# Diffusion mechanisms between La2SiO5 and SiO2 during formation of textured lanthanum silicate oxyapatite crystals

Lizeth Arbelaez, Pierre-Marie Geffroy, Anne Aimable, Maggy Colas, Koichiro

Fukuda, Emilie Béchade

► To cite this version:

Lizeth Arbelaez, Pierre-Marie Geffroy, Anne Aimable, Maggy Colas, Koichiro Fukuda, et al.. Diffusion mechanisms between La2SiO5 and SiO2 during formation of textured lanthanum silicate oxyapatite crystals. Ceramics International, 2023, 49 (19), pp.31428-31438. 10.1016/j.ceramint.2023.07.090. hal-04266023

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Submitted on 23 Nov 2023

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<figure><img src="image_1.png" /></figure>
Diffusion mechanisms between La<sub>2</sub>SiO<sub>5</sub> and SiO<sub>2</sub> during formation of
textured lanthanum silicate oxyapatite crystals

Lizeth Arbelaez<sup>a,*</sup>, Pierre-Marie Geffroy<sup>a</sup>, Anne Aimable<sup>a</sup>, Maggy Colas<sup>a</sup>, Koichiro Fukuda<sup>b</sup>, Emilie Béchade<sup>a</sup>

<sup>a</sup>Université de Limoges, IRCER, CNRS, UMR 7315, 12 Rue Atlantis, F-87000 Limoges, France

<sup>b</sup>Institute of Technology Life Science and Applied Chemistry, Nagoya Institute of Technology, Nagoya

466-8555, Japan

*Corresponding author

E-mail address: lizeth.arbelaez-morales@unilim.fr

**Abstract**

Lanthanum silicate oxyapatite (LSO) is a promising alternative electrolyte for solid oxide fuel cell (SOFC) applications. They exhibit anisotropic oxide-ionic conduction; therefore, a preferential crystal orientation along the c-axis is necessary to achieve optimal conductivity. This study is performed to understand the reaction mechanisms involved in the formation of an LSO layer at the interface of the La<sub>2</sub>SiO<sub>5</sub>/SiO<sub>2</sub> diffusion pair during reactive sintering at high temperatures. Different La<sub>2</sub>SiO<sub>5</sub>/SiO<sub>2</sub> bilayers were fabricated in sandwich-type structures using silica-type quartz or La<sub>2</sub>SiO<sub>5</sub> supports obtained via electrophoresis and uniaxial pressing, respectively. These supports were pre-sintered and then coated with a suspension of the opposite component. The diffusion pairs were isothermally heated at 1500 °C at different holding times (10, 20, and 40 h) and at 1600 °C for 10 h. Their surfaces and cross-sections were investigated via X-ray diffraction, scanning electron microscopy (SEM) observations, energy-dispersive X-ray spectroscopy (EDS), and Raman spectroscopy.
Experimental results show that two different driving forces were involved in the nucleation and growth of apatite crystals. The first is the chemical potential gradient in lanthanum between the components of the layers, and the second is the electric field created to preserve the electroneutrality of the system. The predominant diffusing species in this bilayer system were La<sup>+III</sup> and O<sup>-II</sup>, and their diffusion is enhanced by the formation of a glassy phase on the silica grains through the transformation of silica-type quartz into cristobalite. The formation of a La<sub>2</sub>Si<sub>2</sub>O<sub>7</sub> intermediate phase was detected, which is vital to the interdiffusion of species and the nucleation and growth of oriented apatite crystals.

The porosity gradient observed in the cross-section after reactive diffusion suggests the possibility of achieving an SOFC half-cell device via this process.

**Keywords:** Diffusion mechanism, reactive sintering, lanthanum silicate oxyapatites, textured microstructure, SOFC.

# 1 Introduction

Yttria-stabilized zirconia-based electrolytes are widely used in the fabrication of solid oxide fuel cells (SOFCs). However, the high operating temperature required to ensure favorable ionic conductivity has intensified the search for new electrolyte materials with high ionic conductivity (0.1 S.cm⁻¹). Thus, the operating temperatures can be reduced to an intermediate range (873–1,073 K) without a significant decrease in the power density [1]–[3]. Several studies have demonstrated that apatite-structured materials, such as rare-earth silicate oxyapatites of type La<sub>9.33+x</sub>(SiO<sub>4</sub>)<sub>6</sub>O<sub>2+1.5x</sub>, exhibit high ionic conductivities in this temperature range [4]–[8]. Moreover, these materials present high optimization potential in terms of chemical composition [9]–[11] and microstructure
[12]–[16]. The crystalline structure is formed by large channels along the c-axis, which enhances the conduction of O²⁻ ions in the structure. This characteristic confers strong anisotropy to the properties and conduction mechanisms of this family of materials [17]–[23]. In 1999, Nakayama *et al.*, [24], [25] were the first to measure the ionic conductivity parallel and perpendicular to the c-axis of a single crystal of composition Nd₉.₃三(SiO₄)₆O₂ synthesized via the floating zone method (synthesis temperature >1900 °C) [26]. In 2013, they successfully synthesized La₉.₃₃Si₆O₂₆ single crystals via seeding method at high temperature (1750 °C) [27]. These studies show that the conductivity measured parallel to the c-axis is up to two orders of magnitude higher than that measured perpendicular to the c-axis and that the activation energy remains almost constant.

Subsequently, different techniques for obtaining LSO with a highly oriented structure along the c-axis have been reported. Some of these methods include magnetron sputtering [28]–[30], chemical solution deposition [31], [32], molten salt processes [33], magnetic fields [34], [35], templated grain growth [36], [37] and flux growth [38]–[40]. Meanwhile, Fukuda *et al.* proposed a process that does not require specialized technology and is therefore easier to implement, i.e., the reactive sintering of sandwich-type diffusion pairs [17], [41], [42]. This method is based on the nucleation and growth of oxyapatite crystals via reactive diffusion at the interface of specific component layers shaped by co-pressing.

In their early studies, diffusion pairs of La₂SiO₅/La₂Si₂O₇ were annealed at high temperatures (1600 °C) for long durations (25–100 h). Similarly, other sandwich-type pairs such as La₂SiO₅ / [SiO + 1/2O₂]ₐ [43] and La₂SiO₅/B₂O₃ vapors [44] have been proposed, which yielded outstanding results in terms of apatite orientation.

Based on observations and results obtained from a study pertaining to the La₂SiO₅/La₂Si₂O₇ system [41], researchers proposed reaction mechanisms to explain the
formation of oriented apatite crystals. The authors assumed that the interdiffusion of Si⁴⁺ and La³⁺ at the bilayer interface resulted in the nucleation and growth of oriented apatite crystals in the diffusion path. In this study, two sublayers of oriented apatite that developed differently were formed (Figure 1). At the La₂SiO₅/apatite interface (sublayer I), the apatite phase nucleated and grew via the loss of the La₂O₃ component from La₂SiO₅ (Equation 1) and by the reaction of La₂SiO₅ with SiO₂ (Equation 2) released from the La₂Si₂O₇ layer (Equation 4).

<figure><img src="image_2.png" /><figcaption>Figure 1. La₂SiO₅/La₂Si₂O₇ diffusion pair proposed by Fukuda et al [41].</figcaption></figure>

$$18 \text{ La}_2\text{SiO}_5 - (4 - 3x) \text{ La}_2\text{O}_3 \rightarrow 3\text{La}_{9,33+2x}(\text{SiO}_4)_6\text{O}_{2+3x} \quad (1)$$

$$(14 + 3x) \text{ La}_2\text{SiO}_5 + (4 - 3x) \text{ SiO}_2 \rightarrow 3\text{La}_{9,33+2x}(\text{SiO}_4)_6\text{O}_{2+3x} \quad (2)$$

At the apatite/La₂Si₂O₇ interface (sublayer II), the apatite phase nucleates and grows via the reaction of La₂Si₂O₇ with La₂O₃ (Equation 3), the release from La₂SiO₅ (Equation 1), and the loss of SiO₂ from La₂Si₂O₇ (Equation 4).

$$9 \text{ La}_2\text{Si}_2\text{O}_7 + (5 + 3x) \text{ La}_2\text{O}_3 \rightarrow 3\text{La}_{9,33+2x}(\text{SiO}_4)_6\text{O}_{2+3x} \quad (3)$$

$$(14 + 3x) \text{ La}_2\text{Si}_2\text{O}_7 - (10 + 6x) \text{ SiO}_2 \rightarrow 3\text{La}_{9,33+2x}(\text{SiO}_4)_6\text{O}_{2+3x} \quad (4)$$

Equation 5 describes the global reaction for apatite layer formation.
$$ (10 + 6x) \mathrm{La}_2\mathrm{SiO}_5 + (4 - 3x) \mathrm{La}_2\mathrm{Si}_2\mathrm{O}_7 \rightarrow 3\mathrm{La}_{9,33+2x}(\mathrm{SiO}_4)_6\mathrm{O}_{2+3x} \quad (5) $$

$$ \text{with } 0,01 \le x \le 0,13 $$

They demonstrated that this system was controlled by volume diffusion, in which the growth of the oxyapatite layer increased almost parabolically with time.

In this case, only the solid-state diffusion mechanisms at the interfaces were considered, thus suggesting that interdiffusion was potentially controlled by less mobile species between $Si^{4+}$ and $La^{3+}$. Fukuda et al. suggested that for the $La_2SiO_5/La_2Si_2O_7$ system, silicon controls the volume diffusion kinetics and that the contribution of lanthanum flux is negligible [42], [45]–[47]. In this case, the flux of positive charges provided by $Si^{4+}$ diffusion would be compensated for the flux of $O^{2-}$ in the same direction, coupled with an oxygen vacancy flux from the opposite side. This is the origin of the Kirkendall effect, as evidenced by the high porosity of sublayer II of the apatite [42], [45], [47], [48].

