Surface structures of stoichiometric and oxygen-deficient complex subnanoporous oxide 12CaO·7Al2O3 (C12A7) are generated by simulating lattice rupture under the influence of an external strain. Extra-framework anions are found to serve as buffers, maintaining stability of the lattice cages in both elastic and inelastic stretching regimes. Modification of the local atomic structure in the near-surface region reduces the band gap in stoichiometric insulating C12A7. On the contrary, the band gap appears in the oxygen-deficient form of C12A7, which is metallic in the bulk. This is due to formation of the surface electron traps, which differ both in the type of the local atomic structure and stability of the electronic states. The implications of this electronic structure for the surface chemical and electron emission properties are discussed.
Electrides are crystalline ionic materials, in which electrons serve as anions (Dye 1990, 2003). Over the past decade, several types of organic and inorganic electrides have been synthesized or predicted theoretically, including a room-temperature stable organic electride (Redko et al. 2005), an inorganic electride with a tuneable concentration of the electron anions (Matsuishi et al. 2003; Kim et al. 2007) and high-pressure forms of halogen metals (Pickard & Needs 2009; Gatti et al. 2010). A broader class of related electron-rich materials, including alkali atoms solvated in zeolites (Edwards et al. 1996; Windiks & Sauer 2000) and oxide surfaces (Ricci et al. 2003; Sterrer et al. 2005; Chiesa et al. 2006, 2009; McKenna & Shluger 2008), is actively studied. Owing to the expected low workfunction of these materials, their future applications are thought to include cold electron emitters, catalysts, chemical synthesis agents and components of electronic devices.
Indeed, an electride based on the 12CaO·7Al2O3 (C12A7) mayenite (Matsuishi et al. 2003; Kim et al. 2007) is chemically stable and has a value of the workfunction (2.4 eV) comparable to that of potassium metal (Toda et al. 2007), which ensures its application as an electron emitter in opto-electronic devices (Toda et al. 2004; Yanagi et al. 2009). Tunability of the electron concentration in this material can be used in order to make it simultaneously optically transparent and electrically conductive (Hayashi et al. 2002). Recently, an ability of the C12A7-based electride to promote pinacol coupling has been demonstrated (Buchammagari et al. 2007), and several examples of the catalytic properties of C12A7 surfaces have been reported (Gao et al. 2006; Dong et al. 2007; Ruszak et al. 2008). Synthesis of amorphous forms of the C12A7-based electride (Kim et al. 2005) is promising for advancing large-scale industrial applications of this material.
Understanding mechanisms of the surface-related phenomena in this material requires knowledge of the atomistic structure and electronic properties of C12A7 surfaces in both stoichiometric and electride forms. While electronic properties of C12A7 electride surfaces have been addressed experimentally to some extent (Toda et al. 2007, Yanagi et al. 2009), little information about the C12A7 surface structure is available, apart from the general morphology characterization of sol–gel particles (Zahedi et al. 2008; Gong et al. 2010).
This lack of experimental data is due to exceptional complexity of this system arising not only from the C12A7 lattice structure, which is described in §3, but also owing to a high concentration of charged species that of necessity are stabilized in its lattice.
The purpose of this work is to generate structural models of C12A7 surfaces and analyse their electronic properties using quantum-mechanical simulations based on density-functional theory (DFT). In the following sections, we provide details of the computational methodology (§2), describe the geometrical and electronic structures of the bulk C12A7 (§3) and present new results on the properties of C12A7 surfaces in both stoichiometric and oxygen-deficient, i.e. reduced, forms (§4).
2. Details of the calculations
The cubic unit cell of the stoichiometric bulk C12A7 contains 118 atoms and has a volume of over 1700 Å3. In the case of the surface simulations using a periodic slab model, the minimal cell volume is approximately 3500 Å3. In addition, the complex electronic structure of this material necessitates the use of extended basis sets in order to represent accurately the charge-density distribution, both in the vicinity of the atoms and inside the lattice pores. Quantum-mechanical calculations of these systems would be impractical without access to high-performance computing facilities.
