Direct observation of space-charge-induced electric fields at oxide grain boundaries

Abstract

Space charge layers (SCLs) formed at grain boundaries (GBs) are considered to critically influence the properties of polycrystalline materials such as ion conductivities. Despite the extensive researches on this issue, the presence of GB SCLs and their relationship with GB orientations, atomic-scale structures and impurity/solute segregation behaviors remain controversial, primarily due to the difficulties in directly observing charge distribution at GBs. In this study, we directly observe electric field distribution across the well-defined yttria-stabilized zirconia (YSZ) GBs by tilt-scan averaged differential phase contrast scanning transmission electron microscopy. Our observation clearly reveals the existence of SCLs across the YSZ GBs with nanometer precision, which are significantly varied depending on the GB orientations and the resultant core atomic structures. Moreover, the magnitude of SCLs show a strong correlation with yttrium segregation amounts. This study provides critical insights into the complex interplay between SCLs, orientations, atomic structures and segregation of GBs in ionic crystals.

Here the authors directly observe space-charge-induced electric fields at yttria-stabilized zirconia grain boundaries, revealing how space charge layers corelate with grain boundary orientations, core atomic structures, and yttrium segregation amounts.

Introduction

The study of space charge layers (SCLs) in oxide grain boundaries (GBs) has attracted significant attention due to their impact on various material properties, such as crystal growth, ion conductivity, and electron conductivity^1–3. Many solid-state O-ion and Li-ion conductors are material systems where GB SCLs play a crucial role in determining transport properties^3–6. Yttria-stabilized cubic zirconia (YSZ), for instance, is widely used as an electrolyte for solid oxide fuel cells due to its high oxygen ionic conductivity and thermal stability^7,8. However, numerous studies have indicated that the ionic conductivity across the GBs is significantly lower than that within the grains, and this has been attributed to the formation of SCLs^9,10. According to the SC theory^4,10,11, when the GB core of YSZ is assumed to be positively charged, the positively charged mobile carriers, in this case oxygen vacancies, can be expelled out from the GB core region. Such depletion of oxygen vacancies and the resultant potential barriers can retard oxygen ion conductivity across the YSZ GBs⁴. A thorough analysis of SCLs is thus essential for advancing our understanding of the properties and developing ion conductors with better performances.

So far, some experimental and computational methods have been employed to investigate SCLs^11,12. Conventionally, SCLs have primarily been indirectly investigated through macroscopic measurements of polycrystalline materials using electrochemical impedance spectroscopy¹³. However, such macroscopic measurements are unable to identify the individual contribution of GBs in polycrystalline materials. Since each GB possesses distinct characteristics depending on its orientation and resultant atomic structures^14–17, the SCLs are expected to significantly vary in each GB. Thus, there is a pressing need for the direct observation of the SCLs of individual GBs in conjunction with their orientations, atomic structures and chemistry, in order to design and develop materials with better properties. To address this need, direct observation of SCLs using transmission electron microscopy (TEM) or scanning TEM (STEM)^18–20 has been attempted continuously. However, in the previous studies using S/TEM, the effect of diffraction contrast, which arises from the changes in local structures and distortions around GBs, has made it extremely difficult to extract true and quantitative SCL signals. In addition, while some studies have attempted to measure SC with STEM-electron energy loss spectroscopy (EELS)^21,22 in terms of the chemical change, the sensitivity of the STEM-EELS spectrum in YSZ is typically insufficient to detect subtle changes in oxygen vacancy distribution or Yttrium coordination. As a result, the detailed distribution and origin of SCLs at individual GBs still remain elusive.