Recent studies [49]–[51] pertaining to the reactivity of thermal/chemical barriers containing different rare-earth disilicates or zirconates ($RE_2O_3-RE_2Si_2O_7-RE_2Zr_2O_7$) showed significant diffusion of $RE^{3+}$ when these compounds were in contact with silica-abundant volcanic ashes (known as CMAS, which comprises CaO, MgO, $Al_2O_3$, and $SiO_2$). Rare-earth diffusion into the CMAS layer is enhanced when the glassy phase formed becomes viscous and flows at high temperature (1300 °C).

Sakao et al. [30] investigated $La_2SiO_5/La_2Si_2O_7$ bilayer systems achieved via sputtering and observed the significant diffusion of rare-earth elements, particularly at the grain boundaries of the silica-abundant phase. In contrast to the observations and the hypotheses of Fukuda et al., Sakao et al. suggested that lanthanum diffused from the $La_2SiO_5$ layer to $La_2Si_2O_7$ to form a dense and oriented apatite layer. In this case, porosity due to the Kirkendall effect was detected within the $La_2SiO_5$ layer. These seemingly
contradictory results might be due to differences in the experimental conditions, such as
the reactive sintering temperature and the bilayer fabrication process. Therefore, the
diffusion mechanisms involved in the nucleation and growth of apatite crystals are not
well understood.

Based on the La₂O₃–SiO₂ phase diagram, the apatite phase can be formed by combining
a silica-rich phase (SiO₂ and La₂Si₂O₇) with a lanthanum-rich phase (La₂O₃, La₂O₂CO₃,
and La₂SiO₅). In this study, a La₂SiO₅/SiO₂ diffusion pair was investigated. An original
approach is proposed, in which two sandwich-type La₂SiO₅/SiO₂ diffusion pairs are
developed to determine the critical parameters that govern the preferential orientation
along the c-axis of LSO during the solid-state reaction. Commercial silica-type quartz is
selected to form one of the layers. The La₂SiO₅ compound is synthesized using a method
optimized in our previous study [52].

The effects of the characteristics of the supports (crystalline nature, presintering
temperature, and relative density) as well as the effects of temperature and holding times
on the reactive diffusion technique were investigated via X-ray diffraction, scanning
electron microscopy (SEM), energy dispersive spectroscopy (EDS), and Raman
spectroscopy. Based on the results obtained as well as thermodynamic considerations,
diffusion mechanisms that may occur during the reactive sintering of La₂SiO₅/SiO₂
diffusion pairs are proposed.

**2 Experimental methods**

2.1. *Powder materials*

La₂SiO₅ powders were prepared via a solid-state reaction using high-purity colloidal
silica (monodisperse amorphous silica, 40 wt.% in H₂O: LUDOX AS-40) and La₂O₃
powder (99.9% Sigma-Aldrich) using the optimized synthesis reported in [52]. Based on
the La₂O₃-SiO₂ phase diagram, La₂O₃ and SiO₂ were mixed at a 1:1 molar ratio to obtain
La₂SiO₅. The reagents were dispersed via ultrasonic pulsing using a sonotrode (Vibra-
Cell™, Bioblock Scientific Co., Ltd., Illkirich, France). Subsequently, the mixture was
placed onto a heating plate and stirred at 450 rpm. The temperature was gradually
increased to 160 °C until all water evaporated to obtain a homogeneous and dry powder.
The powder was dried overnight at 110 °C in air and then crushed using an agate mortar
to break the agglomerates. Finally, the dried powder was calcined at 1000 °C for 10 h in
air using Pt crucibles.

Previous studies [52] showed that the use of quartz-type silica, with an average particle
size of 1 µm, was the most appropriate method to crystallize the apatite phase. Thus,
commercial crystallized silica C400 (ground silica-glass CERADEL) that was previously
ground to achieve an average particle size of 1 µm was used to fabricate La₂SiO₅/SiO₂
bilayers. The Brunauer-Emmett-Teller (BET) analysis (3Flex Physisorption
Micromeritics®) was performed after 12 h of degassing at 200 °C, which showed a
specific surface of 7 m².g⁻¹. Inductively coupled plasma spectroscopy and X-ray
fluorescence analyses of the powder indicated the trace amounts of Al₂O₃ (0.66% wt),
Fe₂O₃ (0.09% wt), CaO (0.03% wt), and K₂O (0.49% wt).

## 2.2. Shaping of La₂SiO₅/SiO₂ bilayer

Owing to the difficulty in shaping silica via uniaxial pressing without the use of additives,
two types of La₂SiO₅/SiO₂ bilayers were fabricated in this study.

The first type of bilayer comprised a La₂SiO₅ support shaped by uniaxial pressing, and
the silica layer featured a suspension coating: La₂SiO₅ (support) / SiO₂ (coating)
The second type of bilayer comprised a SiO₂ support shaped by electrophoresis, and the La₂SiO₅ layer featured a suspension coating: SiO₂(support) / La₂SiO₅(coating).

### 2.2.1. La₂SiO₅(support) / SiO₂(coating) bilayer

The La₂SiO₅ supports were obtained via uniaxial pressing (SODEMI press) using a 10 mm diameter steel matrix and an applied pressure of 1.5 t for 1 min. To avoid grain growths that hinder shaping by pressing, only powder obtained via synthesis performed at 1000 °C was used. At this temperature, La₂SiO₅ synthesis was not complete, and traces of La₂O₃ and apatite were detectable, as shown in our complementary study [52]. Hence, the supports were pre-sintered at 1200 °C for 10 h to complete the synthesis and obtain a support of satisfactory purity degree. The La₂SiO₅ supports showed a relative density that was 60% of the theoretical density and did not contain the La₂O₃ reactant.

The silica suspension deposited on the surface of the La₂SiO₅ support was prepared using 0.3 g of ground C400 powder and dispersed in 2 mL of ethanol using the Vibra-CellT.M sonotrode. The dispersion cycle featured 10 s “on” and 5 s “off” cycles for a total of 2 min, with an amplitude of 20%.

The reactive sintering of the La₂SiO₅(support)/SiO₂(coating) bilayer was performed at temperatures of 1500 °C for different holding times (10, 20, and 40 h) and 1600 °C for 10 h, in air with a heating rate of 10 °C/min. The samples were placed in Pt crucibles during sintering.

### 2.2.2. SiO₂(support)/La₂SiO₅(coating) bilayer

The silica quartz C-400 support was shaped via electrophoresis. This technique is based
on the movement of solid charged particles under the application of an external electric field, which allows dense and thick silica layers to be achieved without additives.

Aqueous suspensions of raw silica C-400 at a concentration of 55 wt% were used to prepare the supports. The silica suspension was milled using a high-energy ball mill (Emax, Retsch), with zirconia balls measuring 1 mm in diameter. The volume ratios of the different components were 1/3 zirconia balls (156 g), 1/3 solvent (31.5 g water), and 1/3 powder (55 g). The mill speed was set at 1700 rpm, and the operating temperature limit was set at 70 °C. The particle size was controlled during the milling process to identify the time required to obtain a particle size measuring approximately 1 µm. This was achieved through milling for 20 min. Subsequently, ethanol was added to the suspension (after milling to avoid evaporation) to obtain a 70/30 water/ethanol mass ratio. Ethanol limits the water electrolysis at the anode (release of oxygen at the anode), which is detrimental to the mechanical strength of the support.

The zeta potential of the milled suspension was measured on 0.1%-diluted samples using a Malvern Zetasizer Nano ZS. To increase the zeta potential of the particles and compensate for the addition of ethanol, the pH was increased to 9 by adding ammonia ($NH_4OH$, 1 M). The particles were dominated by deprotonated hydroxyl groups, which corresponded to a zeta potential of -49 mV.

For electrophoretic deposition, two electrodes, one fabricated using copper (cathode) and the other using carbon (Papyex N998 Mersen®, at the anode), were immersed in the suspension and separated by a constant distance of 2 cm. The intensity was set at 10 mA, and the deposition time was varied from 2 to 6 min to obtain a silica support of a few millimeters thick. After drying for 24 h at room temperature, the supports were subjected to pre-sintering between 1200 °C and 1500 °C for 4 h to determine the effects of the
crystalline nature of silica and the density of the supports on the reactivity of the diffusion pair.

A suspension was prepared using the La₂SiO₅ powder synthesized at 1500 °C for 10 h to form a second layer by coating the surface of the silica supports. Specifically, 0.3 g of the La₂SiO₅ powder was dispersed in 2 mL of ethanol using a Vibra-CellT. M sonotrode. The dispersion cycle featured 10 s “on” and 5 s “off” cycles for a total of 2 min, with an amplitude of 20%.

### 2.3. Characterization methods

The particle sizes of the powders were measured using an LA-950V2 Fraunhofer Scientific Analyzer (Horiba, Kyoto, Japan). The specific surface area of the powders was determined via the BET analysis, after degassing performed under vacuum at 200 °C. The thermal behavior of the silica was analyzed using a NETZSCH STA 449 F3 Jupiter device coupled with differential scanning calorimetry analysis and thermogravimetric analysis. In the experiments, approximately 45 mg of powder was placed in a platinum crucible under an air flow rate of 20 mL/min, with a rising and falling rate of 10 °C/min until 1500 °C.

