⁹⁶Zr Tracer Diffusion in AZrO₃ (A = Ca, Sr, Ba)

Abstract

Cation tracer diffusion in polycrystalline AZrO₃ (A = Ca, Sr, Ba) perovskites was studied at 1300–1500 °C in air using the stable isotope ⁹⁶Zr. Thin films of ⁹⁶ZrO₂ were deposited on polished ceramic pellets by drop casting of an aqueous precursor solution containing the tracer. The pellets were subjected to thermal annealing, and the isotope depth profiles were measured by secondary ion mass spectrometry. Two distinct regions with different slopes in the profiles enabled to assess separately the lattice and grain boundary diffusion coefficients using Fick’s second law and Whipple–Le Clair’s equation. The cation diffusion along grain boundaries was 4–5 orders of magnitude faster than the corresponding lattice diffusion. The magnitude of the diffusivity of Zr⁴⁺ was observed to increase with decreasing size of the A-cation in AZrO₃, while the activation energy for the diffusion was comparable 435 ± 67, 505 ± 56, and 445 ± 45 and kJ·mol⁻¹ for BaZrO₃, SrZrO₃, and CaZrO₃, respectively. Several diffusion mechanisms for Zr⁴⁺ were considered, including paths via Zr- and A-site vacancies. The Zr⁴⁺ diffusion coefficients reported here were compared to previous data reported on B-site diffusion in perovskites, and Zr⁴⁺ diffusion in fluorite-type compounds.

1. Introduction

Mixed metal oxides AZrO₃ (A = Ba, Sr, Ca) with perovskite structure have received considerable attention as their properties may be tailored for specific applications by doping at the A or B cation sites. AZrO₃ perovskite materials are attractive due to their high proton conductivity, with potential applications in protonic ceramic fuel cells (PCFC), electrolyzers, gas sensors, and hydrogen membrane technology [1,2,3,4,5,6,7]. The majority of studies on AZrO₃ proton conductors have focused on the transport properties, but a recent study has also addressed the mobility of cations in the BaZrO₃ (BZ)-materials, revealing the challenges with solid state sintering of the ceramics and chemical instability in CO₂ at elevated temperature [8].

AZrO₃ materials belong to the family of A^IIB^IVO₃ perovskites among which cation diffusion has only been investigated in ATiO₃ (A = Ba, Sr), and recently in BZ and BaMO₃ (M = Ti, Zr, Ce) [9,10,11,12,13,14,15,16,17,18]. Systematic studies of factors influencing the cation diffusion, such as A- and B-site cation size, unit cell volume, and concentration of point defects in the materials, are still lacking. Recently, it has been shown that A-site diffusion is faster than B-site diffusion in BZ [17]. Knowledge of the difference in the cation mobility at the different cation sub-lattices is vital for the understanding of the long-term stability of the materials in chemical potential gradients [19]. Moreover, cation diffusion is also relevant for the reactivity of materials with e.g., CO₂, as recently shown for BZ-materials [20]. Cation diffusion in oxides is important for the processing of dense ceramics, and AZrO₃ materials are known for their high melting temperatures and slow sintering rates [21,22,23]. Consequently, the slow migration of the backbone-forming Zr⁴⁺-cations in the perovskites is most likely the reason for the required high sintering temperature for BZ-based ceramics [17].

Recently, we have reported on a systematic investigation of Ba diffusion in BaMO₃ (M = Ti, Zr, Ce) [18], and here, we present a corresponding systematic investigation of ⁹⁶Zr cation tracer diffusion in polycrystalline AZrO₃ (A = Ba, Sr, Ca), measured by secondary ion mass spectrometry (SIMS). The experimental data were obtained by annealing dense AZrO₃ ceramics coated with thin films of ⁹⁶ZrO₂ in the temperature range 1300–1500 °C. The ⁹⁶Zr SIMS depth profiles enabled us to determine lattice and grain boundary diffusion coefficients, and the corresponding activation energies. The cation diffusion data were discussed with respect to the dependence of the Zr⁴⁺ mobility, with respect to the size of the A-cation in the perovskite lattice and the crystal symmetry. Finally, the diffusivity of Zr⁴⁺ in AZrO₃ was compared to the B-site mobility in perovskite oxides in general, and the corresponding diffusion of Zr⁴⁺ in ZrO₂-based fluorite materials.

