When considering the properties of crystalline materials, the impact of defects is essential. Point defects such as vacancies and dopants are the defects most commonly considered in both computational and experimental studies of material properties. Furthermore, the modelling of materials at an atomic level is often confined to bulk systems which contain these point defects (1–4). Considerably less is known about extended defects which appear in polycrystalline systems such as surfaces, dislocations and GBs. As nanostructuring of materials is becoming more prevalent, the behaviour of these extended defects is becoming significantly more important (5–8). GBs give rise to structural discontinuities within materials which result in specific structures and potential non-stoichiometry and can lead to the segregation of point defects to varying degrees, depending on the specific structure (9–13). This can significantly affect the macroscopic properties, for example: ionic conductivity, electronic conductivity, thermal conductivity, thermal expansion, elasticity and strength – all of which are crucial for many applications. Therefore, the understanding of interfaces in these materials is key to optimising their performance. Despite this, relatively little is known about the structure and even less of the effects of these interfaces on material properties due to the inherent complexity of the issues.

An example of the importance of interfaces and polycrystallinity is in the fluorite structured fast oxide ion conductors (14), such as yttria stabilised zirconia (YSZ or ZrO₂-Y₂O₃) or trivalently doped ceria (CeO₂), used in solid oxide cells, oxygen membranes and oxygen sensors (6, 15, 16). It is reported that the ionic conductivity within the GBs of these materials is several orders of magnitude lower than the bulk (17–20) with the effect attributed to a wide range of causes including impurities, dopant segregation, defect cluster formations and space charge layers (7, 8, 20–25). In contradiction it has been observed that other materials, such as Bi₂O₃ (26) and nanostructured YSZ, that the ionic conductivity is enhanced (27, 28). Much of the experimental data is based on average effects observed in impedence spectroscopy, where all GBs are treated equally as an average effect (29, 30). In fact, GBs can take on specific structures, an example of this is shown in Figure 1. That is, the atomistic description of what is happening at the GB is incomplete when obtained from macroscopic observations. Another issue which may arise when only considering average effects is that it is likely that different specifically defined interfaces will behave in different ways. As it is difficult to isolate and study the effects of GBs experimentally, computational studies are invaluable to further our knowledge of these defects and their impact on material properties.

Fig. 1.

The failure to understand the basis of material properties in polycrystalline samples is a significant impediment to the development of new materials and the application of inexpensive processing methods to existing materials. An enhanced understanding of the impact of GBs and polycrystallinity on the properties of materials would allow us to explore alternative routes to optimise their properties and ultimately enhance devices. In order to model the properties of these interfaces we first require a method for accurate prediction of interfacial structures. In this paper we present a computational method for accurately predicting the structure of low angle mirror tilt GBs which can be applied to other interfaces and even heterointerfaces. This method utilises both atomistic simulation and classical molecular dynamic simulation with sophisticated, polarisable force fields derived from ab initio data. Previous theoretical studies of GB structures generally utilise static lattice simulations with empirical force fields and structures based on experimental structures (31, 32). These results often have to be validated using first principles due to the quality and limitations of the force field. In this work the structures are predicted and validated using high-quality force fields derived from ab initio data, this is discussed further in the methodology.

Two fluorite-structured materials are investigated in this study: calcium fluoride (CaF₂) and CeO₂. CaF₂ is the prototypical fluorite material which is a super-ionic conductor at high temperatures (>1100 K) (33). CeO₂ (usually doped) is a highly technologically significant material which is both an ionic and electronic conductor with a wide range of applications including catalysis, solid oxide fuel and electrolysis cells and oxygen sensing (6, 15, 16). We compare their predicted GB structures to experimental structures from the literature obtained via transmission electron microscopy (TEM).

