The Mössbauer effect is the concept that in a solid it is possible for gamma rays to be given off with theoretically no recoil that is always present in a gas. Really it is because the entire solid is acting as a dampener instead of an individual particle creating phonons and so there is essentially no recoil overall. This phenomenon was developed so that it could be used in spectroscopy which was of course named Mössbauer Spectroscopy; which focuses more on the energy changes in nuclei than the shunting about of electrons.
Iron Carbides are compounds containing, unsurprisingly, iron and carbon. But these compounds can take many forms: Fe2C, Fe2C2, Fe3C and many many more. The use of these compounds as catalysts in industry is not affected because as all these chemicals react in close enough to the same way. Chemists would like to know whether they have Fe7C3 or Fe4C but most of these compounds form very similar crystal structures and with the same chemistry it means no chemical method or X-Ray crystallography can determine which are which.
The solution should hopefully be obvious: using Mössbauer Spectroscopy, scientists have been able to develop a method to identify all the iron carbides with incredible accuracy. Using the Mössbauer effect it is also possible to learn about the electron density around the nuclei of the involved atoms and so thermodynamic and magnetic properties can also be predicted along with all the hyperfine structure with extreme precision.