minerals

Article
Predicting the Logarithmic Distribution Factors for
Coprecipitation into an Organic Salt: Selection of
Rare Earths into a Mixed Oxalate
Harry Watts 1,2, * and Yee-Kwong Leong 1
1 Department of Chemical Engineering, University of Western Australia, Crawley, WA 6009, Australia;
yeekwong.leong@uwa.edu.au
2 Watts & Fisher Pty Ltd., Crawley, WA 6009, Australia
* Correspondence: harry@wattsandfisher.com




Received: 30 June 2020; Accepted: 6 August 2020; Published: 12 August 2020


Abstract: Thermodynamic modelling of a leaching system that involves concurrent precipitation

depends on an understanding of how the metals distribute into the precipitate before an assessment of
solubility can be made. It has been suggested in the past that a pair of rare earths (A and B) in solution
will separate from each other by oxalate precipitation according to a logarithmic distribution coefficient
(λ), determined by the kinetics of the precipitation. By contrast, the present study hypothesises that λ
may be approximated from thermodynamic terms, including the solubility product (KSp ) of each
rare earth oxalate and the stability constant (β1 ) for the mono-oxalato complex of each rare earth.
The proposed model was used to calculate λ between pairs of rare earths. An experimental study
was conducted to determine λ between selected pairs using homogenous precipitation through the
hydrolysis of an oxalic acid ester, with fairly close agreement to the values under the proposed model.
Though this model requires more thorough testing, as well as application to other organic salts, it may
provide insight into distribution factors of a precipitate formed by a sequence of organic complexes.

Keywords: rare earths; distribution factor; selective precipitation; oxalates; organic complexes

1. Introduction
In rare earth extraction, a common technique for overcoming the poor solubility of rare earth
minerals is to transfer the rare earth ions into a more stable solid. In sulfuric acid cracking, for example,
the rare earths are transferred into solid sulphates. In caustic conversion, the rare earths are put
into hydroxides. In more recent studies, minerals of rare earth phosphates have been dissolved in
oxalic acid, while the rare earths concurrently precipitate as rare earth oxalates [1,2]. In each of these
techniques, an effective transfer of the rare earths depends on each rare earth having a lower solubility
or a higher stability in the destination compound.
The way that rare earths distribute into an oxalate precipitate has not been modelled, beyond
describing the results of specific experimental conditions. This is despite oxalate coprecipitation being
a common technique in a broad range of areas. Oxalate coprecipitation is a standard method for
producing precursor powders that are calcined into mixed metal oxides. Examples in the literature
abound, such as precursors for magnetic materials [3], piezoelectric oxides [4], superconducting
materials [5,6] and alloys [7]. It is also used to separate rare earths and actinides from other ions in
solution by precipitation. Breakdown of rare earth minerals such as monazite are often done in extreme
conditions [8] that dissolve impurity ions along with the rare earths. The very low solubility of rare
earth and actinide oxalates enables an isolation of rare earths from mixed solutions [9].
The most advanced modelling of oxalate co-precipitation appears to have come from experiments
to separate rare earths from each other in controlled precipitation. Oxalic acid was generated

Minerals 2020, 10, 712; doi:10.3390/min10080712 www.mdpi.com/journal/minerals

Minerals 2020, 10, 712 2 of 9

homogeneously throughout the solution by hydrolysis of dimethyl oxalate, in order to minimize

