# Phase diagram studies on ternary La 2 O 3 -MoO 3 -CaO system

Qiong Ye, M Barré, K Adil, A Rousseau, F Goutenoire

► To cite this version:

Qiong Ye, M Barré, K Adil, A Rousseau, F Goutenoire. Phase diagram studies on ternary La 2 O 3 -MoO 3 -CaO system. Journal of Solid State Chemistry, 2023, 326, pp.124191. 10.1016/j.jssc.2023.124191. hal-04170692

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Submitted on 25 Jul 2023

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# Phase diagram studies on ternary La₂O₃ - MoO₃ - CaO system

Q. Ye *, M. Barré, K. Adil, A. Rousseau and F. Goutenoire

IMMM (Institut des Molécules et Matériaux du Mans), UMR-CNRS 6283, Le Mans Université,
72085 Le Mans Cedex 9, France.

## Abstract

The ternary phase diagram La₂O₃ - MoO₃ - CaO is investigated with long-term thermodynamic equilibration approach followed by qualitative and quantitative analysis with Rietveld refinement on X-ray diffraction data of the equilibrium phases. Three ternary compounds and two solid solutions in the system are determined. In the area corresponding to the range 0 - 70% of the molar percentage of MoO₃, ten zones in agreement with Gibbs' Phase Rule are determined from a thermodynamic point of view.

## Graphical abstract

The ternary phase diagram La₂O₃ - MoO₃ - CaO composed of ten identified zones being in agreement with Gibbs' Phase Rule and of an un-explored zone has been established.

<figure><img src="image_1.png" /></figure>

## Keywords

Ternary phase diagram, Gibbs' Phase Rule, Thermodynamic equilibrium, Solid solution, Rietveld refinement.
# 1. Introduction

Since the discovery of the excellent ionic conductor La₂Mo₂O₉ (σ = 6,0 x 10⁻² S·cm⁻¹ at 800°C) [1], a potential solid electrolyte material for Solid Oxide Fuel Cell (SOFC), the family of lanthanum molybdate LAMOX derived from it has been widely studied. The ionic conductivity of La₂Mo₂O₉ drops sharply below 560°C due to the phase transition (cubic at high temperature ↔ monoclinic at low temperature) [2] [3]. In order to stabilize the structure and improve the conductivity, a widely adopted method is the partial substitution of La³⁺ and/or Mo⁶⁺ with other cations to find new compounds with defect structure, in which the vacancies can form 3D pathway and facilitate the transport of O²⁻/H⁺. This approach has led to the study of the corresponding ternary phase diagram. For example, the partial substitution of La³⁺ and/or Mo⁶⁺ by Ca²⁺ has brought about the investigation of the ternary phase diagram La₂O₃ - MoO₃ - CaO.

The ternary phase diagram La₂O₃ - MoO₃ - CaO has been established by Davydova et al. for the first time in 1991 [4] (Figure 1). Three new compounds Ca₉La₂Mo₄O₂₄, Ca₃La₂MoO₉ with solid solution and CaLa₆Mo₄O₂₂ (molar compositions shown in Table 1) have been reported in the literature.

<figure><img src="image_2.png" /><figcaption>**Figure 1:** Ternary phase diagram La₂O₃ - MoO₃ - CaO established by Davydova et al. in 1991 [4]. Source: Phase Equilibria Diagrams Database (ACerS – NIST).</figcaption></figure>

<table><caption>**Table 1:** Three compounds reported in the research of Davydova et al. in 1991 [4].</caption><thead><tr><th rowspan="2">Compound</th><th colspan="3">Molar composition (%)</th></tr><tr><th>La₂O₃</th><th>MoO₃</th><th>CaO</th></tr></thead><tbody><tr><td>Ca₉La₂Mo₄O₂₄</td><td>7.1</td><td>28.6</td><td>64.3</td></tr><tr><td>Ca₃La₂MoO₉</td><td>20</td><td>20</td><td>60</td></tr><tr><td>CaLa₆Mo₄O₂₂</td><td>37.5</td><td>50.1</td><td>12.5</td></tr></tbody></table>
During our work, we also obtained three new compounds in this system. However, there are significant
differences in the chemical composition between the three compounds reported by Davydova et al. and ours.
Hence, we re-established most areas of this phase diagram based on more accurate data and analysis in this
paper. Two solid solutions and ten zones were determined by quantitative analysis with Rietveld refinement
on the powder X-ray diffraction data.