Previous studies have demonstrated that differential phase contrast (DPC) STEM can directly visualize local electromagnetic field distribution inside materials from nanometer to sub-atomic scale^23–27. In recent years, tilt-scan averaged DPC STEM (tDPC STEM) has been developed for minimizing diffraction contrast effects and extracting true electromagnetic field signals at crystalline interfaces^27–30. Figure 1 shows a schematic illustration of tDPC STEM technique. In tDPC, the incident-beam-tilt conditions are systematically changed while the incident electron probe is stationary at the same sample position. Subsequently, the bright field (BF) disks under multiple beam-tilt conditions are averaged on the detector plane. To a good approximation, the Coulomb deflection of the BF disk by electric fields is insensitive to minor changes in the beam-tilt condition. By contrast, the diffraction contrast is highly sensitive to even slight changes in the beam-tilt condition. Therefore, the electric field component in the DPC signals is mostly unchanged and reinforced by tDPC, whereas the diffraction contrast component changed by beam tilting is effectively averaged and suppressed. Thus, tDPC STEM can extract true electric field signals by suppressing diffraction contrast. By employing tDPC STEM, we recently succeeded in extracting the true electric field signals related to the charge inhomogeneity across semiconductor heterointerfaces quantitatively²⁷. Moreover, other STEM methods such as high-angle annular dark field (HAADF)³¹ and energy dispersive X-ray spectroscopy (EDS)³², can also be used in tDPC STEM, which provides us a comprehensive understanding towards the correlation between local atomic structures, chemistry and electromagnetic fields.

Fig. 1. Schematic illustration of electric field observation across a grain boundary (GB) using tDPC STEM.

The arrangement of the tilt-averaged electron probe, sample, and segmented detector used in this study is shown. By superimposing multiple electron beam tilts, the effect of diffraction contrast is effectively suppressed, enabling quantitative local electric field analysis. As an example, the case with positive charge in the GB core and a negative charge around grain boundary is shown.

In the present study, we employed the tDPC STEM to directly observe the SCLs formed at four different model YSZ GBs. The charge amount was quantified by fitting the experimental electric field profiles with a Poisson-Cahn model³³. We show that it is now possible to directly and quantitatively characterize SCLs at individual GBs. Furthermore, the atomic structures and compositions of these model GBs were thoroughly investigated by HAADF STEM and STEM-EDS, which allow us to establish the one-by-one correlations between atomic structures, segregation behaviors and core charges associated with SCLs.

Results

The atomic structures and segregation behaviors of the four GBs were first studied. Figure 2 shows HAADF STEM images of the four coincident-site-lattice YSZ GBs of a, $\sum 5\left[001\right]/\left(310\right)$, b, $\sum 5\left[001\right]/\left(210\right)$, c, $\sum 9\left[110\right]/\left(221\right)$ and d, $\sum 3\left[110\right]/\left(111\right)$, respectively. The bicrystal fabrication procedure is described in the “Methods”. The GB core atomic structures are clearly resolved, which are consistent with the previous studies^34–38. Atomic-resolution STEM-EDS elemental maps across the GBs are shown in Fig. 3. Quantitative line profiles of the EDS maps are also shown in Fig. 4. Segregation of Y to the GB cores was observed for all the GBs, which was strongly dependent on the GB orientations. It is noted that, although no obvious preferential segregation sites exist in the atomic-scale maps, strong Y segregation was detected in the ∑5[001]/(310) and ∑9[110]/(221) GBs as a total. On the other hand, the $\sum 5\left[001\right]/\left(210\right)$ shows very small Y segregation. In addition, Y segregation was clearly detected at specific GB atomic sites in the $\sum 3\left[110\right]/\left(111\right)$ and partially in the $\sum 5\left[001\right]/\left(210\right)$ GBs. This preferential segregation should be triggered by the strain relaxation of Y³⁺ with a larger ionic size than Zr⁴⁺³⁷(more details will be discussed later). It is also noted that Al and Si impurity segregations were observed for all the GBs except for the $\sum 3\left[110\right]/\left(111\right)$. These impurity atoms may be introduced during the bicrystal fabrication processes^39,40.

Fig. 2. HAADF STEM images of four model YSZ grain boundaries fabricated by bicrystal method.

