% % Program to calculate spurious reflections on Symmetric channel-cut monos % Following [1] Vaclav O. Kostroun, NIM 172(1980) 243-247 % Jordi Juanhuix and I Peral, March 2007 % juanhuix@cells.es, iperal@cells.es setconstants; % Reproduction of the figure from [1] is done when kostroun=1 kostroun=0; % Monochromator characteristics si111=1; % type of crystal, kostroun overides it si311=0; % type of crystal, kostroun overides it sym_mono=1; % type of crystal, kostroun overides it if kostroun % to reproduce the example shown in figure [1], it is enough to use the % following parameters and min=fin=4 D = 10; % dist 1st xtal-screen, m. NOT USED X1 = 18*MILI; % For symmetric mono: gap between xtals, negat. Y1 = 2.0*MILI; hl=20.0*MILI; % h dimension in Vaclav O. Kostroun, NIM 172(1980) 243-247 L=37.0*MILI; alpha = [1; 1; 1]; % reference reflection beta = [-1; 1; 0]; % direction of Bragg axis gamma = [-1; -1; 2]; % orthogonal to previous ones asym=16.0*DEG; % asymmetric cut sym_mono=0; maxEnergy=13.0*KILO; % Maximum energy of the polycromatic beam (in eV) else % other cases different than kostroun publication if and(si111==1,si311==0) alpha = [1; 1; 1]; % reference reflection beta = [-1; 1; 0]; % direction of Bragg axis gamma = [-1; -1; 2]; % orthogonal to previous ones end; if and(si111==0,si311==1) alpha = [3; 1; 1]; % reference reflection beta = [-1; 2; 1]; % direction of Bragg axi gamma = [-1; -4; 7]; % orthogonal to previous ones end; D = 10; % dist 1st xtal-screen (meters) X1 = -3*MILI; % For symmetric mono: gap between xtals, negat. Y1=0.0*MILI; % corresponds to the Y1 dimension in [1], figure 1 hl=50.0*MILI; % width of the crystal (very wide, worst case scenario), % corresponds to the h dimension in [1], L=200.0*MILI; % corresponds to the L dimension in [1], figure 1 asym=0.0*DEG; % asymmetric cut maxEnergy=100.0*KILO; % Maximum energy of the polycromatic beam (in eV) end % X ray characteristics a = 5.4309; %Si - Si(111) 3.1354161 dspacing = a/sqrt(transpose(alpha)*alpha); dim=1; %Two columns Energies in keV and in Agstroms Energy=zeros(dim,1); % Energy in KeV lambda=zeros(dim,1); % wl correspond to energy values in Angstroms Theta=zeros(dim,1); % Theta angles min=8.0; % Minimum energy (in KeV) fin=8.0; % Maximum energy (in KeV) maxrefl = 6; % maximum reflection index to be searched (or plotted) % kostroun figure publication if kostroun==1 min=4; fin=4; end for i=min:fin Energy(i)=i*KILO; % Photon Energy, keV lambda(i)=HCEVA/Energy(i); % Wavelength, A Theta(i) = asin(lambda(i)/2/dspacing); % Bragg angle, rad if kostroun Theta(i)=30.0*(pi/180.0); lambda(i)=2*dspacing*sin(Theta(i)); Energy(i)=HCEVA/lambda(i); end; end % Minimum distance of the extra beams from the main diffracted beam mindisty= 3*MILI; mindistz= 3*MILI; if kostroun mindisty= 15*MILI; mindistz= 8.0*MILI; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % searching for close reflection for a given Theta range for i=min:fin RotBragg = [sin(Theta(i)) 0 cos(Theta(i)); 0 1 0; -cos(Theta(i)) 0 sin(Theta(i))]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Reference reflection position h=alpha(1) ; k=alpha(2) ; l=alpha(3); Halpha = (alpha(1)*h + alpha(2)*k + alpha(3)*l)/ ... sqrt(alpha(1)^2 + alpha(3)^2 + alpha(3)^2)/sqrt(h^2 + k^2 + l^2); Hbeta = (beta(1)*h + beta(2)*k + beta(3)*l)/ ... sqrt(beta(1)^2 + beta(3)^2 + beta(3)^2)/sqrt(h^2 + k^2 + l^2); Hgamma = (gamma(1)*h + gamma(2)*k + gamma(3)*l)/ ... sqrt(gamma(1)^2 + gamma(3)^2 + gamma(3)^2)/sqrt(h^2 + k^2 + l^2); H = RotBragg*[Halpha; Hbeta; Hgamma]; if sym_mono==1 F = X1/((2*H(1)^2-1)*sin(Theta(i)) - 