Effects of merohedric twinning on the diffraction pattern. Erratum and corrigenda

Nespolo, M.; Ferraris, G.; Souvignier, B.

doi:10.1107/S205327331402107X

addenda and errata

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ISSN: 2053-2733

Volume 70| Part 6| November 2014| Pages 683-684

doi:10.1107/S205327331402107X

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Effects of merohedric twinning on the diffraction pattern. Erratum and corrigenda

Massimo Nespolo,^a ^* Giovanni Ferraris ^b and Bernd Souvignier ^c

^aUniversité de Lorraine, Faculté des Sciences et Technologies, Institut Jean Barriol FR 2843, CRM2 UMR CNRS 7036, BP 70239, Boulevard des Aiguillettes, F-54506 Vandoeuvre-lès-Nancy cedex, France, ^bDipartimento di Scienze della Terra, Università di Torino, via Valperga Caluso 35, I-10125 Torino, Italy, and ^cInstitute for Mathematics, Astrophysics and Particle Physics, Faculty of Science, Mathematics and Computing Science, Radboud University Nijmegen, Postbus 9010, 6500 GL Nijmegen, The Netherlands
^*Correspondence e-mail: massimo.nespolo@crm2.uhp-nancy.fr

(Received 8 September 2014; accepted 8 September 2014; online 2 October 2014)

A number of corrections are made to the article by Nespolo et al. [Acta Cryst. (2014), A70, 106–125 ].

Keywords: merohedric twinning; reflection conditions; diffraction symmetry.

On p. 110, the first sentence of the second paragraph should start as follows: `Tables 2 to 5 list the 101 merohedral non-symmorphic types of space groups H that can give rise to 147 twin laws …'

Misalignment of some of the entries the third and fourth columns of Table 3 make this table difficult to read. It is reproduced here with better alignment of the entries in these columns.

Table 3
Classification of the 34 merohedral non-symmorphic space-group types H in the tetragonal crystal family, which can give rise to 42 twin laws

Three twin laws (indicated by the symbol {) have been split into two, because two different coset representatives give different results in terms of G, leading to a total of 45 cases. Among these, ten cannot be extended by a twofold operation s corresponding to the twin operation t (`no extension' in the table), and 16 more do have such an extension but none of the corresponding supergroups G has the same reflection conditions as H (`---' in the table). For these 26 cases (16 for class I and ten for class IIA) the G model is ruled out on the basis of the observed reflection conditions: H in the corresponding row is shown in bold, accompanied by dashes in the last column. For the other 19 cases, the group G^# having the same reflection conditions as H is given; in the tetragonal crystal family, G^# is always a supergroup of H. Entries are ordered according to the diffraction symbol, as given in LVB.

Diffraction symbol	H	No.	t		G^#	No.
Non-centrosymmetric hemihedral (only class I twinning possible)
P-2₁-	P42₁2	90	$[\bar 1]$		---	---
	$[{\bi P}{\bar {\bf 4}}{\bf 2_1} {\bi m}]$	113	$[\bar 1]$		---	---
P4₂--	P4₂22	93			---	---
P4₂2₁-	P4₂2₁2	94			---	---
P4₁--	P4₁22	91			no extension	---
	P4₃22	95			no extension	---
P4₁2₁--	P4₁2₁2	92			no extension	---
	P4₃2₁2	96			no extension	---
P--c	P4₂mc	105			P4₂/mmc	131
	$[P{\bar 4}2c]$	112			P4₂/mmc	131
P-2₁c	$[{\bi P}{\bar {\bf 4}}{\bf 2_1} {\bi c}]$	114			---	---
P-b-	P4bm	100			P4/mbm	127
	$[P{\bar 4}b2]$	117			P4/mbm	127
P-bc	P4₂bc	106			P4₂/mbc	135
P-c-	P4₂cm	101			P4₂/mcm	132
	$[P{\bar 4}c2]$	116			P4₂/mcm	132
P-cc	P4cc	103			P4/mcc	124
P-n-	P4₂nm	102			P4₂/mnm	136
	$[P{\bar 4}n2]$	118			P4₂/mnm	136
P-nc	P4nc	104			P4/mnc	128
I4₁--	I4₁22	98			---	---
I--d	I4₁md	109			---	---
	$[{\bi I}{\bar {\bf 4}}{\bf 2}{\bi d}]$	122			---	---
I-c-	I4cm	108			I4/mcm	140
	$[I{\bar 4}c2]$	120			I4/mcm	140
I-cd	I4₁cd	110			---	---

Centrosymmetric hemihedral (only class IIA twinning possible)
P4₂--	P4₂/m	84	$[\Big\{]$	2_[100]	---	---
			$[\Big\{]$	2_[110]	no extension	---
Pn--	P4/n	85	$[\Big\{]$	2_[100]	---	---
			$[\Big\{]$	2_[110]	P4/nmm	129
P4₂/n--	P4₂/n	86	2_[100]		---	---

Tetartohedral (both class I and class IIA twinning possible)
P4₂--	P4₂	77	$[\bar 1]$		P4₂/m	84
			2_[100]		P4₂22	93
			m_[100]		---	---
P4₁--	P4₁	76	$[\bar {\bf 1}]$		no extension	---
			2_[100]		P4₁22	91
			m_[100]		no extension	---
	P4₃	78	$[\bar {\bf 1}]$		no extension	---
			2_[100]		P4₃22	95
			m_[100]		no extension	---
I4₁--	I4₁	80	$[\bar {\bf 1}]$		---	---
			2_[100]		I4₁22	98
			$[\Big\{]$	m_[100]	---	---
			$[\Big\{]$	m_[110]	no extension	---
I4₁/a--	I4₁/a	88	2_[100]		---	---

In Table 4, the asterisks (*) marking two of the entries in the fifth column should be omitted. The corrected table is given here.

