# Changeset 5bc373b in sasmodels

Ignore:
Timestamp:
Mar 4, 2018 10:40:24 PM (4 years ago)
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
b510b92
Parents:
fc3ae1b
Message:

First edits to core shell parallelipiped docs

Part f ticket 896 effort to ensure the documentation matches the code
now that the code has been fixed and validated.

Location:
sasmodels/models
Files:
2 edited

### Legend:

Unmodified
 r97be877 $A < B < C$. .. image:: img/core_shell_parallelepiped_geometry.jpg .. figure:: img/parallelepiped_geometry.jpg Core of the core shell Parallelepiped with the corresponding definition of sides. There are rectangular "slabs" of thickness $t_A$ that add to the $A$ dimension $(=t_C)$ faces. The projection in the $AB$ plane is then .. image:: img/core_shell_parallelepiped_projection.jpg .. figure:: img/core_shell_parallelepiped_projection.jpg AB cut through the core-shell parllelipiped showing the cross secion of four of the six shell slabs The volume of the solid is .. math:: F(Q) F(q) &= (\rho_\text{core}-\rho_\text{solvent}) S(Q_A, A) S(Q_B, B) S(Q_C, C) \\ &+ (\rho_\text{A}-\rho_\text{solvent}) \left[S(Q_A, A+2t_A) - S(Q_A, Q)\right] S(Q_B, B) S(Q_C, C) \\ \left[S(Q_A, A+2t_A) - S(Q_A, A)\right] S(Q_B, B) S(Q_C, C) \\ &+ (\rho_\text{B}-\rho_\text{solvent}) S(Q_A, A) \left[S(Q_B, B+2t_B) - S(Q_B, B)\right] S(Q_C, C) \\ .. math:: Q_A &= \sin\alpha \sin\beta \\ Q_B &= \sin\alpha \cos\beta \\ Q_C &= \cos\alpha Q_A &= q \sin\alpha \sin\beta \\ Q_B &= q \sin\alpha \cos\beta \\ Q_C &= q \cos\alpha and length $(C+2t_C)$ values, after appropriately sorting the three dimensions to give an oblate or prolate particle, to give an effective radius, for $S(Q)$ when $P(Q) * S(Q)$ is applied. for $S(q)$ when $P(q) * S(q)$ is applied. For 2d data the orientation of the particle is required, described using
 ref07e95 This model calculates the scattering from a rectangular parallelepiped (\:numref:parallelepiped-image\). (:numref:parallelepiped-image). If you need to apply polydispersity, see also :ref:rectangular-prism.