A three-dimensional Hoek–Brown failure criterion based on an elliptical Lode dependence

A new three-dimensional (3D) Hoek–Brown (HB) failure criterion based on an elliptical Lode dependence is proposed to describe failure of rocks and concrete under multiaxial stress states. This criterion not only inherits all benefits of the classical HB criterion that is developed for the triaxial compression (TXC) of rocks but also accounts for the effect of the intermediate principal stress. It is capable of representing the strength difference between the triaxial extension (TXE) and TXC with the introduction of an additional coefficient k (0.5 ≤ k ≤ 1.0), which can be derived from TXE tests or taken as 0.53 for rocks in cases where the TXE test data is unavailable. Other two material constants (m_i and σ_ci) involved in this criterion can be obtained from TXC tests. Additionally, the failure surface of this criterion is smooth and convex on the deviatoric stress plane when 0.5 < k ≤ 1.0. The new criterion achieves very good fit to the test data of TXC/TXE, biaxial compression, and polyaxial compression (PXC) on a wide variety of rock materials and concrete, reported in the literature. Comparison of the new criterion with an existing 3D HB criterion based on the same Lode dependence has demonstrated that the new criterion performs better than the latter for test data of rock and concrete under multiaxial stress states except for PXC test data of one rock type. Finally, the influence of values of k on the accuracy of the new criterion is discussed.     

Processes and kinetics of Cd2+ sorption by a calcareous aquifer sand

The rate of Cd²⁺ sorption by a calcareous aquifer sand was characterized by two reaction steps, with the first step reaching completion in 24 hours. The second step proceeded at a slow and nearly constant rate for at least seven days. The first step includes a fast adsorption reaction which is followed by diffusive transport into either a disordered surface film of hydrated calcium carbonate or into pore spaces. After 24 hours the rate of Cd²⁺ sorption was constant and controlled by the rate of surface coprecipitation, as a solid solution of CdCO₃ in CaCO₃ formed in recrystallizing material. Desorption of Cd²⁺ from the sand was slow. Clean grains of primary minerals, e.g. quartz and aluminosilicates. sorbed much less Cd²⁺ than grains which had surface patches of secondary minerals, e.g. carbonates, iron and manganese oxides. Calcite grains sorbed the greatest amount of Cd²⁺ on a weight-normalized basis despite the greater abundance of quartz. A method is illustrated for determining empirical binding constants for trace metals at in situ pH values without introducing the experimental problem of supersaturation. The binding constants are useful for solute transport models which include a computation of aqueous speciation.     

Molybdenum Mass Fractions and Stable Isotope Compositions of Sedimentary Carbonate and Silicate Reference Materials

A double‐spike method in combination with MC‐ICP‐MS was applied to obtain molybdenum (Mo) mass fractions and stable isotope compositions in a suite of sedimentary silicate (marine, lake, stream, estuarine, organic‐rich sediment, shales, slate, chert) and carbonate reference materials (coral, dolomite, limestones, carbonatites), and a manganese nodule reference material, poorly characterised for stable Mo isotope compositions. The Mo contents vary between 0.076 and 364 μg g^?1, with low‐Mo mass fractions (< 0.29 μg g^?1) found almost exclusively in carbonates. Intermediate Mo contents (0.73–2.70 μg g^?1) are reported for silicate sediments, with the exception of chert JCh‐1 (0.24 μg g^?1), organic‐rich shale SGR‐1b (36.6 μg g^?1) and manganese nodule NOD‐A‐1 (364 μg g^?1). The Mo isotope compositions (reported as δ⁹⁸Mo relative to NIST SRM 3134) range from ?1.77 to 1.03‰, with the intermediate precision varying between ± 0.01 and ± 0.12‰ (2s) for most materials. Low‐temperature carbonates show δ⁹⁸Mo values ranging from 0.21 to 1.03‰ whereas δ⁹⁸Mo values of ?1.77 and ?0.17‰ were obtained for carbonatites CMP‐1 and COQ‐1, respectively. Silicate materials have δ⁹⁸Mo values varying from ?1.56 to 0.73‰. The range of δ⁹⁸Mo values in reference materials may thus reflect the increasingly important relevance of Mo isotope investigations in the fields of palaeoceanography, weathering, sedimentation and provenance, as well as the magmatic realm.     

