Sol—gel approach to low-temperature synthesis of single-phase metastable La2Ga3O7.5 melilite with enhanced grain-boundary oxide ionic conductivity via a kinetically favorable mechanism

Starting with the stoichiometric and highly homogeneous gel-precursor, single-phase metastable melilite La2Ga3O7.5, as the end-member of solid solution La1+xSr1−xGa3O7+x/2 (0≼x≼1), has been synthesized by solid-state reaction at 700 °C for 2 h via a kinetically favorable mechanism and characterized by X-ray diffraction (XRD), Raman, X-ray photoelectron spectroscopy (XPS), field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), AC impedance spectroscopy, etc. It has been revealed that the as-synthesized melilite La2Ga3O7.5 shows an orthorhombic symmetry with crystal cell parameters a = 11.4690(1) Å, b = 11.2825(4) Å, and c = 10.3735(4) Å, while has more Raman active modes than LaSrGa3O7 with a tetragonal structure, which was also synthesized under the same conditions for comparison, but tends to slowly decompose into perovskite LaGaO3 and Ga2O3 when annealed at 700 °C for over 20 h driven by its meta-stability. Moreover, the metastable La2Ga3O7.5 shows a higher XPS binding energy for the excess oxide ions in the crystal structure than those at normal lattice sites. Its intrinsic grain oxide ion conductivity can reach as high as 0.04 and 0.51 mS·cm−1 at 550 and 700 °C, respectively, characterized by a simple Arrhenius relationship ln(σT)—1/T with invariable activation energy, Ea = 1.22 eV, over the temperature range from 300 to 700 °C, along with an apparent grain boundary conductivity that is about double that from the grains thanks to the clean grain boundaries. This paper provides a new strategic approach to the synthesis of complex oxides that may be of high performance but are difficultly achieved by the conventional ceramic method at high temperatures.


Introduction 
Oxide ion conductors are solid electrolyte materials which are widely applied in modern electrochemical devices, including solid oxide fuel cells (SOFCs), oxygen sensors, oxygen pumps, etc. [1][2][3][4], and their to 0.6 by the aerodynamic levitation (ADL) laser heating method through direct crystallization of the undercooled melt. Afterwards, Xu et al. [27] synthesized melilite La 1+x Ca 1−x Al 3 O 7+0.5x (0 ≤ x ≤ 0.6) by the same method, which has not been obtained so far for x > 0 by the conventional solid-state reaction method. More interestingly, Fan et al. [28] successfully obtained metastable melilite La 2 Ga 3 O 7.5 by a similar method, in which the maximum solid solution limit (x max ) is extended to 1 from ~0.64, and the nominal interstitial oxide ion content is as high as 0.5 per unit formula in the crystal structure. Moreover, such a metastable melilite La 2 Ga 3 O 7.5 has been found to possess a greatly suppressed oxide ionic conductivity due to the longrange ordering of the interstitial oxide ions in the crystal structure [29].
Nevertheless, the crystallization of under-cooled melt appears not to be a flawless approach to the synthesis of complex oxides that are difficultly obtained by the conventional methods. The compositional deviation of the melt for different volatilities of raw oxides at high temperatures and incomplete crystallization would yield impurity phases at the grain boundaries, which may significantly deteriorate the grain boundary conductivity. As reported in the literature [28], although Ga-excess recipe can be used empirically to compensate for the loss of Ga during the high temperature melting process of the starting oxides, it is still too difficult to achieve an accurate chemical composition for the desired melilite phase. As a result, the nonconductive impurity phases inevitably remain at the grain boundaries in the crystallization products.