**2. Literature review**

**2.1 The binary phase diagram La<sub>2</sub>O<sub>3</sub> - MoO<sub>3</sub>**

Since the first binary phase diagram La₂O₃ - MoO₃ was published by Fournier *et al.* in 1970 (Figure 2) [5],
many studies were carried out by other teams in the next years [7] [8] [9] [10] [10]. The possible compounds are
listed in Table 2. The diagrams La₂O₃ - MoO₃ and La₂O₃ - WO₃ [23] have comparability in view of the similar
physical and chemical properties of MoO₃ and of WO₃. However, the molybdenum system is much more
complicated than that of tungsten due to the complication of the physic-chemical and structural properties of
MoO₃. The comparison of the compounds located in these two diagrams is presented in Figure 3.

<figure><img src="image_3.png" /><figcaption>**Figure 2:** Binary phase diagram La<sub>2</sub>O<sub>3</sub> - MoO<sub>3</sub> established by Fournier et al. (1970) [5].
Source: Phase Equilibria Diagrams Database (ACerS – NIST).</figcaption></figure>
<table><caption>Table 2: Possible compounds located in the binary phase diagram La₂O₃ - MoO₃.</caption><thead><tr><th rowspan="2">Compound</th><th colspan="2">Composition (mol%)</th><th rowspan="2">Crystal structure</th></tr><tr><th>La<sub>2</sub>O<sub>3</sub></th><th>MoO<sub>3</sub></th></tr></thead><tbody><tr><td>La<sub>6</sub>MoO<sub>12</sub></td><td>75</td><td>25</td><td>1. The structure is still controversial.<br>2. Cubic [a = 11.32(2) Å]---Cros et al. [10]<br>3. Rhombohedral [a = 10.51(1) Å, c = 9.88(2) Å] [4][11]</td></tr><tr><td>La<sub>10</sub>Mo<sub>2</sub>O<sub>21</sub></td><td>71.4</td><td>28.6</td><td>Cubic (a = 11.3100 Å) [10]</td></tr><tr><td>La<sub>34</sub>Mo<sub>8</sub>O<sub>75</sub></td><td>68</td><td>32</td><td>Monoclinic (a = 17.070 Å, b = 12.204 Å, c = 9.742 Å and β = 109.58°, C2/m) [12]</td></tr><tr><td>La<sub>4</sub>MoO<sub>9</sub></td><td>66.7</td><td>13.3</td><td>Hexagonal (a = 8.1970 Å, c = 19.0100 Å) [13]</td></tr><tr><td>La<sub>6</sub>Mo<sub>2</sub>O<sub>15</sub></td><td>60</td><td>40</td><td>Orthorhombic (a = 12.5970 Å, b = 5.9500 Å, c = 8.8880 Å) [10]</td></tr><tr><td>La<sub>2</sub>MoO<sub>6</sub></td><td>50</td><td>50</td><td>Tetragonal [a = 5.797(1) Å, b = 32.035(1) Å, I<sub>4</sub>1/abcd] [14]</td></tr><tr><td>La<sub>2</sub>Mo<sub>2</sub>O<sub>9</sub></td><td>33.3</td><td>66.7</td><td>β-cubic [a = 7.2342(1) Å, P2<sub>1</sub>3, Z = 2,] [15]<br>↓↑ 560°C<br>α-monoclinic [a = 14.325(3) Å, b = 21.482(4) Å, c = 28.585(6) Å and β = 90.40(3)°, P2<sub>1</sub>, Z = 48] [16]</td></tr><tr><td>La<sub>6</sub>Mo<sub>8</sub>O<sub>33</sub></td><td>27.3</td><td>72.7</td><td>Monoclinic [a = 10.7411(3) Å, b = 11.9678(3) Å, c = 11.7722(3) Å and β = 116.062(1)°, P2<sub>1</sub>, Z = 2] [17]</td></tr><tr><td>La<sub>2</sub>Mo<sub>3</sub>O<sub>12</sub></td><td>25</td><td>75</td><td>Monoclinic [a = 17.006(4) Å, b = 11.952(2) Å, c = 16.093(3) Å and β = 108.44(3)°, C2/c, Z = 12] [18]</td></tr><tr><td>La<sub>6</sub>Mo<sub>10</sub>O<sub>39</sub></td><td>23.1</td><td>76.9</td><td>Monoclinic [a = 23.0800(8) Å, b = 14.7146(5) Å, c = 23.0257(7) Å and β = 116.54(1)°, Cc, Z = 8] [19]</td></tr><tr><td>La<sub>4</sub>Mo<sub>7</sub>O<sub>27</sub></td><td>22.2</td><td>77.8</td><td>Orthorhombic [a = 14.1443(14) Å, b = 7.2931(4) Å, c = 22.9916(13) Å, Pca2<sub>1</sub>, Z = 4] [8]</td></tr><tr><td>La<sub>2</sub>Mo<sub>4</sub>O<sub>15</sub></td><td>20</td><td>80</td><td>1.α- type: monoclinic [a = 9.0357(2) Å, b = 12.7737(2) Å, c = 10.6408(2) Å and β = 90.2491(6)°, P2<sub>1</sub>/n, Z = 4] [20]<br>2. β-type: Monoclinic [a = 13.8893(5) Å, b = 13.0757(4) Å, c = 20.0927(8) Å and β = 95.199(2)°, P2<sub>1</sub>/a, Z = 12] [21]</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Figure 3: Comparison of the compounds located in the diagrams La₂O₃ - MoO₃ and La₂O₃ - WO₃. The red arrows indicate the compounds having the same molar composition.</figcaption></figure>

