Fluid flow paths and mechanisms of fluid infiltration in carbonates during contact metamorphism: the Beinn an Dubhaich aureole, Skye

A textural study of marbles from the Beinn an Dubhaich granite contact aureole, Skye, has shown that mass transport by diffusion was probably negligible during the metamorphic event, and that the bulk of the carbonates reacted as a consequence of silica metasomatism, permitting the use of calcsilicates as a tracer for fluid infiltration pathways. Fracture-controlled infiltration was predominant in undeformed marbles, whereas pervasive infiltration occurred during synmetamorphic ductile deformation. Some calcite marbles contain disseminated unoriented calcsilicate minerals that are associated with neither fractures nor a ductile deformation fabric, consistent with an origin via infiltration of fluid along an interconnected grain-edge porosity. The inference of limited pervasive infiltration of undeformed carbonates is consistent with predictions based on experimentally determined fluid–solid dihedral angles.     

Geochemical self-organization of olivine-grade contact metamorphosed chert nodules in dolomite marble, Kilchrist, Skye

Chert nodules in dolostones in the aureole of the Tertiary Beinn an Dubhaich granite, Skye, have developed  mm-scale concentric monomineralic bands of alternating calcite and olivine during breakdown of a diopside core by the reaction 3 Dol+Di=4 Cal+2Fo+2 CO₂. A simple textural progression from thin (<1 cm) homogeneous olivine-calcite rims close to the olivine-in isograd, to total replacement of the diopside core by a ≤10 cm thick well-banded rim close to the carbonate-granite contact demonstrates the developmental stages of the patterning. Correlation of olivine grain size with band spacing, and a greater olivine grain size in banded compared with homogeneous rims support pattern development by post-nucleation geochemical self-organization.     

Effects of dry density and exchangeable cations on the diffusion process of sodium ions in compacted montmorillonite

As a part of the safety assessment of the geological disposal of high-level radioactive waste, the effects of dry density and exchangeable cations on the diffusion process of Na⁺ ions in compacted bentonite were studied from the viewpoint of the activation energy for diffusion. The apparent self-diffusion coefficients of Na⁺ ions in compacted Na-montmorillonite and in a Na- and Ca-montmorillonite mixture were determined by one-dimensional, non-steady diffusion experiments at different temperatures and dry densities. A unique change in activation energy as a function of dry density was found for the Na⁺ ions in compacted Na-montmorillonite. The activation energy suddenly decreased from 18.1 to 14.1 kJ mol^− 1 as the dry density increased from 0.9 to 1.0 Mg m^− 3, whereas it increased to 24.7 kJ mol^− 1 as the dry density increased to 1.8 Mg m^− 3. Examination of the effect of exchangeable cations on the activation energies determined that the activation energies were almost constant, approximately 25 kJ mol^− 1, for the montmorillonite specimens at a dry density of 1.8 Mg m^− 3. However, three different activation energy values were obtained at a dry density of 1.0 Mg m^− 3. These findings cannot be explained by the conventional diffusion model (the pore water diffusion model), which suggests that the predominant diffusion process alternates among pore water diffusion, interlayer diffusion, and external surface diffusion.     

A computational study of oxygen diffusion in olivine

Atomistic modelling techniques are used to study the rate-determining steps that limit diffusion of oxygen in forsterite. The activation energies for diffusion parallel to all three crystallographic axes by the vacancy and interstitial mechanisms are calculated. The activation energy for extrinsic vacancy diffusion is predicted to be isotropic with a barrier height of 119 kJ mol^–1. Conversely, in the interstitial case it is found to be anisotropic, with extrinsic activation energies that range between 94 and 178 kJ mol^–1. The effect of intrinsic defects and two typical impurities, iron and hydrogen, upon diffusion is also considered. We find that the migration energy is slightly higher in iron-rich fayalite compared with forsterite and that the presence of hydrogen defects will not affect the diffusion mechanism. These observations lead us to reinterpret existing experimental results on oxygen diffusion in natural olivine. We suggest that at low oxygen partial pressure the mechanism observed is a vacancy mechanism, while at high oxygen partial pressure the mechanism is interstitial. We believe that this change in mechanism is mediated by iron redox reactions. Taking this process into account, we derive activation energies in excellent agreement with those found experimentally in natural samples of olivine. The anisotropy of activation barriers and hence the change in diffusion rates with temperature could be used to distinguish between the two mechanisms in future experimental work.     