In the following, we present the results of two types of calculations: (i) simulation of a mechanical rupture of a C12A7 lattice with formation of two surfaces and (ii) analysis of the electronic structure of these surfaces in stoichiometric and reduced forms. Both types of calculations are computationally demanding, not only because of the size of the system, but also because of the complex pattern of the rupture-induced lattice deformation and the need for statistical analysis of the electronic-centre distribution in the vicinity of surfaces.
All calculations have been carried out using DFT and the density-functional method of Perdew, Burke and Ernzerhof (PBE) (Perdew et al. 1996) and the projected augmented waves (PAWs) method (Blöchl 1994), as implemented in the Vienna Ab-initio Simulation Package (Kresse & Furthmüller 1996). Eight Monkhorst–Pack k-points have been used for Brillouin-zone integration in calculations of the geometrical and electronic structures of C12A7 bulk and surfaces. The rupture process was modelled using the Γ-point only. We found that, in the case of the bulk stoichiometric C12A7, these two sets of k-points result in a total energy difference of 0.7 meV per atom. A plane-wave basis set cut-off of 500 eV has been used in both cases. Calculations of reduced C12A7 were carried out using a spin-polarized DFT mode. Ten valence electrons have been treated explicitly for Ca atoms, and three and six valence electrons for Al and O atoms, respectively.
3. 12CaO·7Al2O3 bulk
In this section, we describe briefly the electronic structure of stoichiometric and electride forms of the bulk C12A7. More detailed descriptions of these materials can be found in, for example, the works of Hayashi et al. (2002), Matsuishi et al. (2003), Sushko et al. (2003, 2005, 2007), Li et al. (2004), Medvedeva & Freeman (2004) and Kim et al. (2007).
A stoichiometric cubic unit cell of the bulk C12A7 can be represented using the formula [Ca24Al28O64]4+⋅(O2−)2 (C12A7:O2− for brevity), where the positively charged framework [Ca24Al28O64]4+ consists of 12 subnanometer cages per unit cell; the extra-framework oxide ions occupy two of these cages and compensate the charge of the framework. Each cage has an S4 symmetry axis passing through two Ca atoms at the cage poles. The extra-framework anions interact with the atoms of the cage wall and distort it. These distortions are convenient to characterize using the value of the Ca–Ca distance along the S4-axis. Earlier computational studies have predicted that this Ca–Ca distance is 5.54 Å in an empty cage and 4.42 Å in a cage occupied with an extra-framework O2− ion (Sushko et al. 2006). Similar values for the Ca–Ca distance have been obtained experimentally (Boysen et al. 2007; Nomura et al. 2007; Palacios et al. 2007).
The calculated density of states (DOS) for C12A7:O2− is shown in figure 1a. The top of the valence band (VB), formed by the 2p states of the framework oxide ions, is approximately at 1.3 eV. The two peaks at 3 eV (approx. 1.8 eV above the top of the VB) are due to the 2p states of extra-framework oxide ions. The lower energy peak corresponds to the 2p states oriented along the cage S4-axis, and the higher energy peak is due to the 2p states oriented perpendicular to this axis. The relatively narrow feature between 5.2 and 6.9 eV is an unoccupied band formed by the states associated with the empty cages, and is denoted as the cage conduction band (CCB) (Sushko et al. 2003, 2007). Finally, the bottom of the framework conduction band (FCB) is shown at approximately 7.3 eV. This part of the DOS is dominated by the Ca 3d states.
Thermal treatment of C12A7:O2− with Ca and Ti metal vapour leads to extraction of the extra-framework oxygen species from the C12A7 bulk and formation of an electride state (Matsuishi et al. 2003; Kim et al. 2007). The electride chemical composition can be represented as [Ca24Al28O64]4+⋅(e−)4 (C12A7:e− for brevity). The calculated DOS for this system is shown in figure 1b. The positions of the VB and FCB edges and their respective characters remain the same, as in the case of the stoichiometric compound. However, in contrast to C12A7:O2−, the bottom part of the CCB in C12A7:e− is occupied by extra-framework electrons, making it metallic.
