Data-driven design of metal-organic frameworks for wet flue gas CO2 capture.

Limiting the increase of CO2 in the atmosphere is one of the largest challenges of our generation1. Because carbon capture and storage is one of the few viable technologies that can mitigate current CO2 emissions2, much effort is focused on developing solid adsorbents that can efficiently capture CO2 from flue gases emitted from anthropogenic sources3. One class of materials that has attracted considerable interest in this context is metal-organic frameworks (MOFs), in which the careful combination of organic ligands with metal-ion nodes can, in principle, give rise to innumerable structurally and chemically distinct nanoporous MOFs. However, many MOFs that are optimized for the separation of CO2 from nitrogen4-7 do not perform well when using realistic flue gas that contains water, because water competes with CO2 for the same adsorption sites and thereby causes the materials to lose their selectivity. Although flue gases can be dried, this renders the capture process prohibitively expensive8,9. Here we show that data mining of a computational screening library of over 300,000 MOFs can identify different classes of strong CO2-binding sites-which we term 'adsorbaphores'-that endow MOFs with CO2/N2 selectivity that persists in wet flue gases. We subsequently synthesized two water-stable MOFs containing the most hydrophobic adsorbaphore, and found that their carbon-capture performance is not affected by water and outperforms that of some commercial materials. Testing the performance of these MOFs in an industrial setting and consideration of the full capture process-including the targeted CO2 sink, such as geological storage or serving as a carbon source for the chemical industry-will be necessary to identify the optimal separation material.

Molecular dynamics simulations of interfacial structure, dynamics, and interfacial tension of tetrabutylammonium bromide aqueous solution in the presence of methane and carbon dioxide.

The interfacial behavior of tetrabutylammonium bromide (TBAB) aqueous solutions in the absence of gas and the presence of methane and carbon dioxide gases is studied by molecular dynamics simulations. The aqueous TBAB phase, at concentrations similar to the solid semiclathrate hydrate (1:38 mol ratio), has a smaller interfacial tension and an increase in the gas molecules adsorbed at the interface compared to that in pure water. Both these factors may contribute to facilitating the uptake of the gases into the solid phase during the process of semiclathrate hydrate formation. At similar gas pressures, CO2 is adsorbed preferentially compared to CH4, giving it a higher surface density, due to the stronger intermolecular interactions of CO2 molecules of the solution at the interface. The increase in relative adsorption of CH4 at the solution surface compared to that in pure water surface is due to the hydrophobic interactions between the n-alkyl chains of the TBA+ cation and methane gas.

An Ultra-Microporous Metal-Organic Framework with Exceptional Xe Capacity.

Molecular confinement plays a significant effect on trapped gas and solvent molecules. A fundamental understanding of gas adsorption within the porous confinement provides information necessary to design a material with improved selectivity. In this regard, metal-organic framework (MOF) adsorbents are ideal candidate materials to study confinement effects for weakly interacting gas molecules, such as noble gases. Among the noble gases, xenon (Xe) has practical applications in the medical, automotive and aerospace industries. In this Communication, we report an ultra-microporous nickel-isonicotinate MOF with exceptional Xe uptake and selectivity compared to all benchmark MOF and porous organic cage materials. The selectivity arises because of the near perfect fit of the atomic Xe inside the porous confinement. Notably, at low partial pressure, the Ni-MOF interacts very strongly with Xe compared to the closely related Krypton gas (Kr) and more polarizable CO2 . Further 129 Xe NMR suggests a broad isotropic chemical shift due to the reduced motion as a result of confinement.

Prediction of MOF Performance in Vacuum Swing Adsorption Systems for Postcombustion CO2 Capture Based on Integrated Molecular Simulations, Process Optimizations, and Machine Learning Models.

