Generation of EXAFS oscillations through electron-wave interference cartoon 

Matlab code 

% Cartoon of the generation of EXAFS oscillations due to interference

% between the outgoing photoelectron wave and that reflected back from a

% neighbouring scattering atom. 

 

clear; close all; 

 

vid = VideoWriter('EXAFSinterference.mp4','MPEG-4');

vid.Quality = 100;

vid.FrameRate = 30;

open(vid);

figure('units','pixels','position',[0 0 1920 1080]);

set(0,'defaultfigurecolor',[1 1 1]);

set(gca,'linewidth',7);

 

myBlue = [0.4 0.44 0.73];

myGold = [220 166 3]/255;

 

% red - yellow - green - blue - violet custom colormap 

rgb = customcolormap([0 0.25 0.5 0.75 1], {'#ff0000','#ffff00','#00ff00','#0000ff','#7f00ff'});

fliprgb = flip(rgb);

colormap(fliprgb);

 

[xx,yy,zz] = sphere(50);

r1 = 2;

lp = [0.4 0.4 0.7];

gndStatex = -2.5:0.01:2.5; % x-coordinates gnd state

gndStatey = exp(-gndStatex.^2); % y-coordinates gnd state

 

% Generate photon symbol of sine wave and arrow head

phWavex = -4*pi:pi/45:0;

phWavey = sin(2*phWavex);

 

eWavex = 0:pi/45:30;

 

stepFn = 1./(1+exp(10*(phWavex+pi+0.2)));

phWavey = phWavey.*stepFn;

 

x = -5:0.1:10; % x-coordinates potential well

y1 = -0.02*exp(0.7*x); % y-coordinates potential well

for hv = 1/256:1/256:1

    colorIndex1 = 128+round(128*hv); 

    colorIndex2 = round(128*hv); 

    newplot;

    

    hold off

    

    % Plot four curves representing potential well of core electron 

    plot(x-10.5,y1,-x+10.5,y1,-x+40.5,y1,x+19.5,y1,'Color',myBlue,'Linewidth',2)

    hold on

    axis off;

    axis equal;

 

    % Emitting and scattering atoms 

    surf(xx*r1,yy*r1-25,zz*r1,'FaceColor',myBlue,'EdgeColor','none','FaceLighting','gouraud');

    surf(xx*r1+30,yy*r1-25,zz*r1,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

    

    % Dotted linnes showing axis of the two atoms and the zero energy of

    % the electron 

    plot([0 0],[-25 19],'Color','k','Linewidth',1,'Linestyle',':')

    plot([30 30],[-25 19],'Color','k','Linewidth',1,'Linestyle',':')

    plot([-10 40],[0 0],'Color','k','Linewidth',1,'Linestyle',':')

    

    % Plot ground state of core electron 

    plot(gndStatex,4*gndStatey-20,'Color','k','Linewidth',2)

    plot([-2.5 2.5],[-20 -20],'Color','k','Linewidth',1)

    

    % Plot incident photon symbol 

    photon = plot(phWavex,phWavey-8,'Color',fliprgb(colorIndex1,:),...

        'LineWidth',2.5);

    rotate(photon,[0 0 1],-45,[-4*pi -8 0])

    phArrowHd = fill([0.25 -1.4 -1.4]+1,[0 0.5 -0.5]-8,fliprgb(colorIndex1,:),...

        'LineStyle','none','FaceLighting','none');

    rotate(phArrowHd,[0 0 1],-45,[-4*pi -8 0])

    text(-14,-6.4,'h\nu','FontSize',23);

    

    % Plot outgoing andreflected electron waves 

    eWavey = 1.6*sin(1.4*eWavex*hv^0.5)+16*hv; % Outgoing wave from emitting atom

    eWavey2 = -sin(1.4*(eWavex+30)*hv^0.5)+16*hv; % Reflected wave from scattering atom

    plot(eWavex,eWavey,'Color',fliprgb(colorIndex2,:),...

        'LineWidth',3);

    plot(30-eWavex,eWavey2,'Color',fliprgb(colorIndex2,:),...

        'LineWidth',2);

    plot([0 30],[16*hv 16*hv],'Color','k','Linewidth',1)

    

    % Plot of simulated EXAFS spectrum

    xEx = -2:0.01:16;

    % Quasi step-function on a falling slope to represent bare absorption edge

    yE1 = 1./(1+exp(-20*xEx))-xEx/28;

    % chi(E), the EXAFS modulation of the absorption with a period proportional

    % to the square-root of the electron energy (hv - E_B)

    yE2 = 0.28*exp(-xEx/5).*cos(21*abs(xEx).^0.5)./(1+exp(-50*xEx));

    plot(-5.6*(yE1+yE2)+37,xEx,'Color','k','LineWidth',2.0)

    plot([37 37],[0 16],'Color','k','Linewidth',1.5)

    phArrowHd = fill([36.7 37.3 37],[16 16 17.35],'k',...

        'LineStyle','none','FaceLighting','none'); 

    text(37.7,8,'E_e','FontSize',19);

    text(30.7,-1.1,'\mu(E_e)','FontSize',19);

 

    light('Position',lp,'Style','infinite');

    set(gca, 'Projection','perspective'); 

    hold off 

    

    % Store the frame

    frame = getframe(gcf);

    writeVideo(vid,frame);

 

end

% Output the movie as an mpg file

close(vid)