The construction of a reliable potential for GeO2 from first principles

Thermodynamic anomalies, polyamorphism and all that

The appearance and evolution of thermodynamics anomalies, and related properties, are studied for two classes of system, modelling those dominated by covalent and ionic interactions, respectively. Such anomalies are most familiar in the density but are also present in other thermodynamics variables such as the compressibility and heat capacity. By systematically varying key model parameters the emergence and evolution of these anomalies can be tracked across the phase space. The interaction of the anomalies can often be rationalized by thermodynamics 'rules'. The emergence of these anomalies may also be correlated with the appearance of polyamorphism, the existence of multiple amorphous states which differ in density and entropy. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 1)'.

The progression of thermodynamic anomalies in MX2 networks with local tetrahedral geometries

Key thermodynamic anomalies in density and compressibility, as well as the related stability limits, are determined using an ionic model for BeF₂ which includes many-body polarization terms. BeF₂ is chosen as an example of an archetypal network-forming system whose structure can be rationalised in terms of connected local tetrahedral coordination polyhedra. The anion dipole polarizability (which effectively controls the bond angles linking neighbouring tetrahedra) is used as a single free parameter in order to help rationalise the changes in the anomaly locations in phase space, whilst all other potential parameters remain fixed. The anomalies and stability limits systematically shift to lower temperature and higher pressure as the anion polarizability is increased. At high dipole polarizabilities the temperature of maximum density anomaly locus becomes suppressed into the supercooled regime of the phase space. The movements of the anomaly loci are analysed in terms of the network structure and the correlation with the inter-tetrahedral bond angles is considered. The high sensitivity of the anomalies to the details of the potential models applied is discussed with reference to previous works on related systems. The relationship to analogous studies on Stillinger-Weber liquids is discussed.

Structure and dynamics in network-forming materials

The study of the structure and dynamics of network-forming materials is reviewed. Experimental techniques used to extract key structural information are briefly considered. Strategies for building simulation models, based on both targeting key (experimentally-accessible) materials and on systematically controlling key model parameters, are discussed. As an example of the first class of materials, a key target system, SiO₂, is used to highlight how the changing structure with applied pressure can be effectively modelled (in three dimensions) and used to link to both experimental results and simple structural models. As an example of the second class the topology of networks of tetrahedra in the MX₂ stoichiometry are controlled using a single model parameter linked to the M-X-M bond angles. The evolution of ordering on multiple length-scales is observed as are the links between the static structure and key dynamical properties. The isomorphous relationship between the structures of amorphous Si and SiO₂ is discussed as are the similarities and differences in the phase diagrams, the latter linked to potential polyamorphic and 'anomalous' (e.g. density maxima) behaviour. Links to both two-dimensional structures for C, Si and Ge and near-two-dimensional bilayers of SiO₂ are discussed. Emerging low-dimensional structures in low temperature molten carbonates are also uncovered.

Additive polarizabilities in ionic liquids

An extended designed regression analysis of experimental data on density and refractive indices of several classes of ionic liquids yielded statistically averaged atomic volumes and polarizabilities of the constituting atoms. These values can be used to predict the molecular volume and polarizability of an unknown ionic liquid as well as its mass density and refractive index. Our approach does not need information on the molecular structure of the ionic liquid, but it turned out that the discrimination of the hybridization state of the carbons improved the overall result. Our results are not only compared to experimental data but also to quantum-chemical calculations. Furthermore, fractional charges of ionic liquid ions and their relation to polarizability are discussed.

Understanding chemical expansion in perovskite-structured oxides

In this work, chemical expansion in perovskite oxides was characterized in detail, motivated, inter alia, by a desire to understand the lower chemical expansion coefficients observed for perovskites in comparison to fluorite-structured oxides. Changes in lattice parameter and in local atomic arrangements taking place during compositional changes of perovskites, i.e., stoichiometric expansion, were investigated by developing an empirical model and through molecular dynamics and density functional theory atomistic simulations. An accurate empirical expression for predicting lattice constants of perovskites was developed, using a similar approach to previous reports. From this equation, analytical expressions relating chemical expansion coefficients to separate contributions from the cation and anion sublattices, assuming Shannon ionic radii, were developed and used to isolate the effective radius of an oxygen vacancy, rV. Using both experimental and simulated chemical expansion coefficient data, rV for a variety of perovskite compositions was estimated, and trends in rV were studied. In most cases, rV was slightly smaller than or similar to the radius of an oxide ion, but larger than in the fluorite structured materials. This result was in good agreement with the atomistic simulations, showing contractive relaxations of the closest oxide ions towards the oxygen vacancy. The results indicate that the smaller chemical expansion coefficients of perovskites vs. fluorites are largely due to the smaller change in cation radii in perovskites, given that the contraction around the oxygen vacancy appears to be less in this structure. Limitations of applicability for the model are discussed.

Ceria co-doping: synergistic or average effect?

