Molecular dynamics simulations of pressure and temperature effects on MgSiO3 and Mg2SiO4 melts and glasses

Ab-initio interionic potentials for Mg²⁺, Si⁴⁺, and O^2– have been used in molecular dynamics (MD) simulations to investigate diffusivity changes, pressure-induced structural transitions, and temperature effects on polymerization in MgSiO₃ and Mg₂SiO₄ melts and glasses. The potential gives reasonable agreement with the 0.1 MPa radial distribution function of MgSiO₃ glass. Maxima in the diffusion coefficients of Si⁴⁺ and O^2– occur as pressure is increased on the MgSiO₃ melt. The controlling structural mechanism for this behavior is the Q¹ species of SiO₄ tetrahedra. Mg²⁺ diffusion coefficients decrease monotonically with pressure in both melt compositions. Increasing Mg²⁺ coordination number and population of 3- and 4-membered SiO₄ rings with pressure combine to hinder translation of the Mg²⁺ ions. The dominant changes in structure with pressure are a decrease in the intertetrahedral (Si-O--Si) angle up to approximately 4 g/cm³ and coordination changes of the ions above this density. Temperature effects on viscosity in these simulated melts are indirectly studied by analyzing polymerization changes with temperature. Polymerization and coordination numbers increase with decreasing temperature and a small quench rate effect is observed. Fair agreement is found between the MD simulations and experimental equation of state for Mg₂SiO₄, but the equation of state predictions for MgSiO₃ melts are much less accurate. The zero pressure volume, V ₀, is significantly higher and K ₀ is lower in the simulations than empirical values. The inadequacies reflect error in using the ionic approximation for polymerized systems and a need to collect more data for a variety of molecular configurations in the development of ab-initio potentials.     

Surface chemistry and dissolution kinetics of glassy rocks at 25°C

The weathering rates and mechanisms of three types of glassy rocks were investigated experimentally at 25 °C, pH 1.0 to 6.2, and reaction times as much as to 3 months. Changes in major element chemistry were monitored concurrently as a function of time in the aqueous solution and within the near surface region of the glass. Leach profiles, obtained by a HF leaching technique, displayed near-surface zones depleted in major cations. These zones increased in depth with increasing time and decreasing pH of reactions. Release rates into the aqueous solution were parabolic for Na and K and linear for Si and Al. A coupled weathering model, involving surface dissolution with concurrent diffusion of Na, K, and Al, produced a mass balance between the aqueous and glass phases. Steady state conditions are reached at pH 1.0 after approximately 3 weeks of reaction. Steady-state is not reached even after 3 months at pH 6.2.An interdiffusion model describes observed changes in Na diffusion profiles for perlite at pH 1.0. The calculated Na self-diffusion coefficient of 5 × 10^?19 cm²·s^?1 at 25°C approximates coefficients extrapolated from previously reported high temperature data for obsidian. The self-diffusion coefficient for H₃O⁺, 1.2 × 10^?20 cm²·s^?1, is similar to measured rates of water diffusion during hydration of obsidian to form perlite.     

Experimental studies on the solid state diffusion of Cu + In in ZnS and on “Disease”, DIS (Diffusion Induced Segregations), in sphalerite and their geological applications

Isothermal solid state experiments on the diffusion of Cu, Fe, Zn and In and related effects have been carried out in sphalerite single crystals. The driving force for the diffusion and corresponding reactions are chemical potential gradients which are established by differences in sulfur fugacity, oxygen fugacity and the chemical activity between sulfide powders as metal sources and receptor crystals.Studies in the system ZnS-CuInS₂ show replacement rims in sphalerite produced by the formation of solid solutions between ZnS and CuInS₂. These differences reflect the extent of mutual solid solution. The composition profiles of these rims at different temperatures and sulfur fugacities are calculated to diffusion coefficients for the coupled substitution of Cu⁺ + In³⁺ versus 2 Zn²⁺. The interdiffusion coefficients of (Cu + In) in Fe-free sphalerite at the Fe/FeS sulfur fugacity of the sources obey to the relation:     

Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep

Diffusion coefficients of Cr and Al in chromite spinel have been determined at pressures ranging from 3 to 7 GPa and temperatures ranging from 1,400 to 1,700°C by using the diffusion couple of natural single crystals of MgAl₂O₄ spinel and chromite. The interdiffusion coefficient of Cr–Al as a function of Cr# (=Cr/(Cr + Al)) was determined as D _Cr–Al = D ₀ exp {−(Q′ + PV*)/RT}, where D ₀ = exp{(10.3 ± 0.08) × Cr#^0.54±0.02} + (1170 ± 31.2) cm²/s, Q′ = 520 ± 81 kJ/mol at 3 GPa, and V* = 1.36 ± 0.25 cm³/mol at 1,600°C, which is applicable up to Cr# = 0.8. The estimation of the self-diffusion coefficients of Cr and Al from Cr–Al interdiffusion shows that the diffusivity of Cr is more than one order of magnitude smaller than that of Al. These results are in agreement with patterns of multipolar Cr–Al zoning observed in natural chromite spinel samples deformed by diffusion creep.     

Fe–Mg interdiffusion rates in clinopyroxene: experimental data and implications for Fe–Mg exchange geothermometers

Chemical interdiffusion of Fe–Mg along the c-axis [001] in natural diopside crystals (X _Di = 0.93) was experimentally studied at ambient pressure, at temperatures ranging from 800 to 1,200 °C and oxygen fugacities from 10^?11 to 10^?17 bar. Diffusion couples were prepared by ablating an olivine (X _Fo = 0.3) target to deposit a thin film (20–100 nm) onto a polished surface of a natural, oriented diopside crystal using the pulsed laser deposition technique. After diffusion anneals, compositional depth profiles at the near surface region (~400 nm) were measured using Rutherford backscattering spectroscopy. In the experimental temperature and compositional range, no strong dependence of D ^Fe–Mg on composition of clinopyroxene (Fe/Mg ratio between Di₉₃–Di₆₅) or oxygen fugacity could be detected within the resolution of the study. The lack of fO₂-dependence may be related to the relatively high Al content of the crystals used in this study. Diffusion coefficients, D ^Fe–Mg, can be described by a single Arrhenius relation with $$D^{{{\text{Fe}} - {\text{Mg}}}} = 2. 7 7\pm 4. 2 7\times 10^{ - 7} {\text{exp(}}-3 20. 7\pm 1 6.0{\text{ kJ}}/{\text{mol}}/{\text{RT)m}}^{ 2} /{\text{s}}.$$ D ^Fe–Mg in clinopyroxene appears to be faster than diffusion involving Ca-species (e.g., D ^Ca–Mg) while it is slower than D ^Fe–Mg in other common mafic minerals (spinel, olivine, garnet, and orthopyroxene). As a consequence, diffusion in clinopyroxene may be the rate-limiting process for the freezing of many geothermometers, and compositional zoning in clinopyroxene may preserve records of a higher (compared to that preserved in other coexisting mafic minerals) temperature segment of the thermal history of a rock. In the absence of pervasive recrystallization, clinopyroxene grains will retain compositions from peak temperatures at their cores in most geological and planetary settings where peak temperatures did not exceed ~1,100 °C (e.g., resetting may be expected in slowly cooled mantle rocks, many plutonic mafic rocks, or ultra-high temperature metamorphic rocks).     

Diffusion and viscosity of Mg2SiO4 liquid at high pressure from first-principles simulations

We investigate two key transport properties, self-diffusion and viscosity, of Mg₂SiO₄ liquid as a function of temperature and pressure using density functional theory-based molecular dynamics method. Liquid dynamics in a 224-atom supercell was captured in equilibrium simulations of relatively long durations (50-300 ps) to obtain an acceptable convergence. Our results show that Mg and Si are, respectively, the most and least mobile species at most conditions studied and all diffusivities become similar at high pressure. With increasing temperature from 2200 to 6000 K at ambient pressure, the self-diffusivities increase by factors of 25 (Mg), 80 (Si) and 65 (O), and the viscosity decreases by a factor of 30. The predicted temperature variations of all transport coefficients closely follow the Arrhenian law. However, their pressure variations show a significant non-Arrhenian behavior and also are sensitive to temperature. At 3000 K, the diffusivity (viscosity) decreases (increases) by more than one order of magnitude between 0 and 50 GPa with their activation volumes increasing on compression. Over the entire mantle pressure range, the variations at 4000 K are of two orders of magnitude with nearly constant activation volumes whereas the variations at 6000 K are within one order of magnitude with decreasing activation volumes. The predicted complex dynamical behavior of Mg₂SiO₄ liquid can be associated with the structural changes occurring on compression. We also estimate the diffusivity and viscosity profiles along a magma ocean isentrope, which suggest that the melt transport properties vary modestly over the relevant magma ocean depth ranges.     