Assessing Decomposition Rates of Rhizophora mangle and Laguncularia racemosa Leaves in a Tropical Mangrove

Studies exploring leaf decomposition in mangroves in the Brazilian northeast are scarce. Therefore, in a mangrove of the Cachoeira River estuary at Ilhéus, Bahia, the decomposition of senescent leaves of Rhizophora mangle L. and Laguncularia racemosa Gaertn was studied. The litter-bag method and the Olson exponential model were applied to estimate the decomposition rates. The decay pattern of leaf material of both species was similar to those reported in the literature, with rapid initial weight loss, followed by a deceleration and period of slow weight loss. L. racemosa had the highest decay constants at all the study sites which suggest that their leaves are more easily degraded than those of R. mangle. The constantly submerged site presented the highest decay constants of 0.022 g g^?1 day^?1 for R. mangle and 0.031 g g^?1 day^?1 for L. racemosa. Most (95 %) of the leaf material of the two species was lost in 135 and 98 days, respectively. Benthic macrofauna organisms were recorded in the litter bags from the fifth day after the start of the experiment. Such organisms play a key role in the first phase of decomposition in this mangrove system. The decay constants of the leaf litter were generally higher than those reported in other tropical and subtropical regions. This suggests that differences in the process of decomposition are in response to environmental conditions at each location.     

Studies on the spin Hamiltonian parameters and local structure for Rh4+ and Ir4+ in TiO2

The spin Hamiltonian (SH) parameters (g factors g _x , g _y and g _z and the hyperfine structure constants A _x , A _y and A _z ) and local structure for the rhombic Rh⁴⁺ and Ir⁴⁺ centers in TiO₂ (rutile) are theoretically studied from the perturbation formulas of these parameters for a low spin (S = 1/2) d ⁵ ion under rhombically distorted octahedra. In the calculations, the ligand orbital and spin–orbit coupling contributions as well as the influence of the local lattice distortions are taken into account using the cluster approach. The local axial elongation ratios are found to be about 1.7 and 3 times, respectively, larger for the Rh⁴⁺ and Ir⁴⁺ centers than that (≈0.0075) for the host Ti⁴⁺ site in rutile, while the perpendicular distortion angles (≈−0.28° and −0.42°, respectively) are more than one order in magnitude smaller than the host value (≈−9.12°). This means that the impurity centers exhibit further elongations of the oxygen octahedra and much smaller perpendicular rhombic distortions as compared with those of the host Ti⁴⁺ site in TiO₂. The above local lattice distortions can be mainly ascribed to the substitution of the host Ti⁴⁺ by the nd ⁵ impurities, which may induce different physical and chemical properties for the metal–ligand clusters. In addition, the influence of the Jahn–Teller effect on the local structure may not be completely excluded. The calculated SH parameters show reasonable agreement with the observed values.     

How well known are the thermodynamics of Fe–Mg–Ca garnet? Evidence from experimentally determined exchange equilibria

ABSTRACT Many thermodynamic calculations relating to metamorphic rocks hinge on the thermodynamic parameters of garnet. Though some models are widely used, it is not clear whether their underlying premise is correct: that a single set of equations can be written for the activities of the end-members of garnet covering the whole compositional range. A voluminous body of data can be used to constrain the thermodynamics of garnet, namely Fe–Mg exchange experimental data involving garnet and another mineral, particularly clinopyroxene, orthopyroxene and olivine. However, examination of these data reveals inconsistencies, apparently stemming from differences between the thermodynamics of low-Ca and high-Ca garnets, with a boundary of about X^g_Ca= 0.15. In the two regions, for the high P–T of the experimental data, the thermodynamics follow the regular model, with values for the interaction parameters in the low Ca region of about w^g_FeMg= 50R and w_aFe–w^g_MgCa=– 1300R, in which R is the gas constant, and in the high Ca region of about w^g_FeMg= 1100R and w^g_CaFe–w^g_MgCa=– 2200R. Using the subregular, rather than the regular, model does not remove the discrepancy. The cause of the discrepancy needs to be identified if reliable calculations on rocks are to be made.     

