On overestimation of displacements in numerical calculation of zoned dams

Overestimation of displacements in numerical calculations can occur if some requirements are not met by the constitutive relations. Along with consideration for small strain behaviour of soils¹ the stiffening effects of unloading in shear should be taken into account. The latter problem is analysed in the paper using embankment dams as a typical example. Strain and stress paths in their cores and shells were derived from field measurement results and frequent path direction changes during seemingly monotonic loading process were discovered. Proportional loading test results of isotropically and anisotropically consolidated sand allowed interpretation of the in situ paths by the incremental theory of plasticity and distinction between the sections where unloading and reloading in shear develop. Furthermore, the analysis of these tests showed a marked stiffening of the soil due to unloading as well as neutral loading in shear. The strain redistribution due to material inhomogeneity, either inherent or introduced by the loading process, was identified as a common reason for the frequent occurrence of this phenomenon. Consequently, overestimations in displacement calculations can be brought about by neglecting this important effect by the constitutive model used. Accordingly, the unit response envelopes of some typical constitutive laws have been checked from this special point of view, and the models properly describing this phenomenon selected.     

Experimental constraints on hydrogen diffusion in garnet

The incorporation mechanisms and diffusional loss of hydrogen in garnet have been experimentally investigated. A suite of gem-quality hydrous spessartine- and grossular-rich garnets were analysed by Fourier transform infrared spectroscopy (FTIR) and by ion microprobe (SHRIMP-SI) to determine the calibration coefficients for quantification of FTIR data. The excellent agreement between measured absorption and OH/O indicates that the same molar extinction coefficient can be used for spessartine and grossular. The coefficient of 14400 l mol^??1 cm^??2 proposed by Maldener et al. (Phys Chem Miner 30:337–344, 2003) seems the most appropriate for both minerals. A grossular with 6.4% andradite and 1.6% almandine containing 834 ppm H₂O, and an almost pure spessartine with 282 ppm H₂O, were selected for diffusion experiments. 1.5-mm cubes of garnets were heated between 12 h and 10 days at 1 atm under various temperature (750–1050 °C) and oxygen fugacity (\({f_{{{\text{O}}_2}}}\)) conditions, (ΔQFM +?15.2 to ??3.0). Diffusion profiles were acquired from sections through the cubes using FTIR, with a deconvolution algorithm developed to assess peak-specific behaviour. Different families of peaks have been identified based on their diffusive behaviour, representing hydrogen incorporated in different H-bearing defects. A dominant, fast, strongly \({f_{{{\text{O}}_2}}}\)-dependent oxidation-related diffusion mechanism is proposed \(\left( {\{ {{\text{M}}^{2+}}+{{\text{H}}^+}\} +\frac{1}{4}{{\text{O}}_2}={{\text{M}}^{3+}}+\frac{1}{2}{{\text{H}}_2}{\text{O}}} \right)\) (M=Fe, Mn) with a relatively low activation energy (158?±?19 kJ mol^??1). This diffusion mechanism is likely restricted by availability of ferrous iron in grossular. At low oxygen fugacity, this diffusion mechanism is shut off and the diffusivity decreased by more than three orders of magnitude. A second, slower hydrogen diffusion mechanism has been observed in minor bands, where charge balance might be maintained by diffusion of cation vacancies, with much higher activation energy (≈?200–270 kJ mol^??1). Spessartine shows clear differences in peak retentivity suggesting that up to four different H sites might exist. This opens exciting opportunities to use hydrogen diffusion in garnet as speedometer. However, it is essential to constrain the main diffusion mechanisms and the oxygen fugacity in the rocks investigated to obtain timescales for metamorphic or igneous processes.     

Peak metamorphic temperatures from cation diffusion zoning in garnet

A model that relates the characteristic diffusion length and average cooling rate to peak temperature was developed for chemical diffusion in spherical geometries on the basis of geospeedometry principles and diffusion theory. The model is quantitatively evaluated for cation diffusion profiles in garnet. Important model parameters were calibrated empirically using diffusion zoning of Ca in garnet from the Pikwitonei Granulite Domain, a terrane for which the thermal history has been well characterized. The results are used: (i) to empirically test diffusion parameters for Mg and Fe(II) and (ii) to develop a tool that uses the diffusion zoning of these cations in garnet to constrain peak temperature conditions for garnet‐bearing rocks. The thermometric approach was externally tested by applying it to garnet crystals from various metamorphic terranes worldwide and comparing the results to published peak temperature estimates. The results overlap within uncertainties in all cases, but result that are based on Fe(II) and Mg chemical‐diffusion profiles are up to three times more precise than those acquired by conventional methods. The remarkable consistency of the results implies that the model is robust and provides a reliable means of estimating peak temperatures for different types of high‐grade metamorphic rock. The tool could be of particular advantage in rocks where critical assemblages for conventional thermometry do not occur or have been replaced during retrogression.     

Constraints on the duration of high-pressure metamorphism in the Tauern Window from diffusion modelling of discontinuous growth zones in eclogite garnet

An eclogite sample from the Grossgockner region of the Hohe Tauern, Austria contains garnet with a pronounced compositional discontinuity between a Mn‐rich core and an Fe‐rich rim. This jump in composition was caused by a garnet‐consuming reaction followed by growth of the garnet rim + omphacite and marks the prograde transition from epidote–amphibolite to eclogite facies metamorphism. Garnet growth ended at peak metamorphic conditions of 570 °C, 17 kbar, but intracrystalline diffusion continued until about 450 °C, 4 kbar on the retrograde path. This garnet overgrowth texture represents a natural diffusion couple and a time span of 1 Myr was calculated from the diffusion profile developing out of the original sharp compositional step. For typical crustal densities, this time corresponds to a minimum average velocity in the range 4.6–7.4 cm yr^?1 (for vertical movement), which is one of the fastest exhumation rates reported. The diffusion of all divalent cations of four profiles was modelled, both analytically and numerically. Both approaches gave comparable results, but the times computed for each element were always discrepant up to a factor of 2. Variations of diffusion coefficients within 2 in analytical calculations remedied this and gave consistent upper time limits. Numerical modelling does not require the simplifications introduced in the analytical approach. On the other hand, error propagation was computationally unfeasible with this method.     

Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion

Quantification of mass and heat transport in fractured porous rocks is important to areas such as contaminant transport, storage and release in fractured rock aquifers, the migration and sorption of radioactive nuclides from waste depositories, and the characterization of engineered heat exchangers in the context of enhanced geothermal systems. The large difference between flow and transport characteristics in fractures and in the surrounding matrix rock means models of such systems are forced to make a number of simplifications. Analytical approaches assume a homogeneous system, numerical approaches address the scale at which a process is operating, but may lose individual important processes due to averaging considerations. Numerical stability criteria limit the contrasts possible in defining material properties. Here, a hybrid analytical–numerical method for transport modeling in fractured media is presented. This method combines a numerical model for flow and transport in a heterogeneous fracture and an analytical solution for matrix diffusion. By linking the two types of model, the advantages of both methods can be combined. The methodology as well as the mathematical background are developed, verified for simple geometries, and applied to fractures representing experimental field conditions in the Grimsel rock laboratory.     

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     

Harrisitic textures in the Centre Hill complex,Munro Township,Ontario: product of diffusion limited growth

Summary A spectacular occurrence of harrisitic textures has been observed near the upper margin of the Centre Hill complex, a cyclically layered mafic intrusion emplaced within komatiitic and tholeiitic volcanic rocks of the Archean Abitibi Subprovince in the Canadian Shield. The harrisitic textures, interpreted as pseudomorphs after fayalite, reach up to 50 cm in length and consistently extend away from the upper sill margin. They poikilitically enclose crystals of the surrounding matrix, indicating that they originally formed within a crystal-liquid mush. The harrisitic fayalite crystals are interpreted to have grown in situ under far from equilibrium conditions, where growth was limited by the supply of nutrients to the crystal boundaries. Mineral growth conditions were simulated using a diffusion limited aggregation (DLA) algorithm to produce branching clusters qualitatively similar to the observed textures. Based on this model, it is proposed that the original fayalite crystals formed in the late stages of differentiation cycles, where diffusivity was low due to increasing viscosity and Fe-Si enrichment of the interstitial melt. Mineral growth was initiated by an imposed thermal gradient established through the injection of primitive magma into the chamber.

