Diffusion In Silicates Research Articles

Bridging the water solubility and ion diffusivity in the mantle silicates by a thermodynamic model

Water solubility in Mg-endmember silicates is suggested to correlate with cation diffusivity. This study proposes a thermodynamic model by introducing the concept of transient Frenkel defect for Mg ions to quantify the relationship between water solubility and Mg diffusivity in mantle silicates. The formation of the Mg transient Frenkel defect is regarded as the escape of Mg from Mg-O polyhedron, and the concentration of Mg transient vacancy is considered as its statistical probability in silicate minerals. The proposed thermodynamic model reveals that the formation energy for Mg transient vacancy (ΔGtr) is approximately ΔG/6 (ΔG is activation energy for Mg diffusion in silicates) for silicates with Mg-O6 octahedra, such as enstatite, forsterite, wadsleyite, and ringwoodite, and 5ΔG/12 for bridgmanite and post-perovskite. This observation implies a possible diffusion mode of Mg through transient vacancies. Our model connects water solubility and ion diffusivity in silicates.

Rare earth element diffusion in natural enstatite

Chemical diffusion coefficients of La, Nd, Eu, Gd, and Yb in natural enstatite have been measured at 850–1250 °C and 1 atm. Anhydrous diffusion experiments were run in Pt capsules in air, or in sealed silica glass capsules under an iron–wüstite (IW) solid buffer. The sources of diffusant were pre-reacted mixtures of synthetic enstatite powder and microcrystalline rare-earth aluminate garnet. Rutherford Backscattering Spectrometry (RBS) was used to measure diffusion profiles. For Gd diffusion in air over the temperature range 1000–1250 °C, the following Arrhenius relation is found for diffusion normal to (210): D Gd,air = 2.55 × 10 - 9 exp ( 321 ± 85 kJ mol - 1 / RT ) m 2 s - 1 . There is no significant difference between Gd diffusion in air and under IW-buffered conditions. Behavior similar to Gd is also noted for Nd. The Arrhenius relationship for Eu diffusion in enstatite, normal to (210) and at 850–1150 °C and IW-buffered conditions, is D Eu,IW = 6.93 × 10 - 6 exp ( - 384 ± 29 kJ mol - 1 / RT ) m 2 s - 1 . For Eu diffusion in air over the temperature range 1000–1200 °C for the same orientation, the following Arrhenius relation is found: D Eu,air = 1.70 × 10 - 8 exp ( - 350 ± 42 kJ mol - 1 / RT ) m 2 s - 1 . For Eu diffusion under IW-buffered conditions and for experiments run in air, diffusivities normal to (001) are similar to those for diffusion normal to (210). Eu diffusion under IW-buffered conditions is more than an order of magnitude faster than Eu diffusion in air. It is likely that majority of Eu is in the divalent state for diffusion under IW-buffered conditions, but Eu is in the trivalent state for diffusion in air. In the case of Nd and Gd, where valence state does not change under the investigated fO 2 conditions, diffusivities measured for experiments run both in air and under IW-buffered conditions are comparable to those obtained for trivalent Eu. Further, measurements of La, Nd, Eu +3, Gd, and Yb diffusion suggest that diffusion of trivalent REE in enstatite is not sensitive to ionic size, in contrast to that observed for REE diffusion in diopside [Van Orman, J.A., Grove, T.L., Shimizu, N., 2001. Rare earth element diffusion in diopside; influence of temperature, pressure, and ionic radius, and an elastic model for diffusion in silicates. Contrib. Mineral. Petrol. 141, 687–703]. These differences in diffusive behavior of REE between diopside and enstatite, as well as Eu 2+ and Eu 3+ in enstatite, can result in significant REE fractionation between coexisting pyroxenes during partial melting, melt migration, and subsolidus reequilibration processes in the Earth’s mantle and that of the Moon.