An experimental study of Ca-(Fe,Mg) interdiffusion in silicate garnets

Ca-(Fe,Mg) interdiffusion experiments between natural single crystals of grossular (Ca_2.74Mg_0.15 Fe_0.23Al_1.76Cr_0.04Si_3.05O₁₂) and almandine (Ca_0.21Mg_0.40 Fe_2.23Mn_0.13Al_2.00Cr_0.08Si_2.99O₁₂ or Ca_0.43Mg_0.36Fe_2.11 Al_1.95Si_3.04O₁₂), were undertaken at 900–1100 °C and 30 kbar, and pressures of 15.0–32.5 kbar at 1000 °C. Samples were buffered by Fe/FeO in most cases. Diffusion profiles were determined by electron microprobe. Across the experimental couples the interdiffusion coefficients (D˜) were almost independent of composition. The diffusion rates in an unbuffered sample were significantly faster than in buffered samples. The temperature dependence of the D˜ (Ca-Fe,Mg) interdiffusion coefficients may be described by

Temperature-jump induced cation exchange kinetics in (Co<Subscript>0.1</Subscript>Mg<Subscript>0.9</Subscript>)<Subscript>2</Subscript>SiO<Subscript>4</Subscript> olivine: an in situ optical spectroscopic study

In the olivine crystal structure, cations are distributed over two inequivalent octahedral sites, M1 and M2. Kinetics of cation exchange between the two octahedral sites in (Co_0.1Mg_0.9)₂SiO₄ single crystal have been studied in the temperature range from 600 to 800°C by monitoring the time evolution of the absorbance of Co²⁺ ions in M1 or M2 sites using optical spectroscopy after rapid temperature jumps. It was found from such temperature-jump induced relaxation experiments that with increasing temperature the absorbance of Co²⁺ ions in the M1 site decreases while that in the M2 site increases. This indicates a tendency of Co²⁺ cations to populate the M2 site with increasing temperatures and vice versa. The experimental relaxation data can be modeled using a triple exponential equation based on theoretical analysis. Activation energies of 221 ± 4 and 213 ± 10 kJ/mol were derived from relaxation experiments on the M2 site and M1 site, respectively, for the cation exchange processes in (Co_0.1Mg_0.9)₂SiO₄ olivine. Implications for cation diffusion at low temperatures are discussed.     

Interdiffusion of Mg–Fe in olivine at 1,400–1,600 °C and 1 atm total pressure

The interdiffusion coefficient of Mg–Fe in olivine (D _Mg–Fe) was obtained at 1,400–1,600 °C at the atmospheric pressure with the oxygen fugacity of 10^?3.5–10^?2 Pa using a diffusion couple technique. The D _Mg–Fe shows the anisotropy (largest along the [001] direction and smallest along the [100] direction), and its activation energy (280–320 kJ/mol) is ~80–120 kJ/mol higher than that estimated at lower temperatures. The D _Mg–Fe at temperatures of >1,400 °C can be explained by the cation-vacancy chemistry determined both by the Fe³⁺/Fe²⁺ equilibrium and by the intrinsic point defect formation with the formation enthalpy of 220–270 kJ/mol depending on the thermodynamical model for the Fe³⁺/Fe²⁺ equilibrium in olivine. The formation enthalpy of 220–270 kJ/mol for the point defect (cation vacancy) in olivine is consistent with that estimated from the Mg self-diffusion in Fe-free forsterite. The increase in the activation energy of D _Mg–Fe at >1,400 °C is thus interpreted as the result of the transition of diffusion mechanism from the transition metal extrinsic domain to the intrinsic domain at the atmospheric pressure.     

Premelting and high-temperature diffusion of Ca in synthetic diopside: An increase of the cation mobility

A study of Ca self-diffusion along the b axis in synthetic (iron free) diopside single crystal was performed at temperatures ranging from 1273 K to 1653 K. Diffusion profiles of ⁴⁴Ca were measured using α-particles Rutherford Backscattering (α-RBS) micro analysis. We unambiguously find two distinct diffusional regimes, characterized by activation enthalpies H = 280 ± 26 kJ/mol and H = 951 ± 87 kJ/mol at temperatures lower and upper than 1515 K, respectively. This change of diffusion regime takes place near the onset of premelting as detected in calorimetric measurements and can be interpreted in terms of enhanced formation of Frenkel point defects with an activation enthalpy of formation of 1524 ± 266 kJ/mol (H _f/2 = 762 kJ/mol), in accordance with our high-temperature diffusion data. If premelting of diopside is actually related to Ca-Frenkel point defect concentration, this concentration could reach up to few mole percents close to the melting temperature.     

