Recent progress in the experimental and theoretical studies on the barium zirconate proton conductors: A review


 There have been significant developments of solid-state-ion conducting energy materials and perovskite-based oxides those exhibit excellent proton conduction at intermediate temperatures. In contrast to high-temperature oxygen ion-conducting oxides or low-temperature proton-conducting polymers, perovskite oxides have obtained distinguished attention because of their diversified structural aspects and potential applications. Highly stable and conductive electrolytes with improved electrochemical and thermochemical properties are in great demand in numerous fields such as portable electronics and transport systems, energy storage, fuel cells, etc. This review focuses on recent development in the proton-conducting performance of BaZrO 3 (BZO) energy materials. This study aims to integrate the fundamentals of proton conducting BZO perovskites in the prospect of the recent development in materials science and computational engineering. Therefore, in the first half of this review, the basic overview of the BZO perovskites structure, fundamentals of working principles, fabrication, and processing methods underlying the successful development of these materials with superior performance is discussed. The second part principally concentrates on the significant improvement towards higher conductive BZO perovskite fabrication with the help of theoretical studies via density functional theory (DFT) based first-principles calculation and molecular dynamics (MD) simulation followed by the prominent applications in low-temperature solid oxide fuel cells. The presented information on in-depth analysis of the physical properties of barium zirconate from experimental and theoretical studies will guide aspirants in further conducting research in this field near future.


Introduction
The increasing global population and demand for a high-quality life leading to unparalleled industrialization instigate a higher level of energy demand around the globe. Moreover, recent global concern about sustainability and environmental pollution due to toxic by-products and worsening climate crisis, has propelled demand for sustainable and eco-friendly energy conversion methods. Among such efforts, fuel cells, especially solid oxide fuel cells (SOFCs) [1][2][3][4][5][6], are the prime energy conversion devices that got much interest in the last decades. The most common applications are proton-exchange membrane fuel cells (PEMFCs) [7-

Experimental Studies On Bzo Proton Conductor
The preparation of powders and the subsequent electrolyte fabrication process plays a crucial role in any material's nal performance. For BZO, among various synthesis parameters, the addition of transitional metals as dopants and sintering aid during fabrication affects the nal composition and particle grain size. Moreover, these parameters in uence chemical mechanical stability and, most, proton conductivity's behavior.
Therefore, recent literature works are summarized and reviewed in the following subsections by focusing on the above aspects. At the end of this section, a quick view of hydrogen solubility on BZO is also presented.

Doping
Doping with metal ions is a familiar technique to increase the proton conductivity of BZO. In the midst of them, BZY is reported to have high proton conductivity, especially at a temperature below 700 °C [70]. To nd an ideal yttrium doping concentration, the in uence of dopant concentration on BZY was studied by Han et al. [71]. The studied powders having compositions of BaZr 1-x Y x O 3-δ , where x= 0.1-0.25 were prepared using the solid-state reaction (SSR) method [72,73]. The scanning electron microscope (SEM) images of powders (sintered at 1600°C for 24 h in the presence of oxygen) revealed that the 10 to 15 mole % yttrium doped BZY have bimodal microstructure. Moreover, samples containing 14 and 15 mole % of Y 3+ have larger grains compare to ones having 10-13 mole % Y 3+ . The trend of increasing grain size continued up to 16 mole % of Y 3+ and uniform grain size is achieved for BZY having 16-25 mole % yttrium. A similar trend was observed from the total conductivity measurements at wet H 2 ( = 0.05 atm). The total conductivity of BZY material increases with the increasing Y 3+ concentration from 10 to 20 mole %. However, for samples containing a Y 3+ concentration of 20 -25 mole %, total conductivity remains almost unchanged. More importantly, 20 mole % Y 3+ -doped BaZrO 3 showed total conductivity at 500 °C, an essential property for intermediate temperature operated solid oxide fuel cells. The observed in uence of yttrium concentration is attributed to the lowering of grain boundaries resistance with increasing doping concentration. This phenomenon is further con rmed by Iguchi et al. [74] as the as-synthesized BZY samples having 5-15 mole % of yttrium doping showed similar characteristics. The activation energy of 1.03, 0.71, and 0.48 eV were measured for samples of 5, 10, and 15 mole % Y 3+ -dopants, respectively.  [75]. Notably, all the composites were produced using the SSR method. Although the sintering ability is improved with Ca and Sr insertion on BZY, the total transport number decreases with the increasing Sr concentration in the ceramic, which results from the decrease of bulk and apparent grainboundary conductivities.
Similarly, co-doping of Sm 3+ and Y 3+ on BZO is reported by Zhu and co-workers [76]. A citrate-nitrate combustion route was applied to synthesize BaZr 0.8 Y 0.2-x Sm x O 3-δ composite samples. The dilatometry study, conducted in the temperature range of 50-1550 °C, reveals that the sintering shrinkage of co-doped materials improves with the increasing concentration of Sm 3+ . However, the total electrical conductivity decreases with the increment of Sm 3+ concentration. The larger ionic radius of Sm 3+ which is comparable to Y 3+ may be the main reason as the dopants with smaller ionic radii have more stable proton bonds to oxygen at the rst neighbor of dopant. Thus, the activation energy of proton conductivity at the grain boundary increases and a higher proton migration resistance developed through the grain boundary. Recently, Kuroha et al. (2020) [77] reported the effect of Nickel (Ni) addition (Ni = 0 to 0.4) in a 20% In-doped barium zirconate (BaZr 0.8 In 0.2 O 3−δ or BZI20) electrolyte of a tubular fuel cell. The tubular cell's electrolyte surface morphology was investigated by SEM that discovered a highly dense crack-free surface. Due to the increase of Ni-content, the proton diffusivity, electrical conductivity, and density of the samples were decreased, while proton concentration was unchanged. The reason behind the decrement of conductivity might be correlated to the dissolution of Ni in the BZI20 electrolyte.

