Diamond anvil cell partitioning experiments for accretion and core formation: testing the limitations of electron microprobe analysis

Metal-silicate partitioning studies performed in high pressure, laser-heated diamond anvil cells (DAC) are commonly used to explore element distribution during planetary-scale core-mantle differentiation. The small run-products contain suitable areas for analysis commonly less than tens of microns in diameter and a few microns thick. Because high spatial resolution is required, quantitative chemical analyses of the quenched phases is usually performed by electron probe microanalysis (EPMA). Here, EPMA is being used at its spatial limits, and sample thickness and secondary fluorescence effects must be accounted for. By using simulations and synthetic samples, we assess the validity of these measurements, and find that in most studies DAC sample wafers are sufficiently thick to be characterised at 15 kVacc. Fluorescence from metal-hosted elements will, however, contaminate silicate measurements, and this becomes problematic if the concentration contrast between the two phases is in excess of 100. Element partitioning experiments are potentially compromised; we recommend simulating fluorescence and applying a data correction, if required, to such DAC studies. Other spurious analyses may originate from sources external to the sample, as exemplified by 0.5 to > 1 wt.% of Cu arising from continuum fluorescence of the Cu TEM grid the sample is typically mounted on

SiO2 glass density to lower-mantle pressures

The convection or settling of matter in the deep Earth’s interior is mostly constrained by density variations between the different reservoirs. Knowledge of the density contrast between solid and molten silicates is thus of prime importance to understand and model the dynamic behavior of the past and present Earth. SiO2 is the main constituent of Earth’s mantle and is the reference model system for the behavior of silicate melts at high pressure. Here, we apply our recently developed x-ray absorption technique to the density of SiO2 glass up to 110 GPa, doubling the pressure range for such measurements. Our density data validate recent molecular dynamics simulations and are in good agreement with previous experimental studies conducted at lower pressure. Silica glass rapidly densifies up to 40 GPa, but the density trend then flattens to become asymptotic to the density of SiO2 minerals above 60 GPa. The density data present two discontinuities at ∼17 and ∼60  GPa that can be related to a silicon coordination increase from 4 to a mixed 5/6 coordination and from 5/6 to sixfold, respectively. SiO2 glass becomes denser than MgSiO3 glass at ∼40  GPa, and its density becomes identical to that of MgSiO3 glass above 80 GPa. Our results on SiO2 glass may suggest that a variation of SiO2 content in a basaltic or pyrolitic melt with pressure has at most a minor effect on the final melt density, and iron partitioning between the melts and residual solids is the predominant factor that controls melt buoyancy in the lowermost mantle

Non-Analytic Vertex Renormalization of a Bose Gas at Finite Temperature

We derive the flow equations for the symmetry unbroken phase of a dilute 3-dimensional Bose gas. We point out that the flow equation for the interaction contains parts which are non-analytic at the origin of the frequency-momentum space. We examine the way this non-analyticity affects the fixed point of the system of the flow equations and shifts the value of the critical exponent for the correlation length closer to the experimental result in comparison with previous work where the non-analyticity was neglected. Finally, we emphasize the purely thermal nature of this non-analytic behaviour comparing our approach to a previous work where non-analyticity was studied in the context of renormalization at zero temperature.Comment: 21 pages, 4 figure

QED effective action at finite temperature

The QED effective Lagrangian in the presence of an arbitrary constant electromagnetic background field at finite temperature is derived in the imaginary-time formalism to one-loop order. The boundary conditions in imaginary time reduce the set of gauge transformations of the background field, which allows for a further gauge invariant and puts restrictions on the choice of gauge. The additional invariant enters the effective action by a topological mechanism and can be identified with a chemical potential; it is furthermore related to Debye screening. In concordance with the real-time formalism, we do not find a thermal correction to Schwinger's pair-production formula. The calculation is performed on a maximally Lorentz covariant and gauge invariant stage.Comment: 9 pages, REVTeX, 1 figure, typos corrected, references added, final version to appear in Phys. Rev.

Anomalous density, sound velocity, and structure of pressure-induced amorphous quartz

The study of quartz and other silica systems under pressure is one of the most prolific domains of research over the past 50 years because of their applications in material science and fundamental relevance to planetary interiors. The characterization of the amorphous state is essential for the comprehension of pressure-induced amorphization of minerals, the metamorphism observed in shocked materials, and the study of melt structures under pressure. Here, we measured in situ, under static compression the density, sound velocities, and electronic structure of quartz as it passes through its pressure-induced amorphization transition. The transition pressure could be derived from the abrupt increase in density and sound velocity at 24 GPa, and from strong changes in the silicon L2,3 edge and oxygen K edge between 22 and 27 GPa observed in x-ray Raman scattering data, confirming previous results from x-ray diffraction. Above this pressure, our data show an anomalous behavior in density, sound velocity, and electronic fine structure compared to the cold compressed glass and other silica polymorphs. The pressure-induced amorphous quartz has a lower density relative to that of the compressed glass, consistent with the lower average coordination inferred from a different signature in the Si L2,3 and O K electronic absorption edges measured by x-ray Raman scattering spectroscopy. This behavior sheds light on the pressure limit of tetrahedral units in SiO2 components and the existence of polyamorphism in network-forming materials, and highlights the possibility to discriminate between different amorphous states with x-ray Raman scattering spectroscopy

Two-loop HTL Thermodynamics with Quarks

We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure-glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for N_f=2 and with exact numerical results obtained in the large-N_f limit.Comment: 33 pages, 6 figure

Landau-Pomeranchuk-Migdal effect in thermal field theory

In recent studies, the production rate of photons or lepton pairs by a quark gluon plasma has been found to be enhanced due to collinear singularities. This enhancement pattern is very dependent on rather strict collinearity conditions between the photon and the quark momenta. It was estimated by neglecting the collisional width of quasi-particles. In this paper, we study the modifications of this collinear enhancement when we take into account the possibility for the quarks to have a finite mean free path. Assuming a mean free path of order $(g^2T\ln(1/g))^{-1}$, we find that only low invariant mass photons are affected. The region where collision effects are important can be interpreted as the region where the Landau-Pomeranchuk-Migdal effect plays a role in thermal photon production by bremsstrahlung. It is found that this effect modifies the spectrum of very energetic photons as well. Based on these results and on a previous work on infrared singularities, we end this paper by a reasonable physical picture for photon production by a quark gluon plasma, that should be useful to set directions for future technical developments.Comment: 28 pages Latex document, 9 postscript figures, typos corrected, semantics cleanup, final version to appear in Phys. Rev.

Advances in perturbative thermal field theory

The progress of the last decade in perturbative quantum field theory at high temperature and density made possible by the use of effective field theories and hard-thermal/dense-loop resummations in ultrarelativistic gauge theories is reviewed. The relevant methods are discussed in field theoretical models from simple scalar theories to non-Abelian gauge theories including gravity. In the simpler models, the aim is to give a pedagogical account of some of the relevant problems and their resolution, while in the more complicated but also more interesting models such as quantum chromodynamics, a summary of the results obtained so far are given together with references to a few most recent developments and open problems.Comment: 84 pages, 18 figues, review article submitted to Reports on Progress in Physics; v2, v3: minor additions and corrections, more reference