The construction of group theory in crystallography

• Autores: Bernard Maitte
• Localización: The Circulation of Science and Technology: Proceedings of the 4th International Conference of the European Society for the History of Science. Barcelona, 18-20 November 2010 / coord. por Antoni M. Roca Rosell, 2012, ISBN 978-84-9965-108-8, págs. 510-513
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • The French molecular approach led to the distinction of fourteen types of lattice system, while “Naturphilosophie” can count 32 classes of symmetry. At the end of the century, the mathematical study led to 230 different groups belonging to 32 classes, 14 networks and 7 systems.

    In this paper, I will show how, in the continuity of the founding works of Romé de l’Isle (1772) and René-Just Haüy (1801), introducing a triperiodic crystalline structure composed by “integrant molecules” filling the space (7 systems), Gabriel Delafosse (1843) introduces the concept of the crystal lattice repeating “polyhedral molecules” which do not fill the space.

    This view helps explain the “notable exceptions” to the “law of symmetry” of Haüy (the “mériédries”). This approach is generalized in 1848 by Bravais in his study of “systems composed by systems of points” (enumeration of 14 modes of networks ").

    Meanwhile, the German crystallographers, based on continuous view of matter characteristic of “Naturphilosophie”, describe attractive and repulsive forces fighting in space.

    From this idea, they induce the concept of the “axes of symmetry” (Weiss 1805). The combination of these elements of symmetry concurring, discussed by Weiss, continued by Mohs and Hessel, leads in 1830 to the counting of 32 “classes of symmetry”.

    The combination by Sohncke of networks and those of classes that he knew would lead to the enumeration of 61 various “groups of space” (1879). It is with an entirely mathematical approach, without figure, introducing elements of non-concurrent symmetry and introducing the problem of the regular partition of the sphere, that Fedorov and Schoenfliess manage to count, independently of one another, 230 groups of symmetry (1891). .

    The determination of groups of space is now complete. It can bring together the concepts of systems, classes and types of networks. The “groups”, counted without reference to ideas of Galois and its successors, will play an essential role in physics after the work of Pierre Curie (1894).

    It’s a whole century of efforts from crystallographers working in various contexts and with different presupposed that I retrace.