concentration gradients within the solution and allow separations closer to those predicted by
solubility [10]. Feibush, Rowley and Gordon [11] found, however, that the separations were much
lower than predicted, according to solubility for the rare earths tested in their study. There remained no
method to predict the separation from fundamental terms, and the techniques for oxalate coprecipitation
more generally appear to be based on trial and error.
Feibush, Rowley and Gordon [11] did find that the precipitation between pairs of rare earth
oxalates follows a Doerner–Hoskins or logarithmic distribution coefficient. Such a distribution assumes
that the precipitating solid does not re-order its whole self to be in equilibrium with the solution;
rather, the precipitated surface is in equilibrium with the solution and once precipitated it forms an
unchanging substrate for the next surface layer [12]. Doerner and Hoskins were the first to describe
this running equilibrium mathematically [13]. It can be described between concentrations of rare earth
ions [A] and [B] by Equation (1).
d[A] [A]
=λ (1)
d[B] [B]
d[A]
Here, d[B] is the ratio of the concentration of A to B lost from the solution in an infinitesimal
increment, or, in other words, precipitated onto the surface in an infinitesimal increment. The letter λ
signifies the logarithmic distribution coefficient. This expression can be integrated to give Equation (2).

[A] f inal [B] f inal

ln = λln (2)
[A] initial [B] initial

Doerner and Hoskins [13] did not attempt to correlate the coefficient to fundamental terms,
probably in the knowledge that different salts may be governed by different terms. Feibush, Rowley
and Gordon [11] suggested that with rare earth oxalates, the coefficient should be the ratio between the
square roots of the solubility products of the pure rare earth oxalates (square root because each unit of
rare earth oxalate has two rare earth ions), as shown in Equation (3).
p
KSp, A
λ p (3)
KSp, B

This equation is based on KSp, A , as the solubility product for the equation shown in Equation (4).

A2 (C2 O4 )3 → 2A3+ + 3C2 O4 2− (4)

Their experiments, however, showed that the experimental values of the coefficients, while being
logarithmic in nature, were far from what was predicted by solubility in the form of Equation (3).
Equation (3) does not form a basis in the present study for further development of a model.
Some more recent work on the solubility of rare earth oxalates has determined that the saturated
concentration of rare earth A in a solution of concentrated oxalic acid is determined by Equation (5) [14].

KSp, A β1,A 
p p
KSp, A  −3/2 −1/2
[Atotal ] = aC2 O4 2− + aC2 O4 2− (5)
γ3 γ1

In Equation (5), β1,A is the equilibrium constant for the reaction in Equation (6), with the subscript
number denoting the number of oxalates in the complex formed. The expression for β1,A is shown in
Equation (7), where a is the activity of the species denoted as subscript. The symbol γ1 is the activity
co-efficient for the rare earth mono-oxalato complex, and γ3 is the activity co-efficient for the free rare
earth ion, the subscript based on the magnitude of the charge.

A3+ + C2 O4 2− → AC2 O4 1+ (6)

Minerals 2020, 10, 712 3 of 9

aAC2 O4 1+
β1,A = (7)
aA3+ aC2 O4 2−
It can be seen in Equation (5) that the total concentration of rare earth A is made up of two main
species, the free or weakly-complexed rare earth ion in the first term, and the mono-oxalato complex in
the second term. In one sense, Equation (5) represents the saturated concentrations of each of these
species in the particular system. The challenge from a theoretical point of view is how a model of
precipitation can be constructed if there are complexes present. For example, the precipitate may be
formed from a sequence of complexation reactions, where the mono-oxalato complex is the precursor
to the precipitate, rather than the free rare earth ion.

