Changeset eb69cce in sasmodels for sasmodels/models/bcc.py


Ignore:
Timestamp:
Nov 30, 2015 7:18:41 PM (8 years ago)
Author:
Paul Kienzle <pkienzle@…>
Branches:
master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
d18f8a8
Parents:
d138d43
Message:

make model docs more consistent; build pdf docs

File:
1 edited

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  • sasmodels/models/bcc.py

    rd138d43 reb69cce  
    1313The scattering intensity $I(q)$ is calculated as 
    1414 
    15 .. math: 
     15.. math:: 
    1616 
    17     I(q) = \frac{\text{scale}}{V_P} V_\text{lattice} P(q) Z(q) 
     17    I(q) = \frac{\text{scale}}{V_p} V_\text{lattice} P(q) Z(q) 
    1818 
    1919 
    20 where *scale* is the volume fraction of spheres, *Vp* is the volume of the 
    21 primary particle, *V(lattice)* is a volume correction for the crystal 
     20where *scale* is the volume fraction of spheres, $V_p$ is the volume of the 
     21primary particle, $V_\text{lattice}$ is a volume correction for the crystal 
    2222structure, $P(q)$ is the form factor of the sphere (normalized), and $Z(q)$ 
    2323is the paracrystalline structure factor for a body-centered cubic structure. 
    2424 
    2525Equation (1) of the 1990 reference is used to calculate $Z(q)$, using 
    26 equations (29)-(31) from the 1987 paper for *Z1*\ , *Z2*\ , and *Z3*\ . 
     26equations (29)-(31) from the 1987 paper for $Z1$, $Z2$, and $Z3$. 
    2727 
    2828The lattice correction (the occupied volume of the lattice) for a 
     
    3030separation $D$ is 
    3131 
    32 .. math: 
     32.. math:: 
    3333 
    3434    V_\text{lattice} = \frac{16\pi}{3} \frac{R^3}{\left(D\sqrt{2}\right)^3} 
     
    3838in the calculation of $Z(q)$ 
    3939 
    40 .. math: 
     40.. math:: 
    4141 
    4242    \Delta a = g D 
     
    5151For a crystal, diffraction peaks appear at reduced q-values given by 
    5252 
    53 .. math: 
     53.. math:: 
    5454 
    5555    \frac{qD}{2\pi} = \sqrt{h^2 + k^2 + l^2} 
     
    6060correspond to (just the first 5) 
    6161 
    62 .. math: 
     62.. math:: 
    6363 
    64     \begin{eqnarray} 
    65     &q/q_o&&\quad 1&& \ \sqrt{2} && \ \sqrt{3} && \ \sqrt{4} && \ \sqrt{5} \\ 
    66     &\text{Indices}&& (110) && (200) && (211) && (220) && (310) 
    67     \end{eqnarray} 
     64    \begin{array}{lccccc} 
     65    q/q_o          &   1   & \sqrt{2} & \sqrt{3} & \sqrt{4} & \sqrt{5} \\ 
     66    \text{Indices} & (110) &    (200) & (211)    & (220)    & (310)    \\ 
     67    \end{array} 
    6868 
    6969**NB**: The calculation of $Z(q)$ is a double numerical integral that must 
     
    8686model computation. 
    8787 
    88 .. figure:: img/crystal_orientation.gif 
     88.. figure:: img/crystal_orientation.png 
    8989 
    9090    Orientation of the crystal with respect to the scattering plane. 
     
    9494    2D plot using the default values (w/200X200 pixels).* 
    9595 
    96 Reference 
    97 --------- 
     96References 
     97---------- 
    9898 
    9999Hideki Matsuoka et. al. *Physical Review B*, 36 (1987) 1754-1765 
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