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1.
To assess the homogeneity of and provide the first Sr‐Nd‐Hf‐Pb isotopic reference values for the Chinese Geological Standard Glasses CGSG‐1, CGSG‐2, CGSG‐4 and CGSG‐5, we measured these isotopes in several measurement sessions over the course of nearly 3 years. The results were obtained by high‐precision MC‐ICP‐MS and TIMS. Our investigation indicates that these CGSG glass reference materials are homogenous with regard to Sr‐Nd‐Hf‐Pb isotopic distribution and are therefore suitable geochemical materials for Sr‐Nd‐Hf‐Pb isotope measurements. Clear differences in Sr‐Nd‐Hf‐Pb isotopic composition were observed between the glasses and the original powdered rock reference materials (CGSG‐2 and GSR‐7, and especially CGSG‐5 and GSR‐2) because of flux addition during preparation of the glasses. The new Sr‐Nd‐Hf‐Pb isotope data provided here might be useful to the geochemical community for in situ and bulk analysis.  相似文献   

2.
In both nature and synthetic experiments, the common iron oxide haematite (α‐Fe2O3) can incorporate significant amounts of U into its crystal structure and retain radiogenic Pb over geological time. Haematite is a ubiquitous component of many ore deposit types and, therefore, represents a valuable hydrothermal mineral geochronometer, allowing direct constraints to be placed on the timing of ore formation and upgrading. However, to date, no suitable natural haematite reference material has been identified. Here, a synthetic haematite U‐Pb reference material (MR‐HFO) is characterised using LA‐ICP‐MS and ID‐TIMS. Centimetre‐scale ‘chips’ of synthesised α‐Fe2O3 were randomly microsampled via laser ablation‐extraction and analysed using ID‐TIMS. Reproducible U/Pb and Pb/Pb measurements were obtained across four separate chips (n = 13). Subsequently, an evaluation of the suitability MR‐HFO in constraining U‐Pb data via LA‐ICP‐MS is presented using a selection of natural samples ranging from Cenozoic to Proterozoic in age. The MR‐HFO normalised U‐Pb ratios are more concordant and ages more accurate versus the same LA‐ICP‐MS spot analyses normalised to zircon reference material, when compared with independently acquired ID‐TIMS data from the same natural haematite grains. Results establish MR‐HFO as a suitable reference material for LA‐ICP‐MS haematite U‐Pb geochronology.  相似文献   

3.
The Lamont‐Doherty Earth Observatory radiogenic isotope group has been systematically measuring Sr‐Nd‐Pb‐Hf isotopes of USGS reference material BCR‐2 (Columbia River Basalt 2), as a chemical processing and instrumental quality control monitor for isotopic measurements. BCR‐2 is now a widely used geochemical inter‐laboratory reference material (RM), with its predecessor BCR‐1 no longer available. Recognising that precise and accurate data on RMs is important for ensuring analytical quality and for comparing data between different laboratories, we present a compilation of multiple digestions and analyses made on BCR‐2 during the first author's dissertation research. The best estimates of Sr, Nd and Hf isotope ratios and measurement reproducibilities, after filtering at the 2s level for outliers, were 87Sr/86Sr = 0.705000 ± 11 (2s, 16 ppm, n = 21, sixteen digestions, one outlier), 143Nd/144Nd = 0.512637 ± 13 (2s, 25 ppm, n = 27, thirteen digestions, one outlier) and 176Hf/177Hf = 0.282866 ± 11 (2s, 39 ppm, n = 25, thirteen digestions, no outliers). Mean Nd and Hf values were within error of those reported by Weis et al. (2006, 2007) in their studies of RMs; mean Sr values were just outside the 2s uncertainty range of both laboratories. Moreover, a survey of published Sr‐Nd‐Hf data shows that our results fall within the range of reported values, but with a smaller variability. Our Pb isotope results on acid leached BCR‐2 aliquots (n = 26, twelve digestions, two outliers) were 206Pb/204Pb = 18.8029 ± 10 (2s, 55 ppm), 207Pb/204Pb = 15.6239 ± 8 (2s, 52 ppm), 208Pb/204Pb = 38.8287 ± 25 (2s, 63 ppm). We confirm that unleached BCR‐2 powder is contaminated with Pb, and that sufficient leaching prior to digestion is required to achieve accurate values for the uncontaminated Pb isotopic compositions.  相似文献   

