/******************************************************************************* * * McXtrace, x-ray tracing package * Copyright, All rights reserved * DTU Physics, Kgs. Lyngby, Denmark * Synchrotron SOLEIL, Saint-Aubin, France * * Component: Laue_crystal_BC * * %Identification * Written by: Marcus H Mendenhall, NIST * Date: June, 2017 * Version: 1.0 * Origin: NIST * * Perfect, Laue crystal with common cubic structures (diamond, fcc, or bcc, and others if symmetry form factor multipliers provided explicitly) * * %Description * NIST_Laue_crystal_BC.comp is written by Marcus H. Mendenhall, NIST, Gaithersburg, MD, USA * It is based on the full vector math and exact solution of the dispersion relation in * Batterman and Cole, Reviews of Modern Physics 36 number 3, page 681, July 1964 * Perfect crystal with common cubic structures (diamond, fcc, or bcc, and others if symmetry form factor multipliers provided explicitly) * * Reads atomic form factors from a data input file. * The Laue_Crystal code reflects rays in an ideal geometry, does not include surface imperfections or mosaicity. * * The crystal is positioned such that the long axis of the crystal surface coincides with * z-axis and the outer normal to the crystal surface is along +y. * * The ratio of the transmitted beam and forward-diffracted Borrman-effect beam is a hack. The sum of the * two is exactly right, but the actual ratio depends critically on geometry, and I just put in a wild estimate * to allow one to demonstrate what the Borrmann effect looks like. If this is turned on, the displacement of the * transmitted beam and forward diffracted beam at the back side of the crystal will be correctly computed. * This displacement is only exact for symmetrical Laue; asymmetrical computation requires more effort, * and is probably not worth it. * The sampling of these processes are controlled by the 3 variables transmission_sampling, forward_diffraction_sampling, * and Laue_sampling. Since 99% of uses of this will have the transmitted beam turned off, and use Laue diffraction mode, * the values should be just 0,0,1. If the general behavior of the transmitted beams * is interesting, use 1,1,1 which samples all beams equally. Results weights are adjusted for this, * so computed intensities won't be affected. * * Non-copyright notice: * Contributed by the National Institute of Standards and Technology; not subject to copyright in the United States. * This is not an official contribution, in that the results are in no way certified by NIST. * * %Parameters * Input parameters: * width: [m] width of the crystal. * length: [m] zdepth (length) of the crystal. * thickness: [m] thickness of crystal (along y-axis, the surface normal) * material: [ ] Si ("Si.txt"), Ge ("Ge.txt") * form_factors: [ ] "FormFactors.txt" from McXtrace install, usually * V: [AA^3] unit cell volume * h: [ ] 1st Miller index of reflection * k: [ ] 2nd Miller index of reflection * l: [ ] 3rd Miller index of reflection * alphax: [ ] x component of normal (unit vector) to crystal planes. Vector is usually [0,0,1] for symmetric Laue. Crystal surface itself has normal [0,1,0]. * alphay: [ ] y component of normal (unit vector) to crystal planes. * alphaz: [ ] z component of normal (unit vector) to crystal planes. * debye_waller_B: [AA^2] Debye-Waller temperature factor, M=B*(sin(theta)/lambda)^2*(2/3), default=silicon at room temp, 0.4632 * crystal_type: [ ] 1 => Mx_crystal_explicit: provide explicit real and imaginary form factor multipliers structure_factor_scale_r, structure_factor_scale_i, * 2 => Mx_crystal_diamond: diamond * 3 => Mx_crystal_fcc: fcc * 4 => Mx_crystal_fcc: bcc * structure_factor_scale_r: [ ] real part of complex explicit override of structure factor multiplier for crystal structure if Bragg_crystal_explicit * structure_factor_scale_i: [ ] imaginary part of complex explicit override of structure factor multiplier for crystal structure if Bragg_crystal_explicit * transmission_sampling: [ ] enable sampling of transmission diffraction mode. * forward_diffraction_sampling: [ ] enable sampling of forward diffraftion mode. * laue_sampling: [ ] enable sampling of Laue diffraction mode. * * %Link * material datafile obtained from http://physics.nist.gov/cgi-bin/ffast/ffast.pl * * %End *******************************************************************************/ DEFINE COMPONENT Laue_crystal_BC SETTING PARAMETERS (length=0.05, width=0.02, thickness=1e-4, V=160.1826, string form_factors="FormFactors.txt", string material="Si.txt", alphax=0.0, alphay = 0.0, alphaz = 1.0, debye_waller_B=0.4632, int crystal_type=1, int h=1, int k=1, int l=1 , structure_factor_scale_r=0.0, structure_factor_scale_i=0.0, transmission_sampling=1.0, forward_diffraction_sampling=1.0, laue_sampling=1.0) /* X-ray parameters: (x,y,z,kx,ky,kz,phi,t,Ex,Ey,Ez,p) */ SHARE %{ %include "perfect_crystals-lib" %} DECLARE %{ int Z; double rho; double At; double f_rel; double f_nt; t_Table m_t; t_Table f0_t; %} INITIALIZE %{ int status; if (material) { if ((status = Table_Read (&(m_t), material, 0)) == -1) { fprintf (stderr, "Error(%s): Could not parse file \"%s\"\n", NAME_CURRENT_COMP, material); exit (-1); } char** header_parsed; header_parsed = Table_ParseHeader (m_t.header, "Z", "A[r]", "rho", "Z/A", "sigma[a]", NULL); if (header_parsed[2]) { rho = strtod (header_parsed[2], NULL); } if (header_parsed[0]) { Z = strtod (header_parsed[0], NULL); } if (header_parsed[1]) { At = strtod (header_parsed[1], NULL); } } else { fprintf (stderr, "Error(%s): No material file specified\n", NAME_CURRENT_COMP); } if (form_factors) { if ((status = Table_Read (&(f0_t), form_factors, 0)) == -1) { fprintf (stderr, "Error(%s): Could not parse file \"%s\"\n", NAME_CURRENT_COMP, form_factors); exit (-1); } } printf ("INFO: (%s): initialized\n", NAME_CURRENT_COMP); %} TRACE %{ double E; // (keV) x-ray energy double K; // length of k-vector double tin; // 'time' of intersection of ray with y=0 plane (which include the crystal surface) double x_int, y_int, z_int; // intersection with the y=0 plane double dist; // distance from position at t=0 to the y=0 plane double f00, f0h, fp, fpp; // atomic form factors for Q=0 is (f00 + fp + i*fpp) and for Q= ha*+kb*+lc* it is (f0h + fp + i*fpp). /* get the photon's kvector and energy */ K = sqrt (kx * kx + ky * ky + kz * kz); E = K2E * K; /* use built-in constants for consistency */ /* make unit vector in the direction of k :*/ double k0hat[3] = { kx / K, ky / K, kz / K }; // unit vector in the direction of k-vector. double kk0[3] = { kx, ky, kz }; #ifdef MCDEBUG fflush (NULL); // make sure all error messages are in order! #endif /*intersection calculation*/ tin = (-y - thickness / 2) / k0hat[1]; if (tin > 1e-8) { /* check whether our intersection lies within the boundaries of the crystal*/ x_int = x + k0hat[0] * tin; y_int = y + k0hat[1] * tin; z_int = z + k0hat[2] * tin; if (fabs (x_int) <= width / 2 && fabs (z_int) <= length / 2) { dist = sqrt (SQR (x - x_int) + SQR (y - y_int) + SQR (z - z_int)); PROP_DL (dist); /* now the photon is on the crystal surface, ready to be reflected... */ SCATTER; double d = cbrt (V) / (sqrt (h * h + k * k + l * l)); /*this is valid only for cubic structures*/ f00 = Z; f0h = Table_Value (f0_t, 1 / (2 * d), Z); fp = Table_Value (m_t, E, 1) - Z; fpp = Table_Value (m_t, E, 