Grain size
Like doping concentration, the grain size of ceramic powders in uences the proton conductivity. Yamazaki et al. studied the grain size in uence for polycrystalline sintered BZY20 pellets. The precursor powder was synthesized using the wet-chemical method [78]. The variation of sintering temperature results in different grain size boundaries. 1.2 µm average distance between grain boundaries was achieved for sintering temperature below 1150 °C, where for sintering at 1150 -1200 °C reduced the distance to 0.5 µm, which further reduced to 0.44 µm at 1600 °C. The effective grain boundaries conductivity of samples from sintering temperature 850 and 1600 °C were calculated using AC impedance spectroscopy and found to be 2.5-3.2 times (depending on measured temperature) larger for larger grain size. The lower density of grain boundaries is the reason behind the enhancement of the effective grain boundary conductivity and the total conductivity. Where, at 450 °C, the total conductivity of 1.2 µm grain size samples reached ∼70% of the grain interiordominated conductivity, while 0.44 µm grains size gained only 56 % of grain interior-dominated conductivity even at 600 °C. Iguchi et al. [79] investigated the grain growth and grain boundary distribution of BaZr 0.95 Y 0.05 O 3 and observed that the sample preparation method did not affect grain structures and grain boundaries distributions, but the duration of sintering in uenced the grain growth (Fig. 3). Grain size impact on BZY10 materials conductivity was studied by Jarry et al. [80]. The samples' manufacturing process was varied, spark plasma sintering was applied as a sintering technique, and SSR methods followed by sintering with and without sintering aid was applied to produce BZY10 samples having a grain size of 0.3 -5.0 µm.
Noteworthy that all the prepared samples exhibited a similar chemical composition in bulk and grain region. Ambient pressure (AP) X-ray photoelectron spectroscopy (XPS) was applied to study the hydration of the prepared samples and reported that the hydroxylation contribution increases with grain size and is higher at the surface. There was a direct observable correlation among the grain size, grain boundaries, and OHconcentration. When the OH-concentration increases, the larger grain size-based grain boundaries effectively adsorbed more water for the increment of grain size. It was observed that OHconcentration increases at the surface of BZY10 but decreases as AP-XPS analysis depth increases from the sample surface. Hence it is proposed to be one of the contributing factors of higher proton conductivity for the existence of larger grain size in materials. The obtained results concluded that larger grains may enhance the hydration, which raise the catalytic activity of oxidation in a cell.

Sintering aid
Although at intermediate temperature (~500°C), BZY shows good mechanical and chemical stability with moderate proton conductivity, to improve the overall performance it is necessary to operate such fuel cell electrolyte materials at a higher temperature (like ≥ 800 °C). Besides, BZY requires a higher sintering temperature (~1800 °C) to fabricate [81]. In such cases, sintering aid materials like Co, Ni, etc. were applied to overcome the sintering issues [82]. Sample preparation and uses of sintering aids also have in uences on total conductivity [83]. Therefore, to fabricate the BZY electrolyte, the sintering temperature must be considered to develop a cost-effective method. As an example, Ricote et al. reported that the high temperature treated BZY (sintered at 1720 °C while annealed at 2200 °C) having grain size distribution of 1-10 µm acquire 3 times higher total conductivity at 600 °C (measured at 5% H 2 , 0.03 atm H 2 O) than materials sintered at 1600°C using NiO as sintering aid exhibiting grain size distribution of 1-6 µm [83]. The ratio of grain boundary resistance to bulk resistance of the heat-treated sample is half compared to samples sintered using NiO. As a result, the grain boundary activation energy was calculated to be 0.84 eV for the NiO-sintered aid product.
Sintering aid plays a key role in reducing the sintering temperature and the synthesis of densi ed ceramic powders. The uses of CuO, and ZnO as sintering aids for the synthesis of BZY20 ceramics was reported by Kosasang et al. [84]. With the use of 1 wt. % ZnO as a sintering aid, a homogenous particle grain size of 0.5 µm was achieved where 1 µm grain-sized particles were visualized using 1 wt.% CuO. In performance comparison, the ceramic powders prepared with CuO as a sintering abetment have better total proton conductivity than ZnO ones. This is due to the high grain boundary conductivities for the sample with CuO ones where bulk grain boundary conductivity is similar to the ZnO ones. Aktas et al. studied the impact of BaO as a sintering aid on BaZr 0.92 Y 0.08 O 3-δ ceramics earlier [85]. The powders were synthesized by mechanical mixing of BZY powders with BaO followed by the high-temperature sintering process. With the increasing amount of BaO, the nal grain size of ceramic powder decreases, whereas grain boundary activation energy increases. This scenario was viewed for the presence of secondary phase at the grain boundary of BaO crystals.
To investigate the possible inter-diffusion between metal and perovskite ceramics, some research groups incorporated transition metals (Mn, Fe, Co, etc.) as sintering boost into BZY electrolyte by calcination process from the cathode materials (La 1−x Sr x Co 1−y Fe y O 3−δ [86], Ba 1−x Sr x Co 1−y Fe y O 3−δ [87], La 1−x Sr x MnO 3−δ [88], etc.) of an electrolyzer or fuel cell during cell fabrication. However, the impact of the possible inter-diffusion of transition metals into the BZY by the calcination process remains ambiguous, as it may produce an unexpected reduction of cell performance. Han et al. (2020) [89] studied the electrochemical and structural properties of the BZY20proton-conducting electrolyte with individual doping of transition metals like iron (Fe), manganese (Mn), Nickel (Ni), and cobalt (Co) prepared by conventional SSR method instead of calcination process. The X-ray absorption near-edge structure spectroscopy (XANES) analysis was used to determine the success of Fe, Mn, Ni, and Co incorporation into the BZY20 perovskite crystal structure. The transported proton number was measured by the electromotive force (EMF) analysis in the temperature range of 500 °C to 700 °C in the wet reducing (H 2 ) atmosphere and in the wet oxidizing (O 2 ) atmosphere, respectively. The results showed that the incorporation of transitional metals like Co improves the sintering capability, though the proton concentration, transported proton number, and proton conductivity was decreased even after the incorporation of all transitional elements, i.e., Fe, Mn, Ni, or Co. In another study, Han et al. (2018) [69] investigated BZY20 electrolyte materials using ZnO, NiO, and CuO as sintering additives. The experiment showed similar results, i.e., though ZnO, NiO, and CuO improved the sintering ability of BZY20, a signi cant reduction of proton conduction and resultant increment of hole conduction deteriorates the cell performance.
