This is the third and the final post on my series on writing a Powder XRD pattern (diffractogram) simulator from scratch using C.
Till now, we have seen how to calculate the atomic form factor and hence the structure factor.
This was needed for the calculation of the intensity of peaks in an X-ray diffraction pattern (diffractogram).
But that’s not the only thing the intensity depends on. There is also something called the Lorentz-Polarization factor that depends on the value of theta.
Overall, intensity depends upon:
1. Multiplicity
2. Structure Factor
3. Lorentz-Polarization factor
4. Temperature
5. X-Ray Absorption
Out of these we can’t really account for the last two factors in this simple program. This is standard practice in most of the softwares / tools.
So we’ll use the following formula for calculating intensity for given atomic species, atomic positions, hkl values, and theta value.
where M is the multiplicity, 
The next thing we need to completely predict the XRD pattern is the peak positions, i.e. theta (
1. running a loop on the possible hkl values.
2. Then using the lattice information to calculate the interplanar spacing, d(hkl).
3. Then use 
4. Use theta and hkl values to calculate the real and imaginary part of structure factor as explained in the last post.
5. If structure factor is very small, i.e. around 0.01 then the intensity is going to be negligible, i.e. it won’t show up as a peak. So you can reject such small structure factor values by rejecting the corresponding theta values. This would give you the peaks obtained in an XRD pattern.
Now due to a lot of equivalent reflections there would be several repetitions of theta (but not hkl). So you can use these repetitions to calculate the multiplicity as well as remove the repetitions for the output file. This can be done by finding the unique theta values and counting their occurrences.
Finally, to calculate the intensity, just square the structure factor magnitude and then multiply it by the Lorentz-Polarization factor and multiplicity, as already shown above.
Finally just store the output, i.e. the information of reflections, such as miller indices (hkl), theta/2theta, inter-planar spacing d, multiplicity, structure factor and intensity. Now although only information about unique reflections is needed to plot the pattern, but most softwares/tools such as VESTA, also provide information of the equivalent reflections. So the following program also generates two output files. One contains the information about all the reflections (including repetition). Then this data is processed, to find the information about repetitions and another file is generated that contains the data to be plotted.
Now, all the information above as well as in the last two posts should be sufficient to write your own code, but I am posting my own code too for reference and comparison.
One last thing you need to know about the following code is the input file structure.
The input file structure is really absurd and might annoy you. You’re welcome to improve that part of the code.
I am definitely gonna improve it soon.
But for now, let me explain the current expected structure.
The file should end in the .txt extension. That is absolutely necessary.
The first line should contain the number of atoms.
Then the second line contains the code corresponding to the lattice type. The codes are as follows:
1 for cubic, 2 for hexagonal, 3 for rhombohedral, 4 for tetragonal, 5 for orthorhombic, 6 for monoclinic and 7 for triclinic.
The lattice type would then decide what the next part of input looks like. If it’s cubic (1), then the next line should have the one and only needed information, i.e. lattice parameter in Angstrom. If the lattice type is hexagonal (2) then we need lattice parameter a and c, so there will be two more lines giving this information. If lattice type is Monoclinic then there will be ____ lines giving the .
I know the input file structure is embarrassing to say the least, but I’ve included several examples in the end to make it easier to understand. Also pretty soon, I will be making a better input file structure as well as add support for CIF files.
So, the code is finally here:
/*XRD Pattern Simulator By: Manas Sharma mail: [email protected] https://bragitoff.com IG: @___physwhiz___ Forum: physwhiz.bragitoff.com */ #include<stdio.h> #include<string.h> #include<math.h> /* The following function takes the value of q(scattering vector) in the range 0 to 25 (Angstrom)^-1 and the name of the atomic specie using the atomic symbols and returns the atomic form factor at that q value. */ double formFactorCalc(double q, char specie[]){ //variable that will store the resulting form factor double result; int i, found=0,n; //Necessary tables needed for the calculations in array form char elements[211][10]={"H","H1-","He","Li","Li1+","Be","Be2+","B","C","Cval","N","O","O1-","F","F1-","Ne","Na","Na1+","Mg","Mg2+","Al","Al3+","Siv","Sival","Si","P","S","Cl","Cl1-","Ar","K","K1+","Ca","Ca2+","Sc","Sc3+","Ti","Ti2+","Ti3+","Ti4+","V","V2+","V3+","V5+","Cr","Cr2+","Cr3+","Mn","Mn2+","Mn3+","Mn4+","Fe","Fe2+","Fe3+","Co","Co2+","Co3+","Ni","Ni2+","Ni3+","Cu","Cu1+","Cu2+","Zn","Zn2+","Ga","Ga3+","Ge","Ge4+","As","Se","Br","Br1-","Kr","Rb","Rb1+","Sr","Sr2+","Y","Y3+","Zr","Zr4+","Nb","Nb3+","Nb5+","Mo","Mo3+","Mo5+","Mo6+","Tc","Ru","Ru3+","Ru4+","Rh","Rh3+","Rh4+","Pd","Pd2+","Pd4+","Ag","Ag1+","Ag2+","Cd","Cd2+","In","In3+","Sn","Sn2+","Sn4+","Sb","Sb3+","Sb5+","Te","I","I1-","Xe","Cs","Cs1+","Ba","Ba2+","La","La3+","Ce","Ce3+","Ce4+","Pr","Pr3+","Pr4+","Nd","Nd3+","Pm","Pm3+","Sm","Sm3+","Eu","Eu2+","Eu3+","Gd","Gd3+","Tb","Tb3+","Dy","Dy3+","Ho","Ho3+","Er","Er3+","Tm","Tm3+","Yb","Yb2+","Yb3+","Lu","Lu3+","Hf","Hf4+","Ta","Ta5+","W","W6+","Re","Os","Os4+","Ir","Ir3+","Ir4+","Pt","Pt2+","Pt4+","Au","Au1+","Au3+","Hg","Hg1+","Hg2+","Tl","Tl1+","Tl3+","Pb","Pb2+","Pb4+","Bi","Bi3+","Bi5+","Po","At","Rn","Fr","Ra","Ra2+","Ac","Ac3+","Th","Th4+","Pa","U","U3+","U4+","U6+","Np","Np3+","Np4+","Np6+","Pu","Pu3+","Pu4+","Pu6+","Am","Cm","Bk","Cf"}; double