Community‐Derived Standards for LA‐ICP‐MS U‐(Th‐)Pb Geochronology – Uncertainty Propagation,Age Interpretation and Data Reporting

The LA‐ICP‐MS U‐(Th‐)Pb geochronology international community has defined new standards for the determination of U‐(Th‐)Pb ages. A new workflow defines the appropriate propagation of uncertainties for these data, identifying random and systematic components. Only data with uncertainties relating to random error should be used in weighted mean calculations of population ages; uncertainty components for systematic errors are propagated after this stage, preventing their erroneous reduction. Following this improved uncertainty propagation protocol, data can be compared at different uncertainty levels to better resolve age differences. New reference values for commonly used zircon, monazite and titanite reference materials are defined (based on ID‐TIMS) after removing corrections for common lead and the effects of excess ²³⁰Th. These values more accurately reflect the material sampled during the determination of calibration factors by LA‐ICP‐MS analysis. Recommendations are made to graphically represent data only with uncertainty ellipses at 2s and to submit or cite validation data with sample data when submitting data for publication. New data‐reporting standards are defined to help improve the peer‐review process. With these improvements, LA‐ICP‐MS U‐(Th‐)Pb data can be considered more robust, accurate, better documented and quantified, directly contributing to their improved scientific interpretation.     

LA‐(MC)‐ICP‐MS Trends in 2006 and 2007 with Particular Emphasis on Measurement Uncertainties

Research in 2006 and 2007 dealing with laser ablation‐(multicollector)‐inductively coupled plasma‐mass spectrometry, LA‐(MC)‐ICP‐MS, involved studies concerned with optimising the technique itself, as well as applying the method to a variety of problems in the Earth sciences. The causes of elemental and isotopic fractionation produced during laser ablation continues to be of considerable interest, with evidence mounting that processes occurring both at the ablation site and in the argon plasma of the ICP are culpable. There is growing excitement in the use of femtosecond lasers for LA‐(MC)‐ICP‐MS, with the hope that they reduce or eliminate melting and non‐congruent volatilisation at the ablation site and thus approach stoichiometric sampling. Ablation chamber design emerged as a serious concern, particularly with respect to achieving the rapid washout needed for fine‐scale compositional mapping of geological objects. LA‐MC‐ICP‐MS provided data for a wide range of isotopic systems, especially hafnium, but also B, S, Mg, Cu, Fe, Sr, Nd, Pb and U. Measurement uncertainties in LA‐ICP‐MS were discussed by several researchers, and are critically reviewed here ‐ total uncertainties for trace element concentration measurements of silicates including errors on the calibration values of common reference materials are ～10% (95% confidence limits), though the precision of individual spot measurements (50 to 100 μm) is much better, ～1% RSD, using a 193 nm laser and a sector field‐ICP‐MS. LA‐ICP‐MS U‐Pb ages for zircon and other U‐rich accessory phases are claimed by most geoanalysts to have 2s uncertainties of ～0.7 and 1.3% respectively but the actual accuracy of the method is probably only as good as ～2% (2s), when uncertainties associated with laser‐induced Pb/U fractionation are included.     

Matrix Corrections and Error Analysis in High‐Precision SIMS 18O/16O Measurements of Ca–Mg–Fe Garnet

We report technical and data treatment methods for making accurate, high‐precision measurements of ¹⁸O/¹⁶O in Ca–Mg–Fe garnet utilising the Cameca IMS 1280 multi‐collector ion microprobe. Matrix effects were similar to those shown by previous work, whereby Ca abundance is correlated with instrumental mass fractionation (IMF). After correction for this effect, there appeared to be no significant secondary effect associated with Mg/Fe²⁺ for routine operational conditions. In contrast, investigation of the IMF associated with Mn‐ or Cr‐rich garnet showed that these substitutions are significant and require a more complex calibration scheme. The Ca‐related calibration applied to low‐Cr, low‐Mn garnet was reproducible across different sample mounts and under a range of instrument settings and therefore should be applicable to similar instruments of this type. The repeatability of the measurements was often better than ± 0.2‰ (2s), a precision that is similar to the repeatability of bulk techniques. At this precision, the uncertainties due to spot‐to‐spot repeatability were at the same magnitude as those associated with matrix corrections (± 0.1–0.3‰) and the uncertainties in reference materials (± 0.1–0.2‰). Therefore, it is necessary to accurately estimate and propagate uncertainties associated with these parameters – in some cases, uncertainties in reference materials or matrix corrections dominate the uncertainty budget.     