Ceria (CeO2) co-doping has been suggested as a means to achieve ionic conductivities that are significantly higher than those in singly doped systems. Rekindled interest in this topic over the last decade has given rise to claims of much improved performance. The present study makes use of computer simulations to investigate the bulk ionic conductivity of rare earth (RE) doped ceria, where RE = Sc, Gd, Sm, Nd and La. The results from the singly doped systems are compared to those from ceria co-doped with Nd/Sm and Sc/La. The pattern that emerges from the conductivity data is consistent with the dominance of local lattice strains from individual defects, rather than the synergistic co-doping effect reported recently, and as a result, no enhancement in the conductivity of co-doped samples is observed.

Networks under pressure: the development of in situ high-pressure neutron diffraction for glassy and liquid materials

The pressure-driven collapse in the structure of network-forming materials will be considered in the gigapascal (GPa) regime, where the development of in situ high-pressure neutron diffraction has enabled this technique to obtain new structural information. The improvements to the neutron diffraction methodology are discussed, and the complementary nature of the results is illustrated by considering the pressure-driven structural transformations for several key network-forming materials that have also been investigated by using other experimental techniques such as x-ray diffraction, inelastic x-ray scattering, x-ray absorption spectroscopy and Raman spectroscopy. A starting point is provided by the pressure-driven network collapse of the prototypical network-forming oxide glasses B2O3, SiO2 and GeO2. Here, the combined results help to show that the coordination number of network-forming structural motifs in a wide range of glassy and liquid oxide materials can be rationalised in terms of the oxygen-packing fraction over an extensive pressure and temperature range. The pressure-driven network collapse of the prototypical chalcogenide glass GeSe2 is also considered where, as for the case of glassy GeO2, site-specific structural information is now available from the method of in situ high-pressure neutron diffraction with isotope substitution. The application of in situ high-pressure neutron diffraction to other structurally disordered network-forming materials is also summarised. In all of this work a key theme concerns the rich diversity in the mechanisms of network collapse, which drive the changes in physico-chemical properties of these materials. A more complete picture of the mechanisms is provided by molecular dynamics simulations using theoretical schemes that give a good account of the experimental results.

Mechanisms of network collapse in GeO2 glass: high-pressure neutron diffraction with isotope substitution as arbitrator of competing models

The structure of the network forming glass GeO(2) is investigated by making the first application of the method of in situ neutron diffraction with isotope substitution at pressures increasing from ambient to 8 GPa. Of the various models, the experimental results are in quantitative agreement only with molecular dynamics simulations made using interaction potentials that include dipole-polarization effects. When the reduced density ρ/ρ(0) > or approximately equal to 1.16, where ρ(0) is the value at ambient pressure, network collapse proceeds via an interplay between the predominance of distorted square pyramidal GeO(5) units versus octahedral GeO(6) units as they replace tetrahedral GeO(4) units. This replacement necessitates the formation of threefold coordinated oxygen atoms and leads to an increase with density in the number of small rings, where a preference is shown for sixfold rings when ρ/ρ(0) = 1 and fourfold rings when ρ/ρ(0) = 1.64.

Influence of polarizability on metal oxide properties studied by molecular dynamics simulations

We have studied the dependence of metal oxide properties in molecular dynamics (MD) simulations on the polarizability of oxygen ions. We present studies of both liquid and crystalline structures of silica (SiO(2)), magnesia (MgO) and alumina (Al(2)O(3)). For each of the three oxides, two separately optimized sets of force fields were used: (i) long-range Coulomb interactions between oxide and metal ions combined with a short-range pair potential; (ii) extension of force field (i) by adding polarizability to the oxygen ions. We show that while an effective potential of type (i) without polarizable oxygen ions can describe radial distributions and lattice constants reasonably well, potentials of type (ii) are required to obtain correct values for bond angles and the equation of state. The importance of polarizability for metal oxide properties decreases with increasing temperature.

Density-driven structural transformations in network forming glasses: a high-pressure neutron diffraction study of GeO2 glass up to 17.5 GPa

The structure of GeO(2) glass was investigated at pressures up to 17.5(5) GPa using in situ time-of-flight neutron diffraction with a Paris-Edinburgh press employing sintered diamond anvils. A new methodology and data correction procedure were developed, enabling a reliable measurement of structure factors that are largely free from diamond Bragg peaks. Calibration curves, which are important for neutron diffraction work on disordered materials, were constructed for pressure as a function of applied load for both single and double toroid anvil geometries. The diffraction data are compared to new molecular-dynamics simulations made using transferrable interaction potentials that include dipole-polarization effects. The results, when taken together with those from other experimental methods, are consistent with four densification mechanisms. The first, at pressures up to approximately equal 5 GPa, is associated with a reorganization of GeO(4) units. The second, extending over the range from approximately equal 5 to 10 GPa, corresponds to a regime where GeO(4) units are replaced predominantly by GeO(5) units. In the third, as the pressure increases beyond ~10 GPa, appreciable concentrations of GeO(6) units begin to form and there is a decrease in the rate of change of the intermediate-range order as measured by the pressure dependence of the position of the first sharp diffraction peak. In the fourth, at about 30 GPa, the transformation to a predominantly octahedral glass is achieved and further densification proceeds via compression of the Ge-O bonds. The observed changes in the measured diffraction patterns for GeO(2) occur at similar dimensionless number densities to those found for SiO(2), indicating similar densification mechanisms for both glasses. This implies a regime from about 15 to 24 GPa where SiO(4) units are replaced predominantly by SiO(5) units, and a regime beyond ~24 GPa where appreciable concentrations of SiO(6) units begin to form.

