In silico design and experimental validation of a high-entropy perovskite oxide for SOFC cathodes

Abstract

High entropy perovskite oxides have the potential to significantly enhance electrode performance in solid oxide fuel cells (SOFCs) and batteries. However, not all high entropy configurations yield single-phase perovskite oxides. This study focuses on screening La_0.2Sr_0.2A_0.2B_0.2C_0.2MnO₃ (where A/B/C = =Pr, Gd, Nd, Ba, and Ca) for oxygen reduction reaction electrocatalyst applications. Possible configurations are analyzed by evaluating the tolerance factor based on ionic radii and oxidation states, and enthalpy of mixing. Considering these, La_0.2Sr_0.2Ca_0.2Gd_0.2Pr_0.2MnO₃ (LSCGP) is identified as a synthesizable high entropy perovskite oxide, which is experimentally synthesized. In Sr-containing perovskites, Sr is known to segregate to the surface. Hence, LSCGP is first assessed for Sr-cation segregation using density functional theory (DFT), molecular dynamics (MD), and X-ray photoelectron spectroscopy (XPS). The results indicate negligible Sr-cation segregation towards the surface. DFT calculations show that oxygen vacancy formation is facilitated in LSCGP compared to the other high entropy perovskite oxide such as La_0.2Sr_0.2Ba_0.2Nd_0.2Pr_0.2MnO₃ (LSBNP), and simple perovskites such as La_0.8Sr_0.2MnO₃ (LSM20) and La_0.5Sr_0.5MnO₃ (LSM50). MD studies further demonstrate that LSCGP exhibits significantly higher oxygen anion diffusivity compared to LSM20, LSM50, and LSBNP. The electrochemical performance of the LSCGP electrode is characterized in symmetric cell and SOFC configurations. In the symmetric cell, LSCGP showed significantly reduced polarization resistance at the OCV, as compared to the similarly fabricated LSM. The high surface stability and enhanced electrocatalytic properties of LSCGP present it as a promising candidate for electrode applications in energy storage and conversion devices.

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1 Introduction

Solid oxide fuel cells offer an environmentally friendly and effective means of converting chemical energy from renewable energy sources to electrical energy. Their operation produces minimal harmful emissions.^1–3 The La_1–xSr_xMnO_3–δ (LSM) perovskite oxide is a well-studied cathode material for SOFCs.^3–8 It has demonstrated significant electronic conductivity,^5,9,10 thermal stability,^11–14 strong structural stability,^15–17 and high catalytic activity.^18–20 Nevertheless, due to its nature as an electronic conductor, it exhibits a restricted activity region for oxygen evolution and reduction processes, specifically near the triple-phase boundary.^3,21 In addition, Sr cation segregation occurs at high-temperature (1073–1273 K) SOFC operations. Sr enrichment on the LSM surface leads to oxide formation, contributing to surface instability and electrode performance degradation. Researchers have explored various strategies to reduce cation segregation.^22–25 Lee et al. demonstrated that the presence of smaller cations decreases the likelihood of segregation in doped AMnO₃ (A = La, Sm, Ba, Sr, Ca) perovskite oxides.²⁶ It had also been demonstrated that lattice strain also affects the segregation of cations in simple perovskites such as doped LaMnO₃ (LMO)²⁷ and double perovskites like NdBaCo₂O_6–δ (ref. 28) and Sr₂CoNbO_6–δ.²⁹ Similarly, nanostructure strategies have been explored by Anjum et al. in double perovskites for controlling surface cation segregation.^30,31 Sr-cation segregation significantly affects the performance of LSM as a cathode material. Lowering the operating temperature range results in sluggish kinetics of the oxygen reduction reaction caused by cathodic polarization and high overpotential.^32,33 These challenges have hindered its widespread utilization as a cathode in SOFCs. To overcome these limitations, efforts are needed to enhance its surface stability along with high electrocatalytic performance. One promising strategy involves leveraging the concept of high-entropy materials. The high entropy in a structure is introduced by increasing compositional complexity. LSM-based high entropy perovskite oxides could show potential for tailoring the electrocatalytic properties for energy conversion and storage devices.

The concept of high-entropy materials was first introduced independently by Cantor et al.³⁴ and Yeh et al.³⁵ in 2004. High entropy alloys were designed with multiple principal elements in equimolar or nearly equimolar amounts. This results in configurational entropy greater than or equal to 1.5R and hence termed as high entropy materials. Despite the large number of primary components in the alloy, the configurational entropy effect led to the material's single-phase stability.³⁶ Similarly, high-entropy carbides,^37,38 nitrides,³⁹ borides,⁴⁰ and silicides⁴¹ were proposed and investigated. These high entropy materials showed remarkable properties compared to the parent material.⁴² High-entropy perovskite oxides drew attention in 2018 as researchers started developing and exploring the properties of the material.^43,44 High-entropy perovskite oxides have at least five dopants at the A-site, B-site, or both sites in ABO₃-type perovskite oxides.⁴⁰ The high configurational entropy contributes to a decrease in the Gibbs free energy of the system, stabilizing the structure. High-entropy perovskite oxides could be proposed as good candidates for oxygen electrode catalysts.

Perovskite oxides can exhibit significantly enhanced properties when doped with multiple elements at the A-site,^45,46 B-site,⁴⁶ or both sites.^46–50 This had also been evidenced by Sr-doping in LMO.^25,51 Doping multiple elements at the A-site in LSM could further lead to enhancement of the properties of interest. This cocktail effect of synergizing the dopants' effects could help in designing novel materials with improved catalytic activity.⁴⁴ For example, Dabrowa et al. designed La_0.7Sr_0.3(Co_0.2Cr_0.2Fe_0.2Mn_0.2Ni_0.2)O_3–δ high-entropy perovskite oxide with a reduced thermal expansion coefficient (16.0 × 10⁻⁶ K⁻¹).⁵² Similarly, Yan et al. proposed [(Bi, Na)_1/5(La, Li)_1/5(Ce, K)_1/5Ca_1/5Sr_1/5]TiO₃ as a structurally and chemically stable electrode for lithium-ion batteries.⁵³ However, the high-entropy materials are observed to be synthesizable as single-phase materials with only some specific configurations. For example, the La_0.2Nd_0.2Sm_0.2Sr_0.2Ca_0.2MnO₃ configuration is observed to be a single-phase high-entropy perovskite, but La_0.2Nd_0.2Ba_0.2Sr_0.2Ca_0.2MnO₃ is observed to be in a multiphase structure.⁵⁴ Various descriptors have been proposed to predict the synthesizability of high-entropy perovskite oxides.⁵⁵ However, to the best of our knowledge, no universal descriptors can predict a wide range of synthesizable high-entropy configurations.

