[mycotheologist]

I'm trying to figure out how Braggs law is useful for analysing crystal structures. So heres the equation:
nλ =  2dsinθ
where λ is the wavelength of incident radiation, d is the distance between each layer of atoms in the crystal and θ is the angle of incidence. So to keep things simple lets say I beam some x-rays at the crystal at a 90 degree angle of incidence so we can ignore the sinθ part of the equation. How does this equation tell me anything useful? Lets say I beam any old wavelength through the crystal onto a screen. There'll be a diffraction pattern. What then? How do I tell when I have found a wavelength that is an integer multiple of the distance between the atomic layers?

[AWK]

Start from wikipedia, then use texbook on crystallography

Braggs' law gives you information on diffraction only, but together with difraction symmetry and intensity of difraction reflexions you can obtain the whole information with positions of all atoms in the unit cell of crystal. Almost all general chemistry texbooks contains drawings of rock salt, diamond and graphite structure. These are obtained by difraction of X-rays by the crystals.

[cth]

So to keep things simple lets say I beam some x-rays at the crystal at a 90 degree angle of incidence so we can ignore the sinθ part of the equation.

You can't think it like that: if you place the incident beam perpendicular to a given plane, then different planes are not perpendicular anymore.


When you shine an X-ray beam onto a crystal, light is diffracted in specific directions that are governed by Braggs law. You measure the angles of all the reflections. At that point you know λ, you've measured θ, so you can determine distances between planes. And because the intensity of diffracted light is proportional to the number of electrons each atom has, you can mathematically work out a crystal structure.
That's the general principal. In reality crystals are never perfect and we can't measure the diffracted light phase, making solving crystal structures very tricky.