The effects of topology on the structural, dynamic and mechanical properties of network-forming materials

The effects of network topology on the static structural, mechanical and dynamic properties of MX(2) network-forming liquids (with tetrahedral short-range order) are discussed. The network topology is controlled via a single model parameter (the anion polarizability) which effectively constrains the inter-tetrahedral linkages in a physically transparent manner. Critically, it is found to control the balance between the stability of corner- and edge-sharing tetrahedra. A potential rigidity transformation is investigated. The vibrational density of states is investigated, using an instantaneous normal model analysis, as a function of both anion polarizability and temperature. A low frequency peak is seen to appear and is shown to be correlated with the fraction of cations which are linked through solely edge-sharing structural motifs. A modified effective mean atom coordination number is proposed which allows the appearance of the low frequency feature to be understood in terms of a mean field rigidity percolation threshold.

Comparing reduced partial charge models with polarizable simulations of ionic liquids

Molecular ionic liquids are typically characterized by strong electrostatic interactions resulting in a charge ordering and retardation of their translational and rotational behaviour. Unfortunately, this effect is often overestimated in classical molecular dynamics simulations. This can be circumvented in a twofold way: the easiest way is to reduce the partial charges of the ions to sub-integer values of ±0.7-0.9 e. The more realistic model is to include polarizable forces, e.g. Drude-oscillators, but it comes along with an increasing computational effort. On the other hand, charge-scaled models are claimed to take an average polarizability into account. But do both models have the same impact on structure and dynamics of molecular ionic liquids? In the present study several molecular dynamics simulations of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate are performed with different levels of polarization as well as with varying charge scaling factors of 0.74 to 0.90. The analysis of the structural and dynamical results are performed in different levels: from the atomic point of view over the molecular level to collective properties determined by the complete sample.

A dipole polarizable potential for reduced and doped CeO(2) obtained from first principles

In this paper we present the parameterization of a new interionic potential for stoichiometric, reduced and doped CeO(2). We use a dipole polarizable potential (DIPPIM: the dipole polarizable ion model) and optimize its parameters by fitting them to a series of density functional theory calculations. The resulting potential was tested by calculating a series of fundamental properties for CeO(2) and by comparing them against experimental values. The values for all the calculated properties (thermal and chemical expansion coefficients, lattice parameters, oxygen migration energies, local crystalline structure and elastic constants) are within 10-15% of the experimental ones, an accuracy comparable to that of ab initio calculations. This result suggests the use of this new potential for reliably predicting atomic scale properties of CeO(2) in problems where ab initio calculations are not feasible due to their size limitations.

High-pressure behaviour of GeO2: a simulation study

In this work we study the high-pressure behaviour of liquid and glassy GeO(2) by means of molecular dynamics simulations. The interaction potential, which includes dipole polarization effects, was parametrized using first-principles calculations. Our simulations reproduce the most recent experimental structural data very well. The character of the pressure-induced structural transition in the glassy system has been a matter of controversy. We show that our simulations and the experimental data are consistent with a smooth transition from a tetrahedral to an octahedral network with a significant number of pentacoordinated germanium ions appearing over an extended pressure range. Finally, the study of high-pressure, liquid germania confirms that this material presents an anomalous behaviour of the diffusivity as observed in analogous systems such as silica and water. The importance of pentacoordinated germanium ions for such behaviour is stressed.

Cation composition effects on oxide conductivity in the Zr(2)Y(2)O(7)-Y(3)NbO(7) system

Polarizable interaction potentials, parametrized using ab initio electronic structure calculations, have been used in molecular dynamics simulations to study the effect of cation composition on the ionic conductivity in the Zr(2)Y(2)O(7)-Y(3)NbO(7) system and to link the dynamical properties to the degree of lattice disorder. Across the composition range, this system retains a disordered fluorite crystal structure and the vacancy concentration is constant. The observed trends of decreasing conductivity and increasing disorder with increasing Nb(5+) content were reproduced in simulations with the cations randomly assigned to positions on the cation sublattice. The trends were traced to the influences of the cation charges and relative sizes and their effect on vacancy ordering by carrying out additional calculations in which, for example, the charges of the cations were equalized. The simulations did not, however, reproduce all of the observed properties, particularly for Y(3)NbO(7). Its conductivity was significantly overestimated and prominent diffuse scattering features observed in small area electron diffraction studies were not always reproduced. Consideration of these deficiencies led to a preliminary attempt to characterize the consequence of partially ordering the cations on their lattice, which significantly affects the propensity for vacancy ordering. The extent and consequences of cation ordering seem to be much less pronounced on the Zr(2)Y(2)O(7) side of the composition range.