Earth Materials. John O'Brien
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Название: Earth Materials

Автор: John O'Brien

Издательство: John Wiley & Sons Limited

Жанр: География

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isbn: 9781119512219

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СКАЧАТЬ of the mineral's three‐dimensional motif. That the crystal classes were originally defined on the basis of the external symmetry of mineral crystals is another example of the fact that the external symmetry of minerals reflects the internal symmetry of their constituents. The 32 crystal classes belong to 6 (or 7) crystal systems, each with its own characteristic symmetry. Table 4.3 summarizes the crystal systems, the symmetries of the 32 space point groups or crystal classes and their names, which are based on general crystal forms. It is important to remember that a crystal cannot possess more symmetry than that of the motifs of which it is composed. However, it can possess less, depending on how the motifs are arranged and how the crystal developed during growth.

      4.4.2 Bravais lattices, unit cells, and crystal systems

      As noted earlier, any motif can be represented by a point called a node. Nodes, and the motifs they represent, can also be translated in three directions (ta, tb, and tc) to produce three‐dimensional space point lattices and unit cells (Figure 4.10).

      Unit cells are the three‐dimensional analogs of unit meshes. A unit cell is a parallelepiped whose edge lengths and volume are defined by the three unit translation vectors (ta, tb, and tc). The unit cell is the smallest unit that contains all the information necessary to reproduce the mineral by three‐dimensional symmetry operations. Unit cells may be primitive (P), in which case they have nodes only at their corners and a total content of one node (=one motif). Non‐primitive cells are multiple because they contain extra nodes in one or more faces (A, B, C or F) or in their centers (I) and possess a total unit cell content of more than one node or motif.

System Crystal class Class symmetry Total symmetry
Isometric Hexoctahedral 4 slash normal m ModifyingAbove 32 With bar slash normal m 3A4, 4 normal upper A 3 overbar, 6A2, 9m
Hextetrahedral ModifyingAbove 43 With bar normal m 3 normal upper A 4 overbar, 4A3, 6m
Gyroidal 432 3A4, 4A3, 6A2
Diploidal 2 slash normal m ModifyingAbove 3 With bar 3A2, 3m, 4 normal upper A 3 overbar
Tetaroidal 23 3A2, 4A3
Tetragonal Ditetragonal–dipyramidal 4/m2/m2/m i, 1A4, 4A2, 5m
Tetragonal–scalenohedral ModifyingAbove 42 With bar normal m 1 normal upper A 4 overbar, 2A2, 2m
Ditetragonal–pyramidal 4mm 1A4, 4m
Tetragonal–trapezohedral 422 1A4, 4A2
Tetragonal–dipyramidal 4/m i, 1A4, 1m
Tetragonal–disphenoidal ModifyingAbove 4 With bar normal upper A 4 overbar
Tetragonal–pyramidal 4 1A4
Hexagonal(hexagonal) Dihexagonal–dipyramidal 6/m2/m2/m i, 1A6, 6A2, 7m
Ditrigonal–dipyramidal 6m2 СКАЧАТЬ