ТЕРМОДИНАМИЧЕСКИЕ СВОЙСТВА ПОРОДООБРАЗУЮЩИХ ОКСИДОВ α-Al2O3, Cr2O3, α-Fe2O3 И Fe3O4 ПРИ УСЛОВИЯХ ВЫСОКИХ ТЕМПЕРАТУР И ДАВЛЕНИЙ

Equations of state of corundum (α-Al2O3), eskolaite (Cr2O3), hematite (α-Fe2O3), and magnetite (Fe3O4) are constructed based on the Helmholtz free energy by simultaneous optimization of ultrasonic, X-ray diffraction, dilatometric, and thermochemical measurements. The magnetic contribution to Cr2O3, α-Fe2O3, and Fe3O4 Helmholtz free energy was determined via the A.T. Dinsdale model [Dinsdale, 1991]. The calculated thermodynamic properties of rock-forming oxides of aluminum, chromium, and iron are in good agreement with the reference data and experimental measurements at room pressure, as well as with P-V-T measurements at high temperatures and pressures. Thermodynamic functions (x, α, S, CP, CV, KT, KS, γth, G) of corundum, eskolaite, hematite, and magnetite are calculated at different pressures (up to 80, 70, 50 and 20 GPa, respectively) and temperatures (up to 2000 K), and the results are tabulated. The calculated Gibbs energy of rock-forming oxides can be used to construct the phase diagrams of mineral systems, which include the oxides under the conditions of the Earth’s mantle.На основе свободной энергии Гельмгольца построены уравнения состояния корунда (α-Al2O3), эсколаита (Cr2O3), гематита (α-Fe2O3) и магнетита (Fe3O4) путем одновременной оптимизации ультразвуковых, рентгеновских, дилатометрических данных и термохимических измерений теплоемкости при атмосферном давлении и при повышенных температурах и давлениях. Магнитный вклад в свободную энергию Гельмгольца для Cr2O3, α-Fe2O3 и Fe3O4 определен с помощью модели A.T. Динсдала [Dinsdale, 1991]. Предложенный подход к построению уравнений состояния хорошо описывает λ-видную аномалию в теплоемкостях эсколаита, гематита и магнетита, которая связана с изменением магнитных свойств. Полная термодинамическая модель уравнений состояния α-Al2O3, Cr2O3, α-Fe2O3 и Fe3O4 содержит группу из семи фиксированных параметров и группу из девяти подгоночных параметров, значения которых определяются методом наименьших квадратов. Рассчитанные термодинамические функции породообразующих оксидов алюминия, хрома и железа хорошо согласуются со справочными данными и экспериментальными измерениями при атмосферном давлении, а также с современными P-V-T измерениями в алмазных наковальнях и многопуансонных аппаратах высокого давления. Приведена табуляция термодинамических функций (объем, коэффициент термического расширения, изобарная и изохорная теплоемкость, энтропия, адиабатический и изотермиче- ский модули сжатия, термодинамический параметр Грюнейзена и энергия Гиббса) корунда, эсколаита, гематита и магнетита до температуры 2000 K при разных давлениях (до 80, 70, 50 и 20 ГПа, соответственно). Таким образом, полученные уравнения состояния уточняют термодинамику оксидных фаз от стандартных условий до температур и давлений, соответствующих условиям мантии Земли. Рассчитанная энергия Гиббса породообразующих оксидов алюминия, хрома и железа может быть использована для построения фазовых диаграмм минеральных систем с их участием, имеющих принципиальное значение для интерпретации глобальных и промежуточных границ в земной мантии

ТЕРМОДИНАМИЧЕСКИЕ СВОЙСТВА BCC-FE ДО ТЕМПЕРАТУРЫ ПЛАВЛЕНИЯ И ДО ДАВЛЕНИЯ 15 ГПА

Based on Helmholtz’s free energy, an equation of state of iron (bcc-Fe) is constructed with simultaneous optimization of ultrasonic, X-ray diffraction, dilatometric, and thermochemical measurements in the temperature range from 100 K to the melting points and pressures up to 15 GPa. Calculated thermodynamic functions of bcc-Fe are in good agreement with the reference data and experimental measurements at room pressure, as well as with P–V–T measurements at temperatures up to 773 K and pressures up to 16 GPa. The calculated thermodynamic properties of bcc-Fe (x, a, S, CP, CV, KT, KS, K', GT,P) are tabulated up to 1811 K and 15 GPa. The calculated P–V–T relations for bcc-Fe can be used to calculate pressures at given temperatures and volumes.На основе свободной энергии Гельмгольца построено уравнение состояния железа с объемно-центрированной кубической решеткой (bcc-Fe) путем одновременной оптимизации ультразвуковых, рентгеновских, дилатометрических и термохимических измерений в температурном интервале от 100 К до температуры плавления и до давления 15 ГПа. Рассчитанные термодинамические функции bcc-Fe хорошо согласуются со справочными данными и экспериментальными измерениями при атмосферном давлении, а также с P–V–T измерениями в области температур до 773 К и давлений до 16 ГПа. Приведена табуляция термодинамических функций bcc-Fe (x, a, S, CP, CV, KT, KS, K', GT,P) до температуры 1811 К и давления до 15 ГПа. Рассчитанные P–V–T соотношения bcc-Fe могут быть использованы для расчета давления при заданных температурах и объемах

Investigation of structure and hydrogen bonding of super-hydrous phase B (HT) under pressure using first principles density functional calculations

