John A. Purton

The 'zero charge' partitioning behaviour of noble gases during mantle melting

Noble-gas geochemistry is an important tool for understanding planetary processes from accretion to mantle dynamics and atmospheric formation. Central to much of the modelling of such processes is the crystal–melt partitioning of noble gases during mantle melting, magma ascent and near-surface degassing. Geochemists have traditionally considered the ‘inert’ noble gases to be extremely incompatible elements, with almost 100 per cent extraction efficiency from the solid phase during melting processes. Previously published experimental data on partitioning between crystalline silicates and melts has, however, suggested that noble gases approach compatible behaviour, and a significant proportion should therefore remain in the mantle during melt extraction. Here we present experimental data to show that noble gases are more incompatible than previously demonstrated, but not necessarily to the extent assumed or required by geochemical models. Independent atomistic computer simulations indicate that noble gases can be considered as species of ‘zero charge’ incorporated at crystal lattice sites. Together with the lattice strain model, this provides a theoretical framework with which to model noble-gas geochemistry as a function of residual mantle mineralogy.

Atomistic simulation of trace element incorporation into garnets— comparison with experimental garnet-melt partitioning data

Abstract We have studied the energetics of trace element incorporation into pure almandine (Alm), grossular (Gros), pyrope (Py) and spessartine (Spes) garnets (X3Al2Si3O12, with X = Fe, Ca, Mg, Mn respectively), by means of computer simulations of perfect and defective lattices in the static limit. The simulations use a consistent set of interatomic potentials to describe the non-Coulombic interactions between the ions, and take explicit account of lattice relaxation associated with trace element incorporation. The calculated relaxation (strain) energies Urel are compared to those obtained using the Brice (1975) model of lattice relaxation, and the results compared to experimental garnet-melt trace element partitioning data interpreted using the same model. Simulated Urel associated with a wide range of homovalent (Ni, Mg, Co, Fe, Mn, Ca, Eu, Sr, Ba) and charge-compensated heterovalent (Sc, Lu, Yb, Ho, Gd, Eu, Nd, La, Li, Na, K, Rb) substitutions onto the garnet X-sites show a near-parabolic dependence on trace element radius, in agreement with the Brice model. From application of the Brice model we derived apparent X-site Young’s moduli EX(1+, 2+, 3+) and the ‘ideal’ ionic radii r0(1+, 2+, 3+), corresponding to the minima in plots of Urel vs. radius. For both homovalent and heterovalent substitutions r0 increases in the order Py–Alm–Spes–Gros, consistent with crystallographic data on the size of garnet X-sites and with the results of garnet-melt partitioning studies. Each end-member also shows a marked increase in both the apparent EX and r0 with increasing trace element charge (Zc). The increase in EX is consistent with values obtained by fitting to the Brice model of experimental garnet-melt partitioning data. However, the increase in r0 with increasing Zc is contrary to experimental observation. To estimate the influence of melt on the energetics of trace element incorporation, solution energies (Usol) were calculated for appropriate exchange reactions between garnet and melt, using binary and other oxides to simulate cation co-ordination environment in the melt. Usol also shows a parabolic dependence on trace element radius, with inter-garnet trends in EX and r0 similar to those found for relaxation energies. However, r0(i+) obtained from minima in plots of Usol vs. radius are located at markedly different positions, especially for heterovalent substitutions (i = 1, 3). For each end-member garnet, r0 now decreases with increasing Zc, consistent with experiment. Furthermore, although different assumptions for trace element environment in the melt, e.g., REE3+ (VI) vs. REE3+ (VIII), lead to parabolae with differing curvatures and minima, relative differences between end-members are always preserved. We conclude that: 1. The simulated variation in r0 and EX between garnets is largely governed by the solid phase. This stresses the overriding influence of crystal local environment on trace element partitioning. 2. Simulations suggest r0 in garnets varies with trace element charge, as experimentally observed. 3. Absolute values of r0 and EX can be influenced by the presence and structure of a coexisting melt. Thus, quantitative relations between r0, E and crystal chemistry should be derived from well-constrained systematic mineral-melt partitioning studies, and cannot be predicted from crystal-structural data alone.

Calculated solution energies of heterovalent cations in forsterite and diopside: Implications for trace element partitioning

Solution energies are calculated for a wide range of heterovalent impurities in forsterite and diopside, using atomistic simulation techniques and a consistent set of interatomic potentials to represent the non-Coulombic interactions between the ions. The calculations allow explicitly for ionic relaxation. Association between a charged defect and its compensating defect (s) cannot be neglected at low temperatures; however, at concentrations of 10–100 ppm a large proportion will be dissociated at temperatures above 1000 K. The variation of calculated solution energy with ion size reflects the variation in the relaxation energies, and often shows a parabolic variation with ionic radius. For the pure mineral, the calculated solution energies always show a minimum at a radius corresponding to that of the host cation; for impure clinopyroxene (with <1 Ca per formula unit) the optimum cation radius varies with composition, as observed experimentally. A marked variation in the calculated solution energies for trivalent trace elements is predicted depending on which alkali-metal cation is the compensating defect. At the M1 site in diopside the lowest calculated solution energy is for trivalent ions coupled with the substitution of a Na+ ion on the M2 site, i.e. M3+(M1)Na+(M2); at M2 it is X3+(M2)Na+(M2). X3+(M2)Li+(M1) is the lowest energy pairing for forsterite.