In this work, we have systematically screened and identified a new class of compositionally complex materials. These materials incorporate five cations at the A-site in equimolar amounts in the AMnO₃ parent perovskite oxide. Molecular structures are screened for La_0.2Sr_0.2A_0.2B_0.2C_0.2MnO₃ (A/B/C = =Pr, Gd, Nd, Ba, Sr, and Ca) high entropy perovskites based on tolerance factor and enthalpy of mixing. The tolerance factor based on ionic radii and oxidation states of the ions present in the structure is estimated as proposed by Bartel et al.⁵⁶ A decrease in the tolerance factor indicated increasing perovskite structure stability.⁵⁶ An initial screening based on the tolerance factor narrowed down the choices of the possibly synthesizable single-phase high entropy perovskite oxide. Furthermore, DFT simulations are applied to calculate the enthalpy of mixing to predict the synthesizability of the structure. Based on the screening of possible perovskite oxide configurations, a novel Sr-containing La_0.2Sr_0.2Ca_0.2Gd_0.2Pr_0.2MnO₃ high entropy perovskite oxide configuration is proposed. We successfully synthesized LSCGP experimentally to further probe it as a candidate material for energy conversion and storage devices.

2 Methodology

2.1 Theoretical simulations

In order to create structures with random doping, special quasirandom structures (SQS) were generated using the Alloy Theoretic Automated Toolkit (ATAT).^57–59 The initial LMO structure was derived from prior experimental investigations.⁶⁰ 5 × 2 × 1 supercells of the LMO parent structure, containing 50 atoms, were doped with five different cations at the A-site. Subsequently, dopants were randomly distributed at the A-site based on pair correlation functions on each site using the Monte Carlo generator of SQS (mcsqs).⁶¹ Possible high entropy configurations were created by random swapping of the unlike A-site atoms, and then created configurations were assessed according to the Boltzmann probability. Vienna Ab Initio Simulation Package (VASP-5.4.4)⁶² was used for the spin-polarized plane-wave DFT calculations. Projected augmented wave approach⁶³ and Perdew–Burke–Ernzerhof (GGA-PBE)⁶⁴ were employed to handle the electronic states in the core and exchange–correlation interactions between electrons, respectively. We used an energy cutoff of 520 eV. The ionic and electronic relaxation criteria were considered as 10⁻⁵ eV Å⁻¹ and 10⁻⁶ eV, respectively. A Monkhorst–Pack k-mesh^65,66 of 3 × 7 × 11 was used for unit cell relaxation. The unit cells of high entropy structures were optimized in multiple steps. In the first step, only the atomic positions of the atoms were relaxed without relaxing the lattice parameters. In the next step, both atomic positions and lattice parameters are optimized by keeping the volume of the cell fixed. And in the final step, both lattice parameters and atomic positions were fully relaxed with changes in volume allowed. Optimized unit cells (Fig. S1†) were then used to compute and examine the properties of our interest using DFT and MD simulations.

The tolerance factor, introduced by Bartel et al.,⁵⁶ was employed as a screening measure for predicting single-phase synthesizability. The modified tolerance factor (τ) was determined using the ionic radii and oxidation states, which is given as

where r_A, r_B, and r_X represent the radius of A, B, and X ions, respectively, and n_A is the oxidation state of ion A in ABX₃ structures. The enthalpy of mixing⁶⁷ of the high entropy perovskites was calculated using the expressionwhere E_DFT(A_0.2B_0.2C_0.2D_0.2E_0.2MnO₃), E_DFT(AMnO₃), E_DFT(BMnO₃), E_DFT(CMnO₃), E_DFT(DMnO₃), and E_DFT(EMnO₃) represent the stable phase ground state DFT energies for the high entropy oxide A_0.2B_0.2C_0.2D_0.2E_0.2MnO₃ and simple perovskite oxides AMnO₃, BMnO₃, CMnO₃, DMnO₃, and EMnO₃ configurations, respectively.

For surface energy analysis, surface slabs of the synthesized high entropy structure, reference high entropy structure, and simple perovskite structures were prepared. Slabs were terminated along the stable (001) direction with either A-site or B-site cations on the top-most layer with 100 atoms, Fig. S2.† Surface energies of various terminated slabs were obtained using the expression

where E_surface and E_bulk are the DFT energies of the surface slab and bulk structure, respectively. And n is the number of unit cells in the slab structure. Next, to probe the electrocatalytic performance, we computed and examined the oxygen vacancy formation energies for high entropy and reference simple perovskite structures. For this, oxygen vacancies were created by removing the oxygen atom from the possible vacancy site (Fig. S3†), and DFT calculations were performed for non-stoichiometric and stoichiometric structures. The oxygen vacancy formation energies were extracted using the expression

E_OV = E_defect + 0.5 × E_O2 − E_perfect, (4)

where E_perfect, E_defect, and E_O2 are the energies of perfect stoichiometric and non-stoichiometric (structure with oxygen vacancy defect) structures, and gas phase oxygen molecule, respectively.

MD calculations were performed to analyze the time-dependent behavior of ions using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).⁶⁸ Simulations were conducted on surface slabs and the bulk of high entropy and reference perovskite oxides. For this, supercells of 15 × 15 × 15 were created for the analysis. For surface analysis, slabs with A-site cations in the sublayer and Mn cations on the top-most layer were constructed using this supercell. To maintain charge neutrality, we have created oxygen non-stoichiometry (δ) = 0.1, 0.25, and 0.2 for LSM20, LSM50, and high entropy perovskite oxides, respectively. For this, random oxygen vacancies were considered in the structure. A 100 Å vacuum was used to create the slabs in the (001) direction. The NPT ensemble was used for 100 ps with subsequent NVT ensemble run to equilibrate the systems for 100 ps in steps of 1 fs. Subsequently, a production run for 5 ns was conducted using the same ensemble. The average of the findings from ten production runs is considered. In the simulations, the Buckingham pairwise potential⁶⁹ was used to analyze the interaction between cations and oxygen. The coulombic and van Der Waals interactions in the potential are expressed in the form

where the parameters A, ρ, and C represent the strength of the interaction, and z and r_ij denote the ionic charge and interionic separation, respectively. The standard long-range Coulomb potential was used to account for the ionic interactions. Interactions were evaluated using particle–particle particle mesh method⁷⁰ in K-space, with a relative force accuracy of 10⁻⁴ kcal mol⁻¹ Å⁻¹. The Buckingham pairwise potential parameters used in simulations are provided in Table S1.† We used the Verlet algorithm to perform numerical integrations. The constant temperatures were maintained using the Nose–Hoover thermostat^71,72 with a damping parameter of 1 ps. Visual Molecular Dynamics (VMD) was used to analyze and visualize the MD trajectories.⁷³ An analysis of the surface slabs is performed to determine the extent of cation segregation. The degree of cation segregation was measured by calculating the proportion of A-site atoms that move from the sublayer to the uppermost layer on the surface.²⁸

The oxygen anion diffusivity was extracted from the mean square displacement (MSD) vs. time data using the expression

MSD = 6Dt + B, (6)

where D is the oxygen diffusion coefficient, t is the time, and B is a constant. The data on diffusivity were extracted at various temperatures in the range of 773–1273 K. Subsequent analysis of diffusivity with temperature was performed. Activation energies of self-oxygen anion diffusivity were obtained using the Arrhenius equationwhere E_a is the activation energy, D₀ is the pre-exponential factor, k_B is the Boltzmann constant, and T is the temperature.

2.2 Experimental details

The LSCGP cathode precursor for the desired composition was prepared using the auto-combustion synthesis technique following the synthesis protocol described in another report.⁷⁴ The synthesis utilized metal nitrates: La(NO₃)₃·6H₂O, Sr(NO₃)₂, Ca(NO₃)₂·4H₂O, Gd(NO₃)₃·xH₂O, Pr(NO₃)₃·xH₂O (all from Alfa Aesar) and Mn(NO₃)₂·4H₂O (Thermo Scientific), and C₃H₇NO₂L-alanine (SRL Pvt. Ltd) as the fuel. The metal nitrate to fuel ratio was maintained at 2 : 1, thereby preventing undesired hydrolysis of the precursor gel. The saturated aqueous solution of respective metal nitrates was first mixed, and then the aqueous solution of L-alanine was added. The persistent stirring under the controlled temperature of the mixture produced a viscous gel that underwent spontaneous combustion, yielding cathode precursor ash. The temperature for the synthesis process was maintained at 473 K. The resultant cathode precursor ash was calcined at 1273 K for 6 h to get the desired phase of LSCGP. Powder X-ray diffraction (XRD) patterns were recorded on a Bruker D5005 diffractometer equipped with Cu Kα radiation (λ = 1.5418 Å) and a graphic monochromator on the diffracted beam. XRD data were collected in the 2θ range of 20–80° with a step size of 0.01°. The surface oxidation states of the prepared material were studied using the AXIS Supra model of the Kratos analytical limited with 1486.6 eV Al Kα radiation. The high entropy perovskite oxide powder was palletized using a hydraulic press machine and calcined at 1473 K for 5 h. The pallet was connected using silver ink and wire. Total electrical conductivity was measured using the PGSTAT 302N Autolab potentiostat for the temperature range of 673 K to 1073 K in the air atmosphere.

Electrochemical impedance spectroscopy (EIS) measurements were performed by fabricating symmetrical cells of configuration LSCGP|YSZ|LSCGP and LSM|YSZ|LSM. The symmetrical cells were fabricated by first preparing YSZ (1.4 mm) pellets (20 mm diameter) by uniaxial pressing of commercial powders (fuel cell materials) at 200 MPa, followed by sintering at 1723 K for 6 h. The previously prepared YSZ electrolyte discs were brush-painted with LSCGP electrode paste (made of a starch–glycerol-based organic vehicle) on both sides and fired at 1473 K for 6 h, creating symmetrical cells with well-adhered electrode films. The active area of the electrode is measured as 0.305 cm².

AC frequency sweep in the range 10⁻¹ ≤ f ≤ 10⁶ of the electrochemical workstation (IM6 Zahner, Germany) was used for the impedance analysis. The LSCGP electrode material was tested under SOFC operating conditions in both symmetrical SOFC and full-cell SOFC operating configurations. In the case of symmetrical cell operating configurations, an electrolyte support based on YSZ was fabricated. For full cell SOFC applications, YSZ electrolyte was prepared using the same fabrication protocol described previously, and a slurry composed of NiO-YSZ (60 : 40) with 35% of starch as the pore former was printed as the anode film on YSZ electrolyte pellets. LSCGP paste, prepared with the starch-glycerol-based organic vehicle, was subsequently printed as cathode films on the same pellets. The NiO-YSZ (anode) and LSCGP (cathode) films were fired at 1573 K and 1473 K, respectively, each with a holding time of 6 h, to produce single cells of the desired configuration of NiO-YSZ|YSZ|LSCGP. The fabricated single cells were measured to have a thickness of 1.42 mm with an active area of 0.305 cm². Ag wire was used as the current collector for polarisation studies. The cell was fixed on an alumina tube using Ceramabond. The single cell polarisation studies of the developed SOFCs were conducted using an electrochemical workstation (IM6 Zahner, Germany) with the cathode exposed to ambient air and anode kept in a humidified H₂ environment. The fuel flow rate at the anode side was maintained at 50 ml min⁻¹.

3 Results and discussion

3.1 Screening and prediction of the single-phase high entropy perovskite oxide

In order to design LSM-based high entropy perovskite oxides and tune their properties, cation doping at the A-site is considered. Fig. 1(a) shows the possibility of various A-site dopants (e.g., Ca,^26,75 Ba,²⁶ Sr,²⁶ Nd,⁷⁶ Gd,⁷⁷ and Pr⁷⁸) which have been tried in the LMO simple perovskite structure. Stirling approximation⁷⁹ provides a general guideline of doping five or more elements in equal concentration at the A-site, which will likely result in a high entropy structure with configurational entropy greater than 1.5R, Fig. 1(b). Hence, LSM is doped with 5 cations in equimolar amount at the A-site resulting in 1.61R configurational entropy. For 5 possible dopants (Pr, Gd, Nd, Ba, and Ca) at the (A/B/C)-site in La_0.2Sr_0.2A_0.2B_0.2C_0.2MnO₃, ten configurationally complex high entropy materials could be proposed. However, configurational entropy alone does not exclusively determine the stabilization of the single-phase crystalline structure. The presence of multiple elements in a material is likely to introduce numerous competing interactions, resulting in phase segregation.^43,80,81 Thus, not every combination could be synthesized as a phase pure structure.

Fig. 1 (a) A-site dopants (Pr, Gd, Nd, Ba, and Ca) considered in this study to form high entropy perovskites of LSM, and (b) configurational entropy estimated as a function of the number of elements following Stirling's approximation.⁷⁹

The synthesizability of a crystalline material depends on a variety of factors, including synthesis technique and processing conditions such as temperature and pressure.⁸² Descriptors utilizing the Hume-Rothery rule and incorporating different parameters (cation size, electronegativity, and ion valence) have been proposed to theoretically predict the synthesizability of a high entropy material.⁸³ In the case of perovskites, various elements could occupy A or B sites in the ABO₃ structure, but only a few result in the formation of the pure phase perovskite. Bartel et al. proposed a tolerance factor (eqn (1)) to predict the stability of the perovskite structures, which is used here to predict synthesizability.⁵⁶ In addition, DFT simulations are applied to estimate the enthalpy of mixing (eqn (2)). The structural information of the parent perovskite oxides, required for enthalpy of mixing calculations is encapsulated in Tables S2 and S3.† Following this, the synthesizability of high entropy compositions (Fig. 2) is screened to select the candidate material for synthesis. Fig. 2 represents the tolerance factor and enthalpy of mixing for all possible combinations of La_0.2Sr_0.2A_0.2B_0.2C_0.2MnO₃ (dopants = Nd, Pr, Gd, Ba, Ca) type high entropy perovskite oxides. The tolerance factor is calculated using the oxidation state and radii of the ions for high-entropy configurations, eqn (1).

Fig. 2 Screening of possible high entropy configurations based on tolerance factor and enthalpy of mixing (kJ mol⁻¹), where the high entropy configuration in the blue box represents the chosen material LSCGP.

To synthesize a pure-phase perovskite material, the ionic radius and oxidation state of the elements at a site should be similar for solid solubility.⁸³ For this, the tolerance factor should be below 4.18 for a stable perovskite structure. As τ decreases, the solid solubility of the various dopants leading to a single-phase material is expected to increase.⁵⁶ Interestingly, all the high entropy perovskite compositions shown in Fig. 2 satisfy this criterion of the tolerance factor. However, when Shi et al.⁵⁴ synthesized three of the compositions, LSBNP, LSBCP, and LSBCN, they could only make LSBNP as the pure phase (τ = 2.74), while the other two LSBCP (τ = 3.71) and LSBCN (τ = 3.70) resulted in a mixed-phase structure. Thus, we have focused on the compositions in Fig. 2, which have τ < 3. This screening has left us with seven options which are estimated to show tolerance factor <3; LSGNP, LSBNP, La_0.2Sr_0.2Ca_0.2Nd_0.2Pr_0.2MnO₃ (LSCNP), La_0.2Sr_0.2Ba_0.2Gd_0.2Pr_0.2MnO₃ (LSBGP), La_0.2Sr_0.2Ca_0.2Gd_0.2Pr_0.2MnO₃ (LSCGP), La_0.2Sr_0.2Ca_0.2Gd_0.2Nd_0.2MnO₃ (LSCGN) and La_0.2Sr_0.2Ba_0.2Gd_0.2Nd_0.2MnO₃ (LSBGN), as shown in Fig. 2. Further screening of the candidate material is performed using DFT calculated enthalpy of mixing estimates, Fig. 2. LSCGP, LSBGP, and LSCGN are estimated to show the most negative enthalpy of mixing. These top 3 candidates with enthalpy of mixing less than −30 kJ mol⁻¹ may be selected for synthesis. These configurations are expected to have a greater probability of being synthesized as single-phase materials. Out of these three compositions, LSBGP contains Ba, and a bigger Ba cation at the A-site is known to segregate and form secondary phases in perovskite.²⁸ From the remaining two, LSCGP and LSCGN, Pr-based perovskites are known to show superior electrocatalytic properties as compared to Nd-based perovskites.^84,85 Thus, LSCGP has finally been selected as a promising candidate to synthesize and test in experiments. This selection is highlighted in Fig. 2.

Fig. 3(a) shows the XRD pattern of the LSCGP high entropy configuration. Rietveld refinement is carried out, and refined parameters are listed in Table S2 and Fig. S1.† The LSCGP perovskite configuration is fitted to the cubic crystal structure with space group Pm3̄m and a = 3.84 Å. On optimizing the cubic structure of the LSCGP using DFT, the lattice constant is calculated to be 3.87 Å. XRD peaks of the LSCGP are compared with JCPDS # 49-0595 corresponding to LSM, where the principal peak is observed at 32.97381°, which is assigned to the (110) plane, and similarly other peaks are marked in Fig. 3(a). Overall, the LSCGP structure resembles a pure phase simple cubic perovskite with negligible impurities. This confirms the synthesis of LSCGP as a high entropy perovskite oxide. Fig. 3(b) shows the grain size and grain boundaries of the synthesized material in a scanning electron micrograph.

Fig. 3 (a) X-ray diffraction pattern, (b) SEM micrograph, and (c) XPS data of Sr²⁺ in LSCGP.

3.2 Surface analysis and Sr-cation segregation

Since LSCGP contains Sr, it is important to check for the propensity of Sr segregation to the surface. Sr segregation to the surface is likely to form secondary phases and hamper electrocatalytic activity. Fig. 3(c) shows the XPS analysis of the LSCGP, wherein peaks corresponding to Sr²⁺ 3d are marked. As discernible from the figure, only two peaks are observed, at 132.2 ± 0.2 eV and 133.8 ± 0.2 eV, which are likely to originate from 3d_5/2 and 3d_3/2, respectively, of the lattice Sr cations.^86,87 The peaks corresponding to surface Sr, i.e., at 133.5 ± 0.2 eV and 135.2 ± 0.2 eV,^26,86 are not observed in the XPS spectra. This indicates negligible Sr-cation segregation in the high entropy LSCGP structure. A comparison of the XPS spectra of LSCGP with previously reported LSM spectra^26,86,87 reveals that the high-entropy LSCGP exhibits greater stability.