The images of (a), $\sum 5\left[001\right]/\left(310\right)$, (b), $\sum 5\left[001\right]/\left(210\right)$, (c), $\sum 9\left[110\right]/\left(221\right)$ and, (d), $\sum 3\left[110\right]/\left(111\right)$ are shown respectively. The scale bars in (a–d) represent 2 nm.

Fig. 3. Atomic-resolution STEM-EDS cation concentration maps of four model YSZ grain boundaries.

Zr (a–d), Y (e–h), Al (i–l) and Si (m–p) EDS cation concentration maps of the YSZ $\sum 5\left[001\right]/\left(310\right)$, $\sum 5\left[001\right]/\left(210\right)$, $\sum 9\left[110\right]/\left(221\right)$, and $\sum 3\left[110\right]/\left(111\right)$ grain boundaries, respectively. The scale bars represent 0.5 nm.

Fig. 4. Line profiles of cation concentration maps.

Line profiles of Y (a–d), Al (e–h) and Si (i–l) concentration across the $\sum 5\left[001\right]/\left(310\right)$, $\sum 5\left[001\right]/\left(210\right)$, $\sum 9\left[110\right]/\left(221\right)$ and, $\sum 3\left[110\right]/\left(111\right)$ grain boundaries, respectively. The vertical axis is plotted by cation percentage.

Next, the electric field distribution across the GBs were analyzed by tDPC STEM. Figure 5 shows the horizontal electric field component images and the corresponding line profiles (averaging across the field of view) of the $\sum 5\left[001\right]/\left(310\right)$, $\sum 5\left[001\right]/\left(210\right)$ GBs, respectively. From the line profiles, sharp and narrow positive and negative electric field peaks (indicated by red arrows) corresponding to the electric fields converging towards the GB cores, were clearly observed for both GB cores. In addition, in the ∑5[001]/(310) GB, a gentle and wide leftward electric field peak on the left side of the GB, and a gentle and wide rightward electric field peak on the right side of the GB were observed, as indicated by blue arrows (Fig. 5a, b). These signals indicate the presence of a divergent electric field from the GB cores, with approximately 15 nm width on each side of the GB. Conversely, almost no divergent electric fields are found in the $\sum 5\left[001\right]/\left(210\right)$ GB (Fig. 5c, d).

Fig. 5. Electric field maps and corresponding line profiles of $\sum 5$ grain boundaries (GBs) obtained by tDPC STEM.

a Horizontal-component electric field (E_x) map of $\sum 5\left[001\right]/\left(310\right)$ GB and (b), horizontal-component electric field line profile, which is obtained by vertical averaging of (a). c Horizontal-component electric field map of $\sum 5\left[001\right]/\left(210\right)$ GB and (d), horizontal-component electric field line profile, which is obtained by vertical averaging of (c). In the electric field maps in (a) and (c), blue color indicates the leftward and red color indicates the rightward electric fields, respectively. In the line profiles in (b) and (d), the leftward electric field is defined as negative value, and the rightward electric field defined as positive value, respectively.

To interpret these electric field profiles, possible electrostatic potential and associated electric field profiles across GBs with SCLs are schematically illustrated in Fig. 6. From electrostatic point of view, if a GB core is positively charged and negative SCLs exist in adjacent to it, the GB will exhibit positive potential, and result in a diverging electric field from the GB core (Fig. 6a). On the other hand, GB electrostatic potential and resultant electric field profile can also be affected by the structural feature of the GB core. Mean inner potential (MIP), which is defined as a volume average of atomic potential of the specimen, can affect DPC signal in addition to the electric fields originated from charge distribution^41–44. Since the local atomic density of the GB core can be intrinsically lower than that of bulk and the TEM sample thickness along the electron beam direction at GBs is often thinner than the bulk regions due to the selective etching by ion milling, there can be a dip in the MIP along the GB core. The local gradient in MIP results in an electric field, which produces DPC signals, even though the GB were not charged and without charge distribution^45,46. As a result, the GB exhibits a sharp converging electric field towards its core (Fig. 6b). Consider a case of positively charged GB core and negatively charged SCL in real case, where the above two effects coexist in the GB, the overlap of the two potentials shown in Fig. 6a, b is expected. An overlapped electric field profiles should be observed as a total electric field profile by tDPC STEM (Fig. 6c). Our experimental electric field observations and potential profile of $\sum 5\left[001\right]/\left(310\right)$ (see Supplementary Fig. 1) are in consistence with such schematic profile shown in Fig. 6c, indicating that the core of GBs in YSZ is positively charged. Furthermore, it can be concluded that a large amount of SCs exists in $\sum 5\left[001\right]/\left(310\right)$ GB, while the amount of SCs is very small in $\sum 5\left[001\right]/\left(210\right)$ GB.

