Disequilibrium Processes Research Articles

Crystal Size Distribution of Periclase in Contact Metamorphic Dolomite Marbles from the Southern Adamello Massif, Italy

Crystal size distributions (CSD) of periclase in contact metamorphic dolomite marbles are presented for two profiles near the Cima Uzza summit in the southern Adamello Massif (Italy). The database was combined with geochemical and petrological information to deduce the controls on the periclase-forming reaction. The contact metamorphic dolomite marbles are exposed at the contact of mafic intrusive rocks and are partially surrounded by them. Brucite is retrograde and pseudomorphs spherical periclase crystals. Prograde periclase growth is the consequence of limited infiltration of waterrich fluid at T near 6058C. Stable isotope data show depletion in 13 C and 18 O over a narrow region (� 40 cm) near the magmatic contact, whereas the periclase-forming reaction front extends up to 4 m from the contact. CSD analyses along the two profiles show that the median grain size of the periclase crystals does not change, but that there is a progressively greater distribution of grain sizes, including a greater proportion of larger grains, with increasing distance from the contact. A qualitative model, based on the textural and geochemical data, attributes these variations in grain size to changing reaction affinities along a kinetically dispersed infiltration front. This study highlights the need to invoke disequilibrium processes for metamorphic mineral growth and expands the use of CSDs to systems of mineral formation driven by fluid infiltration.

Cognition and equilibrium regulation in development and aging

Changes in emotion-cognition relationships in later life comprise a pattern of both vulnerabilities and strengths. To integrate this pattern of diversity, I propose a neo-Piagetian extension of the concepts of equilibrium and disequilibrium processes to the relationship beyond cognition to encompass emotional activation and arousal, and beyond youth to the full life span. Beginning with a simple, Cannon-type equilibrium based on the response to increasing deviation from ideal end states of correcting through tension reduction, a more complex model is outlined that additionally uses tension amplification aimed at enlargement of the range over which stability is maintained, i.e., permits processes of developmental progression. Parallel to cognitive development, emotional development is described as the emergence of more complex cognitive-affective structures out of original automatic, biologically based ones. In that process, tension thresholds are raised, and the functional range over which equilibrium can be maintained is widened, as higher-order representations become part of the regulatory network. These progressive movements provide well automated emotion regulation whose effectiveness increases well into middle and late life. In contrast to development, aging is ultimately characterized by a lowering of tension thresholds similar to developmental regression. However, as in the purely intellectual realm, that process is offset by the previous automatization and crystallization of cognitive-affective schemas becomes evident only as a result of increasing constraints on fluid capacities, as in advancing age and/or high load of cognitive effort and/or emotional activation.

Melt–rock reaction in the lower oceanic crust and its implications for the genesis of mid-ocean ridge basalt

Primitive cumulates from a 2–3 Ma old gabbro massif exposed in the Kane Megamullion (23°N, Mid-Atlantic Ridge) contain abundant clinopyroxene with high Mg# (86–91). Such magnesian clinopyroxenes have hitherto been taken to signify crystallization at elevated pressures. Kane clinopyroxenes, however, are dominantly oikocrysts that overgrow olivine and plagioclase, indicating crystallization occurred at low pressure. The oikocrysts have textures and compositions indicative of disequilibrium processes. First, many of the oikocrysts enclose resorbed plagioclase with lower anorthite contents than plagioclase in the host rock, and olivine is notably absent as a chadacryst despite being abundant in the host rock. Second, the oikocryst minor element compositions are inconsistent with equilibrium growth from a MORB melt. These data indicate that high-Mg# clinopyroxene in the Kane gabbros formed as a result of reaction between primitive cumulates and migrating melt in the lower oceanic crust, with clinopyroxene and secondary plagioclase growing at the expense of olivine and primary plagioclase. Thus high-Mg clinopyroxene does not result from high-pressure crystallization as has been inferred previously. Assimilation–fractional crystallization modeling indicates that melts undergoing such reactions are enriched in Al 2O 3 and MgO and depleted in CaO and SiO 2. This effect is similar to that expected for fractional crystallization of MORB at elevated pressures, and reacted melts yield higher calculated pressures than starting melts. This suggests that the CaO–Al 2O 3–MgO–SiO 2 relationships of MORB may result from melt–rock reaction, and that calculated pressures of MORB fractionation are overestimated as a result. Melt–rock reaction in the lower oceanic crust may thus account for both lines of evidence for high-pressure fractionation of MORB.

Tariffs, trade and unemployment in a disequilibrium model: issues and policies

This paper studies the disequilibrium transition process engaged by increased openness to trade, and the effect of institutions, market behaviors and economic policies on that transition. The issue is analyzed with a simple two country (north and south), two goods model, amended in order to take into account the time dimension of both the production and the decision processes. Investigating the consequences of a tariff decrease by means of numerical simulations, we show to what extent wage and price setting, and the degree of tightness of monetary policy affect the outcome of the disequilibrium process. The main result is that capturing the gains associated with international trade requires market behaviors and economic policies, which are rather different from what is usually prescribed.

Marshall vs. Walras on Equilibrium and Disequilibrium

In this paper I critically analyse the view that John Hicks sought to establish, according to which Walras’ and Marshall’s approaches to price theory, while differing in scope (that is, general vs. partial analysis), are basically similar in their aims, presuppositions and results. By focusing on a special kind of economy (the pure-exchange, two-commodity economy), which has been formally studied by both economists with the help of similar tools, we can precisely identify the differences between the two approaches. In particular, I am able to prove that there exists a definite trade-off between observability of the disequilibrium process and generality of the equilibrium concept: for Marshall can succeed in modelling a process of exchange in ‘real’ time with observable out-of-equilibrium trades only at the cost of confining his analysis to a partial equilibrium framework; whereas Walras can succeed in developing a truly general equilibrium model only at the cost of accepting that the underlying equilibration process be downgraded to a virtual process in ‘logical’ time.

Li, Be, and B abundances in minerals of peridotite xenoliths from Marsabit (Kenya): Disequilibrium processes and implications for subduction zone signatures

The light elements Li, Be, and B have been analyzed in situ in minerals from three groups of peridotite xenoliths hosted in Quaternary basanites from the Marsabit volcanic field (northern Kenya). Group I and II are fertile lherzolites that experienced deformation, decompression, and cooling in the context of Mesozoic rifting (Group I), followed by heating, static recrystallization, and associated cryptic metasomatism (Group II) as a result of Tertiary‐Quaternary rifting and magmatism. Group III xenoliths are spinel harzburgites and dunites that experienced strong cryptic and modal metasomatism. The Li‐Be‐B systematics in minerals of Group I and II are similar to unmetasomatized subcontinental lithospheric mantle. In contrast, Group III samples are characterized by significant enrichment in all light elements and disequilibrium partitioning between different phases. Light element concentrations levels are similar to that expected for mantle rocks metasomatized by melts and fluids released from subducting slabs, while light element/rare earth element ratios (especially Li/Yb) approach those of typical Island Arc basalts. However, detailed investigation of textures and chemical zoning shows that at least Li concentrations in primary minerals were modified (i.e., decoupled from Yb) during late‐stage melting and/or fluid percolation related to Tertiary‐Quaternary alkaline magmatism in Marsabit (formation of melt pockets consisting of silicate glass, clinopyroxene, olivine, and chromite), ultimately followed by xenolith entrapment and transport to the surface. Mass balance calculations show that the melt pockets formed at the expense of earlier metasomatic phases. During this process the melt pockets mostly preserved the B, Be, and rare earth element budget of the precursor phase assemblage, whereas Li was added. Elevated B/Be and low Ce/B of metasomatic phases prior to late melting could result from metasomatism by a slab fluid. However, similar characteristics are expected for evolved Si‐ and CO2‐rich fluids derived from basanite melt‐peridotite interaction, not related to any subduction zone process. The results of this study imply that the inference of a “slab signature” exclusively based on trace element data of metasomatized peridotite is ambiguous.