2. Results

X-ray diffraction (XRD) patterns of the three materials CZ (CaZrO₃), SZ (SrZrO₃), and BZ (BaZrO₃) could be indexed to single-phase perovskite materials (see Figure S1). The unit cell parameters obtained by Rietveld refinement of the diffraction patterns are summarized in

Table 1. Crystal structure, unit cell parameters, grain size, and relative density of the three materials BZ, SZ, and CZ.

Material	Crystal Structure	Unit Cell Parameters (Å)	Grain Size (μm)	Relative Density (%)
BaZrO3	Cubic $Pm\overline{3}m$	a = 4.193	0.1	97 ± 1
SrZrO3	Orthorhombic $Pbnm$	a = 5.797 b = 5.824 c = 8.209	5.2 ± 0.1	96 ± 2
CaZrO3	Orthorhombic $Pnma$	a = 5.763 b = 8.023 c = 5.596	10.5 ± 0.2	98 ± 1

and in Table S1. The sintered ceramics resulted in phase pure CZ, SZ, and BZ materials with relative density higher than 97% of the theoretical density. Scanning electron microscopy (SEM) micrographs of the three ceramics after thermal etching are shown in Figure 1. The grain size of the three materials were 10.5 ± 0.2, 5.2 ± 0.1, and 1.1 ± 0.1 μm, respectively. The grain size and relative density of the materials are summarized in Table 1.

SEM micrograph of the films of monoclinic ⁹⁶ZrO₂ on one of the materials is shown in Figure 1d. The films were homogeneous and crack-free, and about 1–2 μm thick, with good attachment to the surface of the pellets of CZ, SZ, and BZ. The thickness of the ⁹⁶ZrO₂ layer was controlled by the total amount of tracer in the precursor solution deposited on each pellet. The phase purity of the films was confirmed by XRD (not shown), and the chemical composition was confirmed by SEM/energy dispersive spectroscopy.

The depth profile of ⁹⁶Zr diffusion in SZ after annealing at 1450 °C for 4 h are given in Figure 2. The graph shows the logarithmic normalized intensity of the secondary molecular ion ⁹⁶ZrO⁻ as a function of the depth. The depth profile demonstrates the changes of the tracer concentration from the ⁹⁶ZrO₂/SZ interface towards the bulk. The concentration of the tracer became close to constant at a larger depth, corresponding to the natural abundance of ⁹⁶Zr. Two distinct regions for lattice and grain boundary diffusion were identified as regions A and B in Figure 2, respectively. The parts of the ⁹⁶Zr depth profiles related to lattice and grain boundary diffusion are included in the insets of Figure 2. The data is plotted as a function of x² and x^6/5 in the two regions, and the linear fits to the data according to Equations (5) and (6) (see Section 4) are shown by the red curves. Depth profile, such as the one shown in Figure 2, and corresponding processing of the data were obtained for all the three materials at all the conditions for the tracer annealing.

The critical parameters, α and β, which represent the ratio of the bulk and grain-boundary diffusion to the effective diffusion coefficient, were calculated from the lattice and grain boundary diffusion coefficients, D_L and D_GB [24]. α and β are defined as the partial contribution of the lattice and grain boundary diffusion coefficient, respectively, to the effective diffusion coefficient. The calculated α values were in the range 0.01–0.03, and corresponding β values exceeded 50, demonstrating that the condition to determine D_GB by Equation (6) was fulfilled (β > 10) [24].

The logarithmic tracer diffusion coefficients of ⁹⁶Zr in AZrO₃ (A = Ca, Sr, Ba) as a function of reciprocal temperature, are summarized in Figure 3. The diffusion coefficients follow an Arrhenius behavior. The magnitude of the lattice diffusion coefficient increased in the order BaZrO₃, SrZrO₃, and CaZrO₃, reflecting the decreasing size of the A-cation. The activation energy for lattice diffusion determined by the linear fit to the data is summarized in

Table 2. The pre-exponential factor and activation energy for ⁹⁶Zr lattice and grain boundary diffusion in AZrO₃ perovskites determined by the fit of the tracer diffusion data to the Arrhenius equation.

Material	Do (cm2/s)	Ea, lattice (kJ/mol)	Ea, GB (kJ/mol)
BaZrO3	0.4 ± 0.1	435 ± 67	356 ± 40
SrZrO3	220 ± 90	505 ± 56	523 ± 134
CaZrO3	6.3 ± 1.4	445 ± 45	322 ± 46

. The pre-exponential factor in the Arrhenius expression varied in the range 0.4–220 for the lattice diffusion, see Table 2. The grain boundary diffusion coefficients were 4–5 orders of magnitude higher than the corresponding data for the lattice diffusion. The activation energy for cation transport along grain boundaries is 20–120 kJ·mol⁻¹ lower compared to the corresponding activation energy for lattice diffusion (Table 2).