The bilayers after reactive sintering were characterized via X-ray diffraction (Bruker D8 Advance diffractometer, 2θ-θ mode, CuKα radiation) in the 2θ range 10°-60° (step size: 0.02°; time range: 30 min). Table 1 presents the ICSD database used in this study.
<table><caption>Table 1. Crystallized phases identified via X-ray diffraction.</caption><thead><tr><th>Phase</th><th>N°JCPDS</th><th>Space Group</th><th>Crystal lattice</th></tr></thead><tbody><tr><td>SiO<sub>2</sub> Cristobalite</td><td>98-007-5484</td><td>P 41 21 2</td><td>Tetragonal</td></tr><tr><td>La<sub>2</sub>SiO<sub>5</sub></td><td>98-015-7892</td><td>P 1 21/c 1</td><td>Monoclinic</td></tr><tr><td>La<sub>9,33</sub>(SiO<sub>4</sub>)<sub>6</sub>O<sub>2</sub></td><td>98-015-4068</td><td>P 6<sub>3</sub>/m</td><td>Hexagonal</td></tr><tr><td>La<sub>2</sub>Si<sub>2</sub>O<sub>7</sub></td><td>98-007-1807</td><td>P 1 21/c 1</td><td>Monoclinic</td></tr></tbody></table>

XRD analysis enabled the orientation of the apatite crystallites to be evaluated. In this study, a significant increase in the diffraction peak intensity of {001} (l = 2, 4, and 6) was observed, which is associated with the extinction of the other diffraction peaks. Based on the XRD patterns, the texture fraction of the apatite crystals in the direction of their crystal structure can be calculated using the Lotgering method. The factor (f001) is defined as the fraction of textured area in the crystallographic plane of interest, as expressed in Equation 6 [53], [54].

$$f_{001} = \frac{P_{001} - P_0}{1 - P_0} \quad (6) \quad P_{001} = \frac{\sum I_{001}}{\sum I_{hkl}} \quad \text{and} \quad P_0 = \frac{\sum I_{001}^{\circ}}{\sum I_{hkl}^{\circ}}$$

where $I_{hkl}$ and $I_{hkl}^{\circ}$ are the intensities of the hkl peaks of the textured and randomly oriented samples, respectively. When the fraction of the textured area is equal to one, the material is fully oriented, whereas when it is zero, the material is randomly oriented.

Microstructural analysis was performed using SEM (FEG LEO1530 VP). The samples were polished and sputter coated with a thin layer of metal. Apatite crystals oriented along the c-axis exhibited a characteristic hexagonal morphology in the hkl {001} direction, which can be observed using this characterization technique. EDS was performed to qualitatively and semiquantitatively determine the elements in the sample. In fact, EDS allows the phases in the multilayer material to be identified and the molar percentage of
the elements to be estimated.

The cross-section of the La₂SiO₅/SiO₂ bilayer was investigated via polarized light microscopy using a Zeiss Axio Scope.A1. To perform the analysis, thin sections of the bilayer, i.e., measuring approximately 40 µm, must be prepared.

The chemical and structural properties of the samples were characterized comprehensively via Raman spectroscopy using an InViaReflex spectrometer (Renishaw). Point-by-point analysis of the sample allowed us to map the different phases in the multilayer material, thus complementing the previous EDS analysis. The spectrometer was equipped with a confocal microscope and a 532 nm laser source. Spectra were acquired using a 100x objective, with a step size of 5 µm and an integration time of 5 s in a spectral range of 100–1300 cm⁻¹. The number of spectra for each sample was approximately 1500, and the acquisition time varied from 2h 30 min to 3h depending on the size of the analyzed area.

Multivariate analysis using the direct classical least-squares method was performed using the Wire software (Renishaw). This method was used when the reference spectra for all components in the sample were available (Figure 2). Therefore, reference spectra were obtained by analyzing the pure components (La₂O₃, SiO₂ cristobalite, La₂SiO₅, La₂Si₂O₇, and apatite) using the same imaging instrument.
<figure><img src="image_3.png" /><figcaption>Figure 2. Reference spectra for multivariate analysis using direct classical least-square method.</figcaption></figure>

This method of data analysis resulted in a linear combination of reference data for all spectra in the Raman mapping dataset, thus providing a representation of the component distribution in the study area. The analysis was performed over a long spectral range, thus allowing chemical distribution maps with excellent accuracy to be created, which was mainly due to the measurement step used for acquiring the mapping data. The entire dataset was previously corrected for cosmic rays and the baseline.
### 3. Results

#### 3.1. Characterization of La<sub>2</sub>SiO<sub>5</sub> (support)/SiO<sub>2</sub> (coating) diffusion pair

**Figure 3** shows the cross-section of the La<sub>2</sub>SiO<sub>5</sub> (support)/SiO<sub>2</sub> (coating) bilayers obtained via polarized light microscopy after they were subjected to reactive sintering at 1500 °C under different holding times, i.e., 10, 20, and 40 h. These images show that the crystals grew as a column from the surface in contact with the SiO<sub>2</sub> layer, and the thickness of the oriented apatite layer increased with the reactive sintering time. The thicknesses were 18 µm (10 h), 35 µm (20 h), and 40 µm (40 h). Between 20 and 40 h, the thickness of the apatite layer did not differ significantly, thus indicating that the kinetics of crystal growth decreased considerably over time.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Cross-section of La<sub>2</sub>SiO<sub>5</sub> (support)/SiO<sub>2</sub> (coating) bilayer after reactive sintering at 1500 °C for 10, 20, and 40 h, obtained via polarized light microscopy. Raman mapping of a sample at 1500 °C/40 h.</figcaption></figure>
Based on the general empirical equation shown in **Equation 7**, which was proposed by Wagner and Kidson [55], [56], the growth of the apatite layer thickness can be expressed as follows:

$$e(t) = K (t)^n, \qquad (7)$$

where e(t) represents the thickness of the layer, k is the growth rate constant, t is time [s], and n is the kinetic exponent. Based on the experimental data obtained using **Equation 7**, the value of n associated with the controlling mechanism of the layer growth in the system was estimated. A value of approximately 0.5 was obtained. This implies that the growth of the apatite layer was controlled by volume diffusion [57], [58], as observed for a La₂SiO₅/La₂Si₂O₇ diffusion pair investigated by Fukuda *et al*. In this case, the flow of the species was inversely proportional to the thickness of the apatite layer. Therefore, a decrease in growth kinetics was observed experimentally over time.

The Raman mapping results of the sample annealed at 1500 °C for 40 h is presented in **Figure 3**. Different layers were identified in the samples. The first layer corresponded to residual silica, followed by a thin layer of La₂Si₂O₇ (O₇). The La₂Si₂O₇ layer did not grow as sintering progressed and its thickness did not exceed 10 µm. Subsequently, a layer of apatite measuring approximately 100 µm thick was formed; as a reference, a 40-µm-thick apatite layer corresponds to highly dense and textured apatite. In the second section of the apatite layer, no preferential orientation was observed. Finally, a residual La₂SiO₅ layer (O₅) was observed, thus indicating the presence of the apatite phase in different zones.

The residual silica layer was removed to analyze the sample surfaces using XRD and SEM (**Figure 4**). The strong 002 and 004 reflection peaks in the XRD patterns confirmed
the preferential orientation along the c-axis of the apatite crystals. However, the La₂Si₂O₇
phase and residual silica were detected in all cases. The Lotgering factor *f*₀₀₁ values
obtained for the samples were 0.73 (10 h) and 0.75 (20 and 40 h). These values were
higher than those obtained in a study pertaining to a La₂SiO₅/SiO(g) diffusion pair (0.59)
[43] and lower than those obtained for a sandwich type La₂SiO₅/La₂Si₂O₇ diffusion pair
(0.81) [41].

<figure><img src="image_5.png" /><figcaption>Figure 4. X-ray diffraction and SEM images of the surface of La₂SiO₅ (support)/SiO₂ (coating) bilayers after reactive sintering at 1500 °C for 10, 20, and 40 h.</figcaption></figure>

The SEM images show the hexagonal form of the oxyapatite crystals, with an average
size between 5 and 10 µm.

Based on observation, the microstructure evolved as the reactive sintering progressed. A
higher sintering time favored the densification of the material and the sample surface
annealed at 1500 °C for 40 h became smooth, thus suggesting the presence of a liquid
phase during the reactive sintering. Abnormal grain growth was also observed.

**Figure 5** shows the cross-section obtained via polarized light microscopy and the Raman mapping of the La<sub>2</sub>SiO<sub>5</sub>(support)/SiO<sub>2</sub>(coating) bilayer after the reactive sintering temperature was increased to 1600 °C for 10 h. The thickness of the oriented apatite layer (42 µm) exceeded that obtained after reactive sintering at 1500 °C under the same duration (18 µm), whereas it was similar to that obtained after sintering at 1500 °C (40 µm) for 40 h, as shown in **Figure 3**. This suggests that increasing the temperature by 100 °C is more effective than extending the sintering time. According to the Raman mapping results, the thickness of the apatite layer formed at 1600 °C for 10 h was approximately 200 µm. As in the previous case, this apatite layer comprised two sections with different characteristics. The first one was a region of highly oriented apatite crystals measuring approximately 42 µm, whereas the other region contained randomly oriented apatite crystals. A thin layer of the La<sub>2</sub>Si<sub>2</sub>O<sub>7</sub> phase was observed between the residual silica layers and the oriented apatite layer.

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Cross-section of La<sub>2</sub>SiO<sub>5</sub> (support)/SiO<sub>2</sub> (coating) bilayer after reactive sintering at 1600 °C/10 h, based on polarized light microscopy, and its Raman mapping.</figcaption></figure>
## 3.2. Characterization of SiO₂(support)/La₂SiO₅(coating) diffusion pairs

The silica supports prepared via electrophoresis for the SiO₂(support)/La₂SiO₅(coating) bilayer were pre-sintered at different temperatures (1200 °C, 1300 °C, 1400 °C, and 1500 °C) to investigate the effect of the silica crystallinity (quartz or cristobalite) and the relative density of the silica before the La₂SiO₅ suspension was deposited. An analysis of these supports is presented in the *supporting information*. The reactive sintering of the bilayers was performed at 1600 °C/10 h.

**Figure 6** shows that, after reactive sintering, the previous La₂SiO₅ layer was completely transformed into an oxyapatite layer that appeared porous and did not adhere well to the silica support. The orientation degree of the apatite crystals on the surface, as calculated based on the XRD pattern (not shown), was particularly low ($f_{001} < 0,17$). However, the thin layer at the interface showed vertically oriented crystals, although the orientation degree in this area of the sample could not be calculated.

