Difference between revisions of "Incommensurate composite crystal"
From Online Dictionary of Crystallography
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<Font color="blue">Cristal composite</font> (Fr.) | <Font color="blue">Cristal composite</font> (Fr.) | ||
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An ''incommensurate composite crystal'' is a compound with two or more (''N'') subsystems that are | 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. | themselves modulated structures, with basis structures that are mutually incommensurate. | ||
| − | Each subsystem (numbered by ν) has a reciprocal lattice for its | + | 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 | <math>a_i^{*\nu}</math>. There is a basis of the [[vector module]] of diffraction spots that has at most | ||
3''N'' basis vectors <math>A_j^*</math> such that | 3''N'' basis vectors <math>A_j^*</math> such that | ||
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by AsF<sub>6</sub> octahedra. Another example is nonadecane in the channels of a urea | by AsF<sub>6</sub> octahedra. Another example is nonadecane in the channels of a urea | ||
host crystal. | host crystal. | ||
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| + | [[Category:Fundamental crystallography]] | ||
Revision as of 14:03, 6 February 2012
Cristal composite (Fr.)
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.