# La Substitution into the Melilite Derivative Ca5Ga6O14: Prediction, Synthesis and Ionic Conductivity

Haytem Bazzaoui, Meigeng Gao, Olivier Hernandez, Sébastien Chenu, Lijun He, Cécile Genevois, Emmanuel Veron, L. del Campo, Mathieu Allix, George Darling, et al.

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Haytem Bazzaoui, Meigeng Gao, Olivier Hernandez, Sébastien Chenu, Lijun He, et al. La Substitution into the Melilite Derivative Ca5Ga6O14: Prediction, Synthesis and Ionic Conductivity. Inorganic Chemistry, 2024, 10.1021/acs.inorgchem.4c03172. [https://doi.org/10.1021/acs.inorgchem.4c03172](https://doi.org/10.1021/acs.inorgchem.4c03172)

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# La substitution into the melilite derivative Ca₅Ga₆O₁₄: Prediction, synthesis and ionic conductivity

Haytem Bazzaoui<fnref n="1" />, Meigeng Gao<fnref n="2" />, Olivier Hernandez<fnref n="3" />, Sébastien Chenu<fnref n="4" />,<fnref n="5" />, Lijun He<fnref n="1" />, Cécile Genevois<fnref n="1" />, Emmanuel Veron<fnref n="1" />, Leire Del Campo<fnref n="1" />, Mathieu Allix<fnref n="1" />, George Darling<fnref n="2" />, Matthew S. Dyer<fnref n="2" />* and Michael J. Pitcher<fnref n="1" />*

## Abstract

Layered melilite-type gallates of general formula RE₁+xAE₁-xGa₃O₇+x/₂ are of interest for their ability to host mobile interstitial oxide ions in [Ga₃O₇+x] layers. The crystal structure of Ca₅Ga₆O₁₄ is closely related to melilite, with [Ga₃O₇] layers stacked in a more complex way to accommodate an additional 0.5 interlayer cations per formula unit, suggesting the potential for similar oxide ion conduction behaviour. We used a computational approach to identify the most promising routes to interstitial oxide incorporation into Ca₅Ga₆O₁₄, leading to an experimental investigation of the system Ca₅ₓLaₓGa₆O₁₄+x/₂. Single-phase materials were obtained in the range 0 ≤ x ≤ 0.25 by solid state reactions, producing an ~40× increase in ionic conductivity at 800°C. This limited compositional range presents a challenge for characterisation of the charge-compensating defects. The La substituents were observed directly by X-ray diffraction and STEM-EDX, and a combination of different structural characterization techniques and DFT calculations indicated the presence of interstitial oxide ions indirectly, explaining the conductivity response. As higher carrier concentrations (x > 0.25) are apparently inaccessible in this system, we conclude that its potential as a useful oxide ion conductor is more limited than that of established melilite materials such as La₁+xCa₁-xGa₃O₇+x/₂.

<footnote n="1">¹ CNRS, CEMHTI UPR3079, 1d avenue de la Recherche Scientifique, 45071 Orléans, France</footnote>

<footnote n="2">² Department of Chemistry, University of Liverpool, Crown Street, Liverpool L69 7ZD, UK</footnote>

<footnote n="3">³ Nantes Université, CNRS, Institut des Matériaux de Nantes Jean Rouxel, IMN, F-44000 Nantes, France</footnote>

<footnote n="4">⁴ IRCER, UMR 7315 CNRS, Université de Limoges, 87000 Limoges, France</footnote>

<footnote n="5">⁵ Rennes Institute of Chemical Sciences (ISCR), UMR CNRS 6226, Université de Rennes, 35042 Rennes, France</footnote>
# 1. Introduction

The melilite structure is one of relatively few inorganic oxide structure types that are known to accommodate high concentrations of interstitial oxide ions, which can act as charge carriers at elevated temperatures.<sup>1,2</sup> Alongside other oxide ion conductors based on tetrahedral structural units<sup>3</sup> such as the apatites<sup>4</sup> and scheelites<sup>5</sup>, nonstoichiometric melilites of general formula [*RE<sup>3+</sup>]<sub>1+x</sub> [*AE<sup>2+</sup>]<sub>1-x</sub> Ga<sub>3</sub>O<sub>7+x/2</sub> (where *RE* = La-Yb, Y and *AE* = Ca, Sr or Ba) have been explored as an alternative to established defect-fluorite type materials such as yttria stabilised zirconia or doped ceria for intermediate-temperature oxide electrolytes in solid oxide fuel cell or gas sensor devices, where lower operating temperatures are desirable.<sup>6</sup> Melilites have a layered crystal structure consisting of a two-dimensional framework of vertex-linked GaO<sub>4</sub> tetrahedra that are stacked alternately with sheets of *RE*/*AE* cations. Interstitial oxide is accommodated in the framework layer by forming a non-bridging bond to one Ga<sup>3+</sup> cation, expanding its coordination sphere from tetrahedral GaO<sub>4</sub> to trigonal bipyramidal GaO<sub>5</sub>, and two bonds to different *RE*/*AE* cations from the adjacent layers.<sup>2</sup> Consequently, the ionic conduction is two-dimensional in these systems and proceeds by a cooperative mechanism with dynamic exchange between framework oxide sites and interstitial oxides.<sup>7–10</sup> The gallate melilites show a higher carrier mobility than their aluminate counterparts due to their greater framework flexibility (i.e. the ease of expansion of Ga<sup>3+</sup> from 4- to 5-coordination), and also exhibit more extensive solid solutions allowing higher charge carrier concentrations.<sup>11</sup> Their conductivities increase with increasing interstitial oxide concentrations, and reach a maximum at x ≈ 0.6.<sup>12,13</sup> Stable compositions can be synthesised by solid state reactions in the range 0 ≤ x ≤ 0.64 for La<sub>1+x</sub>Ca<sub>1-x</sub>Ga<sub>3</sub>O<sub>7+x/2</sub>,<sup>12</sup> but it is possible to extend the solid solution into a metastable domain by crystallization of undercooled melts or using sol-gel reactions, for example for the synthesis of the end-member La<sub>2</sub>Ga<sub>3</sub>O<sub>7.5</sub> (x = 1). This produces lower conductivities associated with long-range crystallographic ordering of the interstitial oxides.<sup>14,15</sup>

As the ionic conductivity of the melilites arises from the structure and dynamics of the [Ga<sub>3</sub>O<sub>7</sub>] framework layer, there is a clear motivation to explore other compounds with this structural motif. The calcium gallate Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> is one such example, consisting of melilite-type [Ga<sub>3</sub>O<sub>7</sub>] layers that are stacked alternately with Ca<sup>2+</sup> layers.<sup>16</sup> In contrast to LaSrGa<sub>3</sub>O<sub>7</sub> where adjacent framework layers are eclipsed when viewed along the stacking axis (i.e. only one layer in the unit cell), adjacent [Ga<sub>3</sub>O<sub>7</sub>] layers in Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> are related by a 2<sub>1</sub> screw axis producing two layers per unit cell with opposing orientations (see Figure 1). This produces additional cation sites between the framework layers that can accommodate an extra 0.5 Ca<sup>2+</sup> per formula unit compared to the melilite structure. It was recently reported that gallium deficiency in this material may lead to oxide ion conductivity via an oxide vacancy-mediated mechanism (e.g. for a nominal composition Ca<sub>5</sub>Ga<sub>5.83</sub>O<sub>13.745</sub>),<sup>17</sup> but the enhancement of its ionic conductivity by aliovalent substitution at the Ca<sup>2+</sup> or Ga<sup>3+</sup> sites to produce interstitial oxide charge carriers has not previously been explored.