Transport of oxygen in silicate glasses

Oxygen can be transported through silicate glasses and melts by water, oxygen and silicon monoxide molecules. These molecules dissolve and diffuse in the open glass structure, and oxygen atoms in them can exchange with the oxygen atoms in the silicate silicon–oxygen network. A large variety of measurements of water diffusion in silicates can be understood with the diffusion-reaction and exchange mechanisms of dissolved water molecules. The permeation measurements by Norton of oxygen through silica glass demonstrate the dissolution and diffusion of oxygen molecules. However, measurements of oxygen diffusion with 18O isotope have given widely different results in different studies. The main reason for these differences is the influence of trace amounts of residual water in the oxygen gas and in the glasses. Thus these isotopic exchange measurements of oxygen diffusion in glasses can be understood and interpreted only when the amount of residual water is measured and controlled. Surface exchange between oxygen atoms in the gas phase and the glass is fast; the reason for a lower concentration ratio of oxygen isotope in the glass surface than in the gas phase is not a slow surface reaction but a slow internal exchange between oxygen atoms in dissolved molecules and network oxygen atoms. Diffusion of oxygen in silicates at temperatures above about 1300°C with high activation energy results from diffusion of dissolved SiO molecules, and is related to viscous flow.

Rare earth element diffusion in diopside: influence of temperature, pressure, and ionic radius, and an elastic model for diffusion in silicates

Volume diffusion rates for five rare earth elements (La, Ce, Nd, Dy, and Yb) have been measured in single crystals of natural diopside at pressures of 0.1 MPa to 2.5 GPa and temperatures of 1,050 to1,450 °C. Polished, pre-annealed crystals were coated with a thin film of rare earth element oxides, then held at constant temperature and pressure for times ranging from 20 to 882 h. Diffusion profiles in quenched samples were measured by SIMS (secondary ion mass spectrometry) depth profiling. At 1 atm pressure, with the oxygen fugacity controlled near the quartz–fayalite–magnetite buffer, the following Arrhenius relations were obtained for diffusion normal to (001) (diffusion coefficient D in m2/s): log10 D Yb =(–4.64±0.42)–(411±12 kJ/mol/2.303RT); log10 D Dy =(–3.31±1.44)–(461±41 kJ/mol/2.303RT); log10 D Nd =(–2.95±2.64)–(496±77 kJ/mol/2.303RT); log10 D Ce =(–4.10±1.08)–(463±31 kJ/mol/2.303RT); log10 D Lu =(–4.22±2.66)–(466±78 kJ/mol/2.303RT). Diffusion rates decrease significantly with increasing ionic radius, with La a factor of ~35 slower than Yb. The relationship between diffusivity and ionic radius is consistent with a model in which elastic strain plays a critical role in governing the motion of an ion through the crystal lattice. Activation volumes for Yb and Ce diffusion, at constant temperature and oxygen fugacity, are 9.0±2.0 cm3/mol and 8.9±3.2 cm3/mol, respectively, corresponding to an order of magnitude decrease in diffusivity as pressure is increased from 0 to 3 GPa at 1,200 °C. Diffusion of Nd is such that grain-scale isotopic equilibrium in the mantle can be achieved in ~1 My under conditions near the peridotite solidus (~1,450 °C at 2.5 GPa). The equilibration time is much longer under P, T conditions of the lithospheric mantle or at the eclogite solidus (~1 Gy at 1.5 GPa and 1,150 °C). Because of the relatively strong decrease in diffusivity with pressure (two orders of magnitude between 2.5 and 15 GPa along an adiabatic temperature gradient), Nd transport in clinopyroxene will be effectively frozen at pressures approaching the transition zone, on time scales less than 100 My. Rare earth element diffusion rates are slow enough that significant disequilibrium uptake of REE by growing clinopyroxene phenocrysts may be preserved under natural conditions of basalt crystallization. The relative abundances and spatial distributions of REE in such crystals may provide a sensitive record of the cooling and crystallization history of the host lava.

