Mining, Metallurgy & Exploration

, Volume 36, Issue 1, pp 227–233 | Cite as

Estimation of the Standard Free Energy of Formation of Bastnasite, REFCO3

  • Isehaq Al-Nafai
  • Hojong Kim
  • Kwadwo Osseo-AsareEmail author


The standard Gibbs free energy of formation (ΔGof, 298) of bastnasite, (Ce, La, Nd, Pr)FCO3, was estimated using four different methods. The obtained average values were − 1589.5 kJ/mol for CeFCO3, − 1599.5 kJ/mol for LaFCO3, − 1589.1 kJ/mol for NdFCO3, and − 1595.4 kJ/mol for PrFCO3. The value for cerium bastnasite, CeFCO3, was used to construct a potential vs. pH (Eh-pH) diagram to investigate the stability relations of cerium bastnasite. The diagram shows that CeFCO3 is stable in neutral to basic conditions (pH ~ 6.5–11).


Bastnasite Rare earth elements Cerium Standard free energy of formation Eh-pH diagram 

1 Introduction

Bastnasite, rare-earth flurocarbonate (REFCO3), is one of the most commercially valuable rare-earth minerals, and occurs in large deposits in Mountain Pass, California, and Bayan Obo, China [1]. Four main rare-earth elements are found in bastnasite: cerium, lanthanum, neodymium, and praseodymium. These four elements constitute about 98% of rare-earth contents in bastnasite, with small amounts of yttrium, gadolinium, samarium, and europium [1, 2]. Rare earths are technologically critical elements due to their extensive applications in many areas such as renewable energy technologies, medicine, defense, and electronics [3, 4].

The hydrometallurgical processing of bastnasite is a challenging task because of the similar physical and chemical properties of the rare-earth elements that are present in it [1, 3]. This challenge is not unique to bastnasite; thus there is a continuing search for new techniques to improve the efficiency of extraction and recovery of rare earths from their minerals. One of these methods, which is being pursued in this laboratory, uses Pourbaix diagrams to study the hydrometallurgical behaviors of rare-earth minerals. Previous work focused on monazite (REPO4) hydrometallurgy [5]. Pourbaix diagrams are known for their usefulness in explaining the stability and solubility relations in aqueous systems. Earlier work includes the heterogeneous equilibria of gold- and silver-cyanide systems [6] and the secondary separation of rare earths [7].

The thermodynamic data for all species in a particular system are required to construct the corresponding Eh-pH diagrams. One of the principal challenges in this ongoing study of rare earths’ hydrometallurgy is to determine the necessary thermodynamic data (standard Gibbs free energy of formation, ΔGof) for bastnasite (CeFCO3, LaFCO3, NdFCO3, and PrFCO3). Many theoretical estimation methods such as linear correlation equations have been used to estimate the thermodynamic data of crystalline materials and minerals [8, 9, 10, 11].

The primary objective of the work reported here, is to estimate the standard Gibbs free energy of formation of bastnasite mineral (REFCO3) based on the available thermodynamic properties and methodologies to construct Eh-pH diagrams for the cerium bastnasite system.

2 Methods and Results

Several estimation methods have been used to estimate the standard free energy of formation of crystalline materials and minerals [9, 10, 12, 13, 14, 15]. Four different methods were used in this study to achieve a reasonable estimation of the ΔGof of REFCO3. Each method has its strengths and limitations as will be discussed below. Table 1 summarizes these methods and their required input data.
Table 1

Different methods used to estimate ΔGof of REFCO3


Relevant data needed

Simple thermodynamic approach

Kso, ΔGof of RE3+, F, and CO32−

Single salts approach [1]

ΔHof, ΔHolattice, So of each element and salt

Linear free energy relationship [2]

ΔGon, rM3+, aMvX, bMvX, βMvX

Linear ΔHof–ΔGof relationship [3]

ΔGof and ΔHof of several RE salts

[1] Yoder and Flora [16]; Yoder and Rowand [15]

[2] Ravagan [13]; Ravagan and Adams [14]

[3] Martins [12]

