Li diffusion in zircon

Diffusion of Li under anhydrous conditions at 1 atm and under fluid-present elevated pressure (1.0–1.2 GPa) conditions has been measured in natural zircon. The source of diffusant for 1-atm experiments was ground natural spodumene, which was sealed under vacuum in silica glass capsules with polished slabs of zircon. An experiment using a Dy-bearing source was also conducted to evaluate possible rate-limiting effects on Li diffusion of slow-diffusing REE⁺³ that might provide charge balance. Diffusion experiments performed in the presence of H₂O–CO₂ fluid were run in a piston–cylinder apparatus, using a source consisting of a powdered mixture of spodumene, quartz and zircon with oxalic acid added to produce H₂O–CO₂ fluid. Nuclear reaction analysis (NRA) with the resonant nuclear reaction ⁷Li(p,γ)⁸Be was used to measure diffusion profiles for the experiments. The following Arrhenius parameters were obtained for Li diffusion normal to the c-axis over the temperature range 703–1.151°C at 1 atm for experiments run with the spodumene source:

Two diffusion pathways in quartz: A combined UV-laser and RBS study

The diffusive behavior of argon in quartz was investigated with three analytical depth profiling methods: Rutherford Backscattering Spectroscopy (RBS), 213 nm laser ablation, and 193 nm (Excimer) laser ablation on the same set of experimental samples. The integration of multiple depth profiling methods, each with different spatial resolution and sensitivity, allows for the cross-checking of methods where data ranges coincide. The use of multiple methods also allows for exploration of diffusive phenomena over multiple length-scales. Samples included both natural clear rock crystal quartz and synthetic citrine quartz. Laser analysis of clear quartz was compromised by poor coupling with the laser, whereas the citrine quartz was more easily analyzed (particularly with 193 nm laser). Diffusivity measured by both RBS and 193 nm laser ablation in the outermost 0.3 μm region of citrine quartz are self-consistent and in agreement with previously published RBS data on other quartz samples (including the clear quartz measured by RBS in this study). Apparent solubilities (extrapolated surface concentrations) for citrine quartz are in good agreement between RBS, 213 nm, and 193 nm laser analyses. Deeper penetration of argon measured up to 100 μm depth with the 213 nm laser reveal contributions of a second, faster diffusive pathway, effective in transporting much lower concentrations of argon into the crystal interiors of both clear and citrine quartz. By assuming such deep diffusion is dominated by fast pathways and approximating them as a network of planar features, the net diffusive uptake can be modeled and quantified with the Whipple-LeClaire equation, yielding δD_b values of 1.32 × 10⁻¹⁴ to 9.1 × 10⁻¹⁷ cm³/s. While solubility values from the measured profiles confirm suggestions that quartz has a large capacity for argon uptake (making it a potentially important sink for argon in the crust), the slow rate of lattice diffusion may limit its capability to take up argon in shorter lived geologic environments and in experiments. In such shorter-lived systems, bulk argon diffusive uptake will be dominated by the fast pathway and the quartz lattice (including natural isolated defects that may also be storing argon) may never reach its equilibrium capacity.     

Intellectual property rights and low carbon technology transfer: Conflicting discourses of diffusion and development

Intellectual property rights (IPRs) and the transfer of low carbon technologies to developing countries have been the focus of sustained disagreement between many developed and developing country Parties to the United Nations Framework Convention on Climate Change (UNFCCC). We argue that this disagreement stems from two conflicting political discourses of economic development and low carbon technology diffusion which tend to underpin developing and developed countries’ respective motivations for becoming party to the Convention. We illustrate the policy implications of these discourses by examining empirical evidence on IPRs and low carbon technology transfer and highlight how the two discourses are based on an incomplete understanding of the role of technological capacity in either economic development or technology diffusion. This has important implication for the success of post-2012 international climate agreements.     