2*H(1)*H(3)*cos(Theta(i))); % SYM case else % ASYM case F = (X1*cos(asym)+(L/2.0*cos(asym)+Y1)*sin(asym))/((2.0*H(1)*H(1)-1)*sin(Theta(i)-asym)-2.0*H(1)*H(3)*cos(Theta(i)-asym)); end; % Point source. For extended sources change xyz distribution % xyz: diffraction point at 1st xtal. Lab frame x = 0; y = 0; z = 0; sy0 = 2*H(1)*H(2)*F + y; sz0 = 2*H(1)*H(3)*F + z; hold on; norm=sisf(h,k,l)*(GetAtomicFormFactor('Si',0.5/dspacing))^2; %%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%% % searching over all possible h,k,l, or what is the same, over all possible % energies, assuming maxrefl=15 seems a reasonable hkl limit for h = 0:maxrefl for k = -maxrefl:maxrefl for l = -maxrefl:maxrefl; if check(h,k,l)==1 Halpha = (alpha(1)*h + alpha(2)*k + alpha(3)*l)/ ... sqrt(alpha(1)^2 + alpha(3)^2 + alpha(3)^2)/sqrt(h^2 + k^2 + l^2); Hbeta = (beta(1)*h + beta(2)*k + beta(3)*l)/ ... sqrt(beta(1)^2 + beta(3)^2 + beta(3)^2)/sqrt(h^2 + k^2 + l^2); Hgamma = (gamma(1)*h + gamma(2)*k + gamma(3)*l)/ ... sqrt(gamma(1)^2 + gamma(3)^2 + gamma(3)^2)/sqrt(h^2 + k^2 + l^2); H = RotBragg*[Halpha; Hbeta; Hgamma]; if sym_mono==1 F = X1/((2*H(1)^2-1)*sin(Theta(i)) - 2*H(1)*H(3)*cos(Theta(i))); % SYM case else % ASYM case F = (X1*cos(asym)+(L/2.0*cos(asym)+Y1)*sin(asym))/((2.0*H(1)*H(1)-1)*sin(Theta(i)-asym)-2.0*H(1)*H(3)*cos(Theta(i)-asym)); end; % Point source. For extended sources change xyz distribution % xyz: diffraction point at 1st xtal. Lab frame x = 0; y = 0; z = 0; sx = (2*H(1)^2-1)*F + x; sy = 2*H(1)*H(2)*F + y; sz = 2*H(1)*H(3)*F + z; screen(1) = -D; screen(2) = sy; screen(3) = sz; dist=sqrt((screen(2)/MILI-sy0/MILI)^2+(screen(3)/MILI-sz0/MILI)^2); % distance to the reference point disty=abs(screen(2)/MILI-sy0/MILI) ; distz=abs(screen(3)/MILI-sz0/MILI) ; % distance (y and z) to the reference point if and(disty < mindisty/MILI,distz < mindistz/MILI) % calculating the energy of the h k l reflection s0=[-1,0,0] ; s=s0(:)-2*(s0*H).*H; mods=sqrt((s(1)^2+s(2)^2+s(3)^2)); modH=sqrt(h^2+k^2+l^2)/a; TThetaf = acos(s0*s) ; Ef=HCEVA/(2.0*(1/modH)*sin(TThetaf/2.0)); if Ef < maxEnergy weigth=(sisf(h,k,l)*(GetAtomicFormFactor('Si',0.5*modH))^2)/norm; % "weigth" given by F_hkl^4 weigth=weigth^2; fprintf('Reflection: %3i %3i %3i (Ef= %6.2f keV) at %6.2f mm from 111, weigth= %6.2f | E_mono(keV)= %d \n',h,k,l,Ef/KILO,dist,weigth,Energy(i)/KILO); currpoint = plot(screen(2)/MILI,screen(3)/MILI); if [h;k;l] == alpha; x0 = screen(2)/MILI; y0 = screen(3)/MILI; set(currpoint,'Marker','o','MarkerSize',8,'MarkerFaceColor','r','MarkerEdgeColor','r'); % multicolor: [h k l]./maxrefl text(screen(2)/MILI,screen(3)/MILI,sprintf(' %3i %3i %3i',h,k,l),'FontSize',7); else if(check_plot(h,k,l,alpha)) set(currpoint,'Marker','o','MarkerSize',weigth2size(weigth),'MarkerFaceColor','b','MarkerEdgeColor','b'); % multicolor: [h k l]./maxrefl text(screen(2)/MILI,screen(3)/MILI,sprintf(' %3i %3i %3i',h,k,l),'FontSize',7); end; end; % finishing hkl==alpha condition end % finishing energy max condition end; % finishing distance condition end; % finishing check reflection conditions end; % finishing h,k,l loop end; end; end; % finishing energy loop %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Plot Options title({['Spurious reflections from a Si(' num2str(alpha(1))... num2str(alpha(2)) num2str(alpha(3)) ') monochromator']; ... ['Gap ' num2str(-X1/MILI) ' mm - E = ' num2str(Energy(i)/KILO,'%.3f') ... ' keV - d = ' num2str(dspacing,'%.4f') ' A']}) xlabel('x (mm)'); ylabel('y (mm)'); axis([(sy0-mindisty)/MILI (sy0+mindisty)/MILI (sz0-mindistz)/MILI (sz0+mindistz)/MILI]);