2.1 Empirical Correlation of Thermodynamic Properties Among Rare-Earth Compounds

The free energy formation of bastnasite can be directly estimated upon the availability of suitable thermodynamic quantities such as solubility product (KSP), using thermodynamic relations. For example, the solubility product of cerium bastnasite (CeFCO3) was experimentally measured at ambient temperature (298.15 K) according to the following reaction [17, 18]:
$$ {\mathrm{Ce}\mathrm{FCO}}_{3\left(\mathrm{s}\right)}\leftrightarrow {{\mathrm{Ce}}^{3+}}_{\left(\mathrm{aq}\right)}+{{\mathrm{F}}^{-}}_{\left(\mathrm{aq}\right)}+{{{\mathrm{CO}}_3}^{2-}}_{\left(\mathrm{aq}\right)} $$
$$ {K}_{\mathrm{so}}=\left[{\mathrm{Ce}}^{3+}\right]\left[{\mathrm{F}}^{-}\right]\left[{{\mathrm{CO}}_3}^{2-}\right]={10}^{-16.1} $$
Because the free energy change of this reaction is zero (ΔGr = 0) at equilibrium, the standard Gibbs free energy of the reaction (ΔGor) is calculated as:
$$ \varDelta {G^{\mathrm{o}}}_{\mathrm{r}}=- RT\ln \kern0.28em {K}_{\mathrm{so}}=91.9\ \mathrm{kJ}/\mathrm{mol}. $$
Accordingly, the standard free energy of formation of CeFCO3 can be determined based on the following thermodynamic relation:
$$ \varDelta {G^o}_r=\varDelta {G^o}_{f\left(C{e}^{3+}\right)}+\varDelta {G^o}_{f\left({F}^{-}\right)}+\varDelta {G^o}_{f\left(C{O_3}^{2^{-}}\right)}-\varDelta {G^o}_{f\left( CeFC{O}_3\right)} $$
where \( \varDelta {G}_{f(i)}^o \)is the free energy of formation of species i.
Using the standard free energy of formation of ionic species in Table 2 [19], the free energy of formation of CeFCO3 was estimated as:
$$ {{\Delta \mathrm{G}}^{\mathrm{o}}}_{\mathrm{f}\left({\mathrm{CeFCO}}_3\right)}=-1578.5\ \mathrm{kJ}/\mathrm{mol}. $$
Table 2

Standard free energy of formation of ionic species in CeFCO3 [19]

Ionic species

Standard free energy of formation, ΔGof, (kJ/mol)


− 677.01


− 281.70


− 527.91

Unfortunately, there exists very little information on the thermodynamic properties of bastnasite (REFCO3) with the exception of CeFCO3. According to the analysis on the free energy of formation of various rare-earth compounds summarized in Table 3, we identified a strong linear correlation among the free energy of formation of various rare-earth compounds, possibly due to their close chemical and structural properties, providing a strategy to estimate the free energy of formation of REFCO3 based on CeFCO3. As shown in Fig. 1, using the compounds of cerium and lanthanum as an example, the free energy of formation of the compounds exhibits the linear relationship according to:
$$ {{\Delta \mathrm{G}}^{\mathrm{o}}}_{\mathrm{f}\ \left(\mathrm{La}\;\mathrm{compounds}\right)}=1.0071\;\varDelta {{\mathrm{G}}^{\mathrm{o}}}_{\mathrm{f}\ \left(\mathrm{Ce}\kern0.24em \mathrm{compounds}\right)}+1.2027 $$
with adjusted R2 values > 0.9999. Using this linear relationship, the unknown free energy of formation of LaFCO3 was estimated as − 1588.6 kJ/mol. Using this approach, the free energy of formation of NdFCO3 and PrFCO3 is estimated as − 1582.8 and − 1690.8 kJ/mol, respectively. The validity of this approach was tested with the cerium monazite (CePO4). Using the available free energy of formation of CePO4 [21], the liner correlation estimated the free energy of formation of LaPO4 as − 1851.8 kJ/mol, with only 2.9 kJ (0.16%) difference.
Table 3

Standard free energy of formation (ΔGof, 298) of some RE species in kJ/mol






RE3+ [1]

− 677.01

− 686.18

− 672.13

− 680.28

RECl2+ [1]

− 810.13

− 819.01

− 805.55

− 813.57

RECl3 [1]

− 1068.93

− 1077.45

− 1063.85

− 1072.22

REF3 [1]

− 1576.54

− 1580.80

− 1603.58

− 1612.48

RE(OH)3 [2]

− 1271.51

− 1279.47

− 1276.96

− 1286.03

RE2O3 [2]

