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The method to calculate directions
in a unit cell therefore directions in a crystals
structure will be shown in this video for
vectors in the unit cell. So indicated with arrows the
directions are interested in and we'll go through each of them
determine notations. So we will start off with the
Green Line. So I've indicated x, y and z directions and so
the unit cell in general is going to have
"a", "b" and "c"
indicating the dimension of each
those directions. This is cube of course they're the same
values. That's just looking general case and so
what I am interested in this direction a I'm going to make
this into the arrow the origin and then look at
three axes and what the projection is
on that axis in terms of the unit cell dimensions.
So for the x-axis were at the origin so
that would be zero. For the y-axis
were 1/2 of the dimension "b" so from
here to here that distances is "b". So this is 1/2
of "b" and for the z-axis
we're projection is one of "c"
dimension in the z-direction. So then to create
So this is 0 times "a". We first say
0, 1/2 and 1 removing "a", "b" and "c"
we then make them all integers so 0, 1 and 2
and then our direction would be
0, 1 to 2. So just the x, y and z
vector projections. So this is the direction for
"a" the Green Line. So we can look at
additional curve and do the same thing
so for "b" gonna make this the origin
and we're going to look at the x-axis the y and the z-axes
for the x-axis we are going in a positive direction
So positive is this way on the x-axis. 1/2
of "a". We are starting here we're going to here so
the projection 1/2 of "a". The y-axis is also
one excuse me. The y-axis however
its negative alright and its entire
projection would be entire unit cell
length "b" so this is one times "b" and then the z
axes is 1/2 and the dimension
in z-direction the unit cell c
so again 1/2, 1 and 1/2
making them all integers 1, 2
1 but sorry left of this is minus
and so now I have the unit cell
direction from the unit cell but I don't write -2
instead I write 2 with the minus sign so
for line "b" this is the direction.
For lines c we'll pick this is the origin
and look at "a" we're going negative and projection it's minus
one x-direction times "a"
y direction it's positive one
and "b" dimension and z
this the origin and z is 0 time "c".
-1, 1, 0 direction we put the minus sign here
so this is the direction and this is for lines
"c" or direction "c" in the unit cell
and finally look at "d" where "d" is starting
here so here's our origin now this
is hitting the face so it's hitting this face in the center
sorry x-direction is halfway. 1/2
of "a". The y-direction his one-time
"b" and the z direction is 1/2 times "c"
so the 1/2, 1, 1/2
numbers making the miniatures 1, 2
1 Sp 1, 2, 1 is direction
four "d". So line "d" with the arrow pointing this way
has this notation for each direction