|
|
| Line 1: |
Line 1: |
| '''Friedel's law''', named after [[Georges Friedel]], is a property of [[Fourier transform]]s of real functions.<ref name="Friedel1913">{{cite journal |author=Friedel G |title=Sur les symétries cristallines que peut révéler la diffraction des rayons Röntgen |journal=Comptes Rendus|volume=157 |pages=1533–1536 |year=1913}}</ref>
| | Alyson is the name people use to contact me and I think it sounds quite good when you say it. Ohio is exactly where my house is but my husband wants us to move. He is an order clerk and it's some thing he truly enjoy. She is truly fond of caving but she doesn't have the time recently.<br><br>Feel free to surf to my web-site ... [http://isaworld.pe.kr/?document_srl=392088 live psychic reading] |
| | |
| Given a real function <math>f(x)</math>, its [[Fourier transform]]
| |
| | |
| :<math>F(k)=\int^{+\infty}_{-\infty}f(x)e^{i k \cdot x }dx</math>
| |
| | |
| has the following properties.
| |
| | |
| *<math>F(k)=F^*(-k) \,</math>
| |
| | |
| where <math>F^*</math> is the complex conjugate of <math>F</math>. | |
| | |
| [[Centrosymmetric]] points <math>(k,-k)</math> are called [[Friedel's pairs]].
| |
| | |
| The squared amplitude (<math>|F|^2</math>) is centrosymmetric:
| |
| * <math>|F(k)|^2=|F(-k)|^2 \,</math>
| |
| | |
| The phase <math>\phi</math> of <math>F</math> is [[antisymmetric]]:
| |
| * <math>\phi(k) = -\phi(-k) \,</math>.
| |
| | |
| Friedel's law is used in [[X-ray diffraction]], [[crystallography]] and scattering from real potential within the [[Born approximation]]. Note that a [http://reference.iucr.org/dictionary/Twin_operation twin operation] (aka ''Opération de maclage'') is equivalent to an inversion centre and the intensities from the individuals are equivalent under Friedel's law.<ref name="Nespoloa2004">{{cite journal |author=Nespoloa N, Giovanni Ferraris G |title=Applied geminography - symmetry analysis of twinned crystals and definition of twinning by reticular polyholohedry |journal=Acta Crystal A |volume=60 |issue=1 |pages=89–95 |year=2004 |doi=10.1107/S0108767303025625}}</ref><ref name="Friedel1904">Friedel G (1904). "Étude sur les groupements cristallins". Extract from ''Bullettin de la Société de l'Industrie Minérale'', Quatrième série, Tomes III et IV. Saint-Étienne: Societè de l'Imprimerie Thèolier J. Thomas et C.</ref><ref name="Friedel1923">Friedel G. (1923). ''Bull. Soc. Fr. Minéral.'' '''46''':79-95.</ref>
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| [[Category:Fourier analysis]]
| |
| [[Category:Crystallography]]
| |
Latest revision as of 18:03, 11 December 2014
Alyson is the name people use to contact me and I think it sounds quite good when you say it. Ohio is exactly where my house is but my husband wants us to move. He is an order clerk and it's some thing he truly enjoy. She is truly fond of caving but she doesn't have the time recently.
Feel free to surf to my web-site ... live psychic reading