Changeset e5a8f33 in sasmodels
 Timestamp:
 Mar 27, 2019 6:29:26 AM (4 months ago)
 Branches:
 master, core_shell_microgels, magnetic_model, ticket1257vesicleproduct, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
 Children:
 81d0b9b
 Parents:
 db1c84b
 File:

 1 edited
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sasmodels/models/core_shell_ellipsoid.py
r0507e09 re5a8f33 3 3  4 4 5 Parameters for this model are the core axial ratio X and a shell thickness, 6 which are more often what we would like to determine and makes the model 7 better behaved, particularly when polydispersity is applied than the four 8 independent radii used in the original parameterization of this model. 5 Parameters for this model are the core axial ratio $X_{core}$ and a shell 6 thickness $t_{shell}$, which are more often what we would like to determine 7 and make the model better behaved, particularly when polydispersity is 8 applied, than the four independent radii used in the original parameterization 9 of this model. 9 10 10 11 … … 15 16 the poles, of a prolate ellipsoid. 16 17 17 When *X_core < 1* the core is oblate; when *X_core > 1* it is prolate. 18 *X_core = 1* is a spherical core. 19 20 For a fixed shell thickness *XpolarShell = 1*, to scale the shell thickness 21 prorata with the radius set or constrain *XpolarShell = X_core*. 22 23 When including an $S(q)$, the radius in $S(q)$ is calculated to be that of 24 a sphere with the same 2nd virial coefficient of the outer surface of the 25 ellipsoid. This may have some undesirable effects if the aspect ratio of the 26 ellipsoid is large (ie, if $X << 1$ or $X >> 1$ ), when the $S(q)$ 27  which assumes spheres  will not in any case be valid. Generating a 28 custom product model will enable separate effective volume fraction and 29 effective radius in the $S(q)$. 18 When $X_{core}$ < 1 the core is oblate; when $X_{core}$ > 1 it is prolate. 19 $X_{core}$ = 1 is a spherical core. 20 21 For a fixed shell thickness $X_{polar shell}$ = 1, to scale $t_{shell}$ 22 prorata with the radius set or constrain $X_{polar shell}$ = $X_{core}$. 23 24 .. note:: 25 26 When including an $S(q)$, the radius in $S(q)$ is calculated to be that of 27 a sphere with the same 2nd virial coefficient of the outer surface of the 28 ellipsoid. This may have some undesirable effects if the aspect ratio of the 29 ellipsoid is large (ie, if $X << 1$ or $X >> 1$), when the $S(q)$ 30  which assumes spheres  will not in any case be valid. Generating a 31 custom product model will enable separate effective volume fraction and 32 effective radius in the $S(q)$. 30 33 31 34 If SAS data are in absolute units, and the SLDs are correct, then scale should … … 43 46 where 44 47 48 .. In following equation SK changed radius\_equat\_core to R_e 49 45 50 .. math:: 46 51 :nowrap: 47 52 48 53 \begin{align*} 49 F(q,\alpha) = &f(q, radius\_equat\_core,radius\_equat\_core.x\_core,\alpha) \\50 &+ f(q, radius\_equat\_core + thick\_shell,51 radius\_equat\_core.x\_core + thick\_shell.x\_polar\_shell,\alpha)54 F(q,\alpha) = &f(q,R_e,R_e.x_{core},\alpha) \\ 55 &+ f(q,R_e + t_{shell}, 56 R_e.x_{core} + t_{shell}.x_{polar shell},\alpha) 52 57 \end{align*} 53 58 … … 71 76 $V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid , $R_p$ is the 72 77 polar radius along the rotational axis of the ellipsoid, $R_e$ is the 73 equatorial radius perpendicular to the rotational axis of the ellipsoid 74 and $\Delta \rho$ (contrast) is the scattering length density difference, 75 either $(sld\_core  sld\_shell)$ or $(sld\_shell  sld\_solvent)$. 78 equatorial radius perpendicular to the rotational axis of the ellipsoid, 79 $t_{shell}$ is the thickness of the shell at the equator, 80 and $\Delta \rho$ (the contrast) is the scattering length density difference, 81 either $(\rho_{core}  \rho_{shell})$ or $(\rho_{shell}  \rho_{solvent})$. 76 82 77 83 For randomly oriented particles: … … 104 110 * **Author:** NIST IGOR/DANSE **Date:** pre 2010 105 111 * **Last Modified by:** Richard Heenan (reparametrised model) **Date:** 2015 106 * **Last Reviewed by:** Richard Heenan **Date:** October 6, 2016112 * **Last Reviewed by:** Steve King **Date:** March 27, 2019 107 113 * **Source added by :** Steve King **Date:** March 25, 2019 108 114 """
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