1 | #pragma rtGlobals=1 // Use modern global access method. |
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2 | #pragma IgorVersion=6.1 |
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3 | |
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4 | //////////////////////////////////////////////////// |
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5 | // |
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6 | // calculates the scattering from a rectangular solid |
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7 | // i.e. a parallelepiped with sides a < b < c |
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8 | // |
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9 | // - the user must make sure that the constraints are not violated |
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10 | // otherwise the calculation will not be correct |
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11 | // |
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12 | // From: Mittelbach and Porod, Acta Phys. Austriaca 14 (1961) 185-211. |
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13 | // equations (1), (13), and (14) (in German!) |
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14 | // |
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15 | // note that the equations listed in Feigin and Svergun appears |
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16 | // to be wrong - they use equation (12), which does not appear to |
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17 | // be a complete orientational average (?) |
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18 | // |
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19 | // a double integral is used, both using Gaussian quadrature |
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20 | // routines that are now included with GaussUtils |
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21 | // 20-pt quadrature appears to be enough, 76 pt is available |
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22 | // by changing the function calls |
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23 | // Core Shell version DS 1stJan/7thJan 2008: accounts for contribution from rims on sides A and B of diff SLDs |
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24 | //Shell on longest edge C is not included in this version |
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25 | // |
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26 | //Modified for IgorVersion 6.0 - ACH 1/7/09 |
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27 | //////////////////////////////////////////////////// |
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28 | |
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29 | //this macro sets up all the necessary parameters and waves that are |
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30 | //needed to calculate the model function. |
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31 | // |
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32 | Proc PlotCSParallelepiped(num,qmin,qmax) |
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33 | Variable num=100, qmin=.001, qmax=.7 |
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34 | Prompt num "Enter number of data points for model: " |
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35 | Prompt qmin "Enter minimum q-value (A^1) for model: " |
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36 | Prompt qmax "Enter maximum q-value (A^1) for model: " |
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37 | // |
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38 | Make/O/D/n=(num) xwave_CSPP, ywave_CSPP |
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39 | xwave_CSPP = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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40 | Make/O/D coef_CSPP = {1,35,75,400,10,10,10,2e-6,4e-6,2e-6,1e-6,6e-6,0.06} //CH#2 |
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41 | make/o/t parameters_CSPP = {"Scale Factor","Shortest Edge A (A)","B (A)","Longest Edge C (A)","Rim A ()", "Rim B ()","Rim C ()", "SLD A(A^-2)", "SLD B(A^-2)", "SLD C(A^-2)", "SLD P(A^-2)", "SLD Solv(A^-2)", "Incoherent Bgd (cm-1)"} //CH#3 |
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42 | Edit parameters_CSPP, coef_CSPP |
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43 | |
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44 | Variable/G root:g_CSPP |
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45 | g_CSPP := CSParallelepiped(coef_CSPP,ywave_CSPP, xwave_CSPP) |
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46 | Display ywave_CSPP vs xwave_CSPP |
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47 | ModifyGraph marker=29, msize=2, mode=4 |
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48 | ModifyGraph log=1 |
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49 | Label bottom "q (A\\S-1\\M) " |
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50 | Label left "I(q) (cm\\S-1\\M)" |
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51 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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52 | |
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53 | AddModelToStrings("CSParallelepiped","coef_CSPP","parameters_CSPP","CSPP") |
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54 | // |
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55 | End |
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56 | |
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57 | // |
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58 | //this macro sets up all the necessary parameters and waves that are |
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59 | //needed to calculate the smeared model function. |
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60 | // |
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61 | //no input parameters are necessary, it MUST use the experimental q-values |
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62 | // from the experimental data read in from an AVE/QSIG data file |
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63 | //////////////////////////////////////////////////// |
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64 | Proc PlotSmearedCSParallelepiped(str) |
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65 | String str |
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66 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
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67 | |
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68 | // if no gQvals wave, data must not have been loaded => abort |