Here, we explore the potential for Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> to host mobile interstitial oxide ions by aliovalent substitutions, including partial substitution of M<sup>3+</sup> cations for Ca<sup>2+</sup> according to the nominal formula Ca<sub>5-x</sub>M<sub>x</sub>Ga<sub>6</sub>O<sub>14+x/2</sub>, or substitution of M<sup>4+</sup> or M<sup>5+</sup> for Ga<sup>3+</sup> according to Ca<sub>5</sub>Ga<sub>5-x</sub>M<sub>x</sub>O<sub>14+x/2</sub> or Ca<sub>5-x</sub>Ga<sub>x</sub>M<sub>x</sub>O<sub>14+x</sub>. Substitutions of small concentrations of M<sup>3+</sup> ions such as Eu<sup>3+</sup>, Pr<sup>3+</sup>, Tb<sup>3+</sup> or Bi<sup>3+</sup> for Ca<sup>2+</sup> in Ca<sub>5-x</sub>Ga<sub>x</sub>Ga<sub>6</sub>O<sub>14</sub> (x < 0.15) hosts have recently been explored for luminescence applications,<sup>18-21</sup> but the compositional limits of such systems, as well as the structural response to substitution and charge-compensation mechanism, have not been addressed. From a synthesis viewpoint, it should be noted that Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> forms glass readily<sup>22</sup>, and may be amenable to the glass-crystallisation synthesis
technique that is demonstrated to extend the accessible compositional ranges of related melilite- and
garnet type families,²³⁻²⁷ as well as to sol-gel approaches that extend the accessible range of the
langasite-type oxide ion conductors La₃Ga₅₋ₓGe₁₊ₓO₁₄₊ₓ/₂.²⁸ To focus our synthesis efforts, selection of
the aliovalent M³/₄/₅⁺ substituent is aided by DFT-based prediction to identify the most favourable way
to introduce charge-compensating oxide interstitials. Note that for simplicity, throughout the
manuscript, nominal compositions have been assigned formulae that are charge-balanced by an excess
of oxide e.g. Ca₅₋ₓLaₓGa₆O₁₄₊ₓ/₂, but discussion of other possible defects is included in Sections 3.6 and
4.2. Below, we describe the synthesis of such materials and the response of their structures and
conductivities to aliovalent substitution.

<figure><img src="image_2.png" /><figcaption>**Figure 1:** Crystal structure of Ca₅Ga₆O₁₄. (a) Projection along the stacking axis c, (b) projection along the b-axis with melilite-type layers of alternating orientation labelled as A and B. The unit cell is marked by dashed lines. (c) The individual melilite-type layers A and B projected along c, which are related by a 2₁ screw operation (Ca²⁺ excluded for clarity).</figcaption></figure>
## 2. Experimental

### 2.1 Computational

The phase stability of aliovalent substitution into Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> was assessed by periodic DFT calculations performed using VASP.<sup>29</sup> Substitution by higher-valence cations was initially performed based on the introduction of interstitial oxide to keep charge neutrality within a single crystallographic cell of Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub>. For example, calculations for La<sup>3+</sup> substitution of Ca<sup>2+</sup> were carried out in a supercell with composition Ca<sub>18</sub>La<sub>2</sub>Ga<sub>24</sub>O<sub>57</sub> (Ca<sub>4.5</sub>La<sub>0.5</sub>Ga<sub>6</sub>O<sub>14.25</sub>). All different symmetrically unique configurations for a given composition were effectively obtained using the code SimDope.py.<sup>30</sup> All the configurations were structurally optimized using the PBE exchange correlation density functional,<sup>31</sup> the projector augmented wave (PAW) method<sup>32,33</sup> was used to represent the ion cores with a cutoff energy of 550 eV, and a *k*-point spacing of 0.3. We compared the calculated energy of the most stable configuration to the energies of all-possible competing phases, involving bi-, tri-, ternary phases published in the Inorganic Crystal Structure Database (ISCD) in order to get the enthalpy of the substituted phase to estimate its stability. These calculations are presented in Section 3.1. To evaluate the potential competing charge compensation of Ca vacancies following La substitution, additional equivalent calculations were performed with the same settings in cells with composition Ca<sub>17</sub>La<sub>2</sub>Ga<sub>24</sub>O<sub>56</sub> (Ca<sub>4.25</sub>La<sub>0.5</sub>Ga<sub>6</sub>O<sub>14</sub>), and these are presented in Section 3.6.

### 2.2 Synthesis

The same ceramic synthesis route was used for substituted and un-substituted samples, using similar conditions to a previously reported Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> powder synthesis protocol.<sup>34</sup> Stoichiometric amounts of La<sub>2</sub>O<sub>3</sub> (STREM, 99.9% purity, dried overnight at 900°C), CaO (STREM, 99.95%) and Ga<sub>2</sub>O<sub>3</sub> (STREM, 99.998%), were weighed according to the nominal formula Ca<sub>5-x</sub>La<sub>x</sub>Ga<sub>6</sub>O<sub>14+x/2</sub> for 0 ≤ x ≤ 0.5. The precursors were mixed in an agate mortar under ethanol, dried in air at approximately 100°C using a drying oven, and pressed into pellets of 13 mm diameter. The pellet was placed on a platinum foil and fully covered with freshly made sacrificial powder of the same composition to suppress gallium evaporation, then fired at 1275°C in air for 48 hours. After firing, the loose sacrificial powder was removed manually using a metal spatula, and the remainder was removed using abrasive paper. This pellet was then crushed into powder for analysis, or for further processing (e.g. by SPS). Note that alternative sol-gel and glass-crystallisation routes to Ca<sub>5</sub>La<sub>x</sub>Ga<sub>6</sub>O<sub>14+x/2</sub> were also explored during the course of this study, but offered no advantages compared to the solid state route: these are described in the Supporting Information (Figures S1-S3). All of the materials characterisation reported in this manuscript was conducted on materials synthesised by the ceramic route.