Comparison of geotechnical uncertainties linked to different soil characterization methods

One of the essential inputs in settlement prediction models is the soil modulus, which may be obtained from laboratory tests or estimated from in situ measurements. The total uncertainty in predicting the confined modulus of a sandy soil is quantified with data from side-by-side in situ testing using the standard penetration test, the static cone penetration test, the light dynamic probing and the laboratory oedometer test. To estimate transformation errors, correlations are proposed between in situ and laboratory data. The results indicate that similar magnitudes of total uncertainties are associated with the in situ methods, which are approximately twice as high as those from the direct oedometer method. The quantified uncertainties are an important input for reliability-based designs of foundations under similar soil conditions.     

Thermo‐hydro‐mechanical modeling of damage in unsaturated porous media: Theoretical framework and numerical study of the EDZ

The damage model presented in this article (named ‘THHMD’ model) is dedicated to non‐isothermal unsaturated porous media. It is formulated by means of three independent strain state variables, which are the thermodynamic conjugates of net stress, suction and thermal stress. The damage variable is a second‐order tensor. Stress/strain relationships are derived from Helmholtz free energy, which is assumed to be the sum of damaged elastic potentials and ‘crack‐closure energies’. Damage is assumed to grow with tensile strains due to net stress, with pore shrinkage due to suction and with thermal dilatation. Specific conductivities are introduced to account for the effects of cracking on the intensification and on the orientation of liquid water and vapor flows. These conductivities depend on damage and internal length parameters. The mechanical aspects of the THHMD model are validated by comparing the results of a triaxial compression test with experimental measurements found in the literature. Parametric studies of damage are performed on three different heating problems related to nuclear waste disposals. Several types of loading and boundary conditions are investigated. The thermal damage potential is thoroughly studied. The THHMD model is expected to be a useful tool in the assessment of the Excavation Damaged Zone, especially in the vicinity of nuclear waste repositories. Copyright © 2011 John Wiley & Sons, Ltd.     

SLRS‐5 Elemental Concentrations of Thirty‐Three Uncertified Elements Deduced from SLRS‐5/SLRS‐4 Ratios

The fifth version of natural river water certified reference material, SLRS‐5 (National Research Council – Conseil National de Recherches Canada), is commonly used to control the quality of major and trace element measurements. Concentrations of silicon and thirty‐one uncertified trace elements have been reported for the certified reference material SLRS‐4, but they are not yet available for SLRS‐5. Here, SLRS‐5/SLRS‐4 ratios were deduced from SLRS‐5 and SLRS‐4 measurements by inductively coupled plasma‐atomic emission spectrometry and high‐resolution inductively coupled plasma‐mass spectrometry for certified elements and thirty‐five uncertified elements (rare earth elements, B, Bi, Br, Cs, Ga, Ge, Hf, Li, Nb, P, Pd, Rb, Rh, S, Sc, Si, Sn, Th, Ti, Tl, Y). Both reference materials were measured directly one after the other, so that calculated elemental ratios would not be notably influenced either by calibration uncertainties or by eventual long‐term instrumental drift. The computed ratios are in good agreement with those deduced from the certified values. We also report concentrations for thirty‐three uncertified elements in SLRS‐5 by combining the measured SLRS‐5/SLRS‐4 ratios and the published SLRS‐4 values. The resulting new data set provides target SLRS‐5 values, which will be useful in quality control procedures.     

Numerical characterization of dispersion coefficients by meshless‐based inverse analysis

This study presents the preliminary development of a meshless‐based indirect inverse analysis. Two goals are desired to be attained: (a) identifying fewer quantities in an indirect inverse analysis and (b) getting the interpolation results of spatial variation of a quantity insensitive to the replacement of one or few interpolation points with other points. This idea is illustrated by modifying a meshless local Petrov‐Galerkin (MLPG) formulation of a two‐dimensional (2D) contaminant transport problem under the concept of boundary control. Thus, dispersion coefficients to be identified are solved from measured or prescribed pollutant concentrations. A field problem is introduced to test the performance of resulting meshless‐based indirect inverse analysis procedure. This test finds a major motive and a minor one for performing a meshless‐based indirect inverse analysis. The major motive is attaining the aforementioned Goal (b), while the above‐mentioned Goal (a) is the minor motive. In conclusion, the development of a meshless‐based indirect inverse analysis procedure can be a valuable application of the MLPG method. Copyright © 2010 John Wiley & Sons, Ltd.     