Cation diffusion in olivine—II. Ni-Mg,Mn-Mg,Mg and Ca

Diffusivities of bivalent cations. Mg, Ni. Mn and Ca, in olivine were determined experimentally. The diffusivities of Ni and Mn in forsterite were determined by couple annealing between Ni₂SiO₄ and Mg₂SiO₄, and Mn₂SiO₄ and Mg₂SiO₄, respectively. The diffusivities of Mg and Ca in forsterite were determined by the use of ²⁶Mg and Ca tracers, respectively. Combined with other published results, the diffusion coefficients for bivalent cation diffusion in pure forsterite along the c crystallographic axis range from 2.45 × 10^?11 to 1.4 × 10^?13 cm² sec^?1 at 1200°C, in the order of Fe > Mn > Co > Ni > Mg > Ca. The results suggest that the diffusivity is governed by at least two factors, i.e. the size of the diffusing ionic species and the change of defect density in the crystal structure which is induced by substitution of diffusing ion for Mg ion.     

Experimental determination of cation diffusivities in aluminosilicate garnets

Data from experimentally-induced diffusion profiles at approximately 40 Kbar, 1,300–1,500° C in spessartine-almandine couples and a pyrope-almandine couple at 40 Kbar, 1,440° C, described in Part I, were used to derive tracer diffusion coefficients (D ^*) of Fe, Mn and Mg in garnet. The experimental data were fitted by numerical simulations that model multicomponent, compositionally-dependent difussion, including the effects of nonideal thermodynamic mixing. The simulations use the formalism of irreversible thermodynamics and an eigenvector technique of solution. We were able to fit the asymmetrical spessartine-almandine profiles using constant D ^* and either the Darken/Hartley-Crank or Manning-Lasaga models relating D ^* and interdiffusion coefficients, and both models yielded D _Mg ^* consistent with the direct measurement of D _Mg ^* in by Cygan and Lasaga (1985) at lower temperatures (750–900° C). The results (equations 4.1–4.3 and Table 1) indicate that D _Fe ^* D _Mg ^* <D _Mn ^* and Q _FeQ _Mg>Q _Mn, where Q is the activation energy. In contrast, the asymmetry of pyrope-almandine profiles is too great to fit with either tracer model assuming constant D ^* and indicates that D _Mg ^* is similar to its value in spessartine-almandine couples but D _Fe ^* is an order of magnitude less. The fit also suggests that D _Ca ^* < D _Fe ^* Mg ^* in pyrope-almandine couples. Synthesis of data from the two types of diffusion couples suggests that D _Mg ^* is insensitive to compositional changes, whereas D _Fe ^* is affected by Mn/Mg and Fe/Mg ratios and probably by other factors. These compositional effects on tracer coefficients are compatible with those documented by Morioka (1983) for cation diffusion in olivine.     

Thermal expansion,Debye temperature and Grüneisen parameter of synthetic (Fe,Mg)SiO3 orthopyroxenes