To understand the comparative Sr-cation segregation tendencies at the atomic scale, we performed the surface energy calculations for LSCGP, reference LSBNP,⁵⁴ LSM20, and LSM50 structures, eqn (3). The obtained surface energies from DFT calculations allow the prediction of the energetic favorability of different surface terminations and, hence, cation segregation tendencies.^30,88,89 To compute the surface energies, A/Mn and Mn/A-terminated slabs (where the first atom before '/' is present at the top-most layer and the second atom after '/' is present in the sublayer) of LSM20, LSM50, LSBNP, and LSCGP were considered. These terminated surfaces are shown in Fig. S2.† The obtained surface energy results are provided in Table 1. The effect of multiple dopants at the A-site and level of Sr doping is estimated to show effects on Sr-cation segregation in LSM-based perovskites and high entropy perovskite oxides. Various experimental studies on LSM-based perovskites have shown evidence of significant Sr-cation presence on the surface compared to the bulk in LSM.^22–24 Experimental and theoretical studies performed by Lee et al. have reported Sr-cation segregation in LSM20 thin films.²⁶ In our DFT simulations, 20% Sr doping at the A-site in LMO resulted in lower surface energies of the A/Mn-terminating slab (7.53 kJ mol⁻¹ Å⁻²) as compared to the Mn/A-terminating slab (7.98 kJ mol⁻¹ Å⁻²). This indicated a driving force for preferential Sr cation segregation to the surface due to the energetic favorability of the Sr-terminating slab. Increasing Sr cation content also had a significant effect on Sr cation segregation. For example, Decorse et al. have performed studies with increasing Sr concentration in LSM.⁹⁰ The experimental study reported maximal Sr cation segregation for x = 0.5 in La_1–xSr_xMnO₃.⁹⁰ On 50% Sr-doping at the A-site, the surface energy of the A/Mn-terminating slab (7.61 kJ mol⁻¹·Å⁻²) is further lowered as compared to the Mn/A-terminating slab (8.40 kJ mol⁻¹·Å⁻²), suggesting more pronounced Sr-cation segregation. In the case of LSBNP high entropy configuration, the difference between the A/Mn-terminating slab (7.44 kJ mol⁻¹·Å⁻²) and Mn/A-terminating slab (7.76 kJ mol⁻¹·Å⁻²) is observed to be decreased. This indicates that the high entropy configurations could exhibit stable surfaces. For the LSCGP high entropy configuration, we observed the least difference between the A/Mn-terminating slab (7.26 kJ mol⁻¹·Å⁻²) and the Mn/A-terminating slab (7.45 kJ mol⁻¹·Å⁻²). This shows comparable energetic favorability of the two terminations and the least likelihood of segregation.

Table 1 Surface energies of AO-terminated and MnO₂-terminated slabs from DFT simulations and degree of Sr-cation segregation from MD simulations in LSM20, LSM50, LSBNP, and LSCGP

S. No.	Surface energies (kJ mol^−1·Å^−2)	LSCGP	LSBNP	LSM20	LSM50
1	AO-terminated slab	7.26	7.44	7.53	7.61
2	MnO2-terminated slab	7.45	7.76	7.98	8.40
3	Degree of Sr-cation segregation (%)	2.22	6.67	8.33	19.67

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To gain information regarding the segregation dynamics of ions at different temperatures, MD simulations were performed for the considered structures. In particular, Mn/A terminating surface slabs of La_0.8Sr_0.2MnO_2.9 (LSM20), La_0.5Sr_0.5MnO_2.75 (LSM50), La_0.2Sr_0.2Ba_0.2Nd_0.2Pr_0.2MnO_2.8 (LSBNP), and La_0.2Sr_0.2Ca_0.2Gd_0.2Pr_0.2MnO_2.8 (LSCGP) along the (001) direction are simulated at 1073 K temperature. The A-site cations, B-site Mn, and oxygen ions' trajectories are traced every 10 ps on equilibrated structures for 1 ns, as shown in the cation density profiles in Fig. 4(a–d). In line with the surface energy results from DFT, the Sr-cation distortion is observed to be the maximum at the surface of LSM50, Fig. 4(b), which is likely to reduce the surface stability of the material. Following LSM50, the Sr-cation surface segregation is observed more on LSM20 (Fig. 4(a)) than LSBNP (Fig. 4(c)). The Sr cation segregation is observed to be negligible in the LSCGP material (Fig. 4(d)). The corresponding radial distribution functions of Sr²⁺–O²⁻ ions pairs further show evidence of suppression of cation segregation in LSCGP as compared to LSBNP, LSM20, and LSM50 (Fig. S4†).

Fig. 4 Cation density profiles of Mn/A terminated slabs of (a) LSM20, (b) LSM50, (c) LSBNP, and (d) LSCGP at 1073 K temperature.

For quantitative analysis of segregation, the degree of A-site cation segregation²⁸ is calculated for all these structures. The degree of cation segregation is evaluated as the percentage of Sr-cations segregating on the surface from the sub-layer after the equilibration.²⁸ The values of the degree of cation segregation predict suppressed segregation tendencies of Sr cations in LSCGP (2.22%) as compared to the simple perovskites LSM20 (8.33%), LSM50 (19.67%), double perovskite oxides,²⁸ and LSBNP high entropy structure (6.67%). Here, the presence of different surrounding cations near Sr is expected to result in the suppression of Sr segregation. In the case of LSM20 and LSM50, only La and Sr cations are at the A-site, with a cation size difference of about 0.1 Å. As the concentration of Sr cations increases at the A-site, elastic interactions are expected to play a significant role. These interactions drive the segregation of Sr cations toward the surface due to the increasing size mismatch between A-site dopants.²⁶ In our previous study, we reported a systematic decrease in the level of total A-site cation segregation on the introduction of smaller-sized cations at the A-site in NdBa_1–x(Sr/Ca)_xCo₂O_5+d.²⁸ However, in the case of high entropy configurations, a diverse cationic environment is present at the A-site. The presence of different ion sizes at the A-site could further result in lattice strain in the structure. The parent LMO cubic structure has a lattice parameter of 3.94 Å,⁶⁰ while in LSBNP, the lattice parameter is 3.88 Å.⁵⁴ On the introduction of comparatively lesser-sized dopants at the A-site in LSCGP, the lattice parameter of the cubic structure is further reduced to 3.84 Å. The compressive strain introduced due to the high entropy effect could reduce the available space for segregating cations. Smaller-sized cations could find it easy to accommodate in bulk without the need to migrate towards the surface. Due to such reasons, La, Sr, Ba, Nd, and Pr with varied cation sizes with the biggest Ba²⁺ cation in LSBNP, are expected to show increased segregation as compared to LSCGP with La, Sr, Ca, Gd, and Pr at the A-site. The effect of Ba-cation at the A-site is likely to show an increase in Sr cation segregation as well in LSBNP. It can be observed that in LSBNP, both Ba and Sr cations are segregating towards the surface, while in the case of LSCGP, only Sr may segregate with negligible Ca cation segregation on the surface, Fig. 4. The segregation trend is in line with the XPS and DFT surface energy analysis for Sr segregation. Unlike LSM and reference high entropy perovskite oxide LSBNP, LSCGP is observed to exhibit significantly reduced Sr segregation.