### 2.3 Powder diffraction analysis

Phase identification and lattice parameter determination were carried out in Bragg-Brentano geometry using a Bruker D8 Advance X-ray powder diffractometer with Ni-filtered Cu Kα<sub>1,2</sub> radiation and a LynxEye position-sensitive detector. Samples were dispersed on a silicon wafer from an ethanol mull. High-intensity high-resolution powder X-ray diffraction (SXRD) data were collected on the CRISTAL beamline at the Soleil synchrotron (Gif-sur-Yvette, France) with incident wavelengths λ = 0.5817 or 0.6713 Å, using a curved 1D position sensitive detector consisting of 9 Dectris Mythen2 modules. Samples were contained in borosilicate capillaries. Powder neutron diffraction (PND) data were collected at ambient temperature on the D2B beamline at the Institut Laue-Langevin (Grenoble, France) using an incident wavelength λ = 1.594 Å. Powder samples of mass ~5 g were contained in thin-
walled vanadium cans. Rietveld analyses were performed using Topas Academic (v.6)³⁵ for the SXRD data. Rietveld Maximum Entropy Method (MEM) calculations were carried out using Rietan-FP³⁶ and Dysnomia³⁷ against the PND data.

## 2.4 Electron Microprobe Analysis

Elemental compositions were analyzed with a JEOL IHP-200F electron probe microanalyzer. Measurements were conducted on sintered pellets. After firing and phase verification by laboratory PXRD, these were subjected to a two-stage polishing protocol, with an initial coarse polish to remove any residual sintered sacrificial powder, followed by an optical quality polish to ensure a smooth surface for analysis. Finally, a conducting carbon layer was deposited on the freshly polished surface. The following operating conditions were used: 20 kV accelerating voltage, 10 nA beam current, 10 s counting time for all elements on each spot, 1 µm spot size (focused beam).

## 2.5 Transmission Electron Microscopy

Selected area electron diffraction (SAED), atomic resolution high angle annular dark field-scanning transmission electron microscopy (HAADF-STEM) imaging and STEM-energy dispersive X-ray spectroscopy (EDS) elemental mapping were carried out using a JEOL ARM 200 Cold FEG transmission electron microscope operating at 200 kV. This microscope is equipped with a double spherical aberration corrector and fitted with a JEOL SDD CENTURIO EDS system for compositional analysis. In HAADF-STEM imaging mode, a 68-174.5 mrad inner-outer collection angle and a 0.1nm probe size were used while in STEM-EDX mapping a probe size of 0.13nm was chosen. Powder samples of x = 0.25 composition were finely ground and dispersed in ethanol, a droplet of the mixture was deposited on a TEM copper grid layered by an amorphous holey carbon film and left to dry in air at ambient temperature. Measurements were conducted on regions of approximately 50-70 nm thickness.

## 2.6 Spark Plasma Sintering

Prior to SPS processing, powders were ball milled using a planetary mill for 10 min to reduce their grain size. The densification of ceramic powders was achieved by spark plasma sintering (SPS) using a Dr.Sinter 825 Syntex machine (Fuji FDC, Japan). During the SPS process, the temperature was monitored by a thermocouple positioned through the die in the vicinity of the sample. The milled powders were loaded into graphite dies of 10 mm diameter. The powder samples were then sintered by spark plasma sintering process, at 800°C under a 100 MPa pressure for 2 minutes and then at 1150°C under a 100 MPa pressure for 5 minutes (100°C/min for both heating steps). The freshly sintered pellets had a black colour due to carbon diffusion from the graphite die. The pellets were polished to a thickness of ~0.7 mm, then annealed at 900°C for 6 hours under oxygen gas flow to remove carbon from the pellets. The densities of the resulting (partially-transparent) pellets were close to 100% of the theoretical crystallographic values. Phase-purity was confirmed by laboratory PXRD.

## 2.7 AC Impedance Spectroscopy

Dense pellets obtained by spark plasma sintering (see above), were polished to obtain two parallel faces. Silver paste was coated on both faces and cured in air at 600°C for 30 minutes. AC impedance measurements were then carried out using a Solartron SI 1260 impedance analyser. Data were acquired in the 0.1Hz – 32MHz frequency range from room temperature to 800°C in air.
## 3. Results

### 3.1 Calculated energies for different aliovalent substituents

Introduction of interstitial oxide into Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> can be envisaged by aliovalent substitution at the Ca<sup>2+</sup> site (by analogy to classic melilite systems such as La<sub>1+x</sub>Ca<sub>1-x</sub>Ga<sub>3</sub>O<sub>7+x/2</sub>)<sup>13</sup> or at the Ga<sup>3+</sup> site (by analogy to the langasites La<sub>3</sub>Ga<sub>5-x</sub>Ge<sub>1+x</sub>O<sub>14+x/2</sub>)<sup>28</sup>. We evaluated five model systems theoretically to identify the most promising candidate for synthesis: Ca<sub>5-x</sub>La<sub>x</sub>Ga<sub>6</sub>O<sub>14+x/2</sub> (La@Ca), Ca<sub>5-x</sub>Y<sub>x</sub>Ga<sub>6</sub>O<sub>14+x/2</sub> (Y@Ca), Ca<sub>5</sub>Ga<sub>6-x</sub>Si<sub>x</sub>O<sub>14+x/2</sub> (Si@Ga), Ca<sub>5</sub>Ga<sub>6-x</sub>Ge<sub>x</sub>O<sub>14+x/2</sub> (Ga@Ga) and Ca<sub>5</sub>Ga<sub>6-x</sub>Nb<sub>x</sub>O<sub>14+x</sub> (Nb@Ga). In this way, large- and small-ionic radius M<sup>3+/4+</sup> cations were sampled at both cation sublattices (introducing 0.5 additional O<sup>2-</sup> per cation substitution), as well as a higher-valence substituent (Nb<sup>5+</sup>) at the B sublattice (1 additional O<sup>2-</sup> per substitution). DFT calculations were performed in 1x1x1 cells containing a single charge compensating interstitial oxide anion, using all of the symmetrically-inequivalent configurations generated using SimDope.py<sup>30</sup> (approximately 600 configurations per system). The melilite system La<sub>1+x</sub>Ca<sub>1-x</sub>Ga<sub>3</sub>O<sub>7+x/2</sub> was also evaluated for comparison. The resulting decomposition energies (defined as the energy difference between the model and the most-stable configuration of the system – higher values mean lower stability) are shown in Figure 2. The substitution of La<sup>3+</sup> for Ca<sup>2+</sup> (Ca<sub>5-x</sub>La<sub>x</sub>G<sub>6</sub>O<sub>14+x/2</sub>) is predicted to be the most favourable way to introduce interstitial oxide into the Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> structure (1.18 eV per oxide interstitial ion). The substitution of Nb<sup>5+</sup> for Ga<sup>3+</sup> was found to be slightly less favourable (1.35 eV/interstitial), whilst the other models were substantially higher in energy (2.01 – 2.35 eV/interstitial). All of the calculated energies were significantly higher than La<sup>3+</sup> for Ca<sup>2+</sup> substitution in the melilite La<sub>1+x</sub>Ca<sub>1-x</sub>Ga<sub>3</sub>O<sub>7+x/2</sub> (0.30 eV/interstitial), suggesting that Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> may be less amenable to such modifications. Guided by these results, synthesis efforts targeted the most stable predicted substituted system Ca<sub>5-x</sub>La<sub>x</sub>Ga<sub>6</sub>O<sub>14+x/2</sub>.