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Textures harrisitiques dans le complexe de Centre Hill, canton de Munro, Ontario: produit de croissance limitée par la diffusion

Résumé De spectaculaires textures harrisitiques furent observées près de la marge supérieure du complexe de Centre Hill, une intrusion mafique à stratification cyclique mise en place à l'intérieur de roches volcaniques komatiitiques et tholéiitiques de la Sous-province de l'Abitibi du bouclier canadien. Les textures harrisitiques, interprétées comme étant des pseudomorphes après la fayalite, atteignent 50 cm de hauteur et s'étendent invariablement vers le centre du filon-couche. Ils englobent des cristaux de la matrice environnante, indiquant qu'ils se sont formés à l'origine dans un mélange de cristaux et de fondu silicaté. Les cristaux de fayalite semblent s'être développés en place dans des conditions éloignées de l'équilibre, où leur croissance était limitée par l'approvisionnement de substances nutritives á la bordure des cristaux. Les conditions de croissance furent simulées à l'aide d'un algorithme d'agrégation limitée par la diffusion (DLA), produisant des agrégats en forme de branches qualitativement similaire aux textures observées. A partir de ce modèle, il est interprété que les cristaux de fayalite se sont formes durant les stages tardifs de cycles de différentiation, où la diffusion était réduite dû à une augmentation de la viscosité et à un enrichissement en Fe et Si du liquide interstitiel. La croissance des cristaux fut initiée suite à l'établissement d'un gradient thermique relié à l'injection de magma primitif dans la chambre magmatique.

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With 3 Figures     

Thermodynamic modelling of diffusion-controlled garnet growth

Numerical thermodynamic modelling of mineral composition and modes for specified pressure-temperature paths reveals the strong influence of fractional garnet crystallisation, as well as water fractionation, on garnet growth histories in high pressure rocks. Disequilibrium element incorporation in garnet due to the development of chemical inhomogeneities around porphyroblasts leads to pronounced episodic growth and may even cause growth interruptions. Discontinuous growth, together with pressure- and temperature-dependent changes in garnet chemistry, cause zonation patterns that are indicative of different degrees of disequilibrium element incorporation. Chemical inhomogeneities in the matrix surrounding garnet porphyroblasts strongly affect garnet growth and lead to compositional discontinuities and steep compositional gradients in the garnet zonation pattern. Further, intergranular diffusion-controlled calcium incorporation can lead to a characteristic rise in grossular and spessartine contents at lower metamorphic conditions. The observation that garnet zonation patterns diagnostic of large and small fractionation effects coexist within the same sample suggests that garnet growth is often controlled by small-scale variations in the bulk rock chemistry. Therefore, the spatial distribution of garnet grains and their zonation patterns, together with numerical growth models of garnet zonation patterns, yield information about the processes limiting garnet growth. These processes include intercrystalline element transport and dissolution of pre-existing grains. Discontinuities in garnet growth induced by limited element supply can mask traces of the thermobarometric history of the rock. Therefore, thermodynamic modelling that considers fractional disequilibrium crystallisation is required to interpret compositional garnet zonation in terms of a quantitative pressure and temperature path of the host rock.     

Correlation factors for impurity diffusion on the sublattice of dodecahedral sites in garnet

The method of Koiwa and Ishioka (Philos Mag A 47:927–938, 1983) is used, with slight modification, to evaluate the correlation factor for vacancy-mediated diffusion of impurity atoms on the sublattice of dodecahedral sites in garnet, as a function of the relevant vacancy-jump frequencies. The required values of the lattice Green’s function were obtained from multiple Monte Carlo simulations in lattices of progressively larger size, extrapolated to an infinite lattice using a model that linearizes the dependence of the functional value on lattice size. As Online Resources, codes are provided that permit evaluation of the correlation factor for any chosen set of vacancy-jump frequencies, for implementation in either Mathematica ^® or Matlab ^®.     

Effect of grossular on garnet-biotite,Fe–Mg exchange reactions: evidence from garnet with mixed growth and diffusion zoning

Garnets that exhibit mixed growth and diffusion zoning are used to evaluate the effect of grossular content on garnet Fe–Mg exchange reactions. These garnets from the uppermost amphibolite-facies to granulite-facies gneiss of the Wissahickon Group, southeastern Pennsylvania, show variation in grossular content (0.035<X _Ca<0.14) but nearly constant Mg? (X _Mg/(X _Mg+X _Fe) and X _Mn through the interior indicating re-equilibration of garnet and matrix minerals with respect to iron, magnesium, and manganese. Mg? is not correlated with calcium content, evidence that the effect of calcium on garnet Fe–Mg exchange reactions is small or is offset by other interactions in almandine-rich garnets. In either case, the data presented here indicate that correction for calcium content of garnets in the application of garnet-biotite geothermometry to high-grade metapelites is unnecessary and may lead to an overestimate of peak temperature.     

