Law of rational indices - Revision history

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

2017-11-14T18:02:27Z

Tidied translations and corrected German (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-15T15:25:02Z

Style edits to align with printed edition

MassimoNespolo: Ja

2016-04-14T11:52:08Z

MassimoNespolo: change of category

2014-08-24T19:40:30Z

change of category

BrianMcMahon at 15:58, 6 February 2012

2012-02-06T15:58:54Z

AndreAuthier at 15:45, 19 April 2011

2011-04-19T15:45:27Z

MassimoNespolo: /* History */ typo in the year

2007-05-28T13:53:57Z

‎History: typo in the year

BrianMcMahon at 10:23, 25 May 2007

2007-05-25T10:23:16Z

BrianMcMahon at 10:22, 25 May 2007

2007-05-25T10:22:03Z

GiovanniFerraris at 15:39, 17 March 2006

2006-03-17T15:39:10Z

← Older revision		Revision as of 18:02, 14 November 2017
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−	<~~Font~~ color="blue">Loi des indices rationnels simples</~~Font~~> (''Fr''). <~~Font~~ color="red">Gesetz der ~~Rationalität~~</~~Font~~> (''Ge''). <~~Font~~ color="~~green~~">~~Ley de la racionalidad de los indices~~</~~Font~~> (''Sp''). <~~Font~~ color="~~black~~">~~Legge della razionalità degli indici~~</~~Font~~> (''It''). <~~Font~~ color="~~purple~~">~~有理指数の法則~~</~~Font~~> (''Ja'').	+	<font color="blue">Loi des indices rationnels simples</font> (''Fr''). <font color="red">Gesetz der rationalen Indices</font> (''Ge''). <font color="black">Legge della razionalità degli indici</font> (''It''). <font color="purple">有理指数の法則</font> (''Ja''). <font color="green">Ley de la racionalidad de los indices</font> (''Sp'').

	== Definition ==		== Definition ==

@@ Line 1: / Line 1: @@
-<Font color="blue">Loi des indices rationnels simples</Font> (''Fr''); <Font color="red">Gesetz der Rationalität</Font> (''Ge''); <Font color="green">Ley de la racionalidad de los indices</Font> (''Sp.''); <Font color="black">Legge della razionalità degli indici</Font> (''It''); <Font color="purple">有理指数の法則</Font> (''Ja'')
+<Font color="blue">Loi des indices rationnels simples</Font> (''Fr''). <Font color="red">Gesetz der Rationalität</Font> (''Ge''). <Font color="green">Ley de la racionalidad de los indices</Font> (''Sp''). <Font color="black">Legge della razionalità degli indici</Font> (''It''). <Font color="purple">有理指数の法則</Font> (''Ja'').
 == Definition ==
-The law of rational indices states that the intercepts, ''OP'', ''OQ'', ''OR'', of the natural faces of a crystal form with the unit-cell axes '''a''', '''b''',  '''c''' (see Figure 1) are inversely proportional to prime integers, ''h'', ''k'', ''l''. They are called the [[Miller indices]] of the face. They are usually small because the corresponding lattice planes are among the densest and have therefore a high interplanar spacing and low indices.
+The law of rational indices states that the intercepts, ''OP'', ''OQ'', ''OR'', of the natural faces of a crystal form with the unit-cell axes '''a''', '''b''',  '''c''' (see Fig. 1) are inversely proportional to prime integers, ''h'', ''k'', ''l''. They are called the [[Miller indices]] of the face. They are usually small because the corresponding lattice planes are among the densest and have therefore a high interplanar spacing and low indices.
 [[image:MILLER-1.gif|center]]
@@ Line 15: / Line 15: @@
 </center>
-(Models from Haüy's ''Traité de Minéralogie'' (1801) - the crystal forms have been redrawn in red).
+Models from Haüy's ''Traité de Minéralogie'' (1801) - the crystal forms have been superimposed in heavy lines.
 == History ==
-In 1690, C. Huyghens (1629-1695) advanced the hypothesis that the cleavage rhombohedron of calcite was the result of a stacking of flat ellipsoids and used that hypothesis to explain the cleavage properties and the double refraction of calcite. In 1773, the Swedish mineralogist T.O. Bergman (1735-1784) related the cleavage rhombohedron to the {<math> 2{\bar 1}0</math>} scalenohedron and other forms of calcite, but it is the French mineralogist R.-J.Haüy (1743-1822) who showed that the crystal forms could be reconstructed by appropriate stacking laws of minute cleavage rhombohedra for calcite and cubes for garnets (''Essai d'une théorie sur la structure des cristaux'', 1784; ''Traité de Minéralogie'', 1801).
+In 1690, C. Huyghens (1629-1695) advanced the hypothesis that the cleavage rhombohedron of calcite was the result of a stacking of flat ellipsoids and used that hypothesis to explain the cleavage properties and the double refraction of calcite. In 1773, the Swedish mineralogist T. O. Bergman (1735-1784) related the cleavage rhombohedron to the {<math> 2{\bar 1}0</math>} scalenohedron and other forms of calcite, but it is the French mineralogist R.-J. Haüy (1743-1822) who showed that the crystal forms could be reconstructed by appropriate stacking laws of minute cleavage rhombohedra for calcite and cubes for garnets (''Essai d'une théorie sur la structure des cristaux'', 1784; ''Traité de Minéralogie'', 1801).
 == See also ==
-[[Miller indices]]<br>
+*[[Miller indices]]
 [[Category:Morphological crystallography]]<br>