3.3 Electrocatalytic performance

Theoretical and experimental investigations have shown synthesized LSCGP with good surface stability as compared to parent simple perovskite oxides,^22–24 double perovskite oxides,^28,30,88 and high entropy perovskite oxides.⁵⁴ This indicates that the synthesized LSCGP perovskite has high surface stability and suitability for electrode applications for energy storage devices. To probe the electrocatalytic performance, oxygen vacancy formation energies (E_OV) are estimated for various possible sites using DFT. E_OV provides a reasonable description of the electrocatalytic performance of perovskite oxides.^25,91 For an oxygen electrode catalyst, oxygen vacancy concentration should exist in the material for oxygen anion transport. For example, the oxygen vacancy formation energies of Sr-doped LMO perovskite oxides have been studied using both DFT simulations and experiments.²⁶ The DFT studies performed by Lee et al. have reported 415.85 kJ mol⁻¹, 390.77 kJ mol⁻¹, and 338.66 kJ mol⁻¹ formation energy for single oxygen vacancy in LMO, LSM25, and LSM50, respectively.⁹² The oxygen vacancy formation energy calculations are performed on LMO, LSM20, LSM50, LSBNP, and LSCGP high entropy structures using eqn (4). The corresponding data of oxygen vacancy formation energies from DFT simulations are encapsulated in Table S4† and Fig. 5(a). LMO, LSM20, and LSM50 exhibit oxygen vacancy formation energy of 409.10 kJ mol⁻¹, 362.78 kJ mol⁻¹, and 302.94 kJ mol⁻¹ in the La_1–xSr_x/O plane, respectively. For comparison, Sr-doped LSBNP⁵⁴ and LSCGP high entropy perovskite configurations are evaluated. As the A-site is doped with five different cations, five different sites for oxygen vacancy could be considered (Fig. S3†). As evident from Table S4,† oxygen vacancy formation is observed to be more favorable in the MnO₂ plane as compared to the AO-plane in LSCGP (166.82 kJ mol⁻¹ for MnO₂-plane) and LSBNP (212.02 kJ mol⁻¹ for MnO₂-plane). The oxygen vacancy formation energies of LSCGP high entropy perovskite oxides are observed to be much lesser than those of LMO, LSM20, LSM50, and LSBNP (Fig. 5(a) and Table S4†). Among the various possible sites in LSCGP, the vacancy site near Ca and Pr atoms is observed to be more facile than others in the AO plane. This indicates more oxygen vacancy formation and transport in LSCGP. The aliovalent doping at the A-site and smaller cations at the A-site tend to have lesser coordination. This could lead to reduced oxygen vacancy formation energies and, hence, higher oxygen vacancy concentration in bulk LSCGP. Similarly, the vacancies surrounding smaller-sized Pr³⁺ and Nd³⁺ cations are observed to show lower oxygen vacancy formation energy as compared to the vacancy site surrounded by bigger-sized aliovalent Ba²⁺ and Sr²⁺ dopants in LSBNP. We inspect the valency, size, and individual dopant cation properties that are responsible for reduced oxygen vacancy formation energies. In addition to the presence of various other cations, Ca²⁺ and Pr³⁺ are expected to be mostly responsible for increased oxygen vacancy concentration in LSCGP as compared to LSBNP. In the case of LSCGP, the introduction of aliovalent cation doping like Sr²⁺ and Ca²⁺ is expected to result in oxygen non-stoichiometry and, hence, enhanced oxygen vacancies in the structure. This behavior has also been observed in simple perovskite oxides having Ca, Sr, and Ba at the A-site, which exhibit smaller oxygen vacancy formation energies (Table S4† and Fig. 5(a)). Similarly, the iodometric titration performed by Shen et al. has shown the effect of increasing lower-sized Ca²⁺ aliovalent dopants on oxygen non-stoichiometry in La_1–xCa_xCo_0.5Fe_0.5O_3–δ.⁹³ The oxygen non-stoichiometry, hence, oxygen vacancy concentration is observed to increase on increasing x in La_1–xCa_xCo_0.5Fe_0.5O_3–δ.⁹³ In the case of Pr³⁺, the smaller size and redox-active behavior facilitate the formation of oxygen vacancy as compared to other dopants. There is also evidence that Pr³⁺ doping has increased oxygen vacancy concentration in perovskite oxides. Oxygen vacancy concentration is observed to be enhanced greatly on increasing Pr concentration in Sr_1–xPr_xTiO₃,⁹⁴ Pr_0.1Ba_0.9Co_0.7Fe_0.3O_3−δ,⁹⁵ and Pr_1–xCa_xBa_0.94Co₂O_5+δ.⁹⁶

Fig. 5 Comparison of (a) oxygen vacancy formation energies (E_OV) (Table S4†) of LSCGP and LSBNP, and parent perovskite oxides from the present study and literature, and oxygen density profile of (b) LSBNP, (c) LSCGP at 873 K temperature.