The spatial distribution of the charge density, associated with the 2p states of the extra-framework oxide ions, is shown in figure 1c: the charge density of the extra-framework species is fully localized within the two cages occupied by them and has nearly spherical iso-surfaces. Similarly to this, the extra-framework electrons in C12A7:e− are localized in cages. However, in this case, their charge density has ellipsoid-like iso-surfaces elongated along the S4 axes of respective cages, as illustrated in figure 1d.
4. 12CaO·7Al2O3 surfaces
One of the implications of the C12A7 complex structure is the absence of obvious cleavage planes. To illustrate this point, it is instructive to compare the structure of C12A7 with that of rock-salt materials (figure 2a), such as alkali halides and alkaline earth oxides. For example, the lattice constant of MgO is approximately 4.2 Å and the distances between (001), (011) and (012) atomic planes are approximately 2.1, 1.5 and 0.9 Å, respectively. In contrast, the distances between atomic planes in C12A7 are much smaller and do not exceed approximately 0.5 Å for any combination of the Miller indices. This is illustrated in figure 2b using characteristic ‘bar codes’ for several orientations of the atomic planes: separations between the vertical lines correspond to the distances between the parallel atomic planes. Interestingly, unlike in the rock-salt structure, some inter-plane distances found for (112) orientation are comparable to or exceed those found for (011) and (001) orientations.
To the best of our knowledge, no studies of crystalline C12A7 surfaces have been reported so far. Although the general morphology of C12A7 sol–gel particles has been investigated using scanning electron microscopy (Zahedi et al. 2008; Gong et al. 2010), these data are not sufficient to achieve understanding of atomic-scale mechanisms of surface-related processes.
(a) Computational procedure
Experimentally, surfaces of stoichiometric C12A7 are prepared by slicing single crystal ingots into wafers, which are then polished mechanically (Y. Toda 2009, personal communication). In order to prepare electride surfaces, these wafers are annealed in the presence of metal Ti and then either cleaned with Ar+ or cleaved in vacuum. These are complex processes that are difficult to model theoretically. Instead, we attempted to identify the most energetically stable arrangements of the surface atoms by simulating rupture of C12A7 according to the following protocol. The C12A7 cubic cell has been subjected to stretching along the c-axis until the material ruptured and the two newly formed surfaces were sufficiently well separated. For this, the lattice constants in the x–y plane have been fixed at 12.0 Å, which is close to the experimental value of 11.99 Å (Bartl & Scheller 1970) and that obtained for the fully relaxed cell (12.08 Å), while the value of the lattice constant along z (az) was increased with increments of Δaz. The total energy of the system was minimized with respect to the internal coordinates for each value of az.
In calculations of this type, it is desirable to keep the computational cost to a minimum. Therefore, we investigated the dependence of the rupture process and the final surface structure on the numerical parameters of the calculations. To this end, we calculated the potential-energy profiles for relatively small (0.1 Å) and relatively large (0.5 Å) increments of az, and analysed the effect of the number of energy-minimization steps.
(b) Stoichiometric 12CaO·7Al2O3 surfaces
Figure 3 shows the potential-energy of stoichiometric C12A7 as a function of the lattice parameter az. The value of az was incremented by 0.5 Å, and the internal coordinates were fully relaxed for each az. This procedure will be referred to as Pfull. The corresponding geometrical structures of the cell are shown in figure 4. For clarity, each panel in figure 4 shows two simulation cells along the x-axis and the panels are oriented so that the x–z plane of the cell is parallel to the image plane.