2. Materials and Methods

Rare earth oxides at a minimum of 99.9% purity were obtained from Treibacher Industries
in Austria, along with certificates of assay. Dimethyl oxalate (99%) was obtained from Alfa Aesar,
and diethyl oxalate (99%) from Sigma Aldrich. Analytical grade hydrochloric acid was used. Brand-new
Duran 100 mL conical flasks were used for each experimental flask.
The method underwent considerable development. In the original method, each conical flask
was initially weighed. To each conical flask was added at least two, but up to six, rare earth oxides.
The amount of each rare earth oxide added was determined by a random number generator in Microsoft
Excel, to be an amount between 0.00 and 0.10 g. As close to this number as possible was weighed
and added to the flask. Hydrochloric acid was then added to dissolve the rare earth oxides into
chlorides until a clear solution was obtained. The flask was then heated on a hotplate to evaporate
the remaining hydrochloric acid and water, and leave a precipitate of rare earth chlorides. To the
flask was added about 100 g of deionized water. The mass of dimethyl oxalate (DMO) required for
a complete precipitation was calculated, and a fraction of this was chosen at random, weighed and
added to the flask. The solution was swirled until all the dimethyl oxalate was dissolved. This also
had the effect of dissolving any residual rare earth particles (either difficult crystals of chlorides or
hydroxides). A stopper was placed in the opening of the flask. The flask was submerged in a water
bath at 25 ◦ C and left for a week. One week was chosen based on informal testing—after about four
days, the solution could be decanted into another vessel without further precipitation. A sample of the
solution was taken by pipette and diluted with hydrochloric acid (0.1 M), for analysis by ICP-AES.
The density of the solution was checked to be 1 g/mL.
This method produced internally consistent results between yttrium, erbium and thulium.
However, in the case of lanthanum or neodymium, the initial stages of the precipitation proceeded
without the involvement of one or more of the elements. To minimize the impact of this initial
precipitation, a higher initial concentration of rare earths was used so that the final concentration
covered a greater range of concentration. Also, to minimize errors of measurement of the initial
solution, a stock solution was prepared for use in every conical flask. To allow a slower, more gradual
precipitation, diethyl oxalate (DEO) was chosen as the oxalic acid ester. This appears to have a slower
rate of hydrolysis than dimethyl oxalate.
About 5 g of each of lanthanum, neodymium and yttrium oxides were dissolved together in the
one flask in hydrochloric acid, and evaporated to rare earth chlorides. Deionized water and 1 mL
of hydrochloric acid (10 M) was added to a total of 1000 g. The 1 mL of hydrochloric acid was to
dissolve any rare earth hydroxides that may be present. The pH was not measured, since the acidity
during the experiment increases as more of the oxalic acid ester hydrolyses, so that a constant pH
could not be maintained without the use of a buffer that may complex the rare earth ions. To each
100 mL conical flask was added to about 100 g of rare earth solution and a weighed amount of diethyl
oxalate solution. The diethyl oxalate was added by a glass dropper, as diethyl oxalate can be a solvent
of plastic. A sample of the solution was taken by pipette and diluted with hydrochloric acid (0.1 M) for
analysis by ICP-AES. The density of the solution was checked to be 1 g/mL.
Minerals 2020, 10, 712 4 of 9

It was decided to plot the results between two rare earths from every experimental vessel on
the one graph. The graph was based on Equation (2), so that the logarithm of the quotient of the
starting concentration and final concentration was plotted on an axis for one element, while the same
was plotted on the other axis for the other element. In this way, the slope of the graph should give
the logarithmic distribution coefficient. The reason why this graphical method was chosen rather
than tabulating the coefficient for each experiment was because the graph allows checks of internal
consistency. Firstly, the line of best fit should be passing through the origin. This is because any
constants of integration would be cancelled out in the integration of Equation (1) to Equation (2).
Secondly, the ratios between a pair should be expressible in terms of the others; for example, pairs in a
triplet should multiply to one, as illustrated by Equation (8):

KA = KC × KA (8)
B B C

This is because the logarithmic distribution coefficient should be consistent between a pair
regardless of how many rare earths are in the system.

3. Results
Table 1 shows which rare earths and ester were in each experimental vessel or conical flask, as well
as the solution masses used to calculate the initial concentration. The first five experiments used the
original experimental method. In this procedure, the total solution mass was weighed after the rare
earth chlorides and dimethyl oxalate were dissolved. The last four experiments used the stock solution.
In this method, the assayed stock solution was weighed into the conical flask and then the addition of
diethyl oxalate was weighed.

Table 1. Identity of solution components and masses for each experiment.