倾斜台阶重力异常正演计算公式剖析

规则地质体的正演异常是进行实际数据解释的依据,因此其正确性至关重要。现有教材和大部分论文中所列出的倾斜台阶重力异常正演公式在一定条件下会出现畸点,从而对构造模型的数据解释会产生困扰。笔者从台阶的重力积分表达式出发,重新推导了倾斜台阶模型的重力异常正演公式,模型试验表明笔者新推导公式不会出现畸点,这为数据解释提供更准确的基础数据。     

新疆西天山查岗诺尔铁矿床环带石榴子石和绿帘石的发现及意义

查岗诺尔铁矿是新疆西天山阿吾拉勒铁矿带内的重要大型铁矿床之一。矿体赋存在下石炭统大哈拉军山组安山质火山岩中,与普遍发育的石榴子石化、阳起石化和绿帘石化时空关系密切。石榴子石和绿帘石分属不同热液成矿阶段,它们均发育丰富的环带结构,具体表现为明显地颜色、干涉色、背散射图像及成分（FeO、Al₂O₃、SiO₂、MnO、TiO₂）等差异性。石榴子石具有2个世代、3个类型。早世代石榴子石（Grt1和Grt2）产于块状石榴子石-磁铁矿蚀变岩,呈褐黄色,粒度较细,发育核-边结构,呈非均质性,显示异常干涉色,其核部（Grt1-c）均匀相对富钙铝榴石（Gro_51-53And_41-43Spr_4-8）,而边部（Grt1-r）发育振荡成分环带,总体相对富钙铁榴石（Gro_18-35And_60-77Spr_4-6）;Grt2核部（Grt2-c）呈均质性,为钙铁榴石（And_99-100Spr_0-1）,边部显异常干涉色,发育振荡成分环带,为钙铝铁榴石（Gro_34-54And_38-61Spr_6-9）。晚世代的石榴子石（Grt3）以细脉状或角砾胶结物形式分布,呈红褐色,自形粗粒结构,显非均质性,发育振荡成分环带,端员组分总体以钙铁榴石为主,次为钙铝榴石（Gro_27-43And_50-68Spr_3-8）。石榴子石结构和元素含量变化表明,早期石榴子石形成于弱氧化-氧化、中性-碱性流体体系,其中向边部生长过程,由于新注入流体以及周期性压力汇聚和释放,体系的氧逸度、pH值呈振荡变化;晚期石榴子石形成于弱氧化、弱碱性、动荡的开放流体环境。绿帘石发育3个世代（Ep1、Ep2和Ep3）。Ep1发育核-边结构,核部（Ep1-c）均匀无环带,X_Fe值（X_Fe=Fe³⁺/（Al+Fe³⁺）,原子比值）为0.19~0.21,w（MnO）为0.05%~0.18%,w（TiO₂）为0.10%~0.12%,生长边（Ep1-r）多发育振荡环带,X_Fe值为0.26~0.29,w（MnO）为0.01%~0.14%,w（TiO₂）为0.19%~0.26%。Ep2沿Ep1-r边缘生长,不均匀且经历了溶解-再沉淀过程,X_Fe值为0.15~0.20,w（MnO）为0.42%~1.19%,w（TiO₂）为0.02%~0.07%。Ep3呈柱状或不规则粒状交代Ep2、贴近或穿切Ep1-r生长,较均匀、无环带结构,X_Fe值为0.28~0.37,w（MnO）为0.12%~0.77%,w（TiO₂）为0.02%~0.10%。绿帘石成分变化表明,从Ep1-c到Ep1-r,到Ep2,再到Ep3,流体体系氧逸度经历了先增加,后降低,再升高的变化过程。同时,流体成分也在变化,先从相对贫Ti和Mn向相对富Ti贫Mn演化,而后又变为富Mn贫Ti。因此,在热液磁铁矿矿化阶段,查岗诺尔铁矿的成矿热液的物理-化学环境是不断变化的。研究显示,石榴子石和绿帘石结构和成分研究可以刻画热液成矿系统的流体演化历史。     

