Page:EB1911 - Volume 07.djvu/600

Rh Examples are nickel sulphate (NiSO4·6H2O), guanidine carbonate ((CH5N3)2H2CO3), strychnine sulphate ((C21H22N2O2)2·H2SO4·6H2O).



(Bisphenoidal-tetartohedral).

Here there is only a single dyad axis of symmetry, which coincides with the principal axis. All the forms, except the prisms and basal pinacoid, are sphenoids. Crystals possessing this type of symmetry have not yet been observed.

'''3. ORTHORHOMBIC SYSTEM'''

(Rhombic; Prismatic; Trimetric).

In this system the three crystallographic axes are all at right angles, but they are of different lengths and not interchangeable. The parameters, or axial ratios, are a : b : c, these referring to the axes OX, OY and OZ respectively. The choice of a vertical axis, OZ = c, is arbitrary, and it is customary to place the longer of the two horizontal axes from left to right (OY = b) and take it as unity: this is called the “macro-axis” or “macro-diagonal” (from, long), whilst the shorter horizontal axis (OX = a) is called the “brachy-axis” or “brachy-diagonal” (from, short). The axial ratios are constant for crystals of any one substance and are characteristic of it; for example, in barytes (BaSO4), a : b : c = 0.8152 : 1 : 1.3136; in anglesite (PbSO4), a : b : c = 0.7852: 1 : 1.2894; in cerussite (PbCO3), a : b : c = 0.6100 : 1 : 0.7230.

There are three symmetry-classes in this system:—



(Holohedral; Bipyramidal).

Here there are three dissimilar dyad axes of symmetry, each coinciding with a crystallographic axis; perpendicular to them are three dissimilar planes of symmetry; there is also a centre of symmetry. There are seven kinds of simple forms:—

Bipyramid (figs. 54 and 55). This is the general form and is bounded by eight scalene triangles; the indices are {111}, {211}, {221}, {112}, {321}, {123}, &c., or in general {hkl}. The crystallographic axes join opposite corners of these pyramids and in the fundamental bipyramid {111} the parametral plane has the intercepts a : b : c. This is the only closed form in this class; the others are open forms and can exist only in combination. Sulphur often crystallizes in simple bipyramids.

Prism. This consists of four faces parallel to the vertical axis and intercepting the horizontal axes in the lengths a and b or in any multiples of these; the indices are therefore {110}, {210}, {120} or {hko}.

Macro-prism. This consists of four faces parallel to the macro-axis, and has the indices {101}, {201} ... or {hol}.

Brachy-prism. This consists of four faces parallel to the brachy-axis, and has the indices {011}, {021} ... {okl}. The macro- and brachy-prisms are often called “domes.”

Basal pinacoid, consisting of a pair of parallel faces perpendicular to the vertical axis; the indices are {001}. The macro-pinacoid {100} and the brachy-pinacoid {010} each consist of a pair of parallel faces respectively parallel to the macro- and the brachy-axis.

Figs. 56-58 show combinations of these six open forms, and fig. 59 a combination of the macro-pinacoid (a), brachy-pinacoid (b), a prism (m), a macro-prism (d), a brachy-prism (k), and a bipyramid (u).

Examples of substances crystallizing in this class are extremely numerous; amongst minerals are sulphur, stibnite, cerussite, chrysoberyl, topaz, olivine, nitre, barytes, columbite and many others; and amongst artificial products iodine, potassium permanganate, potassium sulphate, benzene, barium formate, &c.



(Hemimorphic).

Here there is only one dyad axis in which two planes of symmetry intersect. The crystals are usually so placed that the dyad axis coincides with the vertical crystallographic axis, and the planes of symmetry are also vertical.

The pyramid {hkl} has only four faces at one end or other of the crystal. The macro-prism and the brachy-prism of the last class are here represented by the macro-dome and brachy-dome respectively, so called because of the resemblance of the pair of equally sloped faces to the roof of a house. The form {001} is a single plane at the top of the crystal, and is called a “pedion”; the parallel pedion {00 1 }, if present at the lower end of the crystal, constitutes a different form. The prisms {hko} and the macro- and brachy-pinacoids are geometrically the same in this class as in the last. Crystals of this class are therefore differently developed at the two ends and are said to be “hemimorphic.”

Fig. 60 shows a crystal of the mineral hemimorphite (H2Zn2SiO5) which is a combination of the brachy-pinacoid {010} and a prism, with the pedion (001), two brachy-domes and two macro-domes at the upper end, and a pyramid at the lower end. Examples of other substances belonging to this class are struvite (NH4MgPO4·6H2O), bertrandite (H2Be4Si2O9), resorcin, and picric acid.



(Hemihedral).

Here there are three dyad axes, but no planes of symmetry and no centre of symmetry. The general form {hkl} is a bisphenoid (fig. 61) bounded by four scalene triangles. The other simple forms are geometrically the same as in the holosymmetric class.

Examples: epsomite (Epsom salts, MgSO4·7H2O), goslarite (ZnSO4·7H2O), silver nitrate, sodium potassium dextro-tartrate (seignette salt, NaKC4H4O6·4H2O), potassium antimonyl dextro-tartrate (tartar-emetic, K(SbO)C4H4O6), and asparagine (C4H8N2O8·H2O).