Changeset eb69cce in sasmodels for sasmodels/models/bcc.py
- Timestamp:
- Nov 30, 2015 7:18:41 PM (8 years ago)
- 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
- File:
-
- 1 edited
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sasmodels/models/bcc.py
rd138d43 reb69cce 13 13 The scattering intensity $I(q)$ is calculated as 14 14 15 .. math: 15 .. math:: 16 16 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) 18 18 19 19 20 where *scale* is the volume fraction of spheres, *Vp*is the volume of the21 primary particle, *V(lattice)*is a volume correction for the crystal20 where *scale* is the volume fraction of spheres, $V_p$ is the volume of the 21 primary particle, $V_\text{lattice}$ is a volume correction for the crystal 22 22 structure, $P(q)$ is the form factor of the sphere (normalized), and $Z(q)$ 23 23 is the paracrystalline structure factor for a body-centered cubic structure. 24 24 25 25 Equation (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*\.26 equations (29)-(31) from the 1987 paper for $Z1$, $Z2$, and $Z3$. 27 27 28 28 The lattice correction (the occupied volume of the lattice) for a … … 30 30 separation $D$ is 31 31 32 .. math: 32 .. math:: 33 33 34 34 V_\text{lattice} = \frac{16\pi}{3} \frac{R^3}{\left(D\sqrt{2}\right)^3} … … 38 38 in the calculation of $Z(q)$ 39 39 40 .. math: 40 .. math:: 41 41 42 42 \Delta a = g D … … 51 51 For a crystal, diffraction peaks appear at reduced q-values given by 52 52 53 .. math: 53 .. math:: 54 54 55 55 \frac{qD}{2\pi} = \sqrt{h^2 + k^2 + l^2} … … 60 60 correspond to (just the first 5) 61 61 62 .. math: 62 .. math:: 63 63 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} 68 68 69 69 **NB**: The calculation of $Z(q)$ is a double numerical integral that must … … 86 86 model computation. 87 87 88 .. figure:: img/crystal_orientation. gif88 .. figure:: img/crystal_orientation.png 89 89 90 90 Orientation of the crystal with respect to the scattering plane. … … 94 94 2D plot using the default values (w/200X200 pixels).* 95 95 96 Reference 97 --------- 96 References 97 ---------- 98 98 99 99 Hideki Matsuoka et. al. *Physical Review B*, 36 (1987) 1754-1765
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