Calculating Crystal Habit

For the shape of a crystal, the equilibrium and growth form have to be distinguished. The equilibrium form follows from the Wulff construction, while the growth form is determined by the relative growth rates of the different faces. 

Several methods exist to calculate relative growth rates. The earliest and simplest of these was initially proposed by Bravais [29] and Friedel [30] and later extended by Donnay and Marker [31]. Known as the Bravais-Friedel-Doimay-Harker (BFDH) model, it states that the growth rate of a given crystallographic face with Miller indices (hkl) is proportional to the inverse of the interplanar distance between 

This model is purely geometric and does not require any knowledge of the crystal structure of the solid, merely the unit cell dimensions need to be known. The smaller the interplanar distance, the larger the relative growth rate, and as the low index faces are those with the largest interplanar distances, it is these that are expressed in the crystal habit. 

Since the BFDH model is purely geometric and takes no account of the crystal structure, it cannot account for specific strong and directional interactions such as hydrogen bonding between distinct molecules. 

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An enlarged view of a crystal is shown in Fig. VII-11 assume for simplicity that the crystal is two-dimensional. Assuming equilibrium shape, calculate 711 if 710 is 275 dyn/cm. Crystal habit may be changed by selective adsorption. What percentage of reduction in the value of 710 must be effected (by, say, dye adsorption selective to the face) in order that the equilibrium crystal exhibit only (10) faces Show your calculation. 

A major weakness in the calculations described above is that they can only be used to represent vapor grown crystals. In crystals grown from solution, the solvent can greatly influence the crystal habit as can small amounts of impurities. Several investigators (68. 69 accounted for discrepancies between observed crystal habit and those obtained using attachment energies by assuming preferential solvent (or impurity) adsorption on crystal faces. 

The work discussed in the previous paragraphs provides the framework for the prediction of crystal habit from internal structure. The challenge is to add realistic methods for the calculation of solvent and impurities effects on the attachment energies (hence the crystal habits) to allow this method to provide prediction of crystal habit. Initial attempts of including solvent effects have been recently described (71. 721. The combination of prediction of crystal habit from attachment energies (including solvent and impurity effects) and the development of tailor made additives (based on structural properties) hold promise that practical routine control and prediction of crystal habit in realistic industrial situations could eventually become a reality. 

Calculation of Crystal Habit and Solvent-Accessible Areas of Sucrose and Adipic Acid... 

The ciystal habit of sucrose and adipic add crystals were calculated from their intern structure and from the attachment energies of the various crystal faces. As a first attempt to indude the role of the solvent on the crystal habit, the solvent accessible areas of the faces of sucrose and adipic add and were calculated for spherical solvent probes of difierent sizes. In the sucrose system the results show that this type of calculation can qualitatively account for differences in solvent (water) adsorption hence fast growing and slow growing faces. In the adipic add system results show the presence of solvent sized receptacles that might enhance solvent interadions on various fares. The quantitative use of this type of data in crystal shape calculations could prove to be a reasonable method for incorporation of solvent effeds on calculated crystal shapes. 

Incorporation of Solvent Effects in Crystal Habit Calculations... 

Even though still in a prelinainaiy stage, it is hoped that this approach will result in a better solvent - effect corrector to the attachment energy calculations (IS) than the broken hydrogen bond model and a better fit of the predicted sucrose crystal habits with the observed ones. It is already clear that the present model can, at least qualitatively, distinguish between the fast growing ri t pole of the crystal and its slow left pole. 

Using the formulae cited, it should be remembered that they apply primarily to natural crystals, whereas the results obtained for man-made crystals may differ widely from the values calculated from the formulae and compiled in Table II at the end of the book, this depending on the manufacturing technology, crystal habit and fineness. 

Figure 8.14 Comparison of the (a) calculated (from ref [96]) and (b) observed (from ref [97]) crystal habit of a-Al203.

System Orthorhombic Crystal Habit columnar Optical Sign - Axial Angle 69 Optic orientation (assigned acc.to crystal habit) XX c YY a ZZ b. Dispersion None observed Refractive Indexes a (w) = 1.517 (3 ( e) = 1.567 y = 1.592 Density 1.379 Refraction Experimental = 111.90 Calculated = 113.99. 

The changes in crystal habit of glycine were studied by atom-atom potential energy calculations the energy results were completely consistent with the abovementioned observations [27a, 28]. 

To simulate the habit of solution-grown crystals, the interactions of solvent molecnles at the crystal-solution interface conld be considered. In most cases, it is assnmed that the solvent affects crystal habit through preferential adsorption of solvent molecnles on specific faces and that removal of solvent molecules before the deposition of oncoming solnte molecules causes retardation of crystal growth. The extent of solvation of a crystal face could be qualitatively understood from the relative polarities of the varions crystal faces, which can be obtained from electrostatic potential maps calculated at closest approach distances (Berkovitch-Yellin 1985). 

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