Thermal expansion properties of synthetic orthopyroxenes (Fe_0.20Mg_0.80)SiO₃, (Fe_0.40Mg_0.60)SiO₃, (Fe_0.50Mg_0.50)SiO₃, (Fe_0.75Mg_0.25)SiO₃ and (Fe_0.83Mg_0.17)SiO₃ were systematically studied by means of single-crystal x-ray diffraction in the temperature range from 296 to 1300 K. The measurements of unit cell dimensions as a function of temperature reveal that the a and c dimensions and the unit cell volume V increase nonlinearly with a positive curvature with rising temperature, whereas the b dimension behaves differently, depending on the total Fe content. For Mg-rich orthopyroxenes (Fe/(Fe+Mg)<30%), the b dimension expands similarly as the a and c dimensions, but it exhibits a nonlinear increase with a negative curvature for orthopyroxenes with Fe/(Fe+Mg)>30%. Together with the high temperature neutron diffraction data on enstatite (MgSiO₃) (McMullan, Haga and Ghose, unpublished) and x-ray diffraction data on ferrosilite (FeSiO₃) (Sueno et al. 1976), the measured unit cell dimensions were analyzed in terms of the Grüneisen theory of thermal expansion. The linear thermal expansion coefficients α _a and α _c both increase as temperature is elevated, with α _c increasing faster, while α _b changes gradually from increasing for Mg-rich orthopyroxenes to decreasing for Fe-rich orthopyroxenes. The relative magnitudes of linear thermal expansion coefficients are always in the order α _b >α _c >α _a between 300 and 500 K, but at higher temperatures, the order changes to α _c >α _b >α _a for Mg-rich orthopyroxenes and α _c >α _a >α _b for Fe-rich ones. The linear thermal expansion behavior is interpreted on the basis of the structural mechanical model of Weidner and Vaughan (1982). The anomalous behavior of α _b is mainly attributed to the changes in the Fe₂₊ population at the M2 site and the relative stiffness of the M2(Fe₂₊)-O bonds compared to the M2(Mg₂₊)-O bonds. The volume thermal expansion coefficients are nonlinear functions of temperature and lie between 23 and 49×10^?6/K. The previously reported results of mean volume thermal expansion coefficients appear to represent the α _V values characteristic of higher temperatures compared to our results. The thermal Debye temperatures are composition-dependent, decreasing linearly from 812 (MgSiO₃) to 561 K (FeSiO₃), and are systematically higher than the corresponding acoustic Debye temperatures. The Grüneisen parameters range from 0.85 to 0.89 and do not seem to vary with composition. The linear compressibilities derived from thermal expansion and elastic moduli data agree very well. The pressure derivatives of the isothermal bulk modulus (dK₀/dP) are also composition-dependent and decrease from 11.2 (MgSiO₃) to 8.77 (FeSiO₃). Such large values indicate possible anomalous elastic behavior of orthopyroxenes at high pressures in the Earth's upper mantle.     

A subsidiary fast-diffusing substitution mechanism of Al in forsterite investigated using diffusion experiments under controlled thermodynamic conditions

Diffusion of Al in synthetic forsterite was studied at atmospheric pressure from 1100 to 1500 °C in air along [100] with activities of SiO₂, MgO and Al₂O₃ (a_SiO2, a_MgO and a_Al2O3) buffered. At low a_SiO2, the buffer was forsterite + spinel + periclase (fo + sp + per) at all temperatures, while at high a_SiO2 and subsolidus conditions a variety of three-phase assemblages containing forsterite and two other phases from spinel, cordierite, protoenstatite or sapphirine were used at 1100–1350 °C. Experiments at high a_SiO2 and 1400 °C used forsterite + protoenstatite + melt (fo + en + melt), and at 1500 °C, fo + melt. The resulting diffusion profiles were analysed by LA–ICP–MS in scanning mode. Diffusion profiles in the high a_SiO2 experiments were generally several hundred microns in length, but diffusion at low a_SiO2 was three orders of magnitude slower than in high a_SiO2 experiments carried out at the same temperature, producing short profiles only a few microns in length and close to the spatial resolution of the analytical method. Interface concentrations of Al in the forsterite, obtained by extrapolating the diffusion profiles to the crystal/buffer interface, were only a fraction of those expected at equilibrium, and varied among the differing buffer assemblages according to (a_Al2O3)^1/2 and (a_SiO2)^3/4, pointing to the substitution of Al in forsterite by an octahedral-site, vacancy-coupled (OSVC) component with the stoichiometry Al _4/3 ³⁺ vac_2/3SiO₄, whereas the main substitution expected from previous equilibrium studies would be the coupled substitution of 2 Al for Mg + Si, giving the stoichiometry MgAl₂O₄. It is proposed that this latter substitution is not seen on the length scales of the present experiments because it requires replacement of Si by Al on tetrahedral sites, and is accordingly rate-limited by the slow diffusivity of Si. Instead, diffusion of Al by the OSVC mechanism is relatively fast, and at high a_SiO2, even faster than Fe–Mg interdiffusion.     

