Revised equation and table for determining the freezing point depression of H2O-Nacl solutions

The concept of strength envelopes, developed in the 1970s, allowed quantitative predictions of the strength of the lithosphere based on experimentally determined constitutive equations. Initial strength envelopes used an empirical relation for frictional sliding to describe deformation along brittle faults in the upper portion of the lithosphere and power law creep equations to estimate the plastic flow strength of rocks in the deeper part of the lithosphere. In the intervening decades, substantial progress has been made both in understanding the physical mechanisms involved in lithospheric deformation and in refining constitutive equations that describe these processes. The importance of a regime of semibrittle behavior is now recognized. Based on data from rocks without added pore fluids, the transition from brittle deformation to semibrittle flow can be estimated as the point at which the brittle fracture strength equals the peak stress to cause sliding. The transition from semibrittle deformation to plastic flow can be approximated as the stress at which the pressure exceeds the plastic flow strength. Current estimates of these stresses are on the order of a few hundred megapascals for relatively dry rocks. Knowledge of the stability of sliding along faults and of the onset of localization during brittle fracture has improved considerably. If the depth to the bottom of the seismogenic zone is determined by the transition to the stable frictional sliding regime, then that depth will be considerably more shallow than the depth of the transition to the plastic flow regime. Major questions concerning the strength of rocks remain. In particular, the effect of water on strength is critical to accurate predictions. Constitutive equations which include the effects of water fugacity and pore fluid pressure as well as temperature and strain rate are needed for both the brittle sliding and semibrittle flow regimes. Although the constitutive equations for dislocation creep and diffusional creep in single-phase aggregates are more robust, few data exist for plastic deformation in two-phase aggregates. Despite the fact that localization is ubiquitous in rocks deforming both in brittle and plastic regimes, only a limited amount of accurate experimental data are available to constrain predictions of this behavior. Accordingly, flow strengths now predicted from laboratory data probably overestimate the actual rock strength, perhaps by a significant amount. Still, the predictions are robust enough that uncertainties in geometry, mineralogy, loading conditions and thermodynamic state are probably the limiting factors in our understanding. Thus, experimentally determined rheologies can be applied to understand a broad range of topical problems in regional and global tectonics both on the Earth and on other planetary bodies.

Strength of the lithosphere: Constraints imposed by laboratory experiments

https://www.whoi.edu/fileserver.do?id=180587&pt=2&p=59967

Water in the oceanic upper mantle: implications for rheology, melt extraction and the evolution of the lithosphere

[1] We describe a newly calibrated model for the thermodynamic properties of magmatic silicate liquid. The new model, pMELTS, is based on MELTS [Ghiorso and Sack, 1995] but has a number of improvements aimed at increasing the accuracy of calculations of partial melting of spinel peridotite. The pMELTS algorithm uses models of the thermodynamic properties of minerals and the phase equilibrium algorithms of MELTS, but the model for silicate liquid differs from MELTS in the following ways: (1) The new algorithm is calibrated from an expanded set of mineral-liquid equilibrium constraints from 2439 experiments, 54% more than MELTS. (2) The new calibration includes mineral components not considered during calibration of MELTS and results in 11,394 individual mineral-liquid calibration constraints (110% more than MELTS). Of these, 4924 statements of equilibrium are from experiments conducted at elevated pressure (200% more than MELTS). (3) The pMELTS model employs an improved liquid equation of state based on a third-order Birch-Murnaghan equation, calibrated from high-pressure sink-float and shockwave experiments to 10 GPa. (4) The new model employs a revised set of end-member liquid components. The revised components were chosen to better span liquid composition-space. Thermodynamic properties of these components are optimized as part of the mineral-liquid calibration. Comparison of pMELTS to partial melting relations of spinel peridotite from experiments near 1 GPa indicates significant improvements relative to MELTS, but important outstanding problems remain. The pMELTS model accurately predicts oxide concentrations, including SiO2, for liquids from partial melting of MM3 peridotite at 1 GPa from near the solidus up to � 25% melting. Compared to experiments, the greatest discrepancy is for MgO, for which the calculations are between 1 and 4% high. Temperatures required to achieve a given melt fraction match those of the experiments near the solidus but are � 60� C high over much of the spinel lherzolite melting interval at this pressure. Much of this discrepancy can probably be attributed to overstabilization of clinopyroxene in pMELTS under these conditions. Comparison of pMELTS calculations to the crystallization and partial melting experiments of Falloon et al. [1999] shows excellent agreement but also suffers from exaggerated calculated stability of clinopyroxene. Finally, comparison of pMELTS

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2001GC000217

The pMELTS: A revision of MELTS for improved calculation of phase relations and major element partitioning related to partial melting of the mantle to 3 GPa

https://fluids.unileoben.ac.at/Publications_files/Bakker2003a.pdf

Package FLUIDS 1. Computer programs for analysis of fluid inclusion data and for modelling bulk fluid properties

Freezing point depression of NaCl-KCl-H 2 O solutions

Synthetic fluid inclusions. V. Solubility relations in the system NaCl-KCl-H2O under vapor-saturated conditions

A new form of equation of state is proposed for use over extremely wide ranges of pressure where conventional equations fail. In particular, fluids including H2O and CO2 as well as argon, etc., remain more compressible at very high densities than can be represented by typical equations with van der Waals or Carnahan and Starling repulsive terms. The new equation is fitted to the data for H2O and CO2 over the entire range from the vapor and liquid below the critical temperature to at least 2000 K and from zero pressure to more than 105 bar (10 GPa) with good agreement. The extension of the equation for mixed fluids is discussed.

Equations of state valid continuously from zero to extreme pressures for h2o and co2

Synthetic fluid inclusions in natural quartz I. Compositional types synthesized and applications to experimental geochemistry

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/27326/0000349.pdf;sequence=1

S. Michael Sterner

Papers

Freezing point depression of NaCl-KCl-H 2 O solutions

Synthetic fluid inclusions. V. Solubility relations in the system NaCl-KCl-H2O under vapor-saturated conditions

Equations of state valid continuously from zero to extreme pressures for h2o and co2

Synthetic fluid inclusions in natural quartz I. Compositional types synthesized and applications to experimental geochemistry

Synthetic fluid inclusions in natural quartz. IV. Chemical analyses of fluid inclusions by SEM/EDA: Evaluation of method