Besides, as the concentration of Zn, Ni, and Cu in the BZY20 crystal increases, the proton conductivity decreases. Therefore, a post-annealing (at 700 °C for 48 h) on the Ni, Cu, and Zn-doped BZY20 was performed in a reducing hydrogen atmosphere for the removal of Ni, Cu, or Zn content from BZY20. Though the postannealing can remove the ZnO, NiO, and/or CuO sintering additives in some cases, nevertheless the kinetics of the process was very slow. Chen et al. (2019) [90] reported the feasibility of formulating dense BZY polycrystalline electrolytes with low amounts of NiO (0.2%) and low sintering temperatures (1500°C). Their approach improves the Ba evaporation issue, grain size distribution, and relative density. However, NiO addition negatively impacts electronic leakage of BZY10 ceramics in humid oxidizing environments due to misdiagnosis of proton ceramic fuel cell (PCFC) cathode material's electrocatalytic activity and reduced faradaic e ciency of proton ceramic electrolysis cells (PCECs). Therefore, care must be taken during incorporation of such metals (Mn, Fe, Co, Ni, Cu, Zn etc.) as sintering aid to achieve higher cell performance.

Composites and thin lms
BZO perovskite found another promising application as a component of polymer-based composites. In general, polymer-based membranes are commonly used in PEMFC [91]. For such an application, Na on is a conventional polymer material, in which polytetra uoroethylene backbone and the sulfonic acid functional group provides the physical and proton transport sites, respectively [92]. However, proton conductivity properties of Na on decreases at a temperature above 80 °C, therefore as an alternative other polymers, i.e., poly(ether ether ketone), poly(phenylene), poly(ether sulfone), and poly(arylene ether) having higher proton conductivity (>60 mS cm−1 at 80°C) has drawn attention [93,94]. To improve the proton conductivity at a higher temperature and relative humidity, the incorporation of doped BZO was studied [95,96]. A perovskite oxide composition of BZY10 nanoparticle was incorporated in sulfonated poly(ether ether ketone) (SPEEK) polymer [97]. In their work, the amounts of nanoparticles, as well as the degree of sulfonation, were varied to optimize the performance of SPEEK based nanocomposite membrane. As a result, the chemical, mechanical, and thermal stability of composites improved with nanoparticle incorporation. Proton conductivity of the composite membrane increased initially with the incorporation of nanoparticles, however, after the application of 1.8 wt. % of nanoparticle in the matrix, the proton conductivity decreased. The reason is mentioned to be the agglomeration of nanoparticles, narrowing of proton conductivity channels, and rearrangements of the hydrogen bond between -OH groups of nanoparticles and -SO 3 H group of SPEEK [98]. The doping of Y 3+ into BZO plays a vital role in the increase of proton conductivity as dopant sites act as water uptake sites and 'proton traps'. In comparison with pristine SPEEK and incorporated SPEEK-BZY10 composite the maximum power density of fuel cell performance increases from 0.16 to 0.43 Wcm -2 at 80 °C. A similar positive in uence of BZY10 nanoparticles in the case of incorporation with the sulfonated poly (1,4-phenylene ether-ether sulfone) (SPEES) membrane is stated by Hooshyari et al. [99]. The chemical and mechanical stability increases compared to the pure polymer membrane. In terms of membrane performance of 9 wt. % doping of BZY10 nanoparticles in SPEES-based nanocomposite, an overall proton conductivity of 117 mS cm -1 , and considerable fuel cell performance of 0.61 Wcm -2 was found at 80 °C. In that study, pure SPESS polymer membranes proton conductivity was reported to be 81 mS cm -1 at 80 °C and 95 % RH.
Afterward, Aruta et al. study the positive impact of Y 3+ doping proton conductivity of BZO perovskite materials by fabricating thin lms of BZY10 on oxide substrate [100]. With the help of hard X-ray photoelectron spectroscopy (HAXPES), scanning transmission electron microscopy (STEM), and DFT calculations, they investigated the thin lm structure and explained the cause of the improved proton transport properties of Y 3+doped BZO on NdGO 3 substrate. The distorted perovskite structure of NdGO 3 compared to the cubic structure of Y-doped BZO, during Pulsed Laser Deposition (PLD), in uences the lm to grow with an in-plane compressing strain of about 8 %. The developed strain was the driving force for the Y 3+ dopants to substitute, preferably Ba 2+ sites, compare to Zr +4 sites in the crystal structure. The HAXRPES investigations and DFT calculations further veri ed this scenario. Due to the smaller size of Y 3+ compare to Ba 2+ , Y 3+ substitutions for Ba 2+ increased the number of fast proton transport pathways by lowering the proton transfer barriers (activation energy required for the migration step) that result in the improved proton conductivity in doped perovskite materials, hence, the lms deposited in their studied composite. Furthermore, the PLD deposition rate and choice of substrates on the formation of BZY10 thin lm and resulting proton conductivity were studied by Bae et al. [101]. Ceramic material was prepared following mechanochemical, where MgO and sapphire substrates were used. In both substrates, the slow deposition rate consequences highly dispersed lms with lower grain boundaries compared to higher deposition rates. The proton conductivity is higher in thin lms deposited applying a slow deposition rate due to the decrease in insulating grain-boundaries' density. In comparison between MgO and sapphire substrate, thin lms grown on the sapphire substrate shows lower proton conductivity due to higher Ba de ciency in the nal deposited layer.
