A relationship to estimate the excess entropy of mixing: Application in silicate solid solutions and binary alloys

AbstractThe paper presents new calorimetric data on the excess heat capacity and vibrational entropy of mixing of Pt–Rh and Ag–Pd alloys. The results of the latter alloy are compared to those obtained by calculations using the density functional theory. The extent of the excess vibrational entropy of mixing of these binaries and of some already investigated binary mixtures is related to the differences of the end-member volumes and the end-member bulk moduli. These quantities are used to roughly represent the changes of the bond length and stiffness in the substituted and substituent polyhedra due to compositional changes, which are assumed to be the important factors for the non-ideal vibrational behaviour in solid solutions

Heat capacity and entropy behavior of andradite: a multi-sample and −methodological investigation

Andradite, ideal end-member formula Ca_3 Fe^(3+)_2Si_3O_(12), is one of the common rock-forming garnets found in the Earth's crust. There are several outstanding questions regarding andradite's thermodynamic and physical property behavior. Three issues are: i) Could there be differences in the thermodynamic properties, namely heat capacity, C_p , between synthetic and natural andradite crystals, as observed in the Ca-garnet grossular, Ca_3Al_2Si_3O_(12)? ii) What is the thermal nature of the low-temperature magnetic-phasetransition behavior of andradite? and iii) How quantitative are older published calorimetric (i. e., adiabatic and DSC) heat-capacity results? In this work, four natural nearly end-member single crystals and two synthetic polycrystalline andradite samples were carefully characterized by optical microscope examination, X-ray powder diffraction, microprobe analysis, and IR and UV/VIS single-crystal spectroscopy. The IR spectra of the different samples commonly show a main intense OH stretching band located at 3563 cm^(-1), but other OH bands can sometimes be observed as well. Structural OH concentrations, calculated from the IR spectra, vary from about 0.006 to 0.240 wt% H_2O. The UV/VIS spectra indicate that there can be slight, but not fully understood, differences in the electronic state between synthetic and natural andradite crystals. The C_p behavior was determined by relaxation calorimetry between 2 and 300 K and by differential scanning calorimetry (DSC) methods between 150/300 and 700/950 K, employing the same andradite samples that were used for the other characterization measurements. The low-temperature C_p results show a magnetic phase transition with a Néel temperature of 11.3 ± 0.2 K, which could be slightly affected by the precise electronic state of Fe^(2+/3+) in the crystals. The published adiabatic calorimetry results on andradite do not provide a full and correct thermal description of this magnetic transition. The calorimetric Cp measurements give a best estimate for the standard third-law entropy at 298.15 K for andradite of S^o ≈ 324 ± 2 J/mol · K vs. the value of 316.4 ± 2.0 J/mol · K, as given in an early adiabatic investigation. Both natural and synthetic crystals give similar S o values within experimental uncertainty of about 1.0%, but one natural andradite, richer in OH, may have a very slightly higher value around S^o≈ 326 J/mol·K. Low-temperature DSC measurements made below 298 K agree excellently with those from relaxation calorimetry. The DSC measurements above 298 K show a similarity in C_p behavior among natural and synthetic andradites. A C_p polynomial for use above room temperature to approximately 1000 K was calculated from the data on synthetic andradite giving: C_p (J/mol·K) = 599.09 (±14) 2709.5 (±480)· T^(0.5) 1.3866 (±0.26)· 10^7 · T^2 + 1.6052 (±0.42) · 10^9 · T^3

A neutron diffraction study of crystal and low-temperature magnetic structures within the (Na,Li)FeGe2O6 pyroxene-type solid solution series

Solid solution compounds along the Li1–x Na x FeGe2O6 clinopyroxene series have been prepared by solid state ceramic sintering and investigated by bulk magnetic and calorimetric methods; the Na-rich samples with x(Na) > 0.7 were also investigated by low-temperature neutron diffraction experiments in a temperature range of 4–20 K. For samples with x(Na) > 0.76 the crystal structure adopts the C2/c symmetry at all measuring temperatures, while the samples display P21/c symmetry for smaller Na contents. Magnetic ordering is observed for all samples below 20 K with a slight decrease of T N with increasing Na content. The magnetic spin structures change distinctly as a function of chemical composition: up to x(Na) = 0.72 the magnetic structure can be described by a commensurate arrangement of magnetic spins with propagation vector k = (½, 0 0), an antiferromagnetic (AFM) coupling within the Fe3+O6 octahedra zig-zag chains and an alternating AFM and ferromagnetic (FM) interaction between the chains, depending on the nature of the tetrahedral GeO4 chains. The magnetic structure can be described in magnetic space group P a21/c. Close to the structural phase transition for sample with x(Na) = 0.75, magnetic ordering is observed below 15 K; however, it becomes incommensurately modulated with k = (0.344, 0, 0.063). At 4 K, the magnetic spin structure best can be described by a cycloidal arrangement within the M1 chains, the spins are within the a–c plane. Around 12 K the cycloidal structure transforms to a spin density wave (SDW) structure. For the C2/c structures, a coexistence of a simple collinear and an incommensurately modulated structure is observed down to lowest temperatures. For 0.78 ≤ x(Na) ≤ 0.82, a collinear magnetic structure with k = (0 1 0), space group P C21/c and an AFM spin structure within the M1 chains and an FM one between the spins is dominating, while the incommensurately modulated structure becomes dominating the collinear one in the samples with x(Na) = 0.88. Here the magnetic propagation vector is k = (0.28, 1, 0.07) and the spin structure corresponds again to a cycloidal structure within the M1 chains. As for the other samples, a transition from the cycloidal to a SDW structure is observed. Based on the neutron diffraction data, the appearance of two peaks in the heat capacity of Na-rich samples can now be interpreted as a transition from a cycloidal magnetic structure to a spin density wave structure of the magnetically ordered phase for the Na-rich part of the solid solution series

