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Weighting scheme
In quantities that are averages over all atoms, nMOLDYN gives the possibility to choose between differents atomic weighting
schemes. Presently, nMOLDYN implements the following schemes:
- Equal weighting:
 |
(4.1) |
- Mass weighting:
 |
(4.2) |
- Atomic number weighting:
 |
(4.3) |
- Incoherent neutron scattering:
 |
(4.4) |
- Coherent neutron scattering:
 |
(4.5) |
where
is the weight for atom
,
is the number of (selected) atoms in the system (or in
the subsystem) for which the analysis is performed and
,
,
, and
are respectively the
mass, the atomic number, the incoherent scattering length and the coherent scattering length of atom
where
the average being done over isotopes and relative spin orientations of neutrons and nucleus.
Using such a definition, we have
.
If we now group atoms into their different species A, B ...(e.g. oxygens, hydrogens ...) such that:
 |
(4.8) |
where
is the total number of selected species and
is the number of atoms of specie I. Then, we can
define the weight for a given atomic specie I as:
- Equal weighting (per specie):
 |
(4.9) |
- Mass weighting (per specie):
 |
(4.10) |
- Atomic number weighting:
 |
(4.11) |
- Incoherent neutron scattering:
 |
(4.12) |
- Coherent neutron scattering:
 |
(4.13) |
and we have
where
is the atomic weight of atom
of specie
defined in equations
4.1 to 4.2. The weigthing scheme based on specie will be useful when dealing with analysis for which
partial terms can be defined.
Next: Atom selection
Up: The Analysis menu
Previous: The Analysis menu
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pellegrini eric
2009-10-06