86Morphology of polyhedral crystals

larger crystals, a characteristic feature shown by ultra-fine particles is the frequent occurrence of multiply twinned particles. This is understood as a size effect upon surface energy: below a critical size, multiple twinning is energetically more favorable than a single crystalline state. Once a crystal is larger than the critical size, it transforms into a single crystalline state.

4.4.7 Factors controlling growth forms

Examples of changes in growth form were introduced in Section 4.4.5 where we discussed the factors involved in causing the changes.

Since the growth forms of crystals are determined by various inter-relating factors, it is inevitable that to form a clear picture we would need to analyze the origin of each example case by case. However, by studying real examples, we see that the factors determining the forms of polyhedral crystals may be generalized as: (1) the relative normal growth rates of interfaces; (2) the interface roughness; (3) the fact that polyhedral crystals are forms exhibited by a crystal grown by the layer- by-layer growth mechanism or the spiral growth mechanism; (4) the degree of smoothness, which depends on crystallographic direction. Therefore, factors which affect these points will affect the growth forms of polyhedral crystals, and to understand them it is necessary to analyze the step patterns observed on crystal faces. In Chapter 5, we will analyze the problem by consideration of surface microtopography.

References

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9R. Kern, The equilibrium form of a crystal, in Morphology of Crystals, Part A, ed. I. Sunagawa, Dordrecht, D. Reidel, 1987, pp. 77–206

10G. A. Wolff and J. D. Broder, The role of ionicity, bonding and adsorption in crystal morphology, in Adsorption et Croissance Cristalline, CNRS, 1965, pp. 172–94

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12C. W. Bunn, Crystal growth from solution, II, Concentration gradients and the rates of growth of crystals, Disc. Faraday Soc., no. 5, 1949, 132–44

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Jpn. J. Appl. Phys., 8, 1969, 1062

19F. Kawamura, I. Yasui, and I. Sunagawa, Investigations on the growth and morphology

of TiO2 in the TiO2-Na2B4O7 system with and without impurities using a new LPE method, J. Crystal Growth, 231, 2001, 186–93

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23T. Kuroda, Kinetik des Eiswachstums aus der Gasphase und seine Wachstumsformen, Thesis, Braunschweig, Germany.

24A. Wells, Crystal habit and internal structure, I, II, Phil. Mag. Ser. 7, 37, 1946, 184–236

25I. Kostov and R. I. Kostov, Crystal Habits of Minerals, Sofia, Pensoft, 1999

26Romé de l’Isle, Essai de Cristallographie, Paris, 1772

27H. E. Buckley, Crystal Growth, New York, John Wiley & Sons, 1951

28Li Lian, K. Tsukamoto, and I. Sunagawa, Impurity adsorption and habit changes in aqueous solution grown in KCl crystals, J. Crystal Growth, 99, 1990, 1156–61

29M. Bienfait, R. Boistelle, and R. Kern, Formes de croissance des halogenures alcalius dans un solvant polaire, Les morphodoromes de NaCl en solution et l’adsorption d’ions etrangers, in Adsorption et Croissance Cristalline, CNRS, 1965, pp. 515–35, 577–94

30P. Hartman, Habit variation of brookite in relation to the paragenesis, in Adsorption et Croissance Cristalline, CNRS, 1965, pp. 597–614

31Z. Berkovitch-Yellin, J. van Mit, L. Addadi, M. Idelson, M. Iahav, and L. Leiserowitz, Crystal morphology engineering by “tailor-made” inhibitors, A new probe to find intermolecular interactions, J. Am. Chem. Soc., 107, 1985, 3111–22

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88 Morphology of polyhedral crystals

33R. Uyeda, Crystallography of metal smoke particles, in Morphology of Crystals, Part B, ed. I. Sunagawa, Dordrecht, D. Reidel, 1987, pp. 367–508

Suggested reading

G. G. Lemmlein, Morphology and Genesis of Crystals, Collected Papers of G. G. Lemmleim, Moscow, Nauk, 1973 (in Russian)

E. I. Givargizov, Highly Anisotropic Crystals, Dordrecht, D. Reidel, 1986

I. Sunagawa (ed.), Morphology of Crystals, Parts A and B, Dordrecht, D. Reidel, 1987 I. Sunagawa (ed.), Morphology of Crystals, Part C, Dordrecht, D. Reidel, 1994

I. Kostov and R. I. Kostov, Crystal Habits of Minerals, Sofia, Professor Martin Drinov Academic Publishing House and Pensoft