1 | #pragma rtGlobals=1 // Use modern global access method. |
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2 | #pragma IgorVersion=6.0 |
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3 | |
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4 | // |
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5 | // |
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6 | // BCC paracrystal, powder average |
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7 | // |
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8 | // VERY slow, since the function is so ill-behaved and needs LOTS of quadrature |
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9 | // points. Adaptive methods were even slower and troublesom to converge, |
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10 | // although in theory they should be a better choice than blindly increasing the number of points. |
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11 | // |
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12 | // 150 points seems to give reasonable reproduction of the peak heights in the paper. |
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13 | // peak locations are correct |
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14 | // 76 points of quadrature for the smearing is only a guess, it's not been tested yet. |
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15 | // |
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16 | // Original implementation - Danilo Pozzo |
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17 | // modified and modernized for more efficient integration SRK Nov 2008 |
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18 | // |
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19 | //REFERENCE |
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20 | //Hideki Matsuoka etal. Physical Review B, Vol 36 Num 3, p1754 1987 ORIGINAL PAPER |
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21 | //Hideki Matsuoka etal. Physical Review B, Vol 41 Num 6, p3854 1990 CORRECTIONS TO PAPER |
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22 | // |
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23 | //////////////////////////////////////////////////// |
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24 | |
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25 | |
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26 | |
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27 | Proc PlotBCC_ParaCrystal(num,qmin,qmax) |
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28 | Variable num=100, qmin=0.001, qmax=0.7 |
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29 | Prompt num "Enter number of data points for model: " |
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30 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
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31 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
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32 | // |
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33 | Make/O/D/n=(num) xwave_BCC_ParaCrystal, ywave_BCC_ParaCrystal |
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34 | xwave_BCC_ParaCrystal = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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35 | Make/O/D coef_BCC_ParaCrystal = {1,220,0.06,40,3e-6,0.} |
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36 | make/o/t parameters_BCC_ParaCrystal = {"scale","Nearest Neighbor (A)","g","Sphere Radius (A)","Contrast (A-2)", "Background (cm-1)"} |
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37 | Edit parameters_BCC_ParaCrystal, coef_BCC_ParaCrystal |
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38 | |
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39 | Variable/G root:gNordBCC=150 |
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40 | |
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41 | Variable/G root:g_BCC_ParaCrystal |
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42 | g_BCC_ParaCrystal := BCC_ParaCrystal(coef_BCC_ParaCrystal, ywave_BCC_ParaCrystal, xwave_BCC_ParaCrystal) |
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43 | Display ywave_BCC_ParaCrystal vs xwave_BCC_ParaCrystal |
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44 | ModifyGraph marker=29, msize=2, mode=4 |
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45 | ModifyGraph grid=1,mirror=2 |
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46 | ModifyGraph log=0 |
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47 | Label bottom "q (\\S-1\\M) " |
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48 | Label left "I(q) (cm\\S-1\\M)" |
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49 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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50 | |
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51 | AddModelToStrings("BCC_ParaCrystal","coef_BCC_ParaCrystal","BCC_ParaCrystal") |
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52 | // |
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53 | End |
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54 | |
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55 | // |
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56 | //this macro sets up all the necessary parameters and waves that are |
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57 | //needed to calculate the smeared model function. |
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58 | // |
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59 | //no input parameters are necessary, it MUST use the experimental q-values |
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60 | // from the experimental data read in from an AVE/QSIG data file |
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61 | //////////////////////////////////////////////////// |
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62 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
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63 | Proc PlotSmearedBCC_ParaCrystal(str) |
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64 | String str |
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65 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
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66 | |
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67 | // if any of the resolution waves are missing => abort |
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68 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
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69 | Abort |
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70 | endif |
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71 | |
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72 | SetDataFolder $("root:"+str) |
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73 | |
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74 | // Setup parameter table for model function |
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75 | Make/O/D smear_coef_BCC_ParaCrystal = {1,220,0.06,40,3e-6,0.} |
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76 | make/o/t smear_parameters_BCC_ParaCrystal = {"scale","Nearest Neighbor (A)","g","Sphere Radius (A)","Contrast (A-2)", "Background (cm-1)"} |
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77 | Edit smear_parameters_BCC_ParaCrystal,smear_coef_BCC_ParaCrystal //display parameters in a table |
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78 | |
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79 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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80 | // make extra copy of experimental q-values for easy plotting |
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81 | Duplicate/O $(str+"_q") smeared_BCC_ParaCrystal,smeared_qvals |
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82 | SetScale d,0,0,"1/cm",smeared_BCC_ParaCrystal |
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83 | |
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84 | Variable/G gNordBCC = 150 |
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85 | Variable/G gs_BCC_ParaCrystal=0 |
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86 | gs_BCC_ParaCrystal := fSmearedBCC_ParaCrystal(smear_coef_BCC_ParaCrystal,smeared_BCC_ParaCrystal,smeared_qvals) //this wrapper fills the STRUCT |
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87 | |
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88 | Display smeared_BCC_ParaCrystal vs smeared_qvals |
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89 | ModifyGraph marker=29,msize=2,mode=4 |