All GBs simulated here were generated using the minimum energy techniques applied to dislocation, interface and surface energies code (METADISE) (34). The most stable GB structures were found by carrying out optimisation scans of the GB. Surfaces with specific Miller indices were first cut and then reflected to form an interface. A potential energy surface (PES) was then calculated using a forcefield by scanning one surface relative to the other. From this scan, a two-dimensional (2D) PES for the boundary was calculated which allowed the minimum energy structure to be identified. The minimum energy GBs were then optimised and the most stable boundary was selected to investigate using molecular dynamics. The 2D potential energy scan along with the GB structure (before and after optimisation) for the Σ9(221) GB in CeO₂ is shown in Figure 2.

Fig. 2.

GBs are defined by a number of parameters: the crystallographic directions of the axes of the two grains which come together to form the interface (h_i, k_i, l_i ), the rotation axis o = (h_o, k_o, l_o ), the misorientation angle θ around the axis o and the normal axis to the GB plane n. When n is parallel to o the boundary is defined as a twist GB and when n is perpendicular to o the boundary is defined as a tilt boundary. The GBs which are studied in this work are high-angle mirror tilt GBs (n ⊥ o) and the rotation axis is (001).

The geometric definition of the GBs used in this work is the coincidence site lattice model (35). A coincidence lattice site can be defined when there exists a finite fraction of coinciding lattice sites between the two lattices (grains). This model is based on the assumption that when the energy of the GB is low, the coincidence of the atomic sites between the two grains is high, i.e. there are few bonds which are broken across the boundary. The reciprocal density of coincidence lattice sites is known as Σ and is used to characterise the geometry of the GB, as given in Equation (i):

(i)

For cubic lattices, the Σ value can be given by the sum of the squares of the Miller indices of the symmetrical tilt boundary, given by Equation (ii):

(ii)

where δ = 1 if is odd and δ = 0.5 if is even, thus in cubic systems Σ is always an odd number (35, 36). For example, the Σ9(221) GB shown above is defined by the (221) Miller index of the surfaces which are scanned to give this boundary, i.e. (2²+2²+1²) = 9, which is odd so δ = 1 and thus this is written as Σ9(221). The other GBs studied here are defined in the same way.

Initial GB structures were generated as outlined above using METADISE with shell model interaction potentials for both CaF₂ (37, 38) and CeO₂ (39). These structures were then expanded to at least 30 Ångström (Å) in the x-direction, 22 Å in the y-direction (parallel to the GB) and 76 Å in the z-direction (perpendicular to the GB). Each simulation cell contained two identical GBs as illustrated in Figure 3, with each grain having a depth of at least ~35 Å.

Fig. 3.

Molecular dynamics simulations were then carried out to determine the average GB structures. The interaction potential used for the molecular dynamics simulations is known as the dipole polarisable ion model (DIPPIM) (40), implemented in the polarisable ion model aspherical ion model (PIMAIM) code (41). The DIPPIM consists of four elements: charge-charge interactions, short-range repulsion, dispersion interactions and polarisation. This is a highly accurate, polarisable, potential, in which the dipoles are solved self consistently at each molecular dynamics step. This leads to a highly accurate description of the dipoles on ions in the simulation which is of particular importance when simulating highly polarisable ions such as F^– and O^2–. The data used to fit the DIPPIM potentials used in this work were calculated using ab initio methods (2, 42, 43). The use of ab initio data allows for non-equilibrium details on the PES to be accounted for which leads to a highly accurate, transferable interatomic potential.

Often interatomic potentials for fluorite materials are derived from equilibrium experimental data or are formed using interatomic potentials from a range of different sources resulting in inconsistent, non-transferable potentials which may have difficulties taking effects of different coordination environments into account, i.e. surfaces and interfaces. Such interatomic potentials are usually better suited to static lattice simulations as opposed to molecular dynamics simulations. In previous work on the surfaces of CeO₂ (44) we have shown that the DIPPIM provides an accurate description of extended defects and the effect of such defects on ionic transport.