The activation energy for ⁹⁶Zr lattice diffusion is plotted against the unit cell volume per formula unit (f.u.) of the AZrO₃ perovskites in Figure 4. The activation energy is decreasing with increasing unit cell volume per formula unit for the two cubic perovskites BZ and SZ (cubic at the measurement temperature), while the orthorhombic CZ has an activation energy intermediate between the two others.

3. Discussion

The possible pathways for Zr⁴⁺ migration through the cubic perovskite BaZrO₃ lattice are visualized in Figure 5. The path A illustrates Zr⁴⁺ diffusion via a Ba-vacancy, while path C shows Zr⁴⁺ diffusion via a Zr-vacancy. The most likely combination of Zr⁴⁺ migration involving both site vacancies is shown in path B in Figure 5. Recently, we have shown that the diffusion pathway for Zr⁴⁺ via Ba-vacancies is most likely in BZ [17], and we propose that this diffusion mechanism can also be expected for cubic SZ also supported by previous studies [15,25].

The crystal structure of CZ is orthorhombic compared to the cubic structure of BZ and SZ at 1300–1500 °C. The phase transition to cubic SZ has been reported at 1087 °C [26], while CZ is orthorhombic up to 2000 °C [27]. Thus, the diffusion mechanism for CZ cannot be argued for based on diffusion in cubic BZ or SZ. The intermediate local configurations along the diffusion path together with activation energy are different, due to the orthorhombic symmetry. The orthorhombic distortion of CZ crystal structure is significant in the temperature region of the present measurements [28]. The activation energy for diffusion for CZ deviates from the trend from BZ to SZ (Figure 4), which support a modified diffusion path for Zr in CZ relative to the one proposed for the two cubic compounds.

Ionic diffusion in solids depends on point defects in the lattice. The main contribution to point defects in the compounds is the frozen-in point defects after processing at higher temperature, and the change in the point defect concentration during tracer anneal at considerably lower temperature is minor [17,18,29]. The possible point defects in AZrO₃ are the oxygen vacancies (${\mathrm{v}}_{\mathrm{O}}^{••}$), A-site vacancies (${\mathrm{v}}_{\mathrm{A}}^{″}$), Zr vacancies (${\mathrm{v}}_{\mathrm{Zr}}^{4\prime }$) [30], Zr anti-site (${\mathrm{Zr}}_{\mathrm{A}}^{••}$) [31], A-interstitials (${\mathrm{A}}_{\mathrm{i}}^{\mathrm{x}}$), and Zr interstitials (${\mathrm{Zr}}_{\mathrm{i}}^{\mathrm{x}}$). The metal interstitial defects are not energetically favored, and less likely to be present [30,32]. Thus, the main point defect equilibria relevant for Zr⁴⁺ diffusion in AZrO₃ perovskites can be described by point defect reactions (1) and (2) [30,32]

$$\mathrm{nill}\to {\mathrm{v}}_{\mathrm{A}}^{″}+{\mathrm{v}}_{\mathrm{Zr}}^{4\prime }+3{\mathrm{v}}_{\mathrm{O}}^{••}$$

(1)

$${\mathrm{A}}_{\mathrm{A}}^{\mathrm{x}}+{\mathrm{O}}_{\mathrm{O}}^{\mathrm{x}}\to {\mathrm{v}}_{\mathrm{A}}^{″}+{\mathrm{v}}_{\mathrm{O}}^{••}+\mathrm{AO}$$

(2)

where Equation (1) corresponds to the full Schottky equilibrium, and Equation (2) to the A-site partly Schottky equilibrium. The energy of formation for these point defect equilibria, available in the literature for the three materials, are summarized in

Table 3. The energy of formation of point defects in BZ, SZ, and CZ according to Equation (5) and (6), taken from the literature.

