1 | #pragma rtGlobals=1 // Use modern global access method. |
---|
2 | |
---|
3 | //////////////////////////////////////////////// |
---|
4 | // GaussUtils.proc and PlotUtils.proc MUST be included for the smearing calculation to compile |
---|
5 | // Adopting these into the experiment will insure that they are always present |
---|
6 | //////////////////////////////////////////////// |
---|
7 | // this function is for the form factor of a right circular cylinder with core/shell scattering length density profile |
---|
8 | // |
---|
9 | // the core dimensions are given and a constant shell thickness is added to the radius and to dach and of the length |
---|
10 | // this way, the scattering amplitude is simply the difference between two cylinders of different dimensions |
---|
11 | // |
---|
12 | // 06 NOV 98 SRK |
---|
13 | //////////////////////////////////////////////// |
---|
14 | |
---|
15 | Proc PlotCoreShellCylinderForm(num,qmin,qmax) |
---|
16 | Variable num=128,qmin=0.001,qmax=0.7 |
---|
17 | Prompt num "Enter number of data points for model: " |
---|
18 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
---|
19 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
---|
20 | |
---|
21 | make/o/d/n=(num) xwave_cscyl,ywave_cscyl |
---|
22 | xwave_cscyl = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
---|
23 | make/o/d coef_cscyl = {1.,20.,10.,400,1.0e-6,4.0e-6,1.0e-6,0.01} |
---|
24 | make/o/t parameters_cscyl = {"scale","core radius (A)","shell THICKNESS (A)","CORE length (A)","SLD core (A^-2)","SLD shell (A^-2)","SLD solvent (A^-2)","incoh. bkg (cm^-1)"} |
---|
25 | Edit parameters_cscyl,coef_cscyl |
---|
26 | ywave_cscyl := CoreShellCylinderForm(coef_cscyl,xwave_cscyl) |
---|
27 | Display ywave_cscyl vs xwave_cscyl |
---|
28 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
29 | Label bottom "q (\\S-1\\M)" |
---|
30 | Label left "Intensity (cm\\S-1\\M)" |
---|
31 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
32 | End |
---|
33 | /////////////////////////////////////////////////////////// |
---|
34 | |
---|
35 | Proc PlotSmearedCSCylinderForm() |
---|
36 | //no input parameters necessary, it MUST use the experimental q-values |
---|
37 | // from the experimental data read in from an AVE/QSIG data file |
---|
38 | |
---|
39 | // if no gQvals wave, data must not have been loaded => abort |
---|
40 | if(ResolutionWavesMissing()) |
---|
41 | Abort |
---|
42 | endif |
---|
43 | |
---|
44 | // Setup parameter table for model function |
---|
45 | make/o/d smear_coef_cscyl = {1.,20.,10.,400,1.0e-6,4.0e-6,1.0e-6,0.01} |
---|
46 | make/o/t smear_parameters_cscyl = {"scale","core radius (A)","shell radius (A)","length (A)","SLD core (A^-2)","SLD shell (A^-2)","SLD solvent (A^-2)","incoh. bkg (cm^-1)"} |
---|
47 | Edit smear_parameters_cscyl,smear_coef_cscyl |
---|
48 | |
---|
49 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
---|
50 | // make extra copy of experimental q-values for easy plotting |
---|
51 | Duplicate/O $gQvals smeared_cscyl,smeared_qvals |
---|
52 | SetScale d,0,0,"1/cm",smeared_cscyl |
---|
53 | |
---|
54 | smeared_cscyl := SmearedCoreShellCylinderForm(smear_coef_cscyl,$gQvals) |
---|
55 | Display smeared_cscyl vs smeared_qvals |
---|
56 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
57 | Label bottom "q (\\S-1\\M)" |
---|
58 | Label left "Intensity (cm\\S-1\\M)" |
---|
59 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
60 | End |
---|
61 | |
---|
62 | /////////////////////////////////////////////////////////////// |
---|
63 | // unsmeared model calculation |
---|
64 | /////////////////////////// |
---|
65 | Function CoreShellCylinderForm(w,x) : FitFunc |
---|
66 | Wave w |
---|
67 | Variable x |
---|
68 | |
---|
69 | //The input variables are (and output) |
---|
70 | //[0] scale |
---|
71 | //[1] cylinder CORE RADIUS (A) |
---|
72 | //[2] shell Thickness (A) |
---|
73 | //[3] cylinder CORE LENGTH (A) |
---|
74 | //[4] core SLD (A^-2) |
---|
75 | //[5] shell SLD (A^-2) |
---|
76 | //[6] solvent SLD (A^-2) |
---|
77 | //[7] background (cm^-1) |
---|
78 | Variable scale,length,delrho,bkg,rcore,thick,rhoc,rhos,rhosolv |
---|
79 | scale = w[0] |
---|
80 | rcore = w[1] |
---|
81 | thick = w[2] |
---|
82 | length = w[3] |
---|
83 | rhoc = w[4] |
---|
84 | rhos = w[5] |
---|
85 | rhosolv = w[6] |
---|
86 | bkg = w[7] |
---|
87 | // |
---|
88 | // the OUTPUT form factor is <f^2>/Vcyl [cm-1] |
---|
89 | // |
---|
90 | |
---|
91 | // local variables |
---|
92 | Variable nord,ii,va,vb,contr,vcyl,nden,summ,yyy,zi,qq,halfheight |
---|
93 | Variable answer |
---|
94 | String weightStr,zStr |
---|
95 | |
---|
96 | weightStr = "gauss76wt" |
---|
97 | zStr = "gauss76z" |
---|
98 | |
---|
99 | |
---|
100 | // if wt,z waves don't exist, create them |
---|
101 | // 20 Gauss points is not enough for cylinder calculation |
---|
102 | |
---|
103 | if (WaveExists($weightStr) == 0) // wave reference is not valid, |
---|
104 | Make/D/N=76 $weightStr,$zStr |
---|
105 | Wave w76 = $weightStr |
---|
106 | Wave z76 = $zStr // wave references to pass |
---|
107 | Make76GaussPoints(w76,z76) |
---|
108 | // printf "w[0],z[0] = %g %g\r", w76[0],z76[0] |
---|
109 | else |
---|
110 | if(exists(weightStr) > 1) |
---|
111 | Abort "wave name is already in use" // execute if condition is false |
---|
112 | endif |
---|
113 | Wave w76 = $weightStr |
---|
114 | Wave z76 = $zStr // Not sure why this has to be "declared" twice |
---|
115 | // printf "w[0],z[0] = %g %g\r", w76[0],z76[0] |
---|
116 | endif |
---|
117 | |
---|
118 | |
---|
119 | // set up the integration |
---|
120 | // end points and weights |
---|
121 | nord = 76 |
---|
122 | va = 0 |
---|
123 | vb = Pi/2 |
---|
124 | halfheight = length/2.0 |
---|
125 | |
---|
126 | // evaluate at Gauss points |
---|
127 | // remember to index from 0,size-1 |
---|
128 | |
---|
129 | qq = x //current x point is the q-value for evaluation |
---|
130 | summ = 0.0 // initialize integral |
---|
131 | ii=0 |
---|
132 | do |
---|
133 | // Using 76 Gauss points |
---|
134 | zi = ( z76[ii]*(vb-va) + vb + va )/2.0 |
---|
135 | yyy = w76[ii] * CoreShellcyl(qq, rcore, thick, rhoc,rhos,rhosolv, halfheight, zi) |
