# Changeset 96153e4 in sasmodels

Ignore:
Timestamp:
May 20, 2018 11:22:28 PM (3 years ago)
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
fc7bcd5
Parents:
c64a68e
Message:

more corrections and normalizations

Addreses #896. Brings parallelepiped and core-shell parallelepiped more
into line with each other and corrects angle definitions refering to
orietnational distribution docs for details. Still need to sort out
with Paul Kienzle the proper order the angles are applied.

Location:
sasmodels/models
Files:
2 edited

### Legend:

Unmodified
 r5bc6d21 Calculates the form factor for a rectangular solid with a core-shell structure. The thickness and the scattering length density of the shell or "rim" can be different on each (pair) of faces. The thickness and the scattering length density of the shell or "rim" can be different on each (pair) of faces. The three dimensions of the core of the parallelepiped (strictly here a cuboid) may be given in *any* size order as long as the particles are randomly oriented (i.e. take on all possible orientations see notes on 2D below). To avoid multiple fit solutions, e specially with Monte-Carlo fit methods, it may be advisable to restrict their ranges. There may be a number of closely similar "best fits", so some trial and error, or fixing of some dimensions at expected values, may help. The form factor is normalized by the particle volume $V$ such that pulled out of the form factor term due to the multiple slds in the model. The core of the solid is defined by the dimensions $A$, $B$, $C$ such that $A < B < C$. The core of the solid is defined by the dimensions $A$, $B$, $C$ here shown such that $A < B < C$. .. figure:: img/parallelepiped_geometry.jpg ~~~~~~~~~~~~~ If the scale is set equal to the particle volume fraction, $\phi$, the returned value is the scattered intensity per unit volume, $I(q) = \phi P(q)$. However, **no interparticle interference effects are included in this calculation.** There are many parameters in this model. Hold as many fixed as possible with known values, or you will certainly end up at a solution that is unphysical. The returned value is in units of |cm^-1|, on absolute scale. NB: The 2nd virial coefficient of the core_shell_parallelepiped is calculated For 2d data the orientation of the particle is required, described using angles $\theta$, $\phi$ and $\Psi$ as in the diagrams below. For further details of the calculation and angular dispersions see :ref:orientation. The angle $\Psi$ is the rotational angle around the *long_c* axis. For example, $\Psi = 0$ when the *short_b* axis is parallel to the *x*-axis of the detector. angles $\theta$, $\phi$ and $\Psi$ as in the diagrams below, for further details of the calculation and angular dispersions see :ref:orientation . The angle $\Psi$ is the rotational angle around the $C$ axis. For $\theta = 0$ and $\phi = 0$, $\Psi = 0$ corresponds to the $B$ axis oriented parallel to the y-axis of the detector with $A$ along the x-axis. For other $\theta$, $\phi$ values, the parallelepiped has to be first rotated $\theta$ degrees in the $z-x$ plane and then $\phi$ degrees around the $z$ axis, before doing a final rotation of $\Psi$ degrees around the resulting $C$ axis of the particle to obtain the final orientation of the parallelepiped. .. note:: For 2d, constraints must be applied during fitting to ensure that the
 rb343226 The three dimensions of the parallelepiped (strictly here a cuboid) may be given in *any* size order. To avoid multiple fit solutions, especially with Monte-Carlo fit methods, it may be advisable to restrict their ranges. There may be a number of closely similar "best fits", so some trial and error, or fixing of some dimensions at expected values, may help. given in *any* size order as long as the particles are randomly oriented (i.e. take on all possible orientations see notes on 2D below). To avoid multiple fit solutions, especially with Monte-Carlo fit methods, it may be advisable to restrict their ranges. There may be a number of closely similar "best fits", so some trial and error, or fixing of some dimensions at expected values, may help. The form factor is normalized by the particle volume and the 1D scattering of the calculation and angular dispersions see :ref:orientation . .. Comment by Miguel Gonzalez: The following text has been commented because I think there are two mistakes. Psi is the rotational angle around C (but I cannot understand what it means against the q plane) and psi=0 corresponds to a||x and b||y. The angle $\Psi$ is the rotational angle around the $C$ axis against the $q$ plane. For example, $\Psi = 0$ when the $B$ axis is parallel to the $x$-axis of the detector. The angle $\Psi$ is the rotational angle around the $C$ axis. For $\theta = 0$ and $\phi = 0$, $\Psi = 0$ corresponds to the $B$ axis of the particle to obtain the final orientation of the parallelepiped. .. note:: For 2d, constraints must be applied during fitting to ensure that the inequality $A < B < C$ is not violated, and hence the correct definition of angles is preserved. The calculation will not report an error, but the results may be not correct. .. _parallelepiped-orientation: