Abstract
By the term “morphology”, we refer to the set of faces and edges which enclose a crystal.
The abundance of characteristic faces and, at least in ideal circumstances, the regular geometric forms displayed externally by crystals result from the fact that internally, crystals are built upon a crystal structure. What is, then, the relationship between the crystal structure (the internal structure) and morphology (the external surfaces)? Figure 5.1 shows the crystal structure and the morphology of the mineral galena (PbS). The faces of a crystal are parallel to sets of lattice planes occupied by atoms, while the edges are parallel to lattice lines occupied by atoms. In Fig. 5.1a, these atoms are represented by points. A lattice plane occupied by atoms is not actually flat. This may be seen for the lattice plane (100), (010) or (001) in Fig. 5.1c when the size of the spherical atoms is taken into account, and is even more marked for crystals of molecular compounds.
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Notes
- 1.
Application of the zonal equation leads to
$$\begin{array}{@{}c|c@{\qquad}c@{\qquad}c@{\qquad}c|c@{}}1 & 0 & 0 & 1 & 0 & 0\\0 & 1 & 1 & 0 & 1 & 1\\\multicolumn{6}{c}{\hbox{-------------------------------}}\\\multicolumn{6}{c}{[0 \quad \overline{1}\quad 1]}\end{array}\qquad\begin{array}{@{}c|c@{\qquad}c@{\qquad}c@{\qquad}c|c@{}}0 & 1 & 0 & 0 & 1 & 0\\1 & 0 & 1 & 1 & 0 & 1\\\multicolumn{6}{c}{\hbox{-------------------------------}}\\\multicolumn{6}{c}{[1 \quad 0\quad \overline{1}]}\end{array}\qquad\begin{array}{@{}c|c@{\qquad}c@{\qquad}c@{\qquad}c|c@{}}0 & \bar{1} & 1 & 0 & \bar{1} & 1\\1 & 0 & \bar{1} & 1 & 0 & \bar{1}\\\multicolumn{6}{c}{\hbox{-------------------------------}}\\\multicolumn{6}{c}{[1 \quad \bar{1} \quad 1]}\end{array} $$If the values of [uvw] are interchanged, the result is \(({\overline 1}\,{\overline 1}\,{\overline 1})\). Two zone circles intersect in two poles. In morphology, (hkl) and \(({\overline {\rm h}{\,}\overline {\rm k}{\,}\overline {\rm l}})\) represent two parallel faces, which are related to only one set of lattice planes, which may be designated as (hkl) or \(({\overline {\rm h}{\,}\overline {\rm k}{\,}\overline {\rm l}})\).
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© 2011 Springer-Verlag Berlin Heidelberg
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Borchardt-Ott, W. (2011). Morphology. In: Crystallography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16452-1_5
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DOI: https://doi.org/10.1007/978-3-642-16452-1_5
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