Rare binary

Most practical separation problems, however, involve multi-component mixtures, simply because mixtures occurring in nature are rarely binary. Certain industrial streams, the products of various processing steps, could include primarily two components to be further separated in downstream unit operations. Even such streams are in fact multi-component mixtures as a result of impurities carried along in the stream. 

Ask about alternative choices, interpretations, and decisions, and define competing options clearly. The status quo is never your only option, and your choices are rarely binary (i.e., to act or not act). In important decisions, always generate a short list of alternatives. 

Activity-coefficient data at infinite dilution often provide an excellent method for obtaining binary parameters as shown, for example, by Eclcert and Schreiber (1971) and by Nicolaides and Eckert (1978). Unfortunately, such data are rare. 

Since the accuracy of experimental data is frequently not high, and since experimental data are hardly ever plentiful, it is important to reduce the available data with care using a suitable statistical method and using a model for the excess Gibbs energy which contains only a minimum of binary parameters. Rarely are experimental data of sufficient quality and quantity to justify more than three binary parameters and, all too often, the data justify no more than two such parameters. When data sources (5) or (6) or (7) are used alone, it is not possible to use a three- (or more)-parameter model without making additional arbitrary assumptions. For typical engineering calculations, therefore, it is desirable to use a two-parameter model such as UNIQUAC. 

In ternary systems, we distinguish between two common types. In type II, two binaries are partially miscible and the third binary is completely miscible in type I, only one binary is partially miscible. (A third type, where all three binaries are only partially miscible, is relatively rare and not considered here.)... 

The breaking up of azeotropic mixtures. The behaviour of constant boiling point mixtures simulates that of a pure compound, because the composition of the liquid phase is identical with that of the vapour phase. The composition, however, depends upon the pressure at which the distillation is conducted and also rarely corresponds to stoichiometric proportions. The methods adopted in practice will of necessity depend upon the nature of the components of the binary azeotropic mixture, and include —... 

Azeotropic compositions are rare for terpolymerization and Ham 14 has shown that it follows from the simplified eqs. 38-40 that ternary azeotropes should not exist. Nonetheless, a few systems for which a ternary azeotrope exists have now been described (this is perhaps a proof of the limitations of the simplified equations) and equations for predicting whether an azeotropic composition will exist for copolymerizations of three or more monomers have been formulated.20113 This work also shows that a ternary azeotrope can, in principle, exist even in circumstances where there is no azeotropic composition for any of the three possible binary copolymerizations of tire monomers involved. 

Moreover, since the mean free path is of the order of 100 times the molecular diameter, i.e., the range of force for a collision, collisions involving three or more particles are sufficiently rare to be neglected. This binary collision assumption (as well as the molecular chaos assumption) becomes better as the number density of the gas is decreased. Since these assumptions are increasingly valid as the particles spend a larger percentage of time out of the influence of another particle, one may expect that ideal gas behavior may be closely related to the consequences of the Boltzmann equation. This will be seen to be correct in the results of the approximation schemes used to solve the equation. 

In Pig. 4-lc, both the input and the output from the coder are binary sequences, but if planes are spotted only rarely, then the output will contain many fewer binary digits than the input. The theory developed later will show exactly how many binary digits are required from the coder. The important point here is that a reduction is possible and that it depends on the frequency (or probability) of l s in the input data. 

C.19 Aluminum oxide, alumina, exists in a variety of crystal structures, some of which are beautiful and rare. Write the formula for aluminum oxide, which is a binary compound of aluminum and oxygen. The mass of a rectangular slab of aluminum oxide of dimensions 2.5 cm X 3.0 cm X 4.0 cm is 102 g. What is the density of aluminum oxide ... 

The crystal structures of the borides of the rare earth metals (M g) are describedand phase equilibria in ternary and higher order systems containing rare earths and B, including information on structures, magnetic and electrical properties as well as low-T phase equilibria, are available. Phase equilibria and crystal structure in binary and ternary systems containing an actinide metal and B are... 

Binary phase diagrams indicate that the rare-earth dodecaborides do not melt congruently . Owing to the difficulty in preparation of single-phase and single-crystal dodecaborides, little information is available on their physical properties. 

Almost all of the rare-earth metal/rare-earth metal tri-iodide systems, R/RI3, contain binary phases with the rare-earth element in an oxidation state lower than -1-3 ( reduced rare-earth metal iodides) [3, 7, 10-13]. More common is the oxidation state -i-2. Elements that form di-iodides RI2 are illustrated in Fig. 4.1. 

After the discovery of the Al6Mn i-QC [1], development of QCs were limited for almost a decade to ternary systems with a major A1 constituent, such as Al-(Pd,Mn)-Si, Al-Zn-(Li,Mg), Al-Cu-TM (TM = Fe, Ru, Os), Al-Pd-(Mn,Re) [2,25,26], (This may be the reason why jargon such as Al-based QCs was coined.) After all, most QC discoveries were achieved by chemical additions to, or substitutions in, known compounds. From the mid-1990s to about 2000, QCs were also found in Zn-Mg-R (R = rare-earth-metal), Cd-Mg-R, and (Yb,Ca)-Cd systems, the last being the first stable binary i-QC at room temperature. Experience and insight are worth a lot — Tsai and coworkers produced 90% of these i-QCs [27],... 

The transition-metal monopnictides MPn with the MnP-type structure discussed above contain strong M-M and weak Pn-Pn bonds. Compounds richer in Pn can also be examined by XPS, such as the binary skutterudites MPn , (M = Co, Rh, Ir Pn = P, As, Sb), which contain strong Pn-Pn bonds but no M-M bonds [79,80], The cubic crystal structure consists of a network of comer-sharing M-centred octa-hedra, which are tilted to form nearly square Pnn rings creating large dodecahedral voids [81]. These voids can be filled with rare-earth atoms to form ternary variants REM Pnn (RE = rare earth M = Fe, Ru, Os Pn = P, As, Sb) (Fig. 26) [81,82], the antimonides being of interest as thermoelectric materials [83]. 

As a final comment on terminology, we note that elemental semiconductors are formed from a single element, e.g., Si or Ge, whereas compound semiconductors are formed from two binary), three ternary), four quaternary), or, rarely, more elements. Semiconductor alloys refer to solid solutions where either one anion or one cation can substitute for another, or possibly two or more such substitutions can occur for a binary semiconductor AB a simple alloy with C would be represented as Ai CjcB. Semiconductors are often classified by the group numbers in the periodic table. Thus, for example, I-VII semiconductors include Cul and AgBr, II-VI semiconductors include ZnS, CdTe, and HgTe, III-V semiconductors include GaAs, GaN, InP, and InSb, and IVx-VIv semiconductors include PbSe and Sn02. Fundamental physical properties are compiled in a recent handbook [22]. 

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