Crystal attachment energy

Docherty, R., Clydesdale, G., Roberts, K.J. and Bennema, P., 1991. Application of the Bravais-Freidel-Donnay-Harker attachment energy and Ising models to predicting and understanding the morphology of molecular crystals. Journal of Physics D Applied Physics, 24, 89-99. 

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. 

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. 

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. 

There are two downsides to the PBC theory the first is that a certain arbitrariness is unavoidable in finding PBCs in real crystal structures, and the second is that PBC analysis is difficult in complicated structures. In answer to the first criticism, Hartman [3] calculated the attachment energy, and correlated this to Jackson s... 

The lattice energy at a half-crystal position (kink site) is defined as the attachment energy and the energy released in forming a slice containing more than two PBCs is denoted by E j These are related to the lattice energy as follows ... 

Hartman and Bennema (19) found that relative growth rate always increases with At low supersaturation, they were able to show that the growth rate of a given crystal face, hkl is direcdy proportional to the attachment energy ... 

Hartman, P., and P. Bennema, The Attachment Energy as a Habit-Controlling Factor, J. Crystal Growth 49 145 (1980). 

Docherty, R., G. Clydesdale, K.J. Roberts, and P. Bennema, Application of Bravais-Friedel-Donnay-Harker, Attachment Energy and Ising Models to Understanding the Morphology of Molecular Crystals, J. Physics D Appl. Physics 24 89 (1991). 

The attachment energy and Hartman-Perdok methods for the calculation of crystal morphology has been extended to ionic crystals and is described by Strom et. al. 1999. 

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