The higher oxygen vacancy concentration in the bulk promotes oxygen anion diffusivity in the material.⁹⁷ This is likely to promote the oxygen anion diffusivity and oxide ion conductivity. Hence, we probe the diffusion kinetics in the high entropy LSBNP and LSCGP structures using MD simulations. The values of oxygen anion diffusivities are extracted from the MSD vs. time plots as given in Table 2. The oxygen anion diffusivity is obtained by tracing the oxygen anion movements every 10 ps for 5 ns of MD run, using eqn (6). The corresponding MSD vs. time plots for LSCGP and LSBNP are shown in Fig. S5.† Yasuda et al. reported oxygen anion tracer diffusivity of LSM5, LSM10, and LSM20 as 2.44 × 10⁻¹³ cm² s⁻¹ at 1173 K, 4.78 × 10⁻¹² cm² s⁻¹ at 1273 K, and 1.27 × 10⁻¹² cm² s⁻¹ at 1173 K, respectively.⁹⁸ Tripathy et al. reported oxygen anion diffusivity of LSM20 and LSM50 as 2.0 × 10⁻¹⁰ cm² s⁻¹ and 1.2 × 10⁻⁹ cm² s⁻¹, respectively, at 800 K with an activation energy of 98.88 and 96.96 kJ mol⁻¹.⁹⁹ De Souza et al. reported the oxygen tracer diffusion of 3.1 × 10⁻¹² cm² s⁻¹ for LSM20 at 973 K temperature.¹⁰⁰ The self-oxygen ion diffusivity of LSCGP is obtained as 2.41 × 10⁻⁸ cm² s⁻¹ at 873 K as compared to 1.30 × 10⁻⁸ cm² s⁻¹ for LSBNP. The oxygen anion diffusivity of LSCGP is observed to be significantly enhanced compared to LSM5, LSM10, LSM20, and LSM50 at 873 K. The oxygen anion density profiles of LSBNP and LSCGP are shown in Fig. 5(b and c). The high entropy effect in LSCGP, with reduced cation segregation, makes it suitable for a more stable electrode material in SOFCs. The superior stability could be attributed to the synergistic effect of tailored compositions of dopants. In addition, various dopants in the structure enhance its electrocatalytic properties compared to the parent perovskite structure. For example, doping small concentrations of Sr and Ca facilitates oxygen anion transport in LSCGP. However, further increasing the concentration of Sr and Ca could likely lead to increased segregation tendencies.^25,81 In addition, the doped atoms at the A-site (Sr, Ca, Gd, and Pr) have less electron affinities than La, further contributing electrons easily to the diffused oxygen. This facilitates oxygen anion mobility and diffusivity within the material, contributing to its ionic conductivity.

Table 2 A comparison of oxygen anion diffusivity values of LSBNP and LSCGP and reference perovskite oxides as calculated from MD simulations and experimental estimates of diffusion coefficient measured from isotope exchange depth profiling (IEDP)

Temperature (K)	Perovskite oxide	Oxygen diffusivity (cm^2 s^−1)	Method
773	LSBNP	1.04 ± 0.14 × 10^—8	MD [this work]
873	LSBNP	1.30 ± 0.42 × 10^—8	MD [this work]
973	LSBNP	1.53 ± 0.31 × 10^—8	MD [this work]
1073	LSBNP	2.57 ± 0.21 × 10^—8	MD [this work]
1173	LSBNP	3.61 ± 0.32 × 10^—8	MD [this work]
1273	LSBNP	4.59 ± 0.24 × 10^—8	MD [this work]
773	LSCGP	1.27 ± 0.21 × 10^—8	MD [this work]
873	LSCGP	2.41 ± 0.12 × 10^—8	MD [this work]
973	LSCGP	2.95 ± 0.18 × 10^—8	MD [this work]
1073	LSCGP	3.03 ± 0.35 × 10^—8	MD [this work]
1173	LSCGP	4.35 ± 0.25 × 10^—8	MD [this work]
1273	LSCGP	5.78 ± 0.53 × 10^—8	MD [this work]
1273	LMO	2.46 × 10^−13	Isotope oxygen exchange experiment [ref. 103]
1173	LSM5	2.44 × 10^−13	IEDP [ref. 98]
1273	LSM10	4.78 × 10^−12	IEDP [ref. 98]
973	LSM20	3.10 × 10^−16	IEDP [ref. 100]
1073	LSM20	4.00 × 10^−15	IEDP [ref. 100]
1173	LSM20	1.60 × 10^−13	IEDP [ref. 100]
1273	LSM20	6.60 × 10^−13	IEDP [ref. 100]
800	LSM20	2.00 × 10^−10 [ref. 99]	MD [ref. 99]
800	LSM50	1.20 × 10^−9 [ref. 99]	MD [ref. 99]

---

The oxygen anion diffusivity is observed to be thermally activated in the material as diffusivity is observed to be increased with temperature, Table 2. From the oxygen diffusion vs. temperature data, activation energies of self-oxygen diffusivity are estimated in LSCGP using the Arrhenius equation (eqn (7)), Fig. 6(a). The activation energy of oxygen diffusion of LSCGP is estimated as 32.78 kJ mol⁻¹. The value of activation energy of the LSCGP structure is observed to be significantly improved as compared to the activation energies of oxygen diffusion in LSM20 (70.43 kJ mol^−1 101 and 67.54 kJ mol^−1 102), LSM50 (65.65 kJ mol⁻¹ (ref. 102)), and LSBNP (35.83 kJ mol⁻¹, present work). The higher oxygen anion diffusion and lower oxygen diffusion activation energy indicate improved oxygen anion transport in the material. Oxygen anion transport reflects the performance of the material for the ORR and OER activation.

Fig. 6 Arrhenius plot for (a) oxygen anion diffusivity in the temperature range of 773–1273 K, and (b) total conductivity of LSCGP.

To probe the oxygen anion and electron conduction further, total conductivity measurements are performed on LSCGP. The conductivity is measured in an ambient air environment within the temperature range of 673 to 1073 K, as shown in the Arrhenius type plot Fig. 6(b). The total conductivity of the synthesized material falls between the range of 355 S cm⁻¹ to 375 S cm⁻¹. Conductivity is observed to be enhanced when compared with the reference perovskites: LSM10 (120 S cm⁻¹ at 1073 K (ref. 9)), LSM20 (180 S cm⁻¹ at 1073 K,¹⁰⁴ 190 S cm⁻¹ at 1173 K (ref. 10)), LSM30 (178 S cm⁻¹ at 1073 K (ref. 5)), and LSM40 (320 S cm⁻¹ at 1073 K (ref. 9)). In fact, LSCGP is observed to show improved conductivity as compared to the other high entropy perovskite oxide, La_0.2Nd_0.2Sm_0.2Ca_0.2Sr_0.2MnO₃ (215.8 S cm⁻¹ at 1073 K (ref. 54)). Additionally, as the temperature increases, a minor decrease in conductivity is observed in LSCGP. The activation energy associated with the electronic conduction is estimated as 14.4 kJ mol⁻¹, Fig. 6(b), which is similar to the value reported for LSBNP (15.7 kJ mol⁻¹ (ref. 54)). The activation energy associated with the electrical conduction of LSM20 (28.3 kJ mol⁻¹ (ref. 54)) is higher than that of LSCGP and LSBNP,⁵⁴ suggesting relatively higher electronic conduction in high entropy perovskites as compared to LSM at high-temperature operations.