The simulation cells were heated to 1473 K for 500 ps in order to simulate annealing of the GB structures, they were then cooled to 573 K for 500 ps and finally simulated at 300 K for 500 ps. Temperature scaling was carried out (at all three temperatures) every 0.025 ps before data collection for analysis began. Final GB structures were generated by averaging over the frames of the trajectory at 300 K. The DIPPIM potential parameters used for CaF₂ were previously derived by Pyper and Wilson et al. (42, 43) and those for CeO₂ were obtained by Burbano et al. (2). All steps of the simulation were carried out using the isothermal-isobaric ensemble (NPT). CaF₂ simulations utilised a timestep of 5 fs and a short-range cut-off of 14 Å and in the case of CeO₂ simulations had a timestep of 4 fs and a short-range cut-off of 11 Å. The GBs which were simulated for CaF₂ were Σ3(111), Σ5(210), Σ5(310), Σ9(221), Σ11(332), Σ13(320) and Σ13(510); and for CeO₂ are Σ3(111), Σ5(210) and Σ9(221).

Here we present the average predicted structures obtained for GBs in fluorite structured materials and compare these with TEM images obtained from experimental studies. As the F^– and O^2– ions present in CaF₂ and CeO₂ are difficult to image due to their low atomic masses we only compare the cation structures obtained with the aforementioned TEM images. First, we discuss the CaF₂ structures followed by those found for CeO₂. To the authors’ knowledge there are no experimental studies of GB structures in CaF₂ so those found in this study are compared to those of other fluorite materials (CeO₂, ZrO₂ and YSZ).

4.1 Calcium Fluoride Grain Boundaries

4.2 Ceria Grain Boundaries

We have presented a computational method for the prediction of the structure of mirror tilt GBs in fluorite structured materials. This method utilises interatomic potentials which are derived from first-principles data meaning the process is entirely predictive. The excellent level of agreement with existing experimental data on the structures of fluorite GBs highlights the power of the method. The ability to accurately predict these structures is an important first step into the computational investigation of the properties of these materials, which is key to future materials and device optimisation. The method presented here can be extended to the prediction of interfaces in different materials, interfaces of different types (i.e. twist GBs) and even heterointerfaces.

Prior to exposing the as-received Pd-Ni and Pd wires to any gases, SEM and EDX analysis was performed on both wire surfaces and their cross-sections. In Figure 2, representative overview images of the wire surface (Figure 2(a)) and the cross‐section (Figure 2(b)) of the 120 μm Pd-Ni alloy are shown. Overall, EDX analysis confirms the cross-sections of the alloys to contain minute quantities of oxygen, with slightly enhanced amounts at the surface, see Table I. In addition, EDX analysis of three randomly selected points on the Pd-Ni cross‐section reveal the Ni content to be in the range from 4.4–5.0 wt%, close to the value provided by the supplier. EDX mapping did not reveal any obvious heterogeneities or impurities, neither within the grains nor along the grain boundaries. Based on this we conclude the Pd-Ni alloy to be a homogeneous solid-solution, of ~95:5 wt% Pd-Ni, within the uncertainty of the EDX analysis. Finally, it should be noted that light microscopy of chemically etched cross-sections reveal sharp grain boundaries and a grain size of 5–20 μm for 76 μm wires, of both Pd and the Pd-Ni alloy, see Figure 2(c) for the Pd-Ni alloy.

Fig. 2.

When the metallic Pd-Ni gauze (wire diameter 76 μm) is exposed to air in the TGA instrument at 900°C for 24 h, a mass gain of 1.47 wt% is recorded, see Figure 3(a). The observed mass gain is slightly larger than the theoretical value (1.36 wt%) for complete oxidation of Ni to NiO for a 95:5 wt% Pd-Ni alloy. When exposing the metallic Pd gauze to similar conditions, only a minor mass gain is observed (not shown). With reference to Ning et al. (10) and Gegner et al. (19), we assign the observed mass gain of the Pd gauze to a small oxygen solubility and formation of PdO on the Pd surface. The minor mass gain observed for pure Pd may indeed contribute in the slightly larger observed mass gain relative to theory for the Pd-Ni sample. The internal oxidation of the Pd-Ni alloy is shown visually in Figure 3(b)–(d). Here, cross-sections of the Pd-Ni wire heated for 1 h and 4 h, analysed by SEM and EDX, show small precipitated particles approaching the wire centre with time. By EDX point analysis, the precipitated particles are found to consist of oxygen and nickel in an approximately 1:1 molar ratio, indicating NiO formation (Figure 3(c)).