Cation diffusion in olivine—III. Mn2SiO4 system

The diffusion coefficients of divalent cations, Ni, Co, Mn, Ca, Sr and Ba in Mn-olivine, Mn₂SiO₄, were determined experimentally by the use of ⁶³Ni, ⁶⁰Co, ⁵⁴Mn, ⁴⁵Ca, ⁸⁵Sr and ¹³³Ba radioactive tracers, respectively. The empirical relationship between the diffusion coefficient and ionic size of diffusional species shows a trend of variation which was similar to that observed in Mg-olivine, Mg₂SiO₄. The similarity in the trend of variation of diffusion in various olivine systems strongly suggests that the trend is characteristic to the crystal structure of olivine. However, the diffusion coefficient of each cation in Mn-olivine was higher than that in Mg-olivine by about two orders of magnitude. It is suggested that this is due to the loose structure of Mn-olivine compared with that of Mg-olivine.     

Cation partitioning versus temperature in (Mg0.70Fe0.23)Al1.97O4 synthetic spinel by in situ neutron powder diffraction

Neutron powder diffraction experiments in the temperature range 300–1770 K were performed at BENSC, Berlin, Germany, on synthetic (Mg_0.70Fe_0.23) Al_1.97O₄. The cation partitioning over the crystallographic tetrahedral and octahedral sites was determined as a function of temperature through joint Rietveld refinements and advanced minimization techniques. The thermal expansion coefficients of the lattice parameter and inter-atomic bond lengths were also obtained from the full-profile structure refinements. The behaviour of the polyhedral bond-lengths, especially the T−O distances, and of the cell constant upon heating, clearly indicate that the interdiffusion of tetrahedral and octahedral Mg/Al cations starts at about 950 K. This result is straightforwardly supported by the direct analysis of the neutron site scattering factors: Fe always retains tetrahedral coordination at all temperatures, and the cation rearrangement is entirely due to Mg and Al diffusion. Received: 18 November 1997 / Revised, accepted: 23 August 1998     

Co2+ and Ni2+ diffusion in olivine determined by secondary ion mass spectrometry

Diffusion coefficients of Co²⁺ and Ni²⁺ in synthetic single crystal forsterite along the c-axis were determined in the temperature ranges, 700–1200?°C and 800–1300?°C, respectively. The synthesized forsterite specimens were coated with thin evaporated films of CoO and NiO on the c-surface and annealed for diffusion experiments. The short penetration distance of diffusing ions in forsterite was measured by secondary ion mass spectrometry using the depth profile method. The diffusion coefficients of Co (700–1200?°C) and Ni (800–1300?°C) are given by: and The observed diffusion coefficient values show good linear relationships in Arrhenius plots and the activation energy values obtained agree well with the previous values, although the diffusion coefficient values observed at the high temperature end of the experimental range deviate from the previous values. These results indicate that Co and Ni diffuse in olivine with a single mechanism within the temperature range observed, possibly with an extrinsic in nature as in the case of Mg tracer diffusion observed by Chakraborty et?al. 1994 and of Fe-Mg interdiffusion by Chakraborty.     

The effect of silica activity on the diffusion of Ni and Co in olivine

The diffusion of Ni and Co was measured at atmospheric pressure in synthetic monocrystalline forsterite (Mg₂SiO₄) from 1,200 to 1,500 °C at the oxygen fugacity of air, along [100], with the activities of SiO₂ and MgO defined by either forsterite + periclase (fo + per buffer) or forsterite + protoenstatite (fo + en buffer). Diffusion profiles were measured by three methods: laser-ablation inductively-coupled-plasma mass-spectrometry, nano-scale secondary ion mass spectrometry and electron microprobe, with good agreement between the methods. For both Ni and Co, the diffusion rates in protoenstatite-buffered experiments are an order of magnitude faster than in the periclase-buffered experiments at a given temperature. The diffusion coefficients D _M (M = Ni or Co) for the combined data set can be fitted to the equation:

$$\log \,D_{\text{M}} \,\left( {{\text{in}}\,{\text{m}}^{2} \,{\text{s}}^{ - 1} } \right) = - 6.77( \pm 0.33) + \Delta E_{\text{a}} (M)/RT + 2/3\log a_{{SiO_{2} }}$$