Developing constitutive models from EPR‐based self‐learning finite element analysis

A constitutive model that captures the material behavior under a wide range of loading conditions is essential for simulating complex boundary value problems. In recent years, some attempts have been made to develop constitutive models for finite element analysis using self‐learning simulation (SelfSim). Self‐learning simulation is an inverse analysis technique that extracts material behavior from some boundary measurements (eg, load and displacement). In the heart of the self‐learning framework is a neural network which is used to train and develop a constitutive model that represents the material behavior. It is generally known that neural networks suffer from a number of drawbacks. This paper utilizes evolutionary polynomial regression (EPR) in the framework of SelfSim within an automation process which is coded in Matlab environment. EPR is a hybrid data mining technique that uses a combination of a genetic algorithm and the least square method to search for mathematical equations to represent the behavior of a system. Two strategies of material modeling have been considered in the SelfSim‐based finite element analysis. These include a total stress‐strain strategy applied to analysis of a truss structure using synthetic measurement data and an incremental stress‐strain strategy applied to simulation of triaxial tests using experimental data. The results show that effective and accurate constitutive models can be developed from the proposed EPR‐based self‐learning finite element method. The EPR‐based self‐learning FEM can provide accurate predictions to engineering problems. The main advantages of using EPR over neural network are highlighted.     

Experimental insights into laser diffraction particle sizing of fine‐grained sediments for use in palaeoceanography

Grain‐size measurements of fine‐grained sediments based on laser diffraction may contain spurious information due to the over‐estimation of the size and proportion of platy particles. Consequently, some regard the use of laser diffraction particle sizing in palaeoceanography inappropriate. Here, it is shown experimentally that such concerns are not warranted. Laser diffraction particle sizing is known to be fast, precise and allows for detailed particle sizing over a broad size range; it is therefore potentially a very powerful technique if the complications associated with it can be overcome. As most sediments are mixtures of different components transported by different mechanisms, inferences of past environmental parameters require decomposition of the grain‐size record in question. Useful decomposition can only be performed if changes in the contribution of the components are registered predictably by the measuring device. This study reports on mixing experiments which show that the Fritsch A22 laser diffraction particle sizer does indeed register small changes in the contribution of the mixing components in a predictable way. Mixing proportions estimated from the measurements do, however, differ from the initial mixing proportions, but these can be converted with only small errors. Application of the conversion equations to a North Atlantic grain‐size record that showed consistent slowdown of deep‐ocean circulation in response to millennial scale ice‐rafting events during the last glacial does not quantitatively affect the original inferences. Laser diffraction particle sizing of fine‐grained sediments therefore yields reproducible and useful data for palaeoceanographic reconstructions.     

Single‐and multi‐objective genetic algorithm optimization for identifying soil parameters

This paper discusses the quality of the procedure employed in identifying soil parameters by inverse analysis. This procedure includes a FEM‐simulation for which two constitutive models—a linear elastic perfectly plastic Mohr–Coulomb model and a strain‐hardening elasto‐plastic model—are successively considered. Two kinds of optimization algorithms have been used: a deterministic simplex method and a stochastic genetic method. The soil data come from the results of two pressuremeter tests, complemented by triaxial and resonant column testing. First, the inverse analysis has been performed separately on each pressuremeter test. The genetic method presents the advantage of providing a collection of satisfactory solutions, among which a geotechnical engineer has to choose the optimal one based on his scientific background and/or additional analyses based on further experimental test results. This advantage is enhanced when all the constitutive parameters sensitive to the considered problem have to be identified without restrictions in the search space. Second, the experimental values of the two pressuremeter tests have been processed simultaneously, so that the inverse analysis becomes a multi‐objective optimization problem. The genetic method allows the user to choose the most suitable parameter set according to the Pareto frontier and to guarantee the coherence between the tests. The sets of optimized parameters obtained from inverse analyses are then used to calculate the response of a spread footing, which is part of a predictive benchmark. The numerical results with respect to both the constitutive models and the inverse analysis procedure are discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of 1013 Ω Amplifiers in Low‐Signal Plasma‐Source Isotope Ratio Measurements by MC‐ICP‐MS: A Case Study with Pt Isotopes

