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Les diagrammes suivants illustrent la mdthode. 1 2 3 1 2 3 4 5 6 I I OIl''2r"ST^A.LS- BY W. F. Ferrier, B.A. Sc, F.G.S., Lithologist to the Geological Survey of Cana(ia. Ottawa, 1895. I H Reprinled fro.ii 'I'Hii Ottawa Natukalist, Vol. IX, No. f. CRYSTALS.* By W. F. Fkrkiek, B.A.Sc, F.(;..S. Lithologist to the Geological Survey of Canada. I have nothing original to offer you on thii subject, nor are my remarks intended to constitute a lecture on crystallograpliy, but merely to bring to your notice some interesting facts with regard to those won- derful forms which we call crystals, and more especially to trace out the progress made in the study of them since the earliest times. The sub- ject is so vast that it will only be possible for me to call attention to some of the more prominent and interesting facts, which constitute, as it were, the milestones along the road of our knowledge of the subject. At the outset we are confronted with the question " What is a crystal ? " So many definitions have been given that it is somewhat difficult to select one which is expressed in simple terms and at the same time is comprehensive and accurate. E. S. Dana says : — "Structure in Inorganic nature is a result of mathematical symmetry in the action of cohesive attraction. The forms produced are regular solids called crystals ; whence morphology is, in the Inorganic kingdom, called crvstallologv. It is the science of structure in this kingdom oi nature." He subdivides the subject as follows : — Crystallology . Crystallography | '•■^^^'"f. ^^ ^^^""^^ '■^^"'^*"g ^--^"^ 1 ^ & 1 ^ I crystallization. j I treating of the methods of making ^ Crystallogeny J crystals, and the theories of their { origin. (Read before the Ottawa Field Naturalists' Club, Dec. 20th. 1894.) a 118 c n) THK OlTAWA NATl'UALISr, Naumann's definition of a crystal is i very concise and satisfactory one. It is this : — " Any rigid inorganic body possessing an essentia' and original (primitive) more or less regular pulyhedric (many-sided) form jv/tic/i is directly connected with its physv-al properties'^ This latter clause of thj definition is very important as explaining why cleavage fragments, pseudomorphs &c. are not to be termed crystals. To the question why calcite, for instance, should assume one form of crystal, and garnet another, science ran return no answer, but must content itself with determining and describing these curious and multi- farious forms. 'I'he word "crystal" is derived from the (Ireek word ";f/JJ-'0'ra\Ao^" meaning " ice ". The ancients first gave this name to the variety of quartz which we call " Rock-crystal, " because, from its transparency, its usual freedom from color, and the way in which it was found to en- close other bodies, they imigined it had been formed by the action of intense cold on water, which thus becime extraordinarily hardened. The name was later transferred to jjure transparent stones, such as were after used for seals and engraved gems. Some of the old writings on this subject are very amusing. Albertus Magnus, in the middle of the 13th century, gravely relates how the intense cold on the summits of s )me lofty mountains dries the ice so thoroughly that it becomes crystal. Even as late as 1672 the learned Robert Boyle goes into a long dissertation to prove that crystal could not be ice, adducing as two of the strongest proofs of this, first, the fact that ice floats on water and crystal does not, and, secondly, that Mada- gascar, India, and other countries in the torrid zone, abound in crystal, and he could not believe that any ice, however hard, could withstand the heat of those countries. Later the term " crystal " was applied to any mineral naturally limited by plane faces. It was not until 1669 that any important discovery regarding the properties of crystals was made, and then it was that Nicolaus Steno, a Danish physician, discovered for the first time the constancy of angles in Rock-crystal. But it is generally admitted that Steno himself did not fully grasp the importance of his dis- Crystal^, 119 covery, which was more a deduction from the mathematical form of the particular body he observed than a broad generalization from a series of observationsofdifferent bodies Itmust bebornein mind that the ancients knew and had described crystals of certain minerals as having a rstuinpfufig= truncation, 2.itschar/un.' = bevel- ling, Z«i/>/VsM«^=acumination, in speaking of similar variations or changes from the fundamental form of crystal, but it is thought that Delisle did not knowofthis at the time he wrote. Uelisleset to work to determine the primitive forms of all substances, which work was greatly facilitated by the invention at this time of the goniometer. This instrument was invented by a Frenchman named Carangeau, who prepared the clay-models used by Delisle to illustrate his theory. It was designed for the measurement of solid angles, particularly those of crystals, and was of the form known as the common or contact goniotneter. A much more elaborate and accurate instrument for the same pur- pose is the re/luting goniometer of Dr. WoUaston, devised by hirh in 1809, of which several elaborate modifications are now employed by crystallo- graphers. Carangeau's goniometer consisted essentially of a graduated arc and two moveable arms. Its form may be learned by referring to the figures Riven in almost all text-books of mineralogy. The great Crystals. 