High pressure behaviour of superhydrous phase B(HT) of Mg10Si3O14(OH)4 (Shy B) is investigated with the help of density functional theory based first principles calculations. In addition to the lattice parameters and equation of state, we use these calculations to determine the positional parameters of atoms as a function of pressure. Our results show that the compression induced structural changes involve cooperative distortions in the full geometry of the hydrogen bonds. The bond bending mechanism proposed by Hofmeister et al [1999] for hydrogen bonds to relieve the heightened repulsion due to short H--H contacts is not found to be effective in Shy B. The calculated O-H bond contraction is consistent with the observed blue shift in the stretching frequency of the hydrogen bond. These results establish that one can use first principles calculations to obtain reliable insights into the pressure induced bonding changes of complex minerals.Comment: 16 pages, 4 figure

Slab melting as a barrier to deep carbon subduction

Interactions between crustal and mantle reservoirs dominate the surface inventory of volatile elements over geological time, moderating atmospheric composition and maintaining a lifesupporting planet1. While volcanoes expel volatile components into surface reservoirs, subduction of oceanic crust is responsible for replenishment of mantle reservoirs2,3. Many natural, ‘superdeep’ diamonds originating in the deep upper mantle and transition zone host mineral inclusions, indicating an affinity to subducted oceanic crust4–7. Here we show that the majority of slab geotherms will intersect a deep depression along the melting curve of carbonated oceanic crust at depths of approximately 300 to 700 kilometres, creating a barrier to direct carbonate recycling into the deep mantle. Low-degree partial melts are alkaline carbonatites that are highly reactive with reduced ambient mantle, producing diamond. Many inclusions in superdeep diamonds are best explained by carbonate melt–peridotite reaction. A deep carbon barrier may dominate the recycling of carbon in the mantle and contribute to chemical and isotopic heterogeneity of the mantle reservoir

Stochastic Inversion of P-to-S Converted Waves for Mantle Composition and Thermal Structure: Methodology and Application

We present a new methodology for inverting P‐to‐S receiver function (RF) waveforms directly for mantle temperature and composition. This is achieved by interfacing the geophysical inversion with self‐consistent mineral phase equilibria calculations from which rock mineralogy and its elastic properties are predicted as a function of pressure, temperature, and bulk composition. This approach anchors temperatures, composition, seismic properties, and discontinuities that are in mineral physics data, while permitting the simultaneous use of geophysical inverse methods to optimize models of seismic properties to match RF waveforms. Resultant estimates of transition zone (TZ) topography and volumetric seismic velocities are independent of tomographic models usually required for correcting for upper mantle structure. We considered two end‐member compositional models: the equilibrated equilibrium assemblage (EA) and the disequilibrated mechanical mixture (MM) models. Thermal variations were found to influence arrival times of computed RF waveforms, whereas compositional variations affected amplitudes of waves converted at the TZ discontinuities. The robustness of the inversion strategy was tested by performing a set of synthetic inversions in which crustal structure was assumed both fixed and variable. These tests indicate that unaccounted‐for crustal structure strongly affects the retrieval of mantle properties, calling for a two‐step strategy presented herein to simultaneously recover both crustal and mantle parameters. As a proof of concept, the methodology is applied to data from two stations located in the Siberian and East European continental platforms.This work was supported by a grant from the Swiss National Science Foundation (SNF project 200021_159907). B. T. was funded by a Délégation CNRS and Congé pour Recherches et Conversion Thématique from the Université de Lyon to visit the Research School of Earth Sciences (RSES), The Australian National University (ANU). B. T. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement 79382

Carbon-depleted outer core revealed by sound velocity measurements of liquid iron-carbon alloy

The relative abundance of light elements in the Earth's core has long been controversial. Recently, the presence of carbon in the core has been emphasized, because the density and sound velocities of the inner core may be consistent with solid Fe(7)C(3). Here we report the longitudinal wave velocity of liquid Fe(84)C(16) up to 70 GPa based on inelastic X-ray scattering measurements. We find the velocity to be substantially slower than that of solid iron and Fe(3)C and to be faster than that of liquid iron. The thermodynamic equation of state for liquid Fe(84)C(16) is also obtained from the velocity data combined with previous density measurements at 1 bar. The longitudinal velocity of the outer core, about 4% faster than that of liquid iron, is consistent with the presence of 4–5 at.% carbon. However, that amount of carbon is too small to account for the outer core density deficit, suggesting that carbon cannot be a predominant light element in the core

THERMODYNAMIC PROPERTIES OF BCC-FE TO MELTING TEMPERATURE AND PRESSURE TO 15 GPA

Based on Helmholtz’s free energy, an equation of state of iron (bcc-Fe) is constructed with simultaneous optimization of ultrasonic, X-ray diffraction, dilatometric, and thermochemical measurements in the temperature range from 100 K to the melting points and pressures up to 15 GPa. Calculated thermodynamic functions of bcc-Fe are in good agreement with the reference data and experimental measurements at room pressure, as well as with P–V–T measurements at temperatures up to 773 K and pressures up to 16 GPa. The calculated thermodynamic properties of bcc-Fe (x, a, S, CP, CV, KT, KS, K', GT,P) are tabulated up to 1811 K and 15 GPa. The calculated P–V–T relations for bcc-Fe can be used to calculate pressures at given temperatures and volumes

Armalcolite and rutile-bearing mantle peridotites, Vitim volcanic field, South Russia: petrography and mineralogy

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