Difference between revisions of "Incommensurate composite crystal"
From Online Dictionary of Crystallography
TedJanssen (talk | contribs) |
TedJanssen (talk | contribs) |
||
| 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> | + | <math> a_i^{*\nu}~=~\sum_{j=1}^n Z_{ij}^{\nu} A_j^* ~~~(i=1,2,3),</math> |
where Z<sub>ij</sub><sup>ν</sup> are integer coefficients. | where Z<sub>ij</sub><sup>ν</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*ν. 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.