121 objection to it is that it is impossible to employ it in the case of very small crystals, whilst the reflecting goniometer may be used to measure accurately the angles of crystals only „;,th of an inch in size. Rome Delisle, as the result of his researches, came to the conclusion that the primitive forms of all known substances were only six in number, namely : — 1. The cube. 2. The regular octahedron. 3. The regular tetrahedron. 4. 'llie rhombohedron. 5. The octahedron with a rhombic base. ^1. The double six-sided pyramid. These were announced in his treatise on Crystallography published in 1783, in which he figures no less than 500 distinct forms of crystals. The weak point of his .ory was the fact that the whole series of forms of any one substance could be derived not only from the primitive form, but from almost any of the series, thus rendering it impossible to lay d jwn an exact rule as to which of these was to be regarded as the true primitive form. He was guided in his choice by the largeness of development and frequency of occurrence of particular faces and the simplicity of the figure they formed. Thus he chose both cube and regular octahedron, although, as we now know, these forms really belong to one and the same series and may be derived the one from the other. Many of his contemporaries doubted not only his choice of primitive forms but the very existence of the series, and Buffon's objections, as set forth in his " Natural History of Minerals " published ten years later (1783), bore testimony to the difficulty of the important step taken by Rome Delisle. It was far from being obvious that all the crystalline forms of a mineral belong to one series. As early as 1773, Bergman, a celebrated Swedish chemist, shewed in his writings that he recognized the importance of cleavage, and by it he tried to explain the relationship of the various forms assumed by the same mineral, which had so interested and puzzled Delisle, who, however, assigned little or no importance to cleavage, speaking, as he does in the preface to his treatise mentioned above, most contempt- n 1 00 1 aJ W TiiK Ottawa Naturalist. uously oi the "/'n'se-m's/aux" or "crystalloclastes." lUit Ber^jituan did not proceed far enough, and it remiined for another to fully develop the theory of the structure of crystals i.s indicated by their cleavage. In 1784 the Abbd Haiiy made his remarkable discovery, which, like Newton's immortal one, was the result of a mere accident. A six-sided prism of calcite (carbonate of lime) had been broken from a large grou[) in the cabinet of M. Defrance, and he noticed that the fractures were smooth and polished, not irregular as in the case of broken glass. He then commenced splitting-up the crystal with his knife and finally reduced the six-sided prism to a rhombnhedron. E.xtending his experiment to other minerals Haiiy arrived at the con elusion that the kernel obtained from a mineral by cleavage was to be regarded as k^ true primitive form. E. S. Dana defines cleavage as the tendency to break or cleave along certain planes due to regularity of internal structure and fracture, produced, in addition to external symmetr) of form, by crystallization; and he states two principles : — (i) In any species, the direction in which cleavage takes place is always parallel to some plane which either actually occurs in the crystals or may ex'st there in accordance with certain general laws. (2) Cleavage is uniform as to ease parallel to all like planes. That is to say that if it may be obtained parallel to oneoilhe faces of a regular octahedron, for instance, it may be obtained with the same facility parallel to each of the remaining octahedral faces. Haiiy's primitive forms were ten in number, four more than those of Romede risle. They were : — 1. The cube. 2. The regular octahedron. 3. The regular tetrahedron. 4. 1 ne rhombic dodecahedron. 5. The rhombohedron, obtuse or acute. 6. The octahedron, with square, rectangular, or rhombic base. 7. The four-sided prism, with edges at right angles to the base, the base being either a square, a rectangle, a rhomb, or merely a parallelo- gram. Crvstals. 1 -'.{ 8 The four-siJ(.(J prism, with edges inclined obliquely to the base, 'he hase being either a recuuigle, a rhomb, or merely a parallelogram. y. The regular six-sided prism, lo. The double six-sided pyramid. He also grouped all these forms in a general way thus; — 1. Figures bounded by parallelograms. 