EXAFS rules of thumb matlab code

Back to spectroscopic techniques animations

Download

matlab code

% Movie depicting cartoons of rules of thumb for changes in the appearance

% of EXAFS spectra according to the number of scatterers in a shell, the

% radius of the shell, and the scattering strength of the atoms in the

% shell

clear; close all;

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

vid.Quality = 100;

vid.FrameRate = 30;

open(vid);

figure('units','pixels','position',[0 0 1920 1080],'ToolBar','none');

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

set(gca,'linewidth',7);

myBlue = [0.4 0.44 0.73];

myGold = [220 166 3]/255;

myGrey = [0.5 0.5 0.5];

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

r1 = 0.5;

r2 = 0.25;

rt32 = (3^0.5)/2;

% Positions of six subplots

pos1 = [0.01 0.52 0.32 0.46]; % Top left 3D cartoon

pos2 = [0.01 0.02 0.32 0.46]; % Bottom left EXAFS plot

pos3 = [0.34 0.52 0.32 0.46]; % Top middle 3D cartoon

pos4 = [0.34 0.02 0.32 0.46]; % Bottom middle EXAFS plot

pos5 = [0.67 0.52 0.32 0.46]; % Top right 3D cartoon

pos6 = [0.67 0.02 0.32 0.46]; % Bottom right EXAFS plot

tt = 0:pi/180:pi*(1 - 1/180); % 180 frames for full cycle

Rn = 1+(sin(tt)).^2; % Shell radius breathing sinusoidally out and in between 1 and 2

ttt = 0;

LL = 2.35;

hold off;

lp = [0.4 -0.4 0.7];

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

for ii = Rn % Breathing radius

ttt = ttt+1;

% -------------------------------------------------------

% Variation of EXAFS signal with number of atoms in shell

subplot('Position',pos1);

newplot;

hold off

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

hold on

surf(xx*1.5,yy*1.5,zz*1.5,'FaceColor',myGrey,'EdgeColor','none','FaceAlpha',0.1,'FaceLighting','gouraud');

twoon = 30;

if (ttt <= twoon)

surf(xx*r2+1.5,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2-1.5,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

end

fouron = 60;

if (ttt > twoon) && (ttt <= fouron)

surf(xx*r2+1.5,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2-1.5,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2+1.5,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2-1.5,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

end

sixon = 90;

if (ttt > fouron) && (ttt <= sixon)

surf(xx*r2+1.5,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2-1.5,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2+1.5,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2-1.5,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2,zz*r2+1.5,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2,zz*r2-1.5,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

end

eighton = 120;

if (ttt > sixon) && (ttt <= eighton)

surf(xx*r2+rt32,yy*r2+rt32,zz*r2+rt32,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2-rt32,yy*r2+rt32,zz*r2+rt32,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2+rt32,yy*r2-rt32,zz*r2+rt32,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2-rt32,yy*r2-rt32,zz*r2+rt32,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2+rt32,yy*r2+rt32,zz*r2-rt32,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2-rt32,yy*r2+rt32,zz*r2-rt32,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2+rt32,yy*r2-rt32,zz*r2-rt32,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2-rt32,yy*r2-rt32,zz*r2-rt32,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

end

sixon2 = 150;

if (ttt > eighton) && (ttt <= sixon2)

surf(xx*r2+1.5,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2-1.5,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2+1.5,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2-1.5,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2,zz*r2+1.5,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2,zz*r2-1.5,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

end

fouron2 = 180;

if (ttt > sixon2) && (ttt <= fouron2)

surf(xx*r2+1.5,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2-1.5,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2+1.5,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2-1.5,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

end

axis off;

axis equal;

