1 | r""" |
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2 | An alternative version of $P(q)$ for the core-shell ellipsoid |
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3 | (see CoreShellEllipsoidModel), having as parameters the core axial ratio X |
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4 | and a shell thickness, which are more often what we would like to determine. |
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5 | |
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6 | This model is also better behaved when polydispersity is applied than the four |
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7 | independent radii in CoreShellEllipsoidModel. |
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8 | |
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9 | Definition |
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10 | ---------- |
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11 | |
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12 | .. figure:: img/core_shell_ellipsoid_fig1.gif |
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13 | |
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14 | |
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15 | The geometric parameters of this model are |
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16 | |
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17 | *equat_core =* equatorial core radius *= R_minor_core* |
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18 | |
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19 | *X_core = polar_core / equat_core = Rmajor_core / Rminor_core* |
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20 | |
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21 | *T_shell = equat_outer - equat_core = Rminor_outer - Rminor_core* |
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22 | |
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23 | *XpolarShell = Tpolar_shell / T_shell = (Rmajor_outer - Rmajor_core)/ |
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24 | (Rminor_outer - Rminor_core)* |
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25 | |
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26 | In terms of the original radii |
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27 | |
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28 | *polar_core = equat_core * X_core* |
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29 | |
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30 | *equat_shell = equat_core + T_shell* |
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31 | |
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32 | *polar_shell = equat_core * X_core + T_shell * XpolarShell* |
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33 | |
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34 | (where we note that "shell" perhaps confusingly, relates to the outer radius) |
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35 | When *X_core < 1* the core is oblate; when *X_core > 1* it is prolate. |
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36 | *X_core = 1* is a spherical core. |
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37 | |
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38 | For a fixed shell thickness *XpolarShell = 1*, to scale the shell thickness |
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39 | pro-rata with the radius *XpolarShell = X_core*. |
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40 | |
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41 | When including an $S(q)$, the radius in $S(q)$ is calculated to be that of |
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42 | a sphere with the same 2nd virial coefficient of the outer surface of the |
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43 | ellipsoid. This may have some undesirable effects if the aspect ratio of the |
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44 | ellipsoid is large (ie, if $X << 1$ or $X >> 1$ ), when the $S(q)$ |
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45 | - which assumes spheres - will not in any case be valid. |
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46 | |
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47 | If SAS data are in absolute units, and the SLDs are correct, then scale should |
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48 | be the total volume fraction of the "outer particle". When $S(q)$ is introduced |
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49 | this moves to the $S(q)$ volume fraction, and scale should then be 1.0, |
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50 | or contain some other units conversion factor (for example, if you have SAXS data). |
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51 | |
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52 | References |
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53 | ---------- |
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54 | |
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55 | R K Heenan, *Private communication* |
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56 | |
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57 | """ |
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58 | |
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59 | from numpy import inf, sin, cos, pi |
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60 | |
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61 | name = "core_shell_ellipsoid_xt" |
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62 | title = "Form factor for an spheroid ellipsoid particle with a core shell structure." |
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63 | description = """ |
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64 | [core_shell_ellipsoid_xt] Calculates the form factor for an spheroid |
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65 | ellipsoid particle with a core_shell structure. |
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66 | The form factor is averaged over all possible |
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67 | orientations of the ellipsoid such that P(q) |
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68 | = scale*<f^2>/Vol + bkg, where f is the |
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69 | single particle scattering amplitude. |
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70 | [Parameters]: |
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71 | equat_core = equatorial radius of core, |
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72 | x_core = polar radius of core, |
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73 | t_shell = equatorial radius of outer surface, |
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74 | x_polar_shell = polar radius (revolution axis) of outer surface |
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75 | core_sld = SLD_core |
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76 | shell_sld = SLD_shell |
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77 | solvent_sld = SLD_solvent |
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78 | background = Incoherent bkg |
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79 | scale =scale |
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80 | Note:It is the users' responsibility to ensure |
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81 | that shell radii are larger than core radii. |
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82 | oblate: polar radius < equatorial radius |
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83 | prolate : polar radius > equatorial radius - this new model will make this easier |
