Balance crystal

In formulating a population balance, crystals are assumed sufficiently numerous for the population distribution to be treated as a continuous function. One of the key assumptions in the development of a simple population balance is that all crystal properties, including mass (or volume), surface area, and so forth are defined in terms of a single crystal dimension referred to as the characteristic length. For example, Eq. (19) relates the surface area and volume of a single crystal to a characteristic length L. In the simple treatment provided here, shape factors are taken to be constants. These can be determined by simple measurements or estimated if the crystal shape is simple and known—for example, for a cube area = 6 and kY0 = 1. 

Figure 7-24 presents a unique resolution configuration. This configuration provides intrinsically balanced crystal growth rates, avoids optical contamination, and resolves the diasteromers in a simple, direct manner. The essential feature is to seed the crystallizer with the faster-growing diastereomer and leave the slower-growing diastereomer in the dissolver. The crystal growth rates are balanced automatically by the overall material balance. Optical contamination is not an issue either. 

A considerable amount of academic research in the area of advanced crystallizer dynamics followed the development of the population balance crystallizer model (Randolph and Larson 1962 Hulbert and Katz 1964). Much of this work was primarily motivated by the occurrence of limit-cycle behavior in continuous... 

Madeluag constant For an ionic crystal composed of cations and anions of respective change z + and z, the la ttice energy Vq may be derived as the balance between the coulombic attractive and repulsive forces. This approach yields the Born-Lande equation,... 

Tbe pbenol should be weighed out carefully on a piece of glazed paper on the balance pan. If spilt crystals of phenol are allowed to remain on the balance pans, the latter may become corroded. If phenol is allowed to come in contact with the hands, it should be washed off without delay,... 

This fundamental relationship points out that the temperature at which crystal and liquid are in equilibrium is determined by the balancing of entropy and enthalpy effects. Remember, it is the difference between the crystal and... 

Benzene, toluene, and a mixed xylene stream are subsequently recovered by extractive distillation using a solvent. Recovery ofA-xylene from a mixed xylene stream requires a further process step of either crystallization and filtration or adsorption on molecular sieves. o-Xylene can be recovered from the raffinate by fractionation. In A" xylene production it is common to isomerize the / -xylene in order to maximize the production of A xylene and o-xylene. Additional benzene is commonly produced by the hydrodealkylation of toluene to benzene to balance supply and demand. Less common is the hydrodealkylation of xylenes to produce benzene and the disproportionation of toluene to produce xylenes and benzene. 

The common structural element in the crystal lattice of fluoroaluminates is the hexafluoroaluminate octahedron, AIF. The differing stmctural features of the fluoroaluminates confer distinct physical properties to the species as compared to aluminum trifluoride. For example, in A1F. all corners are shared and the crystal becomes a giant molecule of very high melting point (13). In KAIF, all four equatorial atoms of each octahedron are shared and a layer lattice results. When the ratio of fluorine to aluminum is 6, as in cryoHte, Na AlF, the AIFp ions are separate and bound in position by the balancing metal ions. Fluorine atoms may be shared between octahedrons. When opposite corners of each octahedron are shared with a corner of each neighboring octahedron, an infinite chain is formed as, for example, in TI AIF [33897-68-6]. More complex relations exist in chioUte, wherein one-third of the hexafluoroaluminate octahedra share four corners each and two-thirds share only two corners (14). 

Total hafnium available worldwide from nuclear zirconium production is estimated to be 130 metric tons annually. The annual usage, in all forms, is about 85 t. The balance is held in inventory in stable intermediate form such as oxide by the producers Teledyne Wah. Chang (Albany, Oregon) and Western Zirconium in the United States Ce2us in France Prinieprovsky Chemical Plant in Ukraine and Chepetsky Mechanical Plant in Russia (crystal bar). 

Rutile pigments, prepared by dissolving chromophoric oxides in an oxidation state different from +4 in the mtile crystal lattice, have been described (25,26). To maintain the proper charge balance of the lattice, additional charge-compensating cations of different metal oxides also have to be dissolved in the mtile stmcture. Examples of such combinations are Ni " + Sb " in 1 2 ratio as NiO + Sb202, + Sb " in 1 1 ratio as Cr202 + Sb O, and Cr " +... 

