Crystal sphere

“ But the notion of material crystal spheres perpetually recurs in Greek astronomy after his day, and was universally held by the vulgar.
Consider, for an instant, what is involved in the theory of revolving material crystal shells. The stars are at an immense distance, all fixed to a crystal surface, which revolves once in twenty-four hours. The sun is situated on the surface of another shell, but it can not be in one fixed spot on the surface, for we see it rise and set at different points of our horizon at different times of the year. ”

“ As light at any spot in the world-space creates a central point, the nucleus of a comet, around which more of the mass of æther is constantly accumulating till it finally coagulates into the solid condition; so does the process of crystallization evoke some particular spot, point or nucleus in the water, wherein the crystallizing forces are excited, which attract the mass that is susceptible of fixation and fashion it into a crystal. The process of crystallization is a process of fixation, and with it also is furnished the theory of crystallization. ”

“ It becomes obvious 124that the atoms—in their stereometric positions in the molecule, being thus fixed in the solid crystal when the molecules set themselves rigidly in the regular organisation of the space-lattice—form the points of the regular point-system of the crystal structure, which determines to which of the thirty-two classes of symmetry the crystal shall belong. Any movement of the atoms in the crystal, other than that which accompanies change of temperature, and possibly change of pressure, is thus improbable ”

“ At the present day, crystals are considered as belonging to one or other of thirty-two classes, corresponding with these thirty-two types of symmetry, and are grouped in six systems. More recently, theories of crystal structure have attracted attention, and have been studied as purely geometrical problems of the homogeneous partitioning of space. ”

“ EFFECT OF THE SYMMETRY OF CRYSTALS ON THE PASSAGE OF LIGHT THROUGH THEM. QUARTZ, CALCITE, AND GYPSUM AS EXAMPLES. The action of transparent crystals on the rays of light which they transmit is a subject not only of the deepest interest, but also of the utmost importance. For it is immediately possible to detect a cubic crystal, and to discriminate between two groups, optically uniaxial and biaxial respectively, of the other six systems of symmetry, three systems going to each group, by this means alone. For a cubic crystal is singly refractive in all directions. ”

“ A given substance may, according to circumstances, crystallize in a variety of forms or combinations of forms, but, with very few exceptions, all crystals of a given substance exhibit the same kind or grade of symmetry. There are three kinds of crystal symmetry, namely, in respect to a plane, a line or axis, and a point or center. A plane of symmetry divides a crystal into halves in such a way that for every point on one side of the plane there is a corresponding point directly opposite on the other side. Crystals may be cut into halves along various surfaces which are not symmetry planes. ”

“ Every solid matter and thus the Terrestrial generally, is crystallized upon a small as well as large scale. There cannot be an atom that were not crystallized, not arranged according to central and polar forces. Every crystal is therefore, and especially by reason of the infinity of the subordinate poles, crystallized again upon an infinitely small scale, or in other words it consists of infinitely numerous crystals. Every lamella or every particle of the lamella of a crystal consists again of crystals. These are what are called the integral parts, properly integral forms of the crystal. ”

“ Water crystallises like quartz, in the trigonal system, its normal forms being the hexagonal prism and the rhombohedron. A slab of lake ice is generally a huge crystal plate perpendicular to the trigonal axis, or in the case of disturbed growth an interlacing mass of such crystals, all perpendicular to the optic axis, the axis of the hexagonal prism and of trigonal symmetry. ”

“ One of the most beautiful illustrations of cohesive attraction is seen in crystallization. In every instance in which substances pass into the form of a solid, they tend to assume regular shapes called crystals. Each material has its own characteristic form, so that a crystal is a type of a species in the mineral world, even as a plant or an animal is in the organic kingdom. A crystal is a substance bounded by plain surfaces and symmetrically arranged about imaginary lines called axes. The final form depends upon certain smaller forms in its interior structure. ”

“ They show that there are two modes of closely packing equal spheres, which give rise respectively to a cubic and a hexagonal crystal structure, the latter having a specific axial ratio of the vertical to the three equal equatorial horizontal axes; and that the chemical elements which are solids and crystallise, and the structural units of which can naturally be assumed to be equal spheres, being those of the similar atoms of the same chemical element, do practically all crystallise either in the cubic system or in the hexagonal system with the specific axial ratio indicated by them. ”

“ The space-lattice arrangement of the molecules in the crystal structure thus causes the crystal to follow the law of rational indices, by limiting and restricting the number of possible facial forms which can be developed. It also determines which one of the seven systems of symmetry or styles of crystal architecture the crystal shall adopt. ”

“ That it must be true follows from the fact that the crystal faces merely outwardly express in definite form the definite internal structure or arrangement of particles which have built up the crystal. In other words, the real structural symmetry of a crystal never varies no matter how much its geometric symmetry may vary. The practical application of the law of constancy of interfacial angles lies in the fact that in many cases a mineral may actually be identified merely by measuring the interfacial angles of its crystal form. ”

“ There are just 32 classes or combinations of the symmetry elements among crystals and just 232 definite crystal forms. Not only is it demonstrable that no more can exist, but actual experience with crystals of hundreds of species of minerals has never revealed any more. Obviously, then, symmetry furnishes us with a very scientific basis of classification of crystals, all of the 232 crystal forms constituting the 32 symmetry classes being in turn referable to seven fundamental crystal systems. ”