Recently, Exner et al. (2020) [102] proposed a novel method known as powder aerosol deposition (PAD) [103][104][105][106] to produce highly dense BZY20 lm to analyze the electrical, optical, and mechanical behavior at high temperatures (800 °C to 1000 °C). Uniform and crack free PAD lms with dense microstructure were observed from the SEM micrographs. Bulk sintered samples were also prepared for a direct comparison of mechanical properties with PAD lms. Vickers' microhardness test con rms that the hardness of lms was about 2.4 times higher than the sintered bulk samples. Film crystallites size was about 9 times lower than that of the mixed powder, and nally, the XRD, SEM, and hardness test results con rm that the PAD lm is suitable for electrical studied [105,[107][108][109][110][111][112]. At lower temperature (400 °C) lm sample showed a lower conductivity of 2.5 x 10 −8 S/cm, which is 3.5 order lower than the bulk one. On the other hand, at higher temperatures (800 °C to 1000 °C), almost similar conductivity (2 x 10 −2 S/cm) was observed both in bulk and lm samples. BZY20 revealed more than 0.9 ionic transfer numbers even at high temperatures (~800 °C) it suggests that BZY20 is favorable for proton conduction above 700 °C. By the feasibility study, the PAD lm functionality as a membrane was con rmed after successful deposition of PAD-BZY20 lm onto the porous NiO electrode. As the lm exhibits the higher conductivity in the high-temperature region (800 °C to 1000 °C), it may be assumed that the PAD lm is bene cial as a functional lm in the electrochemical membrane devices in hightemperature operation.
3.5 BZO as fuel cell electrolyte materials BZO has much potential as fuel cell electrolytes due to its improved chemical stability. However, BZO has a lower power output compared to barium cerate. Therefore, numerous research efforts were focused on the codoping of rare-earth metals on BZO to increase the power density and chemical stability. In short, the most common synthesis technique was the SSRs method. Followed by combustion, sol-gel, spray pyrolysis, citric acid (CA) -ethylenediaminetetraacetic acid(EDTA), etc. methods, different types of techniques like-drypressing, uniaxially-pressing, co-pressing, tape-casting, solution casting, PLD, etc. were applied for electrolyte fabrication. Furthermore, for calcination, the temperature range of 600-1400 o C and the holding time in the range of 2 to 6 h was applied. For example, Xie et al. (2018) [113] used 1100 o C and 3 h for calcination. On the other hand, Wallis et al. (2020) [114] used the spark plasma sintering method as it reduces the sintering temperature signi cantly (elapsed 20 minutes only). The relative density of the electrolyte depends on the composition, fabrication process, and temperature. For example, Zhu and S. Wang (2019) [76] pointed out that using Sm 3+ doping improves the sintering activity, thus increased the density. Chen et al. (2019) [90] found out that using Bi doping relative density increases from 82% to 95%. In this section, based on the recent research works, a tabulated summary containing the composition of BZO, their preparation method, and relative density is presented in Table 1 [15,76,77,90,99,113,.
BaZr 0. 8  upto 1 mm in depth due to CO 2 attack, and an explicit Y-content and grain size dependency observed. EDS line scanning con rmed the decreased Ba-but increased Zr-and Y-content at the CO 2 exposed BZY10 surface.
Due to the increase of CO 2 exposure temperatures, the Vicker's hardness was unchanged, but with the increase of exposure temperature (in the range of 550 °C-750 °C), the fracture toughness was decreased due to the increase of lateral cracks and induced stress at the surface. On account of the CO 2 reaction, grain boundaries become weak, which resulted in reduced fracture toughness. SEM micrographs showed that the reduction of fracture toughness does not affect the amount of large BaCO 3 crystal formation on the sample surface.
Although the formation of BaCO 3 does not potentially affect the hardness of the experimental sample, the overall mechanical performance was reduced for the generation of micro-cracking on the surface of the sample after the attack of CO 2 . Therefore, care must be taken when BZO-ceramics would be used in the CO 2 containing atmosphere.
Conductivity values of BZY10 show 2 order of magnitude difference, measured by various research groups [71,130,[146][147][148][149][150]. The reasons for this discrepancy are the variation of sintering temperatures and times, sintering methods, and conductivity measuring atmospheres, etc. [71,130,[147][148][149][150]. Another reason might be the changes of Y 3+ mole % caused by the variation of sintering conditions [148], but this phenomenon needs further investigation for clari cation [146]. For example, due to the variation of sample synthesis techniques, sintering processes, and sintering conditions, Ba-de ciency was observed, which reduce the conductivity of BZY10 [141,151].

Hydrogen solubility and diffusivity
The proton-conducting oxides have a potential application in the fusion reactor's isotope separation systems [15,103,[152][153][154][155][156][157][158][159], hydrogen pump for tritium puri cation and recovery [160][161][162][163][164][165], and also as hydrogen sensors [31][32][33][34][35][36][37]and fuel cells [5][6][7][8][9][10]. Therefore, to advance in practical usage of oxide proton conductors as functional materials, it is essential to understand the hydrogen behavior in the proton-conducting materials, such as the amount of dissolution and internal diffusion of hydrogen [166][167][168][169][170]. Nevertheless, solubility and diffusivity data are limited and somewhat scattered for oxide materials. The authors of the current manuscript mentioned in their early studies that [60,171], the hydrogen solubility and diffusivity can be measured and calculated by using a tritium tracer method, for instance, a tritium imaging plate (TIP) [167][168][169]171,172] for the BZY10, BaZr 0.955 Y 0.03 Co 0.015 O 3-δ (BZYC) [171], and CaZr 0.90 In 0.10 O 3-δ (CZI) [60]. In this method, the samples were vacuum-annealed at 1273 K for 1 h, and then samples were exposed for a different duration from 15 min to 16 h at various exposure temperatures of 623 to 1273 K in a 1.3 kPa HT (the tritium and hydrogen ratio was 10 -4 ) [171] or DTO (the tritium and deuterium ratio was 10 - hydrogen solubility (S BZY ~ 10 -4 H/M) was found for HT exposed BZY sample was obtained from the Arrhenius plot. One order higher solubility (S BZYC ~ 10 -3 H/M) was observed for the BZYC. Hydrogen diffusivity (D) of BZYC (~ 10 -11 m 2 /s) is higher than the diffusivity of BZY (~ 10 -12 m 2 /s), and a trend of increase of D was noticed with the increase of exposure temperature. Both higher solubility and diffusivity were observed for BZYC as compared with BZY (Fig. 5). This may be due to cobalt participant in the BZO perovskite as a catalyst in the HT reaction (HT→H+T) during HT exposure. The hydrogen (H) solubility and diffusivity in CZI was lower than that of BZY and BZYC, and the activation energy of H-diffusion for CZI was approximately double of that for BZY and BZYC [60].Therefore, a small amount of cobalt doping (1.5%) may play a vital role in enhancing the electrochemical activity of the proton conducting BZO.

Theoretical Studies On Bzo Proton Conductor
In obtaining insight into the structural properties, and characteristic attributes of perovskite materials, computational approaches play an instrumental role. Two important approaches in this regard are the rst principles DFT study and MD simulation mode. While DFT uses functionals from the quantum mechanical consideration to determine properties of the system of interest, MD simulation provides a dynamic evolution of physical movement in a system of atoms or molecules. The discussions of DFT and MD simulation are gravely relevant to the current review. These methods provide critical insight regarding BZO, which, in some cases, deem unapproachable or too inconvenient by experimental studies. Therefore, these computational approaches can be effectively used to complement experimental studies or validate speci c experimental ndings.
The ground-state structure of BZO was investigated by the neutron scattering experiment and First Principles (FP) calculations. It reveals that unstable phonon mode is a transition phenomenon, which is associated with rotations of ZrO 6 octahedra. These calculations, dependent on the exchange-correlation functionals, suggested the stable cubic perovskite structure of BZO [173].
FP calculations suggested that different types of doping affect the proton conduction signi cantly in a different manner. For example, B-site doped BZO shows that Ga-doping provides the highest chemical stability, whereas La-doping leads the maximum proton conduction [59,174]. This section highlights how DFT studies contribute to extract critical insight regarding BZO in appropriate detail. The abundance of such research works substantiates the strength of BZO as a proton-transporting perovskite candidate and its applicability in related elds.
A combination of XPS, STEM, and DFT calculations show that BZY can accommodate a substantial Y dopant while providing lesser scope for other cations (Zr 4+ and Ba 2+ ) [100]. The most critical insight of this study is the mechanism of the fast proton transport pathway-which is connected to the rich regions due to Ysubstitutions, as they provide a negligible energy barrier for proton transportation. Therefore, it is evident that the ultrathin strain lm's structural and conductivity properties are controlled by epitaxial strain. Acceptor dopants' ability to affect proton mobility is substantiated in a separate DFT study, which suggests similar attractive interaction between the proton and substituting trivalent dopants such as Ga, Sc, In, Y, and Gdleading to structural stability [192]. However, the DFT calculations underestimate the experimental values of the required energy for proton migration. Furthermore, the study attempts to compensate for this aspect by implementing a jump-diffusion model, showing that DFT can be a useful tool for creating a reliable model for such perovskite materials. Solely from the oxygen vacancy perspective, the energetically favorable oxygen vacancy distribution was studied for BCO and BZO and the comparison shows that the vacancies tend to prefer Zr, while they prefer the dopant with the increase of Ce in the solid solution [200]. Therefore, it is substantiated that doping can invoke signi cant structural optimization in the geometry of BZO, which can be explained via DFT investigation. For example, one FP DFT study has shown the optimized con gurations of ions in BZO (Fig. 6) [177].
While considering structural aspects, the defects and local distortions must be included in the discussion in perovskites, as they are directly related to proton mobility [213]. Defect engineering is always mentioned as a suitable approach to manipulate proton conductivity of perovskites such as SrZrO 3 (SZO), CaZrO 3 (CZO), and BZO [207]. Proton conductivity, as a thermally activated phenomenon, is dependent on the percentage of doping (as it increases localized lattice distortion), and surpassing a threshold point, or incorporating a grain boundary defect those frameworks can signi cantly vary the conductivity [173]. This study suggests that the proton conductivity can be improved pronouncedly by embodying dopant-lattice polaronic interaction, and this approach can be extended to other perovskite materials as well. The positive effect of manipulating dopant percentage (tested with 6.25% and 12.5% Y dopant), which results in local distortion in the structure and hence effect in proton conduction, was substantiated by multiple studies based on DFT calculations [214]. Aside from the dopant percentage, non-stoichiometry can affect the proton conductivity, as suggested by manual incorporation of planar and spherical defects by heat treatment-results in a lesser value of activation energy for proton transport [208]. This study strengthens previously suggested mechanisms of improving proton transport by decreasing dopant-lattice interaction [173,215]. For speci c insight on the tilt grain boundary effect, Kim et al. [216], utilize space charge layer and structural disorder to incorporate proton and oxygen vacancies into the system. Based on segregation energies, the energy barriers for proton transport are calculated. Also, the applicability of BZO as an electrochemical device is justi ed in a separate grain boundary study, which suggests that BZO and BCO show high grain boundary resistance [217], which means their proton conductivity is limited by grain boundaries in a polycrystalline state, which can be quanti ed by the space-charge potential. Space-charge modeling in this study also shows that proton formation energies can be different in separate perovskite material in bulk form based on hydrogen bond formation. Focusing on grain boundary segregation, another study substantiated the space-charge formation due to defect segregation [218]. Furthermore, co-adsorption of H 2 O and CO 2 study along with the space-charge attribute of BZO have shown that space-charge formation and adsorbate interaction contribute to de ning defect concentrations [219]. For a speci c study on defect chemistry and solubility of perovskites, DFT calculations have played an instrumental role. It showed that metal (Ni) can be absorbed in the structure identi ed by grain boundary [220].