In this paper, the highly homogeneous gel-precursors with precisely controlled chemical compositions, instead of the under-cooled melt or glassy materials, were adopted to synthesize the single-phase melilite La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 by the solid-state reactions at low temperatures. After a full characterization by X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), Raman, AC impedance spectroscopy, etc., we found that the single-phase melilite La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 can be easily synthesized from their gelprecursors at 700 ℃ for 2 h, and the as-synthesized La 2 Ga 3 O 7.5 shows an orthorhombic symmetry, but can spontaneously decompose into the perovskite LaGaO 3 and Ga 2 O 3 when annealed at 700 ℃ for a prolonged time due to its meta-stability. More interestingly, its www.springer.com/journal/40145 total oxide ion conductivity exhibits a simple Arrhenius relationship ln(T)-1/T with invariable activation energy over the temperature range in this study without the bending reported previously in the literature [28]. In addition, based on the analysis of the relevant experimental results, a kinetically favorable mechanism is proposed, which provides a way to better understand how the precursors or reactants with different spatial inhomogeneity of chemical species would likely give rise to the formation of different products.

2 Preparation of samples
Using analytic grade La 2 O 3 , SrCO 3 , and Ga 2 O 3 as raw materials and EDTA-CA as co-complexant, the single-phase La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 samples were synthesized and prepared through the EDTA-CA co-complex sol-gel process, solid-state reaction, and sintering at elevated temperatures. Specifically, the calculated amounts of La 2 O 3 , SrCO 3 , and Ga 2 O 3 according to the targeted melilite phases were dissolved in an appropriate volume of concentrated nitric acid to obtain a clear and transparent nitrate solution. Then, EDTA ammonia buffer solution and CA·H 2 O were added to the nitrate solution in the molar ratio 1 : 1.5 : 1 of total metal ions M to CA to EDTA. Ammonia was subsequently introduced dropwise to adjust the pH to 7, and then the solvent was evaporated under continuous stirring in a water bath at 80 ℃ to obtain a viscous transparent gel. The gels were dried in an oven at 120 ℃ and calcined in a muffle furnace at 700 ℃ for 2 h to synthesize the La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 powders. These powders were ball-milled with ethanol as a dispersant for 12 h, and dried before uniaxially pressed into pellets of 12 mm in diameter and 1 mm in thickness at 300 MPa with PVA as the binder. The binder was removed by calcining the pellets in the air at 300 ℃ for 1 h, and then the sintering was carried out at 700 ℃ for 2 h to obtain the sintered La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 samples.

3 Structural characterization
A Fourier infrared spectrometer (FTIR, iN10, Nicolet) with the wavenumber range from 400 to 4000 cm −1 was used to determine the complexation state of the gels. The reaction process of the gels was tracked by a thermogravimetry-differential scanning calorimeter (TG-DSC, STA 449 F1, NETZSCH) in a temperature range from room temperature to 900 ℃ at a ramping rate of 5 ℃/min in the air. An X-ray diffractometer (40 kV/ 30 mA, λ = 1.5418 Å/Cu Kα, SmartLabTM 3kW, Rigaku) was used for phase identification and structural characterization of the samples in the 2θ range from 10° to 80°. The morphology of the samples was characterized by a field emission scanning electron microscope (FESEM, SU8200, Hitachi). A highresolution transmission electron microscope (HRTEM, Tecnai G2 F30, FEI) was used to observe the grain microstructure and crystal structure of the samples. The relative densities of the sintered samples were determined by the Archimedes drainage method. To determine the constituent elements and their chemical states, the XPS spectra of the samples were recorded by an X-ray photoelectron spectrometer (K-Alpha, Thermo Fisher Scientific) and analyzed by XPSPEAK 4.1 software after the calibration of binding energy by C 1s (284.8 eV) of carbon. The Raman spectra of the synthesized samples were measured by a Raman spectrometer (LabRAM HR Evolution, HORIBA) with a laser excitation wavelength of 514 nm to deeply investigate the structural characteristics.

4 Electrical property measurements
The sintered bulk samples were ground, polished, and ultrasonically cleaned, and then coated with Ag paste on both sides to form thin film electrodes for measuring the oxide ion conductivities. The samples were measured by an electrochemical workstation (SI-1260, Solartron Metrology) with a constant amplitude AC signal of 5 mV in the frequency range of 0.1 Hz to 1 MHz at temperatures ranging from 300 to 700 ℃. Based on the appropriate equivalent circuit, the measured impedance spectra were numerically analyzed by ZSimpWin software, and then the oxide ion conductivities of the La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 bulk samples at different conditions were obtained.

