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Crystalline substances such as minerals have characteristic planar features that include: (1) crystal faces that develop during growth, (2) cleavage surfaces that develop during breakage, and (3) crystal lattice planes that reflect X‐rays and other types of electromagnetic radiation. All these types of planes possess a number of shared properties.

Figure 4.17 (a) Common open forms: pedions, pinacoids, domes, sphenoids, and pyramids. (b) Different types of prisms that characterize the orthorhombic, trigonal, tetragonal, and hexagonal systems. The illustrated prisms are bounded by pinacoids at the top and bottom.

Source: Klein and Hurlbut (1985). © John Wiley & Sons.

Each type of plane is part of a large set of parallel lattice planes of which it is representative. As a mineral with a particular crystal form grows freely it may be bounded by a sequence of planar faces. When it stops growing, it is bounded by crystal faces that are parallel to many other lattice planes that bounded the mineral as it grew over time. When a mineral cleaves, it breaks along a specific set of parallel planes of relative weakness, but these cleavage planes are parallel to large numbers of planes of weakness or potential cleavage surfaces in the mineral structure along which the mineral did not happen to rupture. When X‐rays are reflected from a reflecting plane, they are reflected simultaneously from all the planes in the crystal that are parallel to one another to produce a “reflection peak” that is characteristic of the mineral and can be used to identify it.

In addition, any set of parallel planes in a crystal is ideally characterized by a particular molecular content; all the parallel planes in the set possess closely similar molecular units, spacing, and arrangement. A molecular image of one of these planes is sufficient to depict the general molecular content of all the planes that are parallel to it. All planes in a set of parallel planes have the same general spatial relationship to the three crystallographic axes. This means that they can be collectively identified in terms of their spatial relationship to the three crystallographic axes. This is true for crystal faces, for cleavage surfaces, for X‐ray reflecting planes or for any set of parallel crystallographic planes that we wish to identify. A universally utilized language has evolved that uses the relationship between the planar features in minerals and the crystallographic axes to identify different sets of planes. A discussion of this language and its use follows.

Figure 4.18 depicts several representative crystal planes with different relationships to the three crystallographic axes. Some crystal planes, or sets of parallel planes, intersect one crystallographic axis and are parallel to the other two (Figure 4.18a, b). Alternatively, a set of crystal planes may intersect two crystallographic axes and be parallel to the third (Figure 4.18c, d). Still other sets of planes intersect all three crystallographic axes (Figure 4.18e, f). No other possibilities exist in Euclidean space; sets of planes in crystalline substances must intersect one, two, or three axes and be parallel to those they do not intersect.

Figure 4.18 Representative crystal faces that cut one, two or three crystallographic axes. See text for further discussion of parts (a–f).

Of course, some sets of planes or their projections intersect the positive ends of crystallographic axes (Figure 4.18b, c, and e). Others, with different spatial orientations with respect to the axes, intersect the negative ends of crystallographic axes (Figure 4.18a). Still others, with yet different orientations, intersect the positive ends of one or more axes and the negative ends of other crystallographic axes (Figure 4.18d, f). Given the myriad possibilities, a simple language is needed that allows one to visualize and communicate to others the relationship and orientation of any set of crystal planes to the crystallographic axes. The language for identifying and describing crystallographic planes involves the use of symbols called Miller indices, which has been employed since the 1830s and is explained in the following sections.