Fig. 6. Schematic illustration of the electric field profiles and corresponding potential profiles across a grain boundary (GB) in YSZ.

In the electric field profile, the leftward electric field is defined to be negative value and the rightward one is defined to be positive values, respectively. a Electric field and potential profiles due to SCLs with positive core charge. b Electric field and potential profiles due to abrupt decrease in mean inner potential. c Electric field and potential profiles resulted from both SC and mean inner potential decrease at the core.

Figure 7 shows the line profiles of the horizontal electric field component images for all the GBs studied here. Note that the plot range of Fig. 7 is modified from that in Fig. 5 in order to emphasize the diverging electric fields of each GB. The original profiles are shown in Supplementary Fig. 2. Strong converging electric field peaks are found at the cores for all the GBs, which can be attributed to the structural-induced abrupt mean inner potential decreases at the cores as discussed above. On the other hand, the diverging electric fields surrounding the GB cores were significantly different among the four GBs. The magnitude of the diverging electric fields follows in the order of $\sum 9\left[110\right]/\left(221\right)$ $\ge$ $\sum 5\left[001\right]/\left(310\right)$ > $\sum 5\left[001\right]/\left(210\right)$ > $\sum 3\left[110\right]/\left(111\right)$. The differences in the diverging electric fields can be attributed to the amount of core charges, which equal to the accumulated SCs. Therefore, the widths of SCLs can also be estimated to be about 15 nm, based on the measured width of the divergent electric fields.

Fig. 7. Horizontal-component electric field line profiles of four YSZ grain boundaries (GBs).

The leftward electric field is defined to be negative value, and the rightward one is defined to be positive value. Note that the y-axis range has been modified from Fig. 5b, d in order to highlight the differences in the diverging electric field of each GB.

Next, we attempted to quantify the SCs and core charges from the distribution of the diverging electric fields. Here, we fitted the electric field line profiles obtained via the tDPC STEM experiment shown in Fig. 7 using a Poisson-Cahn model^33,47. The Poisson-Cahn model can describe space charge over the entire Y₂O₃ concentration range, from dilute to high dopant concentrations. This model combines the Poisson-Boltzmann equation with Cahn-Hilliard theory, incorporating chemical interactions of point defects. Within the Cahn-Hilliard framework⁴⁸, the electrochemical potentials of the acceptor dopant ${\lambda }_{\mathrm{a}}$ and oxygen vacancy ${\lambda }_{\mathrm{v}}$ are described as follows³³:

$${\lambda }_{\mathrm{a}}=f_{\mathrm{aa}}{n}_{\mathrm{a}}\left(x\right)+f_{\mathrm{av}}{n}_{\mathrm{v}}\left(x\right)+{\mathrm{k}}_{\mathrm{B}}T\ln \frac{n_{\mathrm{a}}\left(x\right)}{1-n_{\mathrm{a}}\left(x\right)}-e\varphi \left(x\right)-{\beta }_{\mathrm{a}}\frac{{\mathrm{d}}^2{n}_{\mathrm{a}}\left(x\right)}{{\mathrm{d}x}^2}$$ 1