Dislocation and diffusion creep of synthetic anorthite aggregates

Synthetic fine‐grained anorthite aggregates were deformed at 300 MPa confining pressure in a Paterson‐type gas deformation apparatus. Creep tests were performed at temperatures ranging from 1140 to 1480 K, stresses from 30 to 600 MPa, and strain rates between 2×10−6 and 1×10−3 s−1. We prepared samples with water total contents of 0.004 wt % (dry) and 0.07 wt % (wet), respectively. The wet (dry) material contained <0.7 (0.2) vol % glass, associated with fluid inclusions or contained at triple junctions. The arithmetic mean grain size of the specimens varied between 2.7±0.1 μm for the dry material and 3.4±0.2 μm for wet samples. Two different creep regimes were identified for dry and wet anorthite aggregates. The data could be fitted to a power law. At stresses >120 MPa we found a stress exponent of n = 3 irrespective of the water content, indicating dislocation creep. However, the activation energy of wet samples is 356±9 kJ mol−1, substantially lower than for dry specimens with 648±20 kJ mol−1. The preexponential factor is log A = 2.6 (12.7) MPa−n s−1 for wet (dry) samples. Microstructural observations suggest that grain boundary migration recrystallization is important in accommodating dislocation creep. In the low‐stress regime we observed a stress exponent of n = 1, suggesting diffusion creep. The activation energies for dry and wet samples are 467 ±16 and 170 ± 6 kJ mol−1, respectively. Log A is 12.1 MPa−n μmm s−1 for the dry material and 1.7 MPa−n μmm s−1 for wet anorthite. The data show that the strengths of anorthite aggregates decrease with increasing water content in both the dislocation and diffusion creep regimes. A comparison of the creep data of synthetic plagioclase from this study with published data for feldspar, olivine, and quartz indicates a linear relationship between activation energy and log A similar to the suggested compensation law for diffusion in silicates.

Empirical constraints on closure temperatures from a single diffusion coefficient

The elucidation of thermal histories by geochronological and isotopic means is based fundamentally on solid-state diffusion and the concept of closure temperatures. Because diffusion is thermally activated, an analytical solution of the closure temperature (Tc*) can only be obtained if the diffusion coefficient D of the diffusion process is measured at two or more different temperatures. If the diffusion coefficient is known at only one temperature, however, the true closure temperature (Tc*) cannot be calculated analytically because there exist an infinite number of possible (apparent) closure temperatures (T¯c) which can be generated by this single datum. By introducing further empirical constraints to limit the range of possible closure temperatures, however, mathematical analysis of a modified form of the closure temperature equation shows that it is possible to make both qualitative and quantitative estimates of Tc* given knowledge of only one diffusion coefficient DM measured at one temperature TM. Qualitative constraints of the true closure temperature Tc* are obtained from the shapes of curves on a graph of the apparent Tc (T¯c) vs. activation energy E, in which each curve is based on a single diffusion coefficient measurement DM at temperature TM. Using a realistic range of E, the concavity of the curve shows whether TM is less than, approximately equal to, or greater than Tc*. Quantitative estimates are obtained by considering two dimensionless parameters [lnERT^c vs. Tc*/TM] derived from these curves. When these parameters are plotted for known argon diffusion data and for a given diffusion size and cooling rate, it is found that the resultant curves are almost identical for all of the commonly dated K–Ar minerals – biotite, phlogopite, muscovite, hornblende and orthoclase – in spite of differences in their diffusion parameters. A common curve for Ar diffusion can be derived by least-squares fitting of all the Ar diffusion data and provides a way of predicting a “model” closure temperature Tcm from a single diffusion coefficient DM at temperature TM. Preliminary diffusion data for a labradorite lead to a Tcm of 507 ± 17 °C and a corresponding activation energy of about 65 kcal/mol, given a grain size of 200 μm and a cooling rate of 5 °C/Ma. Curves for He diffusion in silicates (augite, quartz and sanidine) also overlap to a significant degree, both among themselves and with the Ar model curve, suggesting that a single model curve may be a good representation of noble gas closure temperatures in silicates. An analogous model curve for a selection of 18O data can also be constructed, but this curve differs from the Ar model curve. A single model curve for cationic species does not appear to exist, however, suggesting that chemical bonding relationships between the ionic size/charge and crystal structure may influence the closure temperatures of diffusing cations. An indication of the degree of overlap among the various curves for Ar, He, 18O and cations is also obtained by considering the dimensionless parameter E/RTc*; for the noble gases and 18O, E/RTc* values for the respective minerals are very similar, whereas for cations, there is significant dispersion. Given these constraints, this may be a potential method of estimating closure temperatures for certain diffusing species when there are limited diffusion data.

