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PROFESSOR CIMA: What do we mean by a plane? Well, I'll do one over here.
Sometimes I'll get this looking right and sometimes I won't.
But let's look at the (111) plane. I'll describe what this is here.
A plane will connect three points, like I've drawn there.
So here is just one of many different planes I could draw.
So I have to connect three points to define a plane.
In describing a particular plane in a crystal, and you'd like to share it
with somebody, that we have a mathematical formalism to describe a
given plane. And it's based on the three points as being
intercepts on the various axes. I should label this an x, y, and z.
We call these, the description of a plane, Miller indices.
And they usually have an (hkl) listed as h, k, and l.
So what we do to determine the Miller indices for any plane that we have a
picture of, you find the intercepts of the axes x, y, and z. You determine the reciprocals of those intercepts.
And then just like we did, where'd I do it, up here.
You get rid of any fractions. Now let's do some examples.
Well, this one's easy right? We have it right here.
The intercepts-- Maybe I'll do it this way.
So x, y, z. I'll just list intercepts.
In each case it's 1 in this particular plane. We take the reciprocals.
So that's 1 over 1, 1 over 1, 1 over 1, or 1, 1, 1.
So this case, we don't have any fractions. So we don't have to worry about the last step.
So when we describe a plane, now we put the normal paren: (111).