Material	Cation Sublattice	Cation Size [34] (Å)	Partly Schottky Defect (eV/Defect)	Schottky Defect (eV/Defect)	Reference
BaZrO3	Zr	0.72	3.75	3.20	[30]
	Ba	1.61	2.80
SrZrO3	Zr	0.72	4.45	3.51	[32]
	Sr	1.44	2.68
CaZrO3	Zr	0.72	3.09	2.22
	Ca	1.34	1.26

. The formation of A-site partly Schottky-type defects is significantly lower in energy than for the corresponding B-site. According to Table 3, the formation energies for full Schottky-type defects, reaction (1), are decreasing in the order SZ, BZ, and CZ [29,31], while the energies of formation for the AO partly Schottky-type defects decrease in the order BZ, SZ, and CZ. Higher energy of formation implies lower concentration of the frozen-in defects, and slower cation diffusivity is inferred. It is, however, important to note that the formation and loss of volatile BaO at high temperatures has been detected in BZ-materials [8,33], while evidence for the loss of SrO and CaO, from SZ and CZ, has not been reported.

In general, the diffusion coefficient for a mechanism involving ionic jumps to a vacant adjacent site is expressed by an Arrhenius expression [35]:

$$D=D_0\exp \left(-\frac{E_a}{RT}\right)=D_0\exp \left(-\frac{\Delta H_f+\Delta H_m}{RT}\right)$$

(3)

where, $E_a$ is the activation energy of diffusion, $\Delta H_f$ is the enthalpy of formation of the vacancy, $\Delta H_m$ is enthalpy of migration of the diffusing species, R is the gas constant, T is temperature, and D₀ is the pre-exponential factor. The pre-exponential factor is a temperature-independent constant experimentally determined from the fit to the Arrhenius equation and can be expanded as Equation (4) [36]:

$$D_0={\mathsf{\lambda }}^2\mathsf{\eta }\exp \left(\frac{S_f+S_m}{k_B}\right)$$

(4)

where, λ is the jump distance, η is the vibration frequency, and S_f and S_m are the entropy of formation and migration of cation vacancies, respectively.

We have recently argued that the activation energy barrier for Ba²⁺ diffusion in BZ is mainly dominated by the enthalpy of migration [18]. Including the fact that AZrO₃ materials are refractory in terms of sintering, and the defect chemistry is dominated by frozen-in point defects especially on the A-site after sintering, the contribution of the enthalpy of formation to the activation energy is assumed negligible at 1300–1500 °C. The experimental activation energies for Zr⁴⁺ diffusion in all three materials given in Figure 4 imply that increased A-cation size energetically favors Zr⁴⁺ mobility in BZ compared to SZ. The reasons could be attributed to more space for the migration, and lower Coulomb’s repulsion between the two cations A–A or A–B (see Figure 5). A similar trend has been previously observed for Ba²⁺ diffusion in cubic Ba-based perovskites [18]. The activation energy for Zr⁴⁺ diffusion in CZ is the lowest, meaning that the environment of the intermediate diffusion configurations is different compared to cubic perovskites. We proposed that the low energy of formation of the partly and full Schottky-type defects for CZ, compared to the two other compounds (Table 3), and corresponding higher frozen-in defect concentration, favor the Zr⁴⁺ diffusivity in CZ.

The cation transport along grain boundaries in all three materials is stimulated by the lower activation energy compared to activation energy for lattice diffusion. One could argue that the mobility along grain boundaries is facilitated by the higher concentration of cation vacancies at grain boundaries, more space available for the diffusion, and reduced Coulomb’s repulsion due to longer distances between the ions at the grain boundary.

The Arrhenius-type relationship of for Zr⁴⁺ diffusion in AZrO₃ perovskites encouraged us to assess the value of pre-exponential factor, D₀, and calculate the entropy of the diffusion process according to Equation (4). Referring to previous studies, the pre-exponential factor includes the entropy term, which consists of entropy of formation and migration for cation vacancies [18,36]. Based on the consideration of the activation enthalpy of migration, we also propose that the entropy term is dominated by the entropy of migration [37]. In the comparison of all three materials, it can be seen that the dependence of migration entropy on the unit cell volume per formula unit is similar to the corresponding enthalpy of migration (Figure 4), and is decreasing in the order SZ, CZ, and BZ. The lowest entropy value is estimated for BZ, meaning that the disorder due to migration is lower, and correspondingly, the Zr⁴⁺ mobility in BZ will be less favored compared to the other materials.