Formation and destruction of periclase by fluid flow in two contact aureoles

Periclase formed in steeply dipping marbles from the Beinn an Dubhaich aureole, Scotland, and the Silver Star aureole, Montana, by the reaction dolomite = periclase + calcite + CO₂. Equilibrium between rock and fluids with X _{CO 2} < 1 requires that reaction was infiltration-driven. Brucite pseudomorphs after periclase occur in the Beinn an Dubhaich aureole either as bed-by-bed replacement of dolomite or in a lens along the contact between dolomite and a pre-metamorphic dike. Transport theory predicts that infiltration drove both periclase reaction and ¹⁸O-depletion fronts which moved at significantly different velocities along the flow path. The distributions of brucite and ¹⁸O-depleted rocks are identical in surface exposures, thus indicating upward flow. Time-integrated flux (q) was <500 mol/cm² and the fluid source was magmatic. Because periclase and its hydrated equivalent brucite are unaltered to dolomite by retrograde reactions, the exposure of brucite marbles accurately images the flow paths of peak metamorphic fluids. In the Silver Star aureole brucite pseudomorphs after periclase exclusively occur in tabular bodies that are beds with elevated Mg/Ca. The spatial pattern of ¹⁸O-depletion requires upward vertical fluid flow. Estimated prograde q ≈ 10³–10⁴ mol/cm² and the fluid source was magmatic. Low Mg/Ca, ¹⁸O-depleted, brucite-free rocks pose a dilemma because the periclase reaction front should have traveled ≈18 times further through them than the isotope alteration front. The dilemma is resolved by reaction textures that indicate periclase and brucite were destroyed in low Mg/Ca rocks by infiltration-driven retrograde carbonation reactions. Values of retrograde q were ≈10³–10⁴ mol/cm². Brucite (after periclase) was preserved only in high Mg/Ca layers where periclase developed in greater abundance. The geometry of brucite marbles at Silver Star thus reflects the location of high Mg/Ca beds rather than the geometry of fluid flow. Retrograde reactions must be considered before the mineralogical record of prograde fluid flow can correctly be interpreted. In both aureoles fluid flow, mineral reaction, and isotope depletion were structurally controlled by bedding and lithologic contacts. Received: 30 July 1996 / Accepted: 21 March 1997     

Effect of impurities on grain growth in synthetic calcite aggregates

 We investigated grain growth of calcite aggregates fabricated from crushed natural single crystals with different impurity content. The total trace-element concentration of the starting powders varied from about 170 ppm to more than 930 ppm with Mn as the major component. Samples were produced by hot-isostatic pressing of the different powders at 300 MPa confining pressure at 600 °C for 2 h. The starting material for the anneals was dry and had a uniform microstructure with an average grain size of about 5 μm and a porosity of <2.1%. Three disks with Mn concentrations of 10, 350, and 670 ppm, respectively, were annealed in the same run at a confining pressure of 300 MPa, and temperatures between 700 and 900 °C for up to 20 h. Grain growth was fastest in samples with the highest Mn concentrations. A multivariable fit to the data yields grain-growth exponents of 2.0 ± 0.3 for samples with 10 ppm Mn and 2.3 ± 0.2 for those with 670 ppm Mn. The activation energies for grain growth vary from 99 ± 12 kJ mol⁻¹ to 147 ± 14 kJ mol⁻¹ for the respective calcite compositions. Received: 22 August 2000 / Accepted: 12 March 2001     

Palæohydrology of the calcsilicate aureole of the Beinn an Dubhaich granite, Skye, Scotland: a stable isotopic study

The contact aureole developed in siliceous carbonates surrounding the Beinn an Dubhaich granite, Skye, shows textural and stable isotope evidence for infiltration of aqueous fluids during both prograde and retrograde metamorphism. Strongly depleted isotope compositions of reaction-product calcite correlate with high silica and fluorine contents, demonstrating a strong link between isotopic alteration and metasomatism by fluids with a significant magmatic component, even at the margins of the aureole. The oxygen and carbon isotope compositions of the carbonates form a linear cluster with a positive slope of about five, consistent with the depletion of isotope compositions by the infiltration of magmatic and/or meteoric fluids. Rayleigh fractionation during devolatilization played a minor role in determining the final isotope composition. Stable isotope compositions of coexisting calcite–dolomite pairs show varying amounts of isotopic disequilibrium, which correlate with the inferred fluid infiltration mechanism. Much of the calcite in dolostones is the product of infiltration-driven reactions along fractures, and is greatly depleted isotopically relative to the host dolomite, especially at talc grade. At higher grades the calcite–dolomite fractionation is smaller, probably due to both increased fluid–rock interaction and a greater tendency for fluid infiltration to be pervasive on the grain-scale. Limestones generally show near-equilibrium fractionation of oxygen and carbon owing to the overwhelming compositional influence of the host calcite. Veins formed during late-stage hydrothermal circulation have strongly ¹⁸O-depleted compositions relative to the host rock. No small-scale spatial patterns to the isotopic depletion were observed, but the extent of fluid infiltration was greatest in the west of the aureole. Fluid infiltration was clearly highly heterogeneous, with no evidence of a consistent flow direction. It is not possible to determine fluid fluxes or flow directions from one-dimensional flow models based on continuum flow in the Beinn an Dubhaich aureole.     

Metasomatism and self-organization of dolerite dyke–marble contacts: Beinn an Dubhaich, Skye

Dolerite dykes which intrude dolomitic marble in the aureole of the Beinn an Dubhaich granite on the Isle of Skye have developed metasomatized margins close to the contact with the (younger) granite in the southern part of Torrin Quarry. These margins display well-defined mineralogical zones which can be divided into two groups on the basis of composition. Chlorite-bearing margins display the sequence dolerite | diopside+spinel | chlorite+calcite+magnetite | olivine+calcite+spinel | dolomite, whereas phlogopite-bearing sequences have a phlogopite+calcite±fluorapatite layer in place of the chlorite-bearing layer. No spatial pattern is seen in the distribution of the two margin types, but textural and compositional evidence points to an importance of metasomatism by localized infiltration of magmatic fluids in the development of the phlogopite-bearing sequences. Extensive patterning of the phlogopite-bearing margins by a process of self-organization during grain growth has resulted in the formation of alternating silicate-only/calcite-only layers parallel to the dyke margin on a millimetre to centimetre scale. Early development of chlorite-bearing sequences at the dolerite–dolomite contact during contact metamorphism was followed by metasomatism-controlled growth of phlogopite and patterning at or after the peak of metamorphism associated with the expulsion of aqueous fluids from the crystallizing pluton.     

Activation energy for diffusion of helium in water-saturated, compacted Na-montmorillonite

It is important to clarify the migration behavior of hydrogen gas dissolved in water-saturated, compacted bentonite, which is a promising material for geologic disposal of high-level waste and TRU waste disposal. The diffusion coefficients of helium, which can be detected under extremely low background conditions, in water-saturated, compacted Na-montmorillonite were determined as a function of temperature by a transient diffusion method. The activation energies for diffusion of helium were then obtained. The activation energies were from 6.9 ± 4.8 to 19 ± 2.8 kJ mol^− 1 and were regarded to be independent of dry density. The activation energies of helium in water-saturated Na-montmorillonite were roughly equal to those in bulk water, 14.9 kJ mol^− 1, and in ice, from 11 to 13 kJ mol^− 1. It is possible that helium diffuses not only in pore water but also in interlayer water.     

Electrical conduction and polarization of calcite single crystals

The electrical conductivity and polarization properties of calcite single crystals with three orientations, namely, a (00.1) plane perpendicular to the crystallographic c axis (10.0) plane parallel to the crystallographic c axis, and a (10.4) cleavage plane, were studied by both complex impedance and thermally stimulated depolarization current (TSDC) measurements. Conductivities for (00.1)-, (10.0)-, and (10.4)-oriented single calcite crystals at 400–600?°C were 1.16?×?10^?7?–?1.05?×?10^?5, 7.40?×?10^?8?–?4.27?×?10^?6, and 4.27?×?10^?7?–?2.86?×?10^?5 Ω^?1 m^?1, respectively, and the activation energies for conduction were 112, 103, and 101?kJ?mol^?1, respectively. The TSDC spectra verified the electrical polarizability of calcite crystals. The activation energy for depolarization, estimated from TSDC spectra, of the (00.1)-, (10.0)-, and (10.4)-oriented calcite substrates were 112, 119, and 114?kJ?mol^?1, respectively. Considering the correlation between the processes of conduction and electric polarization, we proposed the mechanisms of conduction and polarization in calcite on the assumption of oxide ion transport.     

Dissolution kinetics of dolomite: Effects of lithology and fluid flow velocity

The dissolution kinetics of three stoichiometric dolomite specimens (hydrothermal single crystal, microcrystalline sedimentary rock, coarse-grained marble) were studied in aqueous carbonate solutions. Hydrodynamic conditions were controlled through use of a rotating dolomite disk in which one face was exposed to solution and fluid flow regime was defined by spinning rate. The resulting mass transfer properties were uniform across the disk surface. The dissolution experiments were begun at an initially undersaturated condition set by CO₂ at ~ 1 atm dissolved in deionized water. The reaction was followed by measuring concentrations of Ca²⁺, Mg²⁺, HCO₃^?, and pH over time in a free-drift type of experiment at 0, 15, and 25°C.Dissolution rates for all three samples were similar in form and value; grain size effects were insignificant. Ca/Mg was constant throughout each run at 0.81–0.96. From initial conditions, the dissolution rate decreased as the solution became more saturated. At solution conditions still far from equilibrium (ion activity product = 10^?19), rate dropped off sharply to a very low value. Surface morphology, determined by SEM, showed deep narrow holes in the single crystal, while the rocks dissolved along grain boundaries. These features suggested preferential dissolution of energetically favored sites and surface reaction rate control. Initial rates were used to calculate an apparent activation energy of 32 kJ mol^?1 (sedimentary dolomite) and 27 kJ mol^?1 (single crystal).Initial dissolution rates at 25°C and pH ~ 4 for all samples varied with spinning speed and ranged from 1–3 μmol m^?2 s^?1 for laminar flow conditions to almost 3–6 μmol m^?2 s^?1 as the transition to turbulence began. At lower temperatures, the rate was lower, and increasing spinning velocity had less effect. The strongest spinning rate dependence occurred far from equilibrium, and it became a less important factor as the saturation state increased.     

Interfacial energies for quartz and albite in pelitic schist

Interfacial energies of quartz/quartz (qz/qz), albite/albite (ab/ab), and quartz/albite (qz/ab) boundaries in low-grade pelitic schist were determined based on measured values of dihedral angles. Three kinds of microstructures were investigated, and the interfacial energies were obtained in two independent ways. (1) Relative values of interfacial energy were calculated from dihedral angles formed at quartz and albite triple junctions. (2) Subgrain boundary energy was calculated using the Read-Shockley theory for a boundary connected to an intergranular pore. Dihedral angles formed at the corners of intergranular pores were measured. From the interfacial tension balance equation, the value of the qz/qz grain boundary energy was then obtained. (3) Dihedral angles formed at intersections of either pericline or albite twin boundaries with either ab/ab or qz/ab boundaries were measured. The twin boundary energy was calculated based on a previously derived equation using Landau potential, twin wall thickness, and critical temperature for a phase transition in albite. With a modified interfacial tension balance equation for a twin boundary fixed to a facet orientation, the interfacial energies of ab/ab and qz/ab boundaries were obtained. Energies obtained by methods of (2) and (3) are in good agreement. The interfacial energies for qz/qz, ab/ab, and qz/ab boundaries obtained in this study are 270뀶, 300끞, and 250끀 mJ/m², respectively.     

