Centrifugation of cinnabar, powellite and wulfenite

For powellite and wulfenite, I think at least electrolysis is more reasonable than centrifugation. After all, they are compounds rather than mixtures.
I did find some information about how they process, although not many people studied them because their reserves are far less than molybdenite and smelting difficulties (the same is true in the game, they are only generated in bedrock veins and molybdenum veins at the end, and the generation probability is far less than molybdenite).

As an element of the same group as tungsten, the smelting of molybdate minerals is similar to that of tungstate. However, for gt6, molybdenum is not as important as tungsten (unless you really intend to use high-speed steel as an important material in the later stage rather than manufacturing high-performance tools like gt5u), so it is not necessary to add complex processing like tungsten.

For wulfenite, there are two main leaching methods: sodium hydroxide leaching and sodium sulfide leaching to separate molybdenum and lead. In addition, some people have been studying other leaching methods in recent years, but it seems that they have not been applied on a large scale:

Sodium Hydroxide process:
PbMoO4+2NaOH=Na2MoO4+Pb(OH)2

Lead hydroxide forms precipitates and separates from the solution. However, it should be noted that if excessive alkali is added, sodium plumbite will be produced and lead will be re dissolved. This is also the biggest disadvantage of sodium hydroxide method.

Sodium Sulfide process:
PbMoO4+Na2S=Na2MoO4+PbS
Lead forms lead sulfide precipitation and is separated from the solution. The main advantage of this method is that it can reduce the possible residual lead. The disadvantage is that it requires a relatively high leaching temperature, and excessive sodium sulfide will produce sodium thiomolybdate, which increases the difficulty of subsequent treatment.
Sodium molybdate solution needs to be purified by removing impurities for many times (it is pure by default in the game, so it is not necessary), and then hydrochloric acid is added to form molybdic acid precipitation. In reality, there are impurities in the crude molybdic acid, Ammonia needs to be added to form Ammonium heptamolybdatefor recrystallization and purification (molybdate is troublesome, and it is easy to form heteropoly acid according to the pH, resulting in huge molecular weight and difficult to balance, so this step can be omitted in the game, just like tungsten), and ammonium paramolybdate is heated to decompose into molybdenum trioxide (in some places, acid is added again to form refined molybdic acid, and then heated and dried to form molybdenum trioxide). Finally, like tungsten, And reduced to molybdenum with hydrogen.
Na2MoO4+2HCl=H2MoO4+2NaCl
H2MoO4=heat=MoO3+H2O
MoO3+3H2=Mo+3H2O

As for powellite, because it is too rare, it is almost impossible to find information about how it is processed (most of the information found is collected by minerals…). Fortunately, I have found some information about recovering calcium molybdate from waste liquid containing molybdenum and then treating it into molybdenum trioxide, which should be used as a reference.

The data shows that calcium molybdate can be directly decomposed into calcium chloride and molybdic acid by hydrochloric acid, just like scheelite. There is no need to worry about this. Some places still have to go through ammonium heptamolybdate (really annoying), because impurities and excessive hydrochloric acid may produce molybdenum chloride (but there is no need to worry in the game).
Ca2MoO4+2HCl=H2MoO4+CaCl2

Of course, if you think these are too troublesome, put them directly into the electrolyzer. Anyway, molybdenum is not very important.

Note: molybdenum is a possible option (though not common) in the process of upgrading the crucible. Pay attention to the possible consequences.

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