# Priority rule

### From Online Dictionary of Crystallography

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- | < | + | <font color="blue">Règle de priorité</font> (''Fr''). <font color="red">Prioritätsregel</font> (''Ge''). <font color="black">Regola di priorità</font> (''It''). <font color="green">Regla de prioridad</font> (''Sp''). |

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When more than one kind of [[symmetry element]] occurs for a given symmetry direction, the choice for defining the appropriate Hermann–Mauguin symbol for the [[space group]] is made in order of descending priority: | When more than one kind of [[symmetry element]] occurs for a given symmetry direction, the choice for defining the appropriate Hermann–Mauguin symbol for the [[space group]] is made in order of descending priority: | ||

- | *''m'', ''e'', ''a'', ''b'', ''c'', ''n'' | + | *''m'', ''e'', (''a'', ''b'', ''c''), ''n'' |

*rotation axes before screw axes of the same rotational order. | *rotation axes before screw axes of the same rotational order. | ||

+ | |||

+ | The ''d'' glide does not appear explicitly because it always come last in the order of priority. | ||

There are a few exceptions to this choice: | There are a few exceptions to this choice: | ||

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#For orthorhombic space groups, the priority rule is applied only to the ‘standard symbol’. The symbols for the other ﬁve settings are obtained from the standard symbol by the appropriate transformations, without invoking the priority rule again. | #For orthorhombic space groups, the priority rule is applied only to the ‘standard symbol’. The symbols for the other ﬁve settings are obtained from the standard symbol by the appropriate transformations, without invoking the priority rule again. | ||

#Space-group types ''I''222 and ''I''2<sub>1</sub>2<sub>1</sub>2<sub>1</sub> are two distinct types. Both contain parallel twofold rotation and screw axes and thus would receive the same symbol according to the priority rule. In ''I''222, the three rotation axes and the three screw axes intersect, whereas in ''I''2<sub>1</sub>2<sub>1</sub>2<sub>1</sub> neither the three rotation axes nor the three screw axes intersect. | #Space-group types ''I''222 and ''I''2<sub>1</sub>2<sub>1</sub>2<sub>1</sub> are two distinct types. Both contain parallel twofold rotation and screw axes and thus would receive the same symbol according to the priority rule. In ''I''222, the three rotation axes and the three screw axes intersect, whereas in ''I''2<sub>1</sub>2<sub>1</sub>2<sub>1</sub> neither the three rotation axes nor the three screw axes intersect. | ||

- | #For space groups of type No. | + | #For space groups of type No. 73, the standard symbol ''Ibca'' was adopted, instead of ''Ibaa'' according to the rule, because ''Ibca'' displays the equivalence of the three symmetry directions clearly. |

# In tetragonal space groups with both ''a'' and ''b'' glide planes containing the [001] direction, the preference was given to ''b'', as in ''P4bm''. | # In tetragonal space groups with both ''a'' and ''b'' glide planes containing the [001] direction, the preference was given to ''b'', as in ''P4bm''. | ||

#In cubic space groups where tertiary symmetry planes with glide components 1/2, 0, 0; 0, 1/2, 0; 0, 0, 1/2 and 1/2, 1/2 , 1/2 coexist, the tertiary symmetry element was called ''n'' in ''P'' groups (instead of ''a'', ''b'' or ''c'') but ''c'' in ''F'' groups, because these symmetry elements intersect the origin. | #In cubic space groups where tertiary symmetry planes with glide components 1/2, 0, 0; 0, 1/2, 0; 0, 0, 1/2 and 1/2, 1/2 , 1/2 coexist, the tertiary symmetry element was called ''n'' in ''P'' groups (instead of ''a'', ''b'' or ''c'') but ''c'' in ''F'' groups, because these symmetry elements intersect the origin. | ||

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==See also== | ==See also== | ||

- | + | *Chapter 1.4.1.4 of ''International Tables for Crystallography, Volume A'', 6th edition | |

[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] |

## Latest revision as of 10:11, 17 November 2017

Règle de priorité (*Fr*). Prioritätsregel (*Ge*). Regola di priorità (*It*). Regla de prioridad (*Sp*).

When more than one kind of symmetry element occurs for a given symmetry direction, the choice for defining the appropriate Hermann–Mauguin symbol for the space group is made in order of descending priority:

*m*,*e*, (*a*,*b*,*c*),*n*- rotation axes before screw axes of the same rotational order.

The *d* glide does not appear explicitly because it always come last in the order of priority.

There are a few exceptions to this choice:

- For glide planes in centred monoclinic space groups, the priority rule is purposely not followed in order to bring out the relations between the three ‘cell choices’ given for each setting.
- For orthorhombic space groups, the priority rule is applied only to the ‘standard symbol’. The symbols for the other ﬁve settings are obtained from the standard symbol by the appropriate transformations, without invoking the priority rule again.
- Space-group types
*I*222 and*I*2_{1}2_{1}2_{1}are two distinct types. Both contain parallel twofold rotation and screw axes and thus would receive the same symbol according to the priority rule. In*I*222, the three rotation axes and the three screw axes intersect, whereas in*I*2_{1}2_{1}2_{1}neither the three rotation axes nor the three screw axes intersect. - For space groups of type No. 73, the standard symbol
*Ibca*was adopted, instead of*Ibaa*according to the rule, because*Ibca*displays the equivalence of the three symmetry directions clearly. - In tetragonal space groups with both
*a*and*b*glide planes containing the [001] direction, the preference was given to*b*, as in*P4bm*. - In cubic space groups where tertiary symmetry planes with glide components 1/2, 0, 0; 0, 1/2, 0; 0, 0, 1/2 and 1/2, 1/2 , 1/2 coexist, the tertiary symmetry element was called
*n*in*P*groups (instead of*a*,*b*or*c*) but*c*in*F*groups, because these symmetry elements intersect the origin. - Space groups of type
*I*23 and*I*2_{1}3 (199) are two distinct types of space groups. For this pair, the same arguments apply as given above for*I*222 and*I*2_{1}2_{1}2_{1}.

## See also

- Chapter 1.4.1.4 of
*International Tables for Crystallography, Volume A*, 6th edition