Recent developments in amplifier hardware enable low‐noise measurements of exceedingly small ion beams in isotope ratio analysis, yielding higher precision from smaller samples than ever before. To date, these amplifiers have largely been employed in thermal ionisation instruments, with few applications using plasma‐source (i.e., MC‐ICP‐MS) instruments. Here, we demonstrate the utility of these new generation 10¹³ Ω amplifiers in MC‐ICP‐MS, employing Pt isotopes as a case study, a system that could greatly benefit from the promised advances. The data demonstrate that for samples with low Pt abundance, for a modest increase in uncertainties, the amount of sample required can be reduced by a factor of 50–100. This technique thereby opens up new possibilities for analysis of samples that have low Pt mass fractions or were otherwise impossible to obtain in sufficient quantities.     

Simulation of localization failure with strain‐gradient‐enhanced damage mechanics

Strain gradient implies an important characteristic in localized damage deformation, which can be observed in the softening state of brittle materials, and strain gradients constitute the basic behaviours of localization failure area of the materials. The most important point in strain gradient is its damaging function including an internal length scale, which can be used to express the scale effects of mechanical responses of brittle rock mass. By extending the strain gradient theory and introducing an intrinsic material length scale into the constitutive law, the authors develop an isotropic damage model as well as a micro‐crack‐based anisotropic damage model for rock‐like materials in this paper. The proposed models were used to simulate the damage localization under uniaxial tension and plain strain compression, respectively. The simulated results well illustrated the potential of these models in dealing with the well‐known mesh‐sensitivity problem in FEM. In the computation, elements with C₁ continuity have been implemented to incorporate the proposed models for failure localization. When regular rectangle elements are encountered, the coupling between finite difference method (FDM) and conventional finite element method (FEM) is used to avoid large modification to the existing FEM code, and to obtain relatively higher efficiency and reasonably good accuracy. Application of the anisotropic model to the 3D‐non‐linear FEM analysis of Ertan arch dam has been conducted and the results of its numerical simulation coincide well with those from the failure behaviours obtained by Ertan geophysical model test. In this paper, new applications of gradient theories and models for a feasible approach to simulate localized damage in brittle materials are presented. Copyright © 2002 John Wiley & Sons, Ltd.     

High‐Precision,High‐Accuracy Oxygen Isotope Measurements of Zircon Reference Materials with the SHRIMP‐SI

Analytical protocols for SHRIMP‐SI oxygen isotope analysis (δ¹⁸O) of a suite of zircon reference materials (RMs) are presented. Data reduction involved a robust estimate of uncertainties associated with the individual spot as well as for groups where the spot data are combined. The repeatability of δ¹⁸O measurements is dependent on both the analytical conditions and the choice of the primary reference material. Under optimised conditions, repeatability was often better than 0.4‰ (2s) allowing sample uncertainties to be obtained to better than 0.2‰ (at 95% confidence limit). Single spot uncertainty combined the within‐spot precision with the scatter associated with repeated measurements of the primary zircon reference material during a measurement session. The uncertainty for individual spots measured under optimised conditions was between 0.3 and 0.4‰ (at 95% confidence). The analytical protocols described were used to assess a variety of zircon RMs that have been used for geochronology and for which laser fluorination oxygen isotope data are available (Temora 2, FC1, R33, QGNG and Ple?ovice), as well as zircons that have been used as RMs for trace element or other types of determination (Mud Tank, Monastery, 91500, AS57, AS3, KIM‐5, OG1, SL13, CZ3 and several other Sri Lankan zircons). Repeated analyses over nine sessions and seven different mounts show agreement within analytical uncertainty for Temora 2, FC1, R33, QGNG, Ple?ovice and 91500, when normalised to Mud Tank. For existing ion microprobe mounts with these materials, an appropriate δ¹⁸O can be determined. However, care should be taken when using zircons from the Duluth Complex (i.e., FC1, AS57 and AS3) as reference materials as our data indicated an excess scatter on δ¹⁸O values associated with low‐U zircon grains.     

