Difference between revisions of "Incommensurate composite crystal"
From Online Dictionary of Crystallography
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themselves modulated structures, with basis structures that are mutually incommensurate. | 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 | Each subsystem (numbered by ν) has a reciprocal lattice for its basic structure with three basis vectors | ||
| − | + | <math>a_i^{*\nu}</math>. There is a basis of the [[vector module]] of diffraction spots that has at most | |
| − | 3''N'' basis vectors | + | 3''N'' basis vectors <math>A_j^*</math> such that |
<math> a_i^{*\nu}~=~\sum_{j=1}^n Z_{ij}^{\nu} 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 | + | where <math>Z_{ij}^{\nu}</math> are integer coefficients. |
If ''n'' is larger than the dimension of space (three), the composite crystal is an aperiodic crystal. | If ''n'' is larger than the dimension of space (three), the composite crystal is an aperiodic crystal. | ||
| + | ''n'' is the rank of the vector module. | ||
'''Applications''' | '''Applications''' | ||
Revision as of 06:20, 19 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 [math]a_i^{*\nu}[/math]. There is a basis of the vector module of diffraction spots that has at most 3N basis vectors [math]A_j^*[/math] such that
[math] a_i^{*\nu}~=~\sum_{j=1}^n Z_{ij}^{\nu} A_j^* ~~~(i=1,2,3),[/math]
where [math]Z_{ij}^{\nu}[/math] are integer coefficients. If n is larger than the dimension of space (three), the composite crystal is an aperiodic crystal. n is the rank of the vector module.
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.