<figure><img src="image_3.png" /></figure>

**Figure 2.** Predicted decomposition energies of Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> substituted to introduce interstitial oxide ion as calculated by DFT. All energies represent the decomposition energy of the lowest energy configuration calculated in a 1x1x1 cell of Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> containing a single interstitial oxide ion (eV per interstitial oxide). The red line is the calculated decomposition energy of the substituted melilite with composition La<sub>1.25</sub>Ca<sub>0.75</sub>Ga<sub>3</sub>O<sub>7.125</sub> (Ca<sub>6</sub>La<sub>10</sub>Ga<sub>24</sub>O<sub>57</sub>). (La,Y)@Ca = Ca<sub>18</sub>(La,Y)<sub>2</sub>Ga<sub>24</sub>O<sub>57</sub>, (Si,Ge)@Ga = Ca<sub>20</sub>Ga<sub>22</sub>(Si,Ge)<sub>2</sub>O<sub>57</sub>, Nb@Ga = Ca<sub>20</sub>Ga<sub>23</sub>NbO<sub>57</sub>.

### 3.2 Synthesis and compositional limits of La-substituted Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub>
Using a ceramic synthesis method, single-phase samples of Ca₅ₓLaₓGa₆O₁₄+x/₂ were obtained in the range 0 ≤ x ≤ 0.25, with a linear evolution of the lattice parameters (see Figure 3). The absence of secondary phases was confirmed by collection of high-intensity synchrotron powder diffraction data (SXRD) for samples in this range. Beyond this limit (x > 0.25), the lattice parameters reached a plateau, and the samples contained an increasing weight fraction of LaCaGa₃O₇ melilite as a secondary phase. Attempts to extend the solid solution limit beyond x = 0.25 by glass-crystallisation and sol-gel methods were unsuccessful, producing mixtures of Ca₅Ga₆O₁₄ and Ca₃Ga₄O₉ for x = 0, or mixtures of Ca₅ₓLaₓGa₆O₁₄+x/₂ and LaCaGa₃O₇ for x > 0.25 (see Supporting Information, Figures S1-S3). Consequently, all of the materials characterisation was carried out on materials synthesised by the ceramic method. Attempts to synthesise a Y-substituted material in this solid solution range (i.e. Ca₄.75Y₀.25Ga₆O₁₄.125), using the same ceramic method, produced only multi-phase samples (see Supporting Information, Figure S4).

Electron microprobe analysis of as-synthesised pellets of x = 0 and x = 0.25 showed them to be compositionally homogeneous at the micron scale, with average compositions of Ca₅.07(4)Ga₅.94(3)O₁₄ and Ca₄.80(3)La₀.25(1)Ga₆.0(3)O₁₄.125 respectively based on 30 data points selected at random (see Supporting Information, Figure S5). These values are consistent with the nominal compositions and indicate that no significant Ga₂O₃ volatilisation has occurred during the synthesis. Furthermore, we did not detect any outlying points indicative of secondary phase formation in either sample (i.e. no disproportionately Ca-, Ga- or La-rich particles), consistent with absence of secondary crystalline phases in the SXRD patterns.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Determination of the solid solution limit of Ca₅ₓLaₓGa₆O₁₄+x/₂ by SXRD (0 ≤ x ≤ 0.30) and laboratory PXRD (x = 0.40, 0.50). (a) Diffractograms which are fully indexed to the Ca₅Ga₆O₁₄ structure (green hkl markers) in the range 0 ≤ x ≤ 0.25, but contain a secondary melilite phase (LaCaGa₃O₇, magenta arrows) when x > 0.25. (b) Normalised lattice parameters ((yₓ/y₀) - 1, where y₀ = lattice parameter of the parent x = 0) extracted by profile fitting, showing a linear trend in the range 0 ≤ x ≤ 0.25 followed by a plateau when x ≥ 0.30 (left axis). LaCaGa₃O₇ appears at x = 0.30 and its weight fraction increases steadily at higher x values (right axis).</figcaption></figure>

The corresponding SEM images revealed a significant amount of porosity in these pellets (sintered under ambient pressure), consistent with a measured density (Archimedes method, ethanol) of 67% for the x = 0.25 member (see Supporting Information, Figure S6). Increasing the sintering temperature
is not practical for these compositions whose synthesis temperature (1275°C) is already close to their melting points (~1325°C)³⁴, whilst the volatility of Ga₂O₃ precludes the use of longer sintering times. Instead, highly dense pellets of compositions x = 0, 0.125 and 0.25 were obtained by a spark plasma sintering protocol under 100 MPa pressure with a maximum temperature of 1150°C (see Section 2.6). PXRD confirmed that the SPS pellets still consisted of single-phase Ca₅-xLaₓGa₆O₁₄+x/2. These pellets were subsequently used for AC impedance measurements (see Section 3.3).

### 3.3 Conductivity of Ca₅-xLaₓGa₆O₁₄ (0 ≤ x ≤ 0.25)

The conductivities of SPS-densified pellets of x = 0, x = 0.125 and x = 0.25 were compared by AC impedance spectroscopy, at temperatures up to 800°C. The resulting Nyquist and Arrhenius plots are shown in Figure 4. Total conductivities are reported here (x-intercept method), as the bulk and grain boundary contributions could not be resolved individually from the Nyquist plots. The Arrhenius plots show a significant jump in conductivity at 800°C from 5 × 10⁻⁷ S·cm⁻¹ to 1.3 × 10⁻⁵ S·cm⁻¹ when La³⁺ is substituted into the system (x = 0 to x = 0.125), followed by a smaller increase to 2 × 10⁻⁵ S·cm⁻¹ when x is increased to 0.25. The scale of this conductivity increase with x is similar to that found in the langasite interstitial oxide ion conductors,²⁸ and the absolute values (< 10⁻⁴ S·cm⁻¹ at 800°C) remain far lower than those attainable in typical melilites at this temperature (e.g. ~0.1 S·cm⁻¹).¹² The activation energies show little variation with x, and remain in the range 1.21 – 1.27 eV. These activation energies are comparable with previously reported melilite oxide ion conductors such as La₂Ga₃O₇.₅ (~1.2 eV),¹⁴ and are also close to those of the oxide-rich langasites La₃Ga₅-xGe₁+xO₁₄+x/2 (1.1 – 1.4 eV).²⁸,³⁸ However, they are significantly higher than best-in-class melilite materials such as La₁.₅₄Sr₀.₄₆Ga₃O₇.₂₇ (~0.4 eV).²

<figure><img src="image_5.png" /><figcaption>**Figure 4:** Conductivities of the x = 0, 0.125 and 0.25 dense ceramics by AC impedance spectroscopy. (a – c) Nyquist plots from each sample at different temperatures in the range 600 – 800 °C. Note that</figcaption></figure>
individual bulk and grain boundary contributions were not resolved, so we consider only the total conductivities ($R_{tot}$). (d) Arrhenius plots, overlaid with fits (red line) and activation energies for each sample.