To explain high proton mobility in BZO and create a link between macroscopic proton conductivity and microscopic proton motion, nanoscale percolation has been taken into account, which shows that at low concentration, acceptors can trap protons and hence limit their mobility -while at higher concentration, they tend to create percolation pathways by leading the opposite effect [209]. Proton transfer in BZO has also been considered from a lattice perspective, and it suggests that structural defect can originate from the deformation of oxygen octahedra, which can introduce self-trapping distortion and reorganization of the compound [221]. Intuitively, ion rotation and proton transfer vary according to the availability of ion vacancies, and the associated parameters can be extracted by DFT study to obtain relative energy information due to lattice deformation (Fig. 7) [62].
Furthermore, kinetic Monte Carlo (KMC) associated with DFT calculations has shown that proton conduction can be hampered by the presence of other protons [210], as suggested by calculation of proton transporting energy barriers at high temperature in doped BZO. It is relevant to mention that oxidation and hole conductivity can be affected by polaronic contribution in the doped state of BZO perovskite [175]. By implementing local and semi-local exchange-correlation functionals along with hybrid functionals, the polaronic contributions in conductivity can be quanti ed, and energetically favorable self-trapped holes can be identi ed in the structure, which is prone to delocalization at high temperature, showing consistency with earlier modeling [176].
Moreover, 50% In-doped BZO study using DFT showed that dopant-proton interaction does not affect the diffusion of protons due to the presence of the percolation paths of dopants, which facilitate dopant transport throughout the lattice [179]. The In-doped study has also explored the effect of doping in affecting the proton conduction [177], and the Sc-doped study has discovered hydration energy [222]. As the dopants of BZO are discussed in detail in the previous section, these aspects are not repeated here.
Plane-wave based DFT calculation demonstrate that the proton diffusion coe cient is affected by applied strain in ABO 3 perovskite structure [223], and the enhanced proton diffusion is explained by the formation of preferable proton transport path due to compressive strain in the structure. To analyze the proton diffusion mechanism in the cubic perovskite structure at high temperature, rst-principles MD simulation was performed, which showed that proton diffusion could be enhanced under the application of compressive condition due to the formation of preferential diffusion path (which can be attributed to charge redistribution under this condition). However, there is no evidence of enhancing diffusion from the application of tensile strain or relaxed bulk condition [223]. Speci cally, the proton-oxygen pair correlation is highly affected by the compressive strain. Analyzing electronic and structural parameters from a plane wave-based DFT calculation by incorporating Car-Parrinello MD, it is obtained that applied strain leads to a nonlinear effect on proton diffusion constant. A separate study suggested that "A-site" ion vacancy can positively affect the proton conduction in BZY that reduces the barrier for proton diffusion by accounting for the proton conduction mechanism and hydroxide ion rotation [62]. Fig. 8 shows that the hydroxide ion gets reoriented during rotation and H-O interaction processes, and the bond length also changes due to the larger space provided by the Asite ion vacancy. Due to speci c benchmarking of proton diffusion, this study provides important insights on proton diffusion as well as designing proton conductors [62].
Also, alkali metals (Na, K, Rb, and Cs) were found to be e cient acceptor dopants in BZO because of its comparable or lower energy barriers for proton transport than that of Y-dopants, which suggest an unlike DFT study [178]. Speci cally, the high-temperature attribute of BZO has been addressed in multiple studies, which show that BZO is impressively stable at high temperatures due to phonon contributions [224,225], which further validates its applicability in such a eld. Interestingly, the DFT study has explored a novel structural aspect, is the electrostatic potential of BZO in its doped state. Spectroscopy studies suggest that Ba vacancy at the grain boundary contributes to the potential well, while DFT justi es that statement by demonstrating reduced atomic density at the grain boundary region [226].
It is relevant to mention that surface energy for different surfaces and interfaces of ABO 3 perovskites are calculated by the ab initio method [180], which found that (001) surface energies for zirconates are almost always smaller than the (011) and (111) surface energies, suggesting inward relaxation in (001) surface, and the interface bandgap in the surface depends more strongly upon the upper augmented layer than the substrate augmented layer. Moreover, the formation volume of point defects in BZO is studied by DFT in terms of the defect strain tensor, which suggested that vacancy and hydroxide ion radii are smaller than the oxygen ion radius. These calculations have also been successful in calculating dopant ionic radius agreeable with experiments [181]. Interfacial proton migration in BZO is separately studied in another work, which suggests a curved pathway for proton transport through the ZrO 2 -terminated (100) surface, where the energy barrier can be signi cantly reduced by the addition of carbonate ion [227]. Having an agreement with experimental results on BZ-molten carbonate electrolyte [228], this study suggests an enhanced facile interfacial proton migration between the electrolyte phases. To enhance the transport properties of electrochemical materials, chargecarrier interface studies are carried out well. This scenario suggests that heterogeneous doping can decrease the energy barrier for the transport of protons [229]. This observation is particularly important for designing novel nanostructured composite material.
Aside from the structural attributes, rst principles (FP) phonon calculations have also attempted to address the thermodynamic properties of doped BZO. For example, hydration and defect property analysis has shown that the stable structure of BZO perovskite is cubic and that the vibrational formation entropy for oxygen vacancy is signi cantly higher than that of the protonic defect [56]. That defect characteristic speci cally contributes to the formation of entropy, while being dependent on the size of dopants ion. The entropic calculations fairly agree with earlier experimentations [182,183] as well. The hydration ability and proton conduction were investigated for Y and Sn co-doped BZO by Dawson et al., suggesting that BZO is indeed a potential material for electrode applications [55]. This study investigates the effect of all available defect sites and their contributions to analyze the hydration ability. The previous studies have shown, the most similar favorable and exothermic pathway for hydration when the location is in Y's vicinity. The synergy study of Sn and Y doping substantiated the applicability of BZO in the next-generation solid oxide fuel cells [228]. Defect formation based on thermodynamic modeling has facilitated the calculation of formation energy in BZO with different dopants, which showed that most dopants could substitute Zr without sacri cing favorable conditions energetically [230].
As a continued discussion on the thermodynamic properties of BZO, a notable DFT study is on hightemperature modeling [184]. Apart from strengthening its potency at high-temperature applications, this study shows that BZO possesses moderate mechanical properties and low thermal conductivity, making it competitive with other silicates and ceramic materials. Notably, this study makes about 20% loss of Young's modulus at high temperature with a signi cant decrease in thermal conductivity. A high-temperature tracer diffusion study has also been performed, which facilitated the calculation of grain boundary diffusion [127].