LSCGP is estimated to show superior electrocatalytic activity when measured in terms of conductivity and diffusivity compared to simple perovskites. LSM and manganite-based perovskite oxide electrodes have been observed to show the desired chemical stability with YSZ-based electrolytes for intermediate temperature (773 to 1073 K) operations.¹ In order to test the electrochemical performance of LSCGP, a symmetric SOFC cell consisting of the LSCGP|YSZ|LSCGP configuration is fabricated to analyze electrode impedance under the working SOFC conditions, with one side of the electrode kept in ambient air as the cathode and another in a dry hydrogen (H₂) environment as the anode. Fig. 7(a) represents the EIS spectra in the symmetrical cell configuration measured at two different temperatures (1073 K and 1023 K) at the OCV. The total polarization resistance of the LSCGP electrode, measured as the span of the semicircular impedance arc at the OCV is 0.618 and 0.320 Ω cm² at 1023 and 1073 K, respectively. To compare the electrode polarization resistance with the standard LSM electrode, a similarly fabricated LSM|YSZ|LSM symmetric cell is tested under SOFC working conditions at the same temperature, Fig. 7(b). In both the cells, the thickness of the YSZ electrolyte (1.4 mm) and sintering conditions (T = 1473 K) are kept similar to obtain comparable cell microstructures. As compared to the LSCGP, the similarly fabricated LSM symmetric cell measured a significantly higher polarization resistance at the OCV, 2.106 and 0.865 Ω cm² at 1023 and 1073 K, respectively.

Fig. 7 Symmetric cell impedance spectra measured at the OCV under working SOFC conditions for (a) LSCGP|YSZ|LSCGP and (b) LSM|YSZ|LSM configurations fabricated in a similar fashion.

The LSCGP electrode is further evaluated in a full cell configuration with the NiO-YSZ anode fabricated on the other side of the electrolyte. As represented in Fig. 8(a), the maximum power density values of the NiO-YSZ|YSZ|LSCGP cell are measured to be 124 and 182 mW cm⁻² at 1073 and 1123 K. The corresponding polarization resistance of the cell is measured from the impedance plot in Fig. 8(b), as 0.385 and 0.255 Ω cm² at 1073 and 1123 K, respectively. Considering the thickness of the YSZ electrolyte at 1.4 mm, the cell performance is significant and can be further improved by reducing the electrolyte thickness and engineering the cell microstructure.

Fig. 8 (a) Power density and j–V curves and corresponding (b) impedance spectra of the NiO-YSZ|YSZ|LSCGP SOFC cells tested at 1073 and 1123 K.

4 Conclusions

A single-phase synthesizable, high entropy perovskite structure La_0.2Sr_0.2A_0.2B_0.2C_0.2MnO₃ (A/B/C = =Pr, Nd, Gd, Ba, Ca) is predicted by a two-step screening strategy using the tolerance factor and enthalpy of mixing. A smaller tolerance factor, based on ionic radii and oxidation states, stabilizes the perovskite structure. In the first step, the selection of promising high entropy configurations was narrowed down by focusing on configurations with smaller tolerance factors. In the next step, the enthalpy of mixing calculations was used to exclude likely mixed-phase structures. Through this screening process, LSCGP was proposed as a suitable candidate, which was successfully synthesized. The two-step screening process focuses on identifying configurations that should be synthesized rather than exploring all possible configurations. It provides a targeted strategy to discover synthesizable, single-phase high-entropy configurations. This approach has the potential to be extended to high-entropy materials beyond those used in SOFC applications.

The high entropy effect on surface stability was investigated for LSCGP and reference LSBNP perovskite structures and compared with traditionally used simple perovskites LSM20 and LSM50. DFT calculations were performed to compute the surface energies of A-site terminated and B-site terminated surface slabs of perovskite oxides. Surface energetics predicted the least Sr-cation segregation in LSCGP compared to LSBNP, LSM20, and LSM50. MD simulations observed ion dynamics over time at various temperatures. Simulations showed minimal Sr-cation segregation in LSCGP as observed from the degree of cation segregation and cation density profiles. XPS analysis further confirmed negligible Sr-cation surface segregation, indicating high surface stability in LSCGP.

Oxygen vacancy formation energies calculated from DFT showed that LSCGP had much higher oxygen vacancy concentration than LSBNP, LSM20, and LSM50. MD simulations further demonstrated significantly higher oxygen diffusivity and low activation energies for oxygen anion diffusion in LSCGP. Experimental measurements of the conductivity and symmetric cell performance revealed LSCGP's improved electrocatalytic performance as compared to LSM. LSCGP emerges as a promising and stable candidate material for the cathode in SOFC operations, with enhanced electrocatalytic performance. The high-entropy concept holds significant promise for advancing energy storage and conversion technologies. Realizing its full potential requires rigorous performance evaluations under increasingly complex and realistic conditions. Furthermore, systematic exploration of cation doping at the A and B-sites presents an opportunity to optimize these materials for SOFC applications with improved electrocatalytic activity.

Data availability

The data supporting this article have been included as part of the ESI.†

Conflicts of interest

The authors declare no conflicts of interest. They have no known financial interests or personal relationships that could have influenced the work presented in this paper.

Acknowledgements

JK acknowledges financial support from the Council of Scientific & Industrial Research (CSIR), India [Grant No. 09/086(1412)/2019-EMR-I]. MAH acknowledges the support from the Department of Science and Technology, India, under DST/TDT/AM/2022/138 (G)/2. The results presented in this paper are derived from computations performed at the High-Performance Computing (HPC) cluster, Rudra, at the Inter-University Accelerator Centre Delhi, and Padum, at the Indian Institute of Technology Delhi.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ta08251f

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