Thermodynamic investigation of the reduction-distillation process for rare earth metals production

W.D. Judge1 and G. Azimi1,2,*

1Department of Materials Science and Engineering, University of Toronto, 184 College street, Toronto, Ontario M5S3E4 Canada

2Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College street, Toronto, Ontario M5S3E5 Canada

*Correspondence to: Gisele Azimi ()

SUPPLEMENTAL MATERIAL

The Ellingham diagram presented in Fig. S1 reveals the high thermodynamic stability of samarium, europium, thulium, and ytterbium oxides, and outlines some possible contending reductants. For reduction to occur, it is a thermodynamic requirement that the reductant forms an oxide of higher stability than the given rare earth oxide. Fig. S1 provides a valuable notion of stability based on the relative positions of the lines, but it must be borne in mind Ellingham diagrams are constructed based on standard state thermodynamics which are not strictly obeyed during reduction-distillation.

Fig. S1 – Ellingham diagram showing standard Gibbs free energies of formation versus temperature for samarium, europium, thulium, and ytterbium oxides and some possible reductants. Calculated using FactSage 7.0 software [13].

The vapour pressures presented in Fig. S2 reveal the volatile tendency of samarium, europium, thulium, and ytterbium metals. Calcium and magnesium are equally as volatile as the targeted rare earth metals and, therefore, are not suitable reductants. While aluminum is less volatile than the targeted rare earth metals by a few orders of magnitude, it still tends to carryover to the distillate. Zirconium and thorium have low enough vapour pressures, but to utilize them relies on solid-state reactions with unfavourable kinetics. Lanthanum is the preferred reductant because of its low vapour pressure and low melting point. In some cases, vacuum-melted commercial mischmetal is used in place of lanthanum, but some carryover of neodymium may be expected.

Fig. S2 – Vapour pressures versus temperature for pure rare earth metals, reductants, and crucible materials. Calculated from Ref. [9] and FactSage 7.0 software [13]. The vapour pressure of calcium approximately overlaps europium while that of magnesium slightly exceeds ytterbium.

The standard Gibbs free energy change of reactions (1) and (2) were calculated using FactSage 7.0 thermochemical software [13] over the temperature ranges of interest. These data were fitted using nonlinear regression to generate equations of the type

∆GTo=A+BTlogT+CT

logpREo=a+bT-1+clogT

which are presented in Table S1.

The standard Gibbs free energy change of reactions (1) and (2) were combined to determine the standard Gibbs free energy change of reaction (4) which is presented in Table S1. The equilibrium vapour pressures of reaction (4) were calculated from the standard Gibbs free energy change of reaction (4) and are also presented in Table S1.

Table S1 – Calculated standard Gibbs free energy change and equilibrium vapour pressures over reduction-distillation reactions.

RE / Standard Gibbs free energy change (J per mole RE2O3) / Equilibrium vapour pressure (atm) / Temperature range (K)
2La(l) + RE2O3(s) = La2O3(s) + 2RE(l)
Sm / ∆GTo=20 060-43.21Tlog T+137.36T / logpSmo=15.00-11 270 T-1-2.88logT / 1223–1923a
Eu / ∆GTo=-150 730+46.05Tlog T-147.85T / logpEuo=9.96-9 400 T-1-1.36logT / 1223–1723b
Tm / ∆GTo=75 720-43.29Tlog T+140.25T / logpTmo=13.50-12 260 T-1-2.38logT / 1223–1923a
Yb / ∆GTo=7 510-22.62Tlog T+82.12 T / logpYbo=11.51-7 960 T-1-1.92logT / 1223–1723b
2La(l) + RE2O3(s) = La2O3(s) + 2RE(v)
Sm / ∆GTo=451 710+67.00Tlog T-437.05T / logpSm=11.41-11 800 T-1-1.75logT / 1223–1923
Eu / ∆GTo=209 390+98.28Tlog T-529.22T / logpEu=13.82-5 470 T-1-2.57logT / 1223–1723
Tm / ∆GTo=545 160+48.00Tlog T-376.68T / logpTm=9.84-14 240 T-1-1.25logT / 1223–1923
Yb / ∆GTo=312 140+51.02Tlog T-358.76T / logpYb=9.37-8 150 T-1-1.33logT / 1223–1723

aTemperature range includes hypothetical supercooled liquid metal.

bTemperature range includes hypothetical superheated liquid metal.

The maximum theoretical evaporate rates of rare earth elements are given in Table S2. These were determined from the Hertz-Knudsen-Langmuir relation [14] using the equilibrium vapour pressures of the rare earths over the reaction mixtures (pRE) given in Table S1. The higher evaporation rates in Table S2, mainly for europium and ytterbium, cannot be achieved in practice owing to backscattering effects. However, the purpose of the analysis is to show reduction-distillation of europium and ytterbium should proceed without much kinetic hindrance, while for samarium and thulium this is not expected to be the case.

Table S2 – Calculated maximum evaporation rates for reduction-distillation reactions in vacuo.

RE / Maximum evaporation rate (g cm–2 min–1) / Temperature range (K)
Sm / logrevp=15.93-11 800 T-1-2.25logT / 1223–1923
Eu / logrevp=18.34-5 470 T-1-3.07logT / 1223–1723
Tm / logrevp=14.29-14 240 T-1-1.75logT / 1223–1923
Yb / logrevp=13.91-8 150 T-1-1.83logT / 1223–1723