Heat capacity and entropy behavior of andradite: a multi-sample and −methodological investigation

Andradite, ideal end-member formula Ca_3 Fe^(3+)_2Si_3O_(12), is one of the common rock-forming garnets found in the Earth's crust. There are several outstanding questions regarding andradite's thermodynamic and physical property behavior. Three issues are: i) Could there be differences in the thermodynamic properties, namely heat capacity, C_p , between synthetic and natural andradite crystals, as observed in the Ca-garnet grossular, Ca_3Al_2Si_3O_(12)? ii) What is the thermal nature of the low-temperature magnetic-phasetransition behavior of andradite? and iii) How quantitative are older published calorimetric (i. e., adiabatic and DSC) heat-capacity results? In this work, four natural nearly end-member single crystals and two synthetic polycrystalline andradite samples were carefully characterized by optical microscope examination, X-ray powder diffraction, microprobe analysis, and IR and UV/VIS single-crystal spectroscopy. The IR spectra of the different samples commonly show a main intense OH stretching band located at 3563 cm^(-1), but other OH bands can sometimes be observed as well. Structural OH concentrations, calculated from the IR spectra, vary from about 0.006 to 0.240 wt% H_2O. The UV/VIS spectra indicate that there can be slight, but not fully understood, differences in the electronic state between synthetic and natural andradite crystals. The C_p behavior was determined by relaxation calorimetry between 2 and 300 K and by differential scanning calorimetry (DSC) methods between 150/300 and 700/950 K, employing the same andradite samples that were used for the other characterization measurements. The low-temperature C_p results show a magnetic phase transition with a Néel temperature of 11.3 ± 0.2 K, which could be slightly affected by the precise electronic state of Fe^(2+/3+) in the crystals. The published adiabatic calorimetry results on andradite do not provide a full and correct thermal description of this magnetic transition. The calorimetric Cp measurements give a best estimate for the standard third-law entropy at 298.15 K for andradite of S^o ≈ 324 ± 2 J/mol · K vs. the value of 316.4 ± 2.0 J/mol · K, as given in an early adiabatic investigation. Both natural and synthetic crystals give similar S o values within experimental uncertainty of about 1.0%, but one natural andradite, richer in OH, may have a very slightly higher value around S^o≈ 326 J/mol·K. Low-temperature DSC measurements made below 298 K agree excellently with those from relaxation calorimetry. The DSC measurements above 298 K show a similarity in C_p behavior among natural and synthetic andradites. A C_p polynomial for use above room temperature to approximately 1000 K was calculated from the data on synthetic andradite giving: C_p (J/mol·K) = 599.09 (±14) 2709.5 (±480)· T^(0.5) 1.3866 (±0.26)· 10^7 · T^2 + 1.6052 (±0.42) · 10^9 · T^3

The Specific Heat of Astro-materials: Review of Theoretical Concepts, Materials, and Techniques

We provide detailed background, theoretical and practical, on the specific heat of minerals and mixtures thereof, ‘astro-materials,’ as well as background information on common minerals and other relevant solid substances found on the surfaces of solar system bodies. Furthermore, we demonstrate how to use specific heat and composition data for lunar samples and meteorites as well as a new database of endmember mineral heat capacities (the result of an extensive literature review) to construct reference models for the isobaric specific heat cP as a function of temperature for common solar system materials. Using a (generally linear) mixing model for the specific heat of minerals allows extrapolation of the available data to very low and very high temperatures, such that models cover the temperature range between 10 K and 1000 K at least (and pressures from zero up to several kbars). We describe a procedure to estimate cP(T) for virtually any solid solar system material with a known mineral composition, e.g., model specific heat as a function of temperature for a number of typical meteorite classes with known mineralogical compositions. We present, as examples, the cP(T) curves of a number of well-described laboratory regolith analogs, as well as for planetary ices and ‘tholins’ in the outer solar system. Part II will review and present the heat capacity database for minerals and compounds and part III is going to cover applications, standard reference compositions, cP(T) curves, and a comparison with new and literature experimental dat

Physics and Chemistry of Minerals / A neutron diffraction study of crystal and low-temperature magnetic structures within the (Na,Li)FeGe2O6 pyroxene-type solid solution series

