The Construction of Group Theory in Crystallography
This article sets out to retrace the manner in which Group Theory evolved in crystallography. To engage in this study it is necessary to select, amongst all the approaches to crystals, those which, from the point of view of modern science, mark a step tow
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Abstract This article sets out to retrace the manner in which Group Theory evolved in crystallography. To engage in this study it is necessary to select, amongst all the approaches to crystals, those which, from the point of view of modern science, mark a step towards the establishment of our current understanding. In this way it favours our current perspective. To compensate this distortion, we recall the context in which each explanation that marks history appears. It so becomes clear that notions of triperiodic assemblages and the crystallographic laws of crystal systems and symmetrical classes do not derive from “natural” observations but were compiled and belong to precise theories.
1 Preamble: Contexts I am going to recount the history of the construction of group theory in crystallography. This construction will prove to be extremely rich in that it allows the connection between physical and symmetrical properties, leads Pierre Curie to make symmetry a tool of reasoning, is used in the twentieth century as a cross-border theory between different disciplines and marks the origins of radio crystallography and spectroscopic studies. As we shall see, this history extends over two centuries, crossing diverse branches of science (natural philosophy, physics, mineralogy, crystallography, chemistry and mathematics), and developing varying characteristics depending on the geographical location concerned. Different scientific traditions are set in motion and give rise to the use of different methodologies. In the
B. Maitte () Centre d’Histoire des Sciences et Epist´emologie (CHSE/UMR STL-8163), Universit´e de Lille 1, Lille, France e-mail: [email protected] E. Barbin and R. Pisano (eds.), The Dialectic Relation Between Physics and Mathematics in the XIXth Century, History of Mechanism and Machine Science 16, DOI 10.1007/978-94-007-5380-8 1, © Springer ScienceCBusiness Media Dordrecht 2013
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seventeenth century it is Kepler and Hooke who, amidst the fever of observations and interpretations which are typical of the birth of a “new science”, study both with the naked eye and under microscope the regular shape of crystals and attempt to explain them through a subjacent structure, inaccessible to the best instruments at their disposal. Their efforts are taken up by Christiaan Huygens who contributes to the creation of a geometric and “hypothetical-deductive” science, based on mechanisms which apply in the world of Descartes: a world filled with infinitely liquid ether, composed of elements which resemble hard spheres, in contact with one another. He observes calcite, its patterns, its cleavages, its birefringence, and shows that all these properties possess a common symmetry. He represents them as a repetition in the three directions of space (a triperiodic assemblage underlying etherimmersed molecules), a mass which slows down the speed of passing light waves. He deducts from this hypothesis various physical properties, not yet, but soon to be observed, and accurately predicts the numerica
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