The angular dependence of neutral potassium emission in the form of ground-state atoms as well as Rydberg species is studied from a fused iron catalyst. The catalyst is of the type used for ammonia synthesis in so-called pre-reduced (metallic) condition. The angular distributions observed by surface ionization detection have a more peaked shape than the cosine distribution expected for thermal equilibrium. In the case of a catalyst sample used in the industrial process even a sharp peak on top of a cosine distribution is found. Using detection by field ionization, i.e. detection of Rydberg species only, a rather sharp lobe in the normal direction is found. A theoretical description of cluster formation outside the sample surface from atoms with velocity distributions characteristic for thermal equilibrium is used to interpret the results. The cluster formation is probably due to the long-range interaction between the Rydberg atoms formed on the surface, and the clusters are at least partially formed in an excited state. The cluster sizes contributing to the distributions are estimated from fits to the experimental results. The main cluster size observed with surface ionization detection is concluded to be quite small, containing just a few atoms. There also exist contributions of larger clusters of the size around 10–30 atoms in the case of the pre-reduced catalyst. The used catalyst also gives mainly small clusters, but it does not give clusters of the size 10–30 atoms. Both types of catalyst also give a small number, less than 5%, of very large clusters, with more than 100 atoms according to the model. The field ionization data for the pre-reduced catalyst are well matched by a single cluster size of approximately 30 atoms, which indicates that such clusters have a longer lifetime in the initial excited state than the small clusters.