Twinning by metric merohedry - Revision history

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

2017-11-20T14:30:41Z

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

BrianMcMahon: Style edits to align with printed edition

2017-05-17T17:46:05Z

Style edits to align with printed edition

MassimoNespolo: title

2008-04-10T13:07:23Z

title

AndreAuthier at 12:28, 10 April 2008

2008-04-10T12:28:03Z

MassimoNespolo at 20:42, 9 April 2008

2008-04-09T20:42:05Z

MassimoNespolo at 09:43, 15 May 2006

2006-05-15T09:43:08Z

MassimoNespolo at 13:05, 26 April 2006

2006-04-26T13:05:43Z

New page

Mériédrie métrique(Fr). Meroedria metrica(It)


Twinning by metric merohedry is a special case of [[twinning by merohedry]] which occurs when:
* the lattice of the individual has accidentally a specialized metric which corresponds to a higher holohedry
* the twin operation belongs to this higher holohedry only

If H is the individual point group, D(H) the corresponding holohedry and D(L) the point group of the lattice, twinning by metric merohedry corresponds to D(L) ⊃ D(H) &supe; H

Twinning by metric merohedry can be seen as the degeneration of [[twinning by reticular merohedry]] to [[twin index]] 1, or of [[twinning by pseudomerohedry]] to [[twin obliquity]] zero.

==Example==
A monoclinic crystal of point group H = 2 with angle β = 90º has a orthorhombic lattice. It may undergo two types of twinning by merohedry:
* if the twin operation belongs to the monoclinic holohedry D(H) = 2/''m'', twinning is the classical twinning by merohedry, also termed [[twinning by syngonic merohedry]];
* if the twin operation belongs to the orthorhombic holohedry D(L) = ''mmm'', twinning is by metric merohedry.

==Historical note==
Friedel (1904, p. 143; 1926, p. 56-57) called metric merohedry '''mériédrie d’ordre supérieur''' (higher order merohedry) but stated that it was either unlikely or equivalent to a pseudo-merohedry of low obliquity. Nowadays several examples of true metric merohedry (within experimental uncertainty) are known.

[[Category: Fundamental crystallography]]

← Older revision		Revision as of 14:30, 20 November 2017
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−	~~<p>~~<font color="blue"> Maclage par mériédrie métrique</font>(<i>Fr</i>). <font color="black"> Geminazione per meroedria metrica</font>(<i>It</i>).	+	<font color="blue">Maclage par mériédrie métrique</font> (''Fr''). <font color="red">Verzwillingung durch metrische Meroedrie</font> (''Ge''). <font color="black">Geminazione per meroedria metrica</font> (''It''). <font color="green">Macla por meroedría métrica</font> (''Sp'').
−	~~</p>~~	+

@@ Line 1: / Line 1: @@
-<p><font color="blue"> Maclage par mériédrie métrique</font>(<i>Fr</i>); <font color="black"> Geminazione per meroedria metrica</font>(<i>It</i>)
+<p><font color="blue"> Maclage par mériédrie métrique</font>(<i>Fr</i>). <font color="black"> Geminazione per meroedria metrica</font>(<i>It</i>).
 </p>
 Twinning by metric merohedry is a special case of [[twinning by merohedry]] which occurs when:
-* the lattice of the individual has accidentally a specialized metric which corresponds to a higher holohedry
+* the lattice of the individual has accidentally a specialized metric which corresponds to a higher holohedry,
-* the twin operation belongs to this higher holohedry only
+* the twin operation belongs to this higher holohedry only.
-If H is the individual point group, D(H) the corresponding holohedry and D(L) the point group of the lattice, twinning by metric merohedry corresponds to D(L) &sup; D(H) &supe; H
+If ''H'' is the individual point group, ''D''(''H'') the corresponding holohedry and ''D''(''L'') the point group of the lattice, twinning by metric merohedry corresponds to ''D''(''L'') &sup; ''D''(''H'') &supe; ''H''.
 Twinning by metric merohedry can be seen as the degeneration of [[twinning by reticular merohedry]] to [[twin index]] 1, or of [[twinning by pseudomerohedry]] to [[twin obliquity]] zero.
 ==Example==
-A monoclinic crystal of point group H = 2 with angle &beta; = 90º has a orthorhombic lattice. It may undergo two types of twinning by merohedry:
+A monoclinic crystal of point group ''H'' = 2 with angle &beta; = 90º has an orthorhombic lattice. It may undergo two types of twinning by merohedry:
-* if the twin operation belongs to the monoclinic holohedry D(H) = 2/''m'', twinning is the classical twinning by merohedry, also termed ''twinning by syngonic merohedry'';
+* if the twin operation belongs to the monoclinic holohedry ''D''(''H'') = 2/''m'', twinning is the classical twinning by merohedry, also termed ''twinning by syngonic merohedry'';
-* if the twin operation belongs to the orthorhombic holohedry D(L) = ''mmm'', twinning is by metric merohedry.
+* if the twin operation belongs to the orthorhombic holohedry ''D''(''L'') = ''mmm'', twinning is by metric merohedry.
 ==Historical note==
-Friedel (1904, p. 143; 1926, p. 56-57) called metric merohedry '''mériédrie d’ordre supérieur''' (higher order merohedry)  but stated that it was either unlikely or equivalent to a pseudo-merohedry of low obliquity. Nowadays several examples of true metric merohedry (within experimental uncertainty) are known.
+Friedel (1904, p. 143; 1926, pp. 56-57) called metric merohedry '''mériédrie d’ordre supérieur''' (higher order merohedry)  but stated that it was either unlikely or equivalent to a pseudo-merohedry of low obliquity. Nowadays several examples of true metric merohedry (within experimental uncertainty) are known.
 [[Category:Twinning]]

← Older revision		Revision as of 13:07, 10 April 2008
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−	<p><font color="blue"> Maclage par mériédrie métrique</font>(<i>Fr</i>). <font color="black"> ~~Meroedria~~ metrica</font>(<i>It</i>)	+	<p><font color="blue"> Maclage par mériédrie métrique</font>(<i>Fr</i>); <font color="black"> Geminazione per meroedria metrica</font>(<i>It</i>)
	</p>		</p>

← Older revision		Revision as of 12:28, 10 April 2008
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−	<p><font color="blue"> ~~Mériédrie~~ métrique</font>(<i>Fr</i>). <font color="black"> Meroedria metrica</font>(<i>It</i>)	+	<p><font color="blue"> Maclage par mériédrie métrique</font>(<i>Fr</i>). <font color="black"> Meroedria metrica</font>(<i>It</i>)
	</p>		</p>

← Older revision		Revision as of 09:43, 15 May 2006
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	Friedel (1904, p. 143; 1926, p. 56-57) called metric merohedry '''mériédrie d’ordre supérieur''' (higher order merohedry) but stated that it was either unlikely or equivalent to a pseudo-merohedry of low obliquity. Nowadays several examples of true metric merohedry (within experimental uncertainty) are known.		Friedel (1904, p. 143; 1926, p. 56-57) called metric merohedry '''mériédrie d’ordre supérieur''' (higher order merohedry) but stated that it was either unlikely or equivalent to a pseudo-merohedry of low obliquity. Nowadays several examples of true metric merohedry (within experimental uncertainty) are known.

−		+	[[Category:Twinning]]
−	[[Category: ~~Fundamental crystallography~~]]