Figure 6 compares the Zr⁴⁺ diffusivity in AZrO₃ to the B-site diffusivities in perovskites reported in the literature. The B-site diffusion in AZrO₃ is slower than in most of the A^IIIB^IIIO₃ perovskites, with tolerance factor less than 1, due to increased charge of Zr⁴⁺ [38]. Unfortunately, the dominating diffusion mechanisms are usually not known for most of the data for A^IIIB^IIIO₃ perovskites, which challenge the comparison of data in the literature. The B-site diffusion in AZrO₃ is favored by higher activation energy than in A^IIIB^IIIO₃ perovskites, revealing that the increased charge and tolerance factor reduces the B-site mobility in AZrO₃. One could envisage that the lower tolerance factor facilitates cation diffusion as in A^IIIB^IIIO₃ compared to A^IIB^IVO₃ [17]. Correspondingly, the current diffusion data in CZ gives additional information that the decrease in the tolerance factor with corresponding distortion favors Zr⁴⁺ mobility, shifting it closer to the B-site mobility in A^IIIB^IIIO₃.

The diffusion coefficients of fluorite-type materials are summarized in Figure 7, and compared to experimental Zr⁴⁺ diffusion coefficients from the current study. It can be seen that the mobility of Zr⁴⁺ in AZrO₃ perovskites is of the same order of magnitude as in fluorite-type oxides, such as YSZ. Figure 7 implies that Zr⁴⁺ in the AZrO₃ materials is as slow as in ZrO₂-based oxides, with fluorite structure revealing the low mobility of B-site in the cubic and orthorhombic AZrO₃ perovskites.

The low mobility of Zr⁴⁺ in the current materials, evident by the comparison in Figure 7, is beneficial with respect to the chemical stability in potential gradients, but will shift the sintering temperature of the materials to high temperatures. High sintering temperatures are needed to obtain high density AZrO₃ materials, reflecting that the slow diffusion of Zr⁴⁺ is rate limiting for the sintering [8].

4. Materials and Methods

4.1. Sample Preparation

Dense BZ ceramics were sintered from fine and homogeneous spray-pyrolyzed powders (CerPoTech AS, Trondheim, Norway) at 1600 °C for 10 h in air within sacrificial powder consisting of BZ and 10 wt % BaCO₃. The pre-consolidation, consolidation, and sintering procedures of the BZ ceramics have been described previously [8]. Fine CZ powder (Sigma-Aldrich Norway AS, Oslo, Norway) was pressed into pellets by uniaxial pressing with subsequent cold isostatic press (200 MPa), and sintered at 1550 °C for 2 h in air with the heating rate of 700 °C/h. SZ powder was synthesized by solid state reaction using SrCO₃ (supplier name) and nanosized ZrO₂ powder (Sigma-Aldrich). The precursors were mixed for 8 h by ball milling with YSZ balls and isopropanol, dried (150 °C), ground, and sieved (150 μm). The synthesis was performed at 1200 °C for 5 h in air. The SZ powder was milled and pressed to pellets, and dense ceramics of SZ were prepared by sintering at 1600 °C for 10 h in air, with a heating rate of 700 °C/h.

The surface of the sintered pellets of the three different ceramics was polished by SiC papers and diamond suspension (down to ¼ μm grade) to obtain a flat and smooth surface. The pellets were pre-annealed at 900 °C for 8 h in synthetic air to clean the surfaces and remove any possible traces of carbonates and water.

The detailed procedure for the deposition of the ⁹⁶ZrO₂ films has been reported previously [17]. ⁹⁶ZrO₂ with enrichment higher than 85% (Trace Sciences International, Canada) was first transformed to ⁹⁶ZrO(NO₃)₂·xH₂O, which was dissolved in deionized water (0.05 M), and the solution was drop casted on AZrO₃ pellets at 90 °C. The coated pellets were dried at 150 °C. The ⁹⁶ZrO(NO₃)₂·xH₂O layer was decomposed at 800 °C for 3 h in flowing N₂, resulting in a dense and homogeneous layer of ⁹⁶ZrO₂ (~1–2 μm).

The pellets with the films containing the ⁹⁶Zr tracer were subjected to diffusion annealing temperatures in the range 1300–1500 °C. The annealing time varied in the range 2–90 h. The conditions for the diffusion anneal was estimated for five samples of each material regarding a constant penetration depth, $x=\sqrt{2Dt}=const$, where D is the diffusion coefficient dependent on temperature and t is time, s.