δ98/95Mo values and Molybdenum Concentration Data for NIST SRM 610, 612 and 3134: Towards a Common Protocol for Reporting Mo Data

Molybdenum concentration and δ^98/95Mo values for NIST SRM 610 and 612 (solid glass), NIST SRM 3134 (lot 891307; liquid) and IAPSO seawater reference material are presented based on comparative measurements by MC‐ICP‐MS performed in laboratories at the Universities of Bern and Oxford. NIST SRM 3134 and NIST SRM 610 and 612 were found to have identical and homogeneous ⁹⁸Mo/⁹⁵Mo ratios at a test portion mass of 0.02 g. We suggest, therefore, that NIST SRM 3134 should be used as reference for the δ–Mo notation and to employ NIST SRM 610 or 612 as solid silicate secondary measurement standards, in the absence of an isotopically homogeneous solid geological reference material for Mo. The δ^98/95Mo_{JMC Bern} composition (Johnson Matthey ICP standard solution, lot 602332B as reference) of NIST SRM 3134 was 0.25 ± 0.09‰ (2s). Based on five new values, we determined more precisely the mean open ocean δ^98/95Mo_{SRM 3134} value of 2.09 ± 0.07‰, which equals the value of δ^98/95Mo_{JMC Bern} of 2.34 ± 0.07‰. We also refined the Mo concentration data for NIST SRM 610 to 412 ± 9 μg g^?1 (2s) and NIST SRM 612 to 6.4 ± 0.7 μg g^?1 by isotope dilution. We propose these concentration data as new working values, which allow for more accurate in situ Mo determination using laser ablation ICP‐MS or SIMS.     

Measurement of the Dielectric Properties of Volcanic Scoria and Basalt at 9370 MHz

Dielectric data for volcanic scoria and basalt on the earth at microwave frequency are extremely sparse, and also crucial for volcanic terrains imaging, and development. In consideration of their similarity to lunar regolith (soils and rocks) in chemical and mineral composition, the dielectric data is significative for passive and active microwave remote sensing on the Moon. This study provides the data about the dielectric properties of three kinds of scoria and two kinds of basalt in China. The method put forward in this paper is also applicable for measuring the dielectric properties of dry rocks and other granular ground materials with low complex dielectric constants. Firstly, the authors measured the ε‘ and tanδ values of strip specimens prepared from the mixture of scoria or basalt powder and polythene with the resonant cavity perturbation method at 9370 MHz. Secondly, from the ε‘ and tang values of the mixture, the ε‘s and tanδs values of sofid scoria and basalt were calculated using Lichtenecker‘s mixture formulae. Finally, the effective complex dielectric constants, ε‘e and tanδs, of scoria at different bulk densities were calculated. The results have shown that the ε‘s and tang svalues of all solid basaltic materials measured (both solid basaltic scoria or basalt) are approximately 7 and 0.05,respectively. With increasing bulk density of scoria, the ε‘s and tanδs values of scoria increase significantly.     

