Changeset 40a87fa in sasmodels for sasmodels/models/correlation_length.py
- Timestamp:
- Aug 8, 2016 9:24:11 AM (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:
- 2472141
- Parents:
- 2d65d51
- File:
-
- 1 edited
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sasmodels/models/correlation_length.py
r2c74c11 r40a87fa 8 8 9 9 .. math:: 10 I(Q) = \frac{A}{Q^n} + \frac{C}{1 + (Q\xi)^m} + B10 I(Q) = \frac{A}{Q^n} + \frac{C}{1 + (Q\xi)^m} + \text{background} 11 11 12 The first term describes Porod scattering from clusters (exponent = n) and the 13 second term is a Lorentzian function describing scattering from polymer chains 14 (exponent = m). This second term characterizes the polymer/solvent interactions 15 and therefore the thermodynamics. The two multiplicative factors A and C, the 16 incoherent background B and the two exponents n and m are used as fitting 17 parameters. (Respectively $porod\_scale$, $lorentz\_scale$, $background$, $exponent\_p$ and 18 $exponent\_l$ in the parameter list.) The remaining parameter \ |xi|\ is a correlation 19 length for the polymer chains. Note that when m=2 this functional form becomes the 20 familiar Lorentzian function. Some interpretation of the values of A and C may be 21 possible depending on the values of m and n. 12 The first term describes Porod scattering from clusters (exponent = $n$) and 13 the second term is a Lorentzian function describing scattering from 14 polymer chains (exponent = $m$). This second term characterizes the 15 polymer/solvent interactions and therefore the thermodynamics. The two 16 multiplicative factors $A$ and $C$, and the two exponents $n$ and $m$ are 17 used as fitting parameters. (Respectively *porod_scale*, *lorentz_scale*, 18 *exponent_p* and *exponent_l* in the parameter list.) The remaining 19 parameter $\xi$ (*cor_length* in the parameter list) is a correlation 20 length for the polymer chains. Note that when $m=2$ this functional form 21 becomes the familiar Lorentzian function. Some interpretation of the 22 values of $A$ and $C$ may be possible depending on the values of $m$ and $n$. 22 23 23 24 For 2D data: The 2D scattering intensity is calculated in the same way as 1D, 24 25 where the q vector is defined as 25 26 26 .. math:: 27 q = \sqrt{q_x^2 + q_y^2} 27 .. math:: q = \sqrt{q_x^2 + q_y^2} 28 28 29 29 References
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