Crystal structure

“ 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 ”

“ Hence, at a series of ascending or descending temperatures, assuming the pressure to remain the ordinary atmospheric, these different types of homogeneous crystal structures will be most liable to be produced, each at its own particular temperature, for which stable equilibrium of that crystal structure occurs. ”

“ Flowing crystals are produced, however, by a relatively few substances of very complex molecular constitution, involving a large number of atoms in the molecule; they are mostly compounds of carbon, and in number possibly not one per cent. of the innumerable substances known to produce ordinary solid crystals. That the theory of crystal structure can eventually be made to include these few remarkable substances is highly probable, when many more facts have been accumulated. ”

“ It may be quite definitely stated, however, that there is a considerable amount of experimental evidence that the unit of the space-lattice of the crystal structure is certainly not more complex than the chemical molecule, the idea of an aggregation of chemical molecules to form a “physical molecule” acting as a structural unit having proved to be a misleading myth. ”

“ That crystalline structure is intimately related to chemical constitution will have been made abundantly plain during the course of this book. Yet in spite of the great work of Mitscherlich, essentially a chemist, and of a large amount of striking work which has been steadily accumulating during the last thirty years, with results of vital importance to chemistry, it is only at the eleventh hour that chemists are really awakening to the vast significance which crystal structure has for them. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ One of the remarkable attributes of a crystal is its ability to grow and act as a unit, as if it had a life of its own, despite the evident variety and great number of its parts. Take a crystal of alum, break off a corner and then immerse the broken mass in its mother liquor; at once the crystal will repair itself, new molecules building themselves into its structure as if they knew where to go. ”

“ A crystal possesses two further fundamental properties besides its style of architecture. The first is that it is bounded externally by plane faces, arranged on the definite geometrical plan just alluded to and mutually inclined at angles which are peculiar to the substance, and which are, therefore, absolutely constant for the same temperature and pressure. The second is that a crystal is essentially a homogeneous solid, its internal structure being similar throughout, in such wise that the arrangement about any one molecule is the same as about every other. ”

“ Even so may the particles of dissolved salt be endowed with a movement which enables them to enter into partnership and cohere, and so to build themselves into the orderly structure which makes up a crystal. And even so do crystals grow out of a mixed solution as a pure and homogeneous substance and reject the other materials which are dissolved in the liquid. ”

“ With these prefatory theoretical remarks, which are necessary in order that the experiments now to 187be described should be understood, we may proceed to consider a graduated series of experimental demonstrations which it is hoped will render clear some of the more important features of crystal structure which have been dealt with in previous chapters. Our principal agent will be polarised light, that is, light which has been reduced to vibration in a single plane by means of the well-known Nicol’s prism. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ This structure is, in fact, that of one of the 230 homogeneous structures ascertained by geometricians to be possible to crystals with plane faces. The first property, that of the planeness of the crystal faces, and their arrangement with geometrical symmetry, is actually determined by the second, that of specific homogeneity. For, as with human nature developed to its highest 7type, the external appearance is but the expression of the internal character. ”

“ Fig. 1.—Sand Grains with Quartz Crystals growing from them.
This marvellously everlasting power possessed by a crystal, of silent imperceptible growth, that is, of adding to its own regular structure further accretions of infinitesimal particles, the chemical molecules, of its own substance, is one of the strangest 4functions of solid matter, and one of the fundamental facts of science which is rarely realised, compared with many of the more obvious phenomena of nature.
A crystal in the ordinary sense of the word is solid matter in its most perfectly developed and organised form. ”

“ 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. ”

“ Whatever dead substance, unacceptant of this energy, comes in their way, is either rejected, or forced to take some beautiful subordinate form; the purity of the crystal remains unsullied, and every atom of it bright with coherent energy. Then the second condition is, that from the beginning of its whole structure, a fine crystal seems to have determined that it will be of a certain size and of a certain shape ”

“ 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 ”

“ 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. ”

“ Chemical phenomena, crystallization, magnetic and electrical phenomena show each in their way that the properties of atoms are not alike on opposite faces. Atoms combine to form molecules, and molecules arrange themselves in certain definite geometric forms such as cubes, tetrahedra, hexagonal prisms and stellate forms, with properties emphasized on certain faces or ends. Thus quartz will twist a ray of light in one direction or the other, depending upon the arrangement which may be known by the external form of the crystal. ”

“ 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. ”

“ We can only picture these liquids as consisting of particles which, while they are free to move in all directions, always continue to face the same way, like a group of dancers who in all their evolutions continue to face the audience, instead of turning as they move. When the mechanism which renders possible this remarkable behaviour is better understood, we may be sure that it will bring about a better understanding of the manner in which a solid crystal is constructed. ”

“ It is certainly a very remarkable fact in Natural History, discovered by these observations, that, when the molecules come together to form a crystal out of the watery solution, there should be so much more decided a bias in favour of continued homogeneousness of the assemblage than when, by cooling, they are allowed to settle from their agitations in a rigid, but nearly melting, solid. ”

“ LIQUID CRYSTALS. We have seen in the foregoing pages that a crystal is usually a solid, highly organised in a homogeneous manner, and, unless the symmetry be developed to its highest extent, the crystal then belonging to the cubic system, it is also in general anisotropic, that is, it exhibits double refraction. Section-plates of it, more or less thin according to the strength of the double refraction, exhibit colours in parallel polarised light, and show the phenomenon of a single optic axis, or of two optic axes, in convergent polarised light. ”

“ 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. ”

“ 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. ”

“ Hence, according to the configuration and the molecular forces of the particular crystalline molecule in natural crystallization, there may be necessarily, or almost necessarily, the twin, when growth proceeds simultaneously on the two sides: or the twin growth may be impossible, because the first occupation of the wider hollows on one side, may compel the continuity of the crystalline quality throughout, by leaving only the narrower hollows p q r free for occupation by molecules attaching themselves on the other side. ”