### 3.4 Location of La³⁺ within the host structure

In section 3.2, we confirmed that La³⁺ has been incorporated into the structure by analysis of lattice parameter evolution and phase purity. In this section, we probe the distribution of La³⁺ over the possible cationic host sites Ca1, Ca2 and Ca3 within the crystal structure, taking advantage of the very good X-ray scattering contrast between Ca²⁺ and La³⁺. Samples from the two extremes of the solid solution, of nominal compositions Ca₅Ga₆O₁₄ (x = 0) and Ca₄.75La₀.25Ga₆O₁₄.₁₂₅ (x = 0.25), were selected for comparison. Rietveld refinements against high resolution PXRD data were conducted using the published crystal structure of Ca₅Ga₆O₁₄¹⁶ as a starting model. Both samples, which were prepared at small scale (1 g), were found to be phase pure (see Supporting Information, Figure S7). Good agreement factors were obtained directly for the x = 0 parent phase (R<sub>wp</sub> = 2.19%, χ = 3.31, see Supporting Information Figure S8 and Table S1). For x = 0.25 the Rietveld starting model was set up with equal concentrations of La³⁺ substituted onto each of the three crystallographically-independent Ca²⁺ sites. Due to the insensitivity of X-rays to low concentrations of interstitial oxide, these species were not included in the Rietveld model. Initially, unconstrained refinement of La site occupancy factors at the three Ca sites produced values close to zero at Ca1 and Ca2, and close to 0.25 at Ca3, consistent with the nominal composition. The La³⁺ occupancy at Ca1 and Ca2 was therefore fixed to zero for the final rounds of refinement. Further tests, allowing the site occupancy parameters of Ca²⁺ at the Ca1 and Ca2 sites to refine freely produced values between 0.995 – 1.011, and these were therefore fixed to 1 in the final refinement. This produced a good fit to the data with agreement factors R<sub>wp</sub> = 1.39%, χ = 2.19 (Figure 5a), and a refined La³⁺ site occupancy factor of 0.261(3) at the Ca3 site.

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>
**Figure 5:** Location of La³⁺ in Ca₄.75La₀.25Ga₆O₁₄.125 (x = 0.25) by Rietveld and STEM analysis. (a) Rietveld refinement against synchrotron PXRD (λ = 0.6713 Å). Red points = yobs, black line = ycalc, blue line = yobs-ycalc, green = allowed hkl. (b) Rietveld-refined structure (cations only) projected along the stacking axis (001); red = La, blue = Ca3, grey = Ca(1,2), green = Ga. (c) HAADF-STEM image and (d) STEM-EDX (La L₃-edge) image of x = 0.25 in the [001] zone axis. These are overlaid with the unit cell (yellow box), with the Ca(1,2) and Ca3 columns indicated by gray and red circles respectively.

The accommodation of La³⁺ by the Ca3 sites in x = 0.25 was examined by HAADF-STEM imaging. An atomic-resolution HAADF-STEM image of a crystallite oriented along the layer stacking direction ([001] zone axis) shows the cation arrangement in the structure, and the columns of Ca3 sites are clearly resolved from columns of Ca(1,2) sites (Figure 5c and Supporting Information, Figure S9). An atomic resolution STEM-EDX analysis from the same zone axis reveals periodic maxima in the La³⁺ signal that coincide with the Ca3 positions (Figure 5d; note that the spatial resolution of this map is similar to those obtained from the related langasite-type structures with multiple-occupancy of cation sites).³⁹ A similar analysis of the [010] zone axis (orthogonal to the stacking axis) is shown in Supporting Information (see Figures S10 and S11). This is consistent with the conclusions of the Rietveld PXRD analysis: La³⁺ occupies the Ca3 sites only, with 25 % of these sites substituted by La³⁺ when x = 0.25.

## 3.5 Response of the oxide sublattice to La³⁺ substitution

High resolution neutron powder diffraction data were collected at ambient temperature on two samples of composition x = 0 and 0.25 on scaled-up powder samples (approximate mass 5 g). In parallel with neutron diffraction analysis, SXRD was used to check phase purity on these powders: this revealed very weak CaO peaks in both of the scaled-up samples, corresponding to < 0.6 wt.% CaO (see Supporting Information, Figures S7, S12 and Tables S5-S6). This is most likely due to incomplete reaction of the scaled-up material (see Discussion, Section 4.2). Rietveld refinements using the SXRD models for starting structural parameters (from Section 3.4) produced a good fit to both neutron data sets (Figure 6a,b), indicating at first sight for the x = 0.25 sample that the contribution of any interstitial oxygen to the neutron structure factors is very low. A strong increase of the isotropic atomic displacement parameter (Biso) of the oxide position O2 was noted as a possible indication of a perturbation to the oxide sublattice (Figure 6c), and a significant increase in Biso of Ca1 and Ca2 sites was also observed. However, attempts to locate interstitial oxide ions by Fourier difference mapping of the x = 0.25 sample did not reveal any excess nuclear density above the background. The refined structural parameters from both compositions are tabulated in the Supporting Information (Tables S3-S6), and an alternative Rietveld model of x = 0.25 with atomic displacement parameter refined anisotropically for O2 is shown in Figure S13 and Table S7.

To extract more information on the positions of weak scatterers (i.e. any partially-occupied interstitial oxide sites) and displacement of framework ions, we carried out MEM calculations against the neutron diffraction patterns of both samples (x = 0 and x = 0.25). The extracted Fobs from 671 and 652 independent reflections (for x = 0 and x = 0.25 respectively) were then used as F-constraints to reconstruct the most probable nuclear density in real space by MEM. A flat initial density and the 0th order single-pixel approximation optimization algorithm was used as well as second-order F-constraints. The resulting nuclear density maps are shown in Figure 6e. Inspection of these maps did not reveal any localised additional nuclear density that could be ascribed directly to the presence of interstitial oxide ions. However, there are clear differences in the density distributions around the framework oxides in the two samples. In x = 0, nuclear density is confined to a near-spherical distribution about each oxide site, confirming that the structure is well described by the average Rietveld model. In x = 0.25, the density centred at the O2 site shows a pronounced anharmonic shape,
which may be due to local framework relaxation about an interstitial oxide defect (see Sections 3.6 and 4.2): this is consistent with the disproportionately large increase in atomic displacement parameter of O2 by Rietveld analysis when La³⁺ is substituted into the Ca₅Ga₆O₁₄ structure.

