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Difference between revisions of "Atomic modulation function"

From Online Dictionary of Crystallography

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

Revision as of 16:08, 5 April 2015

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

[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.