The phase purity and microstructure of the materials and the tracer layer were characterized by X-ray powder diffraction (XRD) (Bruker, Billerica, MA, USA) and scanning electron microscopy (SEM) (Hitachi, Chiyoda, Tokyo, Japan). The unit cell parameters for the three materials were obtained by Rietveld refinement using previous reported structural models for the three materials [28,56]. The grain size of the materials was evaluated by linear intercept method, from 50 to 60 grains from the SEM images. The chemical composition of the materials was confirmed by energy dispersive X-ray spectroscopy (EDS) (Oxford Instruments, Abingdon, Oxfordshire, UK).

4.2. Secondary Ion Mass Spectrometry

The distribution of the isotopes ⁹⁰Zr and ⁹⁶Zr in the ceramics was measured by SIMS using a Cameca IMS 4f instrument (Cameca SAS, Gennevilliers CEDEX, France). The experimental conditions and optimization are given elsewhere [17]. The secondary molecular ⁹⁰ZrO^–, and ⁹⁶ZrO^– ion signals were measured as a function of the sputter time. The intensities of the diffusing tracers were collected until the natural abundance of the tracer isotope was approached. The noise in the raw depth profiles was observed only at low intensity levels, which confirmed stable experimental conditions and good charge compensation. The final depth profiles of the isotope tracer were normalized by subtraction of the isotopic ratio of natural abundance [57], in order to avoid instrumental variations. The crater depth was measured with a 3D Laser Scanning Confocal Microscope KEYENCE VK-X100 (KEYENCE, Osaka, Japan). The craters exhibited no considerable roughness at the bottom.

The lattice diffusion coefficient was calculated from the first part of the depth profile (not including the region of the tracer layer with constant concentration) by fitting the experimental data to a solution of the Fick’s second law in a case of a thin film source, Equation (5) [20,35]:

$$-\frac{\partial \ln {[}^z{\mathrm{M}}_{\mathrm{norm}}]}{\partial x^2}=-\frac{1}{4D_{L}t}$$

(5)

where, D_L is lattice diffusion coefficient (cm²·s⁻¹) of isotope ^zM with normalized concentration [^zM_norm] in depth x (cm) at an appropriate time t (s).

Grain boundary transport occurred in the Harrison B-type kinetic regime, where the condition $\mathsf{\delta }<\sqrt{Dt}<d or 1<d/\sqrt{Dt}$ is fulfilled [20], where d is the average grain size and δ is the grain boundary width. The grain boundary diffusion coefficients were estimated from the part of the depth profiles at deeper sputter depth using the Whipple–Le Clair’s equation [20,24]:

$$s\mathsf{\delta }{D}_{GB}=1.322\sqrt{\frac{D_{eff}}{t}}{\left(-\frac{\partial \ln {[}^z{\mathrm{M}}_{\mathrm{norm}}]}{\partial x^{6/5}}\right)}^{-5/3}$$

(6)

where, s is a segregation factor, δ is grain boundary width (cm), D_GB is grain boundary diffusion coefficient (cm²·s⁻¹), D_eff is an effective diffusion coefficient (cm²·s⁻¹), and t is annealing time (s). The effective diffusion coefficient, D_eff, represents a combined lattice and grain boundary diffusivity, calculated by, D_eff = gD_GB + D_L, where g = 3δ/d.

5. Conclusions

The lattice and grain boundary diffusion of Zr⁴⁺ in polycrystalline AZrO₃ (A = Ca, Sr, Ba) was determined by ⁹⁶Zr tracer diffusion experiments. The activation energies for Zr⁴⁺ lattice diffusion were shown to be 435 ± 67, 505 ± 56, and 445 ± 45 and kJ·mol⁻¹, respectively for BaZrO₃, SrZrO₃, and CaZrO₃. It was suggested that lattice diffusion of Zr⁴⁺ occurs via A- and B-vacancies based on the previously reported agreement between experiments and calculations in case of BaZrO₃. Enhanced diffusivity along grain boundaries was observed for Zr⁴⁺ in BaZrO₃, SrZrO₃, and CaZrO₃, with activation energies of 356 ± 40, 523 ± 134, and 322 ± 46 kJ·mol⁻¹, respectively. The pre-exponential factor in the Arrhenius expression for diffusion and the activation entropy of diffusion were shown to depend on the unit cell volume per formula unit in a similar manner as the activation enthalpy. The B-site lattice diffusivities for AZrO₃ perovskites were lower than in A^IIB^IVO₃, and most A^IIIB^IIIO₃ perovskites, and in the same range as most fluorite-type oxides. The low Zr⁴⁺ diffusivity makes the materials robust with respect to B-site mobility in electrochemical potential gradients.