Priority rule - Revision history

BrianMcMahon: Tidied translations and added German and Spanish (U. Mueller)

2017-11-17T10:11:04Z

Tidied translations and added German and Spanish (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-16T13:30:44Z

Style edits to align with printed edition

MassimoNespolo: Adapted to ITA6

2017-04-10T16:31:55Z

Adapted to ITA6

MassimoNespolo: precision

2015-07-08T04:11:50Z

precision

MassimoNespolo at 13:21, 17 March 2009

2009-03-17T13:21:17Z

New page

Règle de priorité (''Fr''). Regola di priorità (''It'')

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'', ''d'';
*rotation axes before screw axes.

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''212121 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''212121 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''213 (199) are two distinct types of space groups. For this pair, the same arguments apply as given above for ''I''222 and ''I''212121.

==See also==
Sections 4.1.2.3 of ''International Tables for Crystallography, Volume A''

[[Category:Fundamental crystallography]]

← Older revision		Revision as of 10:11, 17 November 2017
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−	<~~Font~~ color="blue">Règle de priorité </~~Font~~>(''Fr''). <~~Font~~ color="black">Regola di priorità </~~Font~~>(''It'').	+	<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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-<Font color="blue">Règle de priorité </Font>(''Fr''). <Font color="black">Regola di priorità </Font>(''It'')
+<Font color="blue">Règle de priorité </Font>(''Fr''). <Font color="black">Regola di priorità </Font>(''It'').
@@ Line 13: / Line 13: @@
 #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.
-#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.
+#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.
@@ Line 19: / Line 19: @@
 ==See also==
-Sections 1.4.1.4 of ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
+*Chapter 1.4.1.4 of ''International Tables for Crystallography, Volume A'', 6th edition
 [[Category:Fundamental crystallography]]

@@ Line 1: / Line 1: @@
 <Font color="blue">Règle de priorité </Font>(''Fr''). <Font color="black">Regola di priorità </Font>(''It'')
 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'', ''d'';
+*''m'', ''e'', (''a'', ''b'', ''c''), ''n''
 *rotation axes before screw axes of the same rotational order.
 There are a few exceptions to this choice:
@@ Line 18: / Line 19: @@
 ==See also==
-Sections 4.1.2.3 of ''International Tables for Crystallography, Volume A''
+Sections 1.4.1.4 of ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
 [[Category:Fundamental crystallography]]