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Cross-section of SiO₂ (support) pre-sintered 1200 °C/La₂SiO₅ (coating) bilayer after reactive sintering at 1600 °C/10 h, obtained via polarized light microscopy. Right: zoom-in and EDS images of SiO₂ layer.</figcaption></figure>
The silica support that indicated the best reactivity was the one pre-sintered at 1200 °C, which preserved the quartz structure with a relative density of 66%. However, based on the architecture of this bilayer (see **Figure 6**), the thickness of the oriented apatite layer obtained at 1600 °C for 10 h was extremely low (18 µm) compared with those obtained from the La₂SiO₅ (support)/SiO₂ (coating) bilayers. In this case, only a small fraction of the silica support was consumed, in contrast to the La₂SiO₅ layer, which was completely transformed. Moreover, the EDS analysis showed that lanthanum, which was characterized by small round and white spots, diffused extremely well through the silica grains (dark zone).

**Figure 7** shows the SEM images at different depths of the SiO₂ (support)/La₂SiO₅ (coating) bilayer. At the surface (Figure 7 (a)), apatite crystals were observed. The apatite crystals appeared to have nucleated and begun growing from a dense and glassy silicate layer (Figure 7 (b)). Under this glassy layer, rectangular prisms were formed and their morphology was similar to the monoclinic crystal structure of lanthanum disilicate La₂Si₂O₇ (Figure 7 (d)). The La/Si ratio obtained from the EDS analysis in this area confirmed that they were crystals of the disilicate phase. Additionally, lanthanum diffused into the silica layer, which mainly occurred at the grain boundaries (Figure 7 (c)).
<figure><img src="image_8.png" /><figcaption>**Figure 7.** SEM observations in different areas on surface of SiO₂ (support)/La₂SiO₅ (coating) bilayer: a) and b) lanthanum-rich areas; c) and d) silica-rich areas.</figcaption></figure>

The analysis of the silica supports provided in the *supporting information* reveals the appearance of a glassy phase during the transformation of quartz-α into cristobalite between 1300 °C and 1400 °C. Other studies [59], [60] similarly indicated that the transformation into cristobalite at approximately 1380 °C was accompanied by an intermediate glassy phase, which coated the surface of silica grains. The diffusion of lanthanum through silica is favored by the formation of a liquid-solid interface. This might have contributed to the better reactivity observed in the SiO₂ (support)/La₂SiO₅ (coating) bilayers using silica supports pre-sintered at 1200 °C, which preserved their quartz crystallinity. The formation of this glassy phase can be enhanced when the silica contains trace of elements such as alumina, calcium, and/or other melts. This glassy phase might be vital to the diffusion mechanisms of the species as well as to the nucleation and growth of lanthanum silicate phases.
## 4. Discussion:

### 4.1 Proposed diffusion mechanism during reactive sintering of La₂SiO₅/SiO₂ bilayer

The characterization of the La₂SiO₅ (support)/SiO₂ (coating) diffusion pair showed that both temperature and reactive sintering time significantly affected the thickness of the oriented oxyapatite layer formed. After reactive sintering at 1600 °C for 10 h, an oriented 42-µm-thick apatite layer was formed. Meanwhile, to obtain a similar thickness via sintering at 1500 °C, a holding time of 40 h is required. Furthermore, an analysis of different reactive sintering times revealed that the growth kinetics of the oriented oxyapatite layer decreased after 20 h. The orientation degree of the apatite layer, which is reflected by the Lotgering factor, increased slightly as the reactive sintering temperature increased (the highest value obtained in this study was 0.78). In addition, a higher temperature resulted in a greater conversion of the La₂SiO₅ support into apatite, which was likely due to the better diffusion of species arising from the formation of a liquid-solid interface. Hence, 1600 °C appeared to be a more favorable temperature for the diffusion and nucleation/growth processes during the heat treatment.

An analysis of the SiO₂ (support)/La₂SiO₅ (coating) bilayers showed that the growth of apatite crystals was favored when silica presented quartz crystallinity. The glassy phase generated during the allotropic transformation of quartz into cristobalite appeared to favor the diffusion of rare earth (RE) elements. The La₂SiO₅ layer coating the silica support was consumed rapidly owing to the high lanthanum diffusion, thus resulting in an extremely thin layer of oriented apatite measuring approximately 18 µm.

Some studies pertaining to the diffusion of RE elements demonstrated the strong dissolution and mobility of Y³⁺/RE³⁺ (RE: La→Yb) cations in silica melt phases [49],
[50], [61], [62]. Furthermore, Perrudin et al. [51] indicated that the dissolution kinetics (associated with the basic character of RE element cations) of RE₂O₃ oxides in a CAS matrix (CaO–Al₂O₃–SiO₂) composed primarily of silica increased with the ionic radius of the RE elements. The cationic field strengths FS<fnref n="1" /> of Y³⁺/RE³⁺ (RE: La→Yb) (FS ~ 0.46–0.57 Å⁻²) were similar to that of the well-known lattice modifier Mg²⁺ (FS ~ 0.44 Å⁻²) and might have functioned as a nucleating agent. Lanthanum, which has the largest ionic radius among RE elements, is highly soluble in silica and hence significantly affects the depolymerization of the glass lattice. This breaks the Si–O–Si bonds in the melt, thus promoting the nucleation/growth of microcrystals within the glass. Therefore, when lanthanum oxide was in contact with silica, which is an acidic medium, rapid dissolution and precipitation of di- or ortho-lanthanum silicate crystals (particularly the apatite phase and/or the La₂Si₂O₇ compound) occurred, which is consistent with our observations. Moreover, impurities such as CaO and Al₂O₃, which appeared in trace amounts in the silica used in this study, might enhance the dissolution/precipitation mechanism of these silicate phases. These oxides significantly affect the basicity index, melting temperature, and viscosity of glassy phases [63].

After reactive sintering of the La₂SiO₅/SiO₂ diffusion pair, an intermediate phase of La₂Si₂O₇ was detected on the surface of the obtained oriented apatite layer. The formation of lanthanum disilicate has commonly been observed as a secondary phase during the synthesis of LSO [7], [64], [65]. This can be explained by the enthalpy of formation of the phases, which can also be used to estimate the stability of a compound. The reported enthalpy of formation for La₂Si₂O₇ was -3815.7 ± 4.5 kJ/mol [66], which is significantly

<footnote n="1">¹ The cation field strength is defined as $FS = Z/(Rc+Ra)^2$, where Z is the charge, Rc and Ra are the cation and anion radii, respectively, with the appropriate coordination number, CN.</footnote>
more negative than that reported for the apatite −776.3 ± 17.9 kJ/mol [67]. A more
negative value for the La₂Si₂O₇ indicates that it forms more easily and has higher
thermodynamic stability than the apatite phase.

Other works, including studies pertaining to La₂O₃/SiO₂ systems for catalysis [68]–[70], have also reported the formation of a secondary phase of La₂Si₂O₇. The formation of a core–shell intermediate La₂Si₂O₇ phase was suggested in our previous study [52] pertaining to the synthesis of La₂SiO₅ using La₂O₃ and SiO₂ powders. In this study, we hypothesize that as the La₂Si₂O₇ layer increases, it becomes a diffusion barrier for Si⁴⁺ ions and decelerates the La₂SiO₅ synthesis reaction.

Our current study and previous studies related to the diffusion of RE elements in molten
silica allow us to consider a dissolution-precipitation mechanism at the interface of the
La₂SiO₅/ SiO₂ diffusion pair during reactive sintering. The different steps proposed are
illustrated in **Figure 8** and described below.

<figure><img src="image_9.png" /><figcaption>Figure 8. Schematic illustration of dissolution-precipitation mechanism of La₂SiO₅/SiO₂ bilayer during reactive sintering.</figcaption></figure>
1. In the first step (Figure 8-1), lanthanum diffuses through the glassy phase and $La_2SiO_5$ begins to convert to apatite.

Tests at different sintering temperatures showed that the $La_2SiO_5$ compound in contact with the silica layer rapidly transformed into an apatite layer. Based on the mechanism and equations proposed by Fukuda et al. [41], Equation 8 can be used to explain the dissolution of $La_2O_3$ (i.e., $La^{III}$ and $O^{II}$ species) from lanthanum monosilicate through glassy La–O–Si and new phase formations in apatite.

$$18La_2SiO_{5(s)} - 2(4 - 3x)La^{+III}_{(ss)} - 3(4 - 3x)O^{-II}_{(ss)} \xrightarrow{La-O-Si melt} 3La_{9.33+2x}(SiO_4)_6O_{2+3x(ss)} \quad (8)$$

2. The second step in Figure 8-2 illustrates the crystallization-precipitation of the $La_2Si_2O_7$ phase.

As lanthanum diffusion progressed, the glassy layer of La–Si–O at the interface gradually became enriched with $La^{III}$ species. When the system was saturated, particularly at the grain boundaries, the precipitation of prismatic crystals, which is characteristic of the $La_2Si_2O_7$ phase, occurred (green prisms). Figure 9 shows the progressive growth of these crystals, forming a dense and thin layer of $La_2Si_2O_7$ on the silica surface, as detected via Raman spectroscopy after reactive sintering.

<figure><img src="image_10.png" /><figcaption>Figure 9. Precipitation and formation of $La_2Si_2O_7$ layer.</figcaption></figure>
The phase diagram of La₂O₃–SiO₂ [71] shows that the increase in lanthanum concentration in the glassy of La–Si–O phase results in eutectic equilibrium at 1625 °C, which may explain the precipitation of the La₂Si₂O₇ phase (Equation 9).

$$ \text{Liquid} \overset{1625^{\circ}\text{C}}{\rightleftharpoons} \text{SiO}_{2(\text{s})} + \text{La}_{2}\text{Si}_{2}\text{O}_{7(\text{s})} \quad (9) $$

The temperature at which this equilibrium was attained was similar to the reactive sintering temperature used in the present study and in Fukuda's studies. The formation of this liquid from the eutectic reaction may explain the differences in reactivity between the bilayers sintered at 1500 °C and 1600 °C.