The whole rupture process can be separated into three regimes, as indicated in figure 3. In regime A, the lattice is extended along the c-axis by as much as 15 per cent without signs of bond breaking. This resilience of the lattice is due to its cages, which deform elastically as az increases. Indeed, earlier calculations and the experimental results demonstrate that extra-framework species (Xq−) decrease the Ca–Ca distance along the S4-axis of a cage by approximately 0.5 Å for q=1 and by approximately 1 Å for q=2 (Sushko et al. 2005, 2006; Boysen et al. 2007; Nomura et al. 2007; Palacios et al. 2007), suggesting that the cages could serve as buffers accommodating the effects of the lattice strain.
In regime B, the bonds break and restructure. We identified two sequences of bond stretching, breaking and restructuring for az in the ranges of 14.5–16.0 Å and 16.5–18.0 Å. As is shown in figure 4, the cages are strongly deformed at az=15 Å and precursors of two surfaces have appeared. At this value of az, there are still many bonds connecting the two emerging surfaces. As az increases, these bonds restructure and at az=16 Å, all but two bonds are broken. One of these bonds restructures further and is present, even at az=18 Å.
The transition between regimes A and B, i.e. the onset of the inelastic deformation regime, can be assigned to the value of az, at which the curvature of the potential energy, shown in figure 3, changes its sign. In our case, this occurs at az=14.5 Å.
Finally, in regime C, the rupture process is completed and the two surfaces become independent, forming a C12A7 slab oriented in the x–y plane. The vacuum gap between the surfaces is approximately 12 Å for az=24 Å. One of these surfaces has well-pronounced corrugations owing to both the lattice cages and the debris, which accumulated at the surface. In contrast, the other surface is nearly flat.
The total energy of the ruptured C12A7 is approximately 20 eV per cell higher than the energy of the bulk configuration. Thus, the average energy per surface is approximately 10 eV, which translates into 1.1 J m−2. This value is comparable to the surface free energy of 0.86 J m−2 calculated for a rutile TiO2 (110) surface using the local density approximation (Fox et al. 2006) and that of 0.87 J m−2 found for an MgO (001) surface using the PBE density functional (Alfe & Gillan 2006). We emphasize that the two surfaces clearly have different structures and, therefore, are likely to have different surface energies. Thus, the value of 1.1 J m−2 is only an upper estimate of the surface energy.
In order to investigate the dependence of the rupture pathway on the details of the modelling procedure, we carried out three similar simulations, in which the value of the az increment was fixed at 0.1 Å and the number of the conjugate gradient energy-minimization steps with respect to the internal coordinates was set to 10, 20 and 40, respectively, for each value of az. For simplicity, we will denote these procedures and the corresponding pathways as PN, where N is the number of energy-minimization steps. By comparing these PN pathways with each other, we attempt to find an optimal computational procedure that requires a minimal amount of resources and, at the same time, is sufficiently accurate.
The potential-energy profiles obtained in these calculations are shown in figure 5. We find that all computational procedures give the same profile of the potential-energy surface in the elastic deformation region (12.0 Å <az<14.5 Å). In the inelastic deformation region (az>15 Å), the potential energy for P10 is much higher than that for P20 and P40.
To rationalize this result, we note that each incremental increase of the value of az induces lattice strain and the cell atoms adjust their positions so as to accommodate it. If the number of energy-minimization steps is sufficiently large, the atoms adopt such positions that the strain is relieved at the cost of breaking bonds in a ‘weak’ spot. This is what we observe for P20 and P40. However, if N is too small for the atoms to adopt the lowest energy configuration, the strain remains distributed over the whole cell, and the calculated energy profile resembles that found for the elastic case, as is the case with P10.
Comparison of the rupture pathways calculated for P20 and P40 suggests that, although these pathways are different in the intermediate regime B, the resulting surface structures are identical. Indeed, the two curves shown in figure 5 with diamonds and triangles are within 0.05 eV of each other for all values of az between 20.5 and 24.0 Å.