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90 | ModifyGraph log=0 |
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91 | Label bottom "q (\\S-1\\M)" |
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92 | Label left "I(q) (cm\\S-1\\M)" |
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93 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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94 | |
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95 | SetDataFolder root: |
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96 | AddModelToStrings("SmearedBCC_ParaCrystal","smear_coef_BCC_ParaCrystal","BCC_ParaCrystal") |
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97 | End |
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98 | |
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99 | |
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100 | // nothing to change here |
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101 | // |
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102 | //AAO version, uses XOP if available |
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103 | // simply calls the original single point calculation with |
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104 | // a wave assignment (this will behave nicely if given point ranges) |
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105 | Function BCC_ParaCrystal(cw,yw,xw) : FitFunc |
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106 | Wave cw,yw,xw |
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107 | |
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108 | #if exists("BCC_ParaCrystalX") |
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109 | yw = BCC_ParaCrystalX(cw,xw) |
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110 | #else |
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111 | yw = fBCC_ParaCrystal(cw,xw) |
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112 | #endif |
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113 | return(0) |
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114 | End |
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115 | |
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116 | |
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117 | // |
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118 | // unsmeared model calculation |
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119 | // |
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120 | Function fBCC_ParaCrystal(w,x) : FitFunc |
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121 | Wave w |
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122 | Variable x |
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123 | |
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124 | // Input (fitting) variables are not used |
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125 | // you would give them nice names |
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126 | Variable integral,loLim,upLim |
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127 | loLim = 0 |
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128 | upLim = 2*Pi |
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129 | |
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130 | Variable/G root:gDumY=0 //root:gDumX=0 |
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131 | |
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132 | |
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133 | Variable scale,Dnn,gg,Rad,contrast,background,yy,latticeScale |
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134 | scale = w[0] |
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135 | Dnn = w[1] //Nearest neighbor distance A |
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136 | gg = w[2] //Paracrystal distortion factor |
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137 | Rad = w[3] //Sphere radius |
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138 | contrast = w[4] //SLD contrast |
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139 | background = w[5] |
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140 | |
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141 | //Volume fraction calculated from lattice symmetry and sphere radius |
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142 | latticeScale = 2*(4/3)*pi*(Rad^3)/((Dnn/((3/4)^0.5))^3) |
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143 | |
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144 | NVAR/Z nord=root:gNordBCC |
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145 | if(NVAR_Exists(nord)!=1) |
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146 | nord=20 |
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147 | endif |
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148 | |
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149 | |
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150 | integral = IntegrateFn_N(Integrand_BCC_Outer,loLim,upLim,w,x,nord) |
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151 | |
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152 | integral *= SphereForm_BCC(Rad,contrast,x)*scale*latticeScale |
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153 | // integral *= scale //testing, returns only Z(q) |
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154 | |
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155 | integral += background |
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156 | |
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157 | Return (integral) |
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158 | |
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159 | End |
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160 | |
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161 | // the outer integral is also an integral |
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162 | Function Integrand_BCC_Outer(w,x,dum) |
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163 | Wave w |
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164 | Variable x,dum |
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165 | |
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166 | NVAR yy = root:gDumY |
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167 | yy = dum // save the current dummy yy for use in the inner loop |
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168 | Variable retVal,loLim,upLim |
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169 | // |
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170 | loLim = 0 |
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171 | upLim = Pi |
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172 | |
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173 | NVAR/Z nord=root:gNordBCC |
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174 | if(NVAR_Exists(nord)!=1) |
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175 | nord=20 |
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176 | endif |
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177 | |
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178 | retVal = IntegrateFn_N(Integrand_BCC_Inner,loLim,upLim,w,x,nord) |
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179 | |
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180 | return(retVal) |
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181 | End |
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182 | |
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183 | //returns the value of the integrand of the inner integral |
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184 | Function Integrand_BCC_Inner(w,qq,dum) |
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185 | Wave w |
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186 | Variable qq,dum |
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187 | |
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188 | NVAR yy = root:gDumY //use the yy value from the outer loop |
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189 | Variable xx,retVal |
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190 | xx = dum |
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191 | |
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192 | retVal = BCC_Integrand(w,qq,xx,yy) |
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193 | |
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194 | return(retVal) |
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195 | End |
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196 | |
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197 | Function BCC_Integrand(w,qq,xx,yy) |
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198 | Wave w |
