Van Deemter equation

2013-11-16T20:07:53Z

107.3.215.71: Link to Excel file was not a link to the excel file, but someone's web page, so it was erased. "An automated Excel file for the empiric determination of the Van Deemter equation through matrix regression for a given measurement system (English)"

{{Unreferenced|date=December 2009}}
In [[particle physics]], [[wave|wave mechanics]] and [[optics]], '''momentum transfer''' is the amount of [[momentum]] that one particle gives to another particle.

In the simplest example of [[scattering]] of two colliding particles with initial momenta <math>\vec{p}_{i1},\vec{p}_{i2}</math>, resulting in final momenta <math>\vec{p}_{f1},\vec{p}_{f2}</math>, the momentum transfer is given by
:<math> \vec q = \vec{p}_{i1} - \vec{p}_{f1} = \vec{p}_{f2} - \vec{p}_{i2} </math>
where the last identity expresses [[momentum conservation]]. Momentum transfer is an important quantity because <math>\Delta x = \hbar / |q|</math> is a better measure for the typical distance resolution of the reaction than the momenta themselves.

==Wave mechanics and optics==
A wave has a momentum <math> p = \hbar k </math> and is a vectorial quantity. The difference of the momentum of the scattered wave to the incident wave is called ''momentum transfer''. The [[wave number]] k is the [[Absoluteness (mathematical logic)|absolute]] of the [[wave vector]] <math> k = q / \hbar</math> and is related to the [[wavelength]] <math> k = 2\pi / \lambda</math>. Often, momentum transfer is given in wavenumber units in [[reciprocal length]] <math> Q = k_f - k_i </math>

===Diffraction===
The momentum transfer plays an important role in the evaluation of [[neutron diffraction|neutron]], [[X-ray diffraction|X-ray]] and [[electron diffraction]] for the investigation of [[condensed matter]]. [[Bragg diffraction]] occurs on the atomic [[crystal lattice]], conserves the wave energy and thus is called [[elastic scattering]], where the [[wave number]]s final and incident particles, <math>k_f</math> and <math>k_i</math>, respectively, are equal and just the direction changes by a [[reciprocal lattice]] vector <math> G = Q = k_f - k_i</math> with the relation to the lattice spacing <math> G = 2\pi / d </math>. As momentum is conserved, the transfer of momentum occurs to [[crystal momentum]].

The presentation in <math>Q</math>-space is generic and does not depend on the type of [[radiation]] and wavelength used but only on the sample system, which allows to compare results obtained from many different methods. Some established communities such as [[powder diffraction]] employ the diffraction angle <math> 2\theta </math> as the independent variable, which worked fine in the early years when only a few [[characteristic wavelength]]s such as Cu-K<math>\alpha</math> were available. The relationship to <math>Q</math>-space is

<math> Q = \frac {4 \pi \sin \left ( \theta \right )}{\lambda} </math>

and basically states that larger <math> 2\theta </math> corresponds to larger <math>Q</math>.

==See also==
* [[Mandelstam variables]]
*[[Momentum-transfer cross section]]
* [[impulse (physics)]]

{{DEFAULTSORT:Momentum Transfer}}
[[Category:Particle physics]]
[[Category:Neutron-related techniques]]
[[Category:Synchrotron-related techniques]]
[[Category:Diffraction]]

formulasearchengine - User contributions [en]

Van Deemter equation