1 Synthesis and structures of La 2 Ga 3 O 7.5 and LaSrGa 3 O 7
To track the formation and change of the gels, the FTIR spectra of EDTA, CA·H 2 O, complexed dry gel, and La 2 Ga 3 O 7.5 samples obtained by calcining the dry gel at 700 ℃ were recorded, and the results are shown in Fig. S1 in the Electronic Supplementary Material (ESM). It can be noted that, the metal ions can be complexed well with both EDTA and CA molecules, which allows the well-complexed metal ions to be uniformly distributed in the gel network and leads to the formation of a highly homogeneous gelprecursor by esterification cross-linking. The typical TG-DSC curves of the gel-precursor for La 2 Ga 3 O 7.5 are shown in Fig. 1. It can be seen that the gel decomposition process mainly goes through four stages. The small DSC endothermic peaks at 168 and 212 ℃, accompanied by a weight loss of about 10% in the TG diagram, should be attributed to the volatilization of free water and crystallized water. The sharp DSC exothermic peak at 267 ℃, corresponding to a weight loss of about 35%, may result from the violent oxidation of complexing agents with the nitrate oxidant, which is tailored in quantity so as not to initiate a sustainable auto-combustion but provoke the pyrolysis of complexing agents. A broad exothermic peak at 359 ℃ corresponds to a weight loss of about 25% and can be attributed to the oxidative decomposition of the metal carboxylate in the initial pyrolytic products and the release of large amounts of CO 2 and H 2 O. Similarly, the broad exothermic peak at 444 ℃, corresponding to a weight loss of about 10%, is attributable to the oxidation of pyrolytic product N(CH 2 ) 3 with oxygen in the air [30]. After that, the sample gradually tends to keep a constant weight as the temperature is increased over 500 ℃ , suggesting that the gel's thermal decomposition is going to be close to the end, and the subsequent weight loss of about 6% should come from slow oxidation of the residual carbon. Finally, the sample retains about 14% of the initial weight for the dry gel. . This result manifests that La 2 Ga 3 O 7.5 is of orthorhombic symmetry. With the help of MDI Jade 6.5 software using a Pseudo-Voigt peak function, both XRD patterns were numerically analyzed by whole pattern fitting to determine the lattice parameters. In the meanwhile, the crystal structure relations between  the tetragonal LaSrGa 3 O 7 and the orthorhombic La 2 Ga 3 O 7.5 were considered: a orth ≈ b orth ≈ 2 a tetra and c orth ≈ 2c tetra [28], as shown in Fig. 3. Thus, upon the best-fits with the residual fitting errors R wp = 5.24% and 7.31%, the cell parameters were derived for LaSrGa 3 O 7 and La 2 Ga 3 O 7.5 : a tetra = b tetra = 8.0474(2) Å, c tetra = 5.3283(3) Å, and a orth =11.4690(1) Å, b orth = 11.2825(4) Å, c orth =10.3735(4) Å, which are very close to the data reported in the literature [28,31].
To further characterize the crystal structures of show the SAED images of LaSrGa 3 O 7 and La 2 Ga 3 O 7.5 samples, respectively. As shown in the HRTEM images, both of them exhibit neat lattice stripes. The lattice fringe spacing of LaSrGa 3 O 7 sample is estimated at 0.533 nm, corresponding to the lattice spacing of the (001) plane in its tetragonal structure. For the La 2 Ga 3 O 7.5 sample, a lattice fringe width of 1.085 nm can be determined, which corresponds to the lattice spacing of the (001) plane in its orthorhombic structure. In the SAED image of La 2 Ga 3 O 7.5 sample, the (002) and (004) spots should be from the Ga atomic planes in the [Ga 3 O 7.5 ] polyhedral layers and the La atomic planes between the adjacent [Ga 3 O 7.5 ] polyhedral layers, respectively. More interestingly, additional faint diffraction spots can be seen between the diffraction spots corresponding to the (002) and (004) planes, which may be related to the long-range ordering chain-like arrangement of the interstitial oxide ions. The chain-like arrangement of the interstitial oxide ions is staggered in the adjacent [Ga 3 O 7.5 ] polyhedral layers, resulting in a periodic deviation of the La ions from the (004) crystal plane in the c-axis direction and thus producing the extraordinary diffraction spots.
