in a spray, for example, droplet uniformity index LVfSAMD -Z),)/MMD 433 and relative span factor (D09 -Z)01)/MMD, etc. 

The proper location of data is also important in parameter-estimation situations. For the nitric oxide reduction reaction (K11), for example, the relative sizes of the three-dimensional confidence regions calculated after each observation are shown in Fig. 27. The size of the confidence region after 12 points taken according to a one factor at a time variation of hydrogen and nitric oxide partial pressures is seen to be equivalent the size of the region... 

A bed size factor which is typically expressed as either the mass or volume of adsorbent required to produce 1 tonne day of O2. In either case this factor can be reduced to the relative throughput it is a measure of how long a unit must operate to produce its own volume of purified product O2. 

According to the vendor, pricing is relative to factors including the size of the job and the nature of the treatment as well as the financial arrangements, whether they be lump sum, cost plus, or other (personal communication John T. Corcia, Stablex, 1997). 

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