Piezoelectricity - Revision history

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

2017-11-17T09:49:24Z

Tidied translations and corrected German (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-16T12:54:09Z

Style edits to align with printed edition

MassimoNespolo: /* See also */ 6th edition of ITA

2017-04-10T16:23:21Z

‎See also: 6th edition of ITA

MassimoNespolo: /* Piezoelectric point groups */ broken link fixed; rewording for consistency; two carriace returns removed

2015-03-20T04:59:14Z

‎Piezoelectric point groups: broken link fixed; rewording for consistency; two carriace returns removed

BrianMcMahon at 17:14, 7 February 2012

2012-02-07T17:14:04Z

BrianMcMahon at 09:23, 2 April 2008

2008-04-02T09:23:55Z

BrianMcMahon at 10:12, 25 May 2007

2007-05-25T10:12:24Z

MassimoNespolo at 11:55, 27 February 2007

2007-02-27T11:55:53Z

GiovanniFerraris at 14:20, 28 March 2006

2006-03-28T14:20:35Z

AndreAuthier at 08:21, 6 March 2006

2006-03-06T08:21:35Z

← Older revision		Revision as of 09:49, 17 November 2017
Line 1:		Line 1:
−	<~~Font~~ color="blue"> Piezoélectricité </~~Font~~> (''Fr''). <~~Font~~ color="red"> ~~Piezoelectrizität~~ </~~Font~~> (''Ge''). <font color="~~green~~">~~Piezoelectricidad~~ </~~Font~~> (''Sp''). <~~Font~~ color="~~black~~"> ~~Piezoelettricità~~ </~~Font~~>(''It''). <~~Font~~ color="~~purple~~"> ~~圧電効果~~</~~Font~~> (''Ja'').	+	<font color="blue">Piezoélectricité</font> (''Fr''). <font color="red">Piezoelektrizität</font> (''Ge''). <font color="black">Piezoelettricità</font> (''It''). <font color="purple">圧電効果</font> (''Ja''). <font color="green">Piezoelectricidad</font> (''Sp'').

