The central role of symmetry in condensed matter

I have now finished my first draft of chapter 3, of Condensed Matter Physics: A Very Short Introduction. 

I welcome comments and suggestions. However, bear in mind my target audience is not the typical reader of this blog, but rather your non-physicist friends and family. 
I think it still needs a lot of work. The goal is for it to be interesting, accessible, and bring out the excitement and importance of condensed matter physics.

This is quite hard work, particularly to try and explain things in an accessible manner.
I am also learning a lot.

I have a couple of basic questions.

How is the symmetry of the rectangular lattice and the centred lattice different?

When was the crystal structure of ice determined by X-ray diffraction?
[Pauling proposed the structure in 1935.]


Comments

  1. AnonymousNovember 1, 2019 at 10:15 PM

    This web site and article may be useful. This is by Kenneth G. Libbrecht, Professor of physics at the California Institute of Technology (Caltech)

    http://snowcrystals.com/

    https://arxiv.org/abs/1910.06389

    ReplyDelete
  2. NBCNovember 5, 2019 at 5:38 AM

    If I remember correctly, the crystal structure of ice was NOT determined by x-ray diffraction, but by a combination of x-ray and neutron diffraction. The configuration of oxygen atoms was known from x-ray experiments, but x-rays are not very sensitive to hydrogen (the intensities go as Z^2). Neutrons, by contrast, are very sensitive to hydrogen, and were used by Shull, Davidson and Wollan to confirm Paulings model (Physical Review 75, 1348), in one of the early highlights in the development of neutron scattering.

    ReplyDelete
    Replies
    1. Ross H. McKenzieNovember 8, 2019 at 1:23 PM

      NBC, Thanks for the very helpful comment.

      The Wollan et al. paper from 1949 does look like the definitive study. It is interesting that the classic book on water by Eisenberg and Kauzmann credits the finding to a later study in 1957 by Peterson and Levy.

      Delete
    2. NBCNovember 10, 2019 at 9:17 AM

      I have quickly checked the first page of the Peterson and Levy paper: It appears that their conclusions agree with those of Wollan et al in supporting what they call "the half-hydrogen description", which is Paulings suggestion.

      The main difference between the papers is that Peterson and Levy used single-crystal neutron diffraction, which can give more details than the neutron powder diffraction technique employed by Wollan, Davidson and Shull. But in this particular case, the main conclusion appears to have been the same, however.

      I guess the precise H positions may differ between the two papers (I did not check), but I think it would have been fair if Eisenberg and Kauzmann had also cited the Wollan paper.

      Delete
  3. Ben PowellNovember 5, 2019 at 10:43 AM

    I think that (and haven't checked, and I've mostly thought about the 2d case) that the point groups of the primitive and centred lattices are the same, but their translational symmetries (and therefore space groups) are different.

    If that's wrong I'd be delighted to be corrected.

    ReplyDelete

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