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69 | if(ResolutionWavesMissingDF(str)) |
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70 | Abort |
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71 | endif |
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72 | |
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73 | SetDataFolder $("root:"+str) |
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74 | |
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75 | // Setup parameter table for model function |
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76 | Make/O/D smear_coef_CSPP = {1,35,75,400,10,10,10,2e-6,4e-6,2e-6,1e-6,6e-6,0.06} //CH#4 |
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77 | make/o/t smear_parameters_CSPP = {"Scale Factor","Shortest Edge A (A)","B (A)","Longest Edge C (A)","Rim A ()", "Rim B ()","Rim C ()", "SLD A(A^-2)", "SLD B(A^-2)", "SLD C(A^-2)", "SLD P(A^-2)", "SLD Solv(A^-2)", "Incoherent Bgd (cm-1)"} |
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78 | Edit smear_parameters_CSPP,smear_coef_CSPP //display parameters in a table |
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79 | |
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80 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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81 | // make extra copy of experimental q-values for easy plotting |
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82 | Duplicate/O $(str+"_q") smeared_CSPP,smeared_qvals // |
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83 | SetScale d,0,0,"1/cm",smeared_CSPP // |
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84 | |
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85 | Variable/G gs_CSPP=0 |
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86 | gs_CSPP := fSmearedCSParallelepiped(smear_coef_CSPP,smeared_CSPP,smeared_qvals) //this wrapper fills the STRUCT |
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87 | |
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88 | Display smeared_CSPP vs smeared_qvals // |
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89 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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90 | Label bottom "q (A\\S-1\\M)" |
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91 | Label left "I(q) (cm\\S-1\\M)" |
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92 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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93 | |
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94 | SetDataFolder root: |
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95 | AddModelToStrings("SmearedCSParallelepiped","smear_coef_CSPP","smear_parameters_CSPP","CSPP") |
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96 | End |
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97 | |
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98 | Function CSParallelepiped(cw,yw,xw) : FitFunc |
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99 | Wave cw,yw,xw |
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100 | |
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101 | #if exists("CSParallelepipedX") |
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102 | yw = CSParallelepipedX(cw,xw) |
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103 | #else |
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104 | yw = fCSParallelepiped(cw,xw) |
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105 | #endif |
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106 | return(0) |
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107 | End |
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108 | |
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109 | |
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110 | // calculates the form factor of a rectangular solid |
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111 | // - a double integral - choose points wisely |
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112 | // |
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113 | Function fCSParallelepiped(w,x) : FitFunc |
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114 | Wave w |
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115 | Variable x |
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116 | // Input (fitting) variables are: |
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117 | //[0] scale factor |
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118 | //[1] Edge A (A) |
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119 | //[2] Edge B (A) |
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120 | //[3] Edge C (A) |
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121 | //[4] Rim A (A) |
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122 | //[5] Rim B (A) |
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123 | //[6] Rim C(A) |
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124 | //[7] Rim A SLD(A^-2) |
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125 | //[8] Rim B SLD (A^-2) |
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126 | //[9] Rim C SLD (A^-2) not included at the moment |
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127 | //[10] PPcore SLD (A^-2) |
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128 | //[11] Solvent SLD (A^-2) |
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129 | //[12] incoherent background (cm^-1) |
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130 | // give them nice names |
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131 | Variable scale,aa,bb,cc,ta,tb,tc,rhoA,rhoB,rhoC,rhoP,rhosolv,bkg,inten,qq,ii,arg,mu |
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132 | scale = w[0] |
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133 | aa = w[1] |
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134 | bb = w[2] |
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135 | cc = w[3] |
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136 | ta = w[4] |
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137 | tb = w[5] |
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138 | tc = w[6] // is 0 at the moment |
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139 | rhoA=w[7] //rim A SLD |
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140 | rhoB=w[8] //rim B SLD |
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141 | rhoC=w[9] //rim C SLD |
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142 | rhoP = w[10] //Parallelpiped core SLD |
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143 | rhosolv=w[11] // Solvent SLD |