Silicon diffusion in silicate minerals

Recently obtained silicon self-diffusion data, D Si = D 0exp(− ΔH/RT) , in silicates (quartz, itreous silica, forsterite, San Carlos olivine and diopside) show a compensation law that is a linear relation, log D 0 =logD * +ΔH/2.303RT * . We find ΔH = 532.6 + 30.4 log D 0 ( ΔH in kJ/mol and D 0 in cm 2/s), which corresponds to logD * ⋍ #x02212; 17.5 and T * ⋍ 1588K.D * represents a common value of D Si for all these silicates at T * , but also the value of D Si at ΔH = 0. It has, therefore, a pure entropic signification: D * = fa 2νexp(ΔS/R) ; f is a geometrical factor, a the jump distance and νthe Si-O vibrational stretching optic frequency almost common to all these silicates. Despite the wide range of enthalpies for Si diffusion in silicates, we propose that the compensation law outlines a unique mechanism for Si migration in minerals with structures based on the SiO 4 tetrahedron.

Impact ages of meteorites: A synthesis

Abstract—Isotopic ages of meteorites that indicate chronometer resetting due to impact heating are summarized. Most of the ages were obtained by the39Ar‐40Ar technique, but several Rb‐Sr, Pb‐Pb, and Sm‐Nd ages also suggest some degree of impact resetting. Considerations of experimental data on element diffusion in silicates suggest that various isotopic chronometers ought to differ in their ease of resetting during shock heating in the order K‐Ar (easiest), Rb‐Sr, Pb‐Pb, and Sm‐Nd, which is approximately the order observed in meteorites. Partial rather than total chronometer resetting by impacts appears to be the norm; consequently, interpretation of the event age is not always straightforward.Essentially all39Ar‐40Ar ages of eucrites and howardites indicate partial to total resetting in the relatively narrow time interval of 3.4–4.1 Ga ago (1 Ga = 109years). Several disturbed Rb‐Sr ages appear consistent with this age distribution. This grouping of ages and the brecciated nature of many eucrites and all howardites argues for a large‐scale impact bombardment of the HED parent body during the same time period that the Moon received its cataclysmic bombardment. Other meteorite parent bodies such as those of mesosiderites, some chondrites, and IIE irons also may have experienced this bombardment. These data suggest that the early bombardment was not lunar specific but involved much of the inner Solar System, and may have been caused by breakup of a larger planetismal.Although a few chondrites show evidence of age resetting ∼3.5–3.9 Ga ago, most impact ages of chondrites tend to fall below 1.3 Ga in age. A minimum of ∼4 impact events, including events at 0.3, 0.5, 1.2, and possibly 0.9 Ga appear to be required to explain the younger ages of H, L, and LL chondrites, although additional events are possible. Most L chondrites show evidence of shock, and the majority of39Ar‐40Ar ages of L chondrites fall near 0.5 Ga. The L chondrite parent body apparently experienced a major impact at this time, which may have disrupted it.The observations (1) that lunar highland rocks experienced major impact resetting of various isotopic chronometers ∼3.7–4.1 Ga ago; (2) that the HED parent body experienced widespread impact resetting of the K‐Ar chronometer but only modest disturbance of other isotopic systems, during a similar time period; (3) that ordinary chondrite parent bodies show much more recent and less extensive impact resetting; and (4) that impacts, which initiated cosmic‐ray exposure of most stone meteorites almost never reset isotopic chronometers, may all be a consequence of relative parent body size. Greater degrees of isotopic chronometer resetting occur in larger and warmer impact ejecta deposits that cool slowly. The relatively greater size of bodies like the Moon and Vesta (assumed to be the parent asteroid of HED meteorites) both permit such favorable ejecta deposits to occur more easily compared to smaller parent bodies (generally assumed for chondrites) and also protect parent objects from collisional disruption. Thus, impacts on larger bodies would tend to more easily reset chronometers, consistent with the observed relative ease of resetting of Moon (easiest), HED, chondrites and of K‐Ar (easiest), Rb‐Sr, other chronometers. In contrast, the more recent impact ages of chondrites are postulated to represent collisional disruption of smaller parent objects whose fragments are more readily removed from the meteorite source reservoirs. Impacts that initiate cosmic‐ray exposure are mostly small in scale and produce little heating.