Laboratory Investigations of Enhanced Sulfate Reduction as a Groundwater Arsenic Remediation Strategy

Landfills have the potential to mobilize arsenic via induction of reducing conditions in groundwater and subsequent desorption from or dissolution of arsenic-bearing iron phases. Laboratory incubation experiments were conducted with materials from a landfill where such processes are occurring. These experiments explored the potential for induced sulfate reduction to immobilize dissolved arsenic in situ. The native microbial community at this site reduced sulfate in the presence of added acetate. Acetate respiration and sulfate reduction were observed concurrent with dissolved iron concentrations initially increasing from 0.6 microM (0.03 mg L(-1)) to a maximum of 111 microM (6.1 mg L(-1)) and subsequently decreasing to 0.74 microM (0.04 mg L(-1)). Dissolved arsenic concentrations initially covaried with iron but subsequently increased again as sulfide accumulated, consistent with the formation of soluble thioarsenite complexes. Dissolved arsenic concentrations subsequently decreased again from a maximum of 2 microM (148 microg L(-1)) to 0.3 microM (22 microg L(-1)), consistent with formation of sulfide mineral phases or increased arsenic sorption at higher pH values. Disequilibrium processes may also explain this second arsenic peak. The maximum iron and arsenic concentrations observed in the lab represent conditions most equivalent to the in situ conditions. These findings indicate that enhanced sulfate reduction merits further study as a potential in situ groundwater arsenic remediation strategy at landfills and other sites with elevated arsenic in reducing groundwater.

TEXTURES AND COMPOSITIONAL VARIABILITY IN GERSDORFFITE FROM THE CRESCENCIA Ni (Co U) SHOWING, CENTRAL PYRENEES, SPAIN: PRIMARY DEPOSITION OR RE-EQUILIBRATION?

At the Crescencia showing in the Pyrenees, Spain, three stages of mineral deposition can be distinguished: stage I: nickeline and pararammelsbergite, stage II: gersdorffite, and stage III: uraninite. Gersdorffite has been subdivided into seven groups on the basis of textural and compositional criteria. Some of these groups of gersdorffite clearly show disequilibrium processes that may have been induced by secondary reactions associated with a re-equilibration of the system during cooling. Formation and subsequent growth of gersdorffite nuclei on the nickeline (0001) surface, self-organization, or a coupled dissolution-and-reprecipitation moving interface through pararammelsbergite or nickeline are some of the processes invoked during the re-equilibration. Thus, the compositional variations found in the seven groups of gersdorffite are likely due to intermediate steps during the bulk of the replacement and re-equilibration processes at low temperature, rather than a direct precipitation from the ore-forming fluids under different conditions.

Government Expenditures and Revenues: Evidence from Asymmetric Modeling

In this article, we examine the relationship between U.S. federal revenues and expenditures while relaxing the assumption of a symmetric adjustment process underlying the conventional cointegration and error correction model. Threshold autoregression and momentum threshold autoregression models are used to ascertain the empirical link between the two variables of the budgetary process. Our results suggest that revenues and expenditures are cointegrated and that the adjustment process of the budgetary disequilibrium is asymmetric. The application of the asymmetric error correction model indicates that revenues and expenditures respond to the long‐run requirements of the budgetary balance only when the budget is worsening.

Ureilite petrogenesis: A limited role for smelting during anatexis and catastrophic disruption

Abstract— A popular model for ureilites assumes that during anatexis in an asteroidal mantle, pressure-buffered equilibrium smelting (partial reduction coincident with partial melting) engendered their conspicuous mafic-silicate-core mg diversity (75–96 mol%). Several mass-balance problems arise from this hypothesis. Smelting inevitably consumes a large proportion of any plausible initial carbon while generating significant proportions of Fe metal and copious proportions of CO gas. The most serious problem concerns the yield of CO gas. If equilibrium smelting produced the ureilites' entire 21 mol% range in olivine-core mg, the proportion of gas within the asteroidal mantle (assuming plausibly low pressure <˜80 bar) should have reached ≥85 vol%. Based on the remarkably stepwise cooling history inferred from ureilite texture and mineralogy, a runaway, CO-leaky process that can loosely be termed smelting appears to have occurred, probably triggered by a major impact. The runaway scenario appears likely because, by Le Châtelier's principle, CO leakage would tend to accelerate the smelting process. Also, the copious volumes of gas produced by smelting would have led to explosive, mass-leaky eruptions into the vacuum surrounding the asteroid. Loss of mass would mean diminution of interior pressure, which would induce further smelting, leading to further loss of mass (basalt), and so on. Such a disruptive runaway process may have engendered the ureilites' distinctive reduced olivine rims. But the only smelting, according to this scenario, was a short-lived disequilibrium process that reduced only the olivine rims, not the cores; and the ureilites were cooling, not melting, during the abortive “smelting” episode.

