That involves things like solubility, phase diagrams,and metal-carbon bonds .If you look at a good equilibrium diagram of iron-carbon you will see a line just on the left of the diagram which shows solubility limits of carbon in iron.To the left of the line the iron is in solution and to the right of the line more carbon forms carbides.So each metal has solubility limits in iron.
The attraction of different metals to carbon is different. The weakest bond is with iron followed by chromium .These also are softer more easily ground carbides and the reason that so many tool steels are based on chromium.Some of the other carbides have very strong bonds such as vanadium, tungsten and molybdenum. These are much harder carbides as those who use S30V have found when grinding or polishing. These carbides also resist dissolving into austenite when heat treating .Thus an understanding necessary when HT'ing of the need for longer soak times and higher temperatures.
While vanadium is good to resist grain growth, only about .25% is needed. Additional amounts form carbides.
Another interesting feature of V,Mo, W is the formation of additional , different carbides at high temperature [ ~1000 F] tempering called secondary hardening.