In addition, the structural differences between La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 are also clearly demonstrated by their Raman spectra, as shown in Fig. 5. According to the symmetry group analysis, LaSrGa 3 O 7 with a tetragonal structure should have 45 Raman active vibrational modes, but the experimental Raman spectrum of the LaSrGa 3 O 7 sample gives less than half of its theoretical vibrational bands, which should be due to the degeneration or low intensity of some vibrational modes [32]. Compared with LaSrGa 3 O 7 , the Raman spectrum of La 2 Ga 3 O 7.5 with the orthorhombic structure exhibits more vibrational modes, evidently revealing the lower structural symmetry of La 2 Ga 3 O 7.5 . The characteristic peaks of La 2 Ga 3 O 7.5 at 531 cm −1 and LaSrGa 3 O 7 at 528 cm −1 correspond to the symmetric   To explore the chemical states of the constituent elements, especially of the oxide ions, the full-scale survey spectra of the sintered La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 and local sub-spectra for individual elements were registered by XPS. All XPS spectra, calibrated in terms of the carbon's binding energy at 284.8 eV for C 1s to eliminate charging effects, are demonstrated in Fig. 6. From Fig. 6(a)  since the lower density of the outer electron cloud implies a stronger binding of the nucleus to the inner electrons, namely a higher energy is required to excite the inner electrons into photoelectrons [35].
The O 1s sub-spectra for the two samples are shown in Fig. 6

2 Oxide ionic conductivities of La 2 Ga 3 O 7.5 and LaSrGa 3 O 7
The La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 samples for the measurements of the oxide ion conductivity were those sintered at 700 ℃ for 2 h to reach a relative density of 50%, as indicated by the Archimedean test. The typical cross sectional FESEM image of the La 2 Ga 3 O 7.5 pellet coated with silver films as electrodes on its both sides is shown in Fig. 7. It can be seen that the sample's microstructure is highly homogeneous, and the electrodes are well attached on the sample's side surfaces. Figure 8 shows the typical AC-impedance spectra of the sintered La 2 Ga 3 O 7.5 sample at 300, 400, 500, and 700 ℃, while other impedance spectra at 350, 450, 550, 600, and 650 ℃ are demonstrated in Fig. S2 in the ESM, and those for LaSrGa 3 O 7 at different temperatures are presented in Fig. S3 in the ESM. For La 2 Ga 3 O 7.5 , its impedance spectrum at 300 ℃ shows two complete semicircular arcs corresponding to the grain and grain boundary processes. With the increase of the measurement temperature, the semicircular arc corresponding to the grain process gradually disappears, and at the temperature of 700 ℃, only a partial arc corresponding to the grain boundary process can be observed. This is because the response frequency of the grain process usually increases with the temperature, and  its impedance arc cannot be fully obtained when it exceeds the working frequency of the AC impedance spectrometer. Therefore, only the impedance arc corresponding to the grain boundary with a lower response frequency can be observed at higher temperatures. In addition, AC-impedance measurements were performed on the La 2 Ga 3 O 7.5 sample in humid air by bubbling water and dry air at a flow rate of 50 mL/min. The typical AC-impedance spectra at 400 ℃ and the conductivities at temperatures from 400 to 700 ℃ in humid and dry airs are presented in Figs. S4 and S5 in the ESM. It can be seen that, the AC-impedance spectra and the conductivities derived from them show no differences in the two cases of humid and dry airs, strongly suggesting that no electrical conductivity for the La 2 Ga 3 O 7.5 sample may come from OH groups or protons.
