# Atomic modulation function

### From Online Dictionary of Crystallography

Fonction de modulation atomique (*Fr*). Funzione di modulazione atomica (*It*). 原子変調関数 (*Ja*).

## Definition

A modulated crystal structure is a 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

The occupation probability to find an atom of species *A* at the position *n* + *r*_{j}
is *p*_{A}(*n*,*j*), where the sum over the species of the functions *p*_{A}
is one. Instead of a different species, one may have a vacancy. The functions
*u*(*n*,*j*) and *p*_{A}(*n*,*j*) 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

Modulation functions may be continuous or discontinuous.