Br diffusion in phonolitic melts: Comparison with fluorine and chlorine diffusion

Abstract Bromine diffusion was measured in two natural phonolitic melts: (1) a K2O-rich (~10 wt%) one synthesized from the white pumice phase of the 79 AD eruption of Vesuvius (Italy), and (2) a Na2O-rich (~10 wt%) one corresponding to the most differentiated melt of the 12 000 BC eruption of the Laacher See (Germany). Experiments were performed at 0.5 and 1.0 GPa, 1250 to 1450 °C, at anhydrous and hydrous (2.65 ± 0.35 wt% of dissolved water) conditions. Experiments conducted with the diffusion-couple technique in the piston cylinder were performed with only bromine diffusing and with the simultaneous diffusion of a halogen mixture (F, Cl, Br) to evaluate the interactions between the halogens during diffusion. The diffusion profiles of Br were measured by X-ray fluorescence using synchrotron radiation microprobe (SYXRF), ID18F, at the European Synchrotron Radiation Facility (ESRF, France). Bromine diffusion displays Arrhenian behavior under anhydrous conditions that is similar when it diffuses alone and when it diffuses with F and Cl. The Br diffusion coefficients range between 2 × 10–12 m2/s at 1250 °C and 1.5 × 10–11 m2/s at 1450 °C for the Na-rich melt and between 3 × 10–12 m2/s at 1250 °C and 2.5 × 10–11 m2/s at 1450 °C for the K-rich melt, at 1.0 GPa. Although Br mobility is independent of F and Cl in anhydrous phonolitic melts, its behavior may be dependent on the dominant alkali in the melt, as previously observed for Cl, but not F. For hydrous experiments, although the data are scattered, the Br diffusivity increases slightly with water and the Na/K ratio seems to influence Br diffusivity. Similarly to noble gases, halogen diffusivity at a given temperature in the phonolitic melts appears related to the ionic porosity of the silicate structure. Compared to basaltic melt, Br diffusivities are approximately one order of magnitude lower in the Na-phonolite melt, because of the difference of the pre-exponential factor. Br mobility appears to be decoupled from melt viscosity, considering the results here.

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Effect of iron chloride on the polaronic conduction in potassium phosphateglasses containing iron oxide

Canadian Journal of Physics ◽

10.1139/p00-089 ◽

2000 ◽

Vol 78 (12) ◽

pp. 1091-1105 ◽

Cited By ~ 4

Author(s):

Y M Moustafa

Keyword(s):

Activation Energy ◽

Electrical Conductivity ◽

Structural Changes ◽

Small Polaron ◽

Iron Chloride ◽

Polaron Hopping ◽

Exponential Factor ◽

Order Of Magnitude ◽

The Difference ◽

Fe Ions

DC electrical conductivity measurements of Fe2O3K2OP2O5 glasses containing iron chloride have been carried out in the temperature range from room temperature to 360°C. The DC conductivity was analyzed in terms of small polaron hopping theory. The hopping regime between Fe ions was confirmed to be nonadiabatic. The increase in the conductivity was of the same order of magnitude as the change in the pre-exponential factor upon increasing the FeCl3 content. The decrease in the activation energy with increasing FeCl3 content was interpreted in terms of a decrease in the distance between the iron sites. The increase in electrical conductivity was ascribed to the difference in the activation energy. The variation in the conductivity parameters was interpreted in terms of the structural changes that take place upon increasing the FeCl3 content of the glasses. PACS No.72.20Ee

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Microscopic Interpretation of Arrhenius Parameters

10.1093/oso/9780198805014.003.0008 ◽

2018 ◽

Author(s):

Niels Engholm Henriksen ◽

Flemming Yssing Hansen

Keyword(s):

