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ASYMMETRIC

Online Encyclopedia
Originally appearing in Volume V07, Page 580 of the 1911 Encyclopedia Britannica.
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ASYMMETRIC CLASS (Hemihedral, Pediad). Crystals of this class are devoid of any elements of symmetry. All the forms are pedions, each consisting of a single plane; FtG. 65.-Crystal of they are thus hemihedral with respect to Axinite. crystals of the last class. Although there is a total absence of symmetry, yet the faces are arranged in zones on the crystals. Examples are calcium thiosulphate (CaS2O3.6H20) and hydrogen strontium dextro-tartrate ((C4H40EH)2Sr•5H2O) ; there is no example amongst minerals. 6. HEXAGONAL SYSTEM Crystals of this system are characterized by the presence of a single axis of either triad or hexad symmetry, which is spoken of as the " principal " or " morphological " axis. Those with a triad axis are grouped together in the rhombohedral or trigonal division, and those with a hexad axis in the hexagonal division. By some authors these two divisions are treated as separate systems; or again the rhombohedral forms may be considered as hemihedral developments of the hexagonal. On the other hand, hexagonal forms may be considered as a combination of two rhombohedral forms. Owing to the peculiarities of symmetry associated with a single triad or hexad axis, the crystallographic axes of reference are different in this system from those used in the five other systems of crystals. Two methods of axial representation are in common use; rhonlbohedral axes being usually used for crystals of the rhombohedral division, and hexagonal axes for those of the hexagonal division; though sometimes either one or the other set is employed in both divisions. Rhombohedral axes are taken parallel to the three sets of edges of a rhombohedron (fig. 66). They are inclined to one another at equal oblique angles, and they are all equally inclined to the principal axis; further, they are all of equal length and are interchangeable. With such a set of axes there can be no statement of an axial ratio, but the angle between the axes (or some other angle which may be calculated from this) may be given as a constant of the substance. Thus in calcite the rhombohedral angle (the angle between two faces of the fundamental rhombohedron) is 74° 55', or the angle between the normal to a face of this rhombohedron and the principal axis is 446,, Hexagonal axes are four in number, viz. a vertical axis coinciding with the principal axis of the crystal, and three horizontal axes inclined to one another at 6o° in a plane perpendicular to the principal axis. The three horizontal axes, which are taken either parallel or perpendicular to the faces of a hexagonal prism (fig. 71) or the edge of a hexagonal bipyramid (fig. 70), are equal in length (a) but the vertical axis is of a different length (c). The indices of planes referred to such a set of axes are four in number; they are written as {hikl{, the first three (h+i+k=o) referring to the horizontal axes and the last to the vertical axis. The ratio a : c of the parameters, or the axial ratio, is characteristic of all the crystals of the same substance. Thus for beryl (including emerald) a : c = I : 0'4989 (often written c =0.4989) ; for zinc c =1.3564. Rhombohedral Division. In the rhombohedral or trigonal division of the hexagonal system there are seven symmetry-classes, all of which possess a single triad axis of symmetry.
End of Article: ASYMMETRIC
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