2. Figures bounded by eight triangles. 3. The regular tetrahedron. 4. The regular six-sided prism. 5. I'he double six-sided pyramid. Haiiy was let by his study of cleavage to frame a theory re,j;ardimj the s'n'dun of crystals and to discover a second great law governing their formatior, namely th • one \ 'ch Cinnects the secondary f;.:es with these of the primitive form. fie found thjt the kernels which he obtained by cleavage could be split-up,apparentiy indefinitely, into smaller fragments of the same shape, and, not believing that this process could go on to infinity, came to the conclusion that every crystal of the same substance could, theoretically at least, be cleaved into mmute bricks of a definite size and shape though two small to be separately visible, and therefore that with these bricks a crystal possessing any of the forms in which the particular mineral occurs, might be built up. As the simplest illustration take the case where the bricks are little cubes The conditions to be produced are that the built-up crystal must possess cleavage, and at all its parts the faces obtainable by cleavage are to have the same directions, also that its outer surface must consist of a series of plane faces. A cube composed of these h'ttle bricks could be increased in- definitely in size by adding layers of these bricks to each of its faces. Conversely, it might be decreased in size by taking away the layers. But suppose that the decrease takes place by the regular subtraction of one or several ranges of bricks in each successive layer ; theory, by calculating the number of these ranges required for a particular form, can represent all known forms of crystals and a^so indicate/^.fi//;;^ forms for a particular mineral which may not yet have been observed in the 124 The Ottawa Naturalist. natural cryptals. Figs. 3 and 4 will serve to illustrate what we have just been discussing. Ai "I^'II-TI A ^ /^ ^ A /jT jr Fiy:. 3. Fi^r. 4. Fig. 3 illustrates a cuDe composed of little cubicil bricks, some rows of which are removed to shew the resulting step like arrangement of the layers. All the edges of the steps lie m one plane, as seen in Fig. 4. If we remember that the little bricks are supposed to be so minute as to be separately invisible, it will be seen that the steps will ajipear to lie wholly in the plane, which thus forms a secondary face equally in- clined to two faces of the cube. Haiiy also shewed how a rhombic dodecahedron resulted from the application of successive layers of these little bricks, each less by one row all round, to the faces of the primitive cube, and of course the same result may be obtained by subtracting rows in the same man- ner, (See Fig 4.) Fijr. ?>. He also assumed in some cases that the decrease was parallel, not to the edges of the crystal, but to a diagonal, taking the angles as its point of departure. His theory established the fact that the various I Cry tals. 125 forms of crystals are not irregular or accidental, but definite, and based on certain fixed laws; and he pointed out that whilst certain forms are derivable from a given nucleus, there are others which cannot occur. Moreover he observed that when any change in a crystal took place by its combination with other forms, all similar parts (angles, edges and faces) were modified in the same way. Most important of all, he shewed that these changes could be indicated by rational co-efficients. Thus Haiiy became the discoverer of two of the three great laws of crystallography, namely, the l.wv of symmetry, and the i,aw of WHOLE NUMBERS. The Other, THE LAW OF CONSTANCY OF ANGLES, we have already mentioned. Let us consider for a moment Haiiy's two laws, taking first :— THE LAW OF SYMMETRY. E. S. Dana enunciates this as follows: "The symmetry of crystals is based upon the law that either : /. All parts at a ctystal sitnilar in position wiih reference to the axes are similar in planes or modification, or II. Each half of the similar parts of a crystal, alternate or symmetrical in position or relation to the other half, ?nay be alone similat in its planes or modifications. The forms resulting according to the first method are termed holohedral forms and those according to the second, /lemihedral." An easy experimental way of siudy'ng the symmetry of crystals is to cut one, or the model of one, in two, and place the parts againsc the surface of a mirror, which may or may not i^roduce the e'xact ap- pearance, of the original crystal. If it does produce the exact appearance we have severed the crystal in a plane of symmetry. By referring to Fig. G it will readily be seen that a cube, for in- stance, possesses nine such planes, indicated by the dotted lines. ..