Experiment Number Solution Components Solution Mass, g Ester Ester Mass, g Total Mass, g
1 La, Pr, Nd, Y, Er, Tm 100.00 DMO - 100.00
2 Y, Er, Tm 100.16 DMO - 100.16
3 La, Pr, Nd, Y, Er, Tm 100.01 DMO - 100.01
4 Y, Er, Tm 100.04 DMO - 100.04
5 Y, Er 100.84 DMO - 100.84
6 La, Nd, Y 102.62 DEO 2.04 104.66
7 La, Nd, Y 102.24 DEO 4.20 106.45
8 La, Nd, Y 102.65 DEO 1.05 103.70
9 La, Nd, Y 101.50 DEO 3.15 104.65

Table 2 shows the calculated initial concentrations and the measured final concentrations in each
experimental vessel. In Experiment 7, too much diethyl oxalate was added, and complete precipitation
occurred, so that the rare earths were below the detection limit (BDL).
Figures 1–3 show the results of the experiments with diethyl oxalate and concentrations of
lanthanum, neodymium and yttrium. In addition, Figure 4 shows the result of the experiments with
dimethyl oxalate and yttrium and erbium, in which the intercepts were also small, so that the use of
diethyl oxalate was not required. The graphical results involving thulium also had a small intercept
but are not shown here, as no thermodynamic data for thulium could be found for correlating the
slopes of the graphs.
It can be seen in Figures 1–4 that the results have an internal consistency, with the lines of best fit
having an intercept close to the origin. Also, when the slopes of Figures 1–3 are multiplied together as
a triplet, the product is very close to one, indicating another internal consistency. The data points also
fit fairly closely to a straight line, although deviations will appear to be diminished somewhat by the
logarithmic axes.
Minerals 2020, 10, 712 5 of 9

Table 2. Initial and final solution concentrations for each experiment.

Experiment
Minerals 2020,Number
10, x FOR PEER REVIEW La (ppm) Pr (ppm) Nd (ppm) Y (ppm) Er (ppm) Tm5 (ppm)
of 9
Minerals 2020, 10, x FOR PEER REVIEW 5 of 9
Initial 486 880 183 603 450 883
1
Final
Initial 5603289 - 493 483190 3681508 - 340 - 621
6 Initial
Initial 5603- - - 4831- 3681802 - 661 - 600
26 Final 1300 - 40 910 - -
Final
Final 1300- - - 40 - 910323 - 170 - 168
Initial 5488 - 4732 3606 - -
7 Initial
Initial 5488549 - 115 4732 920 3606430 - 191 - 514
37 Final 𝐵𝐷𝐿 - 𝐵𝐷𝐿 𝐵𝐷𝐿 - -
Final 199
Final 𝐵𝐷𝐿 - 15 𝐵𝐷𝐿66 𝐵𝐷𝐿198 - 57 - 158
Initial
Initial 5656- - - 4877- 3717589 - 493 - 385
48 Initial 5656- - - 4877- 3717330 - 202 - 163
8 Final
Final 3885 - 1410 2600 - -
Final
Initial 3885- - - 1410- 2600962 - 274 - -
59 Initial 5542 - 4779 3642 - -
Initial
Final 5542- - - 4779- 3642667 - 150 - -
9 Final 680 - 4 445 - -
Initial
Final 5603
680 - - 4 4831 4453681 - - - -
6
Final 1300 - 40 910 - -
Figures 1–3 show the results of5488
Initial the experiments
- with4732
diethyl oxalate
3606 and concentrations
- - of
Figures
7 1–3 show the results of the experiments with BDL
diethyl oxalate and concentrations of
lanthanum, neodymium and Finalyttrium.BDL
In addition, Figure
- 4 shows the result
BDLof the experiments
- with
-
lanthanum, neodymium and yttrium. In
Initialand erbium, addition,
5656 in which Figure 4 shows
- the intercepts the result
4877 were also of the experiments with
3717small, so- that the use- of
dimethyl oxalate and yttrium
dimethyl8oxalate and yttrium
Finaland erbium, in which- the intercepts
1410 were also
2600small, so- that the use- of
diethyl oxalate was not required. The3885
graphical results involving thulium also had a small intercept
diethyl oxalate Initial
was not required. The5542 -
graphical results 4779 thulium
involving 3642
also had a -small intercept
-
9 shown
but are not here, as no thermodynamic data for thulium could be found for correlating the
but are not shown here, as Final 680
no thermodynamic - for thulium
data 4 could be 445
found for -correlating -the
slopes of the graphs.
slopes of the graphs.