	== Definition ==		== Definition ==

@@ Line 1: / Line 1: @@
-<Font color="blue"> Piezoélectricité </Font> (''Fr''). <Font color="red"> Piezoelectrizität </Font> (''Ge'').  <font color="green">Piezoelectricidad </Font> (''Sp''). <Font color="black"> Piezoelettricità </Font>(''It''). <Font color="purple"> 圧電効果</Font> (''Ja'')
+<Font color="blue"> Piezoélectricité </Font> (''Fr''). <Font color="red"> Piezoelectrizität </Font> (''Ge'').  <font color="green">Piezoelectricidad </Font> (''Sp''). <Font color="black"> Piezoelettricità </Font>(''It''). <Font color="purple"> 圧電効果</Font> (''Ja'').
 == Definition ==
@@ Line 5: / Line 5: @@
 Piezoelectricity is the property presented by certain materials that exhibit an electric polarization when submitted to an applied mechanical stress such as a uniaxial compression. Conversely, their shape changes when they are submitted to an external electric field; this is the converse piezoelectric effect. The piezoelectric effect and the converse effect are described by third-rank tensors:
-* For a small stress, represented by a second-rank tensor, ''T<sub>ij</sub>'', the resulting polarization, of components P''<sub>k</sub>'' , is given by:
+* For a small stress, represented by a second-rank tensor, ''T<sub>ij</sub>'', the resulting polarization, of components ''P''<sub>''k''</sub>, is given by
 <center>''P<sub>k</sub>'' = ''d<sub>kij</sub>T<sub>ij</sub>''
@@ Line 16: / Line 16: @@
 </center>
-where the first-order term, ''d<sub>ijk</sub>'', represents the inverse piezoelectric effect and the second-order term, ''Q<sub>ijkl</sub>'', a symmetric fourth-rank tensor, the electrostriction effect. The sense of the strain due to the piezoelectric effect changes when the sign of the applied electric field changes , while that due to electrostriction, a quadratic effect, does not.
+where the first-order term, ''d<sub>ijk</sub>'', represents the inverse piezoelectric effect and the second-order term, ''Q<sub>ijkl</sub>'', a symmetric fourth-rank tensor, the electrostriction effect. The sense of the strain due to the piezoelectric effect changes when the sign of the applied electric field changes, while that due to electrostriction, a quadratic effect, does not.
-The matrices associated to the coefficients ''d<sub>kij</sub>'' and ''d<sub>kij</sub>'' of the direct and converse piezoelectric effects, respectively, are transpose of one another.
+The matrices associated with the coefficients ''d<sub>kij</sub>'' and ''d<sub>ijk</sub>'' of the direct and converse piezoelectric effects, respectively, are transpose of one another.
 == Piezoelectric point groups ==
@@ Line 32: / Line 32: @@
 == History ==
-It is considerations of symmetry that led the brothers Jacques (1855-1941) and Pierre Curie (1859-1906) to the discovery of piezoelectricity in materials such as tourmaline, quartz, boracite, sodium chlorate, Rochelle salt [Curie J. and Curie P. (1880), ''C. R. Acad. Sci. Paris'', '''91''', 294-295, ''Développement, par pression, de l'électricité polaire dans les cristaux hémièdres à faces inclinées'']. The inverse piezoelectric effect was predicted by Lippmann G. [(1881), ''Ann. Chim. Phy.'' '''24''', 145-178, ''Principe de conservation de l'électricité'']  and discovered by Curie J. and P.    [(1881), ''C. R. Acad. Sci. Paris'', '''93''', 1137-1140, ''Contractions et dilatations produites par des tensions électriques dans les cristaux hémièdres à faces inclinées''].
+It was considerations of symmetry that led the brothers Jacques (1855-1941) and Pierre Curie (1859-1906) to the discovery of piezoelectricity in materials such as tourmaline, quartz, boracite, sodium chlorate, Rochelle salt [Curie J. and Curie P. (1880), ''C. R. Acad. Sci. Paris'', '''91''', 294-295, ''Développement, par pression, de l'électricité polaire dans les cristaux hémièdres à faces inclinées'']. The inverse piezoelectric effect was predicted by Lippmann G. [(1881), ''Ann. Chim. Phy.'' '''24''', 145-178, ''Principe de conservation de l'électricité'']  and discovered by Curie J. and P.    [(1881), ''C. R. Acad. Sci. Paris'', '''93''', 1137-1140, ''Contractions et dilatations produites par des tensions électriques dans les cristaux hémièdres à faces inclinées''].
 == See also ==
-*[http://www.iucr.org/iucr-top/comm/cteach/pamphlets/18/ An introduction to crystal physics]  (Teaching Pamphlet of the ''International Union of Crystallography'')
+*[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 3.2.2.6 of ''International Tables of Crystallography, Volume A'', 6<sup>th</sup> edition
+*Chapter 3.2.2.6 of ''International Tables for Crystallography, Volume A'', 6th edition
-*Section 1.1.4 of ''International Tables of Crystallography, Volume D''
+*Chapter 1.1.4 of ''International Tables for Crystallography, Volume D''
-[[Category:Physical properties of crystals]]<br>
+[[Category:Physical properties of crystals]]

@@ Line 35: / Line 35: @@
 == See also ==
+*[http://www.iucr.org/iucr-top/comm/cteach/pamphlets/18/ An introduction to crystal physics]  (Teaching Pamphlet of the ''International Union of Crystallography'')
-[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 3.2.2.6 of ''International Tables of Crystallography, Volume A'', 6<sup>th</sup> edition
-Section 10.2 of ''International Tables of Crystallography, Volume A''<br>
+*Section 1.1.4 of ''International Tables of Crystallography, Volume D''
 [[Category:Physical properties of crystals]]<br>

