Studying vibration modes of ice X

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Frank Einstein
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Good afternoon. I am doing an study on ice X, a material with this structure http://postimg.org/image/nub4if9kb/
I want to know why in the centre of the brioullin zone the hidrogen atoms must remain at rest on an even mode.

My reference book is Charles Kittle's, but there is no discussion about this; If someone woul pont me to a book or webpage where this is discused I would really appreciate that.

Thanks for reading.
 
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Frank Einstein said:
Good afternoon. I am doing an study on ice X, a material with this structure http://postimg.org/image/nub4if9kb/
I want to know why in the centre of the brioullin zone the hidrogen atoms must remain at rest on an even mode.

My reference book is Charles Kittle's, but there is no discussion about this; If someone woul pont me to a book or webpage where this is discused I would really appreciate that.

Thanks for reading.
I don't know.
website
http://www1.lsbu.ac.uk/water/ice_x.html

or google ice ten brillouin zone However if you have web of knowledge you could start with these articles
http://pubs.acs.org/doi/abs/10.1021/jp050690z
http://pubs.rsc.org/en/content/articlehtml/2011/cp/c1cp22167a
 
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Thanks for the info.