← Older revision		Revision as of 11:52, 14 April 2016
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−	<Font color="blue"> Loi des indices rationnels simples </Font>(''Fr.''). <Font color="red"> Gesetz der Rationalität </Font> (''Ge.''). <Font color="green"> Ley de la racionalidad de los indices </Font>(''Sp.'').<Font color="black"> Legge della razionalità degli indici </Font>(''It'')	+	<Font color="blue">Loi des indices rationnels simples</Font> (''Fr''); <Font color="red">Gesetz der Rationalität</Font> (''Ge''); <Font color="green">Ley de la racionalidad de los indices</Font> (''Sp.''); <Font color="black">Legge della razionalità degli indici</Font> (''It''); <Font color="purple">有理指数の法則</Font> (''Ja'')

	== Definition ==		== Definition ==

← Older revision		Revision as of 19:40, 24 August 2014
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	[[Miller indices]]<br>		[[Miller indices]]<br>

−	[[Category:~~Fundamental~~ crystallography]]<br>	+	[[Category:Morphological crystallography]]<br>

@@ Line 1: / Line 1: @@
 <Font color="blue"> Loi des indices rationnels simples </Font>(''Fr.''). <Font color="red"> Gesetz der Rationalität </Font> (''Ge.''). <Font color="green"> Ley de la racionalidad de los indices </Font>(''Sp.'').<Font color="black"> Legge della razionalità degli indici </Font>(''It'')
 == Definition ==
@@ Line 8: / Line 7: @@
 [[image:MILLER-1.gif|center]]
-The law of rational indices was deduced by Haüy (1784, 1801) from the observation of the stacking laws required to build the natural faces of crystals by piling up elementary blocks, for instance cubes to construct the {110} faces of the rhomb-dodecahedron observed in garnets or the &#189;{210} faces of the pentagon-dodecahedron observed in pyrite, or rhombohedrons to construct the {21.1} (referred to an hegagonal lattice,  {<math> 2{\bar 1}0</math>}  referred to a rhombohedral lattice) scalenohedron of calcite.
+The law of rational indices was deduced by Haüy (1784, 1801) from the observation of the stacking laws required to build the natural faces of crystals by piling up elementary blocks, for instance cubes to construct the {110} faces of the rhomb-dodecahedron observed in garnets or the &#189;{210} faces of the pentagon-dodecahedron observed in pyrite, or rhombohedrons to construct the {21.1} (referred to an hexagonal lattice,  {<math> 2{\bar 1}0</math>}  referred to a rhombohedral lattice) scalenohedron of calcite.
 <center>
@@ Line 25: / Line 24: @@
 [[Miller indices]]<br>
 [[Category:Fundamental crystallography]]<br>

← Older revision		Revision as of 15:45, 19 April 2011
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−	<Font color="blue"> Loi des indices rationnels simples </Font>(''Fr.''). <Font color="green"> Ley de la racionalidad de los indices </Font>(''Sp.'').<Font color="black"> Legge della razionalità degli indici </Font>(''It'')	+	<Font color="blue"> Loi des indices rationnels simples </Font>(''Fr.''). <Font color="red"> Gesetz der Rationalität </Font> (''Ge.''). <Font color="green"> Ley de la racionalidad de los indices </Font>(''Sp.'').<Font color="black"> Legge della razionalità degli indici </Font>(''It'')

@@ Line 20: / Line 20: @@
 == History ==
-In 1690, C. Huyghens (1629-1695) advanced the hypothesis that the cleavage rhombohedron of calcite was the result of a stacking of flat ellipsoids and used that hypothesis to explain the cleavage properties and the double refraction of calcite. In 1773, the Swedish mineralogist T.O. Bergman (1735-1784) related the cleavage rhombohedron to the {<math> 2{\bar 1}0</math>} scalenohedron and other forms of calcite, but it is the French mineralogist R.-J.Haüy (1743-1822) who showed that the crystal forms could be reconstructed by appropriate stacking laws of minute cleavage rhomohedrons for calcite and cubes for garnets (''Essai d'une théorie sur la structure des cristaux'', 1884; ''Traité de Minéralogie'', 1801).
+In 1690, C. Huyghens (1629-1695) advanced the hypothesis that the cleavage rhombohedron of calcite was the result of a stacking of flat ellipsoids and used that hypothesis to explain the cleavage properties and the double refraction of calcite. In 1773, the Swedish mineralogist T.O. Bergman (1735-1784) related the cleavage rhombohedron to the {<math> 2{\bar 1}0</math>} scalenohedron and other forms of calcite, but it is the French mineralogist R.-J.Haüy (1743-1822) who showed that the crystal forms could be reconstructed by appropriate stacking laws of minute cleavage rhombohedra for calcite and cubes for garnets (''Essai d'une théorie sur la structure des cristaux'', 1884; ''Traité de Minéralogie'', 1801).
 == See also ==

← Older revision		Revision as of 15:39, 17 March 2006
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−	<Font color="blue"> Loi des indices rationnels simples </Font>(''Fr.''). <Font color="green"> Ley de la racionalidad de los indices </Font>(''Sp.'').	+	<Font color="blue"> Loi des indices rationnels simples </Font>(''Fr.''). <Font color="green"> Ley de la racionalidad de los indices </Font>(''Sp.'').<Font color="black"> Legge della razionalità degli indici </Font>(''It'')
		+

	== Definition ==		== Definition ==