Modelling of thermo-chemical properties over the sub-solidus MgO–FeO binary, as a function of iron spin configuration, composition and temperature

Thermo-chemical properties and T–X phase relations diagram of the (Mg,Fe)O solid solution are modelled using mixing Helmholtz energy, ΔF(T,x)mixing, calculated by quantum mechanical and semi-empirical techniques. The sub-solidus MgO–FeO binary has been explored as a function of composition, with iron either in high-spin (HS) or low-spin (LS) configuration. Only the HS model provides physically sound results at room pressure, yielding a correct trend of cell edge versus composition, whereas LS’s issues are at variance with observations. Mixing Helmholtz energy has been parametrized by the following relationship: ΔF(T,x)mixing = x × y × [U0(T) + U1(T) × (x – y) + U2(T) × (x − y)2]−T × S(x,y)config, where y = 1−x and Uj(T) are polynomials in T of the second order. ΔF(T,x)mixing exhibits a quasi-symmetric behaviour and allows one to build the T–X phase relations diagram over the MgO–FeO join. The HS model including vibrational contribution to the Helmholtz energy predicts a solid solution’s critical temperature of some 950 K, remarkably larger than olivine’s and Mg–Fe garnet’s. All this points to a more difficult Mg–Fe mixing in periclase-like structure than olivine and garnet, which, in turn, provide more structure degrees of freedom for atomic relaxation. From ΔF(T,x)mixing, we have then derived ΔH(T,x)excess and ΔS(T,x)excess. The former, characterized by a quasi-regular behaviour, has been parametrized through W × x × (1−x), obtaining WH,Mg–Fe of 17.7(5) kJ/mol. ΔS(T,x)excess, in turn, increases as a function of temperature, showing absolute figures confined within 0.1 J/mol/K. Mixing Gibbs energy, calculated combining the present issues with earlier theoretical determinations of the magnesio-wüstite’s elastic properties, has shown that the HS configuration is stable and promote Mg–Fe solid solution up to ≈15 GPa

Fe-periclase reactivity at Earth's lower mantle conditions: Ab-initio geochemical modelling

Intrinsic and extrinsic stability of the (Mg,Fe)O solid mixture in the Fe-Mg-Si-O system at high P, T conditions relevant to the Earth\u2019s mantle is investigated by the combination of quantum mechanical calculations (Hartree- 26 Fock/DFT hybrid scheme), cluster expansion techniques and statistical thermodynamics. Iron in the (Mg,Fe)O binary mixture is assumed to be either in the low spin (LS) or in the high spin (HS) state. Un-mixing at solid state is observed only for the LS condition in the 23\u201342 GPa pressure range, whereas HS does not give rise to un-mixing. LS (Mg,Fe)O un-mixings are shown to be able to incorporate iron by subsolidus reactions with a reservoir of a virtual bridgmanite composition, for a maximum total enrichment of 0.22 FeO. At very high P (up to 130/3150 GPa/K), a predominant (0.7 phase proportion), iron-rich Fe-periclase mixture (Mg0.50Fe0.50)O is formed, and it coexists, at constrained phase composition conditions, with two iron-poor assemblages [(Mg0.90Fe0.10)O and (Mg0.825Fe0.175)O]. These theoretical results agree with the compositional variability and frequency of occurrence observed in lower mantle Fe-periclase from diamond inclusions and from HP-HT synthesis products. The density difference among the Fe-periclase phases increases up to 10%, between 24 and 130 GPa. The calculated bulk Fe/Mg partitioning coefficient between the bridgmanite reservoir and Fe-periclase, Kd, is 0.64 at 24 GPa; it then drops to 0.19 at 80 GPa, and becomes quasi-invariant (0.18\u20130.16) in the lowermost portion of the Earth\u2019s mantle (80\u2013 130 GPa). These Kd-values represent an approximate estimate for the Fe/Mg-partitioning between actual bridgmanite and Fe-periclase. Consequently, our Kd-values agree with experimental measurements and theoretical determinations, hinting that iron preferentially dissolves in periclase with respect to all the other iron-bearing phases of the lower mantle. The continuous change up to 80 GPa (2000 km depth) of the products (compositions and phase proportions) over the MgO-FeO binary causes geochemical heterogeneities throughout the lower mantle, but it does not give rise to any sharp discontinuity. In this view, anomalies like the ULVZs, explained with a local and abrupt change of density, do not seem primarily ascribable to the mixing behavior and reactivity of (Mg,Fe)O at subsolidus