Siderophile geochemistry of ureilites: A record of early stages of planetesimal core formation

New bulk-compositional data, including trace siderophile elements such as Ir, Os, Au, and Ni, are presented for 25 ureilites. Without exception, ureilites have siderophile abundances too high to plausibly have formed as cumulates. Ureilites undoubtedly underwent a variety of “smelting,” by which C was oxidized to CO gas while olivine FeO was reduced to Fe-metal. However, pressure-buffered equilibrium smelting is not a plausible model for engendering the wide range (75–96 mol%) of mafic-silicate core mg among ureilites. The smelting reaction produces too much CO gas. Even supposing a disequilibrium process with the smelt-gas leaking out of the mantle, none of the ureilites, least of all the ureilite with the most “reduced” (highest) olivine-core mg (ALH84136), has the high Fe-metal abundance predicted by the smelted-cores model. In principle, the Fe-metal generated by smelting could have been subsequently lost, but siderophile data show that ureilites never underwent efficient depletion of Fe-metal. Ureilites display strong correlations among siderophile ratios such as Au/Ir, Ni/Ir, Co/Ir, As/Ir, Se/Ir, and Sb/Ir. Ureilite siderophile depletion patterns loosely resemble siderophile fractionations, presumably nebular in origin, among carbonaceous chondrites. However, Zn, for an element of moderate volatility, is anomalously high in ureilites. A tight correlation between Au and Ni extrapolates to the low-Ni/Au side of the compositional range of carbonaceous chondrites. From this mismatch, mild but nonetheless significant depletions of refractory siderophile elements such as Ir and Os, and moderate depletions of strongly siderophile, weakly chalcophile elements such as Ni and Au, we infer that the ureilite siderophile fractionations are largely the result of a non-nebular process, i.e., removal of S-rich metallic melt, possibly with minor entrainment of Fe-metal. Several lines of trace-element evidence indicate that melt porosity during ureilite anatexis was at least moderate. The ureilite pattern of very mild depletions of extremely siderophile elements, but much deeper depletions of moderately siderophile, chalcophile elements, suggests that asteroidal core formation probably occurs in two discrete stages. In general, separation of a considerable proportion (several wt%) of S-rich metallic melt probably occurs long before, and at a far lower temperature than, separation of the remaining S-poor Fe-metal. Apart from the Fe-metal itself, only extremely siderophile elements wait until the second stage to sequester mainly into the core.

From fluid inclusion microanalysis to large-scale hydrothermal mass transfer in the Earth's interior

This paper illustrates how the recent development of microanalytical techniques for major- and trace-elements in fluid and melt inclusions contributes to the quantitative understanding of lithosphere-scale chemical transport by hydrothermal fluids, including the formation of mineral deposits. After an introductory remark on aspects of instrumentation and data quality assessment, the first-order controls of crustal fluid compositions are discussed, indicating that trace-element concentrations broadly follow silicate rock buffered conditions. However, field-based studies of texturally controlled ore-forming liquid and vapour inclusions in specific upper-crustal magmatic centres show that effective ore formation is a disequilibrium process, requiring deviations of fluid composition from the crustal rock buffers. Microanalytical techniques are also changing experimental approaches in the laboratory, allowing fluid trapping experiments for investigating mineral solubilities, melt-fluid distribution constants, and the chemical properties of fluids responsible for selective element transfer from the downgoing slab to the melting region of calc-alkaline magmas in the mantle wedge.