Postcombustion CO2 capture and storage (CCS) is a key technological approach to reducing greenhouse gas emission while we transition to carbon-free energy production. However, current solvent-based CO2 capture processes are considered too energetically expensive for widespread deployment. Vacuum swing adsorption (VSA) is a low-energy CCS that has the potential for industrial implementation if the right sorbents can be found. Metal-organic framework (MOF) materials are often promoted as sorbents for low-energy CCS by highlighting select adsorption properties without a clear understanding of how they perform in real-world VSA processes. In this work, atomistic simulations have been fully integrated with a detailed VSA simulator, validated at the pilot scale, to screen 1632 experimentally characterized MOFs. A total of 482 materials were found to meet the 95% CO2 purity and 90% CO2 recovery targets (95/90-PRTs)-365 of which have parasitic energies below that of solvent-based capture (∼290 kWhe/MT CO2) with a low value of 217 kWhe/MT CO2. Machine learning models were developed using common adsorption metrics to predict a material's ability to meet the 95/90-PRT with an overall prediction accuracy of 91%. It was found that accurate parasitic energy and productivity estimates of a VSA process require full process simulations.

Molecular dynamics simulations of interfacial properties of the CO2-water and CO2-CH4-water systems.

Molecular dynamics simulations were performed to study the interfacial behavior of the pure carbon dioxide-water system and a binary 40:60 mol. % gas mixture of (carbon dioxide + methane)-water at the temperatures of 275.15 K and 298.15 K and pressures near 4 MPa for CO2 and up to 10 MPa for methane. The simulations are used to study the dynamic equilibrium of the gases at the water-gas interface, to determine the z-density profiles for the gases and water, and calculate the interfacial tension γ under the different temperature/pressure conditions close to those of the formation of clathrate hydrates of these gases. At the same hydrostatic gas phase pressure, the CO2-water interface has a lower interfacial tension than the CH4-water interface. A greater number of CO2 molecules, as much as three times more than methane at the same pressure, were adsorbed at the interfacial layer, which reflects the stronger electrostatic quadrupolar and van der Waals interactions between CO2 and water molecules at the interface. The water surfaces are covered by less than a monolayer of gas even when the pressure of the system goes near the saturation pressure of CO2. The surface adsorbed molecules are in dynamic equilibrium with the bulk gas and with exchange between the gas and interface regions occurring repeatedly within the timescale of the simulations. The effects of the changes in the CO2-water interfacial tension with external temperature and pressure conditions on the formation of the clathrate hydrates and other CO2 capture and sequestration processes are discussed.

Interfacial properties of hydrocarbon/water systems predicted by molecular dynamic simulations.

The presence of small hydrocarbons is known to reduce the interfacial tension of the gas-water interface, and this phenomenon can affect the formation of the clathrate hydrates of these gases. In this work, the interfacial behavior of the pure methane-, ethane-, and propane-water, and the ternary 90:7:3 mol. % gas mixture of (methane + ethane + propane)-water were studied with molecular dynamics simulations. The interfacial tension, γ, and z-density profiles for the gases and water from simulations of the gas-water systems were determined at the temperatures of 275.15 and 298.15 K, and pressures up to 10 MPa for methane and up to near the experimental saturation pressures of ethane and propane. The goal is to accurately calculate the interfacial tension for the hydrocarbon/water systems and to analyze the molecular behaviors at the interfaces which lead to the observed trends. At the same hydrostatic gas phase pressure, propane, ethane, and methane reduce the gas-water interfacial tension in that order. The local density of the gas molecules at the interface is enhanced relative to the bulk gas, and it was determined that about 13%-20%, 33%-40%, and 54%-59% of the gas molecules in the simulation congregated at the interfaces for the CH4-, C2H6-, and C3H8-water systems, respectively, at the different simulated hydrostatic pressure ranges. For all gases in the pressure range studied, a complete monolayer of gas had not formed at the water interface. Furthermore, a dynamic equilibrium with fast exchange between molecules at the interface and in the gas phase was observed. For the gas mixture, deviations were observed between total calculated interfacial tension, γmix, and the "ideal mixture" value, ∑xiγi,pure, calculated from the interfacial tensions of the pure gases, where xi is the mole fraction of each substance in the simulation. Some possible implications of the results on the mechanism of clathrate hydrate formation are discussed.

The utility of polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS) in surface and in situ studies: new data processing and presentation approach.

Infrared spectroscopy is a powerful non-destructive technique for the identification and quantification of organic molecules widely used in scientific studies. For many years, efforts have been made to adopt this technique for the in situ monitoring of reactions. From these efforts, polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS) was developed three decades ago. Unfortunately, because of the complexity of data processing and interpretation, PM-IRRAS had been avoided in lieu of the single potential alteration infrared spectroscopy (SPAIRS) and subtractively normalized interfacial Fourier transform infrared (SNIFTIR). In this work, we present a new approach for PM-IRRAS data processing and presentation, which provides more insight into in situ and surface studies besides dramatically improving the S/N. In this new approach, we recommend three complementary methods of data treatment (eqn (7), (9) and (10)) as the new protocols for presenting PM-IRRAS data. These equations are robust in visualising the surface processes at the solid-liquid and solid-gas interphases. Eqn (7) contrasts the surface adsorbed species with respect to the isotropic background with or without the influence of the applied potential. Eqn (9) highlights the surface potential-driven changes between the sample and the reference spectra. Eqn (10) focuses on the bulk-phase (solution/gas and surface species) potential-driven changes between the sample and the reference spectra, and hence it can be used to track the production of species, which desorb from the surface upon their formation. Examples of ethanol electro-oxidation reaction are provided as a test system for in situ studies and PVP deposited on glassy carbon for thin-film studies to illustrate the utility of the new PM-IRRAS data handling protocol, which is poised to improve the understanding of the chemistry and physics of surface processes.

Ultralow Parasitic Energy for Postcombustion CO2 Capture Realized in a Nickel Isonicotinate Metal-Organic Framework with Excellent Moisture Stability.

Metal-organic frameworks (MOFs) have attracted significant attention as solid sorbents in gas separation processes for low-energy postcombustion CO2 capture. The parasitic energy (PE) has been put forward as a holistic parameter that measures how energy efficient (and therefore cost-effective) the CO2 capture process will be using the material. In this work, we present a nickel isonicotinate based ultramicroporous MOF, 1 [Ni-(4PyC)2·DMF], that has the lowest PE for postcombustion CO2 capture reported to date. We calculate a PE of 655 kJ/kg CO2, which is lower than that of the best performing material previously reported, Mg-MOF-74. Further, 1 exhibits exceptional hydrolytic stability with the CO2 adsorption isotherm being unchanged following 7 days of steam-treatment (>85% RH) or 6 months of exposure to the atmosphere. The diffusion coefficient of CO2 in 1 is also 2 orders of magnitude higher than in zeolites currently used in industrial scrubbers. Breakthrough experiments show that 1 only loses 7% of its maximum CO2 capacity under humid conditions.

The anomalous halogen bonding interactions between chlorine and bromine with water in clathrate hydrates.

Clathrate hydrate phases of Cl2 and Br2 guest molecules have been known for about 200 years. The crystal structure of these phases was recently re-determined with high accuracy by single crystal X-ray diffraction. In these structures, the water oxygen-halogen atom distances are determined to be shorter than the sum of the van der Waals radii, which indicates the action of some type of non-covalent interaction between the dihalogens and water molecules. Given that in the hydrate phases both lone pairs of each water oxygen atom are engaged in hydrogen bonding with other water molecules of the lattice, the nature of the oxygen-halogen interactions may not be the standard halogen bonds characterized recently in the solid state materials and enzyme-substrate compounds. The nature of the halogen-water interactions for the Cl2 and Br2 molecules in two isolated clathrate hydrate cages has recently been studied with ab initio calculations and Natural Bond Order analysis (Ochoa-Resendiz et al. J. Chem. Phys. 2016, 145, 161104). Here we present the results of ab initio calculations and natural localized molecular orbital analysis for Cl2 and Br2 guests in all cage types observed in the cubic structure I and tetragonal structure I clathrate hydrates to characterize the orbital interactions between the dihalogen guests and water. Calculations with isolated cages and cages with one shell of coordinating molecules are considered. The computational analysis is used to understand the nature of the halogen bonding in these materials and to interpret the guest positions in the hydrate cages obtained from the X-ray crystal structures.

Intercalation of Coordinatively Unsaturated Fe(III) Ion within Interpenetrated Metal-Organic Framework MOF-5.

Coordinatively unsaturated Fe(III) metal sites were successfully incorporated into the iconic MOF-5 framework. This new structure, Fe(III) -iMOF-5, is the first example of an interpenetrated MOF linked through intercalated metal ions. Structural characterization was performed with single-crystal and powder XRD, followed by extensive analysis by spectroscopic methods and solid-state NMR, which reveals the paramagnetic ion through its interaction with the framework. EPR and Mössbauer spectroscopy confirmed that the intercalated ions were indeed Fe(III) , whereas DFT calculations were employed to ascertain the unique pentacoordinate architecture around the Fe(III) ion. Interestingly, this is also the first crystallographic evidence of pentacoordinate Zn(II) within the MOF-5 SBU. This new MOF structure displays the potential for metal-site addition as a framework connector, thus creating further opportunity for the innovative development of new MOF materials.

