Mythbusters
- 5
- 0
I have three primitive vectors a1,a2,a3 for the body-centered cubic (bcc) Bravais can be chosen as
a1=ax
a2=ay
a3=(a/2)(x+y+z)
or, for instance, as
b1=(a/2)(y+z-x)
b2=(a/2)(z+x-y)
b3=(a/2)(x+y-z)
where x,y,z are unit vectors.
Now I should show that any vector of the form
R=n1a1+n2a2+n3a3
where n1,n2,n3 are integers
can be presented as
R=m1b1+m2b2+m3b3
where m1,m2,m3 are integers
Do anyone have an idea how I can do this?
Does it help me if I construct reciprocal lattice?
//
Mythbusters - "Well, here's your problem"
a1=ax
a2=ay
a3=(a/2)(x+y+z)
or, for instance, as
b1=(a/2)(y+z-x)
b2=(a/2)(z+x-y)
b3=(a/2)(x+y-z)
where x,y,z are unit vectors.
Now I should show that any vector of the form
R=n1a1+n2a2+n3a3
where n1,n2,n3 are integers
can be presented as
R=m1b1+m2b2+m3b3
where m1,m2,m3 are integers
Do anyone have an idea how I can do this?
Does it help me if I construct reciprocal lattice?
//
Mythbusters - "Well, here's your problem"
… 