a1[]={0.489918 , 0.897661 , 0.8734 , 1.1282 , 0.6968 , 1.5919 , 6.2603 , 2.0545 , 2.31 , 2.26069 , 12.2126 , 3.0485 , 4.1916 , 3.5392 , 3.6322 , 3.9553 , 4.7626 , 3.2565 , 5.4204 , 3.4988 , 6.4202 , 4.17448 , 6.2915 , 5.66269 , 4.43918 , 6.4345 , 6.9053 , 11.4604 , 18.2915 , 7.4845 , 8.2186 , 7.9578 , 8.6266 , 15.6348 , 9.189 , 13.4008 , 9.7595 , 9.11423 , 17.7344 , 19.5114 , 10.2971 , 10.106 , 9.43141 , 15.6887 , 10.6406 , 9.54034 , 9.6809 , 11.2819 , 10.8061 , 9.84521 , 9.96253 , 11.7695 , 11.0424 , 11.1764 , 12.2841 , 11.2296 , 10.338 , 12.8376 , 11.4166 , 10.7806 , 13.338 , 11.9475 , 11.8168 , 14.0743 , 11.9719 , 15.2354 , 12.692 , 16.0816 , 12.9172 , 16.6723 , 17.0006 , 17.1789 , 17.1718 , 17.3555 , 17.1784 , 17.5816 , 17.5663 , 18.0874 , 17.776 , 17.9268 , 17.8765 , 18.1668 , 17.6142 , 19.8812 , 17.9163 , 3.7025 , 21.1664 , 21.0149 , 17.8871 , 19.1301 , 19.2674 , 18.5638 , 18.5003 , 19.2957 , 18.8785 , 18.8545 , 19.3319 , 19.1701 , 19.2493 , 19.2808 , 19.1812 , 19.1643 , 19.2214 , 19.1514 , 19.1624 , 19.1045 , 19.1889 , 19.1094 , 18.9333 , 19.6418 , 18.9755 , 19.8685 , 19.9644 , 20.1472 , 20.2332 , 20.2933 , 20.3892 , 20.3524 , 20.3361 , 20.1807 , 20.578 , 20.2489 , 21.1671 , 20.8036 , 20.3235 , 22.044 , 21.3727 , 20.9413 , 22.6845 , 21.961 , 23.3405 , 22.5527 , 24.0042 , 23.1504 , 24.6274 , 24.0063 , 23.7497 , 25.0709 , 24.3466 , 25.8976 , 24.9559 , 26.507 , 25.5395 , 26.9049 , 26.1296 , 27.6563 , 26.722 , 28.1819 , 27.3083 , 28.6641 , 28.1209 , 27.8917 , 28.9476 , 28.4628 , 29.144 , 28.8131 , 29.2024 , 29.1587 , 29.0818 , 29.4936 , 28.7621 , 28.1894 , 30.419 , 27.3049 , 30.4156 , 30.7058 , 27.0059 , 29.8429 , 30.9612 , 16.8819 , 28.0109 , 30.6886 , 20.6809 , 25.0853 , 29.5641 , 27.5446 , 21.3985 , 30.8695 , 31.0617 , 21.7886 , 32.1244 , 33.3689 , 21.8053 , 33.5364 , 34.6726 , 35.3163 , 35.5631 , 35.9299 , 35.763 , 35.215 , 35.6597 , 35.1736 , 35.5645 , 35.1007 , 35.8847 , 36.0228 , 35.5747 , 35.3715 , 34.8509 , 36.1874 , 35.7074 , 35.5103 , 35.0136 , 36.5254 , 35.84 , 35.6493 , 35.1736 , 36.6706 , 36.6488 , 36.7881 , 36.9185}; double a2[]={0.262003 , 0.565616 , 0.6309 , 0.7508 , 0.7888 , 1.1278 , 0.8849 , 1.3326 , 1.02 , 1.56165 , 3.1322 , 2.2868 , 1.63969 , 2.6412 , 3.51057 , 3.1125 , 3.1736 , 3.9362 , 2.1735 , 3.8378 , 1.9002 , 3.3876 , 3.0353 , 3.07164 , 3.20345 , 4.1791 , 5.2034 , 7.1964 , 7.2084 , 6.7723 , 7.4398 , 7.4917 , 7.3873 , 7.9518 , 7.3679 , 8.0273 , 7.3558 , 7.62174 , 8.73816 , 8.23473 , 7.3511 , 7.3541 , 7.7419 , 8.14208 , 7.3537 , 7.7509 , 7.81136 , 7.3573 , 7.362 , 7.87194 , 7.97057 , 7.3573 , 7.374 , 7.3863 , 7.3409 , 7.3883 , 7.88173 , 7.292 , 7.4005 , 7.75868 , 7.1676 , 7.3573 , 7.11181 , 7.0318 , 7.3862 , 6.7006 , 6.69883 , 6.3747 , 6.70003 , 6.0701 , 5.8196 , 5.2358 , 6.3338 , 6.7286 , 9.6435 , 7.6598 , 9.8184 , 8.1373 , 10.2946 , 9.1531 , 10.948 , 10.0562 , 12.0144 , 18.0653 , 13.3417 , 17.2356 , 18.2017 , 18.0992 , 11.175 , 11.0948 , 12.9182 , 13.2885 , 13.1787 , 14.3501 , 14.1259 , 13.9806 , 15.5017 , 15.2096 , 14.79 , 16.6885 , 15.9719 , 16.2456 , 17.6444 , 17.2535 , 18.5596 , 18.1108 , 19.1005 , 19.0548 , 19.7131 , 19.0455 , 18.933 , 19.0302 , 19.0138 , 18.9949 , 18.997 , 19.0298 , 19.1062 , 19.1278 , 19.297 , 19.1136 , 19.599 , 19.3763 , 19.7695 , 19.559 , 19.8186 , 19.6697 , 19.7491 , 20.0539 , 19.6847 , 19.9339 , 19.6095 , 20.1108 , 19.4258 , 20.2599 , 19.0886 , 19.9504 , 20.3745 , 19.0798 , 20.4208 , 18.2185 , 20.3271 , 17.6383 , 20.2861 , 17.294 , 20.0994 , 16.4285 , 19.7748 , 15.8851 , 19.332 , 15.4345 , 17.6817 , 18.7614 , 15.2208 , 18.121 , 15.1726 , 18.4601 , 15.2293 , 18.8407 , 15.43 , 19.3763 , 15.7189 , 16.155 , 15.2637 , 16.7296 , 15.862 , 15.5512 , 17.7639 , 16.7224 , 15.9829 , 18.5913 , 17.8204 , 16.9029 , 19.0417 , 18.4973 , 18.06 , 19.1584 , 20.4723 , 18.3481 , 13.0637 , 19.5682 , 18.8003 , 12.951 , 19.5026 , 25.0946 , 15.4733 , 19.0211 , 21.2816 , 23.0547 , 22.9064 , 21.67 , 23.1032 , 22.1112 , 23.4219 , 22.4418 , 23.2948 , 23.4128 , 22.5259 , 22.5326 , 22.7584 , 23.5964 , 22.613 , 22.5787 , 22.7286 , 23.8083 , 22.7169 , 22.646 , 22.7181 , 24.0992 , 24.4096 , 24.7736 , 25.1995}; double a3[]={0.196767 , 0.415815 , 0.3112 , 0.6175 , 0.3414 , 0.5391 , 0.7993 , 1.0979 , 1.5886 , 1.05075 , 2.0125 , 1.5463 , 1.52673 , 1.517 , 1.26064 , 1.4546 , 1.2674 , 1.3998 , 1.2269 , 1.3284 , 1.5936 , 1.20296 , 1.9891 , 2.62446 , 1.19453 , 1.78 , 1.4379 , 6.2556 , 6.5337 , 0.6539 , 1.0519 , 6.359 , 1.5899 , 8.4372 , 1.6409 , 1.65943 , 1.6991 , 2.2793 , 5.25691 , 2.01341 , 2.0703 , 2.2884 , 2.15343 , 2.03081 , 3.324 , 3.58274 , 2.87603 , 3.0193 , 3.5268 , 3.56531 , 2.76067 , 3.5222 , 4.1346 , 3.3948 , 4.0034 , 4.7393 , 4.76795 , 4.4438 , 5.3442 , 5.22746 , 5.6158 , 6.2455 , 5.78135 , 5.1652 , 6.4668 , 4.3591 , 6.06692 , 3.7068 , 6.06791 , 3.4313 , 3.9731 , 5.6377 , 5.5754 , 5.5493 , 5.1399 , 5.8981 , 5.422 , 2.5654 , 5.72629 , 1.76795 , 5.41732 , 1.01118 , 4.04183 , 11.0177 , 10.799 , 12.8876 , 11.7423 , 11.4632 , 6.57891 , 4.64901 , 4.86337 , 9.32602 , 4.71304 , 4.73425 , 3.32515 , 2.53464 , 5.29537 , 4.32234 , 2.89289 , 4.8045 , 5.27475 , 4.3709 , 4.461 , 4.47128 , 4.2948 , 3.78897 , 4.4585 , 4.5648 , 3.4182 , 5.0371 , 5.10789 , 2.41253 , 6.14487 , 7.5138 , 7.8069 , 8.9767 , 10.662 , 10.2821 , 10.888 , 10.9054 , 11.3727 , 11.6323 , 11.8513 , 11.9369 , 12.1233 , 12.3856 , 12.1329 , 12.4668 , 12.774 , 12.12 , 13.1235 , 12.0671 , 13.4396 , 11.9202 , 13.7603 , 11.8034 , 11.8509 , 13.8518 , 11.8708 , 14.3167 , 12.2471 , 14.5596 , 11.9812 , 14.5583 , 11.9788 , 14.9779 , 12.1506 , 15.1542 , 12.3339 , 15.3087 , 13.3335 , 12.6072 , 15.1 , 12.8429 , 14.7586 , 12.7285 , 14.5135 , 12.8268 , 14.4327 , 13.0544 , 14.5564 , 14.9305 , 14.7458 , 15.6115 , 13.6145 , 14.2326 , 15.7131 , 13.2153 , 13.7348 , 25.5582 , 14.3359 , 12.7801 , 21.6575 , 16.8883 , 12.8374 , 15.538 , 18.7478 , 11.9328 , 18.442 , 19.1406 , 12.0175 , 16.5877 , 19.1053 , 19.2497 , 13.1138 , 9.49887 , 8.0037 , 12.1439 , 12.4739 , 7.91342 , 12.5977 , 8.19216 , 12.7473 , 9.78554 , 14.1891 , 14.9491 , 12.2165 , 12.0291 , 14.0099 , 15.6402 , 12.9898 , 12.7766 , 14.3884 , 16.7707 , 13.5807 , 13.3595 , 14.7635 , 17.3415 , 17.399 , 17.8919 , 18.3317}; double a4[]={0.049879 , 0.116973 , 0.178 , 0.4653 , 0.1563 , 0.7029 , 0.1647 , 0.7068 , 0.865 , 0.839259 , 1.1663 , 0.867 , -20.307 , 1.0243 , 0.940706 , 1.1251 , 1.1128 , 1.0032 , 2.3073 , 0.8497 , 1.9646 , 0.528137 , 1.541 , 1.3932 , 0.41653 , 1.4908 , 1.5863 , 1.6455 , 2.3386 , 1.6442 , 0.8659 , 1.1915 , 1.0211 , 0.8537 , 1.468 , 1.57936 , 1.9021 , 0.087899 , 1.92134 , 1.5208 , 2.0571 , 0.0223 , 0.016865 , -9.576 , 1.4922 , 0.509107 , 0.113575 , 2.2441 , 0.2184 , 0.323613 , 0.054447 , 2.3045 , 0.4399 , 0.0724 , 2.3488 , 0.7108 , 0.725591 , 2.38 , 0.9773 , 0.847114 , 1.6735 , 1.5578 , 1.14523 , 2.41 , 1.394 , 2.9623 , 1.0066 , 3.683 , 0.859041 , 4.2779 , 4.3543 , 3.9851 , 3.7272 , 3.5375 , 1.5292 , 2.7817 , 2.6694 , -34.193 , 3.26588 , -33.108 , 3.65721 , -2.6479 , 3.53346 , 1.94715 , 0.337905 , 3.7429 , 2.30951 , 0.740625 , 0 , 2.71263 , 1.56756 , 3.00964 , 2.18535 , 1.28918 , -6.1989 , -5.6526 , 0.605844 , 0 , -7.9492 , 1.0463 , 0.357534 , 0 , 1.6029 , 0 , 2.0396 , 0 , 2.4663 , 0.487 , 0.0193 , 2.6827 , 0.288753 , 0 , 2.5239 , 2.2735 , 2.8868 , 1.99 , 1.4953 , 0.9615 , 2.6959 , 0.77634 , 3.28719 , 0.336048 , 3.33049 , 0.612376 , 0.144583 , 2.82428 , 0.97518 , 0.296689 , 2.85137 , 1.51031 , 2.87516 , 2.07492 , 2.89604 , 2.71488 , 2.9227 , 3.87243 , 3.26503 , 3.54545 , 3.7149 , 2.95354 , 3.773 , 2.96577 , 4.50073 , 3.63837 , 4.93676 , 2.98233 , 5.17379 , 2.98706 , 5.38348 , 2.98963 , 5.14657 , 5.47647 , 3.71601 , 5.59415 , 4.30013 , 5.59927 , 4.76492 , 5.38695 , 5.11982 , 5.06412 , 5.44174 , 5.67589 , 5.06795 , 5.83377 , 5.82008 , 5.53672 , 5.7837 , 6.35234 , 5.92034 , 5.86 , 6.58077 , 6.52354 , 5.9676 , 6.48216 , 6.89912 , 5.52593 , 6.82847 , 7.00574 , 5.9696 , 7.01107 , 6.96886 , 6.4692 , 7.10295 , 6.91555 , 7.02588 , 7.42518 , 7.4433 , 2.11253 , 3.21097 , 7.65078 , 4.08655 , 7.05545 , 4.80703 , 5.29444 , 4.17287 , 4.188 , 5.37073 , 4.7984 , 1.21457 , 4.1855 , 5.43227 , 4.92159 , 1.75669 , 3.47947 , 5.66016 , 5.18831 , 2.28678 , 3.49331 , 4.21665 , 4.23284 , 4.24391}; double b1[]={20.6593 , 53.1368 , 9.1037 , 3.9546 , 4.6237 , 43.6427 , 0.0027 , 23.2185 , 20.8439 , 22.6907 , 0.0057 , 13.2771 , 12.8573 , 10.2825 , 5.27756 , 8.4042 , 3.285 , 2.6671 , 2.8275 , 2.1676 , 3.0387 , 1.93816 , 2.4386 , 2.6652 , 1.64167 , 1.9067 , 1.4679 , 0.0104 , 0.0066 , 0.9072 , 12.7949 , 12.6331 , 10.4421 , -0.0074 , 9.0213 , 0.29854 , 7.8508 , 7.5243 , 0.22061 , 0.178847 , 6.8657 , 6.8818 , 6.39535 , 0.679003 , 6.1038 , 5.66078 , 5.59463 , 5.3409 , 5.2796 , 4.91797 , 4.8485 , 4.7611 , 4.6538 , 4.6147 , 4.2791 , 4.1231 , 3.90969 , 3.8785 , 3.6766 , 3.5477 , 3.5828 , 3.3669 , 3.37484 , 3.2655 , 2.9946 , 3.0669 , 2.81262 , 2.8509 , 2.53718 , 2.6345 , 2.4098 , 2.1723 , 2.2059 , 1.9384 , 1.7888 , 1.7139 , 1.5564 , 1.4907 , 1.4029 , 1.35417 , 1.27618 , 1.2148 , 1.18865 , 0.019175 , 1.12446 , 0.2772 , 0.014734 , 0.014345 , 1.03649 , 0.864132 , 0.80852 , 0.847329 , 0.844582 , 0.751536 , 0.764252 , 0.760825 , 0.698655 , 0.696219 , 0.683839 , 0.6446 , 0.646179 , 0.645643 , 0.5946 , 0.597922 , 0.5476 , 0.551522 , 5.8303 , 0.5036 , 5.764 , 5.3034 , 0.467196 , 5.44853 , 4.81742 , 4.347 , 4.3579 , 3.9282 , 3.569 , 3.552 , 3.216 , 3.21367 , 2.94817 , 2.9207 , 2.81219 , 2.77691 , 2.65941 , 2.77393 , 2.6452 , 2.54467 , 2.66248 , 2.52722 , 2.5627 , 2.4174 , 2.47274 , 2.31641 , 2.3879 , 2.27783 , 2.22258 , 2.25341 , 2.13553 , 2.24256 , 2.05601 , 2.1802 , 1.9804 , 2.07051 , 1.91072 , 2.07356 , 1.84659 , 2.02859 , 1.78711 , 1.9889 , 1.78503 , 1.73272 , 1.90182 , 1.68216 , 1.83262 , 1.59136 , 1.77333 , 1.50711 , 1.72029 , 1.42755 , 1.67191 , 1.62903 , 1.37113 , 1.59279 , 1.34323 , 1.30923 , 1.51293 , 1.32927 , 1.24813 , 0.4611 , 1.35321 , 1.2199 , 0.545 , 1.39507 , 1.21152 , 0.65515 , 1.4711 , 1.1008 , 0.6902 , 1.3366 , 1.00566 , 0.704 , 1.2356 , 0.91654 , 0.700999 , 0.68587 , 0.6631 , 0.646453 , 0.616341 , 0.604909 , 0.589092 , 0.579689 , 0.563359 , 0.555054 , 0.547751 , 0.5293 , 0.52048 , 0.516598 , 0.507079 , 0.511929 , 0.502322 , 0.498626 , 0.48981 , 0.499384 , 0.484938 , 0.481422 , 0.473204 , 0.483629 , 0.465154 , 0.451018 , 0.437533}; double b2[]={7.74039 , 15.187 , 3.3568 , 1.0524 , 1.9557 , 1.8623 , 0.8313 , 1.021 , 10.2075 , 0.656665 , 9.8933 , 5.7011 , 4.17236 , 