Solid solution compounds along the Li1xNaxFeGe2O6 clinopyroxene series have been prepared by solid state ceramic sintering and investigated by bulk magnetic and calorimetric methods; the Na-rich samples with x(Na) > 0.7 were also investigated by low-temperature neutron diffraction experiments in a temperature range of 420 K. For samples with x(Na) > 0.76 the crystal structure adopts the C2/c symmetry at all measuring temperatures, while the samples display P21/c symmetry for smaller Na contents. Magnetic ordering is observed for all samples below 20 K with a slight decrease of TN with increasing Na content. The magnetic spin structures change distinctly as a function of chemical composition: up to x(Na) = 0.72 the magnetic structure can be described by a commensurate arrangement of magnetic spins with propagation vector k = (

Search for long-lived neutral particles produced in pp collisions at √s = 13 TeV decaying into displaced hadronic jets in the ATLAS inner detector and muon spectrometer

A search is presented for pair production of long-lived neutral particles using 33     fb − 1 of √ s = 13     TeV proton–proton collision data, collected during 2016 by the ATLAS detector at the LHC. This search focuses on a topology in which one long-lived particle decays in the ATLAS inner detector and the other decays in the muon spectrometer. Special techniques are employed to reconstruct the displaced tracks and vertices in the inner detector and in the muon spectrometer. One event is observed that passes the full event selection, which is consistent with the estimated background. Limits are placed on scalar boson propagators with masses from 125 GeV to 1000 GeV decaying into pairs of long-lived hidden-sector scalars with masses from 8 GeV to 400 GeV. The limits placed on several low-mass scalars extend previous exclusion limits in the range of proper lifetimes c τ from 5 cm to 1 m

Performance of electron and photon triggers in ATLAS during LHC Run 2

Abstract: Electron and photon triggers covering transverse energies from 5 GeV to several TeV are essential for the ATLAS experiment to record signals for a wide variety of physics: from Standard Model processes to searches for new phenomena in both proton–proton and heavy-ion collisions. To cope with a fourfold increase of peak LHC luminosity from 2015 to 2018 (Run 2), to 2.1×1034cm-2s-1, and a similar increase in the number of interactions per beam-crossing to about 60, trigger algorithms and selections were optimised to control the rates while retaining a high efficiency for physics analyses. For proton–proton collisions, the single-electron trigger efficiency relative to a single-electron offline selection is at least 75% for an offline electron of 31 GeV, and rises to 96% at 60 GeV; the trigger efficiency of a 25 GeV leg of the primary diphoton trigger relative to a tight offline photon selection is more than 96% for an offline photon of 30 GeV. For heavy-ion collisions, the primary electron and photon trigger efficiencies relative to the corresponding standard offline selections are at least 84% and 95%, respectively, at 5 GeV above the corresponding trigger threshold

Measurement of the t t ¯ production cross-section and lepton differential distributions in e μ dilepton events from pp collisions at s = 13 TeV with the ATLAS detector

Abstract: The inclusive top quark pair (tt¯) production cross-section σtt¯ has been measured in proton–proton collisions at s=13TeV, using 36.1 fb-1 of data collected in 2015–2016 by the ATLAS experiment at the LHC. Using events with an opposite-charge eμ pair and b-tagged jets, the cross-section is measured to be: σtt¯=826.4±3.6(stat)±11.5(syst)±15.7(lumi)±1.9(beam)pb, where the uncertainties reflect the limited size of the data sample, experimental and theoretical systematic effects, the integrated luminosity, and the LHC beam energy, giving a total uncertainty of 2.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. It is used to determine the top quark pole mass via the dependence of the predicted cross-section on mtpole, giving mtpole=173.1-2.1+2.0GeV. It is also combined with measurements at s=7TeV and s=8TeV to derive ratios and double ratios of tt¯ and Z cross-sections at different energies. The same event sample is used to measure absolute and normalised differential cross-sections as functions of single-lepton and dilepton kinematic variables, and the results are compared with predictions from various Monte Carlo event generators

Measurement of the t t ¯ production cross-section and lepton differential distributions in e μ dilepton events from pp collisions at s = 13 TeV with the ATLAS detector

Abstract: The inclusive top quark pair (tt¯) production cross-section σtt¯ has been measured in proton–proton collisions at s=13TeV, using 36.1 fb-1 of data collected in 2015–2016 by the ATLAS experiment at the LHC. Using events with an opposite-charge eμ pair and b-tagged jets, the cross-section is measured to be: σtt¯=826.4±3.6(stat)±11.5(syst)±15.7(lumi)±1.9(beam)pb, where the uncertainties reflect the limited size of the data sample, experimental and theoretical systematic effects, the integrated luminosity, and the LHC beam energy, giving a total uncertainty of 2.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. It is used to determine the top quark pole mass via the dependence of the predicted cross-section on mtpole, giving mtpole=173.1-2.1+2.0GeV. It is also combined with measurements at s=7TeV and s=8TeV to derive ratios and double ratios of tt¯ and Z cross-sections at different energies. The same event sample is used to measure absolute and normalised differential cross-sections as functions of single-lepton and dilepton kinematic variables, and the results are compared with predictions from various Monte Carlo event generators