Change in the form of CTRs by varying the out-of-plane distance of the top atomic layer - “relaxation”
Matlab code 

% Program plotting the CTR intensity as a function of l and displacement

% dz of the top atomic layer of an elemental simple cubic lattiice between 

% +/- 5%. On the right the movement of this layer is shown, but exaggerated

% by a factor of 5. 

 

close all

vid = VideoWriter('CTRvSurfaceDilation.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);

 

lp = [0. 0. 0.2];

myBlue = [0.32 0.35 0.7];

lightblue = [0.64 0.77 1];

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

 

pos1 = [0.1 0.1 0.5 0.8]; % Top left 3D cartoon

pos2 = [0.64 0.1 0.35 0.8]; % Bottom left EXAFS plot 

 

str1 = '\delta = ';

str3 = ' %';

 

[xx,yy,zz] = sphere(50);  

r1 = 0.35; 

 

z01 = 0:0.0005:0.05; 

z02 = 0.049:-0.0005:-0.05; 

z03 = -0.049:0.0005:0; 

z0 = [z01 z02 z03]; 

l = 0:0.005:3;

for z = z0

    subplot('Position',pos1); 

    newplot 

    F0ctr = (1 - exp(1i*2*pi*l)).^-1 + exp(-1i*2*pi*l);

    I0ctr = (abs(F0ctr)).^2;

    Fctr = (1 - exp(1i*2*pi*l)).^-1 + exp(-1i*2*pi*(1+z)*l);

    Ictr = (abs(Fctr)).^2;

    hold off

    plot(l,log10(I0ctr),'color',lightblue, 'Linewidth', 2)

    hold on

    plot(l,log10(Ictr),'color',myBlue, 'Linewidth', 2)

    set(gca,'fontsize',25,'linewidth',2);

 

    ylim([-2,3]) 

    xlabel('l [r.l.u.]');

    ylabel('log_{10}(CTR intensity)'); 

    

    str2 = num2str(z*100,'% 4.2f'); 

    strTot = [str1,str2,str3]; 

    hText = text(0.5, -1.25, strTot, 'FontSize',25); 

 

    

    subplot('Position',pos2); 

    newplot 

    hold off 

    for atomRow = -3:3 

        hold on

        surf(xx*r1+atomRow,yy*r1,zz*r1,'FaceColor',myBlue,... 

                'EdgeColor','none','FaceLighting','gouraud','FaceAlpha',0.2);

    end 

    

    for atomCol = 0:-1:-5 

        for atomRow = -3:3 

            if (atomCol == 0)

            surf(xx*r1+atomRow,yy*r1,zz*r1+atomCol+z*5,'FaceColor',myBlue,... 

                'EdgeColor','none','FaceLighting','gouraud','FaceAlpha',1+atomCol/5.5);

            else 

                surf(xx*r1+atomRow,yy*r1,zz*r1+atomCol,'FaceColor',myBlue,... 

                'EdgeColor','none','FaceLighting','gouraud','FaceAlpha',1+atomCol/5.5);

            end 

        end 

    end 

    axis off;

    axis equal; 

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

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

    xlim([-4 4]);

    ylim([-1 1]);

    zlim([-6 1]);

    view(0,0);

 

    % Store the frame

    frame = getframe(gcf);

    writeVideo(vid,frame);

    hold off 

end

% Output the movie as an mpg file

close(vid);