Activation Energy ◽

Transition State ◽

Transition State Theory ◽

Average Energy ◽

Zero Point ◽

State Theory ◽

Exponential Factor ◽

Quantum Tunnelling ◽

Microscopic Interpretation ◽

The Difference

This chapter reviews the microscopic interpretation of the pre-exponential factor and the activation energy in rate constant expressions of the Arrhenius form. The pre-exponential factor of apparent unimolecular reactions is, roughly, expected to be of the order of a vibrational frequency, whereas the pre-exponential factor of bimolecular reactions, roughly, is related to the number of collisions per unit time and per unit volume. The activation energy of an elementary reaction can be interpreted as the average energy of the molecules that react minus the average energy of the reactants. Specializing to conventional transition-state theory, the activation energy is related to the classical barrier height of the potential energy surface plus the difference in zero-point energies and average internal energies between the activated complex and the reactants. When quantum tunnelling is included in transition-state theory, the activation energy is reduced, compared to the interpretation given in conventional transition-state theory.

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An experimental and theoretical investigation of diffusion in a two-phase alloy

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1948.0028 ◽

1948 ◽

Vol 192 (1031) ◽

pp. 575-592 ◽

Cited By ~ 15

Keyword(s):

Free Energy ◽

Single Phase ◽

Phase State ◽

Theoretical Treatment ◽

Research Association ◽

Essential Difference ◽

Two Phase ◽

Two Factors ◽

Order Of Magnitude ◽

The Difference

The present paper describes an investigation of diffusion in the solid state. Previous experimental work has been confined to the case in which the free energy of a mixture is a minimum for the single-phase state, and diffusion decreases local differences of concentration. This may be called ‘diffusion downhill’. However, it is possible for the free energy to be a minimum for the two-phase state; diffusion may then increase differences of concentration; and so may be called ‘diffusion uphill’. Becker (1937) has proposed a simple theoretical treatment of these two types of diffusion in a binary alloy. The present paper describes an experimental test of this theory, using the unusual properties of the alloy Cu 4 FeNi 3 . This alloy is single phase above 800° C and two-phase at lower temperatures, both the phases being face-centred cubic; the essential difference between the two phases is their content of copper. On dissociating from one phase into two the alloy develops a series of intermediate structures showing striking X-ray patterns which are very sensitive to changes of structure. It was found possible to utilize these results for a quantitative study of diffusion ‘uphill’ and ‘downhill’ in the alloy. The experimental results, which can be expressed very simply, are in fair agreement with conclusions drawn from Becker’s theory. It was found that Fick’s equation, dc / dt = D d2c / dx2 , can, within the limits of error, be applied in all cases, with the modification that c denotes the difference of the measured copper concentration from its equilibrium value. The theory postulates that D is the product of two factors, of which one is D 0f the coefficient of diffusion that would be measured if the alloy were an ideal solid solution. The theory is able to calculate D/D 0 , if only in first approximation, and the experiments confirm this calculation. It was found that in most cases the speed of diffusion—‘uphill’ or ‘downhill’—has the order of magnitude of D 0 . * Now with British Electrical Research Association.

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Diffusivity, Solubility and Speciation of Sulphur in Silicate Melts

Advances in Science and Technology ◽

10.4028/www.scientific.net/ast.46.93 ◽

2006 ◽

Vol 46 ◽

pp. 93-97 ◽

Cited By ~ 1

Author(s):

J. Stelling ◽

Harald Behrens ◽

Joachim Deubener ◽

Stefan Mangold ◽

Joerg Goettlicher

Keyword(s):

High Temperature ◽

Electron Microprobe ◽

Industrial Production ◽

Silicate Melts ◽

Viscosity Data ◽

Decomposition Products ◽

X Ray ◽

Diffusion Couple Technique ◽

X Ray Absorption ◽

Diffusion Profiles

Diffusion and solubility of sulphur have important effects on the degassing of silicate melts. Both properties are closely related to the structural incorporation of sulphur in the melt. Depending on the oxygen fugacity, sulphur can be present as sulphide (S2-), sulphite (S4+) or sulphate (S6+). Sulphates play an important role in the industrial production of glasses especially in the fining process. The decomposition products of sulphate amass in bubbles which ascend and homogenize the melt. Structural incorporation of sulphur in glasses is studied by XANES (X-ray Absorption Near Edge Spectroscopy). Diffusion of sulphur is investigated in simple silicate systems using the diffusion couple technique. First diffusion profiles were measured in sodium trisilicate glasses by electron microprobe. The results indicate that sulphur diffusivity in high temperature melts is close to the Eyring diffusivity calculated from viscosity data.

