Actions

Difference between revisions of "Incommensurate composite crystal"

From Online Dictionary of Crystallography

Line 13: Line 13:
 
3''N'' basis vectors  '''A'''<sub>j</sub><sup>*</sup> such that
 
3''N'' basis vectors  '''A'''<sub>j</sub><sup>*</sup> such that
  
<math>{\bf a}_i^{*\nu}~=~\sum_{j=1}^n Z_{ij}^{\nu} {\bf A}_j^* ~~~(i=1,2,3),</math>
+
<math> a_i^{*\nu}~=~\sum_{j=1}^n Z_{ij}^{\nu} A_j^* ~~~(i=1,2,3),</math>
  
 
where Z<sub>ij</sub><sup>&nu;</sup> are integer coefficients.
 
where Z<sub>ij</sub><sup>&nu;</sup> are integer coefficients.

Revision as of 18:20, 18 May 2009

Incommensurate Composite Crystal


Cristal composite (Fr.)

Definition

An incommensurate composite crystal is a compound with two or more (N) subsystems that are themselves modulated structures, with basis structures that are mutually incommensurate. Each subsystem (numbered by ν) has a reciprocal lattice for its basic structure with three basis vectors ai. There is a basis of the module of diffraction spots that has at most 3N basis vectors Aj* such that

[math] a_i^{*\nu}~=~\sum_{j=1}^n Z_{ij}^{\nu} A_j^* ~~~(i=1,2,3),[/math]

where Zijν are integer coefficients. If n is larger than the dimension of space (three), the composite crystal is an aperiodic crystal.

Applications

Examples are intergrowth crystals and adsorbed monolayers. To the former belongs Hg3-δAsF6 with two systems of Hg chains inside the host lattice formed by AsF6 octahedra. Another example is nonadecane in the channels of a urea host crystal.