$${\lambda }_{\mathrm{v}}=f_{\mathrm{vv}}{n}_{\mathrm{v}}\left(x\right)+f_{\mathrm{av}}{n}_{\mathrm{a}}\left(x\right)+{\mathrm{k}}_{\mathrm{B}}T\ln \frac{n_{\mathrm{v}}\left(x\right)}{1-n_{\mathrm{v}}\left(x\right)}+2e\varphi \left(x\right)-{\beta }_{\mathrm{v}}\frac{{\mathrm{d}}^2{n}_{\mathrm{v}}\left(x\right)}{{\mathrm{d}x}^2}$$ 2

where $\varphi$ is the electrostatic potential, $n_{\mathrm{a}}$ and $n_{\mathrm{v}}$ are the site fractions of the acceptor dopant and oxygen vacancy, respectively, $f_{ij}$ is the interaction energy between the species i and j, and ${\beta }_i$ is the gradient energy coefficient for species i. The electrostatic potential $\varphi$ follows the Poisson’s equation,

$${\epsilon }_r{\epsilon }_o{\nabla }^2\varphi \left(x\right)=e\left(2N_{\mathrm{v}}^{\mathrm{b}}{n}_{\mathrm{v}}\left(x\right)-N_{\mathrm{a}}^{\mathrm{b}}{n}_{\mathrm{a}}\left(x\right)\right)$$ 3

where ${\epsilon }_{\mathrm{r}}$ and ${\epsilon }_{\mathrm{o}}$ are the relative and vacuum permittivities, respectively, and $N_{\mathrm{i}}^{\mathrm{b}}$ is the bulk site density of the species i. Boundary conditions for species i can be formulated from the mathematical variational analysis of free energy functional⁴⁹:

$${N_i^{\mathrm{b}}\beta }_i{\left(\frac{\mathrm{d}{n}_i\left(x\right)}{\mathrm{d}x}\right.∣}_{x=0}=N_i^{\mathrm{GB}}{\eta }_i^{\mathrm{GB}}$$ 4

where $N_i^{\mathrm{GB}}$ is the site density at the GB, and ${\eta }_i^{\mathrm{GB}}$ is the segregation energy. These equations can be numerically solved using the standard method. We calculated such Poisson-Cahn potential and electric field via Newton-Raphson method, as per the previous studies^33,47. The parameters of $f_{ij}$, ${\beta }_i$, and ${\eta }_i^{\mathrm{GB}}$ were optimized to fit the experimental electric fields. Although structurally induced mean inner potential decrease at the cores is superimposed in the electric field profiles (Fig. 7), we can quantify the space charge using the divergent electric field regions around the GBs. Details of the fitting procedure are shown in the Method. Table 1 shows the results of charge quantification for each GB, along with the amount of Y segregation estimated by STEM-EDS. The space charges was different, resulting in the order of $\sum 9\left[110\right]/\left(221\right)$ $\approx$ $\sum 5\left[001\right]/\left(310\right)$ > $\sum 5\left[001\right]/\left(210\right)$ > $\sum 3\left[110\right]/\left(111\right)$. These findings clearly show that the charge distribution around the GB significantly differs depending on the GB orientation. Moreover, even in the GBs with the same sigma values ($\sum 5\left[001\right]/\left(310\right)$ and $\sum 5\left[001\right]/\left(210\right)$) and with the same rotation axis ($\sum 5\left[001\right]/\left(310\right)$ and $\sum 5\left[001\right]/\left(210\right)$, and $\sum 9\left[110\right]/\left(221\right)$ and $\sum 3\left[110\right]/\left(111\right)$), the amount of SCs and core charges significantly differ.

Table 1.

