1. A method for extracting rare-earth (RE) oxide constituents from a
feedstock containing RE silicates and non-RE contaminants, the method
comprising:
leaching the REs from the feedstock into an acid to form an acid solution;
performing an oxalate precipitation on the acid solution to form an RE oxalate hydrate;
separating the RE oxalate hydrate from the acid solution; and
heat treating the RE oxalate hydrate to form an RE oxide containing the RE elements extracted from the feedstock.
2. The method of claim 1, where separating the RE oxalate hydrate from the acid solution comprises filtering and washing the RE oxalate hydrate.
3. The method of claim 1, further comprising performing a sulfate precipitation on the acid solution and separating the sulfate precipitates from the acid solution prior to performing the oxalate precipitation.
4. The method of claim 1, wherein the feedstock comprises at least one of Yttrium (Y) or Ytterbium (Yb) in the form of at least one of RE2Si2O7 (REDS) or RE2SiO5 (REMS), and the leaching comprises treatment with hydrochloric (HCl) acid, resulting in a residue of substantially Silicon dioxide (SiO2).
5. The method of claim 1, wherein the EBC comprises at least one of Yttrium (Y) or Ytterbium (Yb) in the form of at least one of REDS or REMS, and further performing sulfate precipitation in the acid solution, wherein the sulfate precipitation comprises adding one of Na2SO4 or (NH4)2SO4 to the acid solution to form a precipitate and separating the precipitate from the acid solution prior to oxalate precipitation, wherein the precipitate contains at least one of alkaline earth metals or alkali metals.

6. The method of claim 5, wherein the precipitate is (Ba,Sr)SO4.
7. The method of claim 6, further comprising removing the (Ba,Sr)SO4 precipitate by filtration.
8. The method of claim 1, wherein the EBC comprises at least one of Yttrium (Y) or Ytterbium (Yb) in the form of at least one of REDS or REMS, and performing the oxalate precipitation on the acid solution, wherein performing the oxalate precipitation on the acid solution comprises adding oxalic acid as a solid or in aqueous solution so as to form a RE oxalate hydrate precipitate.
9. The method of claim 8, wherein the oxalic acid solution is added at room temperature while stirring and further comprising washing of the RE oxalate hydrate with water after a first filtration, and thereafter performing a second filtration.
10. The method of claim 1, wherein the feedstock comprises at least one of REDS or REMS and at least one of (Ba,Sr)Si2Al2O8 (BSAS) or Si, and wherein at least one of the Si, Ba, Sr, or Al are removed from the non-deposited feedstock powder.
11. The method of claim 1, wherein the feedstock comprises Yttrium (Y) and Ytterbium (Yb) in the form of YbYDS, and the RE elements extracted from the feedstock comprise a mixed (Yb,Y)2O3.
12. The method of claim 1, wherein the feedstock comprises at least one of Yttrium (Y) or Ytterbium (Yb) in the form of REDS and having at least one of the Y or Yb extracted and recovered therefrom at greater than about 90% yield with each of a plurality of contaminants reduced to less than 100 ppm.
13. The method of claim 1, wherein performing the oxalate precipitation on the acid solution forms RE2(C2O4)3 nH2O.

14. A method for extracting rare-earth (RE) oxide constituents from a
feedstock containing RE silicates, the method comprising:
leaching the REs from the feedstock into an acid to form an acid solution by treatment of the feedstock with hydrochloric acid;
performing an oxalate precipitation on the acid solution to form an RE oxalate hydrate by treatment with oxalic acid;
separating the RE oxalate hydrate from the acid solution; and
heat treating the RE oxalate hydrate to form an RE oxide having the RE elements extracted from the feedstock, wherein the heat treating includes drying and calcining the RE oxalate hydrate.
15. The method of claim 14, wherein separating the RE oxalate hydrate from the acid solution further comprises filtering and washing the RE oxalate hydrate.
16. The method of claim 14, wherein the feedstock comprises at least one of Yttrium (Y) or Ytterbium (Yb) in the form of at least one of REDS or REMS, and further comprising performing a sulfate precipitation on the acid solution that includes dissolving at least one of Na2SO4, (NH4)2SO4, or H2SO4 in the acid solution to form a sulfate precipitate, and further comprising removing the sulfate precipitate by filtration.
17. The method of claim 14, wherein the feedstock comprises at least one of Yttrium (Y) or Ytterbium (Yb) in the form of at least one of REDS or REMS, and performing the oxalate precipitation on the acid solution is performed after performing a sulfate precipitation on the acid solution.
18. The method of claim 14, wherein the oxalic acid solution is added at room temperature and further comprising stirring the RE oxalate, followed by filtration and washing with water.
19. The method of claim 14, wherein the feedstock is a non-deposited feedstock powder including at least one of (Y,Yb)2Si2O7 (YbYDS) or Y2SiO5

(YMS), and at least one of (Ba,Sr)Si2Al2O8 (BSAS) or Si, and wherein the Si, Ba, Sr and Al contaminants are removed to yield a substantially pure RE oxide.
20. A system for rare-earth (RE) element collection and recovery, the
system comprising:
an environmental barrier coating (EBC) fabrication and application system for applying an EBC to an object, the EBC applied as feedstock powder, wherein at least some of the feedstock powder does not deposit on the object and mixes with contaminants; and
a collection and recovery system for chemically extracting the RE elements from the non-deposited powder, the collection and recovery system configured to leach the REs from the non-deposited powder into an acid to form an acid solution, perform an oxalate precipitation on the acid solution to form an RE oxalate hydrate, separate the RE oxalate hydrate from the acid solution, and heat treat the RE oxalate hydrate to form an RE oxide having the RE constituents extracted from the non-deposited powder.
21. The system of claim 20, wherein the EBC comprises Yttrium (Y)
and Ytterbium (Yb) in the form of YbYDS, and the collection and recovery
system is further configured to extract RE elements from the EBC as a mixed
(Y,Yb)2O3.