On the interpretation of peak metamorphic temperatures in light of garnet diffusion during cooling

Abstract Finite difference models of Fe-Mg diffusion in garnet undergoing cooling from metamorphic peak conditions are used to infer the significance of temperatures calculated using garnet-biotite Fe-Mg exchange thermometry. For rocks cooled from high grades where the garnet was initially homogeneous, the calculated temperature (T_calc) using garnet core and matrix biotite depends on the size of the garnet, the ratio of garnet to biotite in the rock (V_garnet/V_biotite) and the cooling rate. For garnets with radii of 1 mm and V_garnet/V_biotite<1, T_calc is 633, 700 and 777°C for cooling rates of 1, 10 and 100°C/Ma. For V_garnet/V_biotite= 1 and 4 and a cooling rate of 10° C/Ma, T_calc is approximately 660 and 610° C, respectively. Smaller and larger garnets have lower and higher T_calc, respectively. These results suggest that peak metamorphic temperatures may be reliably attained from rocks crystallized at conditions below T_calc of the garnet core, provided that V_garnet/V_biotite is sufficiently small (<0.1) and that the composition of the biotite at the metamorphic peak has not been altered during cooling. Numerical experiments on amphibolite facies garnets with nominal peak temperatures of 550–600° C generate a ‘well’in Fe/(Fe + Mg) near the rim during cooling. Maximum calculated temperatures for the assemblage garnet + chlorite + biotite + muscovite + plagioclase + quartz using the Fe/(Fe + Mg) at the bottom of the ‘well’with matrix biotite range from 23–43° C to 5–12° C below the peak metamorphic temperature for cooling rates of 1 and 100° C/Ma, respectively. Maximum calculated temperatures for the assemblage garnet + staurolite + biotite + muscovite + plagioclase + quartz are approximately 70° C below the peak metamorphic temperature and are not strongly dependent on cooling rate. The results of this study indicate that it may be very difficult to calculate peak metamorphic temperatures using garnet-biotite Fe-Mg exchange thermometry on amphibolite facies rocks (T_max > 550° C) because the rim composition of the garnet, which is required to calculate the peak temperature, is that most easily destroyed by diffusion.     

Rare earth diffusion kinetics in garnet: Experimental studies and applications

We determined the diffusion coefficient of Sm in almandine garnet as function of temperature at 1 bar and fO₂ corresponding to that of wüstite-iron buffer, and to a limited extent, that of a few other selected rare earth elements in almandine and pyrope garnets. Both garnets were demonstrated to have metastably survived the diffusion annealing at conditions beyond their stability fields. The experimental diffusion profiles were analyzed by secondary ion mass spectrometry, and in addition, by Rutherford back scattering spectroscopy for two samples. Transmission electron microscopic study of an almandine crystal that was diffusion-annealed did not reveal any near-surface fast diffusion path. Using reasonable approximations and theoretical analysis of vacancy diffusion, the experimental data were used to develop an expression of rare earth element (REE) diffusion coefficient in garnet as a function of temperature, pressure, fO₂, ionic radius, and matrix composition. Calculation of the closure temperature for the Sm-Nd decay system in almandine garnet in a metamorphic terrain shows very good agreement with that constrained independently. Modeling of the REE evolution in melt and residual garnet suggests that for dry melting condition, the REE pattern in the melt should commonly conform closely to that expected for equilibrium melting. However, for much lower solidus temperatures that would prevail in the presence of a H₂O-CO₂ fluid, the concentration of light REE in the melt could be significantly lower than that under equilibrium melting condition. A reported core and rim differences in the REE content of a garnet crystal in a mantle xenolith in kimberlite have been reproduced by assuming that the REE zoning was a consequence of entrapment in a magma derived from an external source for ∼32,000 yr before the eruption.     