4.
Silicon isotope determination of sulfur‐rich samples by MC‐ICP‐MS can be challenging because cation‐exchange chromatography used for Si purification does not efficiently remove anionic sulfur species. Results for pure Si standard solutions with addition of sulfate showed shifts of up to +1.04 ± 0.10‰ (2s) in δ30Si. Doping of both standard solutions and samples with S to a fixed S/Si ratio can eliminate the relative change in instrumental mass fractionation due to variable S/Si in samples and also boosts the relative sensitivity of Si by up to 66%. Moreover, Fe hydroxide precipitation during sample processing adsorbs Si resulting in isotopic fractionations. Tests using Fe‐rich samples showed that this could be a major factor for observed shifts in δ30Si. Acidification of the sample and standard solutions to a pH < 1 aggressively dissolved any Fe hydroxide precipitates, even in relatively Fe‐rich samples such as chondrite meteorites. The pH values of the sample solutions were subsequently adjusted to a range of 2–3 by adding ultra‐pure NaOH solutions. The combination of sulfur doping and the pH adjustment protocol ensured a full recovery of Si and proved to be an efficient and reliable method for Si isotope determination of S‐ and Fe‐rich materials.  相似文献   

5.
The Bayan Obo Fe‐REE‐Nb deposit is the world’s largest rare earth element (REE) resource and its genesis has been the subject of much debate for many years. The most popular are the carbonatite‐related and hydrothermal Fe oxide‐Cu‐Au‐(REE‐U) genetic models. Comparisons of geologic setting, lithology, mineral assemblages, metal associations, geochemistry (particularly REE and light REE/heavy REE ratios), fluid chemistry and isotopics indicate that the Bayan Obo deposit shares features of both types, which are classified differently; that is, the carbonatites model is host‐rock based, while the Fe oxide‐Cu‐Au‐(REE‐U) model is essentially mineral assemblage and metal association based. A speculative classification scheme is tentatively put forward to link the two models, but many questions remain for further studies.  相似文献   

6.
Analytical solutions are presented for linear finite‐strain one‐dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one‐ and two‐way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small‐strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small‐strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non‐linear finite‐strain consolidation. They also clarify a formerly perplexing aspect of finite‐strain solution charts first noted in numerical solutions. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

7.
We report an improved procedure for the determination of the platinum‐group elements (PGE) and Re, and Os isotopes from a single sample aliquot by isotope dilution (ID) using inductively coupled plasma‐mass spectrometry (ICP‐MS) and negative thermal ionisation mass spectrometry (N‐TIMS), respectively. A two‐stage column method was used to purify PGE‐Re from their sample matrix and interfering elements (e.g., Mo, Zr and Hf) after Os had been separated by CCl4 solvent extraction. The first column separation step used cation exchange resin (AG50W‐X8) to concentrate PGE‐Re and some potential interfering elements (e.g., Mo, Zr and Hf). In the second step, N‐benzoyl‐N‐phenylhydroxylamine (BPHA) extraction resin was used to separate PGE‐Re from the remaining interfering elements, which all remained strongly absorbed to the resin. The method was used to determine the PGE and rhenium, and Os isotope ratios in a range of geochemical reference materials (TDB‐1, WGB‐1, BHVO‐2 and UB‐N). The obtained results agree well with those previously published. This new method enables PGE‐Re abundances and Os isotopic ratios to be determined on the same sample digestion, and circumvents the problems created by sample heterogeneity when comparing PGE and Re‐Os isotope data.  相似文献   

