The history of crystallography before X-rays describes how crystallography developed as a science up to the discovery of X-rays by Wilhelm Conrad Röntgen in 1895. The scientific approach to the study of crystals began in the 17th century with the work of Kepler on the structure of snowflakes and Nicolas Steno's discovery that the angles between corresponding faces in a crystalline substance are always the same. The work René Just Haüy published in 1801 and 1802 marked the point where crystallography split from mineralogy to become a science of its own. Some sources state that the history of crystallography started with the investigation of X-ray diffraction by Max von Laue in 1912 but that ignores over a century of previous scientific work in the field.
In the period before X-rays, crystallography can be divided into three broad areas: geometrical crystallography culminating in the discovery of the 230 space groups in 1891–4, physical crystallography, and chemical crystallography.
Up to 1912, crystallography had been largely based on mineralogy. It was the study of minerals in the 18th and 19th centuries that led to a progressive understanding of the relationships between chemical composition, crystal habit and crystal structure. During the 19th century crystallography was progressively transformed into an empirical and mathematical science by the adoption of symmetry concepts.
Origins 16th century
The scientific study of the properties of crystals began in the 16th century. In the first half of the 16th century Paracelsus proposed a theory of mineral formation as an analogy to fruit-bearing plants. In 1546 Georgius Agricola published a study of mineralogy in which morphology, or geometrical shape, was one of the characteristics used to classify minerals. In 1550 Gerolamo Cardano made an early attempt to explain the shape of crystals as the result of a close packing of spheres. In 1591 Thomas Harriot studied the close packing of cannonballs (spheres). In 1597 Andreas Libavius recognised the geometrical characteristics of crystals and identified salts by their crystal shape.
17th century
In 1611 Johannes Kepler published Strena Seu de Nive Sexangula (A New Year's Gift of Hexagonal Snow) which is considered the first treatise on geometrical and atomistic crystallography. Kepler studied the packing of spheres, in order to explain the hexagonal symmetry of snow crystals. He demonstrated that in a compact packing each sphere has six neighbours in the same plane, three in the plane above, and three in the plane below, for a total of twelve touching spheres. Kepler concluded that 0.74084 is the maximum possible density amongst any arrangement of spheres — this became known as the Kepler conjecture. The conjecture was finally proved by Thomas Hales in 1998.
In 1665 Robert Hooke attempted to explain crystal morphology based on the stacking of atoms. In his work Micrographia he reported on the regularity of quartz crystals observed with the recently invented microscope, and proposed that they are formed by spherules.
Nicolas Steno rejected Paracelsus's proposed organic origin for crystals. Steno first observed the law of constancy of interfacial angles in 1669 when studying quartz crystals and noted that, although the crystals of a substance differed in appearance from one to another, the angles between corresponding faces were always the same. Steno's work can be considered as the beginning of crystallography as an independent discipline.
In 1678 Christiaan Huygens proposed a structural explanation of the double refraction of calcite based on ellipsoidal atoms. Huygens published his results in his Traité de la Lumière.
A geometrical theory of crystal structure based on polyhedra was proposed by Domenico Guglielmini. Guglielmini's publications of 1688 and 1705 concluded that basic forms (cube, rhombohedron, hexagonal prism, and octahedron) of various salt crystals are characteristic of each substance, are identical in form, indivisible, and have faces with identical inclinations to each other.
By the second half of the 17th century the ideas of Paracelsus had been displaced by a more scientific approach to chemistry, geology, mineralogy, and the emerging field of crystallography. In his book The Sceptical Chymist of 1661, Robert Boyle criticised the traditional composition of materials, as represented by the teaching of Aristotle and Paracelsus, and initiated the modern understanding of chemical elements using the words "perfectly unmingled bodies". Boyle argued that matter's basic elements consisted of various types of particles, termed "corpuscles", which were capable of arranging themselves into groups (molecules). Boyle was one of the earliest researchers to use the term crystal for crystalline substances apart from quartz.
Geometrical crystallography
18th century
In 1723 Moritz Anton Cappeller published Prodromus Crystallographiae, the first treatise on crystal shapes. The introduction of the term crystallography is attributed to Cappeller.
In 1773 Torbern Bergman, a leader in the field of chemical analysis, described the crystal forms of calcite and stated that all the forms could be built up from the cleavage rhombohedron. Bergman, building on the previous work of Carl Linnaeus, developed a classification of minerals based on chemical characteristics, with subclasses organised by their external shapes, and defined seven primary crystal forms. In 1774 Abraham Gottlob Werner published his classification of minerals. Werner postulated seven primary forms, and showed that some geometrical forms could be derived from one another by truncation.
With Jean-Baptiste L. Romé de l'Isle's Essai de cristallographie published in 1772 and Cristallographie published in 1783 the scientific approach to crystal structure began. Romé de l'Isle described over 500 crystal forms and accurately measured the interfacial angles of a great variety of crystals, using the goniometer designed by his student Arnould Carangeot. He noted that the angles are characteristic of a substance, thus generalising the law of constancy of angles postulated by Nicolas Steno. Romé de l'Isle considered that the shape of a crystal is a consequence of the packing of elemental particles, and defined six primitive forms. However, he criticised René Just Haüy and Torbern Bergman for speculating on the internal structure of crystals without sufficient observational data.
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 interfacial 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 his law of decrements: 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. His 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 his Traité de mineralogie (1801). In 1804 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 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. 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.
French scientists did not adopt the dynamic crystallographic theory, but they did attempt to learn from it. 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. Delafosse's approach explained the behaviour of hemihedral crystals, which were not adequately accounted for by Haüy.
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 1824 Carl Friedrich Naumann confirmed Mohs' observation that the triclinic and monoclinic systems required inclined rather than orthogonal axes.
Crystal classes
In 1826 Moritz Ludwig Frankenheim published the first derivation of the 32 crystal classes, but his work was forgotten for many decades. In 1830, Johann Hessel proved that, as a consequence of the law of rational indices, morphological forms can combine to give exactly 32 kinds of crystal symmetry in Euclidean space, since only two-, three-, four-, and six-fold rotation axes can occur (the crystallographic restriction). However, Hessel's work remained practically unknown for over 60 years and, in 1867, Axel Gadolin independently rediscovered his results. Gadolin, who was unaware of the work of his predecessors, found the crystal classes using stereographic projection to represent the symmetry elements of the 32 groups. Gadolin's work had a clarity that attracted widespread attention, and caused Hessel's earlier work to be neglected.
Miller indices