@@ Line 22: / Line 22: @@
 == Piezoelectric point groups ==
-The [[geometric crystal classes]] for which the piezoelectric effect is possible are determined by symmetry considerations (see [[Curie laws]]). They are the non-centrosymmetric classes, with the exception of 432. The 20 piezoelectric crystal classes are therefore:
+The [[geometric crystal class]]es for which the piezoelectric effect is possible are determined by symmetry considerations (see [[Curie laws]]). They are the non-centrosymmetric classes, with the exception of 432. The 20 piezoelectric crystal classes are therefore:
 , 2, ''m'', 222, 2''mm'',
-, 32, 3''m'', 4, <math>{\bar 4}</math>,422, 4''mm'', <math>{\bar 4}</math>2''m'', 6, <math>{\bar 6}</math>,622, 6''mm'', <math>{\bar 6}</math>2''m''
+Quartz, belonging to geometric crystal class 32, is the most widely used piezoelectric crystal.
 == History ==

@@ Line 1: / Line 1: @@
 <Font color="blue"> Piezoélectricité </Font> (''Fr''). <Font color="red"> Piezoelectrizität </Font> (''Ge'').  <font color="green">Piezoelectricidad </Font> (''Sp''). <Font color="black"> Piezoelettricità </Font>(''It''). <Font color="purple"> 圧電効果</Font> (''Ja'')
 == Definition ==
@@ Line 17: / Line 16: @@
 </center>
-where the first-order term, ''d<sub>ijk</sub>'', represents the inverse piezoelectric effect and the second-orer term, ''Q<sub>ijkl</sub>'', a symmetric fourth-rank tensor, the electrostriction effect. The sense of the strain due to the piezoelectric effect changes when the sign of the applied electric field changes , while that due to electrostriction, a quadratic effect, does not.
+where the first-order term, ''d<sub>ijk</sub>'', represents the inverse piezoelectric effect and the second-order term, ''Q<sub>ijkl</sub>'', a symmetric fourth-rank tensor, the electrostriction effect. The sense of the strain due to the piezoelectric effect changes when the sign of the applied electric field changes , while that due to electrostriction, a quadratic effect, does not.
 The matrices associated to the coefficients ''d<sub>kij</sub>'' and ''d<sub>kij</sub>'' of the direct and converse piezoelectric effects, respectively, are transpose of one another.
@@ Line 43: / Line 42: @@
 Section 1.1.4 of ''International Tables of Crystallography, Volume D''
 [[Category:Physical properties of crystals]]<br>

← Older revision		Revision as of 11:55, 27 February 2007
Line 1:		Line 1:
−	<Font color="blue"> Piezoélectricité </Font> (''Fr''). <Font color="red"> Piezoelectrizität </Font> (''Ge''). <font color="green">Piezoelectricidad </Font> (''Sp'').<Font color="black"> Piezoelettricità </Font>(''It'')	+	<Font color="blue"> Piezoélectricité </Font> (''Fr''). <Font color="red"> Piezoelectrizität </Font> (''Ge''). <font color="green">Piezoelectricidad </Font> (''Sp''). <Font color="black"> Piezoelettricità </Font>(''It''). <Font color="purple"> 圧電効果</Font> (''Ja'')

← Older revision		Revision as of 14:20, 28 March 2006
Line 1:		Line 1:
−	<Font color="blue"> Piezoélectricité </Font> (''Fr''). <Font color="red"> Piezoelectrizität </Font> (''Ge''). <font color="green">Piezoelectricidad </Font> (''Sp'').	+	<Font color="blue"> Piezoélectricité </Font> (''Fr''). <Font color="red"> Piezoelectrizität </Font> (''Ge''). <font color="green">Piezoelectricidad </Font> (''Sp'').<Font color="black"> Piezoelettricità </Font>(''It'')
		+

	== Definition ==		== Definition ==