Thermal decomposition of NH4-analcime

The thermal decomposition of ammonium-exchanged natural analcime is characterized by gas chromatography, IR spectroscopy and X-ray diffraction. The de-ammoniation and dehydroxylation proceed in parallel throughout the decomposition, which evidences the instability of the protonated analcime framework. The mechanism of degassing of NH₄-analcime changes throughout its decomposition. At the initial step, the mechanism of de-ammoniation consists in thermal dissociation of NH₄⁺ molecule onto NH₃ and proton (framework OH group) and diffusion of NH₃ out of the structure. Subsequent decomposition and removal of the OH groups lead to a progressive loss of crystallinity. At this step, an apparent activation energy for NH₃ desorption is estimated to be 145(±13) kJ mol^–1. This value is within the upper limit of the activation energy characteristic for the NH₃ desorption from proton centres in large-pore zeolites. At the final step, the adsorption of NH₃ and protons onto the defect centres in the amorphosed aluminosilicate framework results in a significant increase of an apparent activation energy for the de-ammoniation and dehydroxylation up to 270(±20) kJ mol^–1.     

Kinetics and mechanisms of the leaching of low Fe sphalerite

The surface speciation and leaching kinetics of 38- to 75-μm sphalerite (0.45 wt.% Fe) particles reacted in O₂ purged perchloric acid (at pH 1.0) at 25, 40, 60, and 85 °C over a leach period of 144 h were investigated. In all cases, an initial rapid leach rate is observed followed by a slower leach rate. These two leach regimes can each be adequately modeled using straight-line interpolation, and thus two activation energies (E_a) have been derived. E_a for the fast and slow Zn dissolution rates were 33 ± 4 kJ mol⁻¹ and 34 ± 4 kJ mol⁻¹ respectively, suggesting the same rate-determining step.     

The solubility of calcite and aragonite in seawater of 35%. salinity at 25°C and atmospheric pressure

The solubilities of synthetic, natural and biogenic aragonite and calcite, in natural seawater of 35%. salinity at 25°C and 1 atm pressure, were measured using a closed system technique. Equilibration times ranged up to several months. The apparent solubility constant determined for calcite of 4.39(±0.20) × 10^?7 mol² kg^?2 is in good agreement with other recent solubility measurements and is constant after 5 days equilibration. When we measured aragonite solubility we observed that it decreased with increasing time of equilibration. The value of 6.65(±0.12) × 10^?7 mol² kg^?2, determined for equilibration times in excess of 2 months, is significantly less than that found in other recent measurements, which employed equilibration times of only a few hours to days. No statistically significant difference was found among the synthetic, natural and biogenic material. Solid to solution ratio, contamination of aragonite with up to 10 wt% calcite and recycling of the aragonite made no statistically significant difference in solubility when long equilibration times were used.Measured apparent solubility constants of aragonite and calcite are respectively 22( ± 3)% and 20( ± 2)% less than apparent solubility constants calculated from thermodynamic equilibrium constants and seawater total activity coefficients. These large differences in measured and calculated apparent solubility constants may be the result of the formation of surface layers of lower solubility than the bulk solid.     

