Changeset 41345d7e in sasview
 Timestamp:
 Jul 12, 2016 5:33:14 AM (8 years ago)
 Branches:
 master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release4.1.1, release4.1.2, release4.2.2, ticket1009, ticket1094headless, ticket12422dresolution, ticket1243, ticket1249, ticket885, unittestsaveload
 Children:
 d03228e
 Parents:
 eb320682
 Location:
 src/sas/sasgui/perspectives/corfunc/media
 Files:

 1 added
 1 edited
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src/sas/sasgui/perspectives/corfunc/media/corfunc_help.rst
rfb7fcec r41345d7e 15 15 * Extrapolation of the scattering curve to :math:`Q = 0` and 16 16 :math:`Q = \infty` 17 * Fourier Transform of the extrapolated data to give the correlation function 17 * Fourier/Hilbert Transform of the extrapolated data to give the correlation 18 function/volume fraction profile 18 19 * Interpretation of the 1D correlation function based on an ideal lamellar 19 20 morphology … … 60 61 :align: center 61 62 62 ``Figure 1``The value of :math:`\sigma` is a measure of the electron63 **Figure 1** The value of :math:`\sigma` is a measure of the electron 63 64 density profile at the interface between crystalline and amorphous regions. 64 65 … … 83 84 .. math:: 84 85 h_i = \frac{1}{1 + \frac{(x_ib)^2}{(x_ia)^2}} 86 87 Transform 88  89 90 Fourier 91 ^^^^^^^ 92 93 If Fourier is selected for the transform type, the perspective will perform a 94 discrete cosine transform to the extrapolated data in order to calculate the 95 correlation function. The following algoritm is applied: 96 97 .. math:: 98 \Gamma(x_k) = 2 \sum_{n=0}^{N1} x_n \cos{\left[ \frac{\pi}{N} 99 \left(n + \frac{1}{2} \right) k \right] } \text{ for } k = 0, 1, \ldots, 100 N1, N 101 102 Hilbert 103 ^^^^^^^ 104 If Hilbert is selected for the transform type, the perspective will perform a 105 Hilbert transform to the extraplated data in order to calculate the Volume 106 Fraction Profile. 107 108 Interpretation 109  110 Once the correlation function has been calculated by transforming the 111 extrapolated data, it may be interpreted by clicking the "Compute Parameters" 112 button. The correlation function is interpreted in terms of an ideal lamellar 113 morphology, and structural parameters are obtained as shown in Figure 2 below. 114 It should be noted that a small beam size is assumed; no desmearing is 115 performed. 116 117 .. figure:: fig2.gif 118 :align: center 119 120 **Figure 2** Interpretation of the correlation function. 121 122 The structural parameters obtained are: 123 124 * Long Period :math:`= L_p` 125 * Average Hard Block Thickness :math:`= L_c` 126 * Average Core Thickness :math:`= D_0` 127 * Average Interface Thickness :math:`\text{} = D_{tr}` 128 * Polydispersity :math:`= \Gamma_{\text{min}}/\Gamma_{\text{max}}` 129 * Local Crystallinity :math:`= L_c/L_p`
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