Fig. 3.

As shown in Figure 3(e) and Figure 3(f), chemical etching prior to SEM and EDX analysis reveals that the largest NiO precipitates are located at the grain boundaries and that the grain size has increased to 10–30 μm. Additionally, the NiO precipitates are found at equal depth within the grains as in the grain boundaries, indicating that oxygen diffusion is approximately equally fast in grains and grain boundaries (Figure 3(b)–(d)). Notably, at the same time as oxygen diffuses towards the wire centre, EDX mapping show a distinct reduction in Ni concentration in the wire core (Figure 3(b)–(d)). EDX point analysis of the wire core indicate the Ni content to be 4.2 wt% and 2.7 wt% after 1 h and 4 h, respectively. This implies that during the oxidation process the Ni mobility is enhanced, causing a heterogeneous distribution of Ni with more NiO at the outer part of the wire. These observations coincide well with reports by Gegner et al. (19) on internal oxidation of alloys with a non-noble element in a solid solution with a more noble element. Finally, it should be noted that the initial grain growth is seen during the first 24 h, but no significant grain growth is observed after another 20–30 days of heat treatment (see Figure S1 in the Supplementary Information).

When water vapour is included in the feed gas (wet air: 33 vol% H₂O, 14 vol% O₂, 53 vol% N₂), the internal oxidation of Ni to NiO occurs in a similar manner as in dry air, see Figure 4(a). However, based on gravimetry, the Pd-Ni gauze has lost 2.4 wt% of its initial mass after heat treatment for two weeks in wet air at 1050°C. ICP-MS analysis of the exposed gauze give a total Ni concentration of only 2.7 wt% relative to Pd, compared to 4.8 wt% on a comparable sample treated in dry air. In addition, SEM analysis reveal that the outer parts of the Pd-Ni wire is depleted in Ni (Figure 4(b)) and that some surface roughness has appeared (Figure 4(c)). The data also shows that only 0.1 wt% Pd is lost during two weeks’ treatment in wet air; far below the industrial Pd loss observed during ammonia oxidation (see below). There is also no observed Pd loss in dry air. This correlates well with the work of Opila (20), which shows no Pd loss in wet or dry oxygen and Ar and other literature on Pd loss in dry air (21). Notably, these findings are in contradiction to the calculations of Factsage (22, 23), which estimate a significant Pd loss as PdOH (22, 23) in wet gas and a smaller loss as PdO₂ and Pd(OH)₂ (22, 23) (see Figure S2 in the Supplementary Information). This leads to the conclusion that the observed mass loss of Pd-Ni in wet air is due to NiO being hydrolysed by the wet air and forming volatile Ni(OH)₂, which in turn causes Ni depletion. This observation is in line with Chen et al. (24).

Fig. 4.

Finally, after the two weeks’ treatment in wet air the NiO precipitates are no longer seen at the grain boundaries. Unfortunately, chemical etching prior to SEM analysis has not revealed the exact position of the grain boundaries and thus the occurrence of grain growth is uncertain. In many ways the situation is similar to the grain growth observed during the initial oxidation process of Ni to NiO. During the initial oxidation, inwards/outwards diffusion of O-Ni increased the mobility of O-Ni, just as treatment in wet air may have increased Ni mobility by Ni diffusion towards the surface. The increased mobility may again contribute to grain growth. However, we are currently not in position to elaborate in detail on how grain growth is interwoven and connected to diffusion and the oxidation process. We suggest this as a topic for future investigations.

