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This short video I am going to show how
we plot direction in hexagonal close-packed structure
So I have shown the structure.
I have labeled the axes a1 a2
a3 and z. So 1
minus 1. So this corresponds to -1
this is the a1 the a2
the a3 and the z directions.
So if we were one unit distance in
a1 and -1 in a2
so this would be to -1 then the combined
of those two vectors in this plane is perpendicular to the
a3 direction and so therefore a3 is 0 and indeed a1 plus a2
equals a3 in general
and we have now one in the z-direction
I have shown the a1 the a2 and here's the
z-direction vector and then the direction is just the combination of
these three
which is this purple vector so the combination
of this direction plus this direction
is a vector and at an angle inside the
hexagonal structure. This correspondent to the 1,
-1, 0,1 direction
remember this is in a hexagonal close-packed unit cell