Finally, we note that the potential-energy profiles calculated for P20 and P40 pathways are qualitatively similar to the profile found for Pfull pathway (Δaz=0.5 Å), which is also shown in figure 5 for comparison. The differences between P20, P40 and Pfull in the range of az between 15 and 20 Å are due to different sequences of the bond restructuring and rupture. The energy required to break C12A7 along the Pfull pathway is only 0.1 J m−2 higher than that found for P20 and P40, suggesting that the three pathways result in essentially the same surface structures.
(c) Characterization of the surface structure
Figure 6 shows the atomic structures of the two surfaces of ruptured C12A7:O2−, represented as convolutions of the atomic van der Waals surfaces. The surface shown in figure 6a is significantly more rugged than that shown in figure 6b. This difference in their overall roughness is also apparent from the side view for az=19 Å shown in figure 4. For convenience, they will be characterized as the ‘rough’ and the ‘flat’ surfaces, respectively. Figure 6c,d shows the atomistic structure of the rough and the flat surfaces. Visual analysis of these structures suggests that the outermost regions of both surfaces tend to be Ca rich, while the pits in the near-surface region tend to be Ca poor.
In spite of the difference in their overall structures, the two surfaces contain similar features: these are well defined, almost square pits, which are fragments of the cage wall of the broken cages. Part of the cage-wall material, displaced during the rupture process (see figure 4 for 15 Å), is deposited in the form of the hills on the rough surface (figure 6a). In contrast, no such hills or debris are visible on the flat surface.
To characterize these surfaces further, we analysed the local atomic structures of 15 outermost oxygen ions for each surface. In the case of the rough surface, these ions occupy a region of space 4.4 Å thick and have an average coordination number of 3.07. Only four of these ions are in the same local environment as in the bulk, i.e. have four neighbouring cations. Eight of them have three neighbouring cations and three have only two cation neighbours. For comparison, in the case of the flat surface, 15 outermost oxygen ions are located within a 2.4 Å thick layer and their average coordination number is 3.33: the numbers of four-, three- and two-coordinated oxygens are six, eight and one, respectively. Thus, the flat surface is noticeably denser and more ‘bulk-like’ than the rough one. We note, that the central part of the slab maintains the bulk structure: nine out of ten oxygen ions there have four cation neighbours.
It is instructive to analyse the effect of the rupture on the local atomic structure of the extra-framework O2− ions. There are two such ions in our simulation box: one of them is near the flat surface and another is near the rough surface. After rupture, the O2− ion in a cage close to the flat surface remains at its extra-framework site; its local atomic structure, as well as the structure of the cage it occupies, is similar to those in the C12A7 bulk.
In contrast, the cage containing the other extra-framework O2− ion has been deformed so that this ion has displaced towards the cage wall and merged with it, effectively increasing the cage-wall area. Such a restructuring of the cage wall points to a mechanism, by which extra-framework species in C12A7 can maintain the overall lattice structure upon inelastic stretching: they build into the framework, thus suppressing formation and propagation of fractures.
(d) Surfaces of reduced 12CaO·7Al2O3
The procedures used to simulate rupture of the stoichiometric C12A7 have also been applied in order to generate surface models for C12A7 electride. According to the plane-wave PBE calculations, the extra-framework electrons in C12A7:e− are distributed equally between the cages, making them equivalent. This charge-density distribution dramatically affects the lattice response to stretching. Since the lattice no longer has ‘weak’ and ‘hard’ spots, the cages do not break as such. Instead, the lattice atoms rearrange so as to maintain homogeneous distribution of matter along the c-axis for all considered values of az. For az exceeding 16 Å, this results in formation of quasi-one-dimensional structures or ‘strings’ consisting of Ca, Al and O atoms. These string structures (their feasibility is discussed in §5) consume the material of the simulation cell, which makes it impractical to form electride surface models using this procedure.
