Difference between revisions of "Incommensurate composite crystal"
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| − | + | <font color="blue">Cristal composite incommensurable</font> (''Fr''). <font color="red">Inkommensurabler Kompositkristall</font> (''Ge''). <font color="black">Cristallo composito incommensurabile</font> (''It''). <font color="purple">非整合複合結晶</font> (''Ja''). <font color="green">Estructura inconmensurable compuesta crystal</font> (''Sp''). | |
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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 | |
| − | 3''N'' basis vectors | + | 3''N'' basis vectors <math>A_j^*</math> such that |
| − | <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 == | |
Examples are intergrowth crystals and adsorbed monolayers. To the former belongs | Examples are intergrowth crystals and adsorbed monolayers. To the former belongs | ||
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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]] | ||
Latest revision as of 17:15, 14 November 2017
Cristal composite incommensurable (Fr). Inkommensurabler Kompositkristall (Ge). Cristallo composito incommensurabile (It). 非整合複合結晶 (Ja). Estructura inconmensurable compuesta crystal (Sp).
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.