---|
136 | summ += yyy |
---|
137 | |
---|
138 | ii+=1 |
---|
139 | while (ii<nord) // end of loop over quadrature points |
---|
140 | // |
---|
141 | // calculate value of integral to return |
---|
142 | |
---|
143 | answer = (vb-va)/2.0*summ |
---|
144 | |
---|
145 | // contrast is now explicitly included in the core-shell calculation |
---|
146 | |
---|
147 | //normalize by cylinder volume |
---|
148 | //NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl |
---|
149 | //calculate TOTAL volume |
---|
150 | // length is the total core length |
---|
151 | vcyl=Pi*(rcore+thick)*(rcore+thick)*(length+2*thick) |
---|
152 | answer /= vcyl |
---|
153 | //convert to [cm-1] |
---|
154 | answer *= 1.0e8 |
---|
155 | //Scale |
---|
156 | answer *= scale |
---|
157 | // add in the background |
---|
158 | answer += bkg |
---|
159 | |
---|
160 | Return (answer) |
---|
161 | |
---|
162 | End //End of function CoreShellCylinderForm() |
---|
163 | |
---|
164 | /////////////////////////////////////////////////////////////// |
---|
165 | // F(qq, rcore, thick, rhoc,rhos,rhosolv, length, zi) |
---|
166 | // |
---|
167 | Function CoreShellcyl(qq, rcore, thick, rhoc,rhos,rhosolv, length, dum) |
---|
168 | Variable qq, rcore, thick, rhoc,rhos,rhosolv, length, dum |
---|
169 | |
---|
170 | // qq is the q-value for the calculation (1/A) |
---|
171 | // rcore is the core radius of the cylinder (A) |
---|
172 | //thick is the uniform thickness |
---|
173 | // rho(n) are the respective SLD's |
---|
174 | |
---|
175 | // length is the *Half* CORE-LENGTH of the cylinder = L (A) |
---|
176 | |
---|
177 | // dum is the dummy variable for the integration (x in Feigin's notation) |
---|
178 | |
---|
179 | //Local variables |
---|
180 | Variable dr1,dr2,besarg1,besarg2,vol1,vol2,sinarg1,sinarg2,t1,t2,retval |
---|
181 | |
---|
182 | dr1 = rhoc-rhos |
---|
183 | dr2 = rhos-rhosolv |
---|
184 | vol1 = Pi*rcore*rcore*(2*length) |
---|
185 | vol2 = Pi*(rcore+thick)*(rcore+thick)*(2*length+2*thick) |
---|
186 | |
---|
187 | besarg1 = qq*rcore*sin(dum) |
---|
188 | besarg2 = qq*(rcore+thick)*sin(dum) |
---|
189 | sinarg1 = qq*length*cos(dum) |
---|
190 | sinarg2 = qq*(length+thick)*cos(dum) |
---|
191 | |
---|
192 | t1 = 2*vol1*dr1*sin(sinarg1)/sinarg1*bessJ(1,besarg1)/besarg1 |
---|
193 | t2 = 2*vol2*dr2*sin(sinarg2)/sinarg2*bessJ(1,besarg2)/besarg2 |
---|
194 | |
---|
195 | retval = ((t1+t2)^2)*sin(dum) |
---|
196 | |
---|
197 | return retval |
---|
198 | |
---|
199 | End //Function CoreShellcyl() |
---|
200 | |
---|
201 | // this is all there is to the smeared calculation! |
---|
202 | Function SmearedCoreShellCylinderForm(w,x) :FitFunc |
---|
203 | Wave w |
---|
204 | Variable x |
---|
205 | |
---|
206 | Variable ans |
---|
207 | SVAR sq = gSig_Q |
---|
208 | SVAR qb = gQ_bar |
---|
209 | SVAR sh = gShadow |
---|
210 | SVAR gQ = gQVals |
---|
211 | |
---|
212 | //the name of your unsmeared model is the first argument |
---|
213 | ans = Smear_Model_20(CoreShellCylinderForm,$sq,$qb,$sh,$gQ,w,x) |
---|
214 | |
---|
215 | return(ans) |
---|
216 | End |
---|
217 | |
---|