Z and Z' - Revision history

BrianMcMahon: Added reference to the 2025 Nomenclature Report sanctioning fractional values of Z

2025-09-18T00:03:51Z

Added reference to the 2025 Nomenclature Report sanctioning fractional values of Z

GervaisChapuis at 13:03, 23 June 2024

2024-06-23T13:03:04Z

GervaisChapuis at 14:09, 22 June 2024

2024-06-22T14:09:08Z

GervaisChapuis at 14:06, 22 June 2024

2024-06-22T14:06:24Z

GervaisChapuis at 07:14, 20 June 2024

2024-06-20T07:14:27Z

GervaisChapuis at 08:16, 16 June 2024

2024-06-16T08:16:17Z

GervaisChapuis at 08:14, 16 June 2024

2024-06-16T08:14:34Z

GervaisChapuis at 08:05, 16 June 2024

2024-06-16T08:05:08Z

GervaisChapuis at 08:03, 16 June 2024

2024-06-16T08:03:26Z

GervaisChapuis at 07:47, 16 June 2024

2024-06-16T07:47:58Z

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 == Definitions ==
-In the description of a crystal structure, the letter Z characterises the number of (chemical) formula units contained in the unit cell. For 3D-periodic structures, this number is always an integer which is at least 1.
+In the description of a crystal structure, the letter Z characterises the number of (chemical) formula units contained in the unit cell. For 3D-periodic structures, this number is (almost) always an integer which is at least 1. (For the rare circumstances in which a non-integer value may be reported, see ''''Non-integral values of Z''' below.)
 When dealing with molecular structures, it is also convenient to define Z'. Z' indicates the number of formula units in the asymmetric unit. In other words, Z' is the value of Z divided by the multiplicity of the general position of the corresponding space group. Z' can be a fraction or a positive integer.
-uncertainties
 == Examples ==
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 The cubic structure of NaCl belongs to space group <math>Fm\overline{3}m</math>. The unit cell contains 4 Na and 4 Cl atoms. Consequently Z=4. for inorganic structures, Z' might be a fraction. For NaCl, Z' would be 4/196 or 1/48 indicating that each atom lies on highly symmetric special positions with site symmetry <math>m\overline{3}m</math>.
+In molecular structures, Z' is often equal to one, but can be a rational fraction. If the chemical entity sits on or across crystallographic site symmetry, such as mirror planes, rotation axes and inversion centres or combinations thereof, Z' can be a rational fraction < 1 equal to the ratio Z over the multiplicity of the general position of the corresponding space group. When Z' is an integer ''n'' larger than 1, there are ''n'' symmetry-independent chemical entities in the asymmetric unit.  These entities have identical chemical composition, atomic connectivity and stereochemistry. Such species may be conformers with very similar molecular conformations or different conformations of one or more groups within the molecule as a result of rotations about one or more bonds.
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 In some cases, there are however problems and issues to consider when estimating a value of Z' to a structure. The reference below, What is Z'?, lists a series of pitfalls in some complex structures illustrating the problems of assaining a proper value to Z'.
 == See also ==
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 * [http://zprime.co.uk What is Z'?]
 * [https://www.iucr.org/news/newsletter/etc/articles?issue=149786&result_138339_result_page=10 Looking deeper into molecular structures with Z' > 1 ]
 [[Category:Fundamental crystallography]]

← Older revision		Revision as of 13:03, 23 June 2024
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−	In molecular structures, Z' is often equal to one, but can be a rational fraction. If the chemical entity sits on or across crystallographic site symmetry, such as mirror planes, rotation axes and inversion centres or combinations ~~of them~~, Z' can be a rational fraction < 1 equal to the ratio Z over the multiplicity of the general position of the corresponding space group. When Z' is an integer, n, larger than 1, there are n symmetry-independent chemical entities in the asymmetric unit. These entities have identical chemical composition, atomic connectivity and stereochemistry. Such species may ~~have~~ very similar molecular conformations ~~(conformers)~~ or different conformations of one or more groups within the molecule.	+	In molecular structures, Z' is often equal to one, but can be a rational fraction. If the chemical entity sits on or across crystallographic site symmetry, such as mirror planes, rotation axes and inversion centres or combinations thereof, Z' can be a rational fraction < 1 equal to the ratio Z over the multiplicity of the general position of the corresponding space group. When Z' is an integer, n, larger than 1, there are n symmetry-independent chemical entities in the asymmetric unit. These entities have identical chemical composition, atomic connectivity and stereochemistry. Such species may be conformers with very similar molecular conformations or different conformations of one or more groups within the molecule as a result of rotations about one or more bonds.
		+

	== Remark ==		== Remark ==

@@ Line 17: / Line 17: @@
 == Remark ==
-There are however problems and issues to consider when estimating a value of Z' to a structure. The reference below, What is Z'?, lists a series of pitfalls in some complex structures illustrating the problems of assaining a proper value to Z'.
+In some cases, there are however problems and issues to consider when estimating a value of Z' to a structure. The reference below, What is Z'?, lists a series of pitfalls in some complex structures illustrating the problems of assaining a proper value to Z'.
 == See also ==

@@ Line 17: / Line 17: @@
 == Remark ==
-In some rare cases of ionic compounds, the definition of the asymmetric unit is subject to some limitations. The reference below, What is Z'?, gives some further interesting details.
+There are however problems and issues to consider when estimating a value of Z' to a structure. The reference below, What is Z'?, lists a series of pitfalls in some complex structures illustrating the problems of assaining a proper value to Z'.
 == See also ==

@@ Line 12: / Line 12: @@
 The cubic structure of NaCl belongs to space group <math>Fm\overline{3}m</math>. The unit cell contains 4 Na and 4 Cl atoms. Consequently Z=4. for inorganic structures, Z' might be a fraction. For NaCl, Z' would be 4/196 or 1/48 indicating that each atom lies on highly symmetric special positions with site symmetry <math>m\overline{3}m</math>.
-In molecular structures, Z' is very often equal to one. However, when Z' is an integer larger than 1 this gives some interesting information about the stereochemistry of the molecular compound.
 == Remark ==

@@ Line 19: / Line 19: @@
 == See also ==
-*[[Unit cell]]
+* [[Unit cell]]
-*[[Asymmetric unit]]
+* [[Asymmetric unit]]
-* What is Z'?  [http://zprime.co.uk/ http://zprime.co.uk]
+* [http://zprime.co.uk What is Z'?]
-* Looking deeper into molecular structures with Z' > 1 [https://www.iucr.org/news/newsletter/etc/articles?issue=149786&result_138339_result_page=10/]
+* [https://www.iucr.org/news/newsletter/etc/articles?issue=149786&result_138339_result_page=10 Looking deeper into molecular structures with Z' > 1 ]
 [[Category:Fundamental crystallography]]

@@ Line 15: / Line 15: @@
 == Remark ==
-In some rare cases, the definition of the asymmetric unit is subject to some uncertainties. The reference below, What is Z'?, gives some further interesting details.
+In some rare cases of ionic compounds, the definition of the asymmetric unit is subject to some uncertainties. The reference below, What is Z'?, gives some further interesting details.
 == See also ==