8.
Artificial ground freezing (AGF) is a commonly used technique in geotechnical engineering for ground improvement such as ground water control and temporary excavation support during tunnel construction in soft soils. The main potential problem connected with this technique is that it may produce heave and settlement at the ground surface, which may cause damage to the surface infrastructure. Additionally, the freezing process and the energy needed to obtain a stable frozen ground may be significantly influenced by seepage flow. Evidently, safe design and execution of AGF require a reliable prediction of the coupled thermo‐hydro‐mechanical behavior of freezing soils. With the theory of poromechanics, a three‐phase finite element soil model is proposed, considering solid particles, liquid water, and crystal ice as separate phases and mixture temperature, liquid pressure, and solid displacement as the primary field variables. In addition to the volume expansion of water transforming into ice, the contribution of the micro‐cryo‐suction mechanism to the frost heave phenomenon is described in the model using the theory of premelting dynamics. Through fundamental physical laws and corresponding state relations, the model captures various couplings among the phase transition, the liquid transport within the pore space, and the accompanying mechanical deformation. The verification and validation of the model are accomplished by means of selected analyses. An application example is related to AGF during tunnel excavation, investigating the influence of seepage flow on the freezing process and the time required to establish a closed supporting frozen arch. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

9.
Titanite is a common accessory mineral that preferentially incorporates considerable amounts of U and light rare earth elements in its structure, making it a versatile mineral for in situ U‐Pb dating and Sm‐Nd isotopic measurement. Here, we present in situ U‐Pb ages and Sm‐Nd isotope measurement results for four well‐known titanite reference materials (Khan, BLR‐1, OLT1 and MKED1) and eight titanite crystals that could be considered potential reference material candidates (Ontario, YQ‐82, T3, T4, TLS‐36, NW‐IOA, Pakistan and C253), with ages ranging from ~ 20 Ma to ~ 1840 Ma. Results indicate that BLR‐1, OLT1, Ontario, MKED1 and T3 titanite have relatively homogeneous Sm‐Nd isotopes and low common Pb and thus can serve as primary reference materials for U‐Pb and Sm‐Nd microanalysis. YQ‐82 and T4 titanite can be used as secondary reference materials for in situ U‐Pb analysis because of their low common Pb. However, internal structures and mineral inclusions in YQ‐82 will require careful selection of suitable target domains. Pakistan titanite is almost concordant with an age of 21 Ma and can be used as a reference material when dating Cenozoic titanite samples.  相似文献   

10.
To precisely determine the abundances of fifty‐two elements found within natural water samples, with mass fractions down to fg g?1 level, we have developed a method which combines freeze‐drying pre‐concentration (FDC) and isotope dilution internal standardisation (ID‐IS). By sublimation of H2O, the sample solution was reduced to < 1/50 of the original volume. To determine element abundance with accuracy better than 10%, we found that for solutions being analysed by mass spectrometry the HNO3 concentration should be > 0.3 mol l?1 to avoid hydrolysis. Matrix‐affected signal suppression was not significant for the solutions with NaCl concentrations lower than 0.2 and 0.1 cg g?1 for quadrupole ICP‐MS and sector field ICP‐MS, respectively. The recovery yields of elements after FDC were 97–105%. The detection limits for the sample solutions prepared by FDC were ≤ 10 pg g?1, except for Na, K and Ca. Blanks prepared using FDC were at pg‐levels, except for eleven elements (Na, Mg, Al, P, Ca, Mn, Fe, Co, Ni, Cu and Zn). The abundances of fifty‐two elements in bottled drinking water were determined from five different geological sources with mass fractions ranging from the fg g?1 to μg g?1 level with high accuracy.  相似文献   

11.
A measurement procedure for the rapid acquisition of U‐Pb dates for detrital zircons by quadrupole LA‐ICP‐MS was developed. The procedure achieves a threefold increase in measurement efficiency compared with the most commonly used methods. Utilising reduced background counting times and a shortened ablation period, a throughput of ~ 130 measurements/h can be achieved. The measurement procedure was characterised and validated using data from thirty‐nine sessions acquired over a twelve‐month period. Systematic measurement error in 206Pb/238U dates for reference materials used for quality control with ages between 28.2 and 2672 Ma was < 1.5%. Average measurement uncertainty, including both random and systematic components, was 1–4% (2s). Interrogation of time‐resolved calculated dates and signal intensities for each measurement allows for the detection and elimination of portions of measurements exhibiting age heterogeneities, zoning, lead loss and contamination by common lead. The measurement procedure diminishes the need to acquire cathodoluminescence imagery for routine detrital zircon applications further increasing throughput and reducing cost. The utility of the measurement procedure is demonstrated by the measurement of samples previously characterised by LA‐MC‐ICP‐MS.  相似文献   