with E_a(Ni) = ? 284.3 kJ mol^?1 and E_a(Co) = ? 275.9 kJ mol^?1, with an uncertainty of ±10.2 kJ mol^?1. This equation fits the data (24 experiments) to ±0.1 in log D _M. The dependence of diffusion on \(a_{{{\text{SiO}}_{2} }}\) is in agreement with a point-defect model in which Mg-site vacancies are charge-balanced by Si interstitials. Comparative experiments with San Carlos olivine of composition Mg_1.8Fe_0.2SiO₄ at 1,300 °C give a slightly small dependence on \(a_{{{\text{SiO}}_{2} }}\), with D \(\propto\) (\(a_{{{\text{SiO}}_{2} }}^{0.5}\)), presumably because the Mg-site vacancies increase with incorporation of Fe³⁺ in the Fe-bearing olivines. However, the dependence on fO₂ is small, with D \(\propto\) (fO₂)^0.12±0.12. These results show the necessity of constraining the chemical potentials of all the stoichiometric components of a phase when designing diffusion experiments. Similarly, the chemical potentials of the major-element components must be taken into account when applying experimental data to natural minerals to constrain the rates of geological processes. For example, the diffusion of divalent elements in olivine from low SiO₂ magmas, such as kimberlites or carbonatites, will be an order of magnitude slower than in olivine from high SiO₂ magmas, such as tholeiitic basalts, at equal temperatures and fO₂.

     

Interdiffusion of Na,K,and Ca Between Granitic Melts and NaCl Liquid

This study is aimed at determining the diffusion coefficient of net-work modifiers (mainly Na, K, and Ca) in a two-phase melt-NaCl system, in which the melts are granitic and the system is NaCl-rich in composition. The diffusion coefficients of Na, K, and Ca were measured at the temperatures of 750 – 1400°C, pressures of 0.001 × 10⁸ – 2 × 10⁸ Pa, and initial H₂O contents of 0 wt% –6.9 wt% in the granitic melts. The diffusion coefficients of Fe and Mg were difficult to resolve. In all experiments a NaCl melt was present as well. In the absence of H₂O, the diffusion of net-work modifiers follows an Arrhanious equation at 1 × 10⁵ Pa: lgD_ca=−3. 88−5140/T, lgD_k =−3. 79−4040/T, and lgD_Na, =−4.99−3350/T, where D is in cm² /s andT is in K. The diffusion coefficients of Ca, Na, K, and Fe increase non-linearly with increasing H₂O content in the melt. The presence of about 2 wt% H₂O m the melt will lead to a dramatical increase in diffusivity, but higher H₂O content has only a minor effect. This change is probably the result of a change in the melt structure when H₂O is present. The diffusion coefficients measured in this study are significantly different from those in previous works. This may be understood in terms of the “transient two-liquid equilibrium” theory. Element interdiffusion depends not only on its concentration, but also on its activity co-efficient gradient, which is reflected by the distribution coefficient, of the two contacting melts.     

Self-diffusion of Si and O in diopside-anorthite melt at high pressures

Self-diffusion coefficients for Si and O in Di₅₈An₄₂ liquid were measured from 1 to 4 GPa and temperatures from 1510 to 1764°C. Glass starting powders enriched in ¹⁸O and ²⁸Si were mated to isotopically normal glass powders to form simple diffusion couples, and self-diffusion experiments were conducted in the piston cylinder device (1 and 2 GPa) and in the multianvil apparatus (3.5 and 4 GPa). Profiles of ¹⁸O/¹⁶O and ^29,30Si/²⁸Si were measured using secondary ion mass spectrometry. Self-diffusion coefficients for O (D(O)) are slightly greater than self-diffusion coefficients for Si (D(Si)) and are often the same within error. For example, D(O) = 4.20 ± 0.42 × 10⁻¹¹ m²/s and D(Si) = 3.65 ± 0.37 × 10⁻¹¹ m²/s at 1 GPa and 1662°C. Activation energies for self-diffusion are 215 ± 13 kJ/mol for O and 227 ± 13 kJ/mol for Si. Activation volumes for self-diffusion are −2.1 ± 0.4 cm³/mol and −2.3 ± 0.4 cm³/mol for O and Si, respectively. The similar self-diffusion coefficients for Si and O, similar activation energies, and small, negative activation volumes are consistent with Si and O transport by a cooperative diffusion mechanism, most likely involving the formation and disassociation of a high-coordinated intermediate species. The small absolute magnitudes of the activation volumes imply that Di₅₈An₄₂ liquid is close to a transition from negative to positive activation volume, and Adam-Gibbs theory suggests that this transition is linked to the existence of a critical fraction (∼0.6) of bridging oxygen.