Quantitative core charge and space charge estimated from tDPC STEM images

Grain boundary	Space charge [electron cm−3]	Core charge [electron cm−2]	Y concentration [cation %] (Y segregation [%])	Al concentration [cation %]	Si concentration [cation %]
$\sum 5\left[001\right]/\left(310\right)$	4 ± 2 × 1019	14 ± 3 × 1013	23.6 ± 0.3 (24 ± 4)	0.3 ± 0.1	5.3 ± 0.1
$\sum 9\left[110\right]/\left(221\right)$	6 ± 2 × 1019	10 ± 3 × 1013	25.1 ± 0.3 (25 ± 4)	1.6 ± 0.1	5.3 ± 0.1
$\sum 5\left[001\right]/\left(210\right)$	0.5 ± 0.3 × 1019	2 ± 1 × 1013	21.4 ± 0.3 (10 ± 4)	0.0 ± 0.1	1.4 ± 0.1
$\sum 3\left[110\right]/\left(111\right)$	0.0 ± 0.3 × 1019	0 ± 1 × 1013	26.3 ± 0.3 (35 ± 3)	0.0 ± 0.0	0.0 ± 0.0

Y, Al, and Si amounts analyzed by STEM- EDS (line profiles from Fig. 4) are also listed. Space charge represents maximum negative volume charge density at the space charge layer. Core charge represents positive sheet charge density at the grain boundary interface. Y, Al, and Si concentration is the cation % values at the grain boundary interface, which is assumed 1 nm width. Y segregation values inset in Y concentration column is calculated as maximum value of the ratio of Y increase at GBs compared with that within grains. Errors in the table represent the standard errors.

Discussion

Next, we explore the relationship between the charge distribution and segregation amounts at the GBs. The negative charges observed around the GBs suggest the possibility of depletion of positively charged oxygen vacancies in these regions. From the previous studies, oxygen ions were shown to strongly segregate at the $\sum 5\left[001\right]/\left(310\right)$, $\sum 9\left[110\right]/\left(221\right)$ and slightly segregate at the $\sum 5\left[001\right]/\left(210\right)$ GB, but not to segregate at the $\sum 3\left[110\right]/\left(111\right)$ GB^37,38. These findings are consistent with our tDPC experiments, which indicate the amount of SC differes as $\sum 9\left[110\right]/\left(221\right)$ $\approx$ $\sum 5\left[001\right]/\left(310\right)$ > $\sum 5\left[001\right]/\left(210\right)$ > $\sum 3\left[110\right]/\left(111\right)$. As for Y segregaion, different amounts of Y segregation have been observed (Fig. 4 and the previous studies^36–38) in the four GBs. The cation segregation amount is summarized in Table 1. For the $\sum 3\left[110\right]/\left(111\right)$ GB, Y segregation at very specific GB atomic sites has been observed³⁷. The segregation structure of the $\sum 3\left[110\right]/\left(111\right)$ GB can be perfectly reproduced via Monte Carlo simulations combined with static lattice calculations without taking into account any GB core charges. It has been pointed out that the undercoordinated GB atomic sites are considered to be the origin of Y segregation, in order to minimize the local strain³⁷. Such scenario also agrees with our present result, that the SCs and core charges at the $\sum 3\left[110\right]/\left(111\right)$ GB were essentially negligible within the measurement error of the present tDPC STEM. These results suggest that Y segregation to the $\sum 3\left[110\right]/\left(111\right)$ GB is induced solely by the elastic energy minimization mechanism, and has little correlation to GB core charges. On the other hand, it is found that the amount of Y segregation shows a positive correlation with the amount of core charges in the $\sum 5\left[001\right]/\left(310\right)$, $\sum 5\left[001\right]/\left(210\right)$ and $\sum 9\left[110\right]/\left(221\right)$ GBs. The $\sum 5\left[001\right]/\left(310\right)$ and $\sum 9\left[110\right]/\left(221\right)$ GBs show pronounced Y segregation, despite the absence of specific GB core segregation sites like the $\sum 3\left[110\right]/\left(111\right)$ GB. At the $\sum 5\left[001\right]/\left(210\right)$ GB, while some preferential segregation sites were observed, Y segregation in total is less than the $\sum 5\left[001\right]/\left(310\right)$ and $\sum 9\left[110\right]/\left(221\right)$ GBs, suggesting that elastic energy may also affect the Y segregation at specific sites of the $\sum 5\left[001\right]/\left(210\right)$ GB core. These results suggest that the electrostatic interaction between positively charged GB core and Y might be the major origin of Y segregation in general GBs. Positively charged GB cores would attract Y_Zr and repel oxygen vacancy near the GB. Such interaction would result in a GB Y segregation and oxygen vacancy depletion. It is thus revealed that Y segregation behaviors can be determined by the balance of both electrostatic and elastic interactions, which are strongly dependent on the GB orientations and resultant core atomic structures.