Table 4
Classification of the 27 merohedral non-symmorphic space-group types H in the hexagonal crystal family, which can give rise to 61 twin laws

Among these, 29 cannot be extended by a twofold operation s corresponding to the twin operation t (`no extension' in the table), and two more have such an extension but none of the corresponding supergroups G has the same reflection conditions as H (`---' in the table): for these 31 cases (15 for class I and 16 for class IIA) the G model is ruled out on the basis of the observed reflection conditions: H in the corresponding row is shown in bold, accompanied by dashes in the last column. For the other 30 cases, the group G^# having the same reflection conditions as H is given. Entries are ordered according to the diffraction symbol, as given in LVB.

Diffraction symbol	H	No.	t	G^#	No.
Non-centrosymmetric hemihedral (only class I twinning possible)
P--c	P6₃mc	186	$[\bar 1]$	P6₃/mmc	194
	$[P{\bar 6}2c]$	190	$[\bar 1]$	P6₃/mmc	194
P-c-	P6₃cm	185		P6₃/mcm	193
	$[P{\bar 6}c2]$	188		P6₃/mcm	193
R-c	R3c	161		$[R{\bar 3}c]$	167
P6₃--	P6₃22	182		---	---
P6₂--	P6₂22	180		no extension	---
	P6₄22	181		no extension	---
P6₁--	P6₁22	178		no extension	---
	P6₅22	179		no extension	---
P-cc	P6cc	184		P6/mcc	192

Centrosymmetric hemihedral (only class IIA twinning possible)
P6₃--	P6₃/m	176	m_[100]	---	---
P--c	$[P{\bar 3}1c]$	163	m_[001]	P6₃/mmc	194
P-c-	$[P{\bar 3}c1]$	165	m_[001]	P6₃/mcm	193

Tetartohedral or ogdohedral (both class I and class IIA twinning possible)
P3₁--	P3₁	144	$[{\bar {\bf 1}}]$	no extension	---
			2_[210]	P3₁12	151
			2_[100]	P3₁21	152
			2_[001]	P6₄	172
			m_[001]	no extension	---
			m_[100]	no extension	---
			m_[210]	no extension	---
	P3₁12	151	$[\bar {\bf 1}]$	no extension	---
			2_[001]	P6₄22	181
			m_[001]	no extension	---
	P3₁21	152	$[\bar {\bf 1}]$	no extension	---
			2_[001]	P6₄22	181
			m_[001]	no extension	---
	P3₂	145	$[\bar {\bf 1}]$	no extension	---
			2_[210]	P3₂12	153
			2_[100]	P3₂21	154
			2_[001]	P6₂	171
			m_[001]	no extension	---
			m_[100]	no extension	---
			m_[210]	no extension	---
	P3₂12	153	$[\bar {\bf 1}]$	no extension	---
			2_[001]	P6₂22	180
			m_[001]	no extension	---
	P3₂21	154	$[\bar {\bf 1}]$	no extension	---
			2_[001]	P6₂22	180
			m_[001]	no extension	---
P--c	P31c	159	$[\bar 1]$	$[P{\bar 3}1c]$	163
			m_[001]	$[P{\bar 6}2c]$	190
			2_[001]	P6₃mc	186
P-c-	P3c1	158	$[\bar 1]$	$[P{\bar 3}c1]$	165
			m_[001]	$[P{\bar 6}c2]$	188
			2_[001]	P6₃cm	185
P6₃--	P6₃	173	$[\bar 1]$	P6₃/m	176
			2_[100]	P6₃22	182
			m_[100]	no extension	---
P6₂--	P6₂	171	$[\bar {\bf 1}]$	no extension	---
			2_[100]	P6₂22	180
			m_[100]	no extension	---
	P6₄	172	$[\bar {\bf 1}]$	no extension	---
			2_[100]	P6₄22	181
			m_[100]	no extension	---
P6₁--	P6₁	169	$[\bar {\bf 1}]$	no extension	---
			2_[100]	P6₁22	178
			m_[100]	no extension	---
	P6₅	170	$[\bar {\bf 1}]$	no extension	---
			2_[100]	P6₅22	179
			m_[100]	no extension	---

In Table 7, the sixth entry from the bottom of the 13th column, l = 4n, should not be bold.

Acknowledgements

We thank Howard Flack for spotting these errors.

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addenda and errata\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Effects of merohedric twinning on the diffraction pattern. Erratum and corrigenda

Acknowledgements

addenda and errata