− 1706.24

− 1705.82

− 1721.45 [1]

− 1720.88 [1]

RE2(CO3)3 [2]

− 3113.31

− 3141.77

− 3114.99 [4]

− 3125.87

REPO4 [3]

− 1840.11

− 1848.86

− 1837.61

− 1848.68

REFCO3 [5]

− 1578.6

− 1588.6

− 1582.8

− 1590.8

[1] HSC database [19]

[2] Brookins [20]

[3] Liu and Byrne [21]

[4] Schumm et al. [22]

[5] Estimated

Fig. 1

Correlation plot for the free energy of formation ΔGof between La and Ce compounds

2.2 Simple Salts Approach

Yoder and Flora [16] proposed a method to estimate the thermodynamic data of complex salts based on their constituent single salts data [15, 16]. The major assumption of this approach is that the lattice energy of the double salt can be approximated as the sum of the lattice energies of the constituent simple salts, implying that the enthalpy of formation of double salt can be approximated as the sum of the constituent simple salts, namely the mixing enthalpy is zero.

Employing this approach, bastnasite can be represented by its constituent simple salts as:
$$ \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.{\mathrm{RE}\mathrm{F}}_3+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.{\mathrm{RE}}_2{\left({\mathrm{CO}}_3\right)}_3={\mathrm{RE}\mathrm{F}\mathrm{CO}}_3 $$
and the heat of formation and the entropy of bastnasite are approximated as:
$$ \varDelta {H}_{f,{\mathrm{RE}\mathrm{F}\mathrm{CO}}_3}^0=\frac{1}{3}\varDelta {H}_{f,{\mathrm{RE}\mathrm{F}}_3}^0+\frac{1}{3}\varDelta {H}_{f,{\mathrm{RE}}_2{\left({\mathrm{CO}}_3\right)}_3}^0 $$
$$ \varDelta {S}_{{\mathrm{RE}\mathrm{F}\mathrm{CO}}_3}^0=\frac{1}{3}\varDelta {S}_{{\mathrm{RE}\mathrm{F}}_3}^0+\frac{1}{3}\varDelta {S}_{{\mathrm{RE}}_2{\left({\mathrm{CO}}_3\right)}_3}^0 $$
Consequently, the standard free energy of formation of bastnasite can be calculated as:
$$ \varDelta {G^o}_f=\varDelta {H^o}_f- T\varDelta {S}^o $$
Table 4 represents the values of enthalpy of formation and entropy of REF3 and RE2(CO3)3 used in this approximation. Here, the enthalpies of formation, ΔHof, of RE2(CO3)3 were estimated by linear correlation between rare earths salts. Finally, the free energy of formation of cerium bastnasite is calculated as:
$$ \varDelta {{\mathrm{G}}^{\mathrm{o}}}_{\mathrm{f}}=\varDelta {{\mathrm{H}}^{\mathrm{o}}}_{\mathrm{f}}-\mathrm{T}\varDelta {\mathrm{S}}^{\mathrm{o}}=-1575.2\mathrm{kJ}/\mathrm{mol} $$
Table 4

Thermodynamic data used in single salts approach



So(J/mol K)


− 1688.913 [1]

115.269 [1]


− 3406.6 [b]

100.4 [b]

LaF3 (s)

− 1699.541 [1]

106.985 [1]

La2(CO3)3 (s)

− 3438.3 [b]

58 [b]

NdF3 (s)

− 1679.458 [2]

120.792 [2]

Nd2(CO3)3 (s)

− 3408.5 [b]

98 [b]

PrF3 (s)

− 1689.081 [2]

121.211 [2]

Pr2(CO3)3 (s)

− 3420.8 [b]

98.5 [b]

[1] Barin, part I [34]

[2] Barin, part II [23]

[b] Estimated

The estimated ΔGof values for LaFCO3, NdFCO3 and PrFCO3 from this method were − 1587.8, − 1572.8, and − 1579.5 kJ/mol, respectively.