3.5
3.5
3
3 y = 3.3595x - 0.0106
y = 3.3595x - 0.0106
0]/[Nd])

2.5 R² = 0.9996
0]/[Nd])

2.5 R² = 0.9996
2
2
log([Nd

1.5
log([Nd

1.5
1
1
0.5
0.5
0
0
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
log([La0]/[La])
log([La0]/[La])
Figure
Figure 1. 1. Enrichment
Enrichment of Nd
of Nd against
against La:logarithm
La:La: logarithm of the
ofthe quotient
thequotient
quotientof the starting
of the concentration
starting and
concentration and
Figure 1. Enrichment of Nd against logarithm of of the starting concentration and
final concentration for each rare earth.
final concentration for each
final concentration rarerare
for each earth.
earth.

1
1
0.9
0.9
0.8 y = 1.0042x + 0.0066
0.8 y = 1.0042x + 0.0066
0]/[La])

0.7 R² = 0.999
0]/[La])

0.7 R² = 0.999
0.6
0.6
0.5
log([La

0.5
log([La

0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
log([Y0]/[Y])
log([Y0]/[Y])

Figure 2. Enrichment of La against Y: logarithm of the quotient of the starting concentration and final
concentration for each rare earth.
Minerals 2020,
Minerals 2020, 10,
10, xx FOR
FOR PEER
PEER REVIEW
REVIEW 66 of
of 99

Figure
Minerals 2. Enrichment
10,Enrichment
2020, 2.
Figure 712 of La
of La against
against Y:
Y: logarithm
logarithm of
of the
the quotient
quotient of
of the
the starting
starting concentration
concentration and
and final
final 6 of 9
concentration for
concentration for each
each rare
rare earth.
earth.

1
1
0.9
0.9
0.8
0.8 y=
y = 0.2962x
0.2962x -- 0.0032
0.0032
0.7
0.7 R² = 0.9999
]/[Y])

R² = 0.9999
log([Y00]/[Y])

0.6
0.6
0.5
0.5
log([Y

0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0 0.5
0.5 1
1 1.5
1.5 2
2 2.5
2.5 3
3 3.5
3.5
log([Nd00]/[Nd])
log([Nd ]/[Nd])

Figure 3.
Figure 3. Enrichment
Enrichment of Y
Enrichment of Y against
against Nd: logarithm
against Nd: logarithm of
logarithm of the
of the quotient
the quotient of
quotient of the
of the starting
the starting concentration
starting concentration and final
concentration and final
concentration for each rare earth.
concentration for each rare earth.

0.7
0.7
y=
y = 1.469x
1.469x +
+ 0.0198
0.0198
0.6
0.6 R² =
R² = 0.9975
0.9975
0.5
0.5
]/[Y])
log([Y00]/[Y])

0.4
0.4
log([Y

0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0 0.1
0.1 0.2
0.2 0.3
0.3 0.4
0.4 0.5
0.5
log([Er00]/[Er])
log([Er ]/[Er])

Figure 4.
Figure
Figure
4. Enrichment
4. Enrichment
Enrichment of
of Y
of Y
against
Y against
Er:
against Er:
logarithm
Er: logarithm
of
logarithm of
the
of the
quotient
the quotient
of
quotient of
the
of the
starting
the starting
concentration
starting concentration
and
concentration and
final
and final
final
concentration for
concentration for
concentration each
for each rare
each rare earth.
rare earth.
earth.

