Question: Hi George, I think you mentioned K-space in the chat, sounds interesting but no idea what it is : )

George Fulton answered on 7 Mar 2019:

Great question! K space is used a lot in Physics and it has other names such as momentum space or reciprocal space. K space is important for materials scientists as it is what we are looking at when we observe a diffraction pattern in a transmission electron microscope. But what is a diffraction pattern?I

Diffraction is is a fundamental property that waves such as water have. For example, if a water wave passes through a gap, the wave act to bends and bow outwards. If you added two waves and two slits next to one another, then the diffracted waves interfer with one another and generate a new wave. If we were able to take a slice of this wave and observe how high and low the wave was across this slice, then we would be able to see the diffraction pattern. Often this pattern might look like dark and bright fringes. The actual diffraction pattern depends on the spacing of the slits and the wavelength of the waves. Now what does this have to do with electron microscopes!

In an electron microscope, the electrons are the waves (wave-particle duality!) and the gaps between atoms are the slits. This time the slits act in both directions so the slits are now like holes. Therefore, instead of the diffraction pattern being like fringes, the diffraction patterns of materials are seen as lots of spots. These spots have a particular shape and spacing and this tells us about the atomic spacing! It turns out that the spacing of these points is related to 1/(atomic spacing). So we call it reciprocal space. This isn’t normal space but reciprocal space (k space). If the slits are really close to one another, then the seperation in a diffraction pattern is large, while if the slits are really far from one another, then the spots are really close.

Now there is also another way to look at it, but it’s more complicated (but is most elegant way).
It is sometimes called k space because k is the term scientists use to call momentum. A diffraction pattern only shows spots which correspond to certain momentums. If their momentums don’t satisfy a criteria, then they appear as black on the diffraction pattern. So, in k space, we are just looking at all the scattered waves which can pass the material, the momentums required are just given by the size and spacing of the slits. So the momentum of the scattered waves encodes the information about the material.

Sorry if this answer was difficult to understand. K space is not an easy topic!