CRYSTALLOGRAPHY. With very few exceptions (mercury and water), minerals are limited to solid substances: that is. they are solid at the present temperature of the earth. In discussing their formation and character, we must, how ever, revert to the period when the mineral con stituents of the earth existed in a fluid or semi fluid state. When a homogeneous substance passes from a fluid to a solid condition, its par ticles mutually attract each other along certain definite lines and a solid is built up which shows a definite structural relation between all its in tegral parts. which relation finds expression in its outward form. Such a solid, formed from a nucleus by the piling of accretions front with out, is known as a crystal and is characterized by a regular polyhedral form, bounded by more or less smooth surfaces. A crystal is then the normal form of a mineral which has solidified under ideal conditions and, should its formation be uninterrupted by external agenvies, its ap pearance would he that of a symmetrical geomet ric solid with smooth faces and sharp edges and angles. Such are the ideal representations, which serve to illustrate the crystallization of mineral species and which are to be found in all text-books on the subject. But inasmuch as the ideal conditions mentioned above are of compara tively rare occurrence, it is far more eommon to find minerals in more or less distorted forms. (Sec Figs. 1 and 2.) Large and well-formed crys tals are, in general, produced by a slow process of crystallization. whereas a rapid cooling or concentration of a soliition tends to form aggregates often resembling the forms of animate nature: such are the frost patterns which form on window panes, the coral-like forms of calcium carbonate to lie found in some caves, and many other imitative forms deseribed in the terminology of mineralogy. When indi vidual crystals are entirely lacking. the mineral is said to be massive, although its structure as determined by optical and other methods may be distinctly crystalline.
Regarding the nature of the crystalline of accretion, there is at present verl little knowledge. They :ire without• doubt 1•xtrenn ly minute and may possibly consist of a number of chemical molecules. \Vhatever may he the size or shape 1/1 the crystal units or crystal mole cules, it is sufficient tor the purpose of discussion to regard them as points. A fuller discussion of this subject will he found under CuvmtsraY. The crystal molecules of any chemical substance crystallizing under given conditions are believed to be identical in size and shape. They are never in contact with each other, hut arc held in equi librium by attractive and repellent forces acting along lines which differ for each type of crystal molecule. A crystal molecule having these lines of crystallizing force at right angles, as shown in Fig. 3, would attract like which would arrange themselves as shown in Fig. 4. The theoretical grouping of molecules has been dis cussed by Solmcke, Fedorow, Schfmrlies, and Bar low, who have developed 23(1 possible groupings.
These, however, divide themselves into 32 dis tinct groups identical with the 32 groups men tioned under CRYSTALLOURAPH Y.
If we assume the molecules of a substance to be grouped as shown in Fig. 5. it will be readily seen that the lines of minimum cohesion will be art and bit rather than min, because the former planes are further separated from the next adjacent parallel plane. This explains in a meas ure the fact that crystallized substances often tend to break or cleave parallel to a primary crystallographic face. Assuming a crystal mole cule of any given mineral to be held in equi librium by forces acting in definite directions, it will be readily seen that the crystal built up from accretions of such molecules will, of neces sity, present faces which are symmetrically dis posed with respect to those lines of crystallizing force. Thus we have as a fundamental law of crystallization the principle that a mineral can only crystallize in forms whose symmetry is referable to one of the 32 groups mentioned in the foregoing paragraph. This is known as the law of symmetry. The number of planes possible from the grouping together of crystal molecules of a substance is invariably greater than the number occurring on any given crystal; and modi fying planes are common, often running to great complexity. and under unusual eonditions pre dominating over the commoner types. Ifence we frequently find great variety of form in crystals of the same substance, as is the case with the min eral calcite (q.v.). It should, however, be noted that crystals of a mineral from a certain loeality, which are presumably formed under the same conditions. show a marked similarity of type and are readily distinguishable from those of the same mineral front a different locality. This variation in type. which is known as crystal habit. is particularly noticeable in large and widely dis tributed species. Certain mineral species exhibit a tendency to join two crystals or two halves of the same crystal in such a manner that some crystallographic plane or axis is common to hot h. This is ordinarily (listinguishod by angles. is known as clwnnfmg. See FiV.
It will he readily seen from the above that an accurate knowledge of the occurring crystal forms is of primary importance in the investigation of airy umin•ral species. The identification id the faces of the crystal, which is often attended with considerable diflieulty, is accomplished by meas uring the interfacial angles by means of an in strument called a gonionieter (q.v.) and compar ing this with the calculated relations obtained from simple mathematical formulas. based on spherical rigonometry. The optical properties of minerals as well as their presence and relations in rocks, are determined by means of the petro graphic microscope. (See NicnoscoeE.) For exhaustive study the line of physical char acters, elaborate and accurate apparatus is re quired, whit, a I ppol 0101111c:11 laboratory is almost indispensable to the mineralogieal in vestigato•.