<figure><img src="image_10.png" /></figure>

**Figure 6:** Neutron diffraction analysis of compositions x = 0 and x = 0.25 at ambient temperature. (a, b) Rietveld refinements (λ = 1.599 Å). (c) Refined isotropic atomic displacement parameters for the 9 independent oxide sites, with error bars representing Bérar-corrected standard deviations. (d) A single layer of the refined x = 0.25 structure projected along the stacking axis, with oxides labelled according to the histogram. Blue = Ca, black = La, green = Ga and red = O. The Ca3 sites, which host the La³⁺ substituents, are indicated by violet pentagons. (e) MEM nuclear density maps for a single [Ga₃O₇+x/2] layer of each composition, oriented along the c-axis and plotted at the same isosurface level 0.67% of ρmax), with a magnified view of the O2 environment in x = 0.25 oriented along the b-axis.

## 3.6 Calculation of the most-stable defect configurations and their impact on the crystal structure
In this section, we use calculations to identify the most plausible local structural configurations arising from $La^{3+}$ substitution into $Ca_5Ga_6O_{14}$, for comparison with experimental results. Models were derived from a single unit cell (i.e. containing $Ca_{20}Ga_{24}O_{56}$ when $x = 0$). Two different ways of achieving charge balance are considered: (i) interstitial oxide formation (substitution of $2La^{3+} + O_{int}$ into the unit cell), as targeted experimentally (and by analogy with known melilite-type compounds$^6$), and (ii) vacancy formation at the $Ca^{2+}$ sublattice (substitution of $2La^{3+} + []_{Ca}$ into the cell), as exhibited by the related mayenite-type compounds.$^{17}$

The first scenario, featuring interstitial oxide incorporation, is evaluated for the composition $Ca_{18}La_2Ga_{24}O_{57}$ ($x = 0.5$) using the same calculations presented in Section 3.1. The 554 symmetrically-inequivalent configurations of this composition, relaxed by DFT, were ranked in energy and categorised according to the location of the two $La^{3+}$ ions in the unit cell (Figure 7). The lowest-energy grouping consisted of configurations with both $La^{3+}$ accommodated at Ca3 sites, as observed consistently by our crystallographic and STEM-EDX analysis (see Section 3.4). Further analysis of this grouping, categorising it by $O_{int}$ location, shows that the most stable configurations accommodate interstitial oxides in the Ca3-containing channels, rather than the Ca1/Ca2 channels. The two most stable configurations featured interstitial oxide coordinated to two $La^{3+}$ (Ca3) and two $Ga^{3+}$ (Ga2, Ga3). Both of these configurations present a strong local displacement of the framework O2 oxide away from the $O_{int}$ at the centre of the pentagonal channel, with relatively small perturbations to the O4 and O8 positions (the most stable of these configurations is shown in Figure 7). This coordination mode is reminiscent of the $[Ga_2O_8]$ units found experimentally in oxide-rich langasites where they are associated with low ionic mobility$^{28}$ and resembles that proposed for oxide rich melilites by previous DFT studies.$^7$

The lowest energy cation vacancy-compensated ($2La^{3+} + []_{Ca}$) configurations were evaluated using a similar approach with two $La^{3+}$ substituted randomly into a 1x1x1 cell on to the Ca1, Ca2 or Ca3 sites, compensated by formation of a single cation ($Ca^{2+}$) vacancy on the same sublattice. This produced 613 symmetrically-inequivalent configurations of composition $Ca_{17}La_2Ga_{24}O_{56}$ ($x = 0.5$). Again, the lowest energy grouping was found to contain configurations with both $La^{3+}$ ions at the Ca3 site, with the charge-compensating vacancy located on Ca1 or Ca2 sites. The most stable configuration was found to be lower in energy than the most stable ($2La^{3+} + O_{int}$) configuration by approximately 0.5 eV/defect site, implying that Ca-vacancy formation should be favoured thermodynamically compared to interstitial oxide formation. However, the DFT-relaxed vacancy-balanced configurations show a structural response that is very different to the interstitial oxide models, with a much smaller perturbation to the oxide sublattice (notably very little change at the O2 position, with O3 as the most-shifted oxide) but a more pronounced impact on the A-site cations surrounding the vacancy defect, which are displaced towards the empty site. These shifts are highlighted in yellow on the structural fragments shown in Figure 7. Notably, the response of the oxide sublattice to cation vacancy formation does not resemble that found by Rietveld refinements and MEM calculations; and the preferred vacancy hosting sites (Ca1, Ca2) are fully-occupied according to Rietveld analysis. This is discussed in more detail in Section 4.2.
<figure><img src="image_11.png" /><figcaption>**Figure 7:** The lowest-energy configurations calculated by DFT for interstitial oxide and Ca vacancy charge balancing models, displayed alongside the parent phase Ca<sub>20</sub>Ga<sub>24</sub>O<sub>56</sub> (x = 0). Note that only a single defect-containing slice of each configuration (including a single framework layer and a single adjacent Ca/La layer) is shown for clarity. Atoms that show the largest positional shifts relative to the parent phase are highlighted in yellow. The local coordination environment of the oxide interstitial is displayed for Ca<sub>18</sub>La<sub>2</sub>Ga<sub>24</sub>O<sub>57</sub>. Green = Ga, blue = Ca, cyan = La and red = O. For the interstitial model, the energy of each configuration is plotted according to the location of the two La<sup>3+</sup> ions (Ca3 only = 2x La<sup>3+</sup> on the Ca3 sublattice; Ca(1/2) only = 2x La<sup>3+</sup> on the Ca1/Ca2 sublattice; Ca(1/2)+Ca3 = 1x La<sup>3+</sup> at each sublattice). A second plot represents only configurations with 2x La<sup>3+</sup> on the Ca3 sublattice (La@Ca3 only), with energies plotted according to interstitial oxide location (either in Ca3 or Ca1/Ca2 containing channels). Together, these show that the lowest energy configurations are found with La<sup>3+</sup> on the Ca3 sites, and O<sub>int</sub> in the Ca3-containing channels of the structure.</figcaption></figure>