2); double nhat[3] = { 0, 1, 0 }; // crystal surface normal is yhat, and is set up by mcxtrace to be into the crystal double alpha[3] = { alphax, alphay, alphaz }; int fail; double complex chi0, chih; double k0mag, hscale, thetaB; Mx_CubicCrystalChi (&chi0, &chih, &k0mag, &hscale, &thetaB, f00, f0h, fp, fpp, V, h, k, l, debye_waller_B, E, crystal_type, structure_factor_scale_r, structure_factor_scale_i); double selsum, transmitlim, borrmannlim; selsum = transmission_sampling + forward_diffraction_sampling + laue_sampling; transmitlim = transmission_sampling / selsum; borrmannlim = (transmission_sampling + forward_diffraction_sampling) / selsum; double sampling_selector = rand01 (); double Rsig, Rpi, Tsig, Tpi, Asig, Api; double kh[3], sig_axis[3], pi_axis[3]; fail = Mx_LaueReflectivityBC (&Rsig, &Rpi, &Tsig, &Tpi, &Asig, &Api, kh, // these are the return values k0hat, nhat, alpha, chi0, chih, chih, k0mag, hscale, thetaB, thickness); cross (sig_axis, k0hat, kh, 1); /* kin x kout is sigma direction for diffracted ray */ /* pi is a vector perpendicular to k_in and sig i.e. the direction of pi polarization incoming */ cross (pi_axis, k0hat, sig_axis, 1); /* resolve incoming polarization into sig and pi bits, and scale by sqrt(reflectivity) which is amplitude scale */ double Esig = (Ex * sig_axis[0] + Ey * sig_axis[1] + Ez * sig_axis[2]); double Epi = (Ex * pi_axis[0] + Ey * pi_axis[1] + Ez * pi_axis[2]); if (Esig == 0 && Epi == 0) { /* someone didn't set the polarization direction; set it now to a random value and it will propagate */ double psi = rand01 () * PI / 2; Esig = cos (psi); Epi = sin (psi); } /*, now hack out Borrmann (forward diffraction) estimate. Not really right! Total forward beam is exact, just partitioning into split beam is estimated */ double sigpart = 2 * Tsig / (Tsig + Asig); // should be 1 far away from anything interesting, 2 for enhanced Asig = (1 - ((1 - sigpart) * (1 - sigpart))) * Tsig; // when sigpart=1, all is normal atten, otherwise share Tsig = Tsig - Asig; double pipart = 2 * Tpi / (Tpi + Api); // should be 1 far away from anything interesting, 2 for enhanced Api = (1 - ((1 - pipart) * (1 - pipart))) * Tpi; // when sigpart=1, all is normal atten, otherwise share Tpi = Tpi - Api; #ifdef MCDEBUG fprintf (stderr, "Laue %s, Rsig=%.3e, Rpi=%.3e, sigpart=%.3f, pipart=%.3f, Tsig=%.3e, Tpi=%.3e, Asig=%.3e, Api=%.3e\n", NAME_CURRENT_COMP, Rsig, Rpi, sigpart, pipart, Tsig, Tpi, Asig, Api); #endif /* R is the Laue reflected intensity, T is the transmitted Bormann intensity, A is the undiffracted beam */ /* In all cases, the emergence from the crystal is only exactly right in the symmetric case, for now. The assumption is the rays move along the crystal planes. The real answer requires getting the normal to the dispersion surface, which I have not implemented. For usual, thin crystals, this makes only a tiny difference.*/ #ifdef MCDEBUG fprintf (stderr, "LAUE component %s: Rsig=%.3e Rpi=%.3e Tsig=%.3f Tpi=%.3e\n", NAME_CURRENT_COMP, Rsig, Rpi, Tsig, Tpi); #endif if (transmission_sampling && (sampling_selector <= transmitlim)) { double EsigT = Esig * sqrt (Asig); /* Tsig & Tpi are the un-diffracted beam intensity */ double EpiT = Epi * sqrt (Api); double RT = EsigT * EsigT + EpiT * EpiT; /* projected transmitted, squared back to intensity */ Ex = EpiT * pi_axis[0] + EsigT * sig_axis[0]; Ey = EpiT * pi_axis[1] + EsigT * sig_axis[1]; Ez = EpiT * pi_axis[2] + EsigT * sig_axis[2]; p *= RT / (transmission_sampling / selsum); PROP_DL (thickness / k0hat[1]); // continue through crystal to back side in original direction } else { // doing either forward diffraction (Borrman anomalous transmission) or