Crystal growth transformation

Spanos, N. and Koutsoukos, P.G., 1998. The transformation of vaterite to calcite effect of the conditions of the solutions in contact with the mineral phase. Journal of Crystal Growth, 191, 783-790. 

In some cases shape-control has also been achieved tetra( -octyl)ammonium glycolate transforms Pd(N03)2 predominantly into trigonal Pd particles [186]. Recent work has confirmed that the colloidal protective agents not only prevent particle agglomeration but even provide control of the crystal growth during particle synthesis (see e.g., Ref. [187-191]). The drawbacks of this route are the restriction to noble metal salts and the limited industrial availability of A-(octyl)j RC02. 

Polymer crystallization is usually divided into two separate processes primary nucleation and crystal growth [1]. The primary nucleation typically occurs in three-dimensional (3D) homogeneous disordered phases such as the melt or solution. The elementary process involved is a molecular transformation from a random-coil to a compact chain-folded crystallite induced by the changes in ambient temperature, pH, etc. Many uncertainties (the presence of various contaminations) and experimental difficulties have long hindered quantitative investigation of the primary nucleation. However, there are many works in the literature on the early events of crystallization by var-... 

Wada, N., Yamashita, K. and Umegaki, T. (1995) Effects of divalent cations upon nucleation, growth and transformation of calcium carbonate polymorphs under conditions of double diffusion. Journal of Crystal Growth, 148, 297-304. 

A better insight into the mechanisms of the individual steps in the formation of crystals would be of great help in explaining the creation and transformation of sedimentary deposits and biological precipitates. Valuable reviews are available on the principles of nucleation of crystals and the kinetics of precipitation and crystal growth (Zhang and Nancollas, 1990 Steefel and Van Cappellen, 1990 Van Cappellen, 1991). Only a few important considerations are summarized here to illustrate the wide scope of questions to be answered in order to predict rates and mechanisms of precipitation in natural systems. 

In this paper, three methods to transform the population balance into a set of ordinary differential equations will be discussed. Two of these methods were reported earlier in the crystallizer literature. However, these methods have limitations in their applicabilty to crystallizers with fines removal, product classification and size-dependent crystal growth, limitations in the choice of the elements of the process output vector y, t) that is used by the controller or result in high orders of the state space model which causes severe problems in the control system design. Therefore another approach is suggested. This approach is demonstrated and compared with the other methods in an example. 

It Is unknown whether suspended a-form crystal or 3-form crystal In the saturated solution displays a solid-solid transformation or not. The reason for above experimental results may be assumed as follows In the standpoint of Industrial crystallization. Since 3-form crystal Is less soluble than a-form crystal at high temperature above 284K. The state that a-form crystal Is suspended In the saturated solution Is considered to be supersaturated for 3-form crystal. So the state has the potential to take place primary nucleatlon and crystal growth for the 3-form. In this way, 3-form crystal may be produced In the suspension of a form crystal. Rewarding to the formation of 3-form crystal, a part of a-form crystal suspended may be dissolved. Opposite phenomena may take place at low temperature below 284K. 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

Table 3-2 Diffusion coefficients of noble gases in aqueous solutions Table 3-3 Ionic porosity of some minerals Table 4-1 Steps for phase transformations Table 4-2 Measured crystal growth rates of substances in their own melt...

Crystallization and reactivity in two-dimensional (2D) and 3D crystals provide a simple route for mirror-symmetry breaking. Of particular importance are the processes of the self assembly of non-chiral molecules or a racemate that undergo fast racemization prior to crystallization, into a single crystal or small number of enantiomorphous crystals of the same handedness. Such spontaneous asymmetric transformation processes are particularly efficient in systems where the nucleation of the crystals is a slow event in comparison to the sequential step of crystal growth (Havinga, 1954 Penzien and Schmidt, 1969 Kirstein et al, 2000 Ribo et al 2001 Lauceri et al, 2002 De Feyter et al, 2001). The chiral crystals of quartz, which are composed from non-chiral Si02 molecules is an exemplary system that displays such phenomenon. 

These intergrowth relations are formed through the processes of crystal growth, phase transformation or decomposition associated with a decrease in temperature and pressure, or metasomatism due to the supply of new components from outside. 

All crystal growth takes place in low-temperature, low-pressure aqueous solution (at 1 atmospheric pressure and room temperature). This suggests a higher probability of formation of an amorphous state, phases of low crystallinity, and metastable phases as precursors, and therefore subsequent transformation to stable or metastable phases. 

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