Magnesium and iron isotopes in 2.7 Ga Alexo komatiites: Mantle signatures, no evidence for Soret diffusion, and identification of diffusive transport in zoned olivine

Komatiites from Alexo, Canada, are well preserved and represent high-degree partial mantle melts (∼50%). They are thus well suited for investigating the Mg and Fe isotopic compositions of the Archean mantle and the conditions of magmatic differentiation in komatiitic lavas. High precision Mg and Fe isotopic analyses of 22 samples taken along a 15-m depth profile in a komatiite flow are reported. The δ²⁵Mg and δ²⁶Mg values of the bulk flow are −0.138 ± 0.021‰ and −0.275 ± 0.042‰, respectively. These values are indistinguishable from those measured in mantle peridotites and chondrites, and represent the best estimate of the composition of the silicate Earth from analysis of volcanic rocks. Excluding the samples affected by secondary Fe mobilization, the δ⁵⁶Fe and δ⁵⁷Fe values of the bulk flow are +0.044 ± 0.030‰, and +0.059 ± 0.044‰, respectively. These values are consistent with a near-chondritic Fe isotopic composition of the silicate Earth and minor fractionation during komatiite magma genesis. In order to explain the early crystallization of pigeonite relative to augite in slowly cooled spinifex lavas, it was suggested that magmas trapped in the crystal mush during spinifex growth differentiated by Soret effect, which should be associated with large and coupled variations in the isotopic compositions of Mg and Fe. The lack of variations in Mg and Fe isotopic ratios either rules out the Soret effect in the komatiite flow or the effect is effaced as the solidification front migrates downward through the flow crust. Olivine separated from a cumulate sample has light δ⁵⁶Fe and slightly heavy δ²⁶Mg values relative to the bulk flow, which modeling shows can be explained by kinetic isotope fractionation associated with Fe-Mg inter-diffusion in olivine. Such variations can be used to identify diffusive processes involved in the formation of zoned minerals.     

喜马拉雅造山带片麻岩中石榴子石的多期生长

石榴子石是高级变质作用的重要矿物之一,能够保留成分环带和不同变质阶段的矿物或流体包裹体,为示踪寄主岩石经历的变质演化历史提供重要信息。本文对采自雅拉香波片麻岩穹窿内高级变质岩中石榴子石进行了详细的包裹体成分、主量元素环带和微量元素特征的研究,揭示出石榴子石黑云母片麻岩至少记录了五期岩浆或变质热事件。第Ⅰ期石榴子石为来源于源区的岩浆型石榴子石。第Ⅱ期、第Ⅲ期和第Ⅳ期石榴子石为变质型石榴子石,但不同期次变质作用的温压条件和生长介质、矿物组合不同。第Ⅴ期石榴子石为转熔型石榴子石,是黑云母脱水熔融形成,记录了喜马拉雅造山过程早期加厚地壳条件下的深熔作用。喜马拉雅造山带变质岩中石榴子石具有复杂的成因机制和演化历史,在应用石榴子石进行变质作用研究时,需要仔细甄别,否则会得到错误的结论。     

Multicomponent diffusion in aluminosilicate garnet: coupling effects due to charge compensation

ABSTRACT

Three kinds of multicomponent diffusion effects, arising from three distinct physical mechanisms, are evident in stranded diffusion profiles at the rims of partially resorbed garnets from the contact aureole of the Makhavinekh Lake Pluton, northern Labrador. Profiles that display a subtle maximum in Ca concentration are explained by the prevailing ideal mean-field theory of multicomponent diffusion, but models implementing that theory cannot replicate inverted profiles for Li and internal maxima for Nd, Sm, and Eu. The anomalous profiles are quantitatively reproduced, however, by numerical simulations employing a model based on coupled movement of charge-compensating groups during diffusional transport of yttrium and the rare-earth elements (Y+REEs). An alkali-type charge-compensation mechanism for the heterovalent substitution of Y+REEs on dodecahedral sites in garnet produces direct charge coupling between Li⁺ and (Y+REE)³⁺ and leads to co-diffusion of Li⁺-(Y+REE)³⁺ pairs, with the result that Li profiles closely mimic those for Y+REEs. A menzerite-type charge-compensation mechanism produces indirect charge coupling among all Y+REE components, with the result that the fluxes of low-abundance REEs become partly dependent on the fluxes of Y+REEs present in higher abundance. These findings have implications for the robustness of Li profiles in garnet as monitors of fluid–rock interaction, for geochronology based on the Sm–Nd and Lu–Hf systems, and for future experimental attempts to quantify rates of diffusion in garnet.     

Uphill diffusion,zