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From the 1830s Haüy's molecular crystal structure theory started to be combined with the atomic theory of the chemists to produce a view of a crystal as the regular arrangement of atoms or molecules in space. In 1849 Auguste Bravais related the symmetry of the crystal, considered as one of 14 space lattices, to that of its constituting molecules and formalized the reticular interpretation of hemihedry given by Gabriel Delafosse. In 1852 Delafosse attempted to relate the structure of the molecule to the external shape of the crystal. During the 1850s and 1860s a "quiet revolution" took place in structural chemistry according to Alan J. Rocke, a historian of chemistry. The main features of the revolution were the clarification of the concept of atomic weight (Stanislao Cannizzaro), the definition of the idea of valence (then known as atomicity), and new chemical structural ideas, such as the benzene structure of a ring of alternating double and single carbon bonds (August Kekulé). These developments in chemistry were largely independent of the mathematical and geometrical direction of crystallography in the period 18501895 which had little concern with the practicalities of atomic and molecular arrangement. In 1869 Emanuele Paternò predicted that the four valences of carbon have identical chemical properties and illustrated three predicted isomers of dibromethane showing the tetrahedral carbon atom for the first time. While Paternò's work was the first publication of tetrahedral-valent carbon it is not clear that he recognized the full consequences of the hypothesis. In 1874 Jacobus Henricus van 't Hoff and Joseph Le Bel independently proposed the tetrahedral arrangement of the atoms bound to carbon in organic molecules. Van't Hoff's theory validated and explained Pasteur's results with tartrate crystals, and Johannes Wislicenus' work with isomeric lactic acids, and was fundamental to the further development of stereochemistry. Until the use of X-rays there was no way to determine the actual crystal structure of even the simplest substances such as salt (NaCl). For example in the 1880s, William Barlow proposed several crystal structures based on close-packing of spheres some of which were validated later by X-ray crystallography; however, the available data were too scarce in the 1880s to accept his models as conclusive. In the period between the discovery of X-rays (1895) and X-ray diffraction (1912) Barlow and William Jackson Pope developed the principles of packing, and showed how to deduce the structures of some simple compounds. In the 1930s Linus Pauling was impressed that Barlow had assigned many crystal structures of metals (copper, silver, and gold to cubic close packing, and magnesium, zinc, and cadmium to hexagonal close packing) and salts (sodium, potassium and caesium chlorides) which were subsequently proved to be correct by X-ray crystallography. William Johnson Sollas emphasised the importance of different atomic sizes in constructing simple crystals, and correctly concluded that the sodium and chlorine atoms in salt would be of different sizes. In 1887 Johannes Wislicenus published a study of stereoisomerism in unsaturated compounds. Groth made a systematic classification of minerals based on their chemical composition and crystal structure and published his results in his 5-volume Chemische Kristallographie in 19061919, which contained crystalline morphology and physical property data on nearly 10,000 substances. In 1913 Walter Wahl summarised the known connections between chemical composition and crystalline form as isomorphism (Mitscherlich), morphotropism (Groth), and enantiomorphism (Pasteur and van 't Hoff). In his preface to Andreas Fock's An introduction to chemical crystallography Pope summarised the state of chemical crystallography in 1895 as follows:

"Our knowledge of the physical and geometrical properties of crystals is now very complete, but their relations to chemical constitution and composition are as yet but little known." After 1912 crystallography would develop dramatically with the widespread adoption of X-ray diffraction to determine crystal structures.

== Research community ==

Before the 20th century crystallography was not a well-established academic discipline. There were no academic positions specifically in crystallography. Workers in the field normally carried out their crystallographic research as an ancillary to other employment(s), or had independent means. The leading workers in the field of chemical crystallography were employed as follows:

Professors Mathematics or science: Arago, Berzelius, Biot, Curie, Frankenheim, Lehmann, Liebig, Mitscherlich, Ostwald, Pasteur, Reinitzer, Wöhler Mineralogy: Delafosse, Groth, Haüy, Neumann, Other employment: Brewster (editor), Romé de l'Isle (cataloguer), Sohncke (meteorological service), Wollaston (physician) Independently wealthy: Barlow, Herschel, Huygens In the nineteenth century there were informal schools of crystallography researchers in France (Arago, Biot, Curie, Delafosse, Haüy, Pasteur), Germany (Frankenheim, Groth, Lehmann, Liebig, Mitscherlich, Neumann, Reinitzer, Sohncke, Wöhler) and England (Barlow, Brewster, Herschel, Wollaston). Until the founding of Zeitschrift für Krystallographie und Mineralogie by Paul Groth in 1877 there was no lead journal for the publication of crystallographic papers. The majority of crystallographic research was published in the journals of national scientific societies, or in mineralogical journals. The inauguration of Groth's journal marked the emergence of crystallography as a mature science independent of geology.

== See also == History of atomic theory History of molecular theory History of crystallography before X-rays Geometrical crystallography before X-rays Physical crystallography before X-rays Timeline of chemistry Timeline of crystallography

== Citations ==

== Works cited ==