The effect of exposing Pd and Pd-Ni wires to PtO₂ vapour in both dry and wet air is evaluated. First, we investigated if the presence of Ni in the catchment alloy would influence reactivity of PtO₂ toward Pd. Based on this, both materials were heat treated in dry air at 1050°C with Pt gauzes installed upstream. The results of exposing the two catchment materials to PtO₂ in dry air at 1 h, 4 h and 10 h are presented in Figure 5. Both materials undergo an immediate surface reaction and small Pd-Pt particles or crystals (size ~2–3 μm) are already formed on the wire surfaces after 1 h exposure, as shown in Figure 5(a) and Figure 5(d). The crystals show roughness and have several small ladders on their sides, which increase in size from 4 h to 10 h (Figure 5(b)–(c) and Figure 5(e)–(f)). Notably, for Pd-Ni (Figure 5(a)–(c)), some smaller (1–2 μm) and more faceted crystals appear with a darker contrast in the SEM images. EDX mapping and point analysis of these crystals indicate NiO formation, in line with previous observations of Ni-oxidation in air. From the SEM images reported in Figure 5, it appears as if Pd-Pt based crystals develop at a similar rate in both Pd-Ni and Pd (Figure 5). We therefore conclude that the NiO particles are not participating in the reconstruction and growth process of the Pd-Pt crystals.

With further heat treatment (≥1 day), the interior of the Pd and Pd-Ni wires become subject to the earliest stage of grain reconstruction and ladder-like growth, as if PtO₂ is penetrating sub surface from the formed Pt-Pd crystal layer reacting with more fresh metal on the wire, see Figure 6(a) and Figure 6(b). At longer exposure time (≥3 days), the surface crystals show beautiful single crystal shapes. The ladders causing further crystal growth (from ~10–30 μm) are large, slowly growing over a face of an already existing crystal (Figure 6(c)). Prolonged exposure times (20 days) result in complete grain reconstruction to large surface crystals (~20–30 μm) (Figure 6(d)–(f)). The grain reconstruction and crystal formation also causes significant wire swelling; the wire diameter increases by up to 60% after 20 days, see Figure 6(e) and Figure 6(f) and Table II. Additionally, the grain reconstruction of the wire or gauze causes a significant reduction of mechanical strength.

Fig. 5.

Fig. 6.

Selected crystals on both the Pd-Ni and the Pd wires are analysed with respect to Pt content by means of EDX analysis and the results are summarised in Table II. Pt concentration in the average top-layered crystals increases rapidly the first day (~10–12 at%), followed by a slower accumulation. This observation goes hand in hand with the fact that the reconstruction starts to occur below the top layer of crystals, after one day on stream (Figure 6(a) and Figure 6(b)), indicating that Pt catchment is preferred on the Pd rich areas below the outermost Pd-Pt crystals. After 20 days on stream, the average surface crystals reach a Pt content of ~22 at% Pt, while the outermost exposed crystals reach a Pt content up to ~40 at% (65 wt%). This is similar to an industrial sample treated for 47 days, where the average Pd-Pt crystal on the wire surface has a Pt concentration of ~30 at%.

At this point it is worth commenting that the Pd-Pt crystal growth rate depends on how a specific part of the gauze or wire is directed toward the high velocity gas stream. The PtO₂ molecules have better access to such areas, which is reflected in a higher Pt content; more reconstruction and larger crystal facets (Table II). This is more prominent in laboratory-scale experiments, where the gas is not passing equally uniformly through the gauze as in the industrial or pilot plant. Correspondingly, on laboratory-scale samples, reconstruction is slower and Pt catchment lesser at the wire crossings and at the side(s) of the wire not directly exposed to the gas stream. These observations are applicable to both the Pd-Ni and the Pd catchment gauzes.

