Difference between revisions of "Family structure"
From Online Dictionary of Crystallography
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| − | By superposing two or more identical copies of the same [[polytypism|polytype]] translated by a superposition vector (''i | + | By superposing two or more identical copies of the same [[polytypism|polytype]] translated by a superposition vector (''i.e'' a vector corresponding to a submultiple of a translation period) a fictitious structure is obtained, which is termed a ''superposition structure''. Among the infinitely possible superposition structures, that structure having all the possible positions of each [[OD structure|OD layer]] is termed a '''family structure''': it exists only if the shifts between adjacent layers are rational, ''i.e.'' if they correspond to a submultiple of lattice translations. |
| − | The family structure is common to all polytypes of the same family. From a group-theoretical viewpoint, building the family structure corresponds to transforming ( | + | The family structure is common to all polytypes of the same family. From a group-theoretical viewpoint, building the family structure corresponds to transforming ('completing') all the local symmetry operations of a space groupoid into the global symmetry operations of a space group. |
==See also== | ==See also== | ||
| − | Chapter 9.2 of ''International Tables | + | *Chapter 9.2 of ''International Tables for Crystallography, Volume C'' |
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Latest revision as of 11:00, 15 May 2017
By superposing two or more identical copies of the same polytype translated by a superposition vector (i.e a vector corresponding to a submultiple of a translation period) a fictitious structure is obtained, which is termed a superposition structure. Among the infinitely possible superposition structures, that structure having all the possible positions of each OD layer is termed a family structure: it exists only if the shifts between adjacent layers are rational, i.e. if they correspond to a submultiple of lattice translations.
The family structure is common to all polytypes of the same family. From a group-theoretical viewpoint, building the family structure corresponds to transforming ('completing') all the local symmetry operations of a space groupoid into the global symmetry operations of a space group.
See also
- Chapter 9.2 of International Tables for Crystallography, Volume C