Liquid crystal polyesters are made by a different route. Because they are phenoHc esters, they cannot be made by direct ester exchange between a diphenol and a lower dialkyl ester due to unfavorable reactivities. The usual method is the so-called reverse ester exchange or acidolysis reaction (96) where the phenoHc hydroxyl groups are acylated with a lower aHphatic acid anhydride, eg, acetic or propionic anhydride, and the acetate or propionate ester is heated with an aromatic dicarboxyHc acid, sometimes in the presence of a catalyst. The phenoHc polyester forms readily as the volatile lower acid distills from the reaction mixture. Many Hquid crystal polymers are derived formally from hydroxyacids (97,98) and thein acetates readily undergo self-condensation in the melt, stoichiometric balance being automatically obtained. 

Although performance varies with the isotopes for which they are intended, and with the balance in the design between resolution and efficiency, the overall sensitivity of a y-camera collimator is on the order of 5000 counts/(MBqmin) (several hundred counts/(/iCi-min)). In terms of photons detected per photon emitted, this is equivalent to about 2 x lO ". In other words, about two photons out of 10,000 emitted arrives at the crystal. This necessitates exposure times that range from several minutes to the better part of an hour. Fortunately, the large number of photons available from a modest injected radioactive dose more than offsets the poor detector sensitivity. The camera s abiUty to resolve small objects, however, is ultimately limited by the collimator inefficiency. 

Fig. 4. Drainage of salt crystals in a cylindrical screen pusher-discharge centrifuge (8), where the cake thickness is 3.3 cm, the centrifugal field = 320 U, and the crystals 14 wt % <250 p.m. ( ) Represents moisture in the discharge cake, and (° ) moisture in the cake by material balance with drainage flows line A...

In the manufacture of explosives, sodium nitrate is used mainly in blasting agents. In slurries and emulsions, sodium nitrate improves stabiUty and sensitivity. It also improves the energy balance because sodium nitrate replaces water, so that more fuel can be added to the formulation. Sodium nitrate reduces crystal size of slurries, which in turn increases detonating speed. In dynamites sodium nitrate is used as an energy modifier. Typical content of sodium nitrate is 20—50 wt % in dynamites, 5—30 wt % in slurries, and 5—15 wt % in emulsions. Sodium nitrate is used also in permissible dynamites, a special type of dynamite for coal (qv) mining. 

This reaction can also be mn in a continuous fashion. In the initial reactor, agitation is needed until the carbon disulfide Hquid phase reacts fully. The solution can then be vented to a tower where ammonia and hydrogen sulfide are stripped countercurrendy by a flow of steam from boiling ammonium thiocyanate solution. Ammonium sulfide solution is made as a by-product. The stripped ammonium thiocyanate solution is normally boiled to a strength of 55—60 wt %, and much of it is sold at this concentration. The balance is concentrated and cooled to produce crystals, which are removed by centrifiigation. 

Small concentrations of vinylcarboxyhc acids, eg, acryhc acid, methacrylic acid, or itaconic acid, are sometimes included to enhance adhesion of the polymer to the substrate. The abihty to crystalline and the extent of crystallization are reduced with increa sing concentration of the comonomers some commercial polymers do not crystalline. The most common lacquer resins are terpolymers of VDC—methyl methacrylate—acrylonitrile (162,163). The VDC level and the methyl methacrylate—acrylonitrile ratio are adjusted for the best balance of solubihty and permeabihty. These polymers exhibit a unique combination of high solubihty, low permeabihty, and rapid crystallization (164). 

Certain perovskites with Pb on the A site are particularly important and show pronounced piezoelectric characteristics (PbTiO, PZT, PLZT). Different responses are found in BaTiO and PZT to the addition of donor dopants such as La ". In PZT, lead monoxide [1317-36-8] PbO, lost by volatilization during sintering, can be replaced in the crystal by La202, where the excess positive charge of the La " is balanced by lead vacancies, leading to... 

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