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84 | and polydispersity integrals more logical (as previously the shell could disappear). |
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85 | """ |
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86 | category = "shape:ellipsoid" |
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87 | |
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88 | # pylint: disable=bad-whitespace, line-too-long |
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89 | # ["name", "units", default, [lower, upper], "type", "description"], |
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90 | parameters = [ |
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91 | ["equat_core", "Ang", 20, [0, inf], "volume", "Equatorial radius of core"], |
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92 | ["x_core", "None", 3, [0, inf], "volume", "Polar radius of core"], |
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93 | ["t_shell", "Ang", 30, [0, inf], "volume", "Equatorial radius of shell"], |
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94 | ["x_polar_shell", "", 1, [0, inf], "volume", "Polar radius of shell"], |
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95 | ["core_sld", "1e-6/Ang^2", 2, [-inf, inf], "", "Core scattering length density"], |
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96 | ["shell_sld", "1e-6/Ang^2", 1, [-inf, inf], "", "Shell scattering length density"], |
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97 | ["solvent_sld", "1e-6/Ang^2", 6.3, [-inf, inf], "", "Solvent scattering length density"], |
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98 | ["theta", "degrees", 0, [-inf, inf], "orientation", "Oblate orientation wrt incoming beam"], |
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99 | ["phi", "degrees", 0, [-inf, inf], "orientation", "Oblate orientation in the plane of the detector"], |
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100 | ] |
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101 | # pylint: enable=bad-whitespace, line-too-long |
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102 | |
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103 | source = ["lib/gfn.c", "lib/gauss76.c", "core_shell_ellipsoid_xt.c"] |
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104 | |
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105 | demo = dict(scale=0.05, background=0.001, |
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106 | equat_core=20.0, |
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107 | x_core=3.0, |
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108 | t_shell=30.0, |
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109 | x_polar_shell=1.0, |
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110 | core_sld=2.0, |
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111 | shell_sld=1.0, |
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112 | solvent_sld=6.3, |
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113 | theta=0, |
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114 | phi=0) |
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115 | |
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116 | oldname = 'CoreShellEllipsoidXTModel' |
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117 | |
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118 | oldpars = dict(x_polar_shell='XpolarShell', |
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119 | x_core='X_core', |
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120 | t_shell='T_shell', |
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121 | core_sld='sld_core', |
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122 | shell_sld='sld_shell', |
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123 | solvent_sld='sld_solvent', |
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124 | theta='axis_theta', |
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125 | phi='axis_phi') |
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126 | |
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127 | q = 0.1 |
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128 | phi = pi/6 |
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129 | qx = q*cos(phi) |
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130 | qy = q*sin(phi) |
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131 | |
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132 | tests = [ |
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133 | # Accuracy tests based on content in test/utest_coreshellellipsoidXTmodel.py |
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134 | [{'equat_core': 200.0, |
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135 | 'x_core': 0.1, |
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136 | 't_shell': 50.0, |
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137 | 'x_polar_shell': 0.2, |
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138 | 'core_sld': 2.0, |
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139 | 'shell_sld': 1.0, |
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140 | 'solvent_sld': 6.3, |
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141 | 'background': 0.001, |
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142 | 'scale': 1.0, |
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143 | }, 1.0, 0.00189402], |
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144 | |
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145 | # Additional tests with larger range of parameters |
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146 | [{'background': 0.01}, 0.1, 11.6915], |
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147 | |
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148 | [{'equat_core': 20.0, |
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149 | 'x_core': 200.0, |
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150 | 't_shell': 54.0, |
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151 | 'x_polar_shell': 3.0, |
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152 | 'core_sld': 20.0, |
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153 | 'shell_sld': 10.0, |
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154 | 'solvent_sld': 6.0, |
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155 | 'background': 0.0, |
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156 | 'scale': 1.0, |
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157 | }, 0.01, 8688.53], |
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158 | |
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159 | [{'background': 0.001}, (0.4, 0.5), 0.00690673], |
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160 | |
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161 | [{'equat_core': 20.0, |
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162 | 'x_core': 200.0, |
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163 | 't_shell': 54.0, |
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164 | 'x_polar_shell': 3.0, |
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165 | 'core_sld': 20.0, |
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166 | 'shell_sld': 10.0, |
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167 | 'solvent_sld': 6.0, |
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168 | 'background': 0.01, |
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169 | 'scale': 0.01, |
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170 | }, (qx, qy), 0.0100002], |
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171 | ] |
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