4.2944 , 14.7353 , 3.4262 , 8.8422 , 6.1153 , 79.2611 , 4.7542 , 0.7426 , 4.14553 , 32.3337 , 38.6634 , 3.43757 , 27.157 , 22.2151 , 1.1662 , 1.1717 , 14.8407 , 0.7748 , 0.7674 , 0.6599 , 0.6089 , 0.5729 , 7.9629 , 0.5 , 0.457585 , 7.04716 , 6.67018 , 0.4385 , 0.4409 , 0.383349 , 5.40135 , 0.392 , 0.344261 , 0.334393 , 0.3432 , 0.3435 , 0.294393 , 0.283303 , 0.3072 , 0.3053 , 0.3005 , 0.2784 , 0.2726 , 0.238668 , 0.2565 , 0.2449 , 0.22314 , 0.247 , 0.2274 , 0.244078 , 0.2333 , 0.2031 , 0.2412 , 0.22789 , 0.2516 , 0.205855 , 0.2647 , 0.2726 , 16.5796 , 19.3345 , 16.5623 , 17.3151 , 14.7957 , 14.0988 , 12.6963 , 12.8006 , 11.2145 , 11.916 , 10.1483 , 11.766 , 1.13305 , 0.028781 , 1.0958 , 1.03031 , 1.02238 , 8.48061 , 8.14487 , 8.43467 , 8.37164 , 8.12534 , 8.21758 , 7.84438 , 7.62436 , 7.98929 , 7.55573 , 7.14833 , 7.4726 , 7.19123 , 7.18544 , 6.9089 , 6.80639 , 6.3776 , 6.3247 , 0.5031 , 5.8378 , 0.4655 , 0.4607 , 5.22126 , 0.467973 , 0.420885 , 0.3814 , 0.3815 , 0.344 , 0.3107 , 0.3086 , 0.2756 , 0.28331 , 0.244475 , 0.250698 , 0.226836 , 0.23154 , 0.21885 , 0.222087 , 0.214299 , 0.202481 , 0.210628 , 0.199237 , 0.202088 , 0.185769 , 0.196451 , 0.174081 , 0.1942 , 0.17353 , 0.16394 , 0.181951 , 0.155525 , 0.196143 , 0.149525 , 0.202172 , 0.143384 , 0.19794 , 0.139358 , 0.223545 , 0.13729 , 0.238849 , 0.136974 , 0.257119 , 0.15997 , 0.13879 , 9.98519 , 0.142292 , 9.5999 , 0.128903 , 9.37046 , 0.116741 , 9.2259 , 0.104621 , 9.09227 , 8.97948 , 6.84706 , 8.86553 , 7.10909 , 6.71983 , 8.81174 , 7.38979 , 6.60834 , 8.6216 , 7.7395 , 6.82872 , 8.4484 , 7.65105 , 7.05639 , 8.70751 , 0.517394 , 6.53852 , 2.3576 , 0.488383 , 6.10926 , 2.9238 , 6.24149 , 0.39042 , 3.55078 , 3.97458 , 4.0691 , 4.17619 , 3.87135 , 3.5767 , 3.65155 , 3.41437 , 3.46204 , 3.24498 , 3.41519 , 3.3253 , 3.12293 , 3.05053 , 2.8903 , 3.25396 , 3.03807 , 2.96627 , 2.81099 , 3.26371 , 2.96118 , 2.8902 , 2.73848 , 3.20647 , 3.08997 , 3.04619 , 3.00775}; double b3[]={49.5519 , 186.576 , 22.9276 , 85.3905 , 0.6316 , 103.483 , 2.2758 , 60.3498 , 0.5687 , 9.75618 , 28.9975 , 0.3239 , 47.0179 , 0.2615 , 0.442258 , 0.2306 , 0.3136 , 0.2001 , 0.3808 , 0.185 , 31.5472 , 0.228753 , 0.6785 , 0.916946 , 0.2149 , 0.526 , 0.2536 , 18.5194 , 19.5424 , 43.8983 , 213.187 , -0.002 , 85.7484 , 10.3116 , 136.108 , -0.28604 , 35.6338 , 19.5361 , -0.15762 , -0.29263 , 26.8938 , 20.3004 , 15.1908 , 9.97278 , 20.2626 , 13.3075 , 12.8288 , 17.8674 , 14.343 , 10.8171 , 10.4852 , 15.3535 , 12.0546 , 11.6729 , 13.5359 , 10.2443 , 8.35583 , 12.1763 , 8.873 , 7.64468 , 11.3966 , 8.6625 , 7.9876 , 10.3163 , 7.0826 , 10.7805 , 6.36441 , 11.4468 , 5.47913 , 12.9479 , 15.2372 , 0.2609 , 0.2871 , 0.2261 , 0.2748 , 0.1603 , 0.1664 , 24.5651 , 0.125599 , 22.6599 , 0.117622 , 21.6054 , 0.204785 , 10.1621 , 9.28206 , 11.004 , 9.53659 , 8.78809 , 0.058881 , 21.5707 , 24.7997 , 0.017662 , 0.36495 , 25.8749 , 21.2487 , 19.3317 , 25.2052 , 22.5057 , 17.9144 , 24.6605 , 21.7326 , 21.4072 , 24.7008 , 20.2521 , 25.8499 , 17.3595 , 26.8909 , 23.3752 , 14.0049 , 27.9074 , 19.5902 , 14.1259 , 28.5284 , 27.766 , 29.5259 , 26.4659 , 24.3879 , 23.7128 , 20.2073 , 20.0558 , 18.7726 , 17.8211 , 17.6083 , 16.5408 , 15.7992 , 16.7669 , 15.323 , 14.8137 , 15.885 , 14.1783 , 15.1009 , 13.1275 , 14.3996 , 12.1571 , 13.7546 , 11.6096 , 11.311 , 12.9331 , 10.5782 , 12.6648 , 10.0499 , 12.1899 , 9.34972 , 11.4407 , 8.80018 , 11.3604 , 8.36225 , 10.9975 , 7.96778 , 10.6647 , 8.18304 , 7.64412 , 0.261033 , 7.33727 , 0.275116 , 6.76232 , 0.295977 , 6.31524 , 0.321703 , 5.93667 , 0.3505 , 0.382661 , 0.165191 , 0.417916 , 0.204633 , 0.167252 , 0.424593 , 0.263297 , 0.16864 , 1.4826 , 0.356752 , 0.212867 , 1.5729 , 0.443378 , 0.284738 , 1.96347 , 7.43463 , 0.219074 , 8.618 , 6.7727 , 0.147041 , 8.7937 , 0.469999 , 5.71414 , 9.55642 , 11.3824 , 14.0422 , 23.1052 , 19.9887 , 12.601 , 18.599 , 12.9187 , 17.8309 , 13.4661 , 16.9235 , 16.0927 , 12.7148 , 12.5723 , 13.1767 , 15.3622 , 12.1449 , 11.9484 , 12.33 , 14.9455 , 11.5331 , 11.316 , 11.553 , 14.3136 , 13.4346 , 12.8946 , 12.4044}; double b4[]={2.20159 , 3.56709 , 0.9821 , 168.261 , 10.0953 , 0.542 , 5.1146 , 0.1403 , 51.6512 , 55.5949 , 0.5826 , 32.9089 , -0.01404 , 26.1476 , 47.3437 , 21.7184 , 129.424 , 14.039 , 7.1937 , 10.1411 , 85.0886 , 8.28524 , 81.6937 , 93.5458 , 6.65365 , 68.1645 , 56.172 , 47.7784 , 60.4486 , 33.3929 , 41.6841 , 31.9128 , 178.437 , 25.9905 , 51.3531 , 16.0662 , 116.105 , 61.6558 , 15.9768 , 12.9464 , 102.478 , 115.122 , 63.969 , 0.940464 , 98.7399 , 32.4224 , 32.8761 , 83.7543 , 41.3235 , 24.1281 , 27.573 , 76.8805 , 31.2809 , 38.5566 , 71.1692 , 25.6466 , 18.3491 , 66.3421 , 22.1626 , 16.9673 , 64.8126 , 25.8487 , 19.897 , 58.7097 , 18.0995 , 61.4135 , 14.4122 , 54.7625 , 11.603 , 47.7972 , 43.8163 , 41.4328 , 58.1535 , 39.3972 , 164.934 , 31.2087 , 132.376 , -0.0138 , 104.354 , -0.01319 , 87.6627 , -0.10276 , 69.7957 , 28.3389 , 25.7228 , 61.6584 , 26.6307 , 23.3452 , 0 , 86.8472 , 94.2928 , 22.887 , 20.8504 , 98.6062 , -0.01036 , -0.0102 , 76.8986 , 0 , 0.005127 , 99.8156 , 66.1147 , 0 , 87.4825 , 0 , 92.8029 , 0 , 83.9571 , 62.2061 , -0.7583 , 75.2825 , 55.5113 , 0 , 70.8403 , 66.8776 , 84.9304 , 64.2658 , 213.904 , 59.4565 , 167.202 , 51.746 , 133.124 , 54.9453 , 127.113 , 43.1692 , 62.2355 , 143.644 , 36.4065 , 45.4643 , 137.903 , 30.8717 , 132.721 , 27.4491 , 128.007 , 24.8242 , 123.174 , 26.5156 , 22.9966 , 101.398 , 21.7029 , 115.362 , 21.2773 , 111.874 , 19.581 , 92.6566 , 18.5908 , 105.703 , 17.8974 , 102.961 , 17.2922 , 100.417 , 20.39 , 16.8153 , 84.3298 , 16.3535 , 72.029 , 14.0366 , 63.3644 , 12.4244 , 57.056 , 11.1972 , 52.0861 , 48.1647 , 18.003 , 45.0011 , 20.3254 , 17.4911 , 38.6103 , 22.9426 , 16.9392 , 36.3956 , 26.4043 , 18.659 , 38.3246 , 28.2262 , 20.7482 , 45.8149 , 28.8482 , 17.2114 , 47.2579 , 23.8132 , 14.714 , 48.0093 , 20.3185 , 12.8285 , 47.0045 , 45.4715 , 44.2473 , 150.645 , 142.325 , 29.8436 , 117.02 , 25.9443 , 99.1722 , 23.9533 , 105.251 , 100.613 , 26.3394 , 23.4582 , 25.2017 , 97.4908 , 25.4928 , 22.7502 , 22.6581 , 105.98 , 24.3992 , 21.8301 , 20.9303 , 102.273 , 88.4834 , 86.003 , 83.7881}; double c[]={0.001305 , 0.002389 , 0.0064 , 0.0377 , 0.0167 , 0.0385 , -6.1092 , -0.1932 , 0.2156 , 0.286977 , -11.529 , 0.2508 , 21.9412 , 0.2776 , 0.653396 , 0.3515 , 0.676 , 0.404 , 0.8584 , 0.4853 , 1.1151 , 0.706786 , 1.1407 , 1.24707 , 0.746297 , 1.1149 , 0.8669 , -9.5574 , -16.378 , 1.4445 , 1.4228 , -4.9978 , 1.3751 , -14.875 , 1.3329 , -6.6667 , 1.2807 , 0.897155 , -14.652 , -13.28 , 1.2199 , 1.2298 , 0.656565 , 1.7143 , 1.1832 , 0.616898 , 0.518275 , 1.0896 , 1.0874 , 0.393974 , 0.251877 , 1.0369 , 1.0097 , 0.9707 , 1.0118 , 0.9324 , 0.286667 , 1.0341 , 0.8614 , 0.386044 , 1.191 , 0.89 , 1.14431 , 1.3041 , 0.7807 , 1.7189 , 1.53545 , 2.1313 , 1.45572 , 2.531 , 2.8409 , 2.9557 , 3.1776 , 2.825 , 3.4873 , 2.0782 , 2.5064 , 41.4025 , 1.91213 , 40.2602 , 2.06929 , 9.41454 , 3.75591 , -12.912 , -6.3934 , 4.3875 , -14.421 , -14.316 , 0.344941 , 5.40428 , 5.37874 , -3.1892 , 1.42357 , 5.328 , 11.8678 , 11.2835 , 5.26593 , 5.2916 , 13.0174 , 5.179 , 5.21572 , 5.21404 , 5.0694 , 5.11937 , 4.9391 , 4.99635 , 4.7821 , 4.7861 , 3.9182 , 4.5909 , 4.69626 , 4.69263 , 4.352 , 4.0712 , 4.0714 , 3.7118 , 3.3352 , 3.2791 , 2.7731 , 3.02902 , 2.14678 , 2.4086 , 1.86264 , 2.09013 , 1.5918 , 2.0583 , 1.77132 , 1.24285 , 1.98486 , 1.47588 , 2.02876 , 1.19499 , 2.20963 , 0.954586 , 2.5745 , 1.36389 , 0.759344 , 2.4196 , 0.645089 , 3.58324 , 0.691967 , 4.29728 , 0.68969 , 4.56796 , 0.852795 , 5.92046 , 1.17613 , 6.75621 , 1.63929 , 7.56672 , 3.70983 , 2.26001 , 7.97628 , 2.97573 , 8.58154 , 2.39699 , 9.24354 , 1.78555 , 9.8875 , 1.01074 , 10.472 , 11.0005 , 6.49804 , 11.4722 , 8.27903 , 6.96824 , 11.6883 , 9.85329 , 7.39534 , 12.0658 , 11.2299 , 9.0968 , 12.6089 , 12.0205 , 10.6268 , 13.1746 , 12.5258 , 9.8027 , 13.4118 , 12.4734 , 8.08428 , 13.5782 , 12.4711 , -6.7994 , 13.677 , 13.7108 , 13.6905 , 13.7247 , 13.6211 , 13.5431 , 13.5266 , 13.4637 , 13.4314 , 13.376 , 13.4287 , 13.3966 , 13.3092 , 13.2671 , 13.1665 , 13.3573 , 13.2544 , 13.2116 , 13.113 , 13.3812 , 13.1991 , 13.1555 , 13.0582 , 13.3592 , 13.2887 , 13.2754 , 13.2674}; //Search for the input specie in the 'elements' array to start the caclculation for (i=0;i<211;i++){ if(strcmp(specie, elements[i]) == 0 ) { n=i; found = 1; break; } } //If the specie is found in the table if (found==1){ //Use the atomic form factor formula which is the sum of the Gaussians of a particular form result=a1[n]*exp(-b1[n]*pow(q/(4*M_PI),2))+a2[n]*exp(-b2[n]*pow(q/(4*M_PI),2))+a3[n]*exp(-b3[n]*pow(q/(4*M_PI),2))+a4[n]*exp(-b4[n]*pow(q/(4*M_PI),2))+c[n]; }else{ //Return error code in case the input specie is not found in the database result=9898989898989898; } return result; } /* The following function takes the value of h,k,l and atomic species array, as well as the corresponding x,y,z position arrays and returns the real part of the structure factor for a gien value of h,k,l and theta and lambda */ double realStructFactor(int h, int k, int l, double theta, double lambda, int nat, char species[nat][10], double x[], double y[], double z[]){ double result=0; int i; double q=4*M_PI*sin(theta*M_PI/180.0)/lambda; for (i=0;i<nat;i++){ result=result+formFactorCalc(q, species[i])*cos(2*M_PI*(h*x[i]+k*y[i]+l*z[i])); } return result; } /* The following function takes the value of h,k,l and atomic species array, as well as the corresponding x,y,z position arrays and returns the imaginary part of the structure factor for a gien value of h,k,l and theta and lambda. */ double imagStructFactor(int h, int k, int l, double theta, double lambda, int nat, char species[nat][10], double x[], double y[], double z[]){ double result=0; int i; double q=4*M_PI*sin(theta*M_PI/180.0)/lambda; for (i=0;i<nat;i++){ result=result+formFactorCalc(q, species[i])*sin(2*M_PI*(h*x[i]+k*y[i]+l*z[i])); } return result; } /*Function to find out the no. of unique entries in an array, to get the unique entries of an array in a separate array, to count the no. of occurences of a given input in an array, to get the position of each unique entry in the given array*/ int uniqueCount(int size, double array[], double uniqueArray[], int pos[], int count[]){ int i,k,j; double temp; int size2; int found; for(i=0;i<size;i++){ if(i==0){ j=0; uniqueArray[j]=array[i]; pos[j]=i; size2=1; j++; }else{ found=0; for(k=0;k<size2;k++){ if(array[i]==uniqueArray[k]){ found=1; break; } } if(found!=1){ uniqueArray[j]=array[i]; pos[j]=i; j++; size2++; } } } for(k=0;k<size2;k++){ int counter=0; for(i=0;i<size;i++){ if(uniqueArray[k]==array[i]){ counter++; } } count[k]=counter; } return size2; } //Returns the non-zero entries in an array int nonZeroEntries(int size, double array[]){ int i; int count=0; for(i=0;i<size;i++){ if(array[i]!