X-Rays and Electron Microscopy

  • K. H. G. Ashbee
Part of the Nato Advanced Study Institutes Series book series (NSSB, volume 19)


The equation of scalar wave propagation in a simple periodic medium, described by can, by \({\nabla ^2}\mu = \frac{1}{{{c^2}}}\,\frac{{{\partial ^2}u}}{{\partial {t^2}}}\,;\,\frac{1}{{{c^2}}}\, = \,\alpha + 2\beta \cos \,(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{g} \cdot \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{r} )\) the Bloch theorem, be satisfied by a function of the form, \(u = \sum\limits_{n = - \infty }^{n = + \infty } {{a_n}\exp \,i\,\left\{ {(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{h} + n\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{g} ) \cdot \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{r} - \omega t} \right\}}\) For this to be a solution, however, we must set some restriction on the values of the coefficients an.


Migration Quartz Carbide Boron Hexagonal 


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Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • K. H. G. Ashbee
    • 1
  1. 1.H. H. Wills Physics LaboratoryUniversity of BristolBristolUK

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