Neumann's principle - Revision history

BrianMcMahon: Tidied translations and corrected German (U. Mueller)

2017-11-16T13:11:02Z

Tidied translations and corrected German (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-16T09:46:38Z

Style edits to align with printed edition

MassimoNespolo: Ja; operation, not element!

2015-03-20T04:53:52Z

Ja; operation, not element!

BrianMcMahon at 17:08, 6 February 2012

2012-02-06T17:08:17Z

AndreAuthier at 07:48, 11 November 2010

2010-11-11T07:48:13Z

AndreAuthier at 06:29, 12 July 2006

2006-07-12T06:29:46Z

AndreAuthier at 07:43, 4 May 2006

2006-05-04T07:43:09Z

GiovanniFerraris at 16:05, 17 March 2006

2006-03-17T16:05:36Z

AndreAuthier at 07:35, 5 March 2006

2006-03-05T07:35:16Z

AndreAuthier at 09:11, 3 March 2006

2006-03-03T09:11:42Z

← Older revision		Revision as of 13:11, 16 November 2017
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−	<~~Font~~ color="blue">Principe de Neumann</~~Font~~> (''Fr''). <~~Font~~ color="red">~~Neumannsche~~ Prinzip</~~Font~~> (''Ge''). <~~Font~~ color="~~green~~">Principio de Neumann</~~Font~~> (''Sp''). <~~Font~~ color="~~black~~"> ~~Principio di Neumann~~</~~Font~~> (''It''). <~~Font~~ color="~~purple~~">~~ノイマンの法則~~</~~Font~~> (''Ja'').	+	<font color="blue">Principe de Neumann</font> (''Fr''). <font color="red">Neumannsches Prinzip</font> (''Ge''). <font color="black">Principio di Neumann</font> (''It''). <font color="purple">ノイマンの法則</font> (''Ja''). <font color="green">Principio de Neumann</font> (''Sp'').
		+

	== Definition ==		== Definition ==

@@ Line 1: / Line 1: @@
-<Font color="blue">Principe de Neumann</Font> (''Fr''). <Font color="red">Neumannsche Prinzip</Font> (''Ge''). <Font color="green">Principio de Neumann</Font> (''Sp''). <Font color="black"> Principio di Neumann</Font> (''It''). <Font color="purple">ノイマンの法則</Font> (''Ja'')
+<Font color="blue">Principe de Neumann</Font> (''Fr''). <Font color="red">Neumannsche Prinzip</Font> (''Ge''). <Font color="green">Principio de Neumann</Font> (''Sp''). <Font color="black"> Principio di Neumann</Font> (''It''). <Font color="purple">ノイマンの法則</Font> (''Ja'').
 == Definition ==
@@ Line 7: / Line 7: @@
 == Example ==
-This principle may be illustrated by considering the optical indicatrix of a crystal, which is an ellipsoid. If the medium is invariant with respect to a three-fold, a four-fold or a six-fold rotation (as in a trigonal, tetragonal or hexagonal crystal, for instance), its optical indicatrix must also be invariant with respect to the same operation, according to Neumann's principle. As an ellipsoid can only be ordinary or of revolution, the indicatrix of a trigonal, tetragonal or hexagonal crystal is necessarily an ellipsoid of revolution. These crystals are said to be ''uniaxial''. In a cubic crystal which has four three--fold axes, the indicatrix must have several axes of revolution, it is therefore a sphere and cubic media behave as isotropic media for properties represented by a tensor of rank 2.
+This principle may be illustrated by considering the optical indicatrix of a crystal, which is an ellipsoid. If the medium is invariant with respect to a three-fold, a four-fold or a six-fold rotation (as in a trigonal, tetragonal or hexagonal crystal, for instance), its optical indicatrix must also be invariant with respect to the same operation, according to Neumann's principle. As an ellipsoid can only be ordinary or of revolution, the indicatrix of a trigonal, tetragonal or hexagonal crystal is necessarily an ellipsoid of revolution. These crystals are said to be ''uniaxial''. In a cubic crystal which has four three-fold axes, the indicatrix must have several axes of revolution. It is therefore a sphere, and cubic media behave as isotropic media for properties represented by a tensor of rank 2.
 == History ==
-Franz Neumann (1795-1898)'s principle was first stated in his course at the university of Königsberg (1873/1874) and  was published in the printed version of his lecture notes (Neumann F.E., 1885, ''Vorlesungen über die Theorie der Elastizität der festen Körper und des Lichtäthers'', edited by O. E. Meyer. Leipzig, B. G. Teubner-Verlag.
+Franz Neumann's (1795-1898) principle was first stated in his course at the university of Königsberg (1873/1874) and  was published in the printed version of his lecture notes [Neumann, F. E. (1885), ''Vorlesungen über die Theorie der Elastizität der festen Körper und des Lichtäthers'', edited by O. E. Meyer. Leipzig, B. G. Teubner-Verlag].
 == See also ==
-[[Curie laws]]<br>
+*[[Curie laws]]
-[http://www.iucr.org/iucr-top/comm/cteach/pamphlets/18/ An introduction to crystal physics]  (Teaching Pamphlet of the ''International Union of Crystallography'')<br>
+*[http://www.iucr.org/iucr-top/comm/cteach/pamphlets/18/ ''An introduction to crystal physics'']  (Teaching Pamphlet No. 18 of the International Union of Crystallography)
-Section 1.1.4 of ''[http://it.iucr.org/D/ International Tables of Crystallography, Volume D]''
+*Chapter 1.1.4 of ''[http://it.iucr.org/D/ International Tables for Crystallography, Volume D]''
 [[Category:Physical properties of crystals]]<br>