12.
Gilbert‐type deltas are sensitive recorders of short‐term base‐level changes, but the delta‐front record of a base‐level rise tends to be erased by fluvial erosion during a subsequent base‐level fall, which renders the bulk record of base‐level changes difficult to decipher from the delta‐front deposits. The present detailed study of three large Pleistocene Gilbert‐type deltas uplifted on the southern coast of the Gulf of Corinth, Greece, indicates a genetic link between the delta‐front morphodynamic responses to base‐level changes and the delta‐slope sedimentation processes. Sigmoidal delta‐brink architecture signifies a base‐level rise and is accompanied by a debrite‐dominated assemblage of delta foreset deposits, thought to form when the aggrading delta front stores sediment and undergoes discrete gravitational collapses. Oblique delta‐brink architecture tends to be accompanied by a turbidite‐dominated assemblage of foreset deposits, which are thought to form when the delta‐front accommodation decreases and the sediment carried by hyperpycnal effluent bypasses the front. This primary signal of the system response to base‐level changes combines further with the secondary ‘noise’ of delta autogenic variation and possible allogenic fluctuations in fluvial discharge due to regional climatic conditions. Nevertheless, the evidence suggests that the facies trends of delta foreset deposits may be used to decipher the delta ‘hidden’ record of base‐level changes obliterated by fluvial topset erosion. Early‐stage bayhead deltas may be an exception from the hypothetical model, because their narrow front tends to be swept by river floods irrespective of base‐level behaviour and their subaqueous slope deposits are thus mainly turbidites.  相似文献   

13.
A fully coupled formulation of a hydro‐thermo‐poro‐mechanical model for a three‐phase black oil reservoir model is presented. The model is based upon the approach proposed by one of the authors which fully couples geomechanical effects to multiphase flow. Their work is extended here to include non‐isothermal effects. The gas phase contribution to the energy equation has been neglected based on a set of assumptions. The coupled formulation given herein differs in several ways when compared to the earlier work and an attempt is made to link the flow based formulation and mixture theory. The Finite Element Method is employed for the numerical treatment and essential algorithmic implementation is discussed. Numerical examples are presented to provide further understanding of the current methodology. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

14.
By virtue of a pair of scalar potentials for the displacement of the solid skeleton and the pore fluid pressure field of a saturated poroelastic medium, an alternative solution method to the Helmholtz decomposition is developed for the wave propagation problems in the framework of Biot's theory. As an application, a comprehensive solution for three‐dimensional response of an isotropic poroelastic half‐space with a partially permeable hydraulic free surface under an arbitrarily distributed time‐harmonic internal force field and fluid sources is developed. The Green's functions for the poroelastic fields, corresponding to point, ring, and disk loads, are reduced to semi‐infinite complex‐valued integrals that can be evaluated numerically by an appropriate quadrature scheme. Analytical and numerical comparisons are made with existing elastic and poroelastic solutions to illustrate the quality and features of the solution. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

15.
This study presents a high‐precision method to measure barium (Ba) isotope compositions of international carbonate reference materials and natural carbonates. Barium was purified using chromatographic columns filled with cation exchange resin (AG50W‐X12, 200–400 mesh). Barium isotopes were measured by MC‐ICP‐MS, using a 135Ba–136Ba double‐spike to correct mass‐dependent fractionation during purification and instrumental measurement. The precision and accuracy were monitored by measuring Ba isotope compositions of the reference material JCp‐1 (coral) and a synthetic solution obtained by mixing NIST SRM 3104a with other matrix elements. The mean δ137/134Ba values of JCp‐1 and the synthetic solution relative to NIST SRM 3104a were 0.21 ± 0.03‰ (2s,= 16) and 0.02 ± 0.03‰ (2s,= 6), respectively. Replicate measurements of NIST SRM 915b, COQ‐1, natural coral and stalagmite samples gave average δ137/134Ba values of 0.10 ± 0.04‰ (2s,= 18), 0.08 ± 0.04‰ (2s,= 20), 0.27 ± 0.04‰ (2s,= 16) and 0.04 ± 0.03‰ (2s,= 20), respectively. Barium mass fractions and Ba isotopes of subsamples drilled from one stalagmite profile were also measured. Although Ba mass fractions varied significantly along the profile, Ba isotope signatures were homogeneous, indicating that Ba isotope compositions of stalagmites could be a potential tool (in addition to Ba mass fractions) to constrain the source of Ba in carbonate rocks and minerals.  相似文献   