=0){ count++; } } return count; } main(){ int nat,h,k,l,i; double realSF, imagSF, F2; int h_arr[2000], k_arr[2000], l_arr[2000]; double theta; double theta_arr[2000]; double twoTheta_arr[2000]; double lambda=1.54059; double dmin=lambda/2; int ibrav; double a,b,c; double alpha, beta, gamma; double dhkl; double dhkl_arr[2000]; double Freal[2000], Fimag[2000],Fsq[2000]; char input[30]; printf("Enter Input File Name:n"); scanf("%s",&input); char output1[30]; strcpy(output1,input); char output2[30]; strcpy(output2,input); FILE *fp=NULL; //INPUT FILE CONTAINING THE INFORMATION OF LATTICE TYPE, LATTICE PARAMS. AND ATOMIC POSITIONS fp=fopen(strcat(input,".txt"),"r"); //Read the first line that contains the number of atoms fscanf(fp,"%dn",&nat); //Read the second line that contains the bravais lattice type fscanf(fp,"%dn",&ibrav); //Arrays to store the atomic specie as well as the atomic positions double xpos[nat], ypos[nat], zpos[nat]; char elem[nat][10]; //Read the lattice parameters depending on the value of ibrav switch(ibrav){ case 1: //Cubic //Read the lattice parameter fscanf(fp,"%lfn",&a); b=a; c=a; alpha=beta=gamma=90; break; case 2: //Hexagonal //Read the lattice parameters fscanf(fp,"%lfn",&a); fscanf(fp,"%lfn",&c); b=a; alpha=beta=90; gamma=120; break; case 3: //Rhombohedral //Read the lattice parameters fscanf(fp,"%lfn",&a); fscanf(fp,"%lfn",&alpha); b=a; c=a; beta=alpha; gamma=alpha; break; case 4: //Tetragonal //Read the lattice parameters fscanf(fp,"%lfn",&a); fscanf(fp,"%lfn",&c); b=a; alpha=beta=gamma=90; break; case 5: //Orthorhombic //Read the lattice parameters fscanf(fp,"%lfn",&a); fscanf(fp,"%lfn",&b); fscanf(fp,"%lfn",&c); alpha=beta=gamma=90; break; case 6: //Monoclinic //Read the lattice parameters fscanf(fp,"%lfn",&a); fscanf(fp,"%lfn",&b); fscanf(fp,"%lfn",&c); fscanf(fp,"%lfn",&beta); alpha=gamma=90; break; case 7: //Triclinic //Read the lattice parameters fscanf(fp,"%lfn",&a); fscanf(fp,"%lfn",&b); fscanf(fp,"%lfn",&c); fscanf(fp,"%lfn",&alpha); fscanf(fp,"%lfn",&beta); fscanf(fp,"%lfn",&gamma); break; default: //Read the lattice parameters fscanf(fp,"%lfn",&a); fscanf(fp,"%lfn",&b); fscanf(fp,"%lfn",&c); fscanf(fp,"%lfn",&alpha); fscanf(fp,"%lfn",&beta); fscanf(fp,"%lfn",&gamma); break; } //Skip the line containing the phrase "ATOMIC_POsition" the file fscanf(fp,"%*[^n]"); //Start reading the atom symbol and the x,y,z coordinates for(i=0;i<nat;i++){ fscanf(fp,"%st%lft%lft%lfn",&elem[i],&xpos[i],&ypos[i],&zpos[i]); } //RESULT OF XRD SIMULATOR //Store the reflection information in a file FILE *fp2=NULL; strcat(output1,"_reflections.txt"); fp2=fopen(output1,"w"); fprintf(fp2,"htktlt2thetatd_hkltFrealtFimagt|F|^2n"); int j=0; for(h=-a/dmin;h<=a/dmin;h++){ for(k=-b/dmin;k<=b/dmin;k++){ for(l=-c/dmin;l<=c/dmin;l++){ switch(ibrav){ case 1: if(h==0&&k==0&&l==0){ break; } //Get interplanar spacing using the Cubic formula dhkl=a/sqrt(h*h+k*k+l*l); //if the corresponding angle is not possible if((lambda/(2*dhkl))>1||(lambda/(2*dhkl))<(-1)){ break; } //Get theta in radians theta=asin(lambda/(2*dhkl)); //Convert theta to degrees theta=theta*180/M_PI; realSF=realStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); imagSF=imagStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); if(fabs(realSF-0)<=0.01&&fabs(imagSF-0)<=0.01){ break; }else{ F2=realSF*realSF+imagSF*imagSF; //Store inter-planar spacing in an array dhkl_arr[j]=dhkl; //Store theta in array theta_arr[j]=theta; twoTheta_arr[j]=theta*2; Freal[j]=realSF; Fimag[j]=imagSF; Fsq[j]=F2; h_arr[j]=h; k_arr[j]=k; l_arr[j]=l; fprintf(fp2,"%dt%dt%dt%lft%lft%lft%lft%lfn",h,k,l,2*theta,dhkl,realSF,imagSF,F2); j++; break; } case 2: if(h==0&&k==0&&l==0){ break; } //Get interplanar spacing using the Hexagonal formula dhkl=sqrt(pow(4.0/3.0*(h*h+h*k+k*k)/(a*a)+l*l/(c*c),-1)); //if the corresponding angle is not possible if((lambda/(2*dhkl))>1||(lambda/(2*dhkl))<(-1)){ break; } //Get theta in radians theta=asin(lambda/(2*dhkl)); //Convert theta to degrees theta=theta*180/M_PI; realSF=realStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); imagSF=imagStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); if(fabs(realSF-0)<=0.01&&fabs(imagSF-0)<=0.01){ break; }else{ F2=realSF*realSF+imagSF*imagSF; //Store inter-planar spacing in an array dhkl_arr[j]=dhkl; //Store theta in array theta_arr[j]=theta; twoTheta_arr[j]=theta*2; Freal[j]=realSF; Fimag[j]=imagSF; Fsq[j]=F2; h_arr[j]=h; k_arr[j]=k; l_arr[j]=l; fprintf(fp2,"%dt%dt%dt%lft%lft%lft%lft%lfn",h,k,l,2*theta,dhkl,realSF,imagSF,F2); j++; break; } case 3: if(h==0&&k==0&&l==0){ break; } //Get interplanar spacing using the Rhombohedral formula dhkl=sqrt(pow(((h*h+k*k+l*l)*sin(alpha*M_PI/180)*sin(alpha*M_PI/180)+2*(h*k+k*l+h*l)*(cos(alpha*M_PI/180)*cos(alpha*M_PI/180)-cos(alpha*M_PI/180)))/(a*a*(1-3*cos(alpha*M_PI/180)*cos(alpha*M_PI/180)+2*cos(alpha*M_PI/180)*cos(alpha*M_PI/180)*cos(alpha*M_PI/180))),-1)); //if the corresponding angle is not possible if((lambda/(2*dhkl))>1||(lambda/(2*dhkl))<(-1)){ break; } //Get theta in radians theta=asin(lambda/(2*dhkl)); //Convert theta to degrees theta=theta*180/M_PI; realSF=realStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); imagSF=imagStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); if(fabs(realSF-0)<=0.01&&fabs(imagSF-0)<=0.01){ break; }else{ F2=realSF*realSF+imagSF*imagSF; //Store inter-planar spacing in an array dhkl_arr[j]=dhkl; //Store theta in array theta_arr[j]=theta; twoTheta_arr[j]=theta*2; Freal[j]=realSF; Fimag[j]=imagSF; Fsq[j]=F2; h_arr[j]=h; k_arr[j]=k; l_arr[j]=l; fprintf(fp2,"%dt%dt%dt%lft%lft%lft%lft%lfn",h,k,l,2*theta,dhkl,realSF,imagSF,F2); j++; break; } case 4: if(h==0&&k==0&&l==0){ break; } //Get interplanar spacing using the Tetragonal formula dhkl=sqrt(pow((h*h+k*k)/a/a+l*l/c/c,-1)); //if the corresponding angle is not possible if((lambda/(2*dhkl))>1||(lambda/(2*dhkl))<(-1)){ break; } //Get theta in radians theta=asin(lambda/(2*dhkl)); //Convert theta to degrees theta=theta*180/M_PI; realSF=realStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); imagSF=imagStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); if(fabs(realSF-0)<=0.01&&fabs(imagSF-0)<=0.01){ break; }else{ F2=realSF*realSF+imagSF*imagSF; //Store inter-planar spacing in an array dhkl_arr[j]=dhkl; //Store theta in array theta_arr[j]=theta; twoTheta_arr[j]=theta*2; Freal[j]=realSF; Fimag[j]=imagSF; Fsq[j]=F2; h_arr[j]=h; k_arr[j]=k; l_arr[j]=l; fprintf(fp2,"%dt%dt%dt%lft%lft%lft%lft%lfn",h,k,l,2*theta,dhkl,realSF,imagSF,F2); j++; break; } case 5: if(h==0&&k==0&&l==0){ break; } //Get interplanar spacing using the Orthorhombic formula dhkl=sqrt(pow(h*h/a/a+k*k/b/b+l*l/c/c,-1)); //if the corresponding angle is not possible if((lambda/(2*dhkl))>1||(lambda/(2*dhkl))<(-1)){ break; } //Get theta in radians theta=asin(lambda/(2*dhkl)); //Convert theta to degrees theta=theta*180/M_PI; realSF=realStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); imagSF=imagStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); if(fabs(realSF-0)<=0.01&&fabs(imagSF-0)<=0.01){ break; }else{ F2=realSF*realSF+imagSF*imagSF; //Store inter-planar spacing in an array dhkl_arr[j]=dhkl; //Store theta in array theta_arr[j]=theta; twoTheta_arr[j]=theta*2; Freal[j]=realSF; Fimag[j]=imagSF; Fsq[j]=F2; h_arr[j]=h; k_arr[j]=k; l_arr[j]=l; fprintf(fp2,"%dt%dt%dt%lft%lft%lft%lft%lfn",h,k,l,2*theta,dhkl,realSF,imagSF,F2); j++; break; } case 6: if(h==0&&k==0&&l==0){ break; } //Get interplanar spacing using the Monoclinic formula dhkl=sqrt(pow((h*h/a/a+k*k*sin(beta*M_PI/180)*sin(beta*M_PI/180)/b/b+l*l/c/c-2*h*l*cos(beta*M_PI/180)/a/c)/sin(beta*M_PI/180)/sin(beta*M_PI/180),-1)); //if the corresponding angle is not possible if((lambda/(2*dhkl))>1||(lambda/(2*dhkl))<(-1)){ break; } //Get theta in radians theta=asin(lambda/(2*dhkl)); //Convert theta to degrees theta=theta*180/M_PI; realSF=realStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); imagSF=imagStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); if(fabs(realSF-0)<=0.01&&fabs(imagSF-0)<=0.01){ break; }else{ F2=realSF*realSF+imagSF*imagSF; //Store inter-planar spacing in an array dhkl_arr[j]=dhkl; //Store theta in array theta_arr[j]=theta; twoTheta_arr[j]=theta*2; Freal[j]=realSF; Fimag[j]=imagSF; Fsq[j]=F2; h_arr[j]=h; k_arr[j]=k; l_arr[j]=l; fprintf(fp2,"%dt%dt%dt%lft%lft%lft%lft%lfn",h,k,l,2*theta,dhkl,realSF,imagSF,F2); j++; break; } case 7: if(h==0&&k==0&&l==0){ break; } //Get interplanar spacing using the Monoclinic formula dhkl=sqrt(pow((h*h/a/a*pow(sin(alpha*M_PI/180),2)+k*k/b/b*pow(sin(beta*M_PI/180),2)+l*l/c/c*pow(sin(gamma*M_PI/180),2)+2*k*l*cos(alpha*M_PI/180)/b/c+2*h*l*cos(beta*M_PI/180)/a/c+2*h*k*cos(gamma*M_PI/180)/b/a)/(1-pow(cos(alpha*M_PI/180),2)-pow(cos(beta*M_PI/180),2)-pow(cos(gamma*M_PI/180),2)+2*cos(alpha*M_PI/180)*cos(beta*M_PI/180)*cos(gamma*M_PI/180)),-1)); //if the corresponding angle is not possible if((lambda/(2*dhkl))>1||(lambda/(2*dhkl))<(-1)){ break; } //Get theta in radians theta=asin(lambda/(2*dhkl)); //Convert theta to degrees theta=theta*180/M_PI; realSF=realStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); imagSF=imagStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); if(fabs(realSF-0)<=0.01&&fabs(imagSF-0)<=0.01){ break; }else{ F2=realSF*realSF+imagSF*imagSF; //Store inter-planar spacing in an array dhkl_arr[j]=dhkl; //Store theta in array theta_arr[j]=theta; twoTheta_arr[j]=theta*2; Freal[j]=realSF; Fimag[j]=imagSF; Fsq[j]=F2; h_arr[j]=h; k_arr[j]=k; l_arr[j]=l; fprintf(fp2,"%dt%dt%dt%lft%lft%lft%lft%lfn",h,k,l,2*theta,dhkl,realSF,imagSF,F2); j++; break; } default: if(h==0&&k==0&&l==0){ break; } //Get interplanar spacing using the Triclinic formula dhkl=sqrt(pow((h*h/a/a*pow(sin(alpha*M_PI/180),2)+k*k/b/b*pow(sin(beta*M_PI/180),2)+l*l/c/c*pow(sin(gamma*M_PI/180),2)+2*k*l*cos(alpha*M_PI/180)/b/c+2*h*l*cos(beta*M_PI/180)/a/c+2*h*k*cos(gamma*M_PI/180)/b/a)/(1-pow(cos(alpha*M_PI/180),2)-pow(cos(beta*M_PI/180),2)-pow(cos(gamma*M_PI/180),2)+2*cos(alpha*M_PI/180)*cos(beta*M_PI/180)*cos(gamma*M_PI/180)),-1)); //if the corresponding angle is not possible if((lambda/(2*dhkl))>1||(lambda/(2*dhkl))<(-1)){ break; } //Get theta in radians theta=asin(lambda/(2*dhkl)); //Convert theta to degrees theta=theta*180/M_PI; realSF=realStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); imagSF=imagStructFactor(h,k,l,theta,lambda,nat,elem,xpos,ypos,zpos); if(fabs(realSF-0)<=0.01&&fabs(imagSF-0)<=0.01){ break; }else{ F2=realSF*realSF+imagSF*imagSF; //Store inter-planar spacing in an array dhkl_arr[j]=dhkl; //Store theta in array theta_arr[j]=theta; twoTheta_arr[j]=theta*2; Freal[j]=realSF; Fimag[j]=imagSF; Fsq[j]=F2; h_arr[j]=h; k_arr[j]=k; l_arr[j]=l; fprintf(fp2,"%dt%dt%dt%lft%lft%lft%lft%lfn",h,k,l,2*theta,dhkl,realSF,imagSF,F2); j++; break; } } } } } //A lot of extra redundant kind of stuff that probably wasn't needed //Basically this block of code is suposed to give the final information that will be plotted int totalNoOfReflections=nonZeroEntries(2000,theta_arr); double hUnique[2000]; double kUnique[2000]; double lUnique[2000]; double dhklUnique[2000]; double thetaUnique[2000]; int multiplicity[2000]; int