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Quotes of the day

January 14, 2008 Posted by Emre S. Tasci

The Fourteen Bravais Lattices

When one relaxes the restriction to point operations and considers the full symmetry group of the Bravais lattice, there turn out to be fourteen distinct space groups that a Bravais lattice can have. Thus, from the point of view of symmetry, there are fourteen different kinds of Bravais lattice. This enumeration was first done by M.L. Frankenheim (1842). Frankenheim miscounted, however, reporting fifteen possibilities. A. Bravais (1845) was the first to count the categories correctly.


The seven crystal systems and fourteen Bravais lattices described above exhaust the possibilities. This is far from obvious (or the lattices would have been known as Frankenheim lattices).

Ashcroft, Mermin  Solid State Physics Saunders 1976 Ch. 7


I don’t understand why you materials scientists are so busy in working out experimentally the constitution [crystal structure and phase diagram] of multinary systems. We know the structure of the atoms [needing only Atomic Numbers], we have the laws of quantum mechanics, and we have electronic calculation machines, which can solve the pertinent equation rather quickly!

J.C. Slater, 1956 as quoted by Villars et al. Journal of Alloys and Compounds 279 (1998) 1

3 Responses to “Quotes of the day”

  1. Bo Sundman Says:

    I understand the comment is ironic. The fact which physicists and chemists have so big difficulty to understand is that materials properties are not controlled by bonding between atoms or molecules, which I agree can be calculated very well by quantum mechanics, but by defacts which can be small like vacancies but also big like grain boundaries or
    phase interfaces or even voids. To hindle such large defects one need more than 1E6 atoms and with 10 elements I understand it takes a year or so to calculate the eauilibriul state by quantum mechanics. So I think we will still have to learn phase diagrams
    and study microstructures to develop materials
    for another 10-20 years


  2. Hex, Bugs and More Physics | Emre S. Tasci » Blog Archive » Sub-groups of space groups Says:

    […] reference on Bravais Lattices and info on how/why they are called after Bravais but not Frankenheim.. Filed in Coding, Physics, Tools, […]

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