16.
This paper presents an elasto‐plastic model for non‐linear analyses of cement‐treated sand. Various laboratory tests were systematically carried out to investigate the pre‐peak and post‐peak behaviours of a cement‐treated sand. On the basis of these experimental results, the new model was built within the framework of a relatively simple elasto‐plastic theory. Two failure criteria are employed to express tensile and shear failure characteristics observed in the experimental results of the cement‐treated sand. The proposed model can describe strain‐hardening and strain‐softening responses under both failure modes. In the strain‐softening rules, the smeared crack concept is used, and a characteristic length is considered to avoid the issue of mesh‐size dependency. Since the failure criterion and strain‐hardening/softening rules are based on the experimental evidences, the model is relatively easy to understand and the parameters used in the model have clear physical meaning. The proposed model was applied to simulate the behaviour of cement‐treated sand in various laboratory tests, allowing for a reasonable comprehensive evaluation. It was demonstrated that the proposed model is suitable for describing both the tensile and shear failure behaviours of cement‐treated sand. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

17.
Bastnäsite is the end member of a large group of carbonate–fluoride minerals with the common formula (REE) CO3F·CaCO3. This group is generally widespread and, despite never occurring in large quantities, represents the major economic light rare earth element (LREE) mineral in deposits related to carbonatite and alkaline intrusions. Since bastnäsite is easily altered and commonly contains inclusions of earlier‐crystallised minerals, in situ analysis is considered the most suitable method to measure its U‐Th‐Pb and Sr‐Nd isotopic compositions. Electron probe microanalysis and laser ablation (multi‐collector) inductively coupled plasma‐mass spectrometry of forty‐six bastnäsite samples from LREE deposits in China, Pakistan, Sweden, Mongolia, USA, Malawi and Madagascar indicate that this mineral typically has high Th and LREE and moderate U and Sr contents. Analysis of an in‐house bastnäsite reference material (K‐9) demonstrated that precise and accurate U‐Th‐Pb ages could be obtained after common Pb correction. Moreover, the Th‐Pb age with its high precision is preferable to the U‐Pb age because most bastnäsites have relatively high Th rather than U contents. These results will have significant implications for understanding the genesis of endogenous ore deposits and formation processes related to metallogenic geochronology research.  相似文献   

