1 | r""" |
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2 | Definition |
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3 | ---------- |
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4 | |
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5 | This model is a trivial extension of the CoreShell function to a larger number |
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6 | of shells. The scattering length density profile for the default sld values |
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7 | (w/ 4 shells). |
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8 | |
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9 | .. figure:: img/core_multi_shell_sld_default_profile.jpg |
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10 | |
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11 | SLD profile of the core_multi_shell object from the center of sphere out |
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12 | for the default SLDs.* |
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13 | |
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14 | The 2D scattering intensity is the same as $P(q)$ above, regardless of the |
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15 | orientation of the $\vec q$ vector which is defined as |
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16 | |
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17 | .. math:: |
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18 | |
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19 | q = \sqrt{q_x^2 + q_y^2} |
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20 | |
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21 | .. note:: **Be careful!** The SLDs and scale can be highly correlated. Hold as |
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22 | many of these parameters fixed as possible. |
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23 | |
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24 | .. note:: The outer most radius (= *radius* + *thickness*) is used as the |
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25 | effective radius for $S(Q)$ when $P(Q)*S(Q)$ is applied. |
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26 | |
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27 | For information about polarised and magnetic scattering, see |
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28 | the :ref:`magnetism` documentation. |
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29 | |
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30 | Our model uses the form factor calculations implemented in a c-library provided |
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31 | by the NIST Center for Neutron Research (Kline, 2006) [#kline]_. |
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32 | |
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33 | References |
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34 | ---------- |
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35 | |
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36 | .. [#] See the :ref:`core-shell-sphere` model documentation. |
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37 | .. [#kline] S R Kline, *J Appl. Cryst.*, 39 (2006) 895 |
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38 | .. [#] L A Feigin and D I Svergun, *Structure Analysis by Small-Angle X-Ray and |
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39 | Neutron Scattering*, Plenum Press, New York, 1987. |
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40 | |
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41 | Authorship and Verification |
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42 | ---------------------------- |
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43 | |
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44 | * **Author:** NIST IGOR/DANSE **Date:** pre 2010 |
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45 | * **Last Modified by:** Paul Kienzle **Date:** September 12, 2016 |
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46 | * **Last Reviewed by:** Paul Kienzle **Date:** September 12, 2016 |
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47 | """ |
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48 | from __future__ import division |
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49 | |
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50 | import numpy as np |
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51 | from numpy import inf |
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52 | |
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53 | name = "core_multi_shell" |
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54 | title = "This model provides the scattering from a spherical core with 1 to 4 \ |
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55 | concentric shell structures. The SLDs of the core and each shell are \ |
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56 | individually specified." |
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57 | |
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58 | description = """\ |
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59 | Form factor for a core muti-shell (up to 4) sphere normalized by the volume. |
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60 | Each shell can have a unique thickness and sld. |
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61 | |
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62 | background:background, |
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63 | rad_core0: radius of sphere(core) |
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64 | thick_shell#:the thickness of the shell# |
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65 | sld_core0: the SLD of the sphere |
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66 | sld_solv: the SLD of the solvent |
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67 | sld_shell: the SLD of the shell# |
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68 | A_shell#: the coefficient in the exponential function |
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69 | |
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70 | |
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71 | scale: 1.0 if data is on absolute scale |
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72 | volfraction: volume fraction of spheres |
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73 | radius: the radius of the core |
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74 | sld: the SLD of the core |
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75 | thick_shelli: the thickness of the i'th shell from the core |
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76 | sld_shelli: the SLD of the i'th shell from the core |
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77 | sld_solvent: the SLD of the solvent |
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78 | background: incoherent background |
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79 | |
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80 | """ |
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81 | |
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82 | category = "shape:sphere" |
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83 | |
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84 | |
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85 | # ["name", "units", default, [lower, upper], "type","description"], |
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86 | parameters = [["sld_core", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", |
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87 | "Core scattering length density"], |
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88 | ["radius", "Ang", 200., [0, inf], "volume", |
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89 | "Radius of the core"], |
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90 | ["sld_solvent", "1e-6/Ang^2", 6.4, [-inf, inf], "sld", |
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91 | "Solvent scattering length density"], |
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92 | ["n", "", 1, [0, 10], "volume", |
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93 | "number of shells"], |
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94 | ["sld[n]", "1e-6/Ang^2", 1.7, [-inf, inf], "sld", |
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95 | "scattering length density of shell k"], |
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96 | ["thickness[n]", "Ang", 40., [0, inf], "volume", |
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97 | "Thickness of shell k"], |
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98 | ] |
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99 | |
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100 | source = ["lib/sas_3j1x_x.c", "core_multi_shell.c"] |
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101 | have_Fq = True |
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102 | effective_radius_type = ["outer radius", "core radius"] |
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103 | |
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104 | def random(): |
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105 | """Return a random parameter set for the model.""" |
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106 | num_shells = np.minimum(np.random.poisson(3)+1, 10) |
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107 | total_radius = 10**np.random.uniform(1.7, 4) |
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108 | thickness = np.random.exponential(size=num_shells+1) |
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109 | thickness *= total_radius/np.sum(thickness) |
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110 | pars = dict( |
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111 | #background=0, |
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112 | n=num_shells, |
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113 | radius=thickness[0], |
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114 | ) |
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115 | for k, v in enumerate(thickness[1:]): |
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116 | pars['thickness%d'%(k+1)] = v |
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117 | return pars |
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118 | |
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119 | def profile(sld_core, radius, sld_solvent, n, sld, thickness): |
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120 | """ |
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121 | Returns the SLD profile *r* (Ang), and *rho* (1e-6/Ang^2). |
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122 | """ |
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123 | n = int(n+0.5) |
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124 | z = [] |
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125 | rho = [] |
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126 | |
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127 | # add in the core |
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128 | z.append(0) |
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129 | rho.append(sld_core) |
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130 | z.append(radius) |
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131 | rho.append(sld_core) |
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132 | |
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133 | # add in the shells |
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134 | for k in range(int(n)): |
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135 | # Left side of each shells |
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136 | z.append(z[-1]) |
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137 | rho.append(sld[k]) |
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138 | z.append(z[-1] + thickness[k]) |
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139 | rho.append(sld[k]) |
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140 | # add in the solvent |
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141 | z.append(z[-1]) |
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142 | rho.append(sld_solvent) |
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143 | z.append(z[-1]*1.25) |
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144 | rho.append(sld_solvent) |
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145 | |
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146 | return np.asarray(z), np.asarray(rho) |
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147 | |
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148 | demo = dict(sld_core=6.4, |
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149 | radius=60, |
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150 | sld_solvent=6.4, |
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151 | n=2, |
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152 | sld=[2.0, 3.0], |
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153 | thickness=20, |
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154 | thickness1_pd=0.3, |
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155 | thickness2_pd=0.3, |
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156 | thickness1_pd_n=10, |
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157 | thickness2_pd_n=10, |
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158 | ) |
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