^5-=S^ \l/ t / y V\%. (i. In a sphere there would of course be an infinite number of these planes. ■ *-*^ Tin: Ottawa Natuhalist. Now with regard t j the second law :— THE LAW OK WHOi.K NUMBERS. The meaning of this is simply that Hauy found that the secondary faces had only such positions as would result from the omission of whole numbers of rows of bricks and from the layers having a thickness measured by some multiple of that of a single brick. He actually proved by measurements that the number of bricks in the width or height of a step rarely exceeds six. F^.ut Hauy's theory of the structure of crystals had many weak points in it which speedily became objects of attack. One of his first critics was Weiss, Professor of Mineralogy at Berlin, wha translated Hauy's w^rk into German, in 1S04. He shewed that Hauy's "primitive forms," as professor Nichol puts It, "erred both in excess and defect," and that the " bricks" were not needed at ail to explain the facts observed, in fact, the i)lanes, so-called, buik up of them, would not rctlect li-jit. Bernhardi, a doctor residing in Krfurt, pointed out that the dimensions of the " i)rimitive forms " could not be determined from themselves, their height clei)ending on another form. Also that various crystals, which he named, were much more readily explained from other forms than those taken l)y Haiiy as their " i^rimitives ". In f.ict, numberless objections were raised ; thus, it by no means follows that because a crystal m ly be reduced to a certain form by cleavage, that its growth has resulted from the grouping together of fragments having that form ; again, some minerals have no cleavage, whilst others cleave only in one or two dire ons ; again, it is hard to conceive of a crystal built u)), for instance, of little octahedrons, which, in order to have their faces parallel to the cleavages of the resulting crystal, and be parallel to each other, would have only their angular points in contact, thus form- ing a most skeleton like and unstable structure. But Hauy's theory, pointing as it did to the great importance of the angles of the fices and cleavages of crystals, served to direct attention to them, and led to their more accurate study and determination. It was not so much Hauy's data that required correction, but the substitution of a better theory to connect his facts was needed. The development of the atomic theory of the constitution of Crvstai.s. 127 matter furnished this, and, instead of "bricks", we reason about " atomic groups," whose centres of mass are arranged in straight Hnes and parallel planes, as were the centres of the "bricks" in Haiiy's original theory. Weiss was the first, in 1808, to point out the importance of the axes of crystals, although Haiiy had referred to them. He says :~"The axis is truly the line governing every figure round which the whole is uniformly disposed. All the parts look to it, and by It they are bound together as by a common chain and mutual contact." These axes, it must be borne in mind, are not mere geo- metrical lines ; but it is in reference to them that the forces work ivhich have formed the crystals. Weiss proceeded to arrange Haiiy's primitive forms into four classes each distinguished by a purely geometrical character ; and then from these four classes of sets of lines, he deduced all \.\\q priinitive forms by the construction of planes passing : — 1. Through ends of three lines. 2. Through ends of two of the lines and parallel to the third. 3. Through an end of one of the lines and parallel to two of them That is, these planes passed through the end of a line, or else did not meet it at all. These axes were, in fact, the co-ordinates of the crystal faces of the primitive forms of Haiiy. By taking points along each of these lines at distances equal to twice, three times, four times, etc., the original length, he found, constructing planes as before, that he obtained a set including all the secondary planes described by Haiiy as occurring in actual crystals. Thus he was enabled to devise a very simple system of designating the various faces of crystals, which also greatly facilitated the calcula- tion of their angles. Haiiy had attempted this in conformity with his theory, but his symbols were complex and unwieldy. It is a curious coincidence that at the same time as Weiss was developing his system, A'ohs, Werner's successor at Freiberg, working cjuite independently, arrived at the same division of crystals into four classes, but by a very different process of reasoning. These four classes he termed '■' Systems of Crystallization." ■ 128 The Ottawa Naturalist. Mohs also shewed that since all the similar edges and solid angles of his fundamental figures were to be similarly altered, the existence of one derived plane necessitated, as in Rome Delisle's theory, the simultaneous existence ot a number of others having definite positions. Such a set of faces he called a simple form. If the faces of more than one simple form are present, the resulting form was termed a co7nbination. At this time Sir David Brewster was engaged in his wonderful researches on the optical properties of