Bands in the fcc

> restart;

> with(linalg):

Warning, new definition for norm

Warning, new definition for trace

> a1:=vector([1/2,1/2,0]);

> a2:=vector([0,1/2,1/2]);

> a3:=vector([1/2,0,1/2]);

> cellvolume:=dotprod(a1,crossprod(a2,a3));

Reciprocal lattice vectors, without the factor . Use evalm to get a pretty output

> b1:=evalm(crossprod(a2,a3)/cellvolume);

> b2:=evalm(crossprod(a3,a1)/cellvolume);

> b3:=evalm(crossprod(a1,a2)/cellvolume);

First shell:

> G[1]:=b1; G[2]:=b2; G[3]:= b3; G[4]:=vector([1,1,1]);
for i from 1 to 4 do G[i+4]:=-G[i] od;

Second shell

> G[9]:=vector([2,0,0]); G[10]:=vector([0,2,0]); G[11]:=vector([0,0,2]);
G[12]:=-G[9]; G[13]:=-G[10]; G[14]:=-G[11];

> assume(x,real): assume(y,real): assume(z,real):

Empty lattice bands in the x direction

> y:=0; z:=0;

> E[0]:=x^2+y^2+z^2;

> for i from 1 to 14 do E[i]:=dotprod((vector([x,y,z])-G[i]),(vector([x,y,z])-G[i])) od;

> EmptyBands:=[E[n] $n=0..14];

To avoid possible printer problems, select Options, Plot Display, Window

> plot(EmptyBands,x=-1..1,color=[black,red,red]);