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PROFESSOR CIMA: So now that we've created this monochromatic beam of
intense X-rays-- oh, one of the things I'd like to mention here is how do I
make this even more intense? Anybody have any idea?
So for a given setup here, I've got that spectrum, and I'll
measure some intensity. And obviously, I want to pick just this--
what is it? 1.54 angstroms, right?
That's the wavelength for copper K_alpha. But how do I make it more intense?
STUDENT: Increase the currents? PROFESSOR CIMA: Absolutely.
That's what it is. So if I crank this up--
not just the voltage, but I put a power supply here that can put in more
current, then everything will grow here. The bremsstrahlung will grow, all these will
grow in intensity. And in fact, for a real X-ray tube where you're
really trying to do this to make very intense X-rays, you have to worry
about melting the anode. I mean, it's like a welder.
It's an arc discharge, and it could literally make a pool
of copper in there. So what they do have to do--
since a lot of you are engineers in here-- is you have to run cooling water through here.
And not only that, you have to rotate this so that you don't put so much
energy into one spot you melt it. So it's actually rotating and it's called
a rotating anode tube. So they end up being rather expensive because
this is all high vacuum, you've got water going in here, and that's
spinning at high speed. Just an engineering aside there.
Now, what do we do with this monochromatic X-ray beam?
If you'll allow me, I'm going to take that beam that's coming out there at
44.4 degrees and I'm going to have it go this way just to simplify my--
but now, instead of being this white light meaning a lot of different
wavelengths, it's only a single wavelength. And what we're going to use this for is to
look-- interrogate a sample composed of many crystals.
And in my example here, I'm going to assume these crystals are truly--
they're all the same material, but they're truly randomly oriented.
There's no preferred orientation. And so this type of an experiment is called
powder-- because these are small crystals--
powder diffraction. Now, this is kind of an interesting thing
because remember up here, we had a situation, we had sort of this white radiation.
Here, we have monochromatic radiation. But instead of having a single crystal, we've
got sort of random orientation or this is probably not technically
correct, but this is sort of a white orientation of crystals.
They're randomly oriented. So if I go out here--
so here's theta and here's two theta-- I'd have this whole set up on what's called
the goniometer. And all that means is that I can very simply
rotate this powder and this detector up here so that the plane of the
powder is here and the detector is at twice this angle.
And then I ask, what do you think happens? We know that if this is an FCC material in
here, you're just going to have--
if it were a single crystal, you'd only have reflections for 1, 1, 1.
What's the next one? 2, 0, 0, right?
They can either be-- what's the rule for FCC?
All odd or all even. And I just do the first few.
2, 0, 2, and 3, 1, 1. And in fact, in my example, I have it, it's
polycrystalline nickel. So we calculated the lattice constant.
So I can go through here and say with confidence that the only reflections,
the only diffraction from each one of these crystals that you'll get is ones
from these planes. Now, if I have my slip at the calculated angles--
let's say this is for a single crystal.
So this is 22.23 degrees. Theta is that.
So I'll just do it over here. That's 44.4 degrees, two theta.
51.8 degrees, two theta. 76.4 degrees, two theta.
And 92.8 degrees for 3, 1, 1. Bless you.
So that means when this radiation comes in and it interacts
at an angle of 44.4-- or it'll come in here and diffract off the
1, 1, 1 planes at an angle of 44.4 degrees.
And in general, since this crystal is randomly oriented, it
will go off like that. I'll just pick one.
Let's say that one is such that 44.4 degrees two theta is up over here.
So you're not going to see it. This detector's not going to-- this is the
detector-- is not going to see it.
If, however, I have this set up at 44.4 degrees and I have a million of
these crystals in there, what do you think the chances are that there is
one that is oriented so that you get X-rays coming out
that slip, 44.4 degrees? Well, it's probably pretty good.
Let's say this one lights up. I've got one.
Now, if I go to 45 degrees, will there be any that diffract
into that 45 degrees? No, because you don't get diffraction--
you only get diffraction at these angles. So as you move this detector, you see nothing,
nothing, nothing, boom. 44.4 degrees, 51.8 degrees, blah, blah, blah.
You see what I'm saying? So a powder diffraction pattern, if you plot
two theta here, and intensity--
so use monochromatic X-rays, you'll get the peaks for --
that you'd expect. This one being 1-1-1, 2-0-0, 2-0-2, and I
guess I left one off-- 3, 1, 1.
And so it's kind of interesting, we took this monochromatic X-rays and
used a white distribution, a random distribution of crystals, to get this
diffraction pattern. And of course, if they're not random, these
intensities will vary. So Professor Ballinger may not be here today--
we were talking afterwards about the concept of pole figures.
If, however, these are all oriented so that only the 2, 0, 0 planes are
parallel to the surface, you won't see any of the 1, 1, 1 reflections.
You won't see any of the 2, 0, 2 reflections. So you can actually use this measurement to
determine whether there's any preferred orientation into the
pattern.