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199 | Variable qq,xx,yy |
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200 | |
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201 | Variable retVal,temp1,temp2,temp3,temp4,temp5,aa,Da,Dnn,gg |
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202 | Dnn = w[1] //Nearest neighbor distance A |
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203 | gg = w[2] //Paracrystal distortion factor |
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204 | // aa = Dnn*((4/3)^0.5) //Danilo's version (the paper states |bi| = a) |
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205 | aa = Dnn |
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206 | Da = gg*aa |
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207 | |
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208 | temp1 = qq*qq*Da*Da |
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209 | temp3 = qq*aa |
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210 | |
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211 | retVal = BCCeval(xx,yy,temp1,temp3) |
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212 | retVal /=4*Pi |
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213 | |
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214 | return(retVal) |
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215 | end |
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216 | |
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217 | Function BCCeval(Theta,Phi,temp1,temp3) |
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218 | Variable Theta,Phi,temp1,temp3 |
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219 | Variable temp6,temp7,temp8,temp9,temp10 |
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220 | Variable result |
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221 | |
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222 | temp6 = sin(Theta) |
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223 | temp7 = sin(Theta)*cos(Phi)+sin(Theta)*sin(Phi)+cos(Theta) |
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224 | temp8 = -1*sin(Theta)*cos(Phi)-sin(Theta)*sin(Phi)+cos(Theta) |
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225 | temp9 = -1*sin(Theta)*cos(Phi)+sin(Theta)*sin(Phi)-cos(Theta) |
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226 | temp10 = exp((-1/8)*temp1*((temp7^2)+(temp8^2)+(temp9^2))) |
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227 | result = ((1-(temp10^2))^3)*temp6/((1-2*temp10*cos(0.5*temp3*(temp7))+(temp10^2))*(1-2*temp10*cos(0.5*temp3*(temp8))+(temp10^2))*(1-2*temp10*cos(0.5*temp3*(temp9))+(temp10^2))) |
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228 | |
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229 | return (result) |
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230 | end |
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231 | |
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232 | |
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233 | Function SphereForm_BCC(radius,delrho,x) |
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234 | Variable radius,delrho,x |
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235 | |
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236 | // variables are: |
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237 | //[2] radius () |
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238 | //[3] delrho (-2) |
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239 | //[4] background (cm-1) |
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240 | |
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241 | // calculates scale * f^2/Vol where f=Vol*3*delrho*(sin(qr)-qrcos(qr))/qr^3 |
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242 | // and is rescaled to give [=] cm^-1 |
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243 | |
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244 | Variable bes,f,vol,f2 |
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245 | // |
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246 | //handle q==0 separately |
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247 | If(x==0) |
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248 | f = 4/3*pi*radius^3*delrho*delrho*1e8 |
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249 | return(f) |
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250 | Endif |
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251 | |
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252 | bes = 3*(sin(x*radius)-x*radius*cos(x*radius))/x^3/radius^3 |
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253 | vol = 4*pi/3*radius^3 |
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254 | f = vol*bes*delrho // [=] |
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255 | // normalize to single particle volume, convert to 1/cm |
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256 | f2 = f * f / vol * 1.0e8 // [=] 1/cm |
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257 | |
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258 | return (f2) |
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259 | |
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260 | End |
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261 | |
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262 | |
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263 | |
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264 | |
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265 | /////////////////////////////////////////////////////////////// |
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266 | // smeared model calculation |
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267 | // |
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268 | Function SmearedBCC_ParaCrystal(s) : FitFunc |
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269 | Struct ResSmearAAOStruct &s |
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270 | |
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271 | // the name of your unsmeared model (AAO) is the first argument |
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272 | Smear_Model_76(BCC_ParaCrystal,s.coefW,s.xW,s.yW,s.resW) |
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273 | |
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274 | return(0) |
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275 | End |
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276 | |
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277 | |
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278 | ///////////////////////////////////////////////////////////////// |
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279 | //wrapper to calculate the smeared model as an AAO-Struct |
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280 | // fills the struct and calls the ususal function with the STRUCT parameter |
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281 | // |
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282 | // used only for the dependency, not for fitting |
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283 | // |
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284 | Function fSmearedBCC_ParaCrystal(coefW,yW,xW) |
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285 | Wave coefW,yW,xW |
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286 | |
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287 | String str = getWavesDataFolder(yW,0) |
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288 | String DF="root:"+str+":" |
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289 | |
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290 | WAVE resW = $(DF+str+"_res") |
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291 | |
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292 | STRUCT ResSmearAAOStruct fs |
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293 | WAVE fs.coefW = coefW |
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294 | WAVE fs.yW = yW |
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295 | WAVE fs.xW = xW |
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296 | WAVE fs.resW = resW |
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297 | |
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298 | Variable err |
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299 | err = SmearedBCC_ParaCrystal(fs) |
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300 | |
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301 | return (0) |
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302 | End |
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