“ Crystalline form.—A crystal is bounded by plane surfaces symmetrically arranged with reference to certain imaginary lines passing through its centre and called axes. Crystals of the same species are always constant in the angles between like planes, while similar angles usually vary in different species; so that each species has its own peculiar form.
“Besides external symmetry of form, crystallization produces also regularity of internal structure, and often of fracture. This regularity of fracture, or tendency to break or cleave along certain planes, is called cleavage. ”

“ The nucleus is in fact determined by the shell of the crystal, namely by the94 polar axis. But inversely also the shell is determined by the nucleus, by the polar radii. A nucleus alone would be called a centre of a circle without circumference. Microscopic crystals therefore have at once the same perfected form as the largest in size. A crystal is an entire heavenly body; it is determined by central forces, which have, however, been roused and conducted by dualizing forces, forces of light. Everywhere do we meet with the same laws of the fixation of æther, upon a small as well as large scale. ”

“ While considerations of symmetry are a sufficient guide to the classification of crystals, they offer no explanation of the definite architecture of the crystal nor of the nature of the forces that cause the atoms or molecules to arrange themselves in such definite geometric patterns. We are inevitably led to the conclusion that the atoms of the crystal are arranged according to a definite system, which is characteristic of the particular crystalline form, and the unit of structure is repeated indefinitely with continued growth of the crystal. ”

“ Many other crystallized substances, very different from the Iceland spar, exhibit like it a certain single line or axis, round which their double refraction is exerted symmetrically, being insensible for rays parallel to that axis, and increasing with their inclination to it, so as to be strongest for those which are at right angles to the axis. Crystals thus constituted are called crystals with one axis. For instance, quartz, commonly called rock crystal, has an axis parallel to the edges of the hexahedral prism, under the form of which it is generally found. ”

“ Of course in Nature the corners are not cut, nor the edges beveled, but as a result of the interaction of the forces expressed by the axes and the distribution of the molecules, the molecules arrange themselves in a cube, octahedron, dodecahedron or combination of these basal forms.
Crystal formation
Crystals are formed in liquids as they cool or evaporate and can no longer hold the minerals in solution. Crystals start about a center or nucleus, and molecule by molecule, the orderly arrangement is increased and the crystal grows, there being no size which is characteristic. ”

“ My subject this evening is not the physical properties of crystals, not even their dynamics; it is merely the geometry of the structure—the arrangement of the molecules in the constitution of a crystal. Every crystal is a homogeneous assemblage of small bodies or molecules. ”

“ If the word crystallization were to be confined to its most proper sense, as it seems to have been formerly, it could only be applied to operations by which certain substances are disposed to pass from a fluid to a solid state, by the union of their parts, which so arrange themselves, that they form transparent and regularly-figured masses, like native crystal ”

“ For by such a Power they will range themselves uniformly, and without it they will float irregularly, and come together as irregularly. And since the Particles of Island-Crystal act all the same way upon the Rays of Light for causing the unusual Refraction, may it not be supposed that in the Formation of this Crystal, the Particles not only ranged themselves in rank and file for concreting in regular Figures, but also by some kind of polar Virtue turned their homogeneal Sides the same way.
The Parts of all homogeneal hard Bodies which fully touch one another, stick together very strongly. ”

“ We have just seen that in clinorhombic crystals the principal absorption directions of certain bands were completely different from the axis of optical elasticity of the crystal for the corresponding radiations. If we examine this anomaly, we perceive that the crystals manifesting these effects are complex bodies, formed of various matters, one, or sometimes several, of which absorb light and give each different absorption bands. ”

“ Or we may quote the words of P. von Groth (British Assoc. Rep., 1904) : “A crystal—considered as indefinitely extended—consists of n 585 interpenetrating regular point-systems, each of which is formed of similar atoms; each of these point-systems is built up from a number of interpenetrating space-lattices, each of the latter being formed from similar atoms occupying parallel positions. All the space-lattices of the combined system are geometrically identical, or are characterized by the same elementary parallelopipedon.” ”

“ No correlation then is apparent between the form of crystallisation and the chemical composition. But what we have to notice is that the physical properties of the crystallised substances with regard to light, heat, electricity, &c., are closely similar. Light and heat undulations, wherever they enter a crystal of the regular system, spread with equal rapidity in all directions, just as they would in a uniform fluid. Crystals of the regular system accordingly do not in any case exhibit the phenomena of double refraction, unless by mechanical compression we alter the conditions of elasticity. ”

“ But why they do not begin to coalesce as soon as the liquid is supersaturated it is difficult to say. We have to conceive the alum solution as made up of moving particles of alum and of water, and it may be that the particles are constantly coalescing into minute groups, but as rapidly being broken up again, until a moment arrives at which the alum particles are sufficiently dense to cohere permanently; but how they attract one another and arrange themselves into the wonderful structure which makes a crystal, of this we are entirely ignorant. ”

“ It is exhibited by crystals in which there is no centre of symmetry, and the axes of symmetry are uniterminal or polar in character, being associated with different faces on the crystal at their two ends. When a non-conducting crystal possessing this hemimorphic type of symmetry is subjected to changes of temperature a charge of positive electricity will be developed on the faces in the region of one end of the uniterminal axis, whilst the faces at the opposite end will be negatively charged. ”

“ In almost every flattish crystal of considerable dimension its natural joints are apparent when holding it between the eye and the light. If not, a slight blow will cause them to appear; and if by design or accident, the crystal fall flat upon the floor, it immediately breaks parallel with some of the planes of the primitive form and frequently even into the form itself, which is, a right prism with rhombic bases. It follows that a substance whose laminæ are held together by so slight a crystalline polarity, may be cleaved or split by various means ”