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144 | bkg = w[12] |
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145 | |
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146 | // mu = bb*x //scale in terms of B |
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147 | // aa = aa/bb |
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148 | // cc =cc/bb |
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149 | // ta= (aa+2*ta)/(b+2*tb) |
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150 | // tc= (cc+2*tc)/(b+2*tb) |
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151 | |
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152 | inten = IntegrateFn20(CSPP_Outer,0,1,w,x) |
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153 | // inten = IntegrateFn76(PP_Outer,0,1,w,x) |
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154 | |
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155 | inten /= (aa*bb*cc+2*ta*bb*cc+2*aa*tb*cc+2*aa*bb*tc) //divide by outer volume (=Volume of core+edges) |
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156 | // inten /= (aa*bb*cc) // divide by volume here since FF integral has Vol^2 inside |
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157 | inten *= 1e8 //convert to cm^-1 |
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158 | // inten *= contr*contr |
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159 | inten *= scale |
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160 | inten += bkg |
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161 | |
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162 | Return (inten) |
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163 | End |
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164 | |
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165 | // outer integral |
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166 | |
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167 | // x is the q-value - remember that "mu" in the notation = B*Q |
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168 | Function CSPP_Outer(w,x,dum) |
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169 | Wave w |
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170 | Variable x,dum |
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171 | |
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172 | Variable retVal,mu,mu1,aa,bb,cc,mudum, mudum1, arg |
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173 | aa = w[1] |
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174 | bb = w[2] |
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175 | cc = w[3] |
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176 | // ta = w[4] |
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177 | // tb = w[5] |
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178 | // tc = w[6] |
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179 | |
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180 | mu= bb*x |
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181 | // mu1=(bb+2*tb)*x //mu1 needed for including edge C contribution also: none at the moment |
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182 | mudum = mu*sqrt(1-dum^2) |
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183 | // mudum1 = mu1*sqrt(1-dum^2) |
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184 | retval = IntegrateFn20(CSPP_inner,0,1,w,mudum) |
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185 | // retval = IntegrateFn76(CSPP_inner,0,1,w,mudum) |
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186 | |
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187 | cc = cc/bb |
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188 | arg = mu*cc*dum/2 |
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189 | if(arg==0) |
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190 | retval *= 1 |
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191 | else |
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192 | retval *= (sin(arg)/arg)*(sin(arg)/arg) |
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193 | endif |
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194 | |
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195 | return(retVal) |
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196 | End |
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197 | |
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198 | |
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199 | //returns the integrand of the inner integral |
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200 | Function CSPP_Inner(w,mu,uu) |
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201 | Wave w |
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202 | Variable mu, uu //mu1 needed for including edge C contribution also |
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203 | Variable aa,bb,cc, ta,tb,tc, Vin,Vot,V1,V2,V3,rhoA,rhoB,rhoC, rhoP, rhosolv,dr0, drA,drB, drC,retVal,arg0,arg1,arg2,arg3,arg4,arg5,t0,t1,t2, t3, t4,t5 |
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204 | //local variables |
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205 | //NVAR mu = root:gEvalQval //already has been converted to S=2*pi*q |
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206 | aa = w[1] |
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207 | bb = w[2] |
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208 | cc = w[3] |
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209 | ta = w[4] |
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210 | tb = w[5] |
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211 | tc = w[6] |
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212 | rhoA=w[7] |
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213 | rhoB=w[8] |
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214 | rhoC=w[9] |
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215 | rhoP=w[10] |
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216 | rhosolv=w[11] |
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217 | dr0=rhoP-rhosolv |
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218 | drA=rhoA-rhosolv |
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219 | drB=rhoB-rhosolv |
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220 | drC=rhoC-rhosolv |
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221 | Vin=(aa*bb*cc) |
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222 | Vot=(aa*bb*cc+2*ta*bb*cc+2*aa*tb*cc+2*aa*bb*tc) |
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223 | V1=(2*ta*bb*cc) // incorrect V1 (aa*bb*cc+2*ta*bb*cc) |
