en>RjwilmsiBot: fixing page range dashes using AWB

2013-02-25T01:11:01Z

fixing page range dashes using AWB

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	~~Hello~~ and ~~welcome~~. My title is ~~Irwin~~ and ~~I totally dig that title~~. ~~Doing ceramics is what adore performing~~. For ~~many years he~~'~~s been residing~~ in ~~North Dakota and his family members loves~~ it. ~~Since she was eighteen she's been operating~~ as a ~~receptionist but her marketing~~ by ~~no means comes.~~<br><br>~~Also visit my page~~ ... ~~over~~ the ~~counter std test~~ ([~~http~~://~~www~~.~~videoworld~~.~~com~~/~~blog~~/~~211112 linked internet page~~])		The '''Debye–Waller factor''' (DWF), named after [[Peter Debye]] and [[Ivar Waller]], is used in [[condensed matter physics]] to describe the attenuation of [[x-ray scattering]] or coherent [[neutron scattering]] caused by thermal motion.<ref name="Debye1913">{{cite journal
			\|last=Debye
			\|first=Peter
			\|year=1913
			\|title=Interferenz von Röntgenstrahlen und Wärmebewegung
			\|journal=Ann. d. Phys.
			\|volume=348
			\|issue=1
			\|pages=49–92
			\|doi=10.1002/andp.19133480105
			\|language=German
			\|bibcode = 1913AnP...348...49D }}</ref><ref name="Waller1923">{{cite journal
			\|last=Waller
			\|first=Ivar
			\|year=1923
			\|title=Zur Frage der Einwirkung der Wärmebewegung auf die Interferenz von Röntgenstrahlen
			\|journal=Zeitschrift für Physik A
			\|volume=17
			\|pages=398–408
			\|doi=10.1007/BF01328696
			\|url=http://www.springerlink.com/content/n5233k4882468814/
			\|publisher=Springer
			\|location=Berlin / Heidelberg
			\|language=German
			\|bibcode = 1923ZPhy...17..398W }}</ref> It has also been called the '''B factor''' or the '''temperature factor'''. Often, "Debye-Waller factor" is used as a generic term that comprises the [[Lamb-Mössbauer factor]] of incoherent neutron scattering and [[Mössbauer spectroscopy]].

			The DWF depends on the [[scattering vector]] '''q'''. For a given '''q''', DWF('''q''') gives the fraction of elastic scattering; 1 - DWF('''q''') correspondingly gives the fraction of inelastic scattering. (Strictly speaking, this probability interpretation is not true in general.<ref name="Lipkin2004">{{cite arXiv \|last=Lipkin \|first=Harry \|authorlink=Harry J. Lipkin \|eprint=cond-mat/0405023v1 \|title=Physics of Debye-Waller Factors \|year=2004 }}</ref>) In [[diffraction]] studies, only the elastic scattering is useful; in crystals, it gives rise to distinct [[Bragg peak]]s. Inelastic scattering events are undesirable as they cause a diffuse background — unless the energies of scattered particles are analysed, in which case they carry valuable information ([[inelastic neutron scattering]]).

			The basic expression for the DWF is given by

			:<math> \text{DWF} = \left\langle \exp\left(i \mathbf{q}\cdot \mathbf{u}\right) \right\rangle^2</math>

			where '''u''' is the displacement of a scattering center,
			and <...> denotes either thermal or time averaging.

			Assuming [[harmonic oscillator\|harmonicity]] of the scattering centers in the material under study, the [[Boltzmann distribution]] implies that <math>\mathbf{q}\cdot \mathbf{u}</math> is [[Normal distribution\|normally distributed]] with zero mean. Then, using for example the expression of the corresponding [[Characteristic function (probability theory)\|characteristic function]], the DWF takes the form

			:<math> \text{DWF} = \exp\left( -\langle [\mathbf{q}\cdot \mathbf{u}]^2 \rangle \right)</math>

			Note that although the above reasoning is classical, the same holds also quantum mechanically.

			Assuming also [[isotropy]] of the harmonic potential, one may write

			:<math> \text{DWF} = \exp\left( -q^2 \langle u^2 \rangle / 3 \right)</math>

			where ''q'', ''u'' are the magnitudes (or absolute values) of the vectors '''q''', '''u''' respectively, and <math>\langle u^2 \rangle</math> is the [[mean squared displacement]]. Note that if the incident wave has wavelength <math>\lambda</math>, and it is elastically scattered by an angle of <math>2\theta</math>, then

			:<math>q = \frac{4\pi \sin(\theta)}{\lambda}</math>

			In the context of [[protein structure]]s, the term B-factor is used. The B-factor is defined as:

			:<math>B = 8\pi^2 \langle u^2 \rangle</math>

			It is measured in units of [[Angstrom\|Å]]<sup>2</sup>.
			The B-factors can be taken as indicating the relative vibrational motion of different parts of the structure. '''Atoms with low B-factors belong to a part of the structure that is well-ordered. Atoms with large B-factors generally belong to part of the structure that is very flexible.''' Each ATOM record ([[Protein Data Bank (file format)\|PDB file format]]) of a crystal structure deposited with the [[Protein Data Bank]] contains a B-factor for that atom.

			==References==
			{{reflist}}

			{{DEFAULTSORT:Debye-Waller factor}}
			[[Category:Crystallography]]
			[[Category:Scattering]]
			[[Category:Condensed matter physics]]

2001:638:50C:55:C169:7CBF:97F:4C57 at 11:32, 24 August 2012

2012-08-24T11:32:00Z

New page

Hello and welcome. My title is Irwin and I totally dig that title. Doing ceramics is what adore performing. For many years he's been residing in North Dakota and his family members loves it. Since she was eighteen she's been operating as a receptionist but her marketing by no means comes.<br><br>Also visit my page ... over the counter std test ([http://www.videoworld.com/blog/211112 linked internet page])

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en>RjwilmsiBot: fixing page range dashes using AWB

2001:638:50C:55:C169:7CBF:97F:4C57 at 11:32, 24 August 2012