Finally, we briefly discuss the origin of the positive core charges. The origin of the positive core charges in YSZ GBs has conventionally been explained by the difference in the standard chemical potential of oxygen vacancies at the GB core and that within the grains^50,51. In this scenario, oxygen vacancies gradually accumulate at the GB core. The oxygen distribution has been studied in detail in our previous report³⁸. STEM EDS in that study did not detect such oxygen vacancy accumulation in those GBs³⁸. Other mechanisms of positive core charges have been also proposed, including the existence of unintentional impurities such as Si or Al^18,52, or non-stoichiometric anion-cation coordination deficiencies of ionic crystals at the GB cores^53,54. Our STEM-EDS mapping clearly show that Si and Al impurities indeed segregated to the GBs (Figs. 3, 4). If Si substitutes for Zr sites at the GB cores, no formal charge should be formed at these sites. On the other hand, if Al substitutes for Zr at the GB cores, negative formal charges should be formed. Additionally, if these impurities occupy interstitial sites at the GB cores, positive charges should be formed. Thus, impurity segregation at the core can be one of the origins for the positive core charges. Although the atomic-resolution Si and Al EDS maps suggest that the segregated impurity atoms may occupy both Zr sites and interstitial sites at the GB cores (Fig. 3), quantifying charge amount by these impurities remains highly challenging due to the electron channeling effect in atomic-resolution EDS mapping⁵⁵. On the other hand, the two GBs which show the large SCLs, $\sum 5\left[001\right]/\left(310\right)$ and $\sum 9\left[110\right]/\left(221\right)$ GBs, exhibit incoherent GB core atomic structures (Fig. 2). These results may still support the coordination deficient mechanism as the origin of the positive core charges. As the coordination environment at GB is often much different from those within the bulk, our conclusion could be applicable to those general GBs inside practical polycrystalline materials. In polycrystalline materials, asymmetric or random grain boundaries, which often have more disordered core atomic structures, might have larger space charge. Investigating such more realistic grain boundaries using the present technique will be our future work. Furthermore, given the present dose condition detailed in the Method, tDPC STEM observations reported here hold potential for observing more beam-sensitive materials, such as Li-battery materials⁵⁶. The present technique may lead to our general understanding of grain boundary resistivity in many types of ion-conductors. To address the true origin of the positive core charges quantitatively, first-principles calculations with very long-range cells that account for impurity segregation and charge inhomogeneities should be necessary, which is technically difficult to realize at the moment and beyond our scope of this study. However, the ability to directly observe SCLs at individual, well-defined GBs in conjunction with their atomic-scale structures and chemistry finally open the possibility for fundamental understanding of the correlation between SCLs, atomic structures and segregation behaviors of GBs in many oxide materials.

In summary, we directly observed the electric field distribution across the four different YSZ GBs using tDPC STEM. We found that the SCLs are formed at the YSZ GBs, but the magnitude is strongly dependent on their GB orientations. Moreover, the amount of SCs and the amount of Y segregation show a positive correlation for most of the GBs, where the segregation is mainly dominated by the electrostatic effects. The present approach of directly observing SCLs should pave the way for fundamental understanding of the complex interplays between GB orientations, GB core atomic structures, impurity/solute segregation and SCLs in many oxide materials and devices.

