Phase Diagrams for Crystal Growth

In growing single crystals, one is primarily concerned with obtaining a crystal of predetermined size with a high degree of structural perfection and a well-determined chemical composition. 

Growth of a single crystal requires the nucleation, subsequent growth, eventual termination of the process and, finally, removal of the crystal from the apparatus. 

The transition into the soHd/crystaUine state can be realized from the vapor phase, Hquids or a polycrystalHne soHd phase. Liquid phases are melts or high- or low-temperature solutions. The growth from liquid phases plays the most important role. 

Each step of the growth process is affected by controlling the experimental parameters pressure p, temperature T, and concentration (of components) Xi. 

Crystal Growth Technology. Edited by Hans J. Scheel and Peter Capper Copyright 2008 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 978-3-527-31762-2 

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In terms of the phase diagram, ideal crystal growth would begin with nuclei formed in the labile region, but just beyond the metastable. There, growth would occur slowly the solution, by depletion, would return to the metastable state where no more stable nuclei could form and the few nuclei that had established themselves would continue to grow to maturity at a pace free of defect formation. Thus in growing crystals for X-ray diffraction analysis, one attempts, by either dehydration or alteration of physical conditions, to transport... 

Figure 12.15 The Miers phase diagram for crystallization and nucleation as a function of temperature. The three zones of the phase diagram include (1) the stable zone where the solution is undersaturated and no solid phase can exist at equilibrium (2) the metastable zone where the solution is moderately supersaturated and growth of existing crystals continues until the solution reaches the solubility line, but no new nucleation can occur and (3) the labile zone where the solution is highly supersaturated and both crystal growth and nucleation occur simultaneously.

Fig. 14 Binary phase diagram for C246H494 in octacosane. The top curve shows the equilibrium liquidus for extended-chain crystals, and the bottom line the metastable liquidus for once-folded crystals. Experimental dissolution temperatures are fitted to the Flory-Huggins equation with / = 0.15 (solid lines). Vertical dotted lines (a) and (b) indicate the concentrations at which the growth rates were determined as a function of Tc in [29]. Horizontal dotted lines indicate the temperatures at which the rates were determined in [45] as a function of concentration. G(c) at Tc = 106.3 °C, measured along line (c), is shown in Fig. 12. The shading indicates schematically the crystal growth rate (black = fast), and the dashed line the position of the growth rate minimum...

Fig. 6.18 Phase diagram for IJNbO, as determined for crystal growth.

Figure 12.16 The generic protein phase diagram as presented by Muschol and Rosenberger (1997). Zone I depicts the region of supersaturation where well formed lysozyme crystals form. Zone II is a region where lysozyme undergoes a rapid liquid-liquid phase separation, with the resulting concentrated lysozyme phase quickly tranforming to the more stable crystalline form. Crystals formed in Zone II are of poor quality. Zone III depicts a region characterized by gel formation, unsuitable for crystal growth.

Final comment. Complete thermodynamic and kinetic studies have been made to identify new individual polysulfide phases. The static membrane gauge method appears to be the most promising for controlling the equilibrium state in the systems. This method is also the main source in constructing Ps T-x equilibrium diagrams, which provide valuable data for crystal-growth processes of the intermediate polysulfides. 

Using a Calphad analysis we have determine the phase relationship in this binary system and explained the beha iour of the material. The figures 3a and 3b present the calculated phase diagram obtained by this way (17). All the important information for crystal growth (temperatures, compositions, phase stabilities, liquidus shape,.. . ) are indicated in this diagram. 

Fig. 1.8 I mportant phase diagram types being relevant for crystal growth from the melt and from solution.

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