Now we've learned that liquids are interesting

in that neither the potential energy nor the kinetic energy dominates.

Now a really crucial way to distinguish different liquids

is from a measurement of their pair distribution function.

Now immediately we might ask the question, well how do we calculate it?

The most efficient way to do this

is actually to carry an experimental measurement known as x-ray diffraction.

Now let's consider once again, the same situation,

a collection of n particles in a liquid.

Now to probe distances of the order of one angstrom,

we irradiate the sample with x-rays or neutrons.

Now our discussion here we will assume x-ray scattering.

Now a beam of wavelength lambda illuminates the sample.

The incident beam is coherent, that is all the incoming photons are in phase.

Now due to a difference between the refractive index of the particles and

their surrounding, each particle acts as a scattering center.

Now let's compare the path lengths for

scattering between two different particles.