Atomistic simulation techniques have been employed to investigate the effect of molecular adsorption of water on the low-index surfaces of calcite, aragonite, and vaterite. Calculated surface and hydration energies agree with experiment and previous calculations where available. Known experimental surface features are reproduced, i.e., 1 × 1 symmetry and structural features of the calcite {1014} surface and bulk termination of the {1011} and {1120} surfaces. Surface carbonate groups tend to rotate to lie flat in the surface. The morphologies of the hydrated crystals agree with experimentally found morphologies. The bulk lattice energies of the polymorphs reflect their thermodynamic stability.

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Surface Structure and Morphology of Calcium Carbonate Polymorphs Calcite, Aragonite, and Vaterite: An Atomistic Approach

Superionic conductors are compounds that exhibit exceptionally high values of ionic conductivity within the solid state. Indeed, their conductivities often reach values of the order of 1 Ω−1 cm−1, which are comparable to those observed in the molten state. Following Faraday's first observation of high ionic conductivity within the solids β-PbF2 and Ag2S in 1836, a fundamental understanding of the nature of the superionic state has provided one of the major challenges in the field of condensed matter science. However, experimental and theoretical approaches to their study are often made difficult by the extensive dynamic structural disorder which characterizes superionic conduction and the inapplicability of many of the commonly used approximations in solid state physics. Nevertheless, a clearer picture of the nature of the superionic state at the ionic level has emerged within the past few decades. Many different techniques have contributed to these advances, but the most significant insights have been provided by neutron scattering experiments and molecular dynamics simulations. This review will summarize the state of current knowledge concerning the crystal structures and conduction processes of superionic conductors, beginning with a comparison of the behaviour of two of the most widely studied binary compounds, AgI and β-PbF2. Each can be considered a parent of two larger families of highly conducting compounds which are related by either chemical or structural means. These include perovskite-structured oxides and Li+ containing spinel-structured compounds, which have important commercial applications in fuel cells and lightweight batteries, respectively. In parallel with these discussions, the relative importance of factors such as bonding character and the properties of the mobile and immobile ions (charge, size, polarizability, etc) in promoting the extensive lattice disorder which characterizes superionic behaviour will be assessed and the possibilities for predicting a priori which compounds will display high ionic conductivity discussed.

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Superionics: crystal structures and conduction processes

Significant progress has been made both in experimentation and in theoretical modeling of scanning probe microscopy. The theoretical models used to analyze and interpret experimental scanning probe microscope (SPM) images and spectroscopic data now provide information not only about the surface, but also the probe tip and physical changes occurring during the scanning process. The aim of this review is to discuss and compare the present status of computational modeling of two of the most popular SPM methods---scanning tunneling microscopy and scanning force microscopy---in conjunction with their applications to studies of surface structure and properties with atomic resolution. In the context of these atomic-scale applications, for the scanning force microscope (SFM), this review focuses primarily on recent noncontact SFM (NC-SFM) results. After a brief introduction to the experimental techniques and the main factors determining image formation, the authors consider the theoretical models developed for the scanning tunneling microscope (STM) and the SFM. Both techniques are treated from the same general perspective of a sharp tip interacting with the surface---the only difference being that the control parameter in the STM is the tunneling current and in the SFM it is the force. The existing methods for calculating STM and SFM images are described and illustrated using numerous examples, primarily from the authors' own simulations, but also from the literature. Theoretical and practical aspects of the techniques applied in STM and SFM modeling are compared. Finally, the authors discuss modeling as it relates to SPM applications in studying surface properties, such as adsorption, point defects, spin manipulation, and phonon excitation.

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Theories of scanning probe microscopes at the atomic scale

We calculated the free energy profiles of water and three metal ions (magnesium, calcium, and strontium) adsorbing on the [1014] calcite surface in aqueous solution. The approach uses molecular dynamics with parametrized equations to describe the interatomic forces. The potential model is able to reproduce the interactions between water and the metal ions regardless of whether they are at the mineral surface or in bulk water. The simulations predict that the free energy of adsorption of water is relatively small compared to the enthalpy of adsorption calculated in previous papers. This suggests a large change in entropy associated with the water adsorption on the surface. We also demonstrate that the free energy profile of a metal ion adsorbing on the surface correlates with the solvent density and that the rate of formation of an innersphere complex depends on overcoming a large free energy barrier, which is mainly electrostatic in nature. Furthermore, comparison among the rates of desorption of magnesium, calcium, and strontium from the calcite surface suggests that magnesium has a much lower rate of desorption due to its strong interactions with both water and the surface.