It can
It can be seen
be
would seen inbeen
havein Figures
Figures 1–4 that
1–4
preferablethattothe
the results
results
have have
hadhave an internal
an
a greaterinternal
number consistency,
consistency, with the
with
of data points the lines
on lines
each ofof best
best
graph.
fit having
fit having an
However, an
eachintercept
intercept close to
closecomes
data point the origin.
to thefrom
origin. Also, when
Also, when
a separate the slopes
the slopes of
experimental of Figures
Figures
vessel, 1–3
and1–3 are multiplied
arewas
there multiplied together
together
no exclusion of
as aa triplet,
as triplet,
outliers, apartthefrom
the product
product is very
is
Experimentvery 7,
close
close to one,
to
in which one, indicating
theindicating
precipitationanother
another internal consistency.
internal
was complete. consistency. The data
The data points
In terms of repetition, points
in one
also fit
also
sense fiteach
fairly
fairly
dataclosely
closely to
onaathe
point to straight
straight line, isalthough
line,
one graph although deviations
deviations
a repetition will separation,
will
of the same appear to
appear to be
be diminished
diminished
although somewhat
somewhat
repetition of the
by the logarithmic
by thespecific
same logarithmic axes.
axes. would also provide greater confidence. Overall, it seems that the slope values
conditions
It would
It
in Figures would havebebeen
have
1–4 can been preferable
preferable
described to
as theto have had
have
logarithmic had distribution
aa greater
greater number
number of data
of
coefficientdata pointsexperimentally.
points
(λ), found on each
on each graph.
graph.
However, each data point comes from a separate experimental vessel, and
However, each data point comes from a separate experimental vessel, and there was no exclusion of there was no exclusion of
4. Discussion
outliers, apart from Experiment 7, in which the precipitation was complete.
outliers, apart from Experiment 7, in which the precipitation was complete. In terms of repetition, inIn terms of repetition, in
one sense
one sense each
Giveneach data
thatdata point(3)
point
Equation on did
on the not
the onedescribe
one graph is
graph is the
aa repetition
repetition of the
of
distribution the same separation,
same separation,
coefficient λ [11], and although
although repetition
that it isrepetition
based on
of
the the
of the same specific
same specific
solubility conditions
of the conditions would also provide
would also provide
free or weakly-complexed greater
rare greater confidence.
confidence.
earth ion, Overall,
Overall,
an alternative basisit seems
it for
seems that theλslope
that the
describing slope
was
Minerals 2020, 10, 712 7 of 9

needed. It was hypothesized that the precipitation was governed by the energy difference between the
solid rare earth oxalate and the mono-oxalato complex in Equation (9).

AC2 O4 1+ ↔ 0.5 A2 (C2 O4 )3 (9)

Equation (10) was posed as a way to describe λ, because it represents the ratio of the equilibrium
constants for Equation (9), which in turn is based on Equations (4) and (6). It also approximates the
ratio of the saturated concentrations of the mono-oxalato complexes of each rare earth in question
on the basis of Equation (5), assuming that the activity coefficient γ1 is similar between rare earths.
The term in Equation (5) for the free or weakly-complexed rare earth ion was neglected, as it seemed
unlikely that solid rare earth oxalates would form directly from this simple species.
Equation (10) was used to calculate theoretical values in Table 3. The experimentally found values
match these theoretical values fairly closely.
q
KSp, A β1,A
λB  q (10)
A
KSp, B β1,B

Table 3. Comparison between theoretical and experimentally obtained values for the logarithmic
distribution coefficient.

Pair Theoretical Experimental

Nd/La 3.25 3.36
La/Y 0.96 1.00
Y/Nd 0.32 0.30
Y/Er 1.47 1.47

The theoretical values for λ were calculated using Equation (10) on the results obtained by Chung,
Kim, Lee and Yoo [14], shown in Table 4. The theoretical values for λ for the range of rare earths for
which data is available are shown in Table 5.

