View source for Atomic modulation function

<Font color="blue">Fonction de modulation atomique</font> (''Fr''). <Font color="black">Funzione di modulazione atomica</font> (''It''). <Font color="purple">原子変調関数</font> (''Ja'').

== Definition ==

A [[modulated crystal structure]] is a [[crystal pattern|structure]] that may be obtained from a crystalline system with [[space group]] symmetry, and therefore with [[lattice]] periodicity, by a regular displacement of atoms ([[displacive modulation]]) and/or change in the occupation probability of a site in the basic structure. The deviation from the positions in the basic structure are given by

<math>r(n,j) = n~+~r_j+u_j((n+r_j).</math>

The occupation probability to find an atom of species ''A'' at the position <math>n+r_j</math>
is <math>p_A(n,j)</math>, where the sum over the species of the functions <math>p_A</math>
is one. Instead of a different species, one may have a vacancy. The functions
<math>u(n,j)</math> and <math>p_A(n,j)</math> are the  ''atomic modulation functions''.
For a crystal they should have Fourier modules of finite rank,  ''i.e''. the
functions have Fourier transforms with delta peaks on wave vectors  '''k''' of the form

<math>k~=~\sum_{i=1}^n h_i a_i^*,~~(h_i~~{\rm integers},~n~{\rm finite}.)</math>

Modulation functions may be continuous or discontinuous.

[[Category: Fundamental crystallography]]