Effects of H2O, pH, and oxidation state on the stability of Fe minerals on Mars

On Mars, there is evidence that solutions may have been present on the surface episodically in the past. These solutions were derived by weathering minerals such as olivine and sulfides found in mafic‐ultramafic rocks, and possibly sulfates and meteorite fragments. Upon removal of water and/or supersaturation of solutions, secondary minerals formed. We present a theoretical model for the formation of the solutions and the subsequent precipitation of Fe‐bearing phases. The first Fe‐bearing phases to weather via oxidation are sulfides (troilite or pyrrhotite) which produce secondary Fe (hydr)oxides or FeS2(pyrite or marcasite) and Fe2+sulfates such as melanterite. Melanterite may be replaced by Fe sulfates that have decreasing H2O/(3Fe3++ 2Fe2+), increasing oxidation, and increasing bulk OH/(OH + 2SO4). At Meridiani Planum the presence of jarosite indicates that the solutions were oxidized with pH &lt; 4.5. The solutions were likely Fe‐Mg‐(Ca)‐SO4‐(Cl)‐rich and precipitated Fe (hydr)oxides, Fe phosphates, Fe sulfates with low OH/(OH + SO4), Ca‐Mg sulfates, and possible halides, along with Si‐rich phases. The minerals indicating an acid environment were preserved by either removing components such as salts or water from the system (e.g., in dust storms or episodic aqueous events); isolating the mineral surfaces from fluids; using disequilibrium processes; or a combination. At other localities, jarosite is below detection limits, and schwertmannite may be present. If schwertmannite is present, the solution had near‐neutral pH (∼4 &lt; pH &lt; 10) and Fe (hydr)oxides would have crystallized rapidly, leaving Mg‐Na‐(Ca)‐SO4‐Cl‐rich solutions that likely precipitated Ca phosphates, Ca‐Mg‐Na sulfates, Fe sulfates with moderate‐high OH/(OH + SO4), halides, Si‐rich phases, and possibly Fe‐Mg‐Ca carbonates.

Complex speleothem growth processes revealed by trace element mapping and scanning electron microscopy of annual layers

Closely-spaced transects measured by excimer laser ablation inductively-coupled plasma mass spectrometry (ELA-ICPMS) at 5 and 32 μm spatial resolution are used to generate trace element composition maps (Ba, Sr, Mg, U, Na, P and Al) from MND-S1, a previously studied modern stalagmite from southwest Australia ( Treble et al., 2003: EPSL 216: 141). Rainfall at the site is highly seasonal, and trace elements in MND-S1 show strong seasonal variation. Trace element maps show that Ba, Sr, U and Na concentrations coherently follow annual growth layers identified from Scanning Electron Microscopy (SEM) images. The SEM images also reveal that stalagmite growth did not proceed uniformly: growth layers vary in thickness and locally pinch out. Highly preferential crystal growth, determined by nucleation sites left by the previous year’s growth, may be responsible for this uneven growth layering. Differential crystal growth apparently causes variability of trace element concentrations along each annual layer, although additional disequilibrium processes affect Mg, which is less distinctly banded than Ba, Sr, U and Na. Uneven and discontinuous growth layers influence the number of annual cycles, their wavelengths and seasonal amplitudes measured in any one transect. This has clear implications for studies that use annual trace element cycles as chronological markers, growth rate or seasonality proxies.

Strontium in coral aragonite: 3. Sr coordination and geochemistry in relation to skeletal architecture

Use of the coral Sr palaeothermometer assumes that the Sr in coral skeletons is substituted randomly for Ca in the aragonite structure. The presence of Sr in additional phases e.g., strontianite, or the non random distribution of Sr across metal sites in aragonite, would complicate the Sr/Ca-sea surface temperature relationship. We have used Sr K-edge microEXAFS (extended X-ray absorption fine structure) to determine the structural state of Sr across selected microvolumes of four coral skeletons ( Porites lobata, Acropora palmata, Pavona clavus, and Montastrea annularis). We used a 5 × 3 μm beam to analyse specific areas of the coral skeletal architecture, i.e., centres of calcification, fasciculi, and dissepiments. All EXAFS analyses refine, within error, to an ideally substituted Sr in aragonite, and we found no evidence of strontianite or partly ordered structural states. Anisotropy in the first shell responses results from the fact that the analysed microvolumes are not necessarily averaged for the responses of all crystal orientations in the aragonite. Although secondary ion mass spectrometry confirmed that Sr/Ca composition can vary substantially between skeletal components, we find no evidence for any contrast in Sr structural state. Sr heterogeneity may result from kinetic effects, reflecting complex disequilibrium processes during crystal precipitation, or biological effects, resulting from variations in the composition of the calcifying fluid which are biologically mediated.