Laue diffraction. // for both types of diffraction, the beam propagates inside the crystal // along the lattice plane (perpendicular to diffraction plane and alpha) (B&C figure 2, again). double propdir[3]; cross (propdir, sig_axis, alpha, 1); // beam appears to move this direction // now bump beam to back side of crystal x += thickness * propdir[0] / propdir[1]; y += thickness; z += thickness * propdir[2] / propdir[1]; // now, decide between forward (Borrman) diffraction and Laue if (forward_diffraction_sampling && (sampling_selector < borrmannlim)) { // transmitted direction is same as incoming, no k vector change double EsigT = Esig * sqrt (Tsig); /* Fsig and Fpi are the Borrmann intensity */ double EpiT = Epi * sqrt (Tpi); double RT = EsigT * EsigT + EpiT * EpiT; /* projected Borrmann, squared back to intensity */ Ex = EpiT * pi_axis[0] + EsigT * sig_axis[0]; Ey = EpiT * pi_axis[1] + EsigT * sig_axis[1]; Ez = EpiT * pi_axis[2] + EsigT * sig_axis[2]; p *= RT / (forward_diffraction_sampling / selsum); } else if (laue_sampling) { /* update outgoing direction vector kx, ky, kz = kh, fully scaled diffracted k vector */ kx = kh[0]; ky = kh[1]; kz = kh[2]; double pi1_axis[3]; cross (pi1_axis, kh, sig_axis, 1); /* pi1 is now a vector perpendicular to k_out and sig i.e. the direction of pi polarization outgoing */ double EsigR = Esig * sqrt (Rsig); /* Rsig and Rpi are the Laue intensity */ double EpiR = Epi * sqrt (Rpi); double RR = EsigR * EsigR + EpiR * EpiR; /* projected diffracted reflectivity, squared back to intensity */ Ex = EpiR * pi1_axis[0] + EsigR * sig_axis[0]; Ey = EpiR * pi1_axis[1] + EsigR * sig_axis[1]; Ez = EpiR * pi1_axis[2] + EsigR * sig_axis[2]; p *= RR / (laue_sampling / selsum); } else { // no diffraction sampled! illegal. fprintf (stderr, "LAUE component %s: all sampling choices set to zero. cannot run.\n", NAME_CURRENT_COMP); exit (1); } NORM (Ex, Ey, Ez); if (p == 0) ABSORB; } } else { RESTORE_XRAY (INDEX_CURRENT_COMP, x, y, z, kx, ky, kz, phi, t, Ex, Ey, Ez, p); } } %} MCDISPLAY %{ double w2 = width / 2., l2 = length / 2., t2 = thickness / 2., wl2 = (width + length) / 2.0, arrow = wl2 / 10.0; magnify (""); multiline (9, -w2, -t2, -l2, -w2, t2, -l2, w2, t2, -l2, w2, -t2, -l2, // front face w2, -t2, l2, // connector -w2, -t2, l2, -w2, t2, l2, w2, t2, l2, w2, -t2, l2 // back face ); line (-w2, -t2, -l2, -w2, -t2, l2); // extra edges line (-w2, t2, -l2, -w2, t2, l2); // extra edges line (w2, t2, -l2, w2, t2, l2); // extra edges multiline (8, 0., 0., 0., alphax* wl2, alphay* wl2, alphaz* wl2, alphax* wl2, alphay*(wl2 - arrow) + alphaz * arrow, alphaz*(wl2 - arrow) + alphay * arrow, alphax* wl2, alphay*(wl2 - arrow) - alphaz * arrow, alphaz*(wl2 - arrow) + alphay * arrow, alphax* wl2, alphay* wl2, alphaz* wl2, alphax*(wl2 - arrow) + alphaz * arrow, alphay* wl2, alphaz*(wl2 - arrow) + alphax * arrow, alphax*(wl2 - arrow) - alphaz * arrow, alphay* wl2, alphaz*(wl2 - arrow) + alphax * arrow, alphax* wl2, alphay* wl2, alphaz* wl2); // display alpha vector assuming it is mostly in the 'z' direction double nx = 0., ny = 1.0 / 2.0, nz = 0.; // short surface normal multiline (8, 0., 0., 0., nx* wl2, ny* wl2, nz* wl2, nx* wl2, ny*(wl2 - arrow) + nz * arrow, nz*(wl2 - arrow) + ny * arrow, nx* wl2, ny*(wl2 - arrow) + nz * arrow, nz*(wl2 - arrow) - ny * arrow, nx* wl2, ny* wl2, nz* wl2, nx*(wl2 - arrow) + ny * arrow, ny*(wl2 - arrow) + nx * arrow, nz* wl2, nx*(wl2 - arrow) - ny * arrow, ny*(wl2 - arrow) + nx * arrow, nz* wl2, nx* wl2, ny* wl2, nz* wl2); // display surface normal vector, pointing in forward beam direction, // half the size of alpha vector to make it easy to tell them apart %} END