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Difference between revisions of "Displacive modulation"

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<Font color="blue">Modulation displacive </font>(Fr.)
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<Font color="blue">Modulation displacive </font>(''Fr''). <Font color="purple">変位型変調</font>(''Ja'').
 +
 
  
 
For a  ''displacively modulated crystal phase'', the positions of the atoms are
 
For a  ''displacively modulated crystal phase'', the positions of the atoms are
 
displaced from those of a basis structure with space group symmetry (an ordinary
 
displaced from those of a basis structure with space group symmetry (an ordinary
crystal). The displacements are given by the  ''atomic modulation function''  '''u'''<sub>j</sub>('''r'''),
+
[[crystal]]). The displacements are given by the  [[atomic modulation function]] '''u'''<sub>j</sub>('''r'''), where ''j'' indicates the ''j''th atom in the [[unit cell]] of the basic structure.
where ''j'' indicates the ''j''th atom in the unit cell of the basic structure.
 
  
 
<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 13:56, 20 March 2015

Modulation displacive (Fr). 変位型変調(Ja).


For a displacively modulated crystal phase, the positions of the atoms are displaced from those of a basis structure with space group symmetry (an ordinary crystal). The displacements are given by the atomic modulation function uj(r), where j indicates the jth atom in the unit cell of the basic structure.

[math] r( n,j)~=~ n+ r_j+ u_j( n+ r_j).[/math]

The modulation function has a Fourier expansion

[math] u_j( r)~=~\sum_ k \hat{ u}( k) \exp (2\pi i k. r),~with~ k=\sum_{i=1}^n h_i a_i^*,[/math]

with finite value of n. If n=1, the modulated structure is one-dimensionally modulated. A special case of a one-dimensionally modulated structure is

[math]r(n,j)_{\alpha}~=~ n_{\alpha}+ r_{j\alpha}+A_{j\alpha} \sin \left(2\pi i q. n+ r_j)+\phi_{j\alpha}\right), (\alpha=x,y,z).[/math]