## 2.2 The binary phase diagram CaO - MoO₃
The binary phase diagram MoO₃ - CaO reported by Yanushkevich and Zhukovskii in 1973 [24] (Figure 4) is similar to that of WO₃ - CaO [25]. The difference lies in the physical property of Ca₃WO₆ and Ca₃MoO₆. The former is stable at room temperature and the latter only exists at high temperatures (> 1270 °C). Nevertheless, we could observe the phase Ca₃MoO₆ at room temperature in our work. This is because of the doping of a very small amount of lanthanum which stabilized the structure. The stabilized Ca₃MoO₆ crystallizes in the space group P2₁/n with the monoclinic parameters a ≈ 5.55 Å, b ≈ 5.81 Å, c ≈ 8.01 Å and β ≈ 89.81° [26] which belongs to Perovskite family. In contrast, CaMoO₄ is very stable due to its Scheelite-type structure. This phase crystallizes in the space group I4₁/a with the cell parameters a = 5.226 Å, c = 11.430 Å and Z = 4 [27].

<figure><img src="image_5.png" /><figcaption>**Figure 4:** Binary phase diagram CaO - MoO₃ established by Yanushkevich et al. (1973) [24].
Source: Phase Equilibria Diagrams Database (ACerS – NIST).</figcaption></figure>

## 2.3 The binary phase diagram La₂O₃ - CaO

In 1965, Burry realized a preliminary study of the La₂O₃ - CaO binary phase diagram in his doctoral thesis [28] and reported a year later [29]. In 1972, Lopato *et al.* established a more accurate diagram (Figure 5) [30], but did not find new phase in the binary system.
<figure><img src="image_6.png" /><figcaption>**Figure 5:** Binary phase diagram La₂O₃ - CaO established by Lapato et al. in 1972 [30].
Source: Phase Equilibria Diagrams Database (ACerS – NIST).</figcaption></figure>

# 3. Experimental section

## 3.1 Exploring the ternary diagram

As a strategy of this work, a skeleton of 45 compositions was defined in the ternary diagram as shown in **Figure 6**. They are labeled using alphabetic order from A to Z, from AA to AJ and A' to I'. The points inside the triangle are labeled as the inset in **Figure 6**. The molar composition of each point can be directly read from the binary phase diagram. For example, The composition of the point H' located on the diagram La₂O₃ - MoO₃ is 20 mol.% La₂O₃ and 80 mol.% MoO₃. For the points in the equilateral triangle, we can make three straight lines parallel to the three edges of the equilateral triangle from the point to study, and the intersections of the straight lines with the three edges of the triangle give the values of the three components. **Figure 6** gives an example of the point X: La₂O₃: 30 mol.%, MoO₃: 30 mol.% and CaO: 40 mol.%.
<figure><img src="image_7.png" /><figcaption>**Figure 6:** Skeleton of the labeled points from A to Z, AA to AJ and A' to I'. The inset is a zoom around the X point.</figcaption></figure>

**3.2 Synthesis**

The compound was synthesized with three starting compounds $La_2O_3$ (99.9%, Alfa Aesar), $MoO_3$ (99.9%, TCI) and $CaCO_3$ (99.5%, Merck) by conventional solid state ceramic route. Prior to use, $La_2O_3$ was dried and decarbonated at 1000 °C overnight. The different materials were weighted in stoichiometric proportions, and ground together with ethanol as dispersant in an agate mortar. The dry mixed powder was first heated at 500 °C for 12h in order to avoid sublimation of $MoO_3$ at 700 °C, and then annealed at different temperatures with different durations in an alumina crucible with many intermediate grindings until thermodynamic equilibrium.

