This discovery impressed Haüy with the immense influence which the structure of the crystal substance exerts on the external form, and how, in fact, it determines that form. For the observations were only to be explained on the supposition that the crystal was built up of structural units, which he imagined to be miniature crystals shaped like the fundamental form, and that the faces were dependent on the step-like arrangement possible to the exterior of such an assemblage. This brought him inevitably to the intimate relation which cleavage must bear to such a structure, that it really determined the shape of, and was the expression of the nature of, the structural units. Thus, before the conception of the atomic theory by Dalton, whose first paper (read 23rd October 1803), was published in the year 1803 in the Proceedings of the Manchester Literary and Philosophical Society, two years after the publication of Haüy’s last work (his “Traité de Minéralogie,” Paris, 1801), Haüy came to the conclusion that crystals were composed of units which he termed “Molécules Intégrantes,” each of which comprised the whole chemical compound, a sort of gross chemical molecule. Moreover, he went still further in his truly original insight, for he actually suggested that the molécules intégrantes were in turn composed of “Molécules Elémentaires,” representing the simple matter of the elementary substances composing the compound, and hinted further that these elementary portions had properly orientated positions within the molécules intégrantes.
He thus not only nearly forestalled Dalton’s atomic theory, but also our recent work on the stereometric orientation of the atoms in the molecule in a crystal structure. Dalton’s full theory was not published until the year 1811, in his epoch-making book entitled “A New System of Chemical Philosophy,” although his first table of atomic weights was given as an appendix to the memoir of 1803. Thus in the days when chemistry was in the making at the hands of Priestley, Lavoisier, Cavendish, and Dalton do we find that crystallography was so intimately connected with it that a crystallographer well-nigh forestalled a chemist in the first real epoch-making advance, a lesson that the two subjects should never be separated in their study, for if either the chemist or the crystallographer knows but little of what the other is doing, his work cannot possibly have the full value with which it would otherwise be endowed.
The basis of Haüy’s conceptions was undoubtedly cleavage. He describes most graphically on page 10 of his “Essai” of 1784 how he was led to make the striking observation that a hexagonal prism of calcite, terminated by a pair of hexagons normal to the prism axis, similar to the prisms shown in Fig. 6 (Plate III.) except that the ends were flat, showed oblique internal cleavage cracks, by enhancing which with the aid of a few judicious blows he was able to separate from the middle of the prism a kernel in the shape of a rhombohedron, the now well-known cleavage rhombohedron of calcite. He then tried what kinds of kernels he could get from dog-tooth spar (illustrated in Fig. 7) and other different forms of calcite, and he was surprised to find that they all yielded the same rhombohedral kernel. He subsequently investigated the cleavage kernels of other minerals, particularly of gypsum, fluorspar, topaz, and garnet, and found that each mineral yielded its own particular kernel. He next imagined the kernels to become smaller and smaller, until the particles thus obtained by cleaving the mineral along its cleavage directions ad infinitum were the smallest possible. These miniature kernels having the full composition of the mineral he terms “Molécules Constituantes” in the 1784 “Essai,” but in the 1801 “Traité” he calls them “Molécules Intégrantes” as above mentioned. He soon found that there were three distinct types of molécules intégrantes, tetrahedra, triangular prisms, and parallelepipeda, and these he considered to be the crystallographic structural units.
Fig. 12.
Having thus settled what were the units of the crystal structure, Haüy adopted Romé de l’Isle’s idea of a primitive form, not necessarily identical with the molécule intégrante, but in general a parallelepipedon formed by an association of a few molécules intégrantes, the parallelepipedal group being termed a “Molécule Soustractive.” The primary faces of the crystal he then supposed to be produced by the simple regular growth or piling on of molécules intégrantes or soustractives on the primitive form. The secondary faces not parallel to the cleavage planes next attracted his attention, and these, after prolonged study, he explained by supposing that the growth upon the primitive form eventually ceased to be complete at the edges of the primary faces, and that such cessation occurred in a regular step by step manner, by the suppression of either one, two, or sometimes three molécules intégrantes or soustractives along the edge of each layer, like a stepped pyramid, the inclination of which depends on how many bricks or stone blocks are intermitted in each layer of brickwork or masonry. Fig. 12 will render this quite clear, the face AB being formed by single block-steps, and the face CD by two blocks being intermitted to form each step. The plane AB or CD containing the outcropping edges of the steps would thus be the secondary plane face of the crystal, and the molécules intégrantes or soustractives (the steps can only be formed by parallelepipedal units) being infinitesimally small, the re-entrant angles of the steps would be invisible and the really furrowed surface appear as a plane one. Haüy is careful to point out, however, that the crystallising force which causes this stepped development (or lack of development) is operative from the first, for the minutest crystals show secondary faces, and often better than the larger crystals.
Fig. 13.
An instance of a mineral with tetrahedral molécules intégrantes Haüy gives in tourmaline, and the primitive form of tourmaline he considered to be a rhombohedron, conformably to the well-known rhombohedral cleavage of the mineral, made up of six tetrahedra. Again, hexagonal structures formed by three prismatic cleavage planes inclined at 60° are considered by him as being composed of molécules intégrantes of the form of 60° triangular prisms, or molécules soustractives of the shape of 120° rhombic prisms, each of the latter being formed by two molécules intégrantes situated base to base. This will be clear from Figs. 13 and 14, the former representing the structure as made up of equilateral prismatic structural units, and the latter portraying the same structure but composed of 120°-parallelepipeda by elimination of one cleavage direction; each unit in the latter case possesses double the volume of the triangular one, and being of parallelepipedal section is capable of producing secondary faces when arranged step-wise, whereas the triangular structure is not. The points at the intersections in these diagrams should for the present be disregarded; they will shortly be referred to for another purpose.