# 4. Discussion

## 4.1 Synthesis and stability range of Ca<sub>5-x</sub>La<sub>x</sub>Ga<sub>6</sub>O<sub>14+x/2</sub>

The computational identification of La<sup>3+</sup> as the most energetically-favourable aliovalent dopant for Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub> allowed us to focus our synthesis efforts on this system. Here, conventional ceramic synthesis methods based on a literature protocol for Ca<sub>5</sub>Ga<sub>6</sub>O<sub>14</sub><sup>34</sup> were found to produce the same accessible compositional range (x ≤ 0.25) as non-equilibrium methods based on glass-crystallisation and sol-gel chemistry, which have previously been applied to access metastable compositional ranges with very high defect concentrations in melilites<sup>14,15</sup> and langasites.<sup>28</sup> Here, competition from the rapid formation of the compositionally-adjacent phase Ca<sub>3</sub>Ga<sub>4</sub>O<sub>9</sub> precluded the synthesis of single-phase samples with x = 0, and increasing concentrations of the stable melilite LaCaGa<sub>3</sub>O<sub>7</sub> were present for
compositions x > 0.25. The fact that the solid solution cannot be extended into a metastable domain beyond x = 0.25 in Ca₅ₓLaₓGa₃O₁₄+x/₂ by these alternative synthesis approaches contrasts with the behaviour of the oxide-rich melilites¹⁴,¹⁵ and langasites,²⁸ and presents a severe compositional limit for the system. It implies a maximum interstitial oxide concentration of 0.125 Oint per formula unit (0.5 Oint per unit cell), equivalent to a 0.9 mol% excess of oxygen with respect to the parent phase. This compares unfavourably with the melilite system where 3.9 mol% excess of oxygen is associated with best-in-class conductivity behaviour and can be attained by ceramic synthesis (e.g. in La₁+xCa₁-xGa₃O₇+x/₂),¹² with an ultimate limit of 7.1 mol% oxygen excess in the metastable regime (La₂Ga₃O₇.₅).¹⁴ In the langasite system La₃Ga₅ₓGe₁+xO₁₄+x/₂, which has a similar two dimensional framework structure, a maximum oxygen excess of 5.3 mol% (x = 1.5) can be reached by sol-gel synthesis.²⁸ This is consistent with the high calculated energy cost for interstitial oxide ion formation (1.18 eV/interstitial.) in Ca₅ₓLaₓGa₆O₁₄+x/₂ versus the melilite system La₁+xCa₁-xGa₃O₇+x/₂ (0.3 eV/interstitial). Therefore, simply on the basis of these low accessible carrier concentrations, Ca₅ₓLaₓGa₆O₁₄+x/₂ cannot be expected to have high oxide ion conductivities competitive with current established materials. Future exploration of more complex doping strategies may produce ways to access higher interstitial oxide concentrations in Ca₅Ga₆O₁₄, such as combining La@Ca with Nb@Ga substitution, whose calculated decomposition energies are quite close. Unless this can be achieved, the restricted compositional range will complicate efforts characterise the true structures and compositions of these materials (discussed in detail below).

## 4.2 Crystal structure and charge-compensation mechanism

In this section, we consider the impact of aliovalent La³⁺ substitution on the crystal structure of Ca₅Ga₆O₁₄, and attempt to draw conclusions about the nature of the charge-compensation mechanism in the substituted materials. First, from consideration of lattice parameter trends, Rietveld SXRD analysis and atomic-resolution STEM-EDX (sections 3.2 and 3.3), it is clear that La³⁺ can be incorporated into the crystal structure, in concentrations that are consistent with the maximum nominal stoichiometry of Ca₄.₇₅La₀.₂₅Ga₆O₁₄.₁₂₅. La³⁺ preferentially occupies the Ca3 site with a negligible concentration at the Ca1 and Ca2 sites. This experimentally-observed site preference is also supported by DFT calculations (section 3.4) which find La³⁺ at the Ca3 site to be the most stable way for the structure to accommodate this substitution. This reflects major differences in local coordination environments between the (Ca1/Ca2) and Ca3 sites in Ca₅Ga₆O₁₄, where Ca3 is larger (see bond valence sum calculations, Supporting Information Table S8) and more closely resembles that found in melilite as it lies between two antiparallel [GaO₄]₅ pentagons. The availability of only 1/3 of the Ca²⁺ sites for La³⁺ substitution may also be a contributing factor to the low solid solution limit in this system. This site preference offers a contrast with the melilite systems, which only exhibit a weak tendency for La³⁺ and Ca²⁺ to order crystallographically, due to the near-uniformity of available sites.⁴⁰

The identification of possible interstitial oxide sites by diffraction is considerably more difficult than the refinement of the La³⁺ occupancies, because of the low nominal concentration of this defect (0.5 atoms per unit cell for Ca₄.₇₅La₀.₂₅Ga₆O₁₄.₁₂₅), the large volume and low symmetry of the unit cell, and the potential for the defects to be disordered over a large number of possible crystallographic sites which can further disperse their nuclear density. However, it is possible to probe (indirectly) the existence of such defects by considering all of the experimental and theoretical results together. Below, we compare these observations against the two models considered in Section 3.6 (charge compensation by interstitial oxides or Ca vacancies) to identify the most probable scenario in our materials.
Firstly, we note that single-phase samples can be synthesised at the nominal composition Ca₄.75La₀.25Ga₆O₁₄.₁₂₅, with the absence of secondary phases confirmed by SXRD patterns with excellent signal:noise ratio. The composition determined by electron microprobe measurements corresponds closely to this nominal value, and is consistent with the crystallographic site occupancy factors obtained by Rietveld refinement against the SXRD data (Section 3.4). In particular, these refinements indicate that the Ca1 and Ca2 sites are fully occupied by Ca²⁺. The alternative Ca vacancy balanced model Ca₄.625La₀.25Ga₆O₁₄ has a lower Ca:Ga ratio than the reaction precursor, implying that a Ca-rich secondary phase should form during synthesis (most likely CaO, whose Bragg reflections are clearly resolved from those of Ca₅Ga₆O₁₄); cation vacancies, if present, should prefer the Ca1 and Ca2 sites (see calculations, Section 3.6). Only two of our samples – the scaled-up powders of x = 0 and 0.25 prepared for neutron diffraction – contained any detectable amount of CaO by SXRD. Whilst the amount was too small to be refined reliably for x = 0, the x = 0.25 sample contained 0.56(3) wt.% CaO, which is insufficient for full charge balance in this model (0.92 wt.% required). Given the absence of CaO in the smaller-volume samples by SXRD (including x = 0 and x = 0.25), and the consistency of the lattice parameters between small- and large-volume samples (see Supporting Information, Tables S1–S6,) we consider that the formation of CaO is not intrinsic to these compositions, and is most likely due to incomplete reaction associated with the increased difficulty of mixing reagent powders on scale-up. Overall, the synthesis of phase-pure samples across the compositional range 0 ≤ x ≤ 0.25, the consistency of the measured Ca:Ga ratio with the nominal composition, and the absence of vacancies at the Ca1, Ca2 sites by Rietveld refinement, suggest an interstitial oxide charge balance mechanism.