The room temperature X-ray powder diffraction data was collected on a Bragg-Brentano geometry diffractometer (MPD-PRO Panalytical) from 5° to 110° (2θ) with a step of 0.017° for about 2h with a cobalt radiation (λ = 1.7903 Å).

# 4. Results and discussion

**4.1 Cluster analysis**

The cluster analysis was performed by using PCA (Parameters Cluster Analysis) implemented in the software HighScorePlus [31]. This program can realize the automatic classification of the all data by comparison of the peak positions, profiles and intensities, etc. An example clustered is presented in **Figure 7** and an example no clustered is shown in **Figure 8**. In **Figure 7**, we can observe that seven similar X-ray diffraction diagrams (composition: AFAGAC, AIAG, Al, AIAFAG, ABAC, ACAF and ACX) were extracted and fell into one category corresponding to pale blue box in **Figure 9**. In fact, these seven points are all located in the zone ②
in the ternary phase diagram (Figure 10). In Figure 8, the X-ray diffraction diagram of the point E is not clustered which is in agreement with its special position in the edge of triangle. The global result of PCA is shown in Figure 9. These data were classified into thirteen categories. This result is almost identical to that of Rietveld refinement.

<figure><img src="image_8.png" /><figcaption>Figure 7: Example clustered of the automatic classification corresponding to pale blue box in Figure 9.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 8: Example no clustered of the automatic classification corresponding to the point No.8 in Figure 9.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Figure 9: Global result of PCA (Parameters Cluster Analysis).</figcaption></figure>

**4.2 Determination of new compounds**

Three new compounds have been determined. The first is Ca₃La₂Mo₂O₁₂ which is isotype of the phase Ca₂.₀₆La₂.₆₁□₀.₃₃W₂O₁₂ reported by Q. Ye et al. [32]. This compound belongs to a rare small crystallographic family A₅B₂X₁₂ (Space group: R-3c) having a large hexagonal cell with a ~ 9.77 Å, c ~ 55.78 Å and Z = 18. The second compound located at the point DK (molar composition: 15%CaO - 35%MoO₃ - 50%La₂O₃) in the diagram with the chemical formula Ca₃La₂₀Mo₇O₅₄ has a monoclinic Scheelite-related superstructure. It crystallizes in the space group C2/c with the cell parameters a = 11.49 Å, b = 24.14 Å, c = 16.18 Å and β = 90.9° [33]. The last compound is CaLa₄Mo₃O₁₆ which has a cubic structure with the cell parameters a = 11.210 Å [34].

**4.3 Rietveld refinement**

Rietveld refinement was carried out using HighScorePlus [31] on all X-ray diffraction data in order to archive the result of the qualitative and quantitative analysis. The refinement parameters usually involve the appropriate atomic coordinates, temperature factors, cell parameters, specimen displacement, peak shape, background parameters and correction roughness for the Bragg-Brentano geometry [35]. The detailed analysis of the refinement revealed ten different composition zones, labeled **①** to **⑩**. The corresponding phases, their weight percentage and the R-factor [36] are summarized in **Table 3** and **Table 4**.

It should be noted that the zone **⑪** is not explored. The area near the binary phase diagram La₂O₃ - MoO₃ of the zone **⑩** has only two phases, which can be explained by the slow kinetic and thermodynamic
processes of the compound CaLa₄Mo₃O₁₆, since the homogeneous mixed starting reactants must be annealed at 1300 °C for at least 300h in order to obtain 2g of this pure compound.

