# Changeset e5a8f33 in sasmodels

Ignore:
Timestamp:
Mar 27, 2019 6:29:26 AM (6 months ago)
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
81d0b9b
Parents:
db1c84b
Message:

Fixed missing/poor rst/latex markup

File:
1 edited

### Legend:

Unmodified
 r0507e09 ---------- Parameters for this model are the core axial ratio X and a shell thickness, which are more often what we would like to determine and makes the model better behaved, particularly when polydispersity is applied than the four independent radii used in the original parameterization of this model. Parameters for this model are the core axial ratio $X_{core}$ and a shell thickness $t_{shell}$, which are more often what we would like to determine and make the model better behaved, particularly when polydispersity is applied, than the four independent radii used in the original parameterization of this model. the poles, of a prolate ellipsoid. When *X_core < 1* the core is oblate; when *X_core > 1* it is prolate. *X_core = 1* is a spherical core. For a fixed shell thickness *XpolarShell = 1*, to scale the shell thickness pro-rata with the radius set or constrain *XpolarShell = X_core*. When including an $S(q)$, the radius in $S(q)$ is calculated to be that of a sphere with the same 2nd virial coefficient of the outer surface of the ellipsoid. This may have some undesirable effects if the aspect ratio of the ellipsoid is large (ie, if $X << 1$ or $X >> 1$ ), when the $S(q)$ - which assumes spheres - will not in any case be valid.  Generating a custom product model will enable separate effective volume fraction and effective radius in the $S(q)$. When $X_{core}$ < 1 the core is oblate; when $X_{core}$ > 1 it is prolate. $X_{core}$ = 1 is a spherical core. For a fixed shell thickness $X_{polar shell}$ = 1, to scale $t_{shell}$ pro-rata with the radius set or constrain $X_{polar shell}$ = $X_{core}$. .. note:: When including an $S(q)$, the radius in $S(q)$ is calculated to be that of a sphere with the same 2nd virial coefficient of the outer surface of the ellipsoid. This may have some undesirable effects if the aspect ratio of the ellipsoid is large (ie, if $X << 1$ or $X >> 1$), when the $S(q)$ - which assumes spheres - will not in any case be valid.  Generating a custom product model will enable separate effective volume fraction and effective radius in the $S(q)$. If SAS data are in absolute units, and the SLDs are correct, then scale should where .. In following equation SK changed radius\_equat\_core to R_e .. math:: :nowrap: \begin{align*} F(q,\alpha) = &f(q,radius\_equat\_core,radius\_equat\_core.x\_core,\alpha) \\ &+ f(q,radius\_equat\_core + thick\_shell, radius\_equat\_core.x\_core + thick\_shell.x\_polar\_shell,\alpha) F(q,\alpha) = &f(q,R_e,R_e.x_{core},\alpha) \\ &+ f(q,R_e + t_{shell}, R_e.x_{core} + t_{shell}.x_{polar shell},\alpha) \end{align*} $V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid , $R_p$ is the polar radius along the rotational axis of the ellipsoid, $R_e$ is the equatorial radius perpendicular to the rotational axis of the ellipsoid and $\Delta \rho$ (contrast) is the scattering length density difference, either $(sld\_core - sld\_shell)$ or $(sld\_shell - sld\_solvent)$. equatorial radius perpendicular to the rotational axis of the ellipsoid, $t_{shell}$ is the thickness of the shell at the equator, and $\Delta \rho$ (the contrast) is the scattering length density difference, either $(\rho_{core} - \rho_{shell})$ or $(\rho_{shell} - \rho_{solvent})$. For randomly oriented particles: * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Richard Heenan (reparametrised model) **Date:** 2015 * **Last Reviewed by:** Richard Heenan **Date:** October 6, 2016 * **Last Reviewed by:** Steve King **Date:** March 27, 2019 * **Source added by :** Steve King **Date:** March 25, 2019 """