Free energy of adsorption of water and metal ions on the [1014] calcite surface.

Computer simulations allow for the investigation of many materials properties and processes that are not easily accessible in the laboratory. This is particularly true in the Earth sciences, where the relevant pressures and temperatures may be so extreme that no experimental techniques can operate at those conditions. Computer modeling is often the only source of information on the properties of materials that, combined with indirect evidence (such as seismic data), allows one to discriminate among competing planetary models. Many computer simulations are performed using effective interatomic potentials tailored to reproduce some experimentally observed properties of the materials being investigated. The remoteness of the physically interesting conditions from those achievable in the laboratory, as well as the huge variety of different atomic coordination and local chemical state occurring in the Earth interior, make the dependability of semi-empirical potentials questionable. First-principles techniques based on density-functional theory (DFT) (Hohenberg and Kohn 1964; Kohn and Sham 1965) are much more predictive, not being biased by any prior experimental input, and have demonstrated a considerable accuracy in a wide class of materials and variety of external conditions. The importance of thermal effects in the range of phenomena interesting to the Earth sciences makes a proper account of atomic motion essential. Traditionally, this is achieved using molecular dynamics techniques which have been successfully combined with DFT in the first-principles molecular dynamics technique of Car and Parrinello (1985). Well below the melting temperature, the numerical efficiency of molecular dynamics is limited by the lack of ergodicity, which would require long simulation times, and by the importance of long-wavelength collective motions (phonons), which would require large simulation cells. Both difficulties are successfully dealt with in the quasi-harmonic approximation (QHA) where the thermal properties of solid materials are traced back to those of a system of non-interacting …

Density-Functional Perturbation Theory for Quasi-Harmonic Calculations

A computational method, based on the quasiharmonic approximation, has been computer-coded to calculate the temperature dependence of elastic constants and structural features of crystals. The model is applied to calcite, CaCO3; an interatomic potential based on a C-O Morse function and Ca-O and O-O Borntype interactions, including a shell model for O, has been used. Equilibrations in the range 300–800 K reproduce the experimental unit-cell edges and bond lengths within 1%. The simulated thermal expansion coefficients are 22.3 (//c) and 2.6 (⊥ c), against 25.5 and-3.7×10−6K−1 experimental values, respectively. The thermal coefficients of elastic constants tend to be underestimated; for the bulk modulus, -2.3 against-3.7×10−4K−1 is obtained.

Modelling of the thermal dependence of structural and elastic properties of calcite, caco3

Absolute Ionic Diffusion in MgO - Computer Calculations via Lattice Dynamics

Simulation study of pressure-induced structural changes in La2CuO4 and in La1.83Sr0.17CuO4

We present an atomistic simulation method for calculating the defect formation free energy and defect volume using lattice dynamics. The periodic simulation methods have been extended to allow charged systems with subtraction of defect-defect interactions to be studied routinely. This allows constant pressure minimization to be used rather than the more traditional constant volume method, allowing direct calculation of defect formation volumes and defect free energies or enthalpies rather than lattice energy. We have applied this method to the calculation of enthalpies and volumes of vacancy and Schottky formation as a function of pressure and to the solution of Ca in the lower mantle mineral MgSiO3 perovskite. The results indicate that as the pressure increases the defect volume of vacancy formation decreases and above approximately 50 GPa this decrease actually leads to a reduction in the enthalpy of formation rather than the expected increase as the pressure is increased further. The total Schottky enthalpy however continues to increase as a function of pressure although the rate of change of energy decreases with increasing pressure. The solution of Ca with MgSiO3 perovskite is shown to be very unfavourable and indicates that Ca will form its own CaSiO3 perovskite phase within the conditions expected within the lower mantle. This result is important when considering the amount and location of trace elements such as Al within the mantle that have been shown to be preferentially located within CaSiO3 perovskite rather than MgSiO3 perovskite.

https://iopscience.iop.org/article/10.1088/0953-8984/12/39/306/pdf

A. Wall

Papers

Modelling of the thermal dependence of structural and elastic properties of calcite, caco3

Absolute Ionic Diffusion in MgO - Computer Calculations via Lattice Dynamics

Simulation study of pressure-induced structural changes in La2CuO4 and in La1.83Sr0.17CuO4

Atomistic simulation of the effect of temperature and pressure on point defect formation in MgSiO3 perovskite and the stability of CaSiO3 perovskite

3 – Lattice Energy and Free Energy Minimization Techniques