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First testing of the fast kappa diffractometers at National Synchrotron Light Source and European Synchrotron Radiation Facility

Review of Scientific Instruments ◽

10.1063/1.1146510 ◽

1995 ◽

Vol 66 (2) ◽

pp. 1765-1767 ◽

Cited By ~ 8

Author(s):

I. K. Robinson ◽

H. Graafsma ◽

A. Kvick ◽

J. Linderholm

Keyword(s):

Synchrotron Radiation ◽

Light Source ◽

European Synchrotron Radiation Facility ◽

National Synchrotron Light Source ◽

Synchrotron Light

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A large-solid-angle X-ray Raman scattering spectrometer at ID20 of the European Synchrotron Radiation Facility

Journal of Synchrotron Radiation ◽

10.1107/s1600577516020579 ◽

2017 ◽

Vol 24 (2) ◽

pp. 521-530 ◽

Cited By ~ 46

Author(s):

S. Huotari ◽

Ch. J. Sahle ◽

Ch. Henriquet ◽

A. Al-Zein ◽

K. Martel ◽

...

Keyword(s):

Synchrotron Radiation ◽

Raman Scattering ◽

Solid Angle ◽

European Synchrotron Radiation Facility ◽

Electronic Excitations ◽

Raman Scattering Spectroscopy ◽

X Ray ◽

Area Detector ◽

Spectroscopic Tool

An end-station for X-ray Raman scattering spectroscopy at beamline ID20 of the European Synchrotron Radiation Facility is described. This end-station is dedicated to the study of shallow core electronic excitations using non-resonant inelastic X-ray scattering. The spectrometer has 72 spherically bent analyzer crystals arranged in six modular groups of 12 analyzer crystals each for a combined maximum flexibility and large solid angle of detection. Each of the six analyzer modules houses one pixelated area detector allowing for X-ray Raman scattering based imaging and efficient separation of the desired signal from the sample and spurious scattering from the often used complicated sample environments. This new end-station provides an unprecedented instrument for X-ray Raman scattering, which is a spectroscopic tool of great interest for the study of low-energy X-ray absorption spectra in materials under in situ conditions, such as in operando batteries and fuel cells, in situ catalytic reactions, and extreme pressure and temperature conditions.

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Trapping Effect on the Kinetic Critical Radius in Nucleation and Growth Processes

Materials Science Forum ◽

10.4028/www.scientific.net/msf.790-791.97 ◽

2014 ◽

Vol 790-791 ◽

pp. 97-102

Author(s):

Zoltán Erdélyi ◽

Zoltán Balogh ◽

Gabor L. Katona ◽

Dezső L. Beke

Keyword(s):

Critical Nucleus ◽

Solid Phase ◽

Kinetic Monte Carlo ◽

Mean Field ◽

Transformation Process ◽

Nucleus Size ◽

Critical Nucleus Size ◽

Acta Mater ◽

Order Of Magnitude ◽

The Difference

The critical nucleus size—above which nuclei grow, below dissolve—during diffusion controlled nucleation in binary solid-solid phase transformation process is calculated using kinetic Monte Carlo (KMC). If atomic jumps are slower in an A-rich nucleus than in the embedding B-rich matrix, the nucleus traps the A atoms approaching its surface. It doesn’t have enough time to eject A atoms before new ones arrive, even if it would be favourable thermodynamically. In this case the critical nucleus size can be even by an order of magnitude smaller than expected from equilibrium thermodynamics or without trapping. These results were published in [Z. Erdélyi et al., Acta Mater. 58 (2010) 5639]. In a recent paper M. Leitner [M. Leitner, Acta Mater. 60 (2012) 6709] has questioned our results based on the arguments that his simulations led to different results, but he could not point out the reason for the difference. In this paper we summarize our original results and on the basis of recent KMC and kinetic mean field (KMF) simulations we show that Leitner’s conclusions are not valid and we confirm again our original results.