@@ Line 1: / Line 1: @@
-<Font color="blue"> Principe de Neumann </Font> (''Fr''). <Font color="red"> Neumannsche Prinzip </Font> (''Ge''). <Font color="green"> Principio de Neumann </Font> (''Sp'').<Font color="black"> Principio di Neumann </Font>(''It'')
+<Font color="blue">Principe de Neumann</Font> (''Fr''). <Font color="red">Neumannsche Prinzip</Font> (''Ge''). <Font color="green">Principio de Neumann</Font> (''Sp''). <Font color="black"> Principio di Neumann</Font> (''It''). <Font color="purple">ノイマンの法則</Font> (''Ja'')
 == Definition ==
-Neumann's principle, or principle of symmetry, states that, if a crystal is invariant with respect to certain symmetry elements, any of its physical properties must also be invariant with respect to the same symmetry elements, or otherwise stated, the symmetry elements of any physical property of a crystal must include the symmetry elements of the point group of the crystal. It is generalized to physical phenomena by [[Curie laws]].
+Neumann's principle, or principle of symmetry, states that, if a crystal is invariant with respect to certain [[symmetry operation]]s, any of its physical properties must also be invariant with respect to the same symmetry operations, or otherwise stated, the symmetry operations of any physical property of a crystal must include the symmetry operations of the point group of the crystal. It is generalized to physical phenomena by [[Curie laws]].
 == Example ==
-This principle may be illustrated by considering the optical indicatrix of a crystal, which is an ellipsoid. If the medium is invariant with respect to a three-fold, a four-fold or a six-fold axis (as in a trigonal, tetragonal or hexagonal crystal, for instance), its optical indicatrix must also be invariant with respect to the same axis, according to Neumann's principle. As an ellipsoid can only be ordinary or of revolution, the indicatrix of a trigonal, tetragonal or hexagonal crystal is necessarily an ellipsoid of revolution. These crystals are said to be ''uniaxial''. In a cubic crystal which has four three--fold axes, the indicatrix must have several axes of revolution, it is therefore a sphere and cubic media behave as isotropic media for properties represented by a tensor of rank 2.
+This principle may be illustrated by considering the optical indicatrix of a crystal, which is an ellipsoid. If the medium is invariant with respect to a three-fold, a four-fold or a six-fold rotation (as in a trigonal, tetragonal or hexagonal crystal, for instance), its optical indicatrix must also be invariant with respect to the same operation, according to Neumann's principle. As an ellipsoid can only be ordinary or of revolution, the indicatrix of a trigonal, tetragonal or hexagonal crystal is necessarily an ellipsoid of revolution. These crystals are said to be ''uniaxial''. In a cubic crystal which has four three--fold axes, the indicatrix must have several axes of revolution, it is therefore a sphere and cubic media behave as isotropic media for properties represented by a tensor of rank 2.
 == History ==