3. The third step describes the factors that promote the mobility of species involved in the nucleation and growth of the oriented apatite crystals.

The continuous diffusion/dissolution of the La⁺⁺⁺ and O⁻⁺ species gradually resulted in the formation of oriented apatite crystals on the La₂Si₂O₇ interlayer. The SEM images in Figure 10 show the manner by which the hexagonal oxyapatite crystals nucleate and develop in the flow direction from the smooth La₂Si₂O₇ layer, which resulted in the formation of a textured apatite layer.

<figure><img src="image_11.png" /><figcaption>Figure 10. Nucleation and growth of oriented apatite crystals from La₂Si₂O₇ layer.</figcaption></figure>
The La₂Si₂O₇ phase was progressively consumed and transformed into a densely oriented apatite, which can be expressed as shown in Equation 10:

$$9\text{La}_2\text{Si}_2\text{O}_7\text{(s)} + 2(5+3x)\text{La}^{+\text{III}}\text{(ss)} + 3(5+3x)\text{O}^{-\text{II}}\text{(ss)} \rightarrow 3\text{La}_{9,33+2x}(\text{SiO}_4)_6\text{O}_{2+3x}(\text{ss}) \quad (10)$$

**Figure 11** summarizes the main diffusion mechanisms that occurred during the reactive sintering of the La₂SiO₅ / SiO₂ diffusion pair. The diffusion of La⁺⁺⁺ from the La₂SiO₅ layer was predominant, not the diffusion of Si⁺⁺⁺ from the SiO₂ layer. Enhanced lanthanum diffusion is associated with the chemical potential gradient in lanthanum between the layers reacting at high temperatures. Therefore, this gradient is the driving force to the mobility of La⁺⁺⁺ species.

<figure><img src="image_12.png" /><figcaption>Figure 11. Diffusion mechanism during reactive sintering of La₂SiO₅-SiO₂ diffusion pair.</figcaption></figure>
Oxygen ions, which exhibit high mobility through an oxyapatite phase [6], [7], [72] can easily be associated with the migration of La<sup>+III</sup> (diffusion of La<sup>+III</sup> and O<sup>-II</sup> ions in the same direction). Hence, the driving force to the mobility of O<sup>-II</sup> species is associated with an electric field $\overrightarrow{F}_{elect}$, which arises from nonequilibrium charges on both sides of the interface. The flow of oxygen ions preserves the electroneutrality of the system. These factors result in a high flux of La<sup>+III</sup> and O<sup>-II</sup> species in one direction and, conversely, a low flux of Si<sup>+IV</sup> species originating from silica in the opposite direction.

This low flux of Si<sup>+IV</sup> species is likely related to the low chemical potential gradient in Si and the presence of lanthanum disilicate (O<sub>7</sub> in **Figure 11**) at the apatite/SiO<sub>2</sub> interface. This phase, which is known to be an extremely poor anionic conductor [73], may result in a slower mobility of the Si<sup>+IV</sup> species and serve as a diffusion barrier. The electrical properties of O<sub>7</sub> suggest that the intensity of the electric field passing through this interphase is relatively high.

As the oxyapatite and lanthanum disilicate (La<sub>2</sub>Si<sub>2</sub>O<sub>7</sub>) layers developed, the driving forces promoting the diffusion of La<sup>+III</sup> and O<sup>-II</sup> species into the silica layer did not change. However, the new phases formed at the interface changed the kinetics and transportation modes of the species (solid-state transitions). The decrease in the diffusion fluxes of La<sup>+III</sup> and O<sup>-II</sup> at the La<sub>2</sub>Si<sub>2</sub>O<sub>7</sub>/apatite interface might have been the origin of the nucleation and particularly of the favored growth of dense apatite crystals in the flow direction.

Using data obtained from the growth kinetics of the apatite layer at 1500 °C and 1600 °C, the activation energy value was calculated using the Arrhenius law. The growth rate constant (k) is an exponential function of temperature.

$$K = k_0 \exp \frac{Q}{RT}, \qquad (11)$$
whereby Q is the activation energy for diffusion-limited growth, k₀ is a constant independent of time and temperature, and R is the global gas constant.

Combining Equations (7) and (11) yields the following equation:

$$e (T, t, n) = k_0 t^n \exp \frac{Q}{RT} \quad (12)$$

The Q value was calculated under the condition that growth was controlled by diffusion (n ≈ 0.5), and the calculated Q value was ≈ 3.8 eV. Because the growth of the apatite layer is diffusion controlled, Q corresponds to the activation energy of diffusion in the apatite layer. Studies showed that the activation energy of oxygen in a textured oxyapatite is low, i.e., 0.32–0.4 eV [17], [19], [25], [41], [44], [46]. Therefore, the calculated activation energy (3.8 eV) may be associated with diffusion of La⁺³³ through the apatite layer. Additionally, this high value of activation energy can explain the need for high temperatures to thermally activate the system.

4. Step 4 refers to the evolution toward a stationary state and the formation of porosity in the previous La₂SiO₅ layer.

The continuous diffusion of La⁺³³ and O⁻² species resulted in matter loss from the previous La₂SiO₅ layer (Equation 8). In fact, the design presented in Figure 8-4 shows the formation of porosity in the previous La₂SiO₅ layer transforming into an apatite. Further microstructural analysis (data not shown) confirmed that this porosity was formed during reactive diffusion. In the silica layer, no porosity evolution was observed.

Porosity formation within the previous La₂SiO₅ layer was induced by the Kirkendall effect. This phenomenon is well known and has been observed in the study of diffusion pairs involving chemical concentration gradients [74], [75]. When the diffusion rate of one chemical species is faster than that of the other, diffusion is generated by a vacancy
mechanism, and the interface shifts in the same direction as the vacancy flow. When the concentration of vacancies is high, they precipitate in the form of pores, which is known as the Kirkendall porosity. These voids serve as vacancy sinks, which can become large and continue to expand to restore equilibrium.

Because of this porosity, the apatite crystals that formed in this zone did not exhibit a well-defined orientation. The numerous voids prevented good diffusion control across the numerous interfaces; thus, the $La^{+III}$ and $O^{-II}$ species diffused in several directions. Furthermore, the presence of this porosity in the previous $La_2SiO_5$ layer can facilitate silica diffusion in a gaseous state (SiO) because a proportion of the silica can vaporize at high temperatures (Equation 13).

$$SiO_{2(s)} \rightarrow SiO_{(g)} + 1/2 O_{2(g)} \quad (13)$$

If gaseous silica diffuses through the $La_2SiO_5$ layer during reactive sintering, non-oriented apatite may form within the $La_2SiO_5$. Once this $La_2SiO_5$ layer is completely consumed and transformed into apatite, the flow of $La^{+III}$ and $O^{-II}$ is insufficient to continue the reactions; thus, the growth of an oriented apatite layer would not occur. This indicates that the system has reached a stationary state.

The SEM image of the cross-section in Figure 8-4 shows an interesting characteristic of the formed apatite layer, which can be categorized into two distinct zones and may facilitate the realization of SOFC half-cell devices. The first is highly dense and textured, which can serve as an electrolyte material and ensure the impermeability of the system. The second is porous and thick (up to 100 µm), which is formed by large apatite grains, and can serve as a cermet electrode after infiltration using a nickel oxide or nickel nitrate suspension. Similar systems have been studied and reported in the literature [76]. Due to the high chemical stability of LSO, some studies using apatite materials as an electrolyte
have highlighted the difficulty of achieving good adhesion with other electrode materials.

In this work, good adhesion between the two apatite layers is observed, resulting in a half-cell having high mechanical properties. Additionally, both layers are composed of the same material, which reduces delamination problems that can arise due to differences in thermal expansion coefficients during operation.

## 5. Conclusion

In this study, the mechanisms involved in the reactive sintering of LSO were elucidated based on La₂SiO₅/SiO₂ diffusion pairs. Characterizations were performed via X-ray diffraction, SEM, EDS, and Raman spectroscopy at the interface and cross-section of the diffusion pairs, which allowed us to determine the critical parameters that govern the preferential orientation along the c-axis of LSO during reactive diffusion. This study suggests that La⁺⁺⁺⁺ and O⁻⁻⁻⁻ are the predominant diffusing species from the La₂SiO₅ layer to the silica layer. The diffusion of the species is expected to be enhanced by the formation of a glassy phase resulting from the transformation of quartz into cristobalite. Additionally, the driving forces for the mobility of the species were explained. The mobilities of lanthanum and oxygen were promoted by a chemical potential gradient and an electric field, respectively. The formation of a thin layer of La₂Si₂O₇ was detected. This layer modified the diffusion flux perpendicular to the interface and controlled the nucleation and growth of the textured LSO. The thicknesses of the c-axis oriented LSO layer vary according to the temperature and reactive sintering time. The temperature of 1600°C allows thicker apatite layers to be obtained in shorter holding times.

In this study, we could not easily determine the diffusion of silica through the La₂SiO₅ layer, as proposed for the La₂Si₂O₇/La₂SiO₅ pair. However, the Si⁺⁺⁺⁺ cations remained
strongly stabilized in the disilicate structure and are expected to exhibit reduced mobility
owing to their position within the oxygen tetrahedra.

The microstructures obtained via reactive diffusion are interesting and exhibit potential
to be used for the development of SOFC half-cells. We plan to focus on separating the
obtained apatite materials in future studies. The dense and oriented apatite layer shall be
used as the electrolyte, whereas the second layer of porous apatite shall be infiltrated with
a nickel oxide or nickel nitrate suspension such that it becomes a mixed conductor and
serves as a cermet electrode.

Acknowledgement

The authors would like to express their gratitude to the PERP H2-Flesixoc project, France 2030, for its support. They would also like to thank Julie Cornette for her technical assistance in the Raman spectroscopy characterizations.

References

[1] J. W. Fergus, Electrolytes for solid oxide fuel cells, *J. Power Sources*, vol. 162, pp. 30–40, 2006, doi: 10.1016/j.jpowsour.2006.06.062.

[2] O. H. Kwon and G. M. Choi, Electrical conductivity of thick film YSZ, *Solid State Ionics*, vol. 177, no. 35–36, pp. 3057–3062, 2006, doi: 10.1016/j.ssi.2006.07.039.

[3] Y. Masubuchi, M. Higuchi, T. Takeda, and S. Kikkawa, Preparation of apatite-type La<sub>0.33</sub>(SiO<sub>4</sub>)<sub>6</sub>O<sub>2</sub> oxide ion conductor by alcoxide-hydrolysis, *J. Alloys Compd.*, vol. 408–412, pp. 641–644, 2006, doi: 10.1016/j.jallcom.2004.12.097.

[4] K. Kobayashi and Y. Sakka, Rudimental research progress of rare-earth silicate oxyapatites: their identification as a new compound until discovery of their oxygen ion conductivity, *J. Ceram. Soc. Japan*, vol. 122, no. 1428, pp. 649–663, 2014, doi: 10.2109/jcersj2.122.649.

[5] A. Chesnaud, C. Bogicevic, F. Karolak, C. Estournès, and G. Dezanneau, Preparation of transparent oxyapatite ceramics by combined use of freeze-drying
and spark-plasma sintering, *Chem. Commun.*, no. 15, pp. 1550–1552, 2007, doi: 10.1039/b615524c.

[6] S. Nakayama and M. Sakamoto, Electrical properties of new type high oxide ionic conductor RE₁₀Si₆O₂₇ (RE = La, Pr, Nd, Sm, Gd, Dy), *J. Eur. Ceram. Soc.*, vol. 18, no. 10, pp. 1413–1418, 1998, doi: 10.1016/s0955-2219(98)00032-6.

[7] E. Béchade, I. Julien, T. Iwata, O. Masson, P. Thomas, E. Champion, K. Fukuda, Synthesis of lanthanum silicate oxyapatite materials as a solid oxide fuel cell electrolyte, *J. Eur. Ceram. Soc.*, vol. 28, no. 14, pp. 2717–2724, 2008, doi: 10.1016/j.jeurceramsoc.2008.03.045.

[8] L. León-Reina, E. R. Losilla, M. Martínez-Lara, S. Bruque, and M. A. G. Aranda, Interstitial oxygen conduction in lanthanum oxy-apatite electrolytes, *J. Mater. Chem.*, vol. 14, no. 7, pp. 1142–1149, 2004, doi: 10.1039/b315257j.

[9] T. Yang, H. Zhao, M. Fang, K. Świerczek, J. Wang, and Z. Du, A new family of Cu-doped lanthanum silicate apatites as electrolyte materials for SOFCs: Synthesis, structural and electrical properties, *J. Eur. Ceram. Soc.*, vol. 39, no. 2–3, pp. 424–431, 2019, doi: 10.1016/j.jeurceramsoc.2018.08.047.

[10] Q. Wang, Z. Huang, and S. Chen, Enhancing conductivity of apatite-type lanthanum silicate by Li and Cu co-doping, *J. Phys. Conf. Ser.*, vol. 2351, no. 1, 2022, doi: 10.1088/1742-6596/2351/1/012010.

[11] S. Afroze, H. Absah, M. Reza, M. Somalu, J. Park, S. Nekoonam, A. Issakhov, A. Azad, Structural and electrochemical properties of lanthanum silicate apatites La₁₀Si₆-x-0.2AlxZn₀.2O₂₇-δ for Solid Oxide Fuel Cells (SOFCs), *Int. J. Chem. Eng.*, vol. 2021, pp. 1–10, 2021, doi: 10.1155/2021/6621373.

[12] Y. Feng, L. Dai, W. Meng, Z. He, Y. Li, and L. Wang, Microstructure and electrical conductivity of alkaline elements doped apatite-type La₁₀Si₆O₂₇ electrolytes, *Ceram. Int.*, vol. 43, no. 1, pp. 289–295, 2017, doi: 10.1016/j.ceramint.2016.09.153.

[13] P. J. Panteix, I. Julien, P. Abélard, and D. Bernache-Assollant, “Influence of porosity on the electrical properties of La₉.₃三(SiO₄)₆O₂ oxyapatite,” *Ceram. Int.*, vol. 34, no. 7, pp. 1579–1586, 2008, doi: 10.1016/j.ceramint.2007.05.004.

[14] A. Chesnaud, G. Dezanneau, C. Estournes, C. Bogicevic, F. Karolak, S. Geiger, G. Geneste, Influence of synthesis route and composition on electrical properties of La₉.₃三+xSi₆O₂₆+3x/2 oxy-apatite compounds, *Solid State Ionics*, vol. 179, no. 33–34, pp. 1929–1939, 2008, doi: 10.1016/j.ssi.2008.04.035.

[15] J. M. Porras-Vázquez, E. R. Losilla, L. León-Reina, D. Marrero-López, and M. A. G. Aranda, Microstructure and oxide ion conductivity in a dense La₉.₃三(SiO₄)₆O₂ oxy-Apatite, *J. Am. Ceram. Soc.*, vol. 92, no. 5, pp. 1062–1068, 2009, doi: 10.1111/j.1551-2916.2009.03032.x.
[16] J. Li, Q. Cai, and B. A. Horri, Synthesis and densification of Mo/Mg Co-doped apatite-type lanthanum silicate electrolytes with enhanced ionic conductivity, *Chem. – A Eur. J.*, 2023, doi: 10.1002/chem.202300021.

[17] K. Fukuda, T. Asaka, M. Okino, A. Berghout, E. Béchade, O Masson, I. Julien, P. Thomas, Anisotropy of oxide-ion conduction in apatite-type lanthanum silicate, *Solid State Ionics*, vol. 217, pp. 40–45, 2012, doi: 10.1016/j.ssi.2012.04.018.

[18] K. Fukuda, T. Asaka, and T. Uchida, Thermal expansion of lanthanum silicate oxyapatite (La<sub>9.33</sub>+2x(SiO<sub>4</sub>)<sub>6</sub>O<sub>2+3x</sub>), lanthanum oxyorthosilicate (La<sub>2</sub>SiO<sub>5</sub>) and lanthanum sorosilicate (La<sub>2</sub>Si<sub>2</sub>O<sub>7</sub>)," *J. Solid State Chem.*, vol. 194, pp. 157–161, 2012, doi: 10.1016/j.jssc.2012.04.043.

[19] E. Béchade, O. Masson, T. Iwata, I. Julien, K. Fukuda, P. Thomas, E. Champion, Diffusion path and conduction mechanism of oxide ions in apatite-type lanthanum silicates, *Chem. Mater.*, vol. 21, no. 12, pp. 2508–2517, 2009, doi: 10.1021/cm900783j.

[20] O. Masson, A. Berghout, E. Béchade, J. Jouin, P. Thomas, T. Asaka, K. Fukuda, Local structure and oxide-ion conduction mechanism in apatite-type lanthanum silicates, *Sci. Technol. Adv. Mater.*, vol. 18, no. 1, pp. 644–653, 2017, doi: 10.1080/14686996.2017.1362939.

[21] K. Matsunaga and K. Toyoura, First-principles analysis of oxide-ion conduction mechanism in lanthanum silicate, *J. Mater. Chem.*, vol. 22, no. 15, pp. 7265–7273, 2012, doi: 10.1039/c2jm16283k.

[22] K. Imaizumi, K. Toyoura, A. Nakamura, and K. Matsunaga, Strong correlation in 1D oxygen-ion conduction of apatite-type lanthanum silicate, *J. Phys. Condens. Matter*, vol. 27, no. 36, p. 365601, 2015, doi: 10.1088/0953-8984/27/36/365601.

[23] A. Yadav, O. N. Verma, R. Pandey, N. Jha, and P. Singh, Ion dynamics and electrical transport in lanthanum silicate apatite (La<sub>9.67</sub>Si<sub>6</sub>O<sub>26.5</sub>), *Appl. Phys. A*, vol. 128, no. 10, p. 862, 2022, doi: 10.1007/s00339-022-05963-6.

[24] S. Nakayama, M. Sakamoto, M. Highchi, and K. Kodaira, Oxide ionic conductivity of apatite type Nd<sub>9.33</sub>(SiO<sub>4</sub>)<sub>6</sub>O<sub>2</sub> Single Crystal,” *J. Eur. Ceram. Soc.*, vol. 19, pp. 507–510, 1999, doi: 10.1016/s0955-2219(98)00215-5.

[25] S. Nakayama, M. Sakamoto, M. Highchi, and K. Kodaira, “Ionic conductivities of apatite type Nd<sub>x</sub>(SiO<sub>4</sub>)<sub>6</sub>O<sub>1.5x-12</sub> (X = 9.20 and 9.33) single crystals, *J. Mater. Sci. Lett.*, vol. 19, no. 2, pp. 91–93, 2000, doi: 10.1023/A:1006674708833.

[26] H. Okudera, Y. Masubuchi, S. Kikkawa, and A. Yoshiasa, Structure of oxide ion-conducting lanthanum oxyapatite, La<sub>9.33</sub>(SiO<sub>4</sub>)<sub>6</sub>O<sub>2</sub>, *Solid State Ionics*, vol. 176, no. 15–16, pp. 1473–1478, 2005, doi: 10.1016/j.ssi.2005.02.014.
[27] S. Nakayama, A. Ikesue, Y. Higuchi, M. Sugawara, and M. Sakamoto, Growth of single-crystals of apatite-type oxide ionic conductor from sintered ceramics by a seeding method, *J. Eur. Ceram. Soc.*, vol. 33, no. 2, pp. 207–210, 2013, doi: 10.1016/j.jeurceramsoc.2012.09.013.

[28] M. M. Vieira, J. C. Oliveira, A. L. Shaula, B. Trindade, and A. Cavaleiro, Structure and ionic conductivity of reactively sputtered apatite-type lanthanum silicate thin films, *Surf. Coatings Technol.*, vol. 247, pp. 14–19, 2014, doi: 10.1016/j.surfcoat.2014.02.064.

[29] M. M. Vieira, J. C. Oliveira, A. L. Shaula, A. Cavaleiro, and B. Trindade, Lanthanum silicate thin films for SOFC electrolytes synthesized by magnetron sputtering and subsequent annealing, *Surf. Coatings Technol.*, vol. 206, no. 14, pp. 3316–3322, 2012, doi: 10.1016/j.surfcoat.2012.01.042.

[30] M. Sakao, T. Ishihara, and H. Yoshioka, Fabrication and ionic conductivity of oriented lanthanum silicate films with apatite-type structure, *Solid State Ionics*, vol. 293, pp. 51–55, 2016, doi: 10.1016/j.ssi.2016.05.018.

[31] S. Hori, Y. Takatani, H. Kadoura, T. Uyama, S. Fujita, and T. Tani, Chemical solution deposition of the highly c-axis oriented apatite type lanthanum silicate thin films, *Dalt. Trans.*, vol. 44, no. 40, pp. 17551–17556, 2015, doi: 10.1039/c5dt02569a.

[32] S. Hori, T. Akashi, H. Funabashi, H. Iguchi, H. Matsuo, and T. Tani, Orientation mechanism during crystallization of apatite-type lanthanum silicate thin films from an amorphous precursor, *J. Eur. Ceram. Soc.*, vol. 37, no. 15, pp. 4773–4779, 2017, doi: 10.1016/j.jeurceramsoc.2017.06.034.

[33] K. Ueda, A. Mineshige, H. Takahashi, A. Saito, Y. Daiko, H. Yoshioka, T. Yazawa, C-Axis oriented apatite-type silicates as solid electrolytes, *ECS Trans.*, vol. 57, no. 1, pp. 1143–1149, 2013, doi: 10.1149/05701.1143ecst.

[34] T. S. Suzuki, S. Takahashi, T. Uchikoshi, T. Ishigaki, and K. Kobayashi, Anisotropic electric conductivity and battery performance in c-axis oriented lanthanum silicate oxyapatite prepared by slip casting in a strong magnetic field, *Mater. Trans.*, vol. 60, no. 9, pp. 1949–1953, 2019, doi: 10.2320/matertrans.YM2019832.

[35] K. Kobayashi, K. Hirai, T. Uchikoshi, Y. Sakka, T. Akashi, and T. S. Suzuki, Production of crystal-oriented lanthanum silicate oxyapatite ceramics with anisotropic electrical conductivity and thermal expansion, *Open Ceram.*, vol. 6, 2021, doi: 10.1016/j.oceram.2021.100100.

[36] K. Fukuda, Y. Tsunoda, D. Urushihara, T. Asaka, and H. Yoshida, Flux growth of doped lanthanum silicate oxyapatite crystals with hexagonal tabular morphology, *J. Ceram. Soc. Japan*, vol. 127, no. 3, pp. 143–149, 2019, doi: 10.2109/jcersj2.18174.
[37] K. Fukuda, F. Maekawa, T. Eguchi, Y. Tsunoda, D. Urushihara, T. Asaka, H. Yoshida, Templated grain growth of textured lanthanum silicate oxyapatite ceramics, *J. Ceram. Soc. Japan*, vol. 128, no. 11, pp. 954–961, 2020, doi: 10.2109/jcersj2.20171.

[38] M. Setoguchi, Crystal growth of silicate apatites by flux method, *J. Cryst. Growth*, vol. 99, no. 1–4, pp. 879–884, 1990, doi: 10.1016/S0022-0248(08)80045-0.

[39] B. M. Wanklyn, F. R. Wondre, G. B. Ansell, and W. Davison, Flux growth of rare earth silicates and aluminosilicates, *J. Mater. Sci.*, vol. 9, no. 12, pp. 2007–2014, 1974, doi: 10.1007/BF00540550.

[40] K. Fukuda, T. Eguchi, F. Maekawa, D. Urushihara, T. Asaka, H. Yoshida, E. Béchade, O. Masson, P. Thomas, Morphology and oxide-ion conductivity of flux grown single crystals of BaO-doped lanthanum silicate oxyapatite, *Solid State Ionics*, vol. 346, 2020, doi: 10.1016/j.ssi.2019.115219.

[41] K. Fukuda, T. Asaka, R. Hamaguchi, T. Suzuki, H. Oka, A. Berghout, E. Béchade, O. Masson, I. Julien, E. Champion, P. Thomas, Oxide-ion conductivity of highly c-axis-oriented apatite-type lanthanum silicate polycrystal formed by reactive diffusion between La₂SiO₅ and La₂Si₂O₇, *Chem. Mater.*, vol. 23, no. 24, pp. 5474–5483, 2011, doi: 10.1021/cm2029905.

[42] K. Fukuda, R. Watanabe, M. Oyabu, R. Hasegawa, T. Asaka, and H. Yoshida, “Oxide-Ion Conductivity Enhancement of Polycrystalline Lanthanum Silicate Oxyapatite Induced by BaO Doping and Grain Alignment,” *Cryst. Growth Des.*, vol. 16, no. 8, pp. 4519–4525, 2016, doi: 10.1021/acs.cgd.6b00638.

[43] K. Fukuda, R. Hasegawa, T. Kitagawa, H. Nakamori, T. Asaka, A. Berghout, E. Béchade, O. Masson, J. Jouin, P. Thomas, Well-aligned polycrystalline lanthanum silicate oxyapatite grown by reactive diffusion between solid La₂SiO₅ and gases [SiO+1/2O₂], *J. Solid State Chem.*, vol. 235, pp. 1–6, 2016, doi: 10.1016/j.jssc.2015.12.007.

[44] S. Ide, H. Takahashi, I. Yashima, K. Suematsu, K. Watanabe, and K. Shimanoe, Effect of boron substitution on oxide-ion conduction in c-axis-oriented apatite-type lanthanum silicate,” *J. Phys. Chem. C*, vol. 124, no. 5, pp. 2879–2885, 2020, doi: 10.1021/acs.jpcc.9b11454.

[45] K. Fukuda, T. Asaka, S. Hara, M. Oyabu, A. Berghout, E. Béchade, O. Masson, I. Julien, P. Thomas, Crystal structure and oxide-ion conductivity along c-axis of si-deficient apatite-type lanthanum silicate, *Chem. Mater.*, vol. 25, no. 10, pp. 2154–2162, 2013, doi: 10.1021/cm400892p.

[46] K. Fukuda, T. Asaka, M. Oyabu, D. Urushihara, A. Berghout, E. Béchade, O. Masson, I. Julien, P. Thomas, Crystal structure and oxide-ion conductivity along c-axis of apatite-type lanthanum silicate with excess oxide ions,” *Chem. Mater.*,
vol. 24, no. 23, pp. 4623–4631, 2012, doi: 10.1021/cm3034643.

[47] K. Fukuda, M. Okabe, and T. Asaka, Microtexture of c-axis oriented polycrystalline lanthanum silicate oxyapatite formed by reactive diffusion, vol. 2822, no. 37965, pp. 2816–2822, 2016, doi: 10.1111/jace.14283.

[48] A. A. El Mel, R. Nakamura, and C. Bittencourt, The Kirkendall effect and nanoscience: hollow nanospheres and nanotubes, *Beilstein J. Nanotechnol.*, vol. 6, no. 1, pp. 1348–1361, 2015, doi: 10.3762/bjnano.6.139.

[49] D. L. Poerschke, T. L. Barth, and C. G. Levi, Equilibrium relationships between thermal barrier oxides and silicate melts, *Acta Mater.*, vol. 120, pp. 302–314, 2016, doi: 10.1016/j.actamat.2016.08.077.

[50] D. L. Poerschke, R. W. Jackson, and C. G. Levi, Silicate deposit degradation of engineered coatings in gas turbines: progress toward models and materials solutions, *Annu. Rev. Mater. Res.*, vol. 47, pp. 297–330, 2017, doi: 10.1146/annurev-matsci-010917-105000.

[51] F. Perrudin, M. H. Vidal-Sétif, C. Rio, C. Petitjean, P. J. Panteix, and M. Vilasi, Influence of rare earth oxides on kinetics and reaction mechanisms in CMAS silicate melts, *J. Eur. Ceram. Soc.*, vol. 39, no. 14, pp. 4223–4232, 2019, doi: 10.1016/j.jeurceramsoc.2019.06.036.

[52] L. Arbelaez, P.-M. Geffroy, A. Aimable, K. Fukuda, and E. Béchade, “High-purity synthesis of La₂SiO₅ by solid-state reaction between La₂O₃ and different characteristics of SiO₂, *Ceram. Int.*, vol. 46, no. 16, pp. 25546–25555, 2020, doi: 10.1016/j.ceramint.2020.07.026.

[53] J. L. Jones, E. B. Slamovich, and K. J. Bowman, Critical evaluation of the Lotgering degree of orientation texture indicator, *J. Mater. Res.*, vol. 19, no. 11, pp. 3414–3422, 2004, doi: 10.1557/JMR.2004.0440.

[54] Z. Zhang, X. Duan, B. Qiu, Z. Yang, D. Cai, P. He, D. Jia, Y. Zhou, Preparation and anisotropic properties of textured structural ceramics: A review, *J. Adv. Ceram.*, vol. 8, no. 3, pp. 289–332, 2019, doi: 10.1007/s40145-019-0325-5.

[55] G. V. Kidson, Some aspects of the growth of diffusion layers in binary systems, *J. Nucl. Mater.*, vol. 3, no. 1, pp. 21–29, 1961, doi: 10.1016/0022-3115(61)90175-1.

[56] C. Wagner, The evaluation of data obtained with diffusion couples of binary single-phase and multiphase systems, *Acta Metall.*, vol. 17, no. 2, pp. 99–107, 1969, doi: 10.1016/0001-6160(69)90131-X.

[57] A. Wierzbicka-Miernik, K. Miernik, R. Filipek, and K. Szyszkiewicz, Kinetics of intermetallic phase growth and determination of diffusion coefficients in solid-solid-state reaction between Cu and (Sn+1at.%Ni) pads, *J. Mater. Sci.*,
vol. 52, no. 17, pp. 10533-10544, 2017, doi: 10.1007/s10853-017-1187-2.

[58] N. Thiyaneshwaran, K. Sivaprasad, and B. Ravisankar, Characterization based analysis on TiAl₃ intermetallic phase layer growth phenomenon and kinetics in diffusion bonded Ti/TiAl₃/Al laminates, *Mater. Charact.*, vol. 174, pp. 110981, 2021, doi: 10.1016/j.matchar.2021.110981.

[59] A. Kazemi, M. A. Faghihi-Sani, and H. R. Alizadeh, Investigation on cristobalite crystallization in silica-based ceramic cores for investment casting, *J. Eur. Ceram. Soc.*, vol. 33, no. 15-16, pp. 3397-3402, 2013, doi: 10.1016/j.jeurceramsoc.2013.06.025.

[60] H. Schneider, A. Majdic, and R. Vasudevan, Kinetics of the quartz-cristobalite transformation in refractory-grade silica materials, *Mater. Sci. Forum*, vol. 7, pp. 91-102, 1986, doi: 10.4028/www.scientific.net/MSF.7.91.

[61] C. S. J. Shaw, Effects of melt viscosity and silica activity on the rate and mechanism of quartz dissolution in melts of the CMAS and CAS systems, *Contrib. to Mineral. Petrol.*, vol. 151, no. 6, pp. 665-680, 2006, doi: 10.1007/s00410-006-0086-3.

[62] Y. Zhang, H. Ni, and Y. Chen, Diffusion data in silicate melts," *Rev. Mineral. Geochemistry*, vol. 72, no. 1, pp. 311-408, 2010, doi: 10.2138/rmg.2010.72.8.

[63] M. Craig, N. L. Ndamka, R. G. Wellman, and J. R. Nicholls, CMAS degradation of EB-PVD TBCs: the effect of basicity, *Surf. Coatings Technol.*, vol. 270, pp. 145-153, 2015, doi: 10.1016/j.surfcoat.2015.03.009.

[64] C. Bonhomme, S. Beaudet-Savignat, T. Chartier, A. Maître, A. L. Sauvet, and B. Soulestin, Sintering kinetics and oxide ion conduction in Sr-doped apatite-type lanthanum silicates, *La<sub>9</sub>Sr<sub>1</sub>Si<sub>6</sub>O<sub>26.5</sub>, Solid State Ionics*, vol. 180, no. 36-39, pp. 1593-1598, 2009, doi: 10.1016/j.ssi.2009.10.009.

[65] P. J. Panteix, I. Julien, D. Bernache-Assollant, and P. Abélard, Synthesis and characterization of oxide ions conductors with the apatite structure for intermediate temperature SOFC, *Mater. Chem. Phys.*, vol. 95, no. 2-3, pp. 313-320, 2006, doi: 10.1016/j.matchemphys.2005.06.040.

[66] M. Bolech, F. J. J. G. Janssen, A. S. Booij, and E. H. P. Cordfunke, The standard molar enthalpies of formation of β-La<sub>2</sub>Si<sub>2</sub>O<sub>7</sub> and β-Ce<sub>2</sub>Si<sub>2</sub>O<sub>7</sub>," *J. Chem. Thermodyn.*, vol. 28, no. 11, pp. 1319-1324, 1996, doi: 10.1006/jcht.1996.0116.

[67] A. S. Risbud, K. B. Helean, M. C. Wilding, P. Lu, and A. Navrotsky, Enthalpies of formation of lanthanide oxyapatite phases, *J. Mater. Res.*, vol. 16, no. 10, pp. 2780-2783, 2001, doi: 10.1557/JMR.2001.0381.

[68] R. E. Przekop, P. Marciniak, B. Sztorch, A. Czapik, M. Stodolny, and A. Martyła, One-pot synthesis method of SiO<sub>2</sub>-La<sub>2</sub>O<sub>2</sub>CO<sub>3</sub> and SiO<sub>2</sub>-La<sub>2</sub>O<sub>3</sub> systems using
metallic lanthanum as a precursor, *J. Non. Cryst. Solids*, vol. 520, pp. 119444, 2019, doi: 10.1016/j.jnoncrysol.2019.05.020.

[69] H. Vidal, S. Bernal, R.T. Baker, D. Finol, J.A. Omil, J.M. Pérez Pintado, J.M. Rodríguez-Izquierdo, Characterization of La₂O₃/SiO₂ mixed oxide catalyst supports, *J. Catal.*, vol. 183, no. 1, pp. 53–62, 1999, doi: 10.1006/jcat.1998.2354.

[70] B. M. Faroldi, E. A. Lombardo, and L. M. Cornaglia, Surface properties and catalytic behavior of Ru supported on composite La₂O₃–SiO₂ oxides, *Appl. Catal. A Gen.*, vol. 369, no. 1–2, pp. 15–26, 2009, doi: 10.1016/j.apcata.2009.08.024.

[71] N. A. Toropov and I. A. Bondar, Silicates of rare-earth elements, *Bull. Acad. Sci. USSR Div. Chem. Sci.*, vol. 10, no. 5, pp. 682–687, 1961, doi: 10.1007/BF00905927.

[72] P. M. Geffroy, A. Pons, E. Béchade, O. Masson, and J. Fouletier, Characterization of electrical conduction and nature of charge carriers in mixed and ionic conductors, *J. Power Sources*, vol. 360, pp. 70–79, 2017, doi: 10.1016/j.jpowsour.2017.06.003.

[73] K. Amezawa, J. Yamada, N. Kitamura, Y. Tomii, T. Handa, and N. Yamamoto, High temperature protonic conduction in Sr-doped La₂Si₂O₇, "*Solid State Ionics*, vol. 176, no. 3–4, pp. 341–347, 2005, doi: 10.1016/j.ssi.2004.07.015.

[74] F. Zhang, B. Zhang, X. Chen, X. Zhang, X. Zhu, and H. Du, Computational simulation of voids formation and evolution in Kirkendall effect, *Phys. A Stat. Mech. its Appl.*, vol. 554, p. 124285, 2020, doi: 10.1016/j.physa.2020.124285.

[75] M. J. M. Hermans and M. H. Biglari, Void formation by Kirkendall effect in solder joints, in *The ELFNET Book on Failure Mechanisms, Testing Methods, and Quality Issues of Lead-Free Solder Interconnects*, G. Grossmann and C. Zardini, Eds. Springer, 2011, pp. 105–122.

[76] A. Brisse, A.-L. Sauvet, C. Barthet, S. Beaudet-Savignat, and J. Fouletier, Electrochemical characterizations of Ni/doped lanthanum silicates cermets deposited by spin coating, "*Fuel Cells*, vol. 6, no. 1, pp. 59–63, 2006, doi: 10.1002/fuce.200500097.

## Figure Captions

**Figure 1.** La₂SiO₅/La₂Si₂O₇ diffusion pair proposed by Fukuda et al [41].

**Figure 2.** Reference spectra for multivariate analysis using direct classical least-square
method.

**Figure 3.** Cross-section of La<sub>2</sub>SiO<sub>5</sub> (support)/SiO<sub>2</sub> (coating) bilayer after reactive sintering at 1500 °C for 10, 20, and 40 h, obtained via polarized light microscopy. Raman mapping of a sample at 1500 °C/40 h.

**Figure 4.** X-ray diffraction and SEM images of the surface of La<sub>2</sub>SiO<sub>5</sub> (support)/SiO<sub>2</sub> (coating) bilayers after reactive sintering at 1500 °C for 10, 20, and 40 h.

**Figure 5.** Cross-section of La<sub>2</sub>SiO<sub>5</sub> (support)/SiO<sub>2</sub> (coating) bilayer after reactive sintering at 1600 °C/10 h, based on polarized light microscopy, and its Raman mapping.

**Figure 6.** Cross-section of SiO<sub>2</sub> (support) pre-sintered 1200 °C/La<sub>2</sub>SiO<sub>5</sub> (coating) bilayer after reactive sintering at 1600 °C/10 h, obtained via polarized light microscopy. Right: zoom-in and EDS images of SiO<sub>2</sub> layer.

**Figure 7.** SEM observations in different areas on surface of SiO<sub>2</sub> (support)/La<sub>2</sub>SiO<sub>5</sub> (coating) bilayer: a) and b) lanthanum-rich areas; c) and d) silica-rich areas.

**Figure 8.** Schematic illustration of dissolution-precipitation mechanism of La<sub>2</sub>SiO<sub>5</sub>/SiO<sub>2</sub> bilayer during reactive sintering.

**Figure 9.** Precipitation and formation of La<sub>2</sub>Si<sub>2</sub>O<sub>7</sub> layer.

**Figure 10.** Nucleation and growth of oriented apatite crystals from La<sub>2</sub>Si<sub>2</sub>O<sub>7</sub> layer.

**Figure 11.** Diffusion mechanism during reactive sintering of La<sub>2</sub>SiO<sub>5</sub>-SiO<sub>2</sub> diffusion pair.

## Tables

**Table 1.** Crystallized phases identified via X-ray diffraction.