In this system two of the angles between the crystallographic axes are right angles, but the third angle is oblique, and the axes are of unequal lengths. The axis which is perpendicular to the other two is taken as OY = b (fig. 62) and is called the ortho-axis or ortho-diagonal. The choice of the other two axes is arbitrary; the vertical axis (OZ = c) is usually taken parallel to the edges of a prominently developed prismatic zone, and the clino-axis or clino-diagonal (OX = a) parallel to the zone-axis of some other prominent zone on the crystal. The acute angle between the axes OX and OZ is usually denoted as β, and it is necessary to know its magnitude, in addition to the axial ratios a : b : c, before the crystal is completely determined. As in other systems, except the cubic, these elements, a : b : c and β, are characteristic of the substance. Thus for gypsum a : b : c = 0.6899 : 1 : 0.4124; β = 80° 42′; for orthoclase a : b : c = 0.6585 : 1 : 0.5554; β = 63° 57′; and for cane-sugar a : b : c = 1.2595 : 1 : 0.8782; β = 76° 30′.
Holosymmetric Class
Here there is a single plane of symmetry perpendicular to which is a dyad axis; there is also a centre of symmetry. The dyad axis coincides with the ortho-axis OY, and the vertical axis OZ and the clino-axis OX lie in the plane of symmetry.
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| Fig. 62.—Monoclinic Axes and Hemi-pyramid. |
Fig. 63.—Crystal of Augite. |
All the forms are open, being either pinacoids or prisms; the former consisting of a pair of parallel faces, and the latter of four faces intersecting in parallel edges and with a rhombic cross-section. The pair of faces parallel to the plane of symmetry is distinguished as the “clino-pinacoid” and has the indices {010}. The other pinacoids are all perpendicular to the plane of symmetry (and parallel to the ortho-axis); the one parallel to the vertical axis is called the “ortho-pinacoid” {100}, whilst that parallel to the clino-axis is the “basal pinacoid” {001}; pinacoids not parallel to the arbitrarily chosen clino- and vertical axes may have the indices {101}, {201}, {102} ... {hol} or {101}, {201}, {102} ... {hol}, according to whether they lie in the obtuse or the acute axial angle. Of the prisms, those with edges (zone-axis) parallel to the clino-axis, and having indices {011}, {021}, {012} ... {okl}, are called “clino-prisms”; those with edges parallel to the vertical axis, and with the indices {110}, {210}, {120} ... {hko}, are called simply “prisms.” Prisms with edges parallel to neither of the axes OX and OY have the indices {111}, {221}, {211}, {321} ... {hkl} or {111} ... {hkl}, and are usually called “hemi-pyramids” (fig. 62); they are distinguished as negative or positive according to whether they lie in the obtuse or the acute axial angle β.
Fig. 63 represents a crystal of augite bounded by the clino-pinacoid (l), the ortho-pinacoid (r), a prism (M), and a hemi-pyramid (s).
The substances which crystallize in this class are extremely numerous: amongst minerals are gypsum, orthoclase, the amphiboles, pyroxenes and micas, epidote, monazite, realgar, borax, mirabilite (Na2SO4·10H2O), melanterite (FeSO4·7H2O) and many others; amongst artificial products are monoclinic sulphur, barium chloride (BaCl2·2H2O), potassium chlorate, potassium ferrocyanide (K4Fe(CN)6·3H2O), oxalic acid (C2O4H2·2H2O), sodium acetate (NaC2H3O2·3H2O) and naphthalene.
Hemimorphic Class
In this class the only element of symmetry is a single dyad axis, which is polar in character, being dissimilar at the two ends.
The form {010} perpendicular to the axis of symmetry consists of a single plane or pedion; the parallel face is dissimilar in character and belongs to the pedion {010}. The pinacoids {100}, {001}, {hol} and {hol} parallel to the axis of symmetry are geometrically the same in this class as in the holosymmetric class. The remaining forms consist each of only two planes on the same side of the axial plane XOZ and equally inclined to the dyad axis (e.g. in fig. 62 the two planes XYZ and XYZ); such a wedge-shaped form is sometimes called a sphenoid.
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| Fig. 64.—Enantiomorphous Crystals of Tartaric Acid. |
Fig. 64 shows two crystals of tartaric acid, a a right-handed crystal of dextro-tartaric acid, and b a left-handed crystal of laevo-tartaric acid. The two crystals are enantiomorphous, i.e. although they have the same interfacial angles they are not superposable, one being the mirror image of the other. Other examples are potassium dextro-tartrate, cane-sugar, milk-sugar, quercite, lithium sulphate (Li2SO4·H2O); amongst minerals the only example is the hydrocarbon fichtelite (C5H8).
Clinohedral Class
Crystals of this class are symmetrical only with respect to a single plane. The only form which is here geometrically the same as in the holosymmetric class is the clino-pinacoid {010}. The forms perpendicular to the plane of symmetry are all pedions, consisting of single planes with the indices {100}, {100}, {001}, {001}, {hol}, &c. The remaining forms, {hko}, {okl} and {hkl}, are domes or “gonioids” (γωνία, an angle, and εἶδος, form), consisting of two planes equally inclined to the plane of symmetry.
Examples are potassium tetrathionate (K2S4O6), hydrogen trisodium hypophosphate (HNa3P2O6·9H2O); and amongst minerals, clinohedrite (H2ZnCaSiO4) and scolectite.
In the anorthic (from ἀν, privative, and ὀρθός, right) or triclinic system none of the three crystallographic axes are at right angles, and they are all of unequal lengths. In addition to the parameters a : b : c, it is necessary to know the angles, α, β, and γ, between the axes. In anorthite, for example, these elements are a : b : c = 0.6347 : 1 : 0.5501; α = 93° 13′, β = 115° 55′, γ = 91° 12′.
Holosymmetric Class
Here there is only a centre of symmetry. All the forms are pinacoids, each consisting of only two parallel faces. The indices of the three pinacoids parallel to the axial planes are {100}, {010} and {001}; those of pinacoids parallel to only one axis are {hko}, {hol} and {okl}; and the general form is {hkl}.
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| Fig. 65.—Crystal of Axinite. |
Several minerals crystallize in this class; for example, the plagioclastic felspars, microcline, axinite (fig. 65), cyanite, amblygonite, chalcanthite (CuSO4·5H2O), sassolite (H3BO3); among artificial substances are potassium bichromate, racemic acid (C4H6O6·2H2O), dibrom-para-nitrophenol, &c.
Asymmetric Class
Crystals of this class are devoid of any elements of symmetry. All the forms are pedions, each consisting of a single plane; they are thus hemihedral with respect to 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 (CaS2O3·6H2O) and hydrogen strontium dextro-tartrate ((C4H4O6H)2Sr·5H2O); there is no example amongst minerals.
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
- ↑ From μόνος, single, and κλίειν, to incline, since one axis is inclined to the plane of the other two axes, which are at right angles.