EPR investigation of the methyl radical,the hydrogen atom and carbon oxide radicals in Maxixe-type beryl

The EPR spectra of Maxixe-type beryl contain a large number of overlapping signals. The angular dependence of the 1:3:3:1 signal typical for the CH₃ radical shows that this radical is located at the center of the channel cavity with its symmetry axis parallel to the crystal c-axis and is rotating around this axis. Its EPR spectrum is axially symmetric with g _// = 2.00263, g _⊥ = 2.00249 and A_// = 2.288 mT, A_⊥ = 2.256 mT. These anisotropies have the opposite signs of those found for surface-adsorbed methyl radicals. Hydrogen atoms are located at position 2a at the center of the beryl cavity and the EPR parameters of the narrow doublet signal are A ₀ = 1,407 MHz and g = 2.00230. Another doublet signal, which is broader and has axial symmetry with g _// = 2.00265, g _⊥ = 2.00625 and A_// = 0.895 mT, A_⊥ = 0.885 mT, could come from a HCO₃ radical. One narrow and easily saturated signal with g _// = 2.00227 and g _⊥ = 2.00386 is interpreted to arise from a carbon monoxide radical in the beryl channel, oriented with its axis parallel to the crystal c-axis. Additional weak doublet lines, which have similar g values as the carbon monoxide radical, are created by nearby hydrogens. A powder spectrum with g _// = 2.0017 and g _⊥ = 2.0004 appears upon UV irradiation of the single crystal and is easily saturated. This spectrum is interpreted to arise from a carbon dioxide radical, which rotates around its symmetry axis.     

High pressure elasticity and phase transformation in brucite, Mg(OH)2

The first pressure derivatives of the second-order elastic constants have been calculated for brucite, Mg(OH)₂ from the second- and third-order elastic constants. The deformation theory and finite strain elasticity theory have been used to obtain the second- and third-order elastic constants of Mg(OH)₂ from the strain energy of the lattice. The strain energy ϕ is calculated by taking into account the interactions up to third nearest neighbors in the Mg(OH)₂ lattice. ϕ is then compared with the strain dependent lattice energy from continuum model approximation to obtain the expressions of elastic constants. The complete set of six second-order elastic constants C _IJ of brucite exhibits large anisotropy. Since C ₃₃ (= 21.6 GPa), which corresponds to the strength of the material along the c-axis direction, is less than the longitudinal mode C ₁₁ (= 156.7 GPa), the interlayer binding forces are weaker than the binding forces along the basal plane of Mg(OH)₂. The 14 nonvanishing components of the third-order elastic constants, C _IJK , of brucite have been obtained. All the C _IJK of brucite are negative except the values of C ₁₁₄ (= 230.36 GPa), C ₁₂₄ (= 75.45 GPa) and C ₁₃₄ (= 36.98 GPa). The absolute values of the C _IJK are, in general, one order of magnitude greater than the C _IJ ’s in the Mg(OH)₂ system as usually expected for a crystalline material. To our knowledge, no previous data are available to compare the pressure derivatives of brucite. The pressure derivatives of the two components viz., C ₁₄ and C ₃₃ become negative indicating an elastic instability in brucite while under pressure. This may be related to the phase transition of brucite largely involving rearrangements of H atoms revealed in the Raman spectroscopic, powder neutron diffraction and synchrotron X-ray diffraction studies.     

A macroscopic damage‐plastic constitutive law for modeling quasi‐brittle fracture and ductile behavior of concrete

A new phenomenological macroscopic constitutive model for the numerical simulation of quasi‐brittle fracture and ductile concrete behavior, under general triaxial stress conditions, is presented. The model is particularly addressed to simulate a wide range of confinement stress states, as also, to capture the strong influence of the mean stress value in the concrete failure mechanisms. The model is based on a two‐surface damage‐plastic formulation. The mechanical behavior in different domains of the stress space is separately described by means of a quasi‐brittle or ductile material response:

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Unified 3D critical state bounding-surface plasticity model for soils incorporating continuous plastic loading under cyclic paths. Part I: Constitutive relations

The unified three-dimensional (3D) critical state bounding-surface plasticity model gUTS enables clays, silts and sands to be treated within a single framework. Furthermore, loose and dense states of a particular soil subjected to a wide range of confinements are viewed as a single material defined by the same set of constants. The model is able to handle both monotonic and complex cyclic paths including those involving a rotation of the principal stress directions. The model incorporates the following features: combined use of radial and deviatoric mapping rules and the use of an apparent normal consolidation line for sands; use of a non-associated flow rule where the ratio of the rates of volumetric plastic strain to deviatoric plastic strain is a function only of the ratio of deviatoric to mean effective stresses and the Lode angle; adoption of a bi-linear critical state line projected onto the plane of the void ratio versus logarithm of mean effective stress; inclusion of a sub-elliptic, or super-elliptic, segment in the plastic dilatancy surface for stress ratios less than critical; use of elliptic segments in the deviatoric planes; movement of the projection centre in the deviatoric mapping region and incorporation of a plastic stiffening effect for cyclic paths which repeatedly load in the same deviatoric direction.     

Determination of Platinum‐Group Elements in Geological Samples by Isotope Dilution‐Inductively Coupled Plasma‐Mass Spectrometry Combined with Sulfide Fire Assay Preconcentration

A method was developed for the determination of platinum‐group elements (PGE) in geological samples by isotope dilution‐inductively coupled plasma‐mass spectrometry combined with sulfide fire assay preconcentration. Samples were fused and PGE analytes were concentrated in sulfide buttons. The buttons were dissolved using HCl leaving PGE analytes in insoluble residues, which were digested in HNO₃ and simultaneously processed for the distillation of Os. The remaining solutions were further prepared for the purification of Ru, Rh, Pd, Ir and Pt using a tandem assembly of cation and Ln resin columns. The eluents were directly analysed by membrane desolvation‐ICP‐MS. Ruthenium, Pd, Os, Ir and Pt were determined by isotope dilution, whereas Rh was determined by conventional reference material calibration combined with ¹⁹³Ir as the internal standard element. The method was validated using a series of PGE reference materials, and the measurement data were consistent with the recommended and the literature values. The measurement precision was better than 10% RSD. The procedural blanks were 0.121 ng for Ru, 0.204 for Rh, 0.960 ng for Pd, 0.111 ng for Os, 0.045 ng for Ir and 0.661 ng for Pt, and the limits of detection (3s) were 0.011 ng g^?1 for Ru, 0.008 ng g^?1 for Rh, 0.045 ng g^?1 for Pd, 0.009 ng g^?1 for Os, 0.006 ng g^?1 for Ir and 0.016 ng g^?1 for Pt when a test portion mass of 10 g was used. This indicates that the proposed method can be used for the determination of trace amounts of PGE in geological samples.     

Reappraisal of the GL‐O Reference Material for K‐Ar Dating: New Insight from Microanalysis,Single‐Grain and Milligram Ar Measurements

The homogeneity and Ar‐dating suitability of the GL‐O reference material were re‐evaluated to determine whether this material is sufficiently homogeneous to be suitable for the calibration of modern high sensitivity instruments. Based on new micro‐analyses and noble gas determinations, our contribution reveals several kinds of inhomogeneity at the grain scale: disparity in the glauconitisation among and within the pellets, variable occurrence of a phosphatic component within pellets (1% m/m on average), and rare occurrences of calcite and detrital grains. Measurements on test portions of ≤ 1 mg reflect such heterogeneity with variability in ⁴⁰Ar* content that exceeds analytical uncertainty, including a few highly anomalous values. The lesser evolved glauconite population yielded ⁴⁰Ar* contents ~ 15% lower than the value of 24.8 nl g^?1 recommended by Odin et al. (1982, Numerical dating in stratigraphy. Wiley (Chichester, UK), 123–148). But the measured concentrations of ⁴⁰Ar* converge towards the aforementioned value as test portion mass increased to > 3 mg. A few rare 3 mg experiments still yielded ⁴⁰Ar* contents lower than the recommended value (down to 24.0 nl g^?1), and we recommend using more conservative minimum masses of 5–10 mg. A further purification step for GL‐O or the intercalibration of its powder version could be considered to diminish the size of the test portions and the intensity of the measured signals.     

Niobium and Tantalum Concentrations in NIST SRM 610 Revisited

Niobium and Ta concentrations in MPI‐DING and USGS (BCR‐2G, BHVO‐2G, BIR‐1G) silicate rock glasses and the NIST SRM 610–614 synthetic soda‐lime glasses were determined by 193 nm ArF excimer laser ablation and quadrupole ICP‐MS. Measured Nb and Ta values of MPI‐DING glasses were found to be consistently lower than the recommended values by about 15% and 25%, respectively, if calibration was undertaken using commonly accepted values of NIST SRM 610 given by Pearce et al. Analytical precision, as given by the 1 s relative standard deviation (% RSD) was less than 10% for Nb and Ta at concentrations higher than 0.1 μg g^?1. A significant negative correlation was found between logarithmic concentration and logarithmic RSD, with correlation coefficients of ‐0.94 for Nb and ‐0.96 for Ta. This trend indicates that the analytical precision follows counting statistics and thus most of the measurement uncertainty was analytical in origin and not due to chemical heterogeneities. Large differences between measured and expected Nb and Ta in glasses GOR128‐G and GOR132‐G are likely to have been caused by the high RSDs associated with their very low concentrations. However, this cannot explain the large differences between measured and expected Nb and Ta in other MPI‐DING glasses, since the differences are normally higher than RSD by a factor of 3. Count rates for Nb and Ta, normalised to Ca sensitivity, for the MPI‐DING, USGS and NIST SRM 612–614 glasses were used to construct calibration curves for determining NIST SRM 610 concentrations at crater diameters ranging from 16 (im to 60 μm. The excellent correlation between the Nb/Ca_1μgg‐1 signal (Nb represents the Nb signal intensity; Ca_{1μg g‐1} represents the Ca sensitivity) and Nb concentration, and between the Ta/Ca_{1μg g‐1} signal (where Ta represents the Ta signal intensity; Ca_{1μg g‐1} represents the Ca sensitivity) and Ta concentration (R²= 0.9992–1.00) in the various glass matrices suggests that matrix‐dependent fractionation for Nb, Ta and Ca was insignificant under the given instrumental conditions. The results confirm that calibration reference values of Nb and Ta in NIST SRM 610 given by Pearce et al. are about 16% and 28% lower, respectively. We thus propose a revision of the preferred value for Nb from 419.4 ± 57.6 μg g^?1 to 485 ± 5 μg g^?1 (1 s) and for Ta from 376.6 ± 77.6 μg g^?1 to 482 ± 4 μg g^?1 (Is) in NIST SRM 610. Using these revised values for external calibration, most of the determined average values of MPI‐DING, USGS and NIST SRM 612–614 reference glasses agree within 3% with the calculated means of reported reference values. Bulk analysis of NIST SRM 610 by standard additions using membrane desolvation ICP‐MS gave Nb = 479 ± 6 μg g^?1 (1 s) and Ta = 468 ± 7 μg g^?1 (1 s), which agree with the above revised values within 3%.     

Lattice vibration spectra. LXVIII. Single-crystal Raman spectra of marcasite-type iron chalcogenides and pnictides,FeX2 (X=S,Se, Te; P,As, Sb)

Single-crystal Raman spectra of marcasite-type FeS₂, FeSe₂, and FeTe₂ and loellingite-type FeP₂, FeAs₂, and FeSb₂ are presented and discussed with reference to the energies of the two X-X stretching modes v _x-x (A _g, B _1g) and the four X₂ librations Rx₂ (A _g, B _1g, B _2g, B _3g). The main results obtained are that (i) the intraionic X-X bonds of FeS₂ marcasite and FeS₂ pyrite are nearly equal in strengths (mean values of the S-S stretching modes 418 and 420 cm^-1, respectively) and (ii) the interactions of the metal ions and the dumbbell-like X₂ units increase on going from the chalcogenides to the respective pnictides and from FeS₂ marcasite to pyrite (as shown from the frequencies of the X₂ librations).     

EPR and ENDOR of the PO 4 2− radical in anhydrite,celestite and barite

Electron paramagnetic resonance (EPR) and eletron nuclear double resonance (ENDOR) low temperature measurements of natural anhydrite CaSO₄, celestite SrSO₄ and barite BaSO₄ have revealed the presence of PO ₄ ^2– radical. The principal values of the g tensor and the A tensor [MHz] of hyperfine interaction (HFI) are found to be g _xx =2.0124, g _yy =2.0159, g _zz =2.0098, A _xx =82.1, A _yy =81.4, A _zz =77.2 in CaSO4, g _xx =2.0250, g _yy =2.0070, g _zz =2.0131, A _xx =84.8, A _yy =82.7, A _zz = 90.5 in SrSO₄, g _xx =2.0302, g _yy =2.0079, g _zz =2.0135, A _xx =85.2, A _yy =82.3, A _zz =90.0 in BaSO₄. The principal axes A _xx , A _yy and A _zz are parallel to the crystallographic axes a, b, c in all three matrices. In anhydrite the principal g axes coincide with the A axes. In celestite and barite such coincidence is found to be only along the b axis (a low symmetry effect). The coherence effect of splitting of ENDOR lines by a strong microwave field has been detected. From the analysis of the relative intensities of the ENDOR lines of the PO ₄ ^2– radical in CaSO₄ the relation of probabilities of cross-relaxation processes W _x/W _xx =3.5 are evaluated.     

Determination of Te,As, Bi,Sb and Se (TABS) in Geological Reference Materials and GeoPT Proficiency Test Materials by Hydride Generation‐Atomic Fluorescence Spectrometry (HG‐AFS)

The study of Te, As, Bi, Sb and Se (TABS) has increased over the past years due to their use in the development of low‐carbon energy technologies. However, there is a scarcity of mass fraction values of TABS in geological reference materials. This underlines the difficulty in undertaking routine determinations of these elements. The mass fractions of TABS were determined in geological reference materials using hydride generation‐atomic fluorescence spectrometry (HG‐AFS), calibrated with standard solutions. Comparisons with literature values were used to validate the method. Samples from the GeoPT proficiency test were also analysed. For most elements, there are no assigned or even provisional values for many of the GeoPT and reference materials because of the wide range of results reported. For mass fractions above the quantification limit of the method, our results are in good agreement with the median of GeoPT results. Thus, we propose GeoPT median values as informational values for these elements. In contrast, at mass fractions < 0.5 µg g^?1 median values of Se from GeoPT are systematically higher than our results. Our Se results are in agreement with the reference materials down to 0.02 µg g^?1, which suggest that many of the results for Se reported in GeoPT testing are too high.     

Non-LTE analysis of the formation of KI lines in the spectra of A-K stars

The non-LTE formation of KI lines in the spectra of A-K stars is analyzed. The computations are based on a 36-level model of the neutral potassium atom for blanketed LTE Kurucz model atmospheres with T _eff=4000–10000 K, logg=0.0–4.5, and [M/H]=(0.0)–(?2.0). The KI atoms in the atmospheres of these stars are in states of moderate and strong “over-recombination.” A number of atomic parameters are refined using the profiles and equivalent widths of five lines in the solar spectrum. The classical van der Waals damping constants must be increased by factors of 2–60 to fit the observed profiles. The non-LTE solar potassium abundance—logε (K)=5.14—corresponds to the meteoritic abundance. Non-LTE corrections to the potassium abundance are important and equal to ?0.4...?0.7 dex for the λ7699 Å line and ?0.15...?0.3 dex for the λλ12522, 12432, and 11769 Å lines.