Secondly, whilst MEM analysis against neutron diffraction data did not resolve any new weak maxima in the nuclear density maps that could be assigned directly to Oint defects, it did show a strongly anisotropic distribution of nuclear density about the O2 atom for x = 0.25, in contrast to the parent (x = 0) phase which exhibited isotropic nuclear densities at all of the oxide positions. This is also seen in Rietveld refinements against NPD data, where the isotropic atomic displacement parameter of O2 undergoes a disproportionately large increase between x = 0 and x = 0.25 (see Section 3.5). Examination of the most-stable DFT-relaxed configurations found that incorporation of Oint is most favourable between two La-substituted Ca3 sites adjacent to O2. This coordination mode causes a major local displacement of O2, which shifts away from the interstitial defect to form a [Ga₂O₈] unit, resembling those formed in oxide-rich langasites²⁸ (see Section 3.6). In contrast, the other framework oxides are calculated to undergo very limited displacement upon Oint incorporation. It follows that the observed nuclear density anharmonicity at the O2 site can be interpreted as an indirect consequence of Oint incorporation.

Finally, the progressively increasing conductivity of the material with x implies that a charge-carrying defect is being introduced into the system. In this case, the charge carrier has a similar activation energy (1.26 eV) to known interstitial oxide hosts such as La₂Ga₃O₇.₅ (~1.2 eV)¹⁴ and the langasite series La₃Ga₅-xGe₁+xO₁₄+x/₂ (0 ≤ x ≤ 1.5, 1.1 – 1.4 eV)²⁸,³⁸. The relation between nominal interstitial oxide ion concentration and conductivity is also comparable to such systems, with the observed 40x increase in conductivity being close to that observed in langasites over the same range of excess oxygen concentration (e.g. an approximately 35x increase between La₃Ga₅GeO₁₄ and La₃Ga₄.₅Ge₁.₅O₁₄.₂₅ is reported by Diaz-Lopez et. al.).²⁸ Indeed, the small increase in conductivity between x = 0.125 and 0.25 implies that Ca₅-xLaₓGa₆O₁₄+x/₂ may already be approaching a plateau in conductivity at x = 0.25, similar to the behaviour of the langasite series. It should be noted that Ca²⁺ mobility has been reported at elevated temperatures in Ca₅Ga₆O₁₄⁴¹ and in the related mayenite-type aluminogallate series Ca₁₂Al₁₄-xGaₓO₃₃, but in these materials it is associated with an activation energy of ~2 eV,¹⁷ significantly higher than what we observe here.
Together, these observations provide a strong indication that interstitial oxide is the dominant charge balancing mechanism in this system, but the possibility of a small concentration of $Ca^{2+}$ vacancies in the La-substituted members cannot be ignored completely. The formation of such defects is energetically plausible, as confirmed by DFT calculations that suggest this is a more stable way for the structure to accommodate $La^{3+}$. Furthermore, whilst the most-stable predicted vacancy-balanced configurations cannot explain the observed perturbation of the oxide sublattice, they do feature large local displacements of Ca1 and Ca2 cations towards the vacant site (Figure 7). It should be noted that significant relative increases in isotropic atomic displacement parameters for the Ca1 and Ca2 sites are observed by Rietveld refinement against both in SXRD and NPD data upon $La^{3+}$ substitution, and these are not fully explained by the most stable predicted interstitial model. The real local structure of the doped materials is thus probably more complex than these idealised configurations, and it is plausible that a small concentration of $Ca^{2+}$ vacancies could be present alongside the dominant interstitial oxide charge-balancing species in our materials.

In summary, whilst we are unable to observe interstitial oxide ions directly by diffraction methods, together our experimental and theoretical analyses provide consistent indirect evidence for charge compensation by interstitial oxide incorporation in La-doped $Ca_5Ga_6O_{14}$: this is likely to be the dominant charge compensation mechanism in this system, and it provides an enhanced ionic conductivity compared to the undoped parent phase ($x=0$). At the same time, DFT calculations suggest that $Ca^{2+}$ vacancies may offer an energetically-plausible alternative charge-balance mechanism in this structure type, and the possible existence of a small concentration of such defects alongside the oxide interstitials in our materials cannot be excluded.

## Conclusions

$La^{3+}$ can be substituted into the melilite-related compound $Ca_5Ga_6O_{14}$ by conventional ceramic synthesis methods, and this produces a ~40x increase in conductivity at high temperature ($T \le 800^\circ C$) with activation energies of ~1.2 eV, consistent with the introduction of interstitial oxide ionic charge carriers. The substituted materials $Ca_{5-x}La_xGa_6O_{14+x/2}$ are accessible for $0 \le x \le 0.25$. Unlike the related melilites and langasites, this range cannot be extended by glass-crystallisation or sol-gel syntheses due to the rapid formation of $Ca_3Ga_4O_9$ and increasing competition from the stable melilite phase $LaCaGa_3O_7$. In $Ca_{5-x}La_xGa_6O_{14+x/2}$, $La^{3+}$ is not distributed over all possible Ca sites: SXRD and STEM-EDX elemental mapping show that it populates only the Ca3 site, whose local coordination environment most closely resembles that found in true melilites such as $LaSrGa_3O_7$. Direct crystallographic assignment of the charge-balancing $O_{int}$ species is hampered by their low nominal concentrations and the large low-symmetry unit cell and acentric space group. Instead, the presence of these species in $Ca_{4.75}La_{0.25}Ga_6O_{14.125}$ is inferred indirectly from a range of different characterisation methods. In particular, MEM nuclear density maps showed characteristic anharmonic displacements of the framework oxides, consistent with DFT prediction of the most stable local configurations arising from interstitial oxide coordination. The proposed configurations incorporate additional oxide by displacing one of the framework oxides (O2) to form $[Ga_2O_8]$ units locally, similar to those observed experimentally in the oxide-excess langasite family $La_3Ga_{5-x}Ge_{1+x}O_{14+x/2}$, where they are associated with low oxide ion mobility. The solid solution range of $0 \le x \le 0.25$ in $Ca_{5-x}La_xGa_6O_{14+x/2}$ is much more restricted than the equivalent melilite systems, and such limited charge carrier concentrations mean that the system cannot challenge the performance of best-in-class interstitial oxide conductors such as $La_{1.56}Sr_{0.44}Ga_3O_{7.28}$.
**Supporting Information:** Glass crystallization and sol-gel synthesis attempts (methods and results); electron microprobe analysis; SEM; SXRD diffractograms; Rietveld refinements (fits and tables); selected area electron diffraction; DFT.

Acknowledgements

This work was funded by the Agence Nationale de la Recherche under projects CAPRE (ANR-20-CE08-0007) and HighFive (ANR-23-CE08-0013-01). Microscopy facilities were provided by the MACLE-CVL platform (CNRS UAR2590), co-funded by the European Union and Centre-Val de Loire Region (FEDER). High-performance computing facilities were provided by the University of Liverpool. We thank Dr. Erik Elkaim for assistance at the CRISTAL beamline (Soleil, Gif-sur-Yvette, France), Dr. Stanislav Savvin for data collection at the D2B beamline under proposals EASY-644 and EASY-645 (Institut Laue-Langevin, Grenoble, France) and Arthur Cachot (CEMHTI) for assistance with AC impedance measurements.
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