We can now combine the two previous experiments and perform a heat treatment with both wet air and PtO₂. If a Pd-Ni gauze is heated for two weeks at 1050°C in wet air with PtO₂, a mass increase of 6.5 wt% is observed. From ICP-MS/OES, the resulting Pd-Ni wire contains only 2.8 wt% Ni relative to Pd, at the same time as the gauze has reached a Pt content of 9.3 wt%. This indicates simultaneous Ni loss and Pt catchment. Furthermore, if the Pd-Ni gauze is heated for 30 days in total, the exterior of the wire becomes completely reconstructed, at the same time as the wire is almost fully depleted of Ni, see Figure 7(a) and Figure 7(b). Only the wire core shows the presence of NiO particles. We therefore state that Ni-loss and grain reconstruction are individual effects, caused by the presence of water vapour and PtO₂, respectively.

Fig. 7.

Comparing with investigations by Pura et al. (18), we have also observed diffusion and segregation of NiO in the grain boundaries. However, this seems not to cause grain reconstruction or porosity in dry or wet air. Our findings coincide well with the statement by Pura et al. (11), i.e. grain reconstruction is not caused by the presence of Ni or loss of Ni from the Pd-Ni alloy, but rather by catchment of Pt.

Finally, two samples have been exposed in the ammonia oxidation pilot plant at the Yara Technology Center industrial facility. Here, NH₃ is included in the gas stream (10 vol% in air) and combusted over an ammonia oxidation catalyst just upstream of the catchment unit. Two scenarios were explored: (i) six pure Pt ammonia combustion gauzes and (ii) a bed of LaCoO₃-based ammonia oxidation catalyst pellets, positioned just upstream of a 76 μm pure Pd catchment gauze. As Ni does not significantly affect Pt catchment it was chosen to use pure Pd and not Pd-Ni gauzes in the pilot plant. The experiments were run for nineteen days at 900°C at total pressure of 5 bar, during which each combustion catalyst produced ca. 28 tonnes of nitric acid.

In the first case, when the ammonia oxidation catalyst was a pure Pt gauze, similar features occurred compared to samples heat-treated in the laboratory scale furnace in wet air with Pt upstream. This includes Pt catchment, grain reconstruction and swelling, see Figure 7(c) and Figure 7(d). The Pd-Pt crystals on the wire surface are in the range of 10–30 μm in size, with an average Pt concentration of ~30 at% (44 wt%), while the gauze in total had a Pt concentration of ~14 at% (23 wt%). The Pt concentration of the surface crystals obtained by EDX is similar to those found in samples treated in the laboratory scale furnace, confirming the validity of the laboratory scale experiments on Pt catchment. In contrast to our laboratory scale experiments, we now observe a significant Pd loss (0.036 g tonne^–1 HNO₃), similar to reports by Holtzmann on Pd loss at real ammonia oxidation plant conditions (5).

In the second case, with the LaCoO₃-based combustion catalyst, we can exclude effects by PtO₂ as it is not present in the gas stream. Still, the Pd catchment gauze is subject to swelling and pore formation, see Figure 7(e) and Figure 7(f). However, the wire surface does not look similar to the Pd-Pt crystals observed previously (Figure 7) and there are no foreign elements present, hence there must be a different mechanism causing this pore formation. This means that the observed swelling of the Pd catchment gauze, which causes the increase in pressure drop across the gauze pack over time, happens regardless of Pt catchment. It is an intrinsic effect of the Pd gauze when placed in the ammonia oxidation reactor. The mechanism causing this porous structure is still unknown and should be a relevant topic for future investigations.

More importantly, mass change studies and ICP-MS analysis reveal a significant Pd loss (0.033 g tonne^–1 HNO₃ produced), very similar to the loss observed with a Pt combustion catalyst (see above). Since the Pd loss in the pilot plant occurs both with a Pt and LaCoO₃ combustion catalyst, it is unlikely to be connected to the Pt catchment or grain reconstruction caused by PtO₂. In addition, there is no known thermal loss mechanism for Pd in wet or dry air that can explain such a large thermal Pd loss in the process gas (20). This leads to the conclusion that Pd loss is most probably caused by interaction with the demanding gas stream conditions of ammonia oxidation and thus by the gas constituents that were not present in the laboratory-scale experiments. Identifying the species or combination of species, present in the combusted process gas that lead to Pd loss is a very relevant topic for future investigations.