To perform a quantitative analysis of the AC-impedance spectra of the sintered La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 , the appropriate equivalent circuits for polycrystalline ceramic electrolytes were utilized, as shown in Fig. 8, where R g and R gb represent the grain resistance and the grain boundary resistance, respectively, and CPE g and CPE gb are the constant phase elements for the corresponding processes. All the parameters of the equivalent circuits were evaluated after a nonlinear fitting analysis of the AC-impedance spectra measured at different temperatures by ZSimpWin software, wherein the results for La 2 Ga 3 O 7.5 and LaSrGa 3 O 7 are listed in Tables S1 and S2 in the ESM, respectively. The grain conductivity (σ g ), grain boundary conductivity (σ gb ), and total conductivity (σ t ) of the samples were then calculated by the formulae: σ g = L/(R g A), σ gb = L/(R gb A), and σ t = L/(R t A), where L and A are the thickness and the electrode area of the samples, respectively, and the total resistance R t = R g + R gb . Figure 9 shows the Arrhenius plots ln(T)-1/T of various conductivities of the LaSrGa 3 O 7 and La 2 Ga 3 O 7.5 samples, including their total conductivities, grain and grain boundary conductivities of La 2 Ga 3 O 7.5 , as well as the grain conductivity of La 2 Ga 3 O 7.5 from the literature [28], while the inset shows the plots of these conductivities versus the temperature. It can be noted that, the sintered La 2 Ga 3 O 7.5 distinctly shows a linear Arrhenius relationship (ln(T)-1/T) with invariable activation energies of 1.22, 1.18, and 1.24 eV for the grain, apparent grain boundary, and total conductivities over the entire temperature range from 300 to 700 ℃, respectively. In addition, the total conductivity of La 2 Ga 3 O 7.5 is about 2 Fig. 9 Arrhenius plots of total conductivity, grain and apparent grain boundary conductivities for La 2 Ga 3 O 7.5 , total conductivity for LaSrGa 3 O 7 , and grain conductivity for La 2 Ga 3 O 7.5 from Ref. [28], as well as the inset showing the diagrams for the conductivities versus temperature. orders of magnitude that of LaSrGa 3 O 7 at the temperatures in this study. It takes a value of 0.36 mS·cm -1 at 700 ℃, alongside an apparent grain boundary conductivity of 1.17 mS·cm -1 , about twice as high as the grain conductivity at the same temperature.
However, it should be more interesting to compare the above results with the data reported in the literature [28]. First of all, the grain conductivity of La 2 Ga 3 O 7.5 prepared in this study is very close to that reported in the above literature in the temperature range from 300 to 550 ℃ , verifying that the La 2 Ga 3 O 7.5 phases achieved by two different methods have almost the same intrinsic properties. However, in the literature [28], the apparent grain boundary conductivity is remarkably smaller than the grain conductivity because of the longer chord made from the intercepts by the impedance response arc of the grain boundary on the real axis Z' (Ω·cm) than that by the grain's arc for the AC impedance spectrum of La 2 Ga 3 O 7.5 at 400 ℃. This is evidently different from our above result. Firstly, it is reasonable to believe that the larger apparent grain boundary conductivity in our La 2 Ga 3 O 7.5 should arise from its clean grain boundaries. Secondly, in contrast to the present study, where the invariable activation energy of 1.22 eV for the grain conductivity of La 2 Ga 3 O 7.5 is clearly shown over the whole temperature range from 300 to 700 ℃, whereas an abrupt change in the activation energy of grain conductivity from 1.21 to 1.62 eV around 550 ℃ can be noticed in the literature [28]. This should be an anomaly. It is well known that a change in the activation energy for the transport of charge carriers usually results from the change of carrier migration mechanism with the temperature mostly because of structural changes like phase transitions. Although the authors simply attributed this anomalous change of the activation energy to the thermally induced disordering of interstitial oxide ions [28], it seems still difficult to understand because thermally induced carrier disordering is normally related to an order parameter that is an asymptotic function of the temperature rather than an abrupt change. Moreover, the increase of the temperature should cause the disordering of carriers and often lead to a decrease rather than an increase in the activation energy. Therefore, it is speculated that this anomalous change, if true, would be closely related to the presence of a peculiar microstructure that might be mediated by the impurity phases formed during the crystallization of the under-cooled melt.