Dietary Patterns at the Individual Level through a Nutritional and Environmental Approach: The Case Study of a School Canteen

The public catering sector has important responsibilities in seeking a change toward more sustainable choices for many aspects related to the environmental impacts of their services. The environmental impact of production processes can be studied through life cycle assessment (LCA), which allows a greater awareness of choices and has rarely been applied to catering. In this work, we studied the impacts of two dishes (braised meat and cauliflower meatballs) in a school canteen, their impacts were studied using the daily energy requirement (expressed in kcal) as a functional unit. Global warming potential (GWP) and nonrenewable energy (NRE) were calculated starting from the supply of raw materials up to distribution. Electricity and the act of cooking the meatballs accounted for more than 60% of the measured impact in terms of GWP, whereas, less markedly, they dominated in terms of nonrenewable energy used. In the case of braised meat, the total impact was, however, attributable to the life cycle of the meat (between 60% and 76%) and the consumption of electricity (between 19% and 27%), whereas for all other factors, the contribution was never particularly high. Additionally, a discussion on the correct functional unit to be used proposed the environmental impact of different recipes as an additional criterion for nutritionists during the composition of the menu. An integrated system appears important for changing policies and behaviors and the application of LCA can be a tool capable of contributing to the construction of a holistic instrument of sustainability

An evaluation of |Vus| and precise tests of the Standard Model from world data on leptonic and semileptonic kaon decays

We present a global analysis of leptonic and semileptonic kaon decay data, including all recent results published by the BNL-E865, KLOE, KTeV, ISTRA+ and NA48 experiments. This analysis, in conjunction with precise lattice calculations of the hadronic matrix elements now available, leads to a very precise determination of |Vus| and allows us to perform several stringent tests of the Standard Model.Comment: LaTeX, 25 pages, 12 figures, 16 tables. Submitted to EPJC. v2: Minor changes for accepted version. No numerical results change

Superallowed 0+ to 0+ nuclear beta decays: A new survey with precision tests of the conserved vector current hypothesis and the standard model

A new critical survey is presented of all half-life, decay-energy and branching-ratio measurements related to 20 0+ to 0+ beta decays. Compared with our last review, there are numerous improvements: First, we have added 27 recently published measurements and eliminated 9 references; of particular importance, the new data include a number of high-precision Penning-trap measurements of decay energies. Second, we have used the recently improved isospin symmetry-breaking corrections. Third, our calculation of the statistical rate function now accounts for possible excitation in the daughter atom. Finally, we have re-examined the systematic uncertainty associated with the isospin symmetry-breaking corrections by evaluating the radial-overlap correction using Hartree-Fock radial wave functions and comparing the results with our earlier calculations, which used Saxon-Woods wave functions; the provision for systematic uncertainty has been changed as a consequence. The new corrected Ft values are impressively constant and their average, when combined with the muon liftime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, V_{ud} = 0.97425(22). The unitarity test on the top row of the matrix becomes |V_{ud}|^2 + |V_{us}|^2 + |V_{ub}|^2 = 0.99995(61). Both V_{ud} and the unitarity sum have significantly reduced uncertainties compared with our previous survey, although the new value of V_{ud} is statistically consistent with the old one. From these data we also set limits on the possible existence of scalar interactions, right-hand currents and extra Z bosons. Finally, we discuss the priorities for future theoretical and experimental work with the goal of making the CKM unitarity test even more definitive.Comment: 36 pages, 11 tables, 9 figure