Therefore, surface models for C12A7:e− have been obtained using a different approach, which mimics formation of electrides by extraction of extra-framework oxygen in highly reducing conditions. To this end, we first calculated the neutral oxygen vacancy formation energies (EV) for all three types of the bulk lattice oxygen sites. These are the bridging and non-bridging sites in the framework coordinated by Ca2Al2 and Ca3Al1 neighbours, respectively, and an extra-framework site located approximately at the cage centre.
Using half of the total energy of a free O2 molecule in its triplet state as the common reference, we found that the vacancy formation energy for the extra-framework oxygen is 4.4 eV, which is considerably less than the vacancy formation energy calculated for the non-bridging (5.8 eV) and bridging (5.9 eV) sites. These data clearly suggest that reducing the C12A7 bulk will result in extraction of the extra-framework oxide ions.
In order to determine which sites are most likely to host neutral oxygen vacancies near the surface, we calculated the vacancy formation energies for the 15 outermost oxygen sites near each surface and compared them with the values of EV calculated for 10 oxygen sites in the inner part of the slab.
The lowest EV site is that of the outermost oxygen at the rough surface. This site is coordinated by one Al and one Ca neighbour, and has an EV of 4.4 eV. Creating a vacancy at this site leaves both of its neighbours three-coordinated. The second-lowest EV site is that of the extra-framework oxygen near the flat surface, for which EV is 5.0 eV. For comparison, EV calculated for the other extra-framework oxygen, which has merged with the cage wall during rupture, is 5.9 eV, which is comparable to the vacancy formation energies calculated for the framework oxygens.
The values of EV calculated for all other oxygen sites in the near-surface regions are between 5.2 and 6.2 eV. The upper end of this range (5.8 eV and higher) is due to mainly four-coordinated oxygen sites. These energies match well the EV values found for the inner region of the slab and are consistent with the vacancy formation energies calculated for the framework oxygen sites in the bulk C12A7. The lower end of this range is due to under-coordinated oxygen ions. For example, oxygen sites, coordinated by two Al neighbours only, have values of EV of 5.2–5.3 eV.
Finally, we note that for all considered oxygen vacancies, the total energy of the system has been minimized with respect to the coordinates of all atoms. However, this did not introduce any significant alterations to the overall structures of the rough and flat surfaces.
(e) Electronic structure
The total DOSs calculated for the stoichiometric and several configurations of reduced C12A7 surfaces are shown in figure 7. To obtain the same level of oxygen non-stoichiometry in reduced C12A7 as that in the bulk C12A7 electride, two oxygen atoms have been removed from the simulation cell.
In order to investigate the effect of the oxygen vacancy stability on the electronic structure of the surface, we considered several oxygen sites: (i) coordinated by one Ca and one Al neighbour (EV=4.4 eV, figure 7b), (ii) coordinated by two Al neighbours (EV=5.3 eV, figure 7c), and (iii) an initial extra-framework ion, which has merged with the cage wall (EV=5.9 eV, figure 7d). All of these sites are at or near to the rough surface. In all of these cases, the second oxygen atom was taken from the extra-framework site in the bulk-like cage near the flat surface (EV=5.0 eV).
The effect of the surface on the electronic structure of stoichiometric C12A7 can be understood from comparing the surface and bulk DOSs shown in figures 7a and 1b, respectively. The tails of the VB and both CCB and FCB elongate owing to the rearrangement of the atoms in the near-surface regions. Consequently, the one-electron levels associated with the extra-framework O2− ions are no longer split from the top of the VB, and the CCB states are no longer clearly defined. The band gap between the top of the VB and the bottom of the CCB decreases from 3.5 eV in the bulk to 2.5 eV at the surface. Interestingly, the difference between the energies of the highest occupied and lowest unoccupied states remained almost unchanged.
The DOSs calculated for the reduced C12A7 surfaces are shown in figure 7b–d. Even though the concentration of the oxygen vacancies is the same as in the bulk C12A7 electride (figure 1d), the systems considered here are insulating and the smallest band gap is 1 eV. A common feature of these plots is the level at 0.1–0.2 eV owing to a state associated with the bulk-like cage near the flat surface and occupied by two electrons. The surface of the constant charge density associated with this state is shown in the bottom part of each plot in figure 8.