Molecular simulations and density functional theory calculations of bromine in clathrate hydrate phases.

Bromine forms a tetragonal clathrate hydrate structure (TS-I) very rarely observed in clathrate hydrates of other guest substances. The detailed structure, energetics, and dynamics of Br2 and Cl2 in TS-I and cubic structure I (CS-I) clathrate hydrates are studied in this work using molecular dynamics and quantum chemical calculations. X-ray diffraction studies show that the halogen-water-oxygen distances in the cages of these structures are shorter than the sum of the van der Waals radii of halogen and oxygen atoms. This suggests that the stabilizing effects of halogen bonding or other non-covalent interactions (NCIs) may contribute to the formation of the unique tetragonal bromine hydrate structure. We performed molecular dynamics simulations of Br2 and Cl2 clathrate hydrates using our previously developed five-site charge models for the dihalogen molecules [Dureckova et al. Can. J. Chem. 93, 864 (2015)] which reproduce the computed electrostatic potentials of the dihalogens and account for the electropositive σ-hole of the halogen bond donor (the dihalogen). Analysis of the radial distribution functions, enthalpies of encapsulation, velocity and orientation autocorrelation functions, and polar angle distributions are carried out for Br2 and Cl2 guests in various cages to contrast the properties of these guests in the TS-I and CS-I phases. Quantum chemical partial geometry optimizations of Br2 and Cl2 guests in the hydrate cages using the M06-2X functional give short halogen-water distances compatible with values observed in X-ray diffraction experiments. NCI plots of guest-cage structures are generated to qualitatively show the relative strength of the non-bonding interactions between dihalogens and water molecules. The differences between behaviors of Br2 and Cl2 guests in the hydrate cages may explain why bromine forms the unique TS-I phase.

The Challenge of Water Competition in Physical Adsorption of CO2 by Porous Solids for Carbon Capture Applications - A Short Perspective.

With ever-increasing efforts to design sorbent materials to capture carbon dioxide from flue gas and air, this perspective article is provided based on nearly a decade of collaboration across science, engineering, and industry partners. A key point learned is that a holistic view of the carbon capture problem is critical. While researchers can be inclined to value their own fields and associated metrics, often, key parameters are those that enable synergy between materials and processes. While the role of water in the chemisorption of CO2 is well-studied, in this perspective, it is hoped to highlight the often-overlooked but critical role of water in assessing the potential of a physical adsorbent for CO2 capture. This is a challenge that requires interdisciplinarity. As such, this document is written for a general audience rather than experts in any specific discipline.

MEPO-ML: a robust graph attention network model for rapid generation of partial atomic charges in metal-organic frameworks.

Accurate computation of the gas adsorption properties of MOFs is usually bottlenecked by the DFT calculations required to generate partial atomic charges. Therefore, large virtual screenings of MOFs often use the QEq method which is rapid, but of limited accuracy. Recently, machine learning (ML) models have been trained to generate charges in much better agreement with DFT-derived charges compared to the QEq models. Previous ML charge models for MOFs have all used training sets with less than 3000 MOFs obtained from the CoRE MOF database, which has recently been shown to have high structural error rates. In this work, we developed a graph attention network model for predicting DFT-derived charges in MOFs where the model was developed with the ARC-MOF database that contains 279,632 MOFs and over 40 million charges. This model, which we call MEPO-ML, predicts charges with a mean absolute error of 0.025e on our test set of over 27 K MOFs. Other ML models reported in the literature were also trained using the same dataset and descriptors, and MEPO-ML was shown to give the lowest errors. The gas adsorption properties evaluated using MEPO-ML charges are found to be in significantly better agreement with the reference DFT-derived charges compared to the empirical charges, for both polar and non-polar gases. Using only a single CPU core on our benchmark computer, MEPO-ML charges can be generated in less than two seconds on average (including all computations required to apply the model) for MOFs in the test set of 27 K MOFs.

