It is assumed, though unclear, that neutronium is a harder substance than rodinium since neutronium seems to be impervious to weapons fire while rodinium can be destroyed by Romulan plasma torpedoes. However, according to Spock, rodinium was the hardest substance known to Federation science as of 2266. (TOS: "Balance of Terror") Neutronium was mentioned in 2267 during the confrontation with the Doomsday Machine. So, it is possible that neutronium was first discovered by the Federation sometime between those two incidents.
The term was coined in 1926 for a hypothesized element with the atomic number 0 and currently is used for a hypothesized phase of matter only present in neutron stars. Since 1942, it has been used in various science fiction material to refer to a super-dense alloy or a trans-uranic element on the periodic table.