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

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

xlim([-LL LL]);

ylim([-LL LL]);

zlim([-LL LL]);

view(16,10);

hold off

subplot('Position',pos2);

newplot;

hold off

if (ttt <= twoon)

noAt = 2;

end

if (ttt > twoon) && (ttt <= fouron)

noAt = 4;

end

if (ttt > fouron) && (ttt <= sixon)

noAt = 6

end

if (ttt > sixon) && (ttt <= eighton)

noAt = 8

end

if (ttt > eighton) && (ttt <= sixon2)

noAt = 6;

end

if (ttt > sixon2) && (ttt <= fouron2)

noAt = 4;

end

% Range of x centred around absorption edge

x = -2:0.01:6;

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

y1 = 1./(1+exp(-20*x))-x/20;

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

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

y2 = 0.28*exp(-x).*cos(20*abs(x+0.2).^0.5)./(1+exp(-50*x));

y3 = 0.4*y2*noAt/8; % Modulation varies as number of atoms in shell

plot(x,y1+y3,'Color',myBlue,'LineWidth',3.0)

axis off;

xlim([-2 6]);

ylim([-0.1 1.25]);

hold off

% ----------------------------------------------

% Variation of EXAFS signal with radius of shell

subplot('Position',pos3);

newplot;

hold off

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

hold on

surf(xx*ii,yy*ii,zz*ii,'FaceColor',myGrey,'EdgeColor','none','FaceAlpha',0.1,'FaceLighting','gouraud');

surf(xx*r2+ii,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2-ii,yy*r2,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2+ii,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2-ii,zz*r2,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2,zz*r2+ii,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2,yy*r2,zz*r2-ii,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

axis off;

axis equal;

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

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

xlim([-LL LL]);

ylim([-LL LL]);

zlim([-LL LL]);

view(16,10);

hold off

subplot('Position',pos4);

newplot;

hold off

% Range of x centred around absorption edge

x = -2:0.01:6;

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

y1 = 1./(1+exp(-20*x))-x/20;

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

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

y2 = 0.28*exp(-x).*cos(20*abs(x*ii+0.2).^0.5)./(1+exp(-50*x));

y3 = y2/ii^2; % Modulation varies as 1/Rn^2

plot(x,y1+y3,'Color',myBlue,'LineWidth',3.0)

axis off;

xlim([-2 6]);

ylim([-0.1 1.25]);

hold off

% ---------------------------------------------------------------------

% Variation of EXAFS signal with scattering strenngth of atoms in shell

subplot('Position',pos5);

newplot;

hold off

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

hold on

surf(xx*1.5,yy*1.5,zz*1.5,'FaceColor',myGrey,'EdgeColor','none','FaceAlpha',0.1,'FaceLighting','gouraud');

surf(xx*r2*ii+1.5,yy*r2*ii,zz*r2*ii,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2*ii-1.5,yy*r2*ii,zz*r2*ii,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2*ii,yy*r2*ii+1.5,zz*r2*ii,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2*ii,yy*r2*ii-1.5,zz*r2*ii,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2*ii,yy*r2*ii,zz*r2*ii+1.5,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

surf(xx*r2*ii,yy*r2*ii,zz*r2*ii-1.5,'FaceColor',myGold,'EdgeColor','none','FaceLighting','gouraud');

axis off;

axis equal;

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

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

xlim([-LL LL]);

ylim([-LL LL]);

zlim([-LL LL]);

view(16,10);

hold off

subplot('Position',pos6);

newplot;

hold off

% Range of x centred around absorption edge

x = -2:0.01:6;

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

y1 = 1./(1+exp(-20*x))-x/20;

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

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

y2 = 0.28*exp(-x).*cos(20*abs(x+0.2).^0.5)./(1+exp(-50*x));

y3 = 0.25*y2*ii^2; % Modulation varies as tj, itself proportional to area

plot(x,y1+y3,'Color',myBlue,'LineWidth',3.0)

axis off;

xlim([-2 6]);

ylim([-0.1 1.25]);

hold off

% Store the frame

frame = getframe(gcf);

writeVideo(vid,frame);

hold off;

end

% Output the movie as an mpg file

close(vid)