pos[2000]; int nUnique=uniqueCount(totalNoOfReflections,theta_arr,thetaUnique,pos,multiplicity); for(i=0;i<nUnique;i++){ printf("%lft%dt%dn",2*thetaUnique[i],pos[i],multiplicity[i]); } //Lorentz-Polarization Correction double intensity[nUnique]; for(i=0;i<nUnique;i++){ intensity[i]=multiplicity[i]*Fsq[pos[i]]; intensity[i]=intensity[i]*(1+cos(twoTheta_arr[pos[i]]*M_PI/180)*cos(twoTheta_arr[pos[i]]*M_PI/180)); intensity[i]=intensity[i]/(sin(theta_arr[pos[i]]*M_PI/180)*sin(theta_arr[pos[i]]*M_PI/180)*cos(theta_arr[pos[i]]*M_PI/180)); } //Final plottable results go in the file given by fp3 FILE *fp3=NULL; strcat(output2,"_plotXRD.txt"); fp3=fopen(output2,"w"); fprintf(fp3,"htktlt2thetatd_hklt|F|^2tIntensitytMultiplicityn"); for(i=0;i<nUnique;i++){ fprintf(fp3,"%dt%dt%dt%lft%lft%lft%lft%dn",h_arr[pos[i]],k_arr[pos[i]],l_arr[pos[i]],2*theta_arr[pos[i]],dhkl_arr[pos[i]],Fsq[pos[i]],intensity[i],multiplicity[i]); } }
Input File Examples:
Fe_BCC.txt
2
1
2.848
ATOMIC_POSITIONS {crystal}
Fe 0.00 0.00 0.00
Fe 0.50 0.50 0.50
Cu_FCC.txt
4
1
3.6149
ATOMIC_POSITIONS {crystal}
Cu 0.000000 0.000000 0.000000
Cu 0.000000 0.500000 0.500000
Cu 0.500000 0.000000 0.500000
Cu 0.500000 0.500000 0.000000
ZnO_Hex.txt
4
2
3.2533
5.2073
Atomic Position
Zn 0.333330 0.666670 0.000000
Zn 0.666670 0.333340 0.500000
O 0.333330 0.666670 0.382000
O 0.666670 0.333340 0.882000
CdS_Cub.txt
8
1
5.94083
ATOMIC_POSITIONS {crystal}
Cd 0.000000 0.000000 0.000000
Cd 0.000000 0.500000 0.500000
Cd 0.500000 0.000000 0.500000
Cd 0.500000 0.500000 0.000000
S 0.250000 0.250000 0.750001
S 0.250000 0.750001 0.250000
S 0.750001 0.250000 0.250000
S 0.750001 0.750001 0.750001
TiO2_Tetra.txt
6
4
4.65178
2.96991
ATOMIC_POSITIONS {crystal}
Ti 0.500000 0.500000 0.500001
Ti 0.000000 0.000000 0.000000
O 0.695090 0.695090 0.000000
O 0.195089 0.804912 0.500001
O 0.304911 0.304911 0.000000
O 0.804912 0.195089 0.500001
OUTPUT:
Output Files Generated:
Fe_BCC_plotXRD.txt and Fe_BCC_reflections.txt
Now, the file with the suffix plotXRD.txt contains the plottable data, i.e. the intensity as well as the 2theta values. 2theta values in the 4th column and the intensity in the 7th column. You can plot these using gnuplot using the impulse chart type. Or using Origin using stem scatter chart.
To make things easier for you guys, I am also attaching a shell script down below, that can be used to create a Gnuplot script that would plot a very neat looking graph even with the peaks labelled using the hkl miller indices.
GNUPLOT Script:
To make the following script work, save it as xrdPlotter.sh and then in your terminal run,
chmod u+x xrdPlotter.sh to make it executable
and then run the script using ./xrdPlotter.sh Fe_BCC
#!/bin/bash
filename=$1
filename=$(echo $1'_plotXRD.txt')
n=$(wc -l <$filename)
echo "
set terminal png size 1000,500
set output '"$1"plot.png'
set xlabel '2{/Symbol Q} (degrees)'
set ylabel 'Intensity (arb. units)'
set title 'Simulated XRD Pattern'" >XRDplotScript.p
for (( i=2; i<=$n; i++ ))
do
h=$(awk 'NR=='$i'{print $1}' $filename)
k=$(awk 'NR=='$i'{print $2}' $filename)
l=$(awk 'NR=='$i'{print $3}' $filename)
index=$(echo $h $k $l)
x=$(awk 'NR=='$i'{print $4}' $filename)
y=$(awk 'NR=='$i'{print $7}' $filename)
echo "
set label '"$index"' at "$x","$y" left rotate by 90 offset 0,0.5 font 'Helvetica,8'" >>XRDplotScript.p
done
echo "
#set key box linestyle 1
plot '"$filename"' u 4:7 w impulse">>XRDplotScript.p
echo "
set terminal postscript enhanced color solid 22
set output '"$1"plot.eps'
set xlabel '2{/Symbol Q} (degrees)'
set ylabel 'Intensity (arb. units)'
set title 'Simulated XRD Pattern'" >>XRDplotScript.p
for (( i=2; i<=$n; i++ ))
do
h=$(awk 'NR=='$i'{print $1}' $filename)
k=$(awk 'NR=='$i'{print $2}' $filename)
l=$(awk 'NR=='$i'{print $3}' $filename)
index=$(echo $h $k $l)
x=$(awk 'NR=='$i'{print $4}' $filename)
y=$(awk 'NR=='$i'{print $7}' $filename)
echo "
set label '"$index"' at "$x","$y" left rotate by 90 offset 0,0.5 font 'Helvetica,8'" >>XRDplotScript.p
done
echo "
#set key box linestyle 1
plot '"$filename"' u 4:7 w impulse">>XRDplotScript.p
gnuplot ./XRDplotScript.p
Gnuplot Output:
On the execution of the above scripts there will two plots generated in .esp and .png format, that look like the following:
References:
http://pd.chem.ucl.ac.uk/pdnn/chapter.htm
http://pd.chem.ucl.ac.uk/pdnn/powintro/introind.htm
http://pd.chem.ucl.ac.uk/pdnn/diff2/dindex2.htm
https://www.bragitoff.com/2017/08/x-ray-diffraction-xrd/
Ph.D. researcher at Friedrich-Schiller University Jena, Germany. I’m a physicist specializing in computational material science. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT, and Machine Learning related apps and software from time to time. Can code in most of the popular languages. I like to share my knowledge in Physics and applications using this Blog and a YouTube channel.
[wpedon id="7041" align="center"]
Hello..,
This is Indira G from India. I am a Ph.D Scholar and my work is characterization of starch using microscopy and spectroscopy techniques. I really need your help with regard to analysis of XRD patterns of starch. Since it is powder diffraction pattern I am unable to find .cif file. Please help me in analyzing the XRD pattern.
Looking forward to hear from you soon.
In order to predict the XRD Pattern we need some important information like the lattice parameters as well as the atomic positions.
If you have some experimental data then maybe you can perform a Rietveld refinement to get the parameters.