Elementcollector1,
This is an interesting but difficult task you’ve set for yourself. From your previous experiments, during which you obtained a purple solution after dissolving your magnet, I suspect that the reason you had a purple solution was that you started with an alloy which consisted of cobalt and neodymium, at least in the main part. Many of the salts of both these elements are purple. The dark green ingredient to which you allude is likely iron (probably a mixture of FeII and FeIII) rather than Praseodymium, as the latter is, from my experience, definitely light green, although you could possibly have praseodymium in there as well as iron.
As for separation using the diffential solubilities of Fe and Nd hydroxides, I’m afraid that’s impractical, as they’re both extremely insoluble and the quantities you’d likely get would be so small as to make recovery very difficult if not impossibe for the amateur chemist using the resources we have available to us.
I looked into producing some simple representitive compounds of neodymium and praseodymium a while back, as I’m a keen element collector and amateur metallurgist, and decided that the chlorides would be way to hygroscopic to be useful. I settled on sulphates/ sulfates, and succeeded in producing some decent crystals stable in humidities of at least 90%. To produce large crystals (~ 1mm)relatively free of basic sulfate, ie Nd/Pr(OH)SO4, however, you need to begin with more metal than will dissolve in the H2SO4 and remain in solution; in other words, you have to exceed the solubility of (Nd/Pr)2(SO4)3 in sulfuric acid, wait intil you have a decent amount of crystals but still have a very acidic solution, then decant off the solution, leaving the crystals, which you will have to dry by tissue paper. You will then need to neutralise any acid you have on your tissue and anywhere else, of course. In the case of neodymium, if you rely on evaporation from a solution of weak acid, then your precipitate will turn orange, because you have produced Nd(OH)SO4.
I started with Neodymium and Praseodymium metals, and I know you’re actually aiming to end up with what I started with, but some of the things I learned may be of use to you. You have almost certainly encountered some of the compounds I did, but for different reasons. Turning these into Nd metal will be very difficult, though, and you may have to settle with a representitive compound. All this needs to be done, of course, with gloves, specs and other protective equipment, an outdoors if you’re going to do any heating, and always have plenty of sodium bicarbonate on hand to soak up and neutralise any acid spills.