MD studies
BZO is one of the highly explored perovskite materials for the analysis of MD studies that might deem as a useful method. Numerous ab initio, classical MD, and DFT studies have investigated its cogency and attributes as a robust proton-conducting oxide. For example, detailed thesis work on BCO and BZO has explored computational modeling of them. The calculations discovered relevant parameters connected to the local protonic environment and proton transfer phenomena, especially in the doped state, which were previously inaccessible to experimental maneuvers [231]. Although ab initio simulations have extracted some insight regarding microscopic processes of dissociative adsorption of hydrogen on structure surface [201], MD simulations performed with reactive force eld have articulated temperature-dependent change of geometrical parameters. This part of the study has provided information regarding how a proton can dictate BZY structural features, even when far from a doping site. The speci c modeling of D-BZ, D-YB, and D-2YB reveals a comparison between the radial distribution functions of protonated and unprotonated (single and double) structures. The simulation results predict that avoiding Y-clustering can improve proton transport in such compounds. Another independent MD simulation study by the same author on Y-doped BZO has shown that classical MD can analyze the Y-doping effect within the framework of the cubic formation of BZO and yttrium induces mutation in the oxygen sites in the vicinity of the local geometry [185]. Besides, topologically different oxygen sites can provide inkling on thermodynamically favorable proton-hopping paths, and further emphasizes the importance of avoiding Y-clustering to prevent protonic traps.
MD simulation on Y-doped BZO has been applied to illustrate the fast oxygen transport phenomenon because of its excellent ion conductivity as well as chemical activity. Through incorporating reactive force eld potentials, the oxygen vacancies, doping effect, and edge dislocations have been explored for the BZO system with or without edge dislocations, and calculations on radial distribution function, expansion coe cient, and ionic self-diffusion coe cient. The MD calculations on the aforementioned entities have been carried out employing the dependencies of temperature and doping percentage [186]. These results manifest that a mole fraction of yttrium can increase oxygen transport which can be characterized by the oxygen transport coe cient. Also, due to the formation of double-bottle diffusion channels and the resulting regeneration of oxygen polyhedrons, dislocations can accelerate oxygen ion diffusion. Therefore, line defects can be considered in future studies to enhance ion conductivity at low temperatures.
Recently, different types of doping effects have been attempted on BZO, such as In and Sc-doping to nd out local proton coordination [232], local structure [179], and vibration dynamics [233], which were studied by the same research group. The proton coordination study can be performed with a combination of experimental and plane-wave based DFT framework. Induced charge density due to the proton's introduction can be visualized by Fig. 9, which shows that there could be a signi cant difference between the charge distribution of stoichiometric and protonated bulk [223]. However, ab initio MD simulation on a hydrated sample of BZO shows that it is possible for overlapping INS spectra of protons to exist in the local structural environment, clari ed by O-H bend, O-H stretch, and higher-order transitions. This study also presents an argument that due to the presence of percolation paths throughout the lattice structure, proton diffusion does not necessarily get affected by dopant-proton interaction. MD simulations have provided independent insights on structural and thermodynamic aspects of BZO, but reactive force eld parameters have been developed for studying electrode-electrolyte interfaces. These parameters have facilitated to re-calculate of the primary energy barrier for proton diffusion in BZY that manifests a very consistent experimental value [234]. Local distortion and dynamics were further explored by DFT-based MD simulations [213]. To further visualize the success of DFTbased MD studies to determine the proton diffusion coe cient, one may refer to the temperature-dependent proton diffusion coe cient for BZO ( Fig. 10(a)) and the comparison with experimental values (Fig. 10(b)) [195,235,236].
Further study suggests the proton-trapping phenomenon in dopant state that invoked from the same perspective with the extended outlook. To achieve a self-intermediate scattering function for small and large momentum values, which facilitates validation against neutron scattering experiments has been investigated [194]. The thermal expansion coe cient results match well with experimental data up to 1200K, although the lattice parameter was overestimated, which was consistent with earlier observation [6,195]. The slightly doped lattice observation showed a little distortion from a cubic to tetragonal structure, which was validated by earlier experimentation [196], but for higher doping concentration, the orthorhombic structure did not sustain. Again, this study proved the reliability of the reactive force eld (ReaxFF) potential to analyze such perovskite attributes by MD simulations and substantiated doping effect in BZO. However, the lattice parameter overestimation suggested that the ReaxFF model can be improved when BZO is modeled for too soft material.
Quantum Mechanical (QM) studies were carried out for different perovskite materials to determine their comparative diffusion coe cients and activation energies for proton transport (only inter-octahedra proton transfer for BZO [197,198]. These ndings substantiate the QM method on BZO, as calculated activation energy is agreeable with statistical uncertainty and can be explained by proton's repulsive interaction with cation (Zr) [199]. The results of such activation energy were further a rmed by a separate research group using the valence-bond approach and reactive force eld MD simulation [195,237] (Refer to Fig. 11, which shows the diffusion trajectory of the proton). Furthermore, path integral MD simulations which incorporate quantum effects into the dynamic analysis showed a signi cant difference between the potential barrier and the minimum energy paths due to the quantum effect. Between these two the translational path shows a decrease of potential barrier with an increase of quantum effect, while for the reorientation motion path the effect reveals the opposite trend [238,239].
