Crystallization growth unit

Fig. 2. Crystal-growth unit for rare earth hexacyanoferrates (III) (l) micro-pump, (2) syringes, (3) details of a syringe, (4) crystal-growth vessel surrounded by a copper-coil heat exchanger (connected with (6)), (5) heater for heating the oil in the outer vessel to slightly below the desired growth temperature, (6) thermostating unit for the heat exchanger.

Here r is the distance between the centers of two atoms in dimensionless units r = R/a, where R is the actual distance and a defines the effective range of the potential. Uq sets the energy scale of the pair-interaction. A number of crystal growth processes have been investigated by this type of potential, for example [28-31]. An alternative way of calculating solid-liquid interface structures on an atomic level is via classical density-functional methods [32,33]. 

In this section we briefly summarize a few modern applications of simulation techniques for the understanding of crystal growth of more complex materials. In principle, liquid crystals and colloids also belong to this class, but since the relative length of their basic elements in units of their diameter is still of order about unity in contrast to polymers, for example, they can be described rather well by the more conventional models and methods as discussed above. 

S. C. Ke, L. J. DeLucas, J. G. Harrison. Computer simulation of protein crystal growth using aggregates as the growth unit. J Phy D 57 1064, 1998. 

Primary crystallization occurs when chain segments from a molten polymer that is below its equilibrium melting temperature deposit themselves on the growing face of a crystallite or a nucleus. Primary crystal growth takes place in the "a and b directions, relative to the unit cell, as shown schematically in Fig. 7.8. Inevitably, either the a or b direction of growth is thermodynamically favored and lamellae tend to grow faster in one direction than the other. The crystallite thickness, i.e., the c dimension of the crystallite, remains constant for a given crystallization temperature. Crystallite thickness is proportional to the crystallization temperature. 

Growth and nucleation interact in a crystalliser in which both contribute to the final crystal size distribution (CSD) of the product. The importance of the population balance(37) is widely acknowledged. This is most easily appreciated by reference to the simple, idealised case of a mixed-suspension, mixed-product removal (MSMPR) crystalliser operated continuously in the steady state, where no crystals are present in the feed stream, all crystals are of the same shape, no crystals break down by attrition, and crystal growth rate is independent of crystal size. The crystal size distribution for steady state operation in terms of crystal size d and population density // (number of crystals per unit size per unit volume of the system), derived directly from the population balance over the system(37) is ... 

Eig. 2.22 Continuous crystal growth around a central screw dislocation axis. The small blocks are unit cells of the crystalline material and are usually well organized. The displacement site acts as a site for nucleation. 

The number of inputs which are available for controlling crystallisation processes is limited. Possible Inputs for a continuous evaporative crystallisation process are, crystalliser temperature, residence time and rate of evaporation. These Inputs affect the crystal size distribution (CSD) through overall changes in the nucleatlon rate, the number of new crystals per unit time, and the growth rate, the increase in linear size per unit time, and therefore do not discriminate directly with respect to size. Moreover, it has been observed that, for a 970 litre continuous crystalliser, the effect of the residence time and the production rate is limited. Size classification, on the other hand, does allow direct manipulation of the CSD. 

The level of impurity uptake can be considered to depend on the thermodynamics of the system as well as on the kinetics of crystal growth and incorporation of units in the growing crystal. The kinetics are mainly affected by the residence time which determines the supersaturation, by the stoichiometry (calcium over sulfate concentration ratio) and by growth retarding impurities. The thermodynamics are related to activity coefficients in the solution and the solid phase, complexation constants, solubility products and dimensions of the foreign ions compared to those of the ions of the host lattice [2,3,4]. 

Figure 14.6 (a) Scoring of the influence of two factors on crystal growth (see text, score is in arbitrary units). Response surface fitted to the result, top view (b) and three-dimensional view (c). 

The specific surface area of a solid is the surface area of a unit mass of material, usually expressed as m g . There is an inverse relationship between surface area and particle size. Massive crystals of hematite from an ore deposit (e. g. specularite) may have a surface area 1 m g". As particle size/crystallinity is governed largely by the chemical environment experienced during crystal growth, the surface area of a synthetic iron oxide depends upon the method of synthesis and that of a natural one, upon the environment in which the oxide formed. 

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