Diminishing availability of rare earth metals prohibits expansion of traditional and quantum computing and low temperature technologies. So - my question is about artificial synthesis of rare earth metals in nuclear reactors? Can this be done, what is cost of this, are there current efforts to do this and are there fundamental limits that prohibits such synthesis.
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4There are vast quantities of rare earth minerals easily accessible on the Earth's surface (e.g., in Nevada) The problem is the cost and environmental impact of extracting, separating, and refining the rare earth elements. – S. McGrew Feb 05 '19 at 14:58
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1And, those environmental impacts would be dwarfed by those involved in large-scale transmutation of elements into rare earths. – Jon Custer Feb 05 '19 at 15:01
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I am fully aware of the evironmental impact of rare earth extraction that is why I am thinking about alternatives. Nevertheless, even if there are no need for synthesis of rare earth then my question is valid justified by curiosity only. – TomR Feb 05 '19 at 15:01
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I've removed a number of comments that seemed to be veering in a less than useful direction. I think we should simply agree that this is a place for physics and leave it at that. – dmckee --- ex-moderator kitten Feb 06 '19 at 04:46
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1Possible duplicates: https://physics.stackexchange.com/q/183801/44126, https://physics.stackexchange.com/q/109985/44126, https://physics.stackexchange.com/q/452050/44126. Transmutation is expensive. – rob Feb 06 '19 at 13:35
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You need to find the primary material near of what you want to obtain on the table of elements . It must exist a correct transmutation with neutrons available in reactors . Neutrons fluxes are low . Probabilities ( cross sections ) are low . So , it needs many time to transmute . It is impossible to transmute all the primary material : you will obtain just some new atoms in the original matrix . It is impossible to avoid transmuting the material you try to obtain ! For example , I suppose you obtain gold in a thermal reactor : gold is immediatly transmuted in 198Au* which decay in 198Hg .
The only industrial application I see that was working , was neutron transmutation doping of silicon .

Jean Jacques
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There are also rare earths in the fission products, initially mostly in the form of radioactive isotopes. The chemistry of separating those out is nasty and dangerous. – Feb 06 '19 at 07:56