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224 | V2=(2*aa*tb*cc) // incorrect V2(aa*bb*cc+2*aa*tb*cc) |
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225 | // V3=(aa*bb*cc+2*aa*bb*tc) |
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226 | aa = aa/bb |
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227 | // bb = bb/bb |
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228 | ta=(aa+2*ta)/bb |
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229 | tb=(aa+2*tb)/bb |
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230 | |
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231 | //Mu*(1-x^2)^(0.5) |
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232 | //handle arg=0 separately, as sin(t)/t -> 1 as t->0 |
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233 | |
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234 | // arg0 = mu*cc*dum/2 |
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235 | arg1 = (mu*aa/2)*sin(Pi*uu/2) |
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236 | arg2 = (mu/2)*cos(Pi*uu/2) |
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237 | arg3= (mu*ta/2)*sin(Pi*uu/2) |
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238 | arg4= (mu*tb/2)*cos(Pi*uu/2) |
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239 | |
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240 | |
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241 | // if(arg0 ==0) |
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242 | // t0=1 |
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243 | // else |
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244 | // t0=sin(arg0)/arg0 |
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245 | // endif |
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246 | if(arg1==0) |
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247 | t1 = 1 |
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248 | else |
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249 | t1 = (sin(arg1)/arg1) //defn for CSPP model sin(arg1)/arg1 test: (sin(arg1)/arg1)*(sin(arg1)/arg1) |
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250 | endif |
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251 | if(arg2==0) |
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252 | t2 = 1 |
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253 | else |
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254 | t2 = (sin(arg2)/arg2) //defn for CSPP model sin(arg2)/arg2 test: (sin(arg2)/arg2)*(sin(arg2)/arg2) |
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255 | endif |
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256 | if(arg3==0) |
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257 | t3 = 1 |
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258 | else |
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259 | t3 = sin(arg3)/arg3 |
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260 | endif |
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261 | if(arg4==0) |
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262 | t4 = 1 |
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263 | else |
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264 | t4 = sin(arg4)/arg4 |
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265 | endif |
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266 | |
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267 | // retval =( (dr0*dr0)*(t1*t1)*(t2*t2)*Vin + (drA*drA)*(t3-t1)*(t3-t1)*(t2*t2)*V1+ (drB*drB)*(t1*t1)*(t4-t2)*(t4-t2)*V2 ) // doesnot include contribution from edge C Incorrect FF |
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268 | retval =( dr0*t1*t2*Vin + drA*(t3-t1)*t2*V1+ drB*t1*(t4-t2)*V2 )*( dr0*t1*t2*Vin + drA*(t3-t1)*t2*V1+ drB*t1*(t4-t2)*V2 ) // correct FF : square of sum of phase factors |
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269 | // retval =t1*t2* dr0*dr0*Vin*Vin //*( dr0*t1*t2*Vin ) //test case of original PP with no rims |
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270 | return(retVal) |
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271 | End |
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272 | |
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273 | |
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274 | // this is all there is to the smeared calculation! |
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275 | Function fSmearedCSParallelepiped(coefW,yW,xW) |
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276 | Wave coefW,yW,xW |
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277 | |
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278 | String str = getWavesDataFolder(yW,0) |
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279 | String DF="root:"+str+":" |
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280 | |
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281 | WAVE resW = $(DF+str+"_res") |
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282 | |
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283 | STRUCT ResSmearAAOStruct fs |
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284 | WAVE fs.coefW = coefW |
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285 | WAVE fs.yW = yW |
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286 | WAVE fs.xW = xW |
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287 | WAVE fs.resW = resW |
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288 | |
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289 | Variable err |
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290 | err = SmearedCSParallelepiped(fs) |
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291 | |
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292 | return (0) |
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293 | End |
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294 | |
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295 | // this is all there is to the smeared calculation! |
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296 | Function SmearedCSParallelepiped(s) :FitFunc |
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297 | Struct ResSmearAAOStruct &s |
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298 | |
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299 | // the name of your unsmeared model (AAO) is the first argument |
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300 | Smear_Model_20(CSParallelepiped,s.coefW,s.xW,s.yW,s.resW) |
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301 | |
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302 | return(0) |
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303 | End |
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