Composition ranges

Convergence is usually accomplished in 2 to 4 iterations. For example, an average of 2.6 iterations was required for 9 bubble-point-temperature calculations over the complete composition range for the azeotropic system ehtanol-ethyl acetate. Standard initial estimates were used. Figure 1 shows results for the incipient vapor-phase compositions together with the experimental data of Murti and van Winkle (1958). For this case, calculated bubble-point temperatures were never more than 0.4 K from observed values. 

As an indication of the types of infonnation gleaned from all-electron methods, we focus on one recent approach, the FLAPW method. It has been used to detennine the band stmcture and optical properties over a wide energy range for a variety of crystal stmctures and chemical compositions ranging from elementary metals [ ] to complex oxides [M], layered dichalcogenides [, and nanoporous semiconductors The k p fonnulation has also enabled calculation of the complex band stmcture of the A1 (100) surface... 

Dentistry. Most casting alloys meet the composition and properties criteria of specification no. 5 of the American Dental Association (37) which prescribes four types of alloy systems constituted of gold—silver—copper with addition of platinum, palladium, and 2inc. Composition ranges are specified, as are mechanical properties and minimum fusion temperatures. Wrought alloys for plates also may include the same constituents. Similarly, specification no. 7 prescribes nickel and two types of alloys for dental wires with the same alloy constituents (see Dental materials). 

T omp practical compensation temperature is found ia a very narrow compositional range around... 

As a result, the internal quantum efficiencydecreases exponentially as the separation between the direct and iadirect minima decreases. This property strongly influences the useful compositional ranges of mixed alloys of direct and iadirect materials. 

The crystallinity of poly(lactide- (9-glycoHde) samples has been studied (36). These copolymers are amorphous between the compositional range of 25—70 mol % glycoHde. Pure polyglycoHde was found to be about 50% crystalline whereas pure poly-L-lactide was about 37% crystalline. An amorphous poly(L-lactide-i (9-glycoHde) copolymer is used in surgical cHps and staples (37). The preferred composition chosen for manufacture of cHps and staples is the 70/30 L-lactide/glycoHde copolymer. 

Titanium alloyed with niobium exhibits superconductivity, and a lack of electrical resistance below 10 K. Composition ranges from 25 to 50 wt % Ti. These alloys are P-phase alloys having superconducting transitional temperatures at ca 10 K. Thek use is of interest for power generation, propulsion devices, fusion research, and electronic devices (52). 

Studies of the copolymerization of VDC with methyl acrylate (MA) over a composition range of 0—16 wt % showed that near the intermediate composition (8 wt %), the polymerization rates nearly followed normal solution polymerization kinetics (49). However, at the two extremes (0 and 16 wt % MA), copolymerization showed significant auto acceleration. The observations are important because they show the significant complexities in these copolymerizations. The auto acceleration for the homopolymerization, ie, 0 wt % MA, is probably the result of a surface polymerization phenomenon. On the other hand, the auto acceleration for the 16 wt % MA copolymerization could be the result of Trommsdorff and Norrish-Smith effects. 

Once initiated, zirconium and carbon powders react exothermically in a vacuum or inert atmosphere to form zirconium carbide. With the greater availabiHty of relatively pure metal powders, this technique is coming into common use for the production of several refractory carbides. Zirconium carbide is not a fixed stoichiometric compound, but a defect compound with a single-phase composition ranging from ZrCQ to ZrCQ at 2400°C. 

Other researchers have reported the trihaUdes to be non stoichiometric with composition ranges of ZrCl2 24 ZrCl2 q, ZrBr2 gy—ZrBr 235 and Zrl2 g —Zrl 43 (176). The composition ranges of the lower iodides were reported to be Zrl 2 Zrl2 and Zrl "Zrl 3 (177). 

The well-known Gibbs-Duhem equation (2,3,18) is a special mathematical redundance test which is expressed in terms of the chemical potential (3,18). The general Duhem test procedure can be appHed to any set of partial molar quantities. It is also possible to perform an overall consistency test over a composition range with the integrated form of the Duhem equation (2). 

For apphcation to distiUation (a nearly isobaric process), as shown in Figs. 13-8 to 13-13, binary-mixture data are frequently plotted, for a fixed pressure, as y versus x, with a line of 45° slope included for reference, and as T versus y and x. In most binary systems, one of the components is more volatile than the other over the entire composition range. This is the case in Figs. 13-8 and 13-9 for the benzene-toluene system at pressures of both 101.3 and 202.6 kPa (1 and 2 atm), where benzene is more volatile than toluene. 

Three types of binary equilibrium cui ves are shown in Fig. 13-27. The y-x diagram is almost always plotted for the component that is the more volatile (denoted by the subscript 1) in the region where distillation is to take place. Cui ve A shows the most usual case, in which component 1 remains more volatile over the entire composition range. Cui ve B is typical of many systems (ethanol-water, for example) in which the component that is more volatile at lowvalues of X becomes less volatile than the other component at high values of X. The vapor and liquid compositions are identical for the homogeneous azeotrope where cui ve B crosses the 45° diagonal. A heterogeneous azeotrope is formed with two liquid phases by cui ve C,... 

Analysts should not rely on databases developed by others unless citations and regression resiilts are available. Many improper conclusions have been drawn when analysts have relied upon the databases supplied with commercial simulators. While they may be accurate in the temperature, pressure, or composition range upon which they were developed, there is no guarantee that they are accurate for the unit conditions in question. Pure component and mixture correlations should be developed for the conditions experienced in the plant. The set of database parameters must be internally consistent (e.g., mixture-phase equilibria parameters based on the pure-component vapor pressures that will be used in the analysis). This ensures a consistent set of database parameters. 

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