Isovalent trace element partitioning between minerals and melts - a computer simulation study

Abstract We present a new approach for the rationalisation of trace element partitioning between silicate melts and minerals, which is not based on the empirical, parameterised continuum models in common use. We calculate the energetics of ion substitution using atomistic simulation techniques, which include an explicit evaluation of the relaxation energy (strain energy) contribution to this process. Solution energies are estimated for isovalent impurities in CaO, diopside, orthoenstatite, and forsterite. These show a parabolic dependence on ionic radius, similar to the variation of mineral-melt partition coefficients with ionic radius. The success of the empirical models, which often include only the strain energy, appear to have been due to the partial cancellation of energy terms, and to the empirical fitting of the parameters included in these models. Our approach can be readily extended to aliovalent substitution.

Guest‐Adaptable and Water‐Stable Peptide‐Based Porous Materials by Imidazolate Side Chain Control

The peptide-based porous 3D framework, ZnCar, has been synthesized from Zn2+ and the natural dipeptide carnosine (β-alanyl-L-histidine). Unlike previous extended peptide networks, the imidazole side chain of the histidine residue is deprotonated to afford Zn–imidazolate chains, with bonding similar to the zeolitic imidazolate framework (ZIF) family of porous materials. ZnCar exhibits permanent microporosity with a surface area of 448 m2 g−1, and its pores are 1D channels with 5 Å openings and a characteristic chiral shape. This compound is chemically stable in organic solvents and water. Single-crystal X-ray diffraction (XRD) showed that the ZnCar framework adapts to MeOH and H2O guests because of the torsional flexibility of the main His-β-Ala chain, while retaining the rigidity conferred by the Zn–imidazolate chains. The conformation adopted by carnosine is driven by the H bonds formed both to other dipeptides and to the guests, permitting the observed structural transformations.

Displacement cascades in Gd2Ti2O7 and Gd2Zr2O7: a molecular dynamics study

We report molecular dynamics simulations of the production of radiation cascades in two pyrochlore compounds that have been proposed as possible materials for high level radioactive waste storage. There are clear differences between the two systems that support the results of recent high energy ion bombardment experiments, in which pyrochlores were increasingly radiation resistant with increasing Zr content.

Non-hexagonal ice at hexagonal surfaces: the role of lattice mismatch

It has long been known that ice nucleation usually proceeds heterogeneously on the surface of a foreign body. However, little is known at the microscopic level about which properties of a material determine its effectiveness at nucleating ice. This work focuses on the long standing, conceptually simple, view on the role of a good crystallographic match between bulk ice and the underlying substrate. We use grand canonical Monte Carlo to generate the first overlayer of water at the surface and find that the traditional view of heterogeneous nucleation does not adequately account for the array of structures that water may form at the surface. We find that, in order to describe the structures formed, a good match between the substrate and the nearest neighbour oxygen-oxygen distance is a better descriptor than a good match to the bulk ice lattice constant.

Ab initio calculation of phase diagrams of ceramics and minerals

A range of methods, based on Monte Carlo and lattice dynamics simulations, are presented for the calculation of the thermodynamic properties of solid solutions and phase diagrams. These include Monte Carlo simulations with the explicit interchange of cations, the use of the semigrand-canonical ensemble and configurational bias techniques, hybrid Monte Carlo/molecular dynamics, and a new configurational lattice dynamics technique. It is crucial to take account of relaxation of the local atomic environment and vibrational effects. Examples studied are (i) the enthalpy and entropy of mixing, the phase diagram and the spinodal of MnO/MgO. The available experimental data disagree widely for this system; (ii) the enthalpy of mixing of CaO/MgO, where the size mismatch between the cations is considerably larger than in (i); (iii) the postulated high-pressure orthorhombic to cubic phase transition in (Mg,Mn)SiO3 perovskite, where we show that impurity cations can have a much larger effect than that expected from a mean-field treatment or linear interpolation between end-member compounds.

Simulation of mineral solid solutions at zero and high pressure using lattice statics, lattice dynamics and Monte Carlo methods

We discuss how two techniques, based on (1) lattice statics/lattice dynamics simulations and (2) Monte Carlo methods may be used to calculate the thermodynamic properties of oxide mixtures at zero and high pressure. The lattice statics/lattice dynamics calculations involve a full free energy structural optimization of each of a number of configurations, followed by thermodynamic averaging. Strategies for generating a suitable set of configurations are discussed. We compare results obtained by random generation with those obtained using radial distribution functions or explicit symmetry arguments to obtain approximate or exact weightings respectively for individual configurations. The Monte Carlo simulations include the explicit interchange of cations and use the semigrand canonical ensemble for chemical potential differences. Both methods are readily applied to high pressures and elevated temperatures without the need for any new parametrization. Agreement between the two techniques is better at high pressures where anharmonic terms are smaller. We compare in detail the use of each technique for properties such as enthalpies, entropies, volume and free energies of mixing at zero and high pressure and thus calculation of the phase diagram. We assess the vibrational contributions to these quantities and compare results with those in the dilute limit. The techniques are illustrated throughout using MnO?MgO and should be readily applicable to more complicated systems.

Ordering in spinels—A Monte Carlo study

Abstract We have extended a recently developed Monte Carlo technique which includes explicit exchange as well as movement of ions to systems involving heterovalent exchange. These Monte Carlo computer simulations, based on analytical inter-atomic potentials, are capable of providing detailed quantitative information concerning the thermodynamics of ordering of spinel (MgAl2O4), gahnite (ZnAl2O4), hercynite (FeAl2O4), NiAl2O4, and magnesioferrite (MgFe2O4) over a range of pressures and temperatures. At all temperatures and pressures ionic relaxation, lattice vibrations, and pressure are explicitly taken into account. Each compound has a larger expansion coefficient and smaller bulk modulus in the normal than in the inverse spinel structure. We predict only a small variation of order parameter with pressure, and that this will be more pronounced for inverse than normal spinels. We examine, briefly, the consequences of our results for the kinetics of cation ordering in these solids.