The volcanic activity of Stromboli in the 1906–1998 AD period: mineralogical, geochemical and isotope data relevant to the understanding of the plumbing system

Volcanic activity of Stromboli in the last 100 years was characterised by regular Strombolian eruptions with some occurrences of major explosions and paroxysms at the summit crater and lava flows down into the Sciara del Fuoco. Two types of juvenile fragments, shoshonitic to high-K basalts in composition, are peculiarly outpoured during major explosions: black scoriae, similar to those erupted by the normal Strombolian activity, representing a highly porphyritic (45–60 vol%), volatile-poor magma (HP magma) and a small volume of light pumice, representing a low-porphyritic (<10 vol%), volatile-rich magma (LP magma). Lava flows are constituted by the HP magma. The LP magma has a less evolved composition, lower incompatible trace element contents and Sr isotope ratios (0.70610) than the HP magma. Mineral phases in equilibrium with the LP and HP magmas have distinct compositions (Fo% in olivine: 80–85 and around 70, Mg# in clinopyroxene: 0.83–0.91 and around 0.75, An% in plagioclase: 80–90 and around 65, respectively), in spite of syn-eruptive mingling, and disequilibrium processes lead to large compositional ranges in minerals of both LP and HP magmas. Olivine and clinopyroxene of pumice were equilibrated at higher temperatures (and probably higher pressures) than the same crystals of scoriae. All these data provide evidence that the two magmas are characterised by sharply distinct physico-chemical conditions. It has also been pointed out that the plumbing system is under overall steady-state conditions. The HP magma resides at shallow level and evolves in a continuously erupting, crystallising (olivine+clinopyroxene+plagioclase) and replenished reservoir, which is fed by the LP magma. The LP magma derives from a deeper reservoir in which it undergoes limited crystallisation of femic phases. Plagioclase begins to crystallise only at lower depth. Significant geochemical, mineralogical and isotope variations with time in scoriae and lavas of the 20th century are observed. The MgO, V, Ni and Cr contents of magmas slightly increase from 1906 to 1930, then decrease from 1965 towards the present. Mineral chemistry data also vary accordingly. An increase of incompatible trace element contents after 1930 and a decrease of Sr isotope ratios after 1980–85 (from 0.70626 to 0.70616) have also been pointed out. These variations are thought to be due to changes in the crystallisation/replenishment equilibrium of the magma reservoir or to compositional modifications of the feeding magma. Some correlations between the main compositional variations and the type of eruptive activity also seem to be present. The occurrence of relatively frequent paroxysms during the first part of the 20th century, associated with the observed decrease of magma evolution, seems to indicate that more energetic explosions are associated with the rise of a higher volume of refreshing magma.

Cumulative Causation and Evolutionary Micro-Founded Technical Change

Cet article developpe une approche alternative a l’analyse des differences en taux de croissance entre economies telle que proposee par les Nouvelles Theories de la Croissance. Notre analyse se place dans une approche de la croissance comme un processus en desequilibre. Ce dernier repose sur le cadre developpe dans la theorie dite de la croissance cumulative pour laquelle le changement technique resulte de processus microeconomiques inspires par les approches evolutionnistes et neo-autrichienne. En ce sens, nous remplacons la traditionnelle loi de Kaldor-Verdoorn par une modelisation explicite de la dynamique industrielle. A l’aide de ce modele, nous cherchons a identifier les sources de divergences entre economies liees notamment a certains parametres macroeconomiques et technologiques. Ceci nous permettra de mettre en evidence differents regimes de divergence, nuancant ainsi certains resultats trouves dans la litterature. JEL Classification: O41, O30, F43

Technical progress, accumulation and financial constraints: is the productivity paradox really a paradox?

