MATLAB: How to add more atoms to FCC structure to look like single unit cell of zincblende

crystalsspheretetrahedronvector

I have
While what I want is
The section of code which adjusts the spheres and their positioning is:
if true
  % function fccgitter = fccgitter(d0,col)
if nargin == 0; 
 d0 = 0; col='r';
end
a = 10;
r = .1;
u = [d0,d0,d0]; 
R1 = [0,0,0]+u;
R2 = [0,0,1]+u;
R3 = [0,1,0]+u;
R4 = [0,1,1]+u;
R5 = [1,0,0]+u;
R6 = [1,0,1]+u;
R7 = [1,1,0]+u;
R8 = [1,1,1]+u;
linie(R1,R2,3,col); hold on;
linie(R1,R3,3,col)
linie(R3,R4,3,col)
linie(R4,R8,3,col)
linie(R8,R7,3,col)
linie(R7,R5,3,col)
linie(R5,R6,3,col)
linie(R6,R8,3,col)
linie(R5,R1,3,col)
linie(R2,R4,3,col)
linie(R2,R6,3,col)
linie(R3,R7,3,col)
linie(R1,R4,2,col); linie(R2,R3,2,col); 
linie(R1,R6,2,col); linie(R2,R5,2,col); 
linie(R1,R7,2,col); linie(R3,R5,2,col); 
linie(R5,R8,2,col); linie(R6,R7,2,col); 
linie(R4,R7,2,col); linie(R3,R8,2,col); 
linie(R2,R8,2,col); linie(R6,R4,2,col);
axis equal;
light('Position',[0 -5 1]);
end
Thanks in advance!

Best Answer

So think about what properties an atom in that structure has, in terms of distance to those other atoms. This is a big part of mathematics.
1. You see a physical problem, where you don't know the answer. (Here, the locations of certain atoms.)
2. Formulate some model for the system. In this case, the model will be in terms of the forces between atoms. The location will be at a stable point of minimal potential energy. For example, suppose potential energy is proportional to the square of the distance between two atoms? Then the total potential energy is given as the sum of squares of the distances.
3. Therefore, to locate an atom, you might choose to find a sphere that passes through each of those neighboring atoms. The center of the sphere is the location of the new atom, since it is equidistant to the connected neighbors.
4. Plot a point for each now located atom.
Ask a question. Formulate a model. Use the model to solve for the unknowns of interest.
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