<table><caption>**Table 3:** Identified phases and their weight fractions of synthesized samples in the different zones. The grey boxes indicate that the number of observed phases is not in agreement with Gibbs' phase rule.</caption><thead><tr><th rowspan="2">Zone i</th><th rowspan="2">Sample</th><th colspan="3">Phase and weight percentage (% ±0.1)</th><th rowspan="2">R<sub>p</sub> (% ±0.01)</th><th rowspan="2">R<sub>wp</sub> (% ±0.01)</th></tr><tr><th>La<sub>2</sub>O<sub>3</sub> (Hex)</th><th>CaO</th><th>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></th></tr></thead><tbody><tr><td rowspan="2">①</td><td>RW</td><td>1.3</td><td>13.8</td><td>84.9</td><td>3.73</td><td>5.20</td></tr><tr><td>RQ</td><td>7.3</td><td>11.9</td><td>80.7</td><td>5.08</td><td>6.60</td></tr><tr><td rowspan="10">②</td><td>Al</td><td>Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub></td><td>CaO</td><td>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>7.54</td><td>10.99</td></tr><tr><td>AF</td><td>51.5</td><td>28.9</td><td>19.6</td><td>6.23</td><td>9.36</td></tr><tr><td>AFAG</td><td>18.2</td><td>24.5</td><td>57.3</td><td>5.21</td><td>8.56</td></tr><tr><td>AIAG</td><td>60.5</td><td>15.5</td><td>24.0</td><td>4.64</td><td>6.87</td></tr><tr><td>ABAF</td><td>21.3</td><td>48.9</td><td>29.8</td><td>6.08</td><td>7.97</td></tr><tr><td>ACAF</td><td>5.6</td><td>25.6</td><td>68.9</td><td>5.11</td><td>7.26</td></tr><tr><td>ABAC</td><td>32.2</td><td>13.5</td><td>54.3</td><td>4.91</td><td>6.78</td></tr><tr><td>R</td><td>18.4</td><td>15.1</td><td>66.6</td><td>4.49</td><td>5.88</td></tr><tr><td>X</td><td>1.9</td><td>8.1</td><td>90.0</td><td>5.30</td><td>7.61</td></tr><tr><td>RX</td><td>20.7</td><td>6.5</td><td>72.8</td><td>4.31</td><td>5.65</td></tr><tr><td rowspan="2">③</td><td>AIC<sub>3b</sub></td><td>Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub></td><td>CaO</td><td>Ca<sub>3</sub>MoO<sub>6</sub></td><td>7.79</td><td>12.06</td></tr><tr><td>AIC<sub>3h</sub></td><td>47.3</td><td>12.5</td><td>40.2</td><td>7.90</td><td>12.51</td></tr><tr><td rowspan="2">④</td><td>AG3</td><td>Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub></td><td>CaMoO<sub>4</sub>-tetra</td><td>Ca<sub>3</sub>MoO<sub>6</sub></td><td>7.09</td><td>12.10</td></tr><tr><td>AG4</td><td>43.5</td><td>19.1</td><td>37.4</td><td>5.71</td><td>9.12</td></tr><tr><td rowspan="6">⑤</td><td>AD</td><td>Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub></td><td>CaMoO<sub>4</sub>-tetra</td><td>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>6.12</td><td>9.12</td></tr><tr><td>Y</td><td>18.5</td><td>62.0</td><td>19.5</td><td>6.12</td><td>8.88</td></tr><tr><td>ACY</td><td>4.0</td><td>48.7</td><td>47.3</td><td>5.98</td><td>7.53</td></tr><tr><td>XY</td><td>30.9</td><td>23.2</td><td>45.9</td><td>4.62</td><td>6.30</td></tr><tr><td>ACXY</td><td>24.5</td><td>16.8</td><td>58.8</td><td>6.82</td><td>9.21</td></tr><tr><td>XS</td><td>28.8</td><td>10.3</td><td>60.9</td><td>5.69</td><td>8.43</td></tr><tr><td rowspan="2">⑥</td><td>RS</td><td>18.1</td><td>10.1</td><td>71.8</td><td>4.62</td><td>6.60</td></tr><tr><td>DL</td><td>Ca<sub>4</sub>Mo<sub>3</sub>O<sub>16</sub></td><td>CaMoO<sub>4</sub>-tetra</td><td>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>6.37</td><td>9.58</td></tr><tr><td rowspan="2">⑦</td><td>DEL</td><td>5.8</td><td>12.3</td><td>82.0</td><td>5.20</td><td>7.48</td></tr><tr><td>D</td><td>Ca<sub>4</sub>Mo<sub>3</sub>O<sub>16</sub></td><td>La<sub>2</sub>MoO<sub>6</sub></td><td>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>7.43</td><td>9.54</td></tr><tr><td rowspan="4">⑧</td><td>DE</td><td>83.5</td><td>1.3</td><td>15.1</td><td>5.33</td><td>7.38</td></tr><tr><td>DE'</td><td>48.1</td><td>13.0</td><td>39.1</td><td>5.07</td><td>7.05</td></tr><tr><td>DEE'</td><td>37.1</td><td>53.8</td><td>9.1</td><td>4.83</td><td>6.62</td></tr><tr><td>EF</td><td>28.2</td><td>49.6</td><td>22.3</td><td></td><td></td></tr><tr><td rowspan="3">⑨</td><td>EF</td><td>Ca<sub>4</sub>Mo<sub>3</sub>O<sub>16</sub></td><td>CaMoO<sub>4</sub>-tetra</td><td>La<sub>2</sub>Mo<sub>2</sub>O<sub>9</sub>-mono</td><td>5.71</td><td>7.97</td></tr><tr><td>MEF</td><td>60.8</td><td>11.2</td><td>28.0</td><td>5.80</td><td>7.69</td></tr><tr><td>MF</td><td>70.3</td><td>14.1</td><td>15.6</td><td>4.80</td><td>6.64</td></tr><tr><td rowspan="3">⑩</td><td>CC'</td><td>La<sub>2</sub>O<sub>3</sub> (Hex)</td><td>La<sub>2</sub>MoO<sub>6</sub></td><td>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>4.13</td><td>5.95</td></tr><tr><td>BC'</td><td>41.0</td><td>48.2</td><td>10.8</td><td>4.15</td><td>6.05</td></tr><tr><td>D'DD'</td><td>50.3</td><td>35.1</td><td>14.5</td><td>4.72</td><td>7.07</td></tr><tr><td rowspan="2">⑩</td><td>EE'F</td><td>La<sub>2</sub>MoO<sub>6</sub></td><td>La<sub>2</sub>Mo<sub>2</sub>O<sub>9</sub>-mono</td><td></td><td>5.30</td><td>7.70</td></tr><tr><td>EF'</td><td>83.9</td><td>7.7</td><td></td><td>5.48</td><td>8.17</td></tr></tbody></table>
<table><caption>**Table 4:** Identified phases and their weight fractions of synthesized samples on the boundary lines between two zones.</caption><thead><tr><th>Line i-j</th><th>Sample</th><th colspan="2">Phase and weight percentage (% ±0.1)</th><th>R<sub>p</sub> (% ±0.01)</th><th>R<sub>wp</sub> (% ±0.01)</th></tr></thead><tbody><tr><td rowspan="4">① - ②</td><td>ABWX</td><td>CaO</td><td>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>5.57</td><td>7.99</td></tr><tr><td>WXR</td><td>16.7</td><td>83.3</td><td>6.35</td><td>8.84</td></tr><tr><td>RK</td><td>10.5</td><td>89.5</td><td>6.16</td><td>9.67</td></tr><tr><td></td><td>9.7</td><td>90.3</td><td></td><td></td></tr><tr><td>① - ⑨</td><td>B</td><td>La<sub>2</sub>O<sub>3</sub> (Hex)</td><td>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>6.51</td><td>11.94</td></tr><tr><td rowspan="5">② - ⑤</td><td>ACAG</td><td>Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub></td><td>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>5.71</td><td>9.24</td></tr><tr><td>AC</td><td>70.7</td><td>29.3</td><td>6.51</td><td>9.80</td></tr><tr><td>XRS</td><td>61.9</td><td>38.1</td><td>5.43</td><td>8.15</td></tr><tr><td>RL</td><td>22.2</td><td>77.8</td><td>4.72</td><td>6.22</td></tr><tr><td>KL</td><td>13.6</td><td>86.4</td><td>3.56</td><td>4.87</td></tr><tr><td>④ - ⑤</td><td>ADAG</td><td>Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub></td><td>CaMoO<sub>4</sub>-tetra</td><td>6.65</td><td>11.59</td></tr><tr><td rowspan="3">⑤ - ⑥</td><td>S</td><td>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>CaMoO<sub>4</sub>-tetra</td><td>6.42</td><td>8.81</td></tr><tr><td>YZ</td><td>68.7</td><td>31.3</td><td>6.54</td><td>8.95</td></tr><tr><td>YT</td><td>40.4</td><td>59.6</td><td>7.37</td><td>11.00</td></tr><tr><td rowspan="3">⑥ - ⑧</td><td>Z</td><td>Ca<sub>4</sub>Mo<sub>3</sub>O<sub>16</sub></td><td>CaMoO<sub>4</sub>-tetra</td><td>5.91</td><td>7.96</td></tr><tr><td>T</td><td>34.3</td><td>65.7</td><td>4.89</td><td>7.50</td></tr><tr><td>M</td><td>63.1</td><td>36.9</td><td>5.21</td><td>8.17</td></tr><tr><td rowspan="3">⑦ - ⑨</td><td>DD'</td><td>La<sub>2</sub>MoO<sub>6</sub></td><td>Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>6.42</td><td>8.79</td></tr><tr><td>DD'E'</td><td>23.0</td><td>77.0</td><td>5.03</td><td>6.93</td></tr><tr><td></td><td>52.9</td><td>47.1</td><td></td><td></td></tr><tr><td>⑧ - ⑪</td><td>N</td><td>La<sub>2</sub>Mo<sub>2</sub>O<sub>9</sub>-mono</td><td>CaMoO<sub>4</sub>-tetra</td><td>8.06</td><td>13.69</td></tr><tr><td></td><td></td><td>87.1</td><td>12.9</td><td></td><td></td></tr></tbody></table>

### 4.3 Solid solution

During the Rietveld refinement we observed a significant variation of the cell volume of the phases Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub> (~ 20 Å<sup>3</sup>) and Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub> (~ 40 Å<sup>3</sup>), which means that there exist solid solutions of these two compounds. The comparison of the cell volume of Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub> and Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub> for some chosen compositions is shown in **Table 5** and **Table 6**, respectively.

<table><caption>**Table 5:** Comparison of the cell volume of Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub> for some compositions chosen.</caption><thead><tr><th>Composition (point)</th><th>Weight percentage of Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub>(% ±0.1)</th><th>Volume of Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub> (Å<sup>3</sup> ±0.1)</th><th>R<sub>Bragg</sub> (% ±0.01)</th><th>R<sub>p</sub> (% ±0.01)</th><th>R<sub>wp</sub> (% ±0.01)</th></tr></thead><tbody><tr><td>RS</td><td>13.9</td><td>4470.7</td><td>1.20</td><td>6.42</td><td>6.60</td></tr><tr><td>XS</td><td>18.1</td><td>4472.2</td><td>2.80</td><td>5.69</td><td>8.43</td></tr><tr><td>AF</td><td>18.2</td><td>4474.9</td><td>3.33</td><td>6.23</td><td>9.36</td></tr><tr><td>X</td><td>20.7</td><td>4476.5</td><td>5.14</td><td>5.30</td><td>7.61</td></tr><tr><td>ACAF</td><td>32.2</td><td>4478.1</td><td>6.53</td><td>5.11</td><td>7.26</td></tr><tr><td>AIAG</td><td>21.3</td><td>4479.2</td><td>4.49</td><td>4.64</td><td>6.87</td></tr><tr><td>AC</td><td>61.9</td><td>4480.6</td><td>4.06</td><td>6.51</td><td>9.80</td></tr><tr><td>ACY</td><td>30.9</td><td>4481.6</td><td>5.81</td><td>5.98</td><td>7.53</td></tr><tr><td>ADAG</td><td>55.2</td><td>4485.5</td><td>3.78</td><td>6.65</td><td>11.59</td></tr><tr><td>Y</td><td>4.0</td><td>4489.7</td><td>9.51</td><td>6.12</td><td>8.88</td></tr></tbody></table>
<table><caption>Table 6: Comparison of the cell volume of Ca₃La₂₀Mo₇O₅₄ for some compositions chosen.</caption><thead><tr><th>Composition (point)</th><th>Weight percentage of Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub>(% ±0.1)</th><th>Volume of Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub>(Å<sup>3</sup> ±0.1)</th><th>R<sub>Bragg</sub> (% ±0.01)</th><th>R<sub>p</sub> (% ±0.01)</th><th>R<sub>wp</sub> (% ±0.01)</th></tr></thead><tbody><tr><td>XS</td><td>71.8</td><td>4478.0</td><td>6.02</td><td>5.69</td><td>8.43</td></tr><tr><td>RX</td><td>82.8</td><td>4484.9</td><td>6.54</td><td>4.31</td><td>5.65</td></tr><tr><td>WXR</td><td>89.5</td><td>4483.3</td><td>8.16</td><td>6.35</td><td>8.84</td></tr><tr><td>XY</td><td>58.8</td><td>4488.2</td><td>6.79</td><td>4.62</td><td>6.30</td></tr><tr><td>DD'E'</td><td>47.1</td><td>4491.3</td><td>6.53</td><td>5.03</td><td>6.93</td></tr><tr><td>DE'</td><td>9.1</td><td>4495.2</td><td>2.04</td><td>5.07</td><td>7.05</td></tr><tr><td>DEL</td><td>53.9</td><td>4498.5</td><td>5.98</td><td>5.59</td><td>7.93</td></tr><tr><td>DD'</td><td>77.0</td><td>4500.2</td><td>6.44</td><td>6.42</td><td>8.79</td></tr><tr><td>DE</td><td>39.1</td><td>4506.1</td><td>5.56</td><td>5.33</td><td>7.38</td></tr><tr><td>DL</td><td>82.0</td><td>4510.8</td><td>8.86</td><td>6.37</td><td>9.58</td></tr></tbody></table>

### 4.4 Establishment of the ternary phase diagram

According to the result of the Rietveld refinements and solid solution analysis, the ternary phase diagram is established as shown in Figure 10.

<figure><img src="image_11.png" /><figcaption>Figure 10: Ternary phase diagram La₂O₃ - MoO₃ - CaO showing the synthesized points (purple) with 10 identified zones (①-⑩) and an un-explored zone (⑪-blue). The bold black line represents the solid solution.</figcaption></figure>
## 5. Conclusion

The ternary phase diagram of the area corresponding to the range 0 - 70% of the molar percentage of MoO₃ has been re-established. By using qualitative and quantitative analysis with Rietveld refinement, ten different zones which are in agreement with Gibbs' Phase Rule and two solid solutions have been determined.

Compared to the ternary phase diagram established by Davydova *et al.* in 1991, the differences are the following:

1) Although three new compounds were found in both studies, there are big differences in composition. The different compounds and corresponding compositions are presented in **Table 7**.

<table><caption>**Table 7:** Comparison of the compounds and corresponding compositions between the two studies.</caption><thead><tr><th colspan="2">Compound and corresponding molar composition reported by Davydova <i>et al.</i> in 1991 <sup>[4]</sup></th><th colspan="2">Compound and corresponding molar composition discovered in present work</th></tr></thead><tbody><tr><td rowspan="3">Ca<sub>3</sub>La<sub>2</sub>MoO<sub>9</sub></td><td>CaO: 60.0%</td><td rowspan="3">Ca<sub>3</sub>La<sub>2</sub>Mo<sub>2</sub>O<sub>12</sub></td><td>CaO: 50.0%</td></tr><tr><td>La<sub>2</sub>O<sub>3</sub>: 20.0%</td><td>La<sub>2</sub>O<sub>3</sub>: ~ 16.7%</td></tr><tr><td>MoO<sub>3</sub>: 20.0%</td><td>MoO<sub>3</sub>: ~ 33.3%</td></tr><tr><td rowspan="3">Ca<sub>9</sub>La<sub>2</sub>Mo<sub>4</sub>O<sub>24</sub></td><td>CaO: ~ 64.3%</td><td rowspan="3">Ca<sub>3</sub>La<sub>20</sub>Mo<sub>7</sub>O<sub>54</sub></td><td>CaO: 15.0%</td></tr><tr><td>La<sub>2</sub>O<sub>3</sub>: ~ 7.1%</td><td>La<sub>2</sub>O<sub>3</sub>: 50.0%</td></tr><tr><td>MoO<sub>3</sub>: ~ 28.6%</td><td>MoO<sub>3</sub>: 35.0%</td></tr><tr><td rowspan="3">Ca<sub>6</sub>Mo<sub>4</sub>O<sub>22</sub></td><td>CaO: 12.5%</td><td rowspan="3">Ca<sub>6</sub>Mo<sub>4</sub>O<sub>16</sub></td><td>CaO: ~ 16.7</td></tr><tr><td>La<sub>2</sub>O<sub>3</sub>: 37.5%</td><td>La<sub>2</sub>O<sub>3</sub>: ~ 33.3%</td></tr><tr><td>MoO<sub>3</sub>: 50.0%</td><td>MoO<sub>3</sub>: 50.0%</td></tr></tbody></table>

The composition in our work is determined by combining the following results using three different analysis methods. The first one is the initial composition where the final synthesis product is 100% pure. However, in reality, it is difficult to obtain absolute single-phase through conventional solid-state synthesis method. The second is the result from the chemical analysis using EDX in TEM or SEM. As we know, the accuracy of this result could be affected by the thickness of the different crystallites. The last one is the crystallographic composition from Rietveld analysis using the powder diffraction data (X ray lab., synchrotron and neutron). The accuracy of this result is also related to the nature of different diffusing atoms. The error of the final result is less than 5 atm.%).

2) Only one large range of solid solution Ca₃La₂MoO₉ (C:L:M = 3:1:1)) located at the center of the phase diagram was reported in the work of Davydova. However, two solid solutions Ca₃La₂Mo₂O₁₂ and Ca₃La₂₀Mo₇O₅₄ have been observed in our work. Their cell volumes present obvious difference (Table 5 and 6) at different compositions. The result of Rietveld refinement of the point XRS (see Supplementary Information Page 46) also shows that the two compounds are coexistent.
**Credit author statement**

**Qiong YE:** Synthesis, Analysis, Investigation, Software, Data curation, Writing - original draft.

**Maud BARRE:** Validation, Supervision.

**Karim ADIL:** Validation, Supervision.

**Anthony ROUSSEAU:** Validation, supervision.

**François GOUTENOIRE:** Validation, Analysis, Investigation, Software, Data curation, Supervision.

All authors contributed to this manuscript.

**Declaration of competing interest**

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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