18.
The Valanginian is a period of global environmental change as illustrated by sedimentary, palaeontological, geochemical and climatic perturbations. A production crisis in most of the carbonate platforms suggests important changes in palaeoenvironmental conditions. During the same time interval, a major positive excursion in δ13C, the Weissert Event, suggests perturbations of the carbon cycle from the latest Early Valanginian to the Early Hauterivian. In order to better understand the link between these changes, sea‐level fluctuations have been reconstructed in detail from the Middle Berriasian to the earliest Hauterivian. Sections from the Peri‐Vocontian Zone (South‐east France) have been investigated because of the good quality of outcrops on the carbonate platforms, their margins and in the Vocontian Basin. Sections ranging from the most proximal zone (Swiss Jura) to the basin were interpreted in terms of sequence stratigraphy and cyclostratigraphy, and correlated at high resolutions. Using the identified small, medium and large‐scale sequences as well as depositional geometries, sea‐level fluctuations were reconstructed. Two main trends are evidenced during the studied interval: (i) the peak amplitude (magnitude) of the sea‐level fluctuations increased gradually from the Middle Berriasian to the Early Valanginian, and reached a maximum (more than 50 m) from the middle Early Valanginian to the Valanginian/Hauterivian boundary; and (ii) sea‐level variations were quite symmetrical during the Late Berriasian, slightly asymmetrical during the Early Valanginian and strongly asymmetrical (fast sea‐level rise, slow fall) from the latest Early Valanginian to the earliest Hauterivian. Moreover, three orders of sea‐level fluctuations were recognized in the sedimentary rocks of the Peri‐Vocontian Zone. Platform‐basin correlations and cyclostratigraphic interpretations of the basinal sections evidence an astronomical control on the sea‐level variations, mainly by the two eccentricity cycles of 100 and 400 kyr. The increase in the amplitude of the sea‐level fluctuations and their change from symmetrical to asymmetrical can be related to the onset of a major cooling event in the Early Valanginian. Fast transgressions followed by slower regressions would correspond to waxing and waning of high‐latitudinal ice during most of the Valanginian, especially from the latest Early Valanginian to the latest Late Valanginian. Glacio‐eustatic sea‐level fluctuations in tune with the 100 and 400 kyr eccentricity cycles are in agreement with glaciations during the Valanginian.  相似文献   

19.
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.  相似文献   

20.
Mineral inclusions are ubiquitous in metamorphic rocks and elastic models for host‐inclusion pairs have become frequently used tools for investigating pressure–temperature (P–T) conditions of mineral entrapment. Inclusions can retain remnant pressures () that are relatable to their entrapment P–T conditions using an isotropic elastic model and P–T–V equations of state for host and inclusion minerals. Elastic models are used to constrain P–T curves, known as isomekes, which represent the possible inclusion entrapment conditions. However, isomekes require a temperature estimate for use as a thermobarometer. Previous studies obtained temperature estimates from thermometric methods external of the host‐inclusion system. In this study, we present the first P–T estimates of quartz inclusion entrapment by integrating the quartz‐in‐garnet elastic model with titanium concentration measurements of inclusions and a Ti‐in‐quartz solubility model (QuiG‐TiQ). QuiG‐TiQ was used to determine entrapment P–T conditions of quartz inclusions in garnet from a quartzofeldspathic gneiss from Goodenough Island, part of the (ultra)high‐pressure terrane of Papua New Guinea. Raman spectroscopic measurements of the 128, 206, and 464 cm?1 bands of quartz were used to calculate inclusion pressures using hydrostatic pressure calibrations (), a volume strain calculation (), and elastic tensor calculation (), that account for deviatoric stress. values calculated from the 128, 206, and 464 cm?1 bands’ hydrostatic calibrations are significantly different from one another with values of 1.8 ± 0.1, 2.0 ± 0.1, and 2.5 ± 0.1 kbar, respectively. We quantified elastic anisotropy using the 128, 206 and 464 cm?1 Raman band frequencies of quartz inclusions and stRAinMAN software (Angel, Murri, Mihailova, & Alvaro, 2019,  234 :129–140). The amount of elastic anisotropy in quartz inclusions varied by ~230%. A subset of inclusions with nearly isotropic strains gives an average and of 2.5 ± 0.2 and 2.6 ± 0.2 kbar, respectively. Depending on the sign and magnitude, inclusions with large anisotropic strains respectively overestimate or underestimate inclusion pressures and are significantly different (<3.8 kbar) from the inclusions that have nearly isotropic strains. Titanium concentrations were measured in quartz inclusions exposed at the surface of the garnet. The average Ti‐in‐quartz isopleth (19 ± 1 ppm [2σ]) intersects the average QuiG isomeke at 10.2 ± 0.3 kbar and 601 ± 6°C, which are interpreted as the P–T conditions of quartzofeldspathic gneiss garnet growth and entrapment of quartz inclusions. The P–T intersection point of QuiG and Ti‐in‐quartz univariant curves represents mechanical and chemical equilibrium during crystallization of garnet, quartz, and rutile. These three minerals are common in many bulk rock compositions that crystallize over a wide range of P–T conditions thus permitting application of QuiG‐TiQ to many metamorphic rocks.  相似文献   

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