In the standard representation of technology, productivity is built into the production function as a given relationship between inputs and output. This representation needs an equilibrium framework, in which the ratios between the factors and output are constant and corresponding to those dictated by the production function coefficients. In this framework, technological advances should be instantaneously mapped into increases in productivity, and the only way to explain the ‘productivity paradox’ is to assume adoption delays. We propose a different approach, by which productivity is the outcome of an out-of-equilibrium process triggered by a technological shock. The potential gains of a superior technology may only be appropriated if agents succeed in reshaping the productive capacity (whose distinguishing feature is to be temporally articulated), and in recovering the intertemporal coordination disrupted by the introduction of the new technique. Physical, human, and financial capital are complementary in this process of reshaping, and may constrain each other. The outcome of the disequilibrium process depends then on the interaction of accumulation choices, learning, and money supply rules. We argue that the different performances of the US and Europe in the last two decades may be explained along these lines.

Nonlinear macrokinetics of heat and mass transfer and chemical or electrochemical reactions

We consider single-phase and multiphase disequilibrium processes in presence of nonlinear heat and mass transfer as well as chemical or electrochemical reactions. An approach accepted distinguishes in each elementary process, diffusive or chemical, two competing (unidirectional) fluxes. They are equal in the state of thermodynamic equilibrium and their difference off equilibrium constitutes the observed resulting flux representing the rate of chemical reaction. We stress the role of nonlinear chemical (electrochemical) resistance and chemical (electrochemical) affinity. The nonequilibrium systems under investigation are described by equations of nonlinear kinetics of Marcelin–de Donder type containing exponential terms with respect to chemical potentials of Planck and temperature reciprocal, that simultaneously are analytical expressions characterizing the transport of the substance or energy by the energy barrier. We show how the kinetics of this sort follows from the law of mass action, what are its consequences closely and far from equilibrium, and also how a basic equation of chemical or electrochemical kinetics (Butler–Volmer) emerges. We also stress the significance of nonlinear chemical (electrochemical) resistance and of the chemical (electrochemical) affinity. Simultaneously we stress restrictiveness of the discrete energy barrier, which is not capable of avoiding mean quantities characteristic of the whole barrier and connected with finite affinities or driving forces. To describe the chemical transformation as a motion through the energy barrier treated as a continuum an effort is made to replace the logarithmic chemical resistance (a mean quantity associated with a finite affinity) by its local counterpart. The result is a continuous description, governed by a principle of Fermat type with an infinite number of infinitesimal refractions of the ray. The results show that the path of chemical complex bends into a direction that ensures its shape associated with longest residence time in regions of lower resistivity. These properties make it possible to predict shapes of chemical paths.

Rb-sr dating of epithermal vein mineralization stages in the eastern Harz Mountains (Germany) by paleomixing lines

A method is evaluated that enables the dating of binary isotopic paleomixing in hydrothermal alteration assemblages by iterative reconstruction and regression of corresponding two-component mixing lines from conventional Rb-Sr data. The model has been applied to illite-bearing granulometric fractions of hydrothermally altered sedimentary rocks associated with epithermal vein mineralization in the eastern Harz Mountains, Germany. These veins are characterized by a principal quartz-sulfide stage containing quartz, base metal sulfides, and siderite and a subsequent dominant calcite-fluorite-quartz stage. Rb-Sr analyses were performed on untreated granulometric fractions, HCl-treated residues, corresponding HCl leachates, and cogenetic vein minerals obtained from two silicified rock samples related to the quartz-sulfide and the calcite-fluorite-quartz mineralization, respectively. Neither the untreated nor the HCl-leached fractions of these rock samples yield statistically robust and geochronologically meaningful isochrons. When applying the binary mixing model, however, two well-defined paleomixing lines can be reconstructed for the HCl-treated fractions of the rock samples and associated vein minerals at model ages of 226 ± 1 Ma (quartz-sulfide alteration) and 209 ± 2 Ma (calcite-fluorite-quartz alteration). We examine the significance and reliability of these model ages and the corresponding paleomixing lines by means of statistical and geological criteria and discuss the effects of leaching experiments performed on the granulometric fractions using 1 N HCl as well as the nature and origin of the components dissolved in the acid leachates. Our results suggest that the mixing model provides a successful dating concept for isotopic disequilibrium processes during low-temperature hydrothermal events that produce binary mixtures among newly formed alteration phases.