Extending the applicability of the Raman carbonaceous‐material geothermometer using data from contact metamorphic rocks

The degree of graphitization of carbonaceous material (CM) has been widely used as an indicator of metamorphic grade. Previous work has demonstrated that peak metamorphic temperature (T) of regional metamorphic rocks can be estimated by an area ratio (R2) of peaks recognized in Raman spectra of CM. The applicability of this method to low‐pressure (<3 kbar) contact metamorphism was tested using Raman spectroscopic analyses of samples from two contact‐metamorphic aureoles in Japan (Daimonji and Kasuga areas). A suitable measurement procedure allows the dependence of the geothermometer on sample type (thin section, chip) and incident angle of laser beam relative to the c‐axes of CM to be tested. Two important general results are: (i) in addition to standard thin sections, chips are also suitable for spectral analysis; and (ii) the incident angle of the laser beam does not significantly affect the temperature estimation, i.e. spectral measurements for the geothermometer can be carried out irrespective of the crystallographic orientation. A laser wavelength of 532 nm was used in this study compared with 514.5 nm in an independent previous study. A comparison shows that the use of a 532‐nm laser results in a slightly, but systematically larger R2 ratio than that of a 514.5‐nm laser. Taking this effect into account, our results show that there is a slight but distinct difference between the R2–T correlations shown by contact and regional metamorphic rocks: the former are slightly better‐crystallized (have slightly lower R2 values) than the latter at the same temperature. This difference is interpreted as due to the degree of associated deformation. Despite the slight difference, the results of this study coincide within the estimated errors of ±50 °C with those of the previously proposed Raman CM geothermometer, thus demonstrating the applicability of this method to contact metamorphism. To facilitate more precise temperature estimates in regions of contact metamorphism, a new calibration for analyses using a 532‐nm laser is derived. Another important observation is that the R2 ratio of metamorphosed CM in pelitic and psammitic rocks is highly heterogeneous with respect to a single sample. To obtain a reliable temperature estimate, the average R2 value must be determined by using a substantial number of measurements (usually N > 50) that adequately reflects the range of sample heterogeneity. Using this procedure (with 532‐nm laser) and adapting our new calibration, the errors of the Raman CM geothermometer for contact metamorphic rocks decrease to ～±30 °C.     

Direct Trace Element Determination in Oil and Gas Produced Waters with Inductively Coupled Plasma‐Optical Emission Spectrometry: Advantages of High‐Salinity Tolerance

Waters co‐produced during petroleum extraction are the largest waste streams from oil and gas development. Reuse or disposal of these waters is difficult due to their high salinities and the sheer volumes generated. Produced waters (PWs) may also contain valuable mineral commodities. While an understanding of produced water trace element composition is required for evaluating the associated resource and waste potential of these materials, measuring trace elements in brines is challenging due to the dilution requirements of typical methods. Alternatively, inductively coupled plasma‐optical emission spectrometry (ICP‐OES) has shown promise as being capable of direct measurements of trace elements within PWs with minimal dilution. Here, we evaluate direct ICP‐OES trace element quantification in PWs for seventeen trace elements (As, Al, Ba, Be, Cd, Cr, Co, Cu, Hg, Mo, Ni, Pb, Rb, Sb, U, V and Zn) within fifteen PWs from five U.S. continuous reservoirs. The total analytical uncertainties associated with the trace element levels determined using ICP‐OES were estimated to be better than ± 30% (2s) except for Rb, which could not be determined due to ionisation interferences. The ICP‐OES results are compared with trace element levels determined using inductively coupled plasma‐mass spectrometry from the same samples. Our results demonstrate the potential for direct analysis of high‐salinity waters using ICP‐OES with minimal dilution and provide trace element concentrations in waters from several important U.S. petroleum‐generating reservoirs where available data are sparse.     

Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading

This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

High‐Precision Iron Isotope Analysis of Geological Reference Materials by High‐Resolution MC‐ICP‐MS

We report high‐precision iron isotopic data for twenty‐two commercially available geological reference materials, including silicates, carbonatite, shale, carbonate and clay. Accuracy was checked by analyses of synthetic solutions with known Fe isotopic compositions but different matrices ranging from felsic to ultramafic igneous rocks, high Ca and low Fe limestone, to samples enriched in transition group elements (e.g., Cu, Co and Ni). Analyses over a 2‐year period of these synthetic samples and pure Fe solutions that were processed through the whole chemistry procedure yielded an average δ⁵⁶Fe value of ?0.001 ± 0.025‰ (2s, n = 74), identical to the expected true value of 0. This demonstrates a long‐term reproducibility and accuracy of < 0.03‰ for determination of ⁵⁶Fe/⁵⁴Fe ratios. Reproducibility and accuracy were further confirmed by replicate measurements of the twenty‐two RMs, which yielded results that perfectly match the mean values of published data within quoted uncertainties. New recommended values and associated uncertainties are presented for interlaboratory calibration in the future.     