On the Use of Changes in Dihedral Angle to Decode Late-stage Textural Evolution in Cumulates

The melt-filled pore structure in the final stages of solidificationof cumulates must lie somewhere between the two end-membersof impingement (in which pore topology is controlled entirelyby the juxtaposition of growth faces of adjacent grains) andtextural equilibrium (in which pore topology is controlled bythe minimization of internal energies). The exact position betweenthese two end-members is controlled by the relative rates ofcrystal growth and textural equilibration. For samples in whichgrowth has stopped, or is very slow, textural equilibrium willprevail. A close examination of dihedral angles in natural examplesdemonstrates that these two end-member textures can be distinguished.The impingement end-member results in a population of apparentsolid–melt dihedral angles with a median of 60° anda standard deviation of 25–30°, whereas the texturallyequilibrated end-member population has a median of 28° anda standard deviation of 14°. For the specific case of cumulatesin the Rum Layered Intrusion, residual porosity in troctoliticcumulates was close to the impingement end-member, whereas thatin peridotites was close to melt-bearing textural equilibrium.Suites of glass-bearing samples from small, or frequently disturbed,magma systems show modification of initial impingement textures.These modifications may be a consequence of textural equilibrationor of diffusion-limited growth during quenching. Distinctioncan be made between these two processes by a consideration ofgrain shape. The geometry of interstitial phases in suites offully solidified cumulates from the Rum Layered Intrusion showsvariable approach to sub-solidus textural equilibrium from aninitial state inherited by pseudmorphing of the last melt. Texturalequilibration at pore corners occurs as a continuous process,with a gradual movement of the entire dihedral angle populationtowards the equilibrium final state. If the initial, pseudomorphedstate is one of disequilibrium (i.e. a melt-present impingementtexture) this change is accompanied by a reduction in the spreadof the population. If it is one of equilibrium, the change isaccompanied by an initial increase in the spread of the population,followed by a decrease. These observations demonstrate thatpreviously published models of dihedral angle change involvingthe instantaneous establishment of the equilibrium angle inthe immediate vicinity of the pore corner are incorrect. KEY WORDS: cumulate; dihedral angle; textural evolution; Rum intrusion; Kula; Santorini     

Empirical tests of carbon isotope thermometry in granulites from southern California

Abstract ‘Peak’metamorphic carbon isotope fractionations between calcite and graphite (Δ_Cal–Gr) in marbles and calc-silicates from the Cucamonga granulite terrane (San Gabriel Mountains, California) range from 3.48 to 2.90%. The data are used to test three previously published calibrations of the calcite–graphite carbon isotope thermometer. An empirical calibration of the calcite–graphite carbon isotope thermometer gives temperatures of 700–750°C; a theoretical–experimental calibration of the system gives temperatures of 760°–870°C; an experimental calibration gives temperatures of 870–1300°C. Temperatures calculated using the empirical calibration are in agreement with those calculated from garnet-based cation exchange thermometry when uncertainty is considered. Temperatures calculated using the theoretical–experimental calibration overlap the upper range of cation exchange thermometry temperatures and range to 50°C higher. The experimental calibration yields temperatures from 50 to 480°C higher than those from cation exchange thermometry. Moreover, temperatures from the experimental calibration are also inconsistent with mineral and melt equilibria in the granulite phase assemblage. Despite the better agreement between cation exchange thermometry and the empirical calibration of the calcite–graphite system, temperatures calculated using the theoretical–experimental calibration may be real peak metamorphic temperatures. If retrograde diffusion partially reset garnet-based cation exchange thermometers by c. 50°C, then the cation exchange temperatures are consistent with those from the theoretical–empirical calibration. Thermometric evidence from biotite dehydration melting equilibria is consistent with either the empirical calibration if melting was fluid-present, or the theoretical–experimental calibration if melting was fluid-absent.     

Rare earth element and gallium diffusion in yttrium aluminum garnet

Diffusion of four rare-earth elements and gallium has been measured in yttrium aluminum garnet (YAG). Sources of diffusant were mixtures of alumina and rare-earth element oxides for REE diffusion, and mixtures of gallium and yttrium oxides for Ga diffusion. Diffusion profiles were measured with Rutherford backscattering spectrometry (RBS). For the rare-earth elements investigated, the following Arrhenius relations were obtained: D_La=6.87×10^–1 exp (–582±21 kJ mol^–1 /RT) m²s^–1 D_Nd=1.63×10^–1 exp (–567±15 kJ mol^–1 /RT) m²s^–1 D_Dy=2.70×10⁰ exp (–603±35 kJ mol^–1 /RT) m²s^–1 D_Yb=1.50×10^–2 exp (–540±26 kJ mol^–1 /RT) m²s^–1 Diffusion rates for the rare earths are quite similar, in contrast with trends noted for zircon. It is likely that these differences are a consequence of the relative ionic radii of the REE and the cations for which they substitute in the mineral lattice. For gallium, the following Arrhenius relation was determined: D_Ga=9.96×10^–6 exp (–404±19 kJ mol^–1 /RT) m²s^–1 Gallium diffuses faster than the REE in YAG and has a smaller activation energy for diffusion. These data mirror relative trends in diffusion rates for YIG, in which trivalent cations occupying tetrahedral and octahedral sites (i.e., Al, Ga, Fe) diffuse faster than trivalent cations occupying dodecahedral sites (i.e., Y and the REE), and suggest that the rate-limiting process in the diffusion-controlled regime of solid-state creep of YAG is the diffusion of yttrium. Received: 10 November 1997 / Revised; accepted: 13 March 1998     

Heat capacity and thermodynamic functions of xenotime YPO<Subscript>4</Subscript>(c) at 0–1600 K

The heat capacity of xenotime YPO₄(c) was measured by adiabatic calorimetry at 4.78–348.07 K. Our experimental and literature data on H ⁰(T)-H ⁰(298.15 K) of Y orthophosphate were utilized to derive the C _p ⁰(T) function of xenotime at 0–1600 K, which was then used to calculate the values of thermodynamic functions: entropy, enthalpy change, and reduced Gibbs energy. These functions assume the following values at 298.15 K: C _p ⁰ (298.15 K) = 99.27 ± 0.02 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 93.86 ± 0.08 J K⁻¹ mol⁻¹, H ⁰(298.15 K) − H ⁰(0) = 15.944 ± 0.005 kJ mol⁻¹, Φ⁰(298.15 K) = 40.38 ± 0.08 J K⁻¹ mol⁻¹. The value of the free energy of formation Δ _f G ⁰(YPO₄, 298.15 K) is −1867.9 ± 1.7 kJ mol⁻¹.     

Comparison of isoleucine epimerization in a model dipeptide and fossil protein

The dipeptide isoleucyl-glycine in aqueous solution has activation energies for isoleucine epimerization and hydrolysis of 23.1 and 20.9 kcal mol^?1, respectively. The activation energy for epimerization of NH₂-terminal isoleucine is 5–8 kcal mol^?1 less than activation energies reported for epimerization of isoleucine in the free state or in various protein systems. Furthermore, the rate of isoleucine epimerization in the NH₂-terminal position exceeds the rate of hydrolysis at temperatures between 0 and 152°C. Consequently, a high rate of epimerization in fossils should only occur when isoleucine is in the terminal position. Partially epimerized isoleucine will be converted through hydrolysis from the terminal form to the slower epimerizing free isoleucine. Over the course of the total isoleucine epimerization reaction, either in dipeptides or proteins, the activation energy will increase and the reaction rate will decrease as terminal isoleucine is converted to free isoleucine. This process may explain the non-linear kinetics observed for isoleucine epimerization in carbonate fossils.The degree of isoleucine epimerization is low in different molecular weight fractions of a fossil protein from Mercenaria in all fractions greater than 500 mol. wt, where most isoleucine is likely to be in the interior position. In the less than 500 mol. wt peptide fraction, where a considerable portion of the isoleucine is likely to be in the terminal position, the degree of epimerization is significantly greater. These analytical results from fossil protein support the interpretation of isoleucine kinetics obtained by study of dipeptides.