Apatite/liquid partition coefficients for the rare earth elements and strontium

Sixteen sets of apatite/liquid partition coefficients (D^ap/liq) for the rare earth elements (REE; La, Sm, Dy, Lu) and six values for Sr were experimentally determined in natural systems ranging from basanite to granite. The apatite + melt (glass) assemblages were obtained from starting glasses artificially enriched in REE, Sr and fluorapatite components; these were run under dry and hydrous conditions of 7.5–20 kbar and 950–1120°C in a solid-media, piston-cylinder apparatus. An SEM-equipped electron microprobe was used for subsequent measurement of REE and Sr concentrations in coexisting apatites and quenched glasses. The resulting partition coefficient patterns resemble previously determined apatite phenocryst/groundmass concentration ratios in the following respects: (1) the rare earth patterns are uniformly concave downward (i.e., the middle REE are more compatible in apatite than the light and heavy REE); (2) D_REE^ap/liq is much higher for silicic melts than for basic ones; and (3) strontium (and therefore Eu²⁺) is less concentrated by apatite than are the trivalent REE. The effects of both temperature and melt composition on D_REE^ap/liq are systematic and pronounced. At 950°C, for example, a change in melt SiO₂ content from 50 to 68 wt.% causes the average REE partition coefficient to increase from ～7 to ～30. A 130°C increase in temperature, on the other hand, results in a two-fold decrease in D_REE^ap/liq. Partitioning of Sr is insenstitive to changes in melt composition and temperature, and neither the Sr nor the REE partition coefficients appear to be affected by variations in pressure or H₂O content of the melt.The experimentally determined partition coefficients can be used not only in trace element modelling, but also to distinguish apatite phenocrysts from xenocrysts in rocks. Reported apatite megacryst/host basalt REE concentration ratios [12], for example, are considerably higher than the equilibrium partition coefficients, which suggest that in this particular case the apatite is actually xenocrystic.A reversal experiment incorporated in our study yielded diffusion profiles of REE in apatite, from which we extracted a REEαCa interdiffusion coefficient of 2–4×10^?14 cm²/s at 1120°C. Extrapolated downward to crustal temperatures, this low value suggests that complete REE equilibrium between felsic partial melts and residual apatite is rarely established.     

Diffusion and partitioning of magnesium in quartz grain boundaries

Experiments were conducted to study Mg diffusion in quartz grain boundaries. A detector particle method was used to study grain-boundary diffusion because Mg was confined exclusively to the grain boundaries. Diffusion couples were assembled by placing a MgF₂ disk against a disk of quartzite, which was placed against a disk of quartzite that contained fayalite (Fe₂SiO₄) ‘detector particles.’ During diffusion experiments, Mg diffused along the grain boundaries of the central quartzite toward the fayalite quartzite where it was incorporated into fayalite detector particles. The only pathway for transport from the diffusant source to fayalite detector particles was through the grain boundaries in the central quartzite. The cross-sectional area of the grain boundaries that delivered Mg to the fayalite detector particles was determined from scanning electron microscope images. The Mg contents of the fayalite detector particles were used to calculate the mass of Mg that fluxed through the grain boundaries. During the diffusion experiments, pyroxene crystallites nucleated and grew in the central quartzites from Mg and Fe that was transported along quartz grain boundaries. The Mg contents of the crystallites vary linearly throughout the quartzites, suggesting that steady-state transport conditions were rapidly established in the quartz grain boundaries. Magnesium concentrations in the pyroxene crystallites are proportional to concentration gradients in the grain boundaries of the central quartzite. Grain-boundary fluxes and linear concentration gradients were used to calculate diffusion of Mg in grain boundaries of the central quartzite component in the diffusion couples.     

An analytic method to account for drag in the Vinti satellite theory

In order to retain separability in the Vinti theory of Earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all, altitudes and simultaneously reduces the variational equations to definite integrals with closed form evaluations whose limits are in terms of the eccentric anomaly. The values of the limits for any arbitrary time interval are obtained from the Vinti program.Results of this technique for the case of the intense air drag satellites San Marco-2 and Air Force Cannonball are given. These results indicate that the satellite ephemerides produced by this theory in conjunction with the Vinti program are of very high accuracy. In addition, since the program is entirely analytic, several months of ephemerides can be obtained within a few seconds of computer time.     

Triangle based interpolation

Triangle based interpolation is introduced by an outline of two classical planar interpolation methods, viz. linear triangular facets and proximal polygons. These are shown to have opposite local bias. By applying cross products of triangles to obtain local gradients, a method designated “slant-top proximal polygon interpolation” is introduced that is intermediate between linear facets and polygonal interpolation in its local bias. This surface is not continuous, but, by extending and weighting the gradient planes, a C¹ surface can be obtained. The gradients also allow a roughness index to be calculated for each data point in the set. This index is used to control the shape of a blending function that provides a weighted combination of the gradient planes and linear interpolation. This results in a curvilinear, C¹,interpolation of the data set that is bounded by the linear interpolation and the weighted gradient planes and is tangent to the slant-top interpolation at the data points. These procedures may be applied to data with two, three, or four independent variables.