Search USGS⌕ Search
Home/Archive/USGS

USGS · 70016423

Solid-solution aqueous-solution equilibria: Thermodynamic theory and representation

P. D. Glynn·E.J. Reardon
View original source ↗Export metadata ↓

Abstract

Thorstenson and Plummer's (1977) "stoichiometric saturation' model is reviewed, and a general relation between stoichiometric saturation Kss constants and excess free energies of mixing is derived for a binary solid-solution B1-xCxA: GE = RT[ln Kss - xln(xKCA) - (l-x)ln((l-x)KBA)]. This equation allows a suitable excess free energy function, such as Guggenheim's (1937) sub-regular function, to be fitted from experimentally determined Kss constants. Solid-phase free energies and component activity-coefficients can then be determined from one or two fitted parameters and from the endmember solubility products KBA and KCA. A general form of Lippmann's (1977,1980) "solutus equation is derived from an examination of Lippmann's (1977,1980) "total solubility product' model. Lippmann's II or "total solubility product' variable is used to represent graphically not only thermodynamic equilibrium states and primary saturation states but also stoichiometric saturation and pure phase saturation states.

Explore related subjects

American Journal of ScienceArticle

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

P. D. Glynn, E.J. Reardon. 1990. Solid-solution aqueous-solution equilibria: Thermodynamic theory and representation. https://doi.org/10.2475/ajs.290.2.164

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related USGS reports

USGS2025

Rare earth element-mineralized carbonatite in the Bear Lodge Alkaline Complex, USA—Ore genesis implications from fluid inclusion characterization

Rare earth element (REE) resources of the Bear Lodge Alkaline Complex, Wyoming, are hosted in variably leached carbonatite spatially related to diatreme breccia pipes. We investigated the genesis of REE and lesser-known gold resources through fluid inclusion analysis of carbonatite, fluorite breccia, and smoky quartz vein samples. Physicochemical characteristics of inclusion-trapped fluids were evaluated using petrography, microthermometry, Raman spectroscopy, decrepitate mound analysis, energy-dispersive spectroscopy, laser ablation inductively coupled plasma mass spectrometry, and noble gas isotope analysis. Microthermometry results reveal three fluid types that affected carbonatite dikes within deeper zones that escaped near-surface, ore-grade REE enrichment: (1) high-temperature (330–432°C) magmatic fluid captured in fine-grained calcite; (2) REE-enriched alkali bicarbonate-sulfate brine; and (3) low-temperature (117–182°C) diluted magmatic or meteoric water. Multiphase brine-like inclusions contain burbankite, nahcolite, strontianite, celestine and alkali sulfate daughter crystals, linking them to early burbankite mineralization. Peripheral smoky quartz and fluorite occurrences at Smith Ridge, 1.5 km from the central carbonatite dike swarm, contain primary inclusions that are Cl-poor and rich in Na-HCO 3 -SO 4 , similar to secondary and pseudosecondary inclusions in carbonatites. Helium isotopes reveal a MORB-like source for carbonatite samples and an older crust signature at Smith Ridge, consistent with the proximal ridge-top exposures of Archean granite. Results from this fluid inclusion study coupled with previous studies of carbonatite mineral paragenesis, show that light REEs (LREEs) were not mobilized great distances. Instead, burbankite crystallized within carbonatite from alkali bicarbonate fluids. With sodium retained in early burbankite, outward-emanating fluids enriched in potassium relative to sodium (higher K:Na) resulted in potassium–ferric iron metasomatism of silicate host rocks. This alkali fractionation was accompanied by fractionation of LREEs and heavy REEs (HREEs), with LREEs dominating the central carbonatite resources. In contrast, areas of peripheral REE mineralization at Bear Lodge are commonly characterized by higher HREE:LREE ratios. The K:Na ratio of associated fenites or alteration assemblages could be indicative of early crystallized burbankite in carbonatites and REE fractionation processes potentially leading to areas of concentrated HREEs with greater supply vulnerabilities.

South Dakota, Wyoming↗
USGS2024

Deformation by pressure solution and grain boundary sliding in a retrograde shear zone in southern New England, USA

Alleghanian phyllonites in a shear zone in southern New England were formed by the retrogression and hydration of a high-grade Acadian pelitic schist. The retrogression was locally incomplete, resulting in both heterogeneous mineralogy and mineral compositions, and in many arrested reaction textures. These features, documented by backscattered electron and element map imaging, and by 40 Ar/ 39 Ar dating, provide a record of the processes active as the schist was converted to a phyllonite. On the margins of the shear zone relic biotite and garnet grains survive but are partially replaced by chlorite. Relic high-grade muscovite flakes containing up to 35 % paragonite (pg) also persist but are entrained in swarms of pg-poor muscovite flakes producing folia with an anastomosing network of muscovite grains of variable composition. Single crystals of pg-rich muscovite are truncated by muscovite in successively younger cross-cutting folia that contain decreasing pg contents, falling to <5% pg in the youngest folia. In the core of the shear zone all high-grade minerals are destroyed, but recrystallization continues with earlier greenschist facies folia replaced by lower grade and pg-poorer muscovite in younger folia. Muscovite grains in truncated folia are commonly kinked and selective recrystallization of muscovite in kink bands to pg-poor-compositions demonstrates that strain energy helped drive recrystallization. The boundaries of these new pg-poor muscovite folia are sharp, and truncations indicate that grain boundary sliding (GBS) involved dissolution. GBS also enabled folding by flexural slip along muscovite grain boundaries. Fold amplitudes increased as chlorite dissolved from fold limbs precipitated in fold hinges producing crescent-shaped saddle-reef-like structures. Together these observations of truncation and replacement by dissolution and precipitation demonstrate that pressure solution and GBS facilitated both the formation of the phyllonitic shear zone and slip along it.

Connecticut↗
USGS2023

The geometry and kinematics of the latest paleozoic Allatoona Fault, one of the youngest thrusts in the southernmost Appalachian Hinterland, Alabama and Georgia, U.S.A.

The Allatoona thrust fault in the southernmost hinterland of the Appalachian Blue Ridge-Piedmont megathrust sheet is among the latest structures in the kinematic sequence of events along the west flank of the orogen. It is an out-of-sequence, craton-directed thrust fault that cuts metamorphic isograds and earlier thrusts, and it has a nearly linear trace of ≥280 km, making it one of the major thrust faults in the orogen. On the northwest, the fault cuts Pennsylvanian or younger(?) regional cross antiforms that cause significant orogenic curvature of older underlying thrust sheets and is likely Permian in age. To the southeast, however, units within the fault hanging wall maintain a nearly constant width resulting in a significant change in the regional structural architecture of the orogen. In the central segment of the fault, where it marks the western/eastern Blue Ridge domain boundary, a ~20 km-long eyelid window (Mulberry Rock window) framed by three amphibolite facies thrust sheets overlying the greenschist facies Talladega belt allochthon, allows a 3-D view into the structural architecture, kinematics, and trajectories of the regional thrusts. Two earlier thrusts within the window (Mulberry Rock and Burnt Hickory Ridge thrusts, with a combined minimum horizontal net slip component of 27 km) are cut by the Allatoona fault, which is a ~15 m-wide high strain zone with top-to-the-northwest displacement, and a >17.2 km horizontal net slip vector. Structural branch points between the Allatoona and Mulberry Rock thrusts indicate that the Mulberry Rock allochthon is a large north-trending horse beneath the Allatoona fault, centered on the Mulberry Rock window, which is likely the result of oblique ramp thrusting over the massive Mulberry Rock Gneiss. The Allatoona fault cuts down obliquely into the tectonostratigraphy progressively deeper both to the northeast and northwest, locally approaching underlying foreland thrust sheets, and cutting older regional structures. To the northeast, the Allatoona fault lies at the base of the Dahlonega gold belt, becoming an internal eastern Blue Ridge thrust at Dawsonville, Georgia. Although that sequence extends another 120 km into North Carolina, continuation of the Allatoona fault that additional distance is in debate. Regardless, the Allatoona is one of the kinematically latest and longest faults in the southern Appalachian orogen.

Alabama, Georgia, South Carolina↗