The applicability of this approach was tested by the estimation of ΔGof of Ca10(PO4)6F2. Its literature value of ΔGof is − 12,982.95 kJ/mol [24]. The constitutent single salts are Ca3(PO4)2 and CaF2 as shown by Eq. 12:
$$ {\mathrm{Ca}}_{10}{\left({\mathrm{PO}}_4\right)}_6{\mathrm{F}}_2=3{\mathrm{Ca}}_3{\left({\mathrm{PO}}_4\right)}_2+{\mathrm{Ca}\mathrm{F}}_2 $$

Following the single salts estimation steps in estimating the free energy of formation of Ca10(PO4)6F2, the obtained value of ΔGof was − 12,790.91 kJ/mol with less than 1.5% difference from the tabulated literature value. All thermodynamic data used in this example were taken from Dean’s Handbook [24].

2.3 Linear Free Energy Relationship

Sverjensky and Molling [10] proposed an empirical linear free energy relationship to estimate the free energy of formation of divalent crystalline compounds based on the free energy of formation of non-solvated ions and their ionic radius in a given coordination state. Later, this method was revised and applied for trivalent lanthanides by Ragavan [13], Ragavan and Adams [14] as:
$$ \varDelta {G^o}_{f,{M}_vX}={a}_{M_vX}\varDelta {G^o}_{n,{M}^{3+}}+{b}_{M_vX}+{\beta}_{M_vX}{r}_{M^{3+}} $$
where \( {{\varDelta G}^o}_{f,{M}_vX} \) is free energy of formation of crystalline material, the coefficients \( {a}_{M_vX},{b}_{M_vX}, \)and \( {\beta}_{M_vX} \) are the regression parameters, and \( {r}_{M^{3+}} \)the Shannon-Prewitt ionic radius in a given coordination state. The parameter \( {{\varDelta G}^o}_{n,{M}^{3+}} \) is the Gibbs free energy of nonsolvation of the metal cation and represents the difference between the standard Gibbs free energy formation of the aqueous cation \( {{\varDelta G}^o}_{f,{M}^{3+}} \), and the Gibbs free energy of solvation of aqueous M3+ ion \( {{\varDelta G}^o}_{s,{M}^{3+}} \) according to:
$$ \varDelta {G^o}_{n,{M}^{3+}}=\varDelta {G^o}_{f,{M}^{3+}}-\varDelta {G^o}_{s,{M}^{3+}} $$

According to Ragavan and Adams [14], the parameter \( {a}_{M_vX} \) can be estimated by correlating known values of \( {a}_{M_vX} \) with the ratio between the charge and the coordination number of the central atom in the ligand (e.g., C in CO32−). In contrast, the value of parameter \( {\beta}_{M_vX} \) depends on the structure of the cation and its coordination number, and the parameter \( {b}_{M_vX} \)depends on the reaction type and conditions of the reactions when the solid forms.

In cerium bastnasite, M3+ is Ce3+ and X is assumed to be (FCO3)3−. For X, the charge of carbon is +4, and its coordination number (CN) is 4 (one F and three oxygens). As a result, the charge/CN ratio is 4/4 = 1, and so a = 0.16. The value of β was estimated to be 26.32 kJ/mol based on the coordination number (= 9) of Ce in bastnasite [25]. Since there is no data for (FCO3)3−, the parameter b is approximated to be the average of RE(OH)3 and RE2O3 which have a similar hexagonal crystal structure to bastnasite [26, 27, 28]. The average was taken because “b” does not depend on the valence or stoichiometry of the species, and this approximation gives b = − 1728.8 kJ/mol. The required data for this method are summarized in Table 5 and the standard free energies of formation ΔGof were estimated to be − 1601.6, − 1603.7, − 1601.6, and − 1603.3 kJ/mol for CeFCO3, LaFCO3, NdFCO3, and PrFCO3, respectively.
Table 5

Data used in the linear free energy relationship approach


\( {{\varDelta G}^o}_{n,{M}^{3+}} \) (kJ/mol) [1]

\( {r}_{M^{3+}} \) (nm) for CN = 9 [2]













[1] Ragavan and Adams [14]

[2] Shannon [29]