KSp β1 .
p
Table 4. Solubility products [14], equilibrium constants [14] and their products

Equilibrium Constant, β1
p
Element Solubility Product, KSp KSp ·β1
Y 5.1 × 10−30 2.3 × 107 5.2 × 10−8
La 6.0 × 10−30 2.2 × 107 5.4 × 10−8
Nd 1.3 × 10−31 4.6 × 107 1.7 × 10−8
Sm 4.5 × 10−32 3.2 × 107 6.8 × 10−9
Eu 4.2 × 10−32 3.3 × 107 6.8 × 10−9
Gd 4.25 × 10−32 3.5 × 107 7.2 × 10−9
Dy 2.0 × 10−31 4.9 × 107 2.2 × 10−8
Er 9.0 × 10−31 8.0 × 107 7.6 × 10−8

The reason why Equation (10) should approximate λ is a conundrum. Firstly, the most abundant
form of each rare earth will be the mono-oxalato complex only in a concentrated solution of oxalic
acid according to Equation (5). In the present case, a hydrolyzing ester will only produce a very dilute
concentration of oxalic acid before precipitation occurs, meaning that the most abundant form of rare
earth in solution will be the free or weakly-complexed ion according to Equation (5). This implies that
the measured final concentrations are mainly made up of free or weakly-complexed rare earth ions,
and that the model is still a relation between the concentration of these ions and the fractions on the
surface of the precipitate. Yet, according to Equation (9), the free rare earth ion is not involved in that
equilibrium directly.
Minerals 2020, 10, 712 8 of 9

Table 5. Calculated logarithmic distribution coefficients (precipitation of the element in the horizontal
row for every one of the elements in the vertical column).

Element La Nd Sm Eu Gd Dy Er
Y 0.96 3.1 7.7 7.7 7.2 2.4 0.68
La 3.25 7.9 8.0 7.5 2.5 0.71
Nd 2.4 2.5 2.3 0.76 0.22
Sm 1.0 0.94 0.31 0.09
Eu 0.94 0.31 0.09
Gd 0.33 0.10
Dy 0.29

Nor is there an obvious kinetic argument, as a higher stability of mono-oxalato complex will
cause less precipitation into the solid oxalate compound under this particular model. It would perhaps
be expected that a higher concentration of mono-oxalato complexes would lead to a higher rate of
collisions leading to precipitation.
The notion of a stepwise formation of organic complexes into an organic salt also does not yield
an adequate explanation. The concentration of the mono-oxalato complex of each rare earth would be
determined by the stability constant in Equation (7), as well as the activity fraction of the free rare earth
ion. Adding the chemical equations for the formation of the mono-oxalato complex (Equation (6)),
and the formation of the precipitate from the mono-oxalato complex (Equation (9)) merely yields
Equation (4), which represents the solubility product.
The system is behaving as though the ratio of the concentrations of the mono-oxalato complex of
each rare earth is the same as that for the free rare earth ions. It may be conjectured that Equation (6)
for the formation of the mono-oxalato complex is not attaining equilibrium before precipitation is
occurring. It is possible that this may be connected to the very low concentration of oxalic acid and the
very low solubility of the oxalate precipitate. Overall, it remains difficult to explain the model from
kinetic and thermodynamic principles.

5. Conclusions
It was found that the logarithmic distribution co-efficient λ for precipitation between a pair of rare
earths was fairly close to the ratio of the equilibrium constants for the step from mono-oxalato complex
to the rare earth oxalate salt. This model relates the total concentration of rare earths (mostly free
rare earth ions) to the fractions precipitating into the solid, so it is unclear why only the last step of
the precipitation counts for λ. There appears to be no simple kinetic explanation either, with λ being
derived from thermodynamic terms, and the curious result that a higher stability of mono-oxalato
complex results in less precipitation.