Moreover, a detailed MD simulation study was carried out on BZO to highlight its microscopic atomic behavior, interatomic separation, and thermal transport properties by simplifying the interatomic potentials into pairwise interactions [202]. This study calculated isothermal compressibility, thermal expansion coe cient, heat capacity, and thermal conductivity for this material over a range of normal to very high temperature and pressure, which are in good agreement with experimental ndings. From a strict interaction perspective, the potential functions have been analyzed to obtain insight regarding binding potential. Peaks at the radial distribution functions at the reference temperature, which broaden in cases of higher temperatures, provide a hint regarding close packing or solid phase, but in the case of BZO, splitting of the peak is observed, which suggests asymmetry to some extent. Also, the coordination numbers suggest structural robustness, i.e., the ability to maintain the perovskite structure even at high temperatures. Summarizing the structural and thermodynamic results from MD simulation, one can easily declare that BZO maintains a cubic perovskite structure but has a larger lattice constant than SrTiO 3 (STO). The lattice parameter of BZO negligibly increases at high temperature, and molar volume increases with temperature. The calculated parameters agree with experimental results [187,188], substantiating the reliability of MD simulation. However, the linear thermal expansion coe cient varies slightly from the experimental value, staying in good harmony with the experiment at room temperature while deviating at high temperatures [240,241]. Comparing with STO material, BZO is slightly less expansible. The calculation on isothermal compressibility shows that BZO is less stiff than STO, which validates the experimental nding [240,242]. A remarkable agreement is found for heat capacity [203][204][205][206] and thermal conductivity result [204] of BZO at room temperature while showing agreement with different consequences at high temperatures. Furthermore, the results of similar related thermal conductivity agree better with the experiment than earlier semi-empirical MD simulation, suggesting a better de nition of pair potentials in this study [243]. The lower Debye temperature of BZO also substantiates the less stiff attribute [244]. In short, this study mainly provides us con dence in MD simulations on perovskite structures, as this approach has successfully reproduced reliable thermodynamic parameters. In this regard, a separate group has also undertaken the analysis of BZO to establish the thermodynamic parameters by using MD simulation and the researchers have organized the obtained results in two different works -one analyzing BZO only [245], and the other comparing SZO with BZO [246]. The earlier one incorporates a newer representation of pair potentials for BZO, and they also calculated lattice parameters, thermal expansion coe cient, isothermal compressibility, heat capacity, and thermal conductivity within a broad temperature and pressure range. These ndings, similar to the previous paragraph, assent with experimental ndings. Furthermore, the latter group has been able to reproduce agreeable results by taking into account thermal expansion and isothermal compressibility of BZO. This reproducibility of MD simulations on BZO suggests that such perovskite materials, especially thermodynamics parameters, can be studied with reliability by this approach.
Further MD analysis has investigated BZO from preference to cubic perovskite structure, distortion, intermediate structure perspectives, and has predicted phonon spectra to compare the stability of materials [189]. MD simulation can run at room temperature with similar structures that display as the outcome at room temperature, i.e., they can invoke free moving among degenerate structures, suggesting that this work attempts to analyze BZO by involving defects by manipulating the atom radii. However, this analysis explicitly admits the importance of studying dopant's role to enhance proton transport in such perovskite materials. The obtained radial distribution function implies that there is no observable distortion above room temperature, suggesting a phase transition and that larger system size can lead to the clustering of various types of distortions.
Moreover, a combination of MD simulations and the DFT method, indicate that in the grain boundary of BZO, proton and oxygen segregate to different grain boundaries clearly [190]. Combining the results from MD simulations and DFT, it can be summarized that for BZO, grain boundary segregation is signi cant to incorporate a positive core charge and electrostatic potential barriers, which has been demonstrated by experiments at different temperatures [149,150,191,193]. The defect-defect interaction can be attributed to the insensitivity of dopant concentration, but it is explained from the DFT perspective as well.

Conclusion
Improved proton-conducting energy materials are in great demand in various electrochemical and thermochemical processes, namely, hydrogen pumps and hydrogen sensors, portable electronics, transport systems, energy storage, fuel cells, and nuclear industry including off-gas capture and isotopic separations, among others. The poor sinterability, high sintering temperature (1700-2100 o C) to promote desired microstructure and grain growth, defects due to dopants, and poor stability make it impractical for the aforementioned devices. During the last decades, the development of material science, microelectronics, and potential demand have forced the excessive development of solid-state-ion conducting ceramic materials, perovskite-based oxides that exhibited excellent proton conduction at low and/or intermediate temperatures.
In the midst of all perovskites, BZO exhibited tremendous potential for good proton-conducting performance at low temperatures. This review has comprehensively discussed the working principle of BZO perovskites, the effect of processing, applications, and prospects of it. The rational selection of dopants and processing conditions govern the successful development of highly stable and conductive BZO electrolytes. The authors declare that they have no competing interests. Figure 1 Schematic of the generation of an oxygen vacancy by the substitution of two Zr4+ ions with two Y3+ ions in perovskite BaZrO3to form BaZr1-xYxO3-α [60].

Figure 2
Page 46/54 Schematic representation of proton diffusion process in ABO3 perovskite with (bottom row) and without (upper row) an A-site ion vacancy. Proton diffusion mechanism (upper left and bottom left gures). Hydroxide ion rotation and proton transfer mechanism (middle four gures). B-O-B bending motion mechanism (upper right and bottom right gures). Here red and brown balls represent the initial and nal positions of the atoms, respectively. Reprinted with permission from Ref. [62].   wet H2, and (f) wet air for the BZY20 and BZYC5 pellets. Reprinted with permission from Ref. [138]. with radioactivity values. Color of red in the standard sample means higher tritium concentration, while blue means lower tritium concentration, (c) color spectrum of tritium concentration, (d) Arrhenius plot of the hydrogen solubilities for the BZY, BZYC [171], and CZI [60]samples, and (e) Arrhenius plot of the hydrogen diffusivities to compare the tritium diffusivity data for BZY, BZY, CZI that were obtained from the present studies [171] with the literature data of the proton diffusivity in BZY at 673-873 K, was reported by Kreuer [172]. Reproduce with permission from Ref. [60,171,172].  The mechanism of how electronic density redistributes itself for (a) hydroxide ion reorientation and (b) OD-H-OA interactions to affect proton transport. Reproduce with permission from Ref. [62].

Figure 11
Mechanism of proton diffusion (white spheres) at 1500 K in the BaZrO3 lattice (smoothed and averaged over successive frames). Legend: O: Red, Ba: Green. It is clear that at square vertices, the oxygen atoms screen Zr