Changeset 7609046 in sasmodels for doc/guide/pd/polydispersity.rst

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Timestamp:
Jul 19, 2018 12:47:44 PM (14 months ago)
Branches:
master
Children:
f41027b
Parents:
9ce5bcb (diff), 1d9998c (diff)
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git-author:
Paul Kienzle <pkienzle@…> (07/19/18 12:47:44)
git-committer:
Message:

Merge branch 'master' into ticket-608-user-defined-weights

File:
1 edited

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Unmodified
 r9ce5bcb P(q) = \text{scale} \langle F^* F \rangle / V + \text{background} where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an average over the size distribution. where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an average over the size distribution $f(x; \bar x, \sigma)$, giving .. math:: P(q) = \frac{\text{scale}}{V} \int_\mathbb{R} f(x; \bar x, \sigma) F^2(q, x)\, dx + \text{background} Each distribution is characterized by a center value $\bar x$ or with larger values of $N_\sigma$ required for heavier tailed distributions. The scattering in general falls rapidly with $qr$ so the usual assumption that $G(r - 3\sigma_r)$ is tiny and therefore $f(r - 3\sigma_r)G(r - 3\sigma_r)$ that $f(r - 3\sigma_r)$ is tiny and therefore $f(r - 3\sigma_r)f(r - 3\sigma_r)$ will not contribute much to the average may not hold when particles are large. This, too, will require increasing $N_\sigma$. These are all implemented as *number-average* distributions. .. note:: In 2009 IUPAC decided to introduce the new term 'dispersity' to replace the term 'polydispersity' (see Pure Appl. Chem., (2009), 81(2), 351-353 _ in order to make the terminology describing distributions of properties unambiguous. Throughout the SasView documentation we continue to use the term polydispersity because one of the consequences of the IUPAC change is that orientational polydispersity would not meet their new criteria (which requires dispersity to be dimensionless). Suggested Applications