Changeset 0f113fb in sasmodels for sasmodels/models/core_shell_parallelepiped.py

Timestamp:

Dec 4, 2017 8:18:21 AM (6 years ago)

Author:

Paul Kienzle <pkienzle@…>

Branches:

master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

c11d09f, a189283

Parents:

10ee838 (diff), 791281c (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.

Message:

Merge branch 'master' into ticket-786

File:

• sasmodels/models/core_shell_parallelepiped.py (modified) (6 diffs)

sasmodels/models/core_shell_parallelepiped.py

@@ -5 +5 @@
 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. However at this time the 1D
-calculation does **NOT** actually calculate a c face rim despite the presence
-of the parameter. Some other aspects of the 1D calculation may be wrong.
-
-.. note::
-   This model was originally ported from NIST IGOR macros. However, it is not
-   yet fully understood by the SasView developers and is currently under review.
+"rim" can be different on each (pair) of faces.
 
 The form factor is normalized by the particle volume $V$ such that
@@ -21 +15 @@
 where $\langle \ldots \rangle$ is an average over all possible orientations
 of the rectangular solid.
-
 
 The function calculated is the form factor of the rectangular solid below.
@@ -41 +34 @@
     V = ABC + 2t_ABC + 2t_BAC + 2t_CAB
 
-**meaning that there are "gaps" at the corners of the solid.**  Again note that
-$t_C = 0$ currently.
+**meaning that there are "gaps" at the corners of the solid.**
 
 The intensity calculated follows the :ref:`parallelepiped` model, with the
 core-shell intensity being calculated as the square of the sum of the
-amplitudes of the core and shell, in the same manner as a core-shell model.
-
-.. math::
-
-    F_{a}(Q,\alpha,\beta)=
-    \left[\frac{\sin(\tfrac{1}{2}Q(L_A+2t_A)\sin\alpha \sin\beta)
-               }{\tfrac{1}{2}Q(L_A+2t_A)\sin\alpha\sin\beta}
-    - \frac{\sin(\tfrac{1}{2}QL_A\sin\alpha \sin\beta)
-           }{\tfrac{1}{2}QL_A\sin\alpha \sin\beta} \right]
-    \left[\frac{\sin(\tfrac{1}{2}QL_B\sin\alpha \sin\beta)
-               }{\tfrac{1}{2}QL_B\sin\alpha \sin\beta} \right]
-    \left[\frac{\sin(\tfrac{1}{2}QL_C\sin\alpha \sin\beta)
-               }{\tfrac{1}{2}QL_C\sin\alpha \sin\beta} \right]
-
-.. note::
-
-    Why does t_B not appear in the above equation?
-    For the calculation of the form factor to be valid, the sides of the solid
-    MUST (perhaps not any more?) be chosen such that** $A < B < C$.
-    If this inequality is not satisfied, the model will not report an error,
-    but the calculation will not be correct and thus the result wrong.
+amplitudes of the core and the slabs on the edges.
+
+the scattering amplitude is computed for a particular orientation of the
+core-shell parallelepiped with respect to the scattering vector and then
+averaged over all possible orientations, where $\alpha$ is the angle between
+the $z$ axis and the $C$ axis of the parallelepiped, $\beta$ is
+the angle between projection of the particle in the $xy$ detector plane
+and the $y$ axis.
+
+.. math::
+
+    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) \\
+    &+ (\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) \\
+    &+ (\rho_\text{C}-\rho_\text{solvent})
+        S(Q_A, A) S(Q_B, B) \left[S(Q_C, C+2t_C) - S(Q_C, C)\right]
+
+with
+
+.. math::
+
+    S(Q, L) = L \frac{\sin \tfrac{1}{2} Q L}{\tfrac{1}{2} Q L}
+
+and
+
+.. math::
+
+    Q_A &= \sin\alpha \sin\beta \\
+    Q_B &= \sin\alpha \cos\beta \\
+    Q_C &= \cos\alpha
+
+
+where $\rho_\text{core}$, $\rho_\text{A}$, $\rho_\text{B}$ and $\rho_\text{C}$
+are the scattering length of the parallelepiped core, and the rectangular
+slabs of thickness $t_A$, $t_B$ and $t_C$, respectively. $\rho_\text{solvent}$
+is the scattering length of the solvent.
 
 FITTING NOTES
+~~~~~~~~~~~~~
+
 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.**
+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.
 
-Constraints must be applied during fitting to ensure that the inequality
-$A < B < C$ is not violated. The calculation will not report an error,
-but the results will not be correct.
-
 The returned value is in units of |cm^-1|, on absolute scale.
 
 NB: The 2nd virial coefficient of the core_shell_parallelepiped is calculated
 based on the the averaged effective radius $(=\sqrt{(A+2t_A)(B+2t_B)/\pi})$
-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.
+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 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` .
+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.
+
+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.
 
 .. figure:: img/parallelepiped_angle_definition.png
@@ -114 +127 @@
     Equations (1), (13-14). (in German)
 .. [#] D Singh (2009). *Small angle scattering studies of self assembly in
-   lipid mixtures*, John's Hopkins University Thesis (2009) 223-225. `Available
+   lipid mixtures*, Johns Hopkins University Thesis (2009) 223-225. `Available
    from Proquest <http://search.proquest.com/docview/304915826?accountid
    =26379>`_
@@ -175 +188 @@
         Return equivalent radius (ER)
     """
-
-    # surface average radius (rough approximation)
-    surf_rad = sqrt((length_a + 2.0*thick_rim_a) * (length_b + 2.0*thick_rim_b) / pi)
-
-    height = length_c + 2.0*thick_rim_c
-
-    ddd = 0.75 * surf_rad * (2 * surf_rad * height + (height + surf_rad) * (height + pi * surf_rad))
-    return 0.5 * (ddd) ** (1. / 3.)
+    from .parallelepiped import ER as ER_p
+
+    a = length_a + 2*thick_rim_a
+    b = length_b + 2*thick_rim_b
+    c = length_c + 2*thick_rim_c
+    return ER_p(a, b, c)
 
 # VR defaults to 1.0
@@ -216 +227 @@
             psi_pd=10, psi_pd_n=1)
 
-# rkh 7/4/17 add random unit test for 2d, note make all params different, 2d values not tested against other codes or models
+# rkh 7/4/17 add random unit test for 2d, note make all params different,
+# 2d values not tested against other codes or models
 if 0:  # pak: model rewrite; need to update tests
     qx, qy = 0.2 * cos(pi/6.), 0.2 * sin(pi/6.)