Hydrogen Adsorption in Ultramicroporous Metal-Organic Frameworks Featuring Silent Open Metal Sites.

In this study, we utilized an ultramicroporous metal-organic framework (MOF) named [Ni3(pzdc)2(ade)2(H2O)4]·2.18H2O (where H3pzdc represents pyrazole-3,5-dicarboxylic acid and ade represents adenine) for hydrogen (H2) adsorption. Upon activation, [Ni3(pzdc)2(ade)2] was obtained, and in situ carbon monoxide loading by transmission infrared spectroscopy revealed the generation of open Ni(II) sites. The MOF displayed a Brunauer-Emmett-Teller (BET) surface area of 160 m2/g and a pore size of 0.67 nm. Hydrogen adsorption measurements conducted on this MOF at 77 K showed a steep increase in uptake (up to 1.93 mmol/g at 0.04 bar) at low pressure, reaching a H2 uptake saturation at 2.11 mmol/g at ∼0.15 bar. The affinity of this MOF for H2 was determined to be 9.7 ± 1.0 kJ/mol. In situ H2 loading experiments supported by molecular simulations confirmed that H2 does not bind to the open Ni(II) sites of [Ni3(pzdc)2(ade)2], and the high affinity of the MOF for H2 is attributed to the interplay of pore size, shape, and functionality.

Characterization of Zn-containing metal-organic frameworks by solid-state 67Zn NMR spectroscopy and computational modeling.

Metal-organic frameworks (MOFs) are an extremely important class of porous materials with many applications. The metal centers in many important MOFs are zinc cations. However, their Zn environments have not been characterized directly by (67)Zn solid-state NMR (SSNMR) spectroscopy. This is because (67)Zn (I=5/2) is unreceptive with many unfavorable NMR characteristics, leading to very low sensitivity. In this work, we report, for the first time, a (67)Zn natural abundance SSNMR spectroscopic study of several representative zeolitic imidazolate frameworks (ZIFs) and MOFs at an ultrahigh magnetic field of 21.1 T. Our work demonstrates that (67)Zn magic-angle spinning (MAS) NMR spectra are highly sensitive to the local Zn environment and can differentiate non-equivalent Zn sites. The (67)Zn NMR parameters can be predicted by theoretical calculations. Through the study of MOF-5 desolvation, we show that with the aid of computational modeling, (67)Zn NMR spectroscopy can provide valuable structural information on the MOF systems with structures that are not well described. Using ZIF-8 as an example, we further demonstrate that (67)Zn NMR spectroscopy is highly sensitive to the guest molecules present inside the cavities. Our work also shows that a combination of (67)Zn NMR data and molecular dynamics simulation can reveal detailed information on the distribution and the dynamics of the guest species. The present work establishes (67)Zn SSNMR spectroscopy as a new tool complementary to X-ray diffraction for solving outstanding structural problems and for determining the structures of many new MOFs yet to come.

The HEALED SBU Library of Chemically Realistic Building Blocks for Construction of Hypothetical Metal-Organic Frameworks.

Advancements in hypothetical metal-organic framework (hMOF) databases and construction tools have resulted in a rapidly expanding chemical design space for nanoporous materials. The bulk of these hypothetical structures are constructed using structural building units (SBUs) derived from experimental MOF structures, often collected from the CoRE-MOF database. Recent investigations into the state of these deposited experimental structures' chemical accuracy identified an array of common structural errors, including omitted protons, missing counterions, and disordered structures. These structural errors propagate into the SBUs mined from experimental MOFs, culminating in inaccurate hMOF structures possessing net charges or missing atoms which were not accounted for previously. This work demonstrates how manual investigation was applied to diagnose structural errors in SBUs obtained from several popular hMOF construction tools and databases. An analysis of the prevailing errors discovered during the examination process is provided along with representative cases to aid with error detection in future studies involving SBU extraction and hMOF construction. A novel repair protocol was established and employed to generate a library of SBUs that are hand-examined and labeled with enhanced detail (HEALED). This repaired library of SBUs contains 952 inorganic SBUs and 568 organic SBUs ideally suited for the generation of hypothetical frameworks that are chemically accurate and properly charge labeled. Additionally, case studies following the effects of SBU errors on electrostatic potential-fitted charges and GCMC-simulated gas adsorption predictions are presented to highlight the significance of using chemically accurate hMOF structures exclusively in all screening efforts going forward.