@@ Line 1: / Line 1: @@
 <Font color="blue"> Principe de Neumann </Font> (''Fr''). <Font color="red"> Neumannsche Prinzip </Font> (''Ge''). <Font color="green"> Principio de Neumann </Font> (''Sp'').<Font color="black"> Principio di Neumann </Font>(''It'')
 == Definition ==
@@ Line 19: / Line 18: @@
 [http://www.iucr.org/iucr-top/comm/cteach/pamphlets/18/ An introduction to crystal physics]  (Teaching Pamphlet of the ''International Union of Crystallography'')<br>
 Section 1.1.4 of ''[http://it.iucr.org/D/ International Tables of Crystallography, Volume D]''
 [[Category:Physical properties of crystals]]<br>

@@ Line 12: / Line 12: @@
 == History ==
-Franz Neumann (1795-1898)'s principle was first stated in his course at the university of Königsberg (1973/1974) and  was published in the printed version of his lecture notes (Neumann F.E., 1885, ''Vorlesungen über die Theorie der Elastizität der festen Körper und des Lichtäthers'', edited by O. E. Meyer. Leipzig, B. G. Teubner-Verlag.
+Franz Neumann (1795-1898)'s principle was first stated in his course at the university of Königsberg (1873/1874) and  was published in the printed version of his lecture notes (Neumann F.E., 1885, ''Vorlesungen über die Theorie der Elastizität der festen Körper und des Lichtäthers'', edited by O. E. Meyer. Leipzig, B. G. Teubner-Verlag.
 == See also ==

← Older revision		Revision as of 16:05, 17 March 2006
Line 1:		Line 1:
−	<Font color="blue"> Principe de Neumann </Font> (''Fr''). <Font color="red"> Neumannsche Prinzip </Font> (''Ge''). <Font color="green"> Principio de Neumann </Font> (''Sp'').	+	<Font color="blue"> Principe de Neumann </Font> (''Fr''). <Font color="red"> Neumannsche Prinzip </Font> (''Ge''). <Font color="green"> Principio de Neumann </Font> (''Sp'').<Font color="black"> Principio di Neumann </Font>(''It'')
		+

	== Definition ==		== Definition ==

@@ Line 11: / Line 11: @@
 == History ==
-Neumann's views on symmetry originate from his conclusion that the axes of the mechanical, thermal and optical axes of a crystal must coincide and his observation of the relations between their orientation and that of the crystalline axes of gypsum (Neumann F.E., 1833, ''Poggendorf Ann. Phys.'', '''27''', 240-274, ''Die thermischen, optischen und kristallographischen Axen des Kristallsystems des Gypses''. They were stated in the printed version of his lecture notes (Neumann F.E., ''Vorlesungen über die Theorie der Elastizität der festen Kö rper und des Lichtäthers'', edited by O. E. Meyer. Leipzig, B. G. Teubner-Verlag.
+Franz Neumann's views on symmetry originate from his conclusion that the axes of the mechanical, thermal and optical axes of a crystal must coincide and his observation of the relations between their orientation and that of the crystalline axes of gypsum (Neumann F.E., 1833, ''Poggendorf Ann. Phys.'', '''27''', 240-274, ''Die thermischen, optischen und kristallographischen Axen des Kristallsystems des Gypses''. They were stated in the printed version of his lecture notes (Neumann F.E., ''Vorlesungen über die Theorie der Elastizität der festen Körper und des Lichtäthers'', edited by O. E. Meyer. Leipzig, B. G. Teubner-Verlag.
 == See also ==