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Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Examples of vibration modes plotted over the first Brillouin zone (frequency νi versus Brillouin radius σa). Note for each vibration mode the curves overlap except for v3, where the difference is small. (Online version in colour.)