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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:

where $\omega_\alpha$ is the weight for atom $\alpha$, $N_{atoms}$ is the number of (selected) atoms in the system (or in the subsystem) for which the analysis is performed and $m_\alpha$, $Z_\alpha$, $b_{\alpha,\mathrm{inc}}$, and $b_{\alpha,\mathrm{coh}}$ are respectively the mass, the atomic number, the incoherent scattering length and the coherent scattering length of atom $\alpha$ where


$\displaystyle b_{\alpha,\mathrm{coh}}$ $\textstyle =$ $\displaystyle \overline{b_\alpha}$ (4.6)
$\displaystyle b_{\alpha,\mathrm{inc}}$ $\textstyle =$ $\displaystyle \sqrt{\overline{b_\alpha^2}-\overline{b_\alpha}^2}$ (4.7)

the average being done over isotopes and relative spin orientations of neutrons and nucleus.

Using such a definition, we have $\sum_{\alpha=1}^N \omega_\alpha=1$.

If we now group atoms into their different species A, B ...(e.g. oxygens, hydrogens ...) such that:

\begin{displaymath}
N = \sum^{N_{species}}_{I = 1}n_I
\end{displaymath} (4.8)

where $N_{species}$ is the total number of selected species and $n_I$ is the number of atoms of specie I. Then, we can define the weight for a given atomic specie I as:

and we have $\sum_{I=1}^{N_{species}} {\cal W_I}=\sum_{I=1}^{N_{species}}\sum_{\alpha=1}^{n_I} \omega_{\alpha,I}= 1$ where $\omega_{\alpha,I}$ is the atomic weight of atom $\alpha$ of specie $I$ 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 up previous contents
Next: Atom selection Up: The Analysis menu Previous: The Analysis menu   Contents
pellegrini eric 2009-10-06