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| title | chunk | source | category | tags | date_saved | instance |
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| Geometrical crystallography before X-rays | 2/4 | https://en.wikipedia.org/wiki/Geometrical_crystallography_before_X-rays | reference | science, encyclopedia | 2026-05-05T16:17:27.087973+00:00 | kb-cron |
In 1781 René Just Haüy (often termed the "Father of crystallography") discovered that crystals always cleave along crystallographic planes. Based on this observation, and the fact that the inter-facial angles in each crystal species always have the same value, Haüy concluded that crystals must be periodic and composed of regularly arranged layers of tiny polyhedra (molécules intégrantes). This theory explained why all crystal planes are related by small rational numbers (the law of rational indices). In 1784 René-Just Haüy published Essai d'une théorie sur la structure des cristaux, appliquée à plusieurs genres de substances cristallisées in which he stated his law of decrements (décroissement): a crystal is composed of molecules arranged periodically in three dimensions without leaving any gaps. Haüy's molecular crystal structure theory assumed that molécules intégrantes were specific in shape and composition for every compound. Haüy developed his mathematical theory of crystal structure over many years. Haüy's theory turned out to be remarkably accurate, and gave crystallography a legitimate place among the sciences. Haüy's crystal structure theory was criticised as over-simplistic by William Hyde Wollaston in 1813 and by Henry James Brooke in 1819. Haüy also tended to ignore experimental results that contradicted his structural theory, such as those achieved with the more accurate reflection goniometer invented by Wollaston in 1809. In 1819 Eilhard Mitscherlich discovered the law of isomorphism which states that compounds which contain the same number of atoms, and have similar structures, tend to exhibit similar crystal forms. The discovery of the phenomena of isomorphism and polymorphism dealt a clear blow to Haüy's crystal structure theory.
== Atomism versus Dynamism ==
Christian Samuel Weiss became familiar with Haüy's theory by translating the 4-volume Traité de mineralogie (1801). Weiss added an appendix to volume 1 of the translation in which he first outlined his dynamical theory of crystals. In contrast to Haüy, Weiss took a purely geometric approach to external crystal morphology, completely disregarding any attempt at modelling the internal structure of crystals. Weiss has been termed "the founder of geometric crystallography". Weiss rejected Haüy's static "atomistic" theory of crystals instead using a "dynamic" approach that was typical of the German natural philosophers of the early 19th century. Weiss understood the external forms of crystals as a consequence of internal attractions and repulsions, and that generative forces were expressed in definite directions which could be observed as one or more axes of rotation. Weiss used crystallographic axes as the basis of his systematic classification of crystals. Weiss and his followers Moritz Ludwig Frankenheim and Johann F. C. Hessel studied the symmetry of crystals. Up until 1800 the concept of symmetry had a variety of meanings, however during the 19th century crystallography was progressively transformed into an empirical and mathematical science by the adoption of symmetry concepts. "In the first half of the 19th century the paramount symmetry problem was that of point symmetry: to enumerate all possible combinations of symmetry elements which pass through a common point, the origin, and therefore leave this point single. The crystallographic symmetry elements were observed to be exclusively 2, 3, 4 and 6-fold axes, mirror planes, and centres of inversion." In 1829 Justus Günther Graßmann published a study of the symmetries of the crystal systems using an algebra of linear combinations. In 1832 Franz Ernst Neumann used symmetry considerations when studying double refraction in crystals. By the second half of the 19th century the study of crystals was focused more on their geometry and mathematical analysis than their physical properties. Gabriel Delafosse continued Haüy's work in France. He was the first to use the terms lattice (réseau) and unit cell (maille). He stated that the orientation of the axes in a substance is constant, which implies symmetry of translation (a defining feature of a lattice), and that the external symmetry of a crystal reflects its inner symmetry, namely the symmetry of the constituent atoms and their arrangement. In other words, the law of symmetry applies to both the inside and the outside of a crystal. French scientists did not adopt the dynamic crystallographic theory, but they did attempt to learn from it. Delafosse built on Haüy's crystallographic approach by stating that the structure and physical properties of crystals should exhibit the same symmetry. Delafosse aimed to resolve the apparent counter-examples to Haüy's law of symmetry by explaining that the symmetry of the physical phenomena revealed the inner structure of crystals. This structure is sometimes more complex than the external morphology. Crystals, in these cases, are of lower symmetry than the lattice. This substructure explained the behaviour of hemihedral crystals, which were not adequately accounted for by Haüy. Delafosse argued that Haüy's molécules intégrante did not necessarily have a physical reality, but rather that its polyhedral form should be regarded instead as the space surrounding a lattice point.
== Crystal systems ==
Christian Samuel Weiss introduced the concept of crystal systems in 1815. Weiss defined seven crystal systems: five based on three orthogonal axes (cubic, tetragonal, orthorhombic, monoclinic and triclinic), and two (trigonal and hexagonal) based on three axes in a plane at 60° to each other and a fourth axis orthogonal to the plane. The number and type of the crystal systems of Weiss correspond to the modern systems apart from the triclinic and monoclinic cases which have non-orthogonal axes. Friedrich Mohs established a classification system for minerals based solely on their external shape. Mohs distinguished four crystal systems rather than the seven identified by Weiss. In 1822 Weiss and Mohs engaged in a priority dispute on who had first discovered the crystal systems.
In 1824 Carl Friedrich Naumann confirmed Mohs' observation that the triclinic and monoclinic systems required inclined rather than orthogonal axes. Naumann attempted a synthesis of the Weiss and Mohs systems by considering four different configuration of axes: orthogonal (three right angles), monoclinic (two right angles and one oblique one), diclinic (one right angle and two oblique ones), and triclinic (three oblique ones). The diclinic system has not survived.
== Crystal classes ==