Methods

Sample preparation

We fabricated four well-defined YSZ bicrystals as model samples by a diffusion bonding method. Two YSZ (10 mol% Y₂O₃) single crystals were precisely cut and joined at 1600 °C for 15 h in air³⁶, forming the bicrystals with $\sum 5\left[001\right]/\left(310\right)$, $\sum 5\left[001\right]/\left(210\right)$, $\sum 9\left[110\right]/\left(221\right)$, and $\sum 3\left[110\right]/\left(111\right)$ GBs. TEM specimens were prepared via mechanical polishing using 9 to 1 µm diamond suspensions followed by Ar ion-beam thinning using 3.5 kV to 0.5 kV accelerating voltages. The sample thickness was estimated to be approximately 30 to 80 nm for each GB using STEM electron energy loss spectroscopy⁵⁷.

STEM observations

The atomic structure and Y segregation of the GBs were examined by HAADF-STEM and STEM-EDS using an aberration-corrected STEM with dual-EDS detectors (JEM-ARM200CF, JEOL). The accelerating voltage and the convergence semi-angle were set to 200 keV and 24 mrad, respectively. NSS3 spectral analysis software (Thermo Fisher Scientific Inc.) was used to perform the EDS analysis. Low magnification two-dimensional EDS maps were taken at all the GBs^37,38. Then, the line profiles across the GBs are formed by integrating the EDS signal parallel to the GBs to obtain quantitative amount of segregation (Fig. 4 and Table 1). The GB chemistry was defined by the cation ratio, namely N_i/N_total, where N_i is the number of atoms for cation i and N_total is the total number of cations.

Electric field distribution was mapped via tDPC STEM using the magnetic-field-free atomic resolution STEM with 40-segmented detector²⁶ and tilt-scan system²⁹ (JEM-ARM200CF equipped with a magnetic-field-free objective lens, JEOL)⁵⁸. The accelerating voltage and the convergence semi-angle were set to be 200 keV and 2 mrad, respectively. The probe current, dwell time, and expected probe size were set to be approximately 12 pA, 98 µsec/pixel, and 0.7 nm, respectively. The electron dose with these conditions is estimated to be about 2000 e^-/Ų. 61-beam-tilt conditions, of which the maximum-tilt angle was set to be 8 mrad, were generated by the tilt coils above the probe corrector, and the tilted beam converged into one BF disk on the detector by the other tilt coils below the objective lens²⁷. The center of mass (CoM) of the BF disk was measured for imaging quantitative electric field maps inside the specimens⁵⁹. The CoM value was measured by weighting the electron intensity of each detector segment by the geometric center of mass of the detector segment at each raster position. The tDPC images were denoised by excluding signals incompatible with the Poisson equation via discrete cosine transformation⁶⁰. The residual diffraction contrast was evaluated using calculated tilt-averaged BF disks via electron-diffraction simulation^27,30,61.

SCs and potentials were quantified by fitting the experimental electric field profiles to the electric field profiles of Poisson-Cahn model. We numerically calculated the Poisson-Cahn electric field by solving Eqs. (1–4) via Newton-Raphson method according to the MATLAB script in the previous study³³. The calculated electric field profiles were adjusted to match the experimental electric field profiles using cubic spline interpolation, and the parameters of $f_{ij}$, ${\beta }_i$, and $f_i^{\mathrm{GB}}$ in Eqs. (1–4) were optimized using the Nelder-Mead method to minimize the squared error between the experimental and model electric fields.

Image calculation, analysis, fitting, and display of the results were performed using common Python3 packages such as Numpy and Scikit-image.

Author contributions

S.T. and N.S. designed the study. S.T. wrote the paper with support from B.F., T.S. and N.S. S.T. and B.F. fabricated the YSZ samples and performed the STEM experiments. S.T. performed the image analysis and model fitting. T.S. and Y.I. contributed to the discussion and comments. N.S. directed the entire study.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The electric field image data generated in this study have been deposited in the figshare database⁶² [10.6084/m9.figshare.25859548]. The data that support this study are available from the corresponding authors upon request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-53014-w.