crystals, and the results of his experiments on the polarization of light brought out in such a remark- able manner the mtimate relations existing between their behaviour with regard to light passing through them, and the number of kinds of axes they possessed, that Whewell has justly said, "Sir D. Brewster's optical experiments must have led to a classification of crystals into the above systems, or something nearly equivalent, even if the crystals had not been so arranged by attention to their forms." Sometimes crystals were observed by both Weiss and Mohs which, instead of being complete simple forms, like the regular octahedron,' presented only /J«//the regular number of faces, as, for example, the regular tetrahedron, which may be derived from the regular octahedron by suppressing its alternate faces. Delisle and Hauy had regarded the tetrahedron as a distinct kind of primitive form, but Weiss and Mohs found it necessary to postulate that simple forms may not only be complete, but semi-complete also, pointing out, however, that the half which presents itself is not an arbitrary one, but can always be derived systematically from the complete simple form. The complete simple forms were termed holohedral, and the semi- complete ones IiemihedraL In 1822, Mohs added two more systems of crystallization to the four already described by Weiss and himself; but Weiss brought forward very strong objections to their recognition, and their independance was not fully established until 1833, when the actions on light of crystals belonging to these systems were first studied. They were what we now call the monochtiic diV\d frt'c/mic systems. The researches of Weiss and Mohs may be said to have given to Crystals. 129 crystallography its present form, in all essential points, as a pure science, and subsequent progress has been along the lines ot working out details rather than modifying its foundations. The accompanying table, (page 130), will shew at a glance the six systems of crystallization now recognized, with their principal synonyms and examples of minerals for each system. Very often crystals are met with in which one or more parts are reversed with regard to the others, often presenting the appearance of two crystals symmetrically united. These are termed hvin crystals, but the theory of their formation is too elaborate to be gone into in the present paper. Time will not permit me, either, to go into details respecting the various methods of designating the faces of crystals by numbers or symbols, and of calculating their angles. That of Naumann is. perhaps, the one most employed. This subject belongs, however,more to pure geometric crystallography, and will be found fully explained in the text-books. I can only briefly mention here some of the many wonderful physical properties possessed by crystals. The researches of Brewster on polarized light have already been referred to. The discovery that the shape of the cleavage-form is intimately related to the action of the crystal upon light is due to him ; and his researches, as already mentioned, confirmed the existence of the two additional systems of crystallization recognized somewhat doubt- fully by Mohs. One of the most remarkable discoveries of recent times was the mathematical demonstration by von Lang, Quenstedt, and others, that six, and only six, systems of symmetry are possible for all crystallized matter. In 1822, Mitscherlich announced his discovery oi isomorphism, the property which substances analogous in chemical composition possess of crystallizing in forms closely resembling each other, and with only a slight difference between their corresponding angles. A good example is siderite and dolomite, the crystal form being a rhombohedron. Mitscherlich also pointed out that the same substance (simple or compound) may crystallize in two distinct systems ( dimorphism ),ox even in three or more (trimorphism:ix\A polymorphism). Thus the sulphide of iron crystallizes in the isometric system (pyrite), and also in the orthorhombic system {marcasite). 130 Tfik Ottawa Naturalist. SYSTEMS OF CRYSTALLIZATION, Name. I. ISOMKTRIC. — Tessiilar, Mohs & Elaidinger. Isomeln'c, I Liusmnnn. Tesscral, Nauniaiin. Rt'i^iihir, Weiss k- Ruse. Culnc, Dufrtnoy & Miller. Aloiionmtric, Dana (early editions.) IL Tetragonal. — Pvraiiiidal, Mohs. Z'iiei-iiii(/-eiiiaxige, Weiss. Tetragonal, Naiur.ann. Monoih'i/ietiii, Ilausniann. Qiiailnilic, von Kohell. /.h'///e/n'/\Dtir\:i (early editions) III. IIexac.onai,. Hhombohedral, Mohs. Drci- u}id-ei)ia.\ige, Weiss. FIexa.;o)ial, Naumann. Mouotrimctric, Haiismann. Note. — This System has a RHOM- liOHEDKAI, DIVISION, which includes forms wiih only 3 planes of symmetry. IV. ORTHOKHOMmC. — Prismatic or Orthotype, Mohs. Ein-und-einaxigc, Weiss. Khoininc and Anisometric, Naumann. Trimctiic and Ort/ior/tonilnc, Hausniann. Triinelric, Dana, (early edi- tions.) A.\ES. Three, of equal length, intersecting e ac li