Diffusion in Mg2SiO4 polymorphs and chemical heterogeneity in the mantle transition zone

DIFFUSION in silicates plays a key role in a number of processes in the Earth's mantle, including viscous flow1–4, electrical conductance5–8 and the homogenization of chemical heterogeneities. Although cation diffusion rates have been measured in olivine at high pressures9,10, no data exist on the chemical transport properties of the silicate phases thought to predominate in the transition zone of the mantle (from 400 to 700 km depth). Here we present measurements of cation diffusion in the α-olivine phase and high-pressure β- and γ-spinel phases of Mg2SiO4 at pressures up to 14 GPa. We find that diffusion rates in both high-pressure phases are about three orders of magnitude faster than that of olivine. When coupled with convective thinning, these faster diffusion rates suggest that the transition zone is more efficient at mixing chemical heterogeneities than the olivine-dominated upper mantle. Furthermore, we calculate that the minimum size of chemical heterogeneities in the transition zone should be of the order of metres.

The effect of hydrogen on oxygen diffusion in quartz: evidence for fast proton transients?

The importance of water in modifying the physico-chemical and mechanical properties of minerals has long been recognized. Water dramatically weakens quartz and enhances oxygen diffusion in silicates at high pressures and temperatures, with important geological consequences, but the underlying mechanisms are poorly understood. Recent attention has focused on the role of H2 and O2 in these mechanisms. Here we report the results of a study of the diffusion of oxygen in quartz at high pressure and temperature in the presence of water and of dry H2 gas, and compare the results with those of experiments in the presence of dry O2 gas. We conclude that oxygen diffusion is inhibited in the presence of dry H2 but enhanced in the presence of H2O, and deduce that fast H+ transients rather than H2 movement may be responsible for oxygen diffusion enhancement in framework silicates. Because of their high mobility, such transients may well be experimentally unquenchable within the silicate framework.

Multicomponent exchange and diffusion in silicates

The treatment of multicomponent diffusion and exchange in silicates is developed. An ionic diffusion model, similar to one proposed by workers in ceramics, is described and applied to the evaluation of diffusion coefficients, D ij , from tracer diffusion values. The general problem of cation exchange between complex silicates is then solved exactly, with particular emphasis on 1. (a) useful approximations to the exact solutions; 2. (b) the influence of the kinetic and thermodynamic parameters on the diffusion process; and 3. (c) the limiting cases, which enable the complex silicates to be treated as binary systems, for the purposes of computing diffusion profiles.

A Discussion on natural strain and geological structure - Diffusion in metamorphic tectonites: lattice-fixed reference frames

The nature of volume diffusion during metamorphism may be studied by examining compositional zoning in metamorphic minerals. Garnets with sharp optical zones and internal fabrics related to deformation are of special interest, because they provide a link between partitioning by growth and by diffusion. Diffusion in the almandine-rich garnets of pelitic schists involves, at the very least, the migration of four ionic components (Fe2+, Mn2+, Mg2+ and Ca2+). Because of the possible occurrence of uphill diffusion and other phenomena we do not intuitively associate with diffusion, the search for evidence of volume diffusion must be preceded by a careful theoretical and experimental examination of diffusion in multicomponent minerals. The theoretical and experimental investigation of diffusion in silicates may be simplified by: (1) the choice of ions as components in the flux equations; (2) the construction of lattice-fixed reference frames to reduce the number of flux equations and diffusion coefficients. Flux equations are developed specifically for diffusion via ionized vacancies, but they may be easily modified to treat diffusion via neutral vacancies or by one to one exchange of ions. Methods are presented for solving the flux equations under the constraint that the crystal remain electrically neutral during diffusion. The transition-state theory of Lane & Kirkaldy (1964), which allows the calculation of the matrix of chemical diffusion coefficients from the mobility of individual ions, is adapted to the particular lattice-fixed frames developed here.