Phosphonate monoesters as carboxylate-like linkers for metal organic frameworks.

Bidentate phosphonate monoesters are analogues of popular dicarboxylate linkers in MOFs, but with an alkoxy tether close to the coordinating site. Herein, we report 3-D MOF materials based upon phosphonate monoester linkers. Cu(1,4-benzenediphosphonate bis(monoalkyl ester), CuBDPR, with an ethyl tether is nonporous; however, the methyl tether generates an isomorphous framework that is porous and captures CO(2) with a high isosteric heat of adsorption of 45 kJ mol(-1). Computational modeling reveals that the CO(2) uptake is extremely sensitive both to the flexing of the structure and to the orientation of the alkyl tether.

Mechanistic analysis of iridium(III) catalyzed direct C-H arylations: a DFT study.

In a recent experimental work the Ir complex [Ir(cod)(py)(PCy(3))](PF(6)) (that is, Crabtree's catalyst) has been shown to catalyze the C-H arylation of electron-rich heteroarenes with iodoarenes using Ag(2)CO(3) as base. For this process, an electrophilic metalation mechanism, (S(E)Ar) has been proposed as operative mechanism rather than the concerted metalation-deprotonation (CMD) mechanism, widely implicated in Pd-catalyzed arylation reactions. Herein we have investigated the C-H activation step for several (hetero)arenes catalyzed by a Ir(III) catalyst and compared the data obtained with the results for the Pd(II)-catalyzed C-H bond activation. The calculations demonstrate that, similar to Pd(II)-catalyzed reactions, the Ir(III)-catalyzed direct C-H arylation occurs through the CMD pathway which accounts for the experimentally observed regioselectivity. The transition states for Ir(III)-catalyzed direct C-H arylation feature stronger metal-C((arene)) interactions than those for Pd(II)-catalyzed C-H arylation. The calculations also demonstrate that ligands with low trans effect may decrease the activation barrier of the C-H bond cleavage.

Molecular dynamics simulation of NMR powder lineshapes of linear guests in structure I clathrate hydrates.

We perform molecular dynamics simulations (up to 6 ns) for the structure I clathrate hydrates of linear molecules CS, CS(2), OCS, and C(2)H(2) in large cages at different temperatures in the stability range to determine the angular distribution and dynamics of the guests in the large cages. The long axes of linear guest molecules in the oblate large structure I clathrate hydrate cages are primarily confined near the equatorial plane of the cage rather than axial regions. This non-uniform spatial distribution leads to well-known anisotropic lineshapes in the solid-state NMR spectra of the guest species. We use the dynamic distribution of guest orientations in the cages during the MD simulations at different temperatures to predict the (13)C NMR powder lineshapes of the guests in the large cages. The length of the guests and intermolecular interactions of the guests in the water cages determine the angular distribution and the mobility of the guests in the sI large cages at different temperatures. At low temperatures the range of motion of the guests in the cages are limited and this is reflected in the skew of the predicted (13)C lineshapes. As the guest molecules reach the fast motion limit at higher temperatures, the lineshapes for CS, OCS, and C(2)H(2) are predicted to have the "standard" powder lineshapes of guest molecules.

A DFT+U study of defect association and oxygen migration in samarium-doped ceria.

A specialized genetic algorithm (GA) is used to search the structural space of samarium-doped ceria (SDC) for the most energetically stable configurations which will predominate in low temperature fuel cells. A systematic investigation of all configurations of 3.2% SDC and a GA investigation of 6.6% SDC are presented for the first time at the DFT+U level of theory. It was found that Sm atoms prefer to occupy the nearest neighbor (NN) position relative to the oxygen vacancy at 3.2%, while at 6.6%, a balance exists between various Sm-vacancy interactions and the vacancies prefer to be separated by ∼6 Å. Also, the migration barriers for oxygen diffusion are calculated amongst the best structures in 3.2% and 6.6% SDC and are found to be comparable to the barriers in Gd-doped ceria at the DFT+U level of theory. While the migration calculations provide insight on the oxygen diffusion mechanism in this material, the favored configurations from our GA enable future research on concentrated SDC and contribute to the atomistic understanding of the influence of dopant-vacancy and vacancy-vacancy interactions on ionic conductivity.