Author Contributions: H.W. was responsible for designing and conducting the experiments and drafting.
Y.-K.L. provided academic supervision and feedback. All authors have read and agreed to the published version
of the manuscript.
Funding: This research received no external funding.
Acknowledgments: Acknowledged is the Minerals Research Institute of Western Australia for its funding of this
project. Also acknowledged is the Australian Government Research Training Program for its funding.
Conflicts of Interest: The authors declare no conflict of interest.

References
1. Lapidus, G.T.; Doyle, F.M. Selective thorium and uranium extraction from monazite: I. Single-stage oxalate
leaching. Hydrometallurgy 2015, 154, 102–110. [CrossRef]
2. Lazo, D.E.; Dyer, L.G.; Alorro, R.D.; Browner, R. Treatment of monazite by organic acids 1: Solution coversion
of rare earths. Hydrometallurgy 2017, 174, 202–209. [CrossRef]
Minerals 2020, 10, 712 9 of 9

3. Gadkari, A.B.; Shinde, T.J.; Vasambekar, P.N. Magnetic properties of rare earth ion (Sm3+ ) added
nanocrystalline Mg–Cd ferrites, prepared by oxalate co-precipitation method. J. Magn. Magn. Mater.
2010, 322, 3823–3827. [CrossRef]
4. Choy, J.H.; Han, Y.H.; Kim, S.J. Oxalate coprecipitation route to the piezoelectric Pb(Zr,Ti)O3 oxide. J. Mater. Chem.
1997, 7, 1807–1813. [CrossRef]
5. Cui, L.J.; Zhang, P.X.; Li, J.S.; Yan, G.; Wang, D.Y.; Pan, X.F.; Liu, G.Q.; Hao, Q.B.; Liu, X.H.; Feng, Y.
Preparation and Characterization of Large-Quantity Bi-2223 Precursor Powder by Oxalate Coprecipitation.
IEEE Trans. Appl. Supercond. 2016, 26, 1–4. [CrossRef]
6. Shter, G.E.; Grader, G.S. YBCO Oxalate Coprecipitation in Alcoholic Solutions. J. Am. Ceram. Soc. 1994, 77,
1436–1440. [CrossRef]
7. Drozd, V.A.; Gabovich, A.M.; Kała, M.P.; Nedilko, S.A.; Gierłowski, P. Oxalate coprecipitation synthesis and
transport properties of polycrystalline Sr1−x Lax PbO3−δ solid solutions. J. Alloy. Compd. 2004, 367, 246–250.
[CrossRef]
8. Krishnamurthy, N.; Gupta, C.K. Extractive Metallurgy of Rare Earths, 2nd ed.; CRC Press: Boca Raton,
FL, USA, 2015.
9. Rodríguez-Ruiz, I.; Teychené, S.; Vitry, Y.; Biscans, B.; Charton, S. Thermodynamic modeling of neodymium
and cerium oxalates reactive precipitation in concentrated nitric acid media. Chem. Eng. Sci. 2018, 183, 20–25.
[CrossRef]
10. Gordon, L.; Shaver, K.J. Fractionation of some rare earth pairs: By precipitation from homogeneous solution.
Anal. Chem. 1953, 25, 784–787. [CrossRef]
11. Feibush, A.M.; Rowley, K.; Gordon, L. Coprecipitation in Some Binary Systems of Rare Earth Oxalates.
Anal. Chem. 1958, 30, 1605–1609. [CrossRef]
12. Matsui, M. The Coprecipitation Behavior of Rare Earth Elements with Calcium Oxalate upon Precipitation
from a Homogeneous System. Bull. Chem. Soc. Jpn. 1966, 39, 1114. [CrossRef]
13. Doerner, H.A.; Hoskins, W.M. Co-precipitation of radium and barium sulfates 1. J. Am. Chem. Soc. 1925, 47,
662–675. [CrossRef]
14. Chung, D.Y.; Kim, E.H.; Lee, E.H.; Yoo, J.H. Solubility of rare earth oxalate in oxalic and nitric acid media.
J. Ind. Eng. Chem. 1998, 4, 277–284.

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