electron diffraction pattern !

Question

Syed Ali Hassan 2020-8-27

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/585371-electron-diffraction-pattern

编辑： Syed Ali Hassan 2020-8-27

This is my code , I started with making and ideal crystal in 2D, then I tried to plot the lattice points and reciprocal lattice coordinates in lattice space, Now I know that I need to formula of 2dsin(theta)=n(lemdda) , I am not sure, I need to calculate the electron diffraction pattren from this simple cube. can anyone help me out !

       % 2D Crystal Translation Vectors
Primitivelattice=0;
Cellsize=0;
switch Primitivelattice
    case 0
        a=[1 0 0];
        b=[0 1 0];
        c=[0 0 100];
    case 1
        a=[1 0 0];
        b=[0 2 0];
        c=[0 0 100]; 
end
% define the size of the cell
 switch Cellsize
     case 0
         n1=5;
         n2=7;
     case 1
         n1=4;
         n2=6;
 end 
 
 %Unit vectors
 x_hat=[1 0 0];
 y_hat=[0 1 0];
 z_hat=[0 0 1];
 
 
%% direct speace lattice points
 %calculating coordinates of each lattice point in real space
 %calculating the distacne (lattice constant) from the origin
 
 [X,Y,Z]= meshgrid(1:n1,1:n2,1);
 Rx=X*dot(a,x_hat)+Y*dot(b,x_hat)+Z*dot(c,x_hat);
 Ry=X*dot(a,y_hat)+Y*dot(b,y_hat)+Z*dot(c,y_hat);
 Rz=X*dot(a,z_hat)+Y*dot(b,z_hat)+Z*dot(c,z_hat);
 % Output of Coordinates for each lattice point
 fprintf(1,'\n\nTable 1: Real Space Lattice Coordinates [in units of a])\n');
fprintf(1,'         [Note: The Rz values are ignored for the 2D Case.\n');
for i=1:n2
    for j=1:n1
        fprintf(1,'%d %d %8.5f %8.5f %8.5f\n',i,j,Rx(i,j),Ry(i,j),Rz(i,j));
    end
end
%plotting of coodinates
figure (1)
plot(Rx,Ry,'o')
hold on
xlabel(['Rx [a]'],'fontsize',14,'fontweight','bold','fontname','Thoma');
ylabel(['Ry [a]'],'fontsize',14,'fontweight','bold','fontname','Thoma');
title(['Lattice Space'],'fontsize',14,'fontweight','bold','fontname','Thoma');
%Calculating Reciprocal lattice Points 
%Calculating the coordiante of reciprocal lattice space
volume=dot(a,cross(b,c));
a_recp=2.0*pi*cross(b,c)/volume;
b_recp=2.0*pi*cross(c,a)/volume;
c_recp=2.0*pi*cross(a,b)/volume;
[X,Y,Z]=meshgrid(1:n1,1:n2,1);
Kx=X*dot(a_recp,x_hat)+Y*dot(b_recp,x_hat)+Z*dot(c_recp,x_hat);
Ky=X*dot(a_recp,y_hat)+Y*dot(b_recp,y_hat)+Z*dot(c_recp,y_hat);
Kz=X*dot(a_recp,z_hat)+Y*dot(b_recp,z_hat)+Z*dot(c_recp,z_hat);
figure (2)
hold on
plot(Kx,Ky,'*')
xlabel(['Kx [1/a]'],'fontsize',14,'fontweight','bold','fontname','Tahoma');
ylabel(['Ky [1/a]'],'fontsize',14,'fontweight','bold','fontname','Tahoma');
title(['Reciprocal Lattice Space'],'fontsize',14,'fontweight','bold','fontname','Tahoma');
box on;