Neutral vacancies at the sites of the two-coordinated oxygens, indicated as Ca2+/2e−/Al3+ and Al3+/2e−/Al3+ in figure 7b,c, respectively, also give rise to localized levels occupied by two electrons each. Stronger binding of the electrons in the Al3+/2e−/Al3+ case is consistent with the larger electrostatic potential produced by the nearest vacancy neighbours. The charge-density distributions associated with these vacancies are shown in figure 8a,b, respectively. Finally, the vacancy formed at the site of an initial extra-framework O2− ion, which has merged with the cage wall in a distorted cage, gives rise to a level which is almost isoenergetic to that formed in the bulk-like cage (figure 7d). In this case, the two electrons are localized in the cage rather than at the vacancy site as such (figure 8c), indicating that the cage structure and its ability to trap electrons have been preserved in spite of its distortion.
Thus, the results of these calculations suggest that even strongly deformed near-surface regions retain cages as elementary lattice building blocks. Unlike in the bulk, these cages are able to trap up to two electrons, which is attributed to enhanced lattice relaxation of the surface atoms. In addition, electrons can also be trapped at the near-surface sites, which belong to the remains of the framework. In all considered cases, reduced C12A7 slabs were insulating.
(a) Effect of the extra-framework species
The results described in §4 suggest that the structure and morphology of cleaved and mechanically treated C12A7 surfaces depend on the type of the extra-framework species. We propose that the effect of these species is twofold.
First, the interaction between the extra-framework species and the atoms of the cage wall stabilizes the occupied cages. In our case, the two cages containing extra-framework O2− ions are more robust towards the lattice stretching than the empty ones because the two Ca ions at the cage poles are bonded to the extra-framework species. Consequently, the occupied cages largely retained their structure; only empty cages have been destroyed in the course of the rupture process. Since the number of cages occupied by extra-framework ions is always smaller than the number of empty cages, the former can be considered as hard inclusions in the otherwise soft lattice. This stabilization effect and, therefore, the structure of the resulting surfaces are likely to depend on the charge state and chemical identity of the extra-framework ions.
Second, extra-framework ions can serve as buffers accommodating external lattice strain. On the atomic scale, this effect has two mechanisms. In the elastic regime, the stretching load applied to an empty cage along the S4 symmetry axis is distributed over the cage wall only. In contrast, in an occupied cage, this load is shared between the cage wall and the Ca–Xq−–Ca bonds, where Xq− is an extra-framework species. Moreover, since the Ca–Ca distances in the occupied cages are smaller than in empty ones, only the Ca–Xq−–Ca bonds will be strained at relatively small loads. In the inelastic regime, an extra-framework species can displace from its site near the centre of the cage towards the cage wall and build itself into the framework, thus suppressing its fracture.
(b) Surface structures
Atomic-scale structures of insulating surfaces can be resolved using surface scanning techniques, such as atomic force microscopy (AFM), as described by Lauritsen & Reichling (2010). Unfortunately, there are no sufficiently well-resolved AFM data that could be used for comparison here. However, features analogous to what we have described above have been observed by Barth & Henry (2003) on cleaved MgO (001) surfaces using non-contact AFM. For example, AFM images shown in fig. 1 in Barth & Henry (2003) demonstrate that irregular adstructures, reminiscent of debris on the rough surface shown in figure 6, are formed alongside well-defined rectangular pits of monoatomic depth.
The origin of these adstructures is unclear as yet. One of the possible mechanisms of their formation may involve quasi-one-dimensional strings that appear when the lattice is stretched and the two surfaces get separated (figure 4, 18 Å). Formation of similar strings has been observed by Shluger et al. (1997) in studies of the contact and subsequent separation of LiF and MgO surfaces using a molecular-dynamics method and classical inter-atomic potentials. Appearance of the strings in our DFT calculations lends further support for them as the origin of the surface adstructures.