2.4 Linear ΔHo f–ΔGo f Relationship

The linear free energy relationship was the starting point of the linear ΔHof–ΔGof relationship. This method is applicable to families of crystalline solids. Martins [12] correlated many solid families and identified the linear relationship between ΔHof–ΔGof among different classes of solid compounds. In this approach, ΔHof–ΔGof was correlated for various families of rare-earth solid compounds (Table 6) and obtained the following linear correlation function (Fig. 2):
$$ {{\Delta \mathrm{H}}^{\mathrm{o}}}_{\mathrm{f}}=1.1312\ {{\Delta \mathrm{G}}^{\mathrm{o}}}_{\mathrm{f},298}+115.16 $$
with adjusted R2 values over 0.999. This linear correlation function allows the estimation of the free energy formation of bastnasite upon the availability of the standard enthalpy of formation. Using the standard enthalpy of formation for bastnasite obtained from single salts approach in Section 2.2, the standard free energies of formation were estimated to be − 1603.7 kJ/mol, − 1615.9 kJ/mol, − 1601.2 kJ/mol, − 1607.5 kJ/mol, respectively for CeFCO3, LaFCO3, NdFCO3 and PrFCO3.
Table 6

Thermodynamic data used in the linear ΔHof–ΔGof relationship


ΔHof (kJ/mol)

ΔGof (kJ/mol)

CeAlO3 [1]

− 1753.51

− 1665.31

CeCrO3 [1]

− 1540.13

− 1451.94

LaAsO4 [1]

− 1556.87

− 1455.66

La2(SeO3)3 [2]

− 2879.43

− 2633.83

CeF3 [1]

− 1688.91

− 1611.88

LaF3 [1]

− 1699.54

− 1623.78

NdF3 [3]

− 1679.46

− 1603.58

PrF3 [3]

− 1689.08

− 1612.48

La(AsO2)3 [4]

− 2153.07

− 1988.92

Nd(AsO2)3 [4]

− 2142.21

− 1977.02

Pr(AsO3)3 [4]

− 2155.89

− 1991.32

Ce2(SO4)3 [1]

− 3954.29

− 3602.92

Nd2(SO4)3 [2]

− 3899.49

− 3547.38

La2(SO4)3 [4]

− 3941.3

− 3595.27

[1] Barin, part I [34]

[2] Wagman et al. [30]

[3] Barin, part II [23]

[4] HSC database [19]

Fig. 2

ΔHof vs. ΔGof relation for several RE salts

This approach was applied to monazite (REPO4) and the free energy of formation for monazite (CePO4) was − 1784.9 kJ/mol, compared to the literature value of − 1781.5 kJ/mol [19] with less than 0.2% error.

3 Discussion

The results from all methods, including average values, are summarized in Table 7. As observed from the table, the results were in a good agreement with less than ± 25 kJ/mol difference among the various approaches. The results from the first method were close to each other with ~ 12 kJ/mol difference between CeFCO3 and PrFCO3. On the other hand, the second method shows values close to the first method with lower difference between different REFCO3 solids. In contrast to the first two methods, the last two methods gave higher values (~ 25 kJ/mol). The values from the linear free energy relationship were very close to each other since REFCO3 species are isostructural, so they have the same values of regression parameters, and the radius of RE3+ ions and their \( {{\Delta \mathrm{G}}^o}_{n,{M}^{3+}} \) are similar.
Table 7

Summary of the estimated values of ΔGof of REFCO3 using different methods


Method 1 (kJ/mol)

Method 2 (kJ/mol)

Method 3 (kJ/mol)

Method 4 (kJ/mol)

Average (kJ/mol)


− 1578.6

− 1574.9

− 1601.6

− 1603.7

− 1589.5


− 1588.6

− 1587.8

− 1603.7

− 1615.9

− 1599.5


− 1582.8

− 1572.8

− 1601.6

− 1601.2

− 1589.1


− 1590.8

− 1579.5

− 1603.3

− 1607.5

− 1595.4

It is interesting to compare the value of − 1589.5 kJ/mol for the estimated free energy of formation of CeFCO3 with the value of − 1709.7 kJ/mol reported by Gysi and Williams-Jones [31]. The research of these authors was based on a combination of experimental and theoretical methods (e.g., high temperature enthalpy measurements plus estimated entropy values). They further acknowledged that the resulting extrapolation down to 298.15 K introduced uncertainties in their reported data. The authors further admitted that it is dangerous to conduct experiments on a natural material (with composition different from the endmember Ce-bastnasite) and then attribute the resulting thermodynamic data to the pure Ce-bastnasite. It is also instructive to note that, on the basis of electrokinetic experiments, Pradip et al. [32] reported that the point of zero charge (pzc) of synthetic Ce-bastnasite was approximately pH 7, whereas the corresponding value for natural Ce-bastnasite was in the neighborhood of pH 9.2. This further demonstrates that it is problematic to assume that the thermodynamic properties of synthetic Ce-bastnasite can be equated to those of natural Ce-bastnasite. Therefore, at this stage in the research on rare-earth metal thermodynamics, the fact that the various predictive models utilized in the current work provide remarkable agreement in the predicted ΔGof, 298 values, not just for Ce-bastanite but for the additional rare earth elements, i.e., La, Nd, and Pr, provides reasonable justification for acceptance of the reported ΔGof, 298 values.