Application of the representer method for parameter estimation in numerical reservoir models

A data assimilation method was applied to estimate poorly known parameters (permeabilities) in a numerical reservoir model. Most variational methods for data assimilation are based on the assumption that the model is perfect except for the poorly known parameters. The representer method allows also for model errors, i.e. for uncertainties in the state variables (pressures and saturations). The method is based on minimizing a cost functional, assuming all the errors and parameters to be multivariate Gaussian random variables with given mean and covariances. The uncertain parameters and variables are expanded into a finite sum of basis functions called representers, and the gradients of the cost functional are obtained with an adjoint method. This approach gives an optimal parametrization in the sense that the final result is equal to the solution of the full inverse problem. The method was tested on a simple one-dimensional model to simulate two-phase (oil-water) flow through a heterogeneous reservoir. The results show that the method is able to provide an acceptable estimate of the permeability field. We used pressure measurements from a small number of observation wells in between the injection and production wells, but the representer method could be used equally well to assimilate data from other sources. The method appears to be a promising data assimilation tool for applications in reservoir engineering.     

Optimisation of Lithium Chromatography for Isotopic Analysis in Geological Reference Materials by MC‐ICP‐MS

The lithium isotope system can be an important tracer for various geological processes, especially tracing continental weathering. The key to this application is the accurate and precise determination of lithium isotopic composition. However, some of the previously established column separation methods are not well behaved when applied to chemically diverse materials, due to the significant variations in matrix/lithium ratios in some materials. Here, we report a new dual‐column system for lithium purification to achieve accurate and precise analysis of lithium isotopic compositions using a multi‐collector inductively coupled plasma‐mass spectrometer (MC‐ICP‐MS). Compared with single‐column systems, our dual‐column system yielded a consistent elution range of the lithium‐bearing fraction (7–16 ml) for samples with a large range of lithium loads and matrix compositions, so that column re‐calibration is not required. In addition, this method achieved complete lithium recovery and low matrix interference (e.g., Na/Li ≤ 1) with a short elution time (~ 6 h, excluding evaporation), with the entire procedure completed in 1.5 days. We report high precision Li isotopic compositions in twelve chemically diverse materials including seawater, silicates, carbonates, manganese nodules and clays. New recommended Li isotopic values and associated uncertainties are presented as reference values for quality control and inter‐laboratory calibration for future research and were consistent with previously published data. However, significant lithium isotopic variances (~ 1‰) in BHVO‐2 from different batches suggest Li isotopic heterogeneity in this reference material and that Li isotopic studies using this reference material should be treated with caution.     

Flux‐Free Fusion of Silicate Rock Preceding Acid Digestion for ICP‐MS Bulk Analysis

We present a new method for the decomposition of silicate rocks by flux‐free fusion in preparation for whole‐rock trace element determination (Sc, Rb, Sr, Y, Zr, Nb, Cs, Ba, rare earth elements and Hf) that is especially applicable to zircon‐bearing felsic rocks. The method was verified by analyses of RMs of mafic (JB‐1a, JB‐2, JGb‐1) and felsic rocks (JG‐3, JR‐3, JSd‐1, GSP‐2, G‐2). Pellets of powdered sample (up to 500 mg) without flux were weighed and placed in a clean platinum crucible. The samples were then fused in a Siliconit® tube furnace and quenched to room temperature. The optimum condition for the fusion of granitic rock was determined to be heating for 2–3 min at 1600 °C. The fused glass in the platinum crucible after heating was decomposed using HF and HClO₄ in a Teflon® beaker. Decomposed and diluted sample solutions were analysed using a quadrupole inductively coupled plasma‐mass spectrometer. Replicate analyses (n = 4 or 5) of the RMs revealed that analytical uncertainties were generally < 3% for all elements except Zr and Hf (～ 6%) in JG‐3. These higher uncertainties may be attributed to sample heterogeneity. Our analytical results for the RMs agreed well with recommended concentrations and recently published concentrations, indicating complete decomposition of our rock samples during fusion.