Rectangular pits and characteristic low-coordinated cation sites, found at both surfaces, are expected to be chemically active and may explain the high catalytic activity and remarkable selectivity of C12A7 observed by Ruszak et al. (2008). Properties of these special sites need to be investigated separately.
(c) Electronic structure of reduced 12CaO·7Al2O3
The electronic structure calculations of the reduced C12A7 surfaces reveal that atom rearrangements in the near-surface region form a distribution of low-coordinated oxygen sites. Oxygen vacancies created at these sites give rise to localized electronic states. This suggests that local amorphization of the crystalline C12A7 electride induced, for example, thermally or mechanically, may convert the lattice from a metallic to a semiconducting or an insulating state. Using this property may provide a pathway for writing three-dimensional semiconducting domains in a metallic host.
We note that the two gap states associated with the cages (figure 7d) are almost isoenergetic, even though the cages have different structures and different local environments, i.e. located near the rough and flat surfaces, respectively. The charge-density distribution in these states is similar to that found in F-centres—neutral vacancies of anions in, for example, alkali halides and alkaline earth oxides. Current proposals for new photocathode materials include alkali halide films supported on metal substrates. It is thought that the F-centres are the main source of emitted electrons (Maldonado et al. 2009). Our results suggest that the near-surface region in reduced C12A7 may host such vacancy-like gap states at concentrations of 1021 cm−3 and, being interfaced with a metal substrate, may perform as a bright photocathode.
We have constructed theoretical models of surfaces of the stoichiometric and reduced forms of C12A7 by simulating rupture of the C12A7 bulk. Our results reveal that extra-framework ions stabilize the lattice cages and suppress their fracture under the influence of external strain. Thus, cages occupied by extra-framework ions tend to remain intact in the processes of rupture and cleavage. In contrast, empty cages destabilize and get destroyed.
Analysis of the obtained surface structures suggests that the lattice undergoes restructuring within an approximately 2–4 Å surface layer, as characterized by the reduced coordination of the near-surface oxygen ions. The surface structures obtained in this work show characteristic features: rectangular pits owing to the broken cages, hills owing to debris formed during the rupture process and flat areas formed by clusters of several atoms.
The DOSs, calculated for several configurations of reduced C12A7, suggest that even at the extra-framework electron concentration of approximately 2×1021 cm−3, the near-surface region does not become metallic. Instead, localized gap states are formed; positions of their energy levels with respect to the band edges and spatial distributions of the electron density are governed by the surface structural defects and the lattice cages in the near-surface region. In our case, these states are within 2 eV from the top of the VB and approximately 1 eV below the lowest unoccupied state in the near-surface region.
These results suggest that judiciously modifying the C12A7 lattice structure, one can convert its metallic electride form into a semiconductor or an insulator by creating a high-density distribution of localized electronic states close to the bottom of the bulk conduction band. It is proposed that, in the case of the surfaces and films, formation of a relatively narrow distribution of electronic states associated with complete cages in the near-surface region will take place. This property could be advantageous for optimizing brightness and emittance properties of photocathodes in order to meet the needs of the fourth generation of light sources. Other applications may include catalytic processes, in which C12A7 surface states can participate as transient charge traps and/or donors.
The authors thank K. Hayashi, S.-W. Kim, T. Kamiya, S. Matsuishi and W. P. Hess for stimulating discussions. This research was supported by the Elements Science and Technology Project, MEXT, and JSPS FIRST Programme. P.V.S. is supported by the Royal Society. Calculations have been performed at the HECTOR facility (access provided via the Materials Chemistry Consortium) and at EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory.
One contribution to a Special feature ‘High-performance computing in the chemistry and physics of materials’.
- Received October 29, 2010.
- Accepted December 17, 2010.
- This journal is © 2011 The Royal Society