The average of the estimated values of CeFCO3, along with the available thermodynamic data for other species in the Ce-F-CO3-H2O system as shown in Table 8, was used to construct Eh-pH diagrams. The diagrams were constructed using HSC Chemistry software [19]. Figures 3 and 4 show the Eh-pH diagrams for the Ce-F-CO3-H2O system with different concentrations of dissolved metal. These diagrams reveal the stability domain of CeFCO3, which is located in neutral to basic media (pH ~ 6–13) depending on the metal concentration. This result is in good agreement with the previously constructed log [M] vs. pH diagrams for CeFCO3 which showed that CeFCO3 is stable in the pH range of 7–13 [17]. Furthermore, cerium carbonate, Ce2(CO3)3, shows no appearance in the Eh-pH diagrams, which was the case in the log [M] vs. pH diagrams [17]. This indicates that Ce2(CO3)3 is less stable than CeFCO3 in aqueous solution and that CeFCO3 dominates in stability domain over Ce2(CO3)3.
Table 8

Thermodynamic data used in the Ce-F-CO3-H2O system diagram


∆Go f, 298 (kJ/mol)






























− 623.198 [1]

− 586.865 [1]

− 689.916 [1]

− 180.609 [1]

− 296.813 [1]

− 578.087 [1]

− 527.908 [1]

− 673.967 [1]

− 281.705 [1]

0.000 [1]

− 677.013 [1]

− 508.482 [1]

− 1027.10 [1]

− 1706.24 [2]

− 877.770 [1]

− 1271.52 [2]

− 986.043 [3]

− 1729.71 [3]

− 1514.90 [3]

− 1754.90 [3]

− 3010.37 [3]

− 1428.67 [4]

− 982.713 [1]

− 1281.75 [1]

− 1868.78 [1]

− 1576.54 [1]

− 1753.85 [1]

− 3113.31 [2]

− 1589.5 [5]

[1] HSC database [19]

[2] Brookins [20]

[3] Baes and Mesmer [33]

[4] Hayes et al. [35]

[5] Estimated in this work

Fig. 3

Ce-F-CO3-H2O system, {Ce} = 10−6 mol/kg, {F} = {C} = 1.0 mol/kg

Fig. 4

Ce-F-CO3-H2O system, {Ce} = {F} = {C} = 10−3 mol/kg

4 Conclusions

The standard free energies of formation (ΔGof) of bastnasite, REFCO3, were estimated using four different methods. The four methods gave close values with a small difference (± 25 kJ/mol) between different methods. The main findings of this work can be summarized as follows:
  • The average values were considered because each method shows its applicability to known literature values of benchmark compounds. These obtained values were − 1589.5, − 1599.5, − 1589.1, and − 1595.4 kJ/mol for CeFCO3, LaFCO3, NdFCO3, and PrFCO3, respectively.

  • The fact that the estimated ΔGof values were close to the ΔGof value derived from Kso gives confidence to the experimental Kso value for CeFCO3.

  • Applying the estimated value of CeFCO3 in constructing the Eh-pH diagrams for cerium bastnasite aqueous systems shows CeFCO3 species in the pH range 6–13 with good agreement to cerium bastnasite in aqueous systems in log [M] vs. pH diagrams [17].



The work reported here was inspired, in part, by the contributions of Fuerstenau and coworkers to rare earths’ metallurgy [17, 18, 32]. As always, KOA says: “Medaase, oyiwala dɔŋŋ, akpe, menɛ wo mkpɛ, asante sana. Thank you.”

Funding Information

The authors received financial support (through a fellowship award to the first author) from Sultan Qaboos University under the Omani Government (R. No. 2172/2013).

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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© Society for Mining, Metallurgy & Exploration Inc. 2019

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringThe Pennsylvania State UniversityUniversity ParkUSA

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