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Berechnung kinetischer Isotopeneffekte für die Reaktion von Methyljodid mit Cyanid-Ion

Zeitschrift für Naturforschung A ◽

10.1515/zna-1966-0909 ◽

1966 ◽

Vol 21 (9) ◽

pp. 1377-1384

Author(s):

A. V. Willi

Keyword(s):

Transition State ◽

Secular Equation ◽

Isotope Effects ◽

Force Constants ◽

Bond Breaking ◽

Bending Force ◽

A Value ◽

Order Of Magnitude ◽

Deuterium Isotope Effects ◽

The Difference

Kinetic carbon-13 and deuterium isotope effects are calculated for the SN2 reaction of CH3I with CN-. The normal vibrational frequencies of CH3I, the transition state I · · · CH3 · · · CN, and the corresponding isotope substituted reactants and transition states are evaluated from the force constants by solving the secular equation on an IBM 7094 computer.Values for 7 force constants of the planar CH3 moiety in the transition state (with an sp2 C atom) are obtained by comparison with suitable stable molecules. The stretching force constants related to the bonds being broken or newly formed (fCC, fCC and the interaction between these two stretches, /12) are chosen in such a way that either a zero or imaginary value for νʟ≠ will result. Agreement between calculated and experimental methyl-C13 isotope effects (k12/ k13) can be obtained only in sample calculations with sufficiently large values of f12 which lead to imaginary νʟ≠ values. Furthermore, the difference between fCI and fCC must be small (in the order of 1 mdyn/Å). The bending force constants, fHCI and fHCC, exert relatively little influence on k12/k13. They are important for the D isotope effect, however. As soon as experimental data on kH/kD are available it will be possible to derive a value for fHCC in the transition state if fHCI is kept constant at 0.205 mdynA, and if fCI, fCC and f12 are held in a reasonable order of magnitude. There is no agreement between experimental and calculated cyanide-C13 isotope effects. Possible explanations are discussed. — Since fCI and fCC cannot differ much it must be concluded that the transition state is relatively “symmetric”, with approximately equal amounts of bond making and bond breaking.

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A Bayesian ensemble data assimilation to constrain model parameters and land-use carbon emissions

Biogeosciences ◽

10.5194/bg-15-2909-2018 ◽

2018 ◽

Vol 15 (9) ◽

pp. 2909-2930 ◽

Cited By ~ 18

Author(s):

Sebastian Lienert ◽

Fortunat Joos

Keyword(s):

Land Use ◽

Carbon Emissions ◽

Latin Hypercube Sampling ◽

Historical Period ◽

Model Parameters ◽

Dynamic Global Vegetation Model ◽

Order Of Magnitude ◽

The Difference ◽

Wood Harvest ◽

Global Vegetation

Abstract. A dynamic global vegetation model (DGVM) is applied in a probabilistic framework and benchmarking system to constrain uncertain model parameters by observations and to quantify carbon emissions from land-use and land-cover change (LULCC). Processes featured in DGVMs include parameters which are prone to substantial uncertainty. To cope with these uncertainties Latin hypercube sampling (LHS) is used to create a 1000-member perturbed parameter ensemble, which is then evaluated with a diverse set of global and spatiotemporally resolved observational constraints. We discuss the performance of the constrained ensemble and use it to formulate a new best-guess version of the model (LPX-Bern v1.4). The observationally constrained ensemble is used to investigate historical emissions due to LULCC (ELUC) and their sensitivity to model parametrization. We find a global ELUC estimate of 158 (108, 211) PgC (median and 90 % confidence interval) between 1800 and 2016. We compare ELUC to other estimates both globally and regionally. Spatial patterns are investigated and estimates of ELUC of the 10 countries with the largest contribution to the flux over the historical period are reported. We consider model versions with and without additional land-use processes (shifting cultivation and wood harvest) and find that the difference in global ELUC is on the same order of magnitude as parameter-induced uncertainty and in some cases could potentially even be offset with appropriate parameter choice.

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