3 Meta-stability and synthetic mechanism of La 2 Ga 3 O 7.5
To explore the meta-stability of La 2 Ga 3 O 7.5 , the assynthesized La 2 Ga 3 O 7.5 samples were annealed at 700, 750, 800, and 850 ℃ for 2 h and then characterized by XRD, with the resulting diffraction patterns shown in Fig. 10(a). It can be noted that some bud-like diffraction peaks attributable to the LaGaO 3 phase may be identified clearly with the samples after calcination at 750 ℃ for 2 h. With the increase of the temperature, the diffraction peaks of LaGaO 3 intensify rapidly, and the La 2 Ga 3 O 7.5 sample is completely decomposed into the LaGaO 3 and Ga 2 O 3 phases after calcination at 850 ℃ for 2 h. Figure 11(a) gives a distinct diagram to describe how fast the La 2 Ga 3 O 7.5 decomposes with increasing temperature, wherein the diffraction intensity fraction of LaGaO 3 with respect to the total diffraction intensity integrated over the whole 2 range is used as an index. Evidently, the decomposition of La 2 Ga 3 O 7.5 should be initiated at some temperatures slightly below 750 ℃ and then accelerated over 775 ℃ at a blasting rate until the end.
To further investigate the meta-stability of La 2 Ga 3 O 7.5 , another attempt was also made to calcine the assynthesized La 2 Ga 3 O 7.5 again at 700 ℃ for different time before the characterization by XRD. As shown in Fig. 10(b), no diffraction peaks of LaGaO 3 can be observed for the sample after the calcination at 700 ℃ for 20 h, implying that no noticeable change with the La 2 Ga 3 O 7.5 sample has taken place at this condition. When the annealing time was extended to 40 h, some slight diffraction peaks for LaGaO 3 can be observed, suggesting that the La 2 Ga 3 O 7.5 sample has undergone a tiny decomposition. In the same way as the above, a diagram of describing how fast the La 2 Ga 3 O 7.5 decomposes with increasing the calcination time at 700 ℃ was determined, as shown in Fig. 11(b). It can be seen that, the decomposition of La 2 Ga 3 O 7.5 heated at 700 ℃ appears to show linear kinetics with a constant but small rate. Obviously, this result unveils the nature of metastable La 2 Ga 3 O 7.5 : It can be synthesized from a highly homogeneous gel-precursor at 700 ℃ for 2 h and can also start to decompose due to heating at the same temperature for over 20 h. It is easy to understand  that, increasing the annealing time or temperature will induce La 2 Ga 3 O 7.5 more effectively to lose its metastability, given a high kinetic barrier between the metastable La 2 Ga 3 O 7.5 and the thermodynamically stable La 2 O 3 + 1.5Ga 2 O 3 .
Although the crystallization of the under-cooled melt was regarded as an appropriate non-equilibrium approach to the synthesis of the metastable La 2 Ga 3 O 7.5 melilite [28], the single-phase metastable La 2 Ga 3 O 7.5 melilite without impurity phases has been obtained indeed from its gel-precursor through a solid phase reaction at as low a temperature as 700 ℃. To better understand the synthetic mechanism of the metastable La 2 Ga 3 O 7.5 , a kinetically favorable mechanism is proposed here. It means that whether La 2 Ga 3 O 7.5 can be synthesized at a temperature high enough to thermodynamically drive the synthetic reactions is mainly controlled by the microscopic inhomogeneity of chemical species of reactants concerned in the reaction system. The smaller the micro-inhomogeneity is, the more favorable the reaction is to take place kinetically. www.springer.com/journal/40145 Assuming that the spatial inhomogeneity of the chemical species concerned in the reaction system can be defined as a characteristic size (), and their average diffusion coefficient is D. Then, the minimum time (τ) required to accomplish an elementary solid-state reaction controlled by the diffusion should be expressed as Eq. (1): (1) It is easy to perceive that here the minimum reaction time is also the time required for the system to change from one state to another by jumping over an energy barrier. Thus, it is a measure of the energy barrier to characterize the kinetics of the reaction. A shorter minimum reaction time means a lower energy barrier. Therefore, a larger probability with which the reaction is accomplished based on Eqs. (2) and (3): where r E  is the kinetic potential barrier of the reaction, and k is the proportional factor, p is the probability with which the reaction is accomplished , k B is the Boltzmann constant, and T is the absolute temperature.
Obviously, the under-cooled oxide melt or glassy precursor obtained at high temperatures usually has an extremely small spatial inhomogeneity size, say a few atoms across. Also, according to the above exponential dependence of reaction probability on the inhomogeneity size, the formation reaction of La 2 Ga 3 O 7.5 can favorably happen at a great probability almost just through a local structural adjustment at a temperature that can satisfy the kinetic requirement. Naturally, it is also true for the formation of La 2 Ga 3 O 7.5 starting with a highly homogeneous gel-precursor, and the kinetic process should be very similar to the above because of the small spatial inhomogeneity size. However, when the mixture of component oxide particles of micros in average diameter is used as a precursor, the formation of La 2 Ga 3 O 7.5 would become kinetically unfavorable and even too difficult to happen because of the large spatial inhomogeneity size of the mixture, which greatly reduces the probability of the elementary reaction, compared to the use of glass or gel-precursor. In this case, to increase the probability of the elementary reaction, the reaction temperature should be increased, but this is seriously detrimental to metastable La 2 Ga 3 O 7.5 and results in the formation of thermodynamically stable phases LaGaO 3 and Ga 2 O 3 .
As to the specific solid-state reactions involved in this paper, the highly homogeneous gel-precursor with a nominal chemical composition of La 2 O 3 + 1.5Ga 2 O 3 strongly tends to form a single-phase La 2 Ga 3 O 7.5 rather than a two-phase product of 2LaGaO 3 + 0.5Ga 2 O 3 . This is because the formation of the two-phase product would destroy the original homogeneity and greatly increase the system's spatial inhomogeneity size, which leads to a much higher potential barrier for the formation of 2LaGaO 3 + 0.5Ga 2 O 3 than for the formation of La 2 Ga 3 O 7.5 , and the probability for the former reaction is then greatly reduced. Besides, the presence of residual Ga 2 O 3 can hinder the growth of LaGaO 3 in space. In other words, if the reaction needs to proceed, additional energy is required to overcome the potential barrier created by the spatial hindrance of the residual Ga 2 O 3 to the growth of LaGaO 3 , which is not favorable for the reaction to proceed at low temperatures. Therefore, the synthesis of the single-phase metastable La 2 Ga 3 O 7.5 from highly homogeneous gel-precursor at low temperatures is a competing result of multiple kinetic processes of different potential barriers.

Conclusions
In summary, the single-phase metastable melilite La 2 Ga 3 O 7.5 with the orthorhombic symmetric structure has been successfully synthesized at 700 ℃ from a highly homogeneous gel-precursor from the EDTA-CA combined complexation sol-gel process, and a kinetically favorable mechanism is proposed to better understand the formation of the single-phase La 2 Ga 3 O 7.5 rather than LaGaO 3 + Ga 2 O 3 . The FTIR spectra and TG-DSC results manifest that the EDTA-CA combined complexation sol-gel process can lead to highly homogeneous gel-precursor. Moreover, the as-synthesized La 2 Ga 3 O 7.5 with the orthorhombic structure shows more Raman active vibrational modes and an additional XPS peak at higher binding energy for the interstitial oxide ions than the tetrahedral LaSrGa 3 O 7 , but tends to slowly decompose into the perovskite LaGaO 3 and Ga 2 O 3 when annealed at 700 ℃ for over 20 h or at higher temperatures driven by its meta-stability. Also, different from the anomalous phenomena reported in the literature [28], the sintered La 2 Ga 3 O 7.5 exhibits linear Arrhenius plots (ln(T)-1/T) with invariable activation energies for its oxide ion conductivities over the temperature range from 300 to 700 ℃ and a significantly higher apparent grain boundary conductivity than the grain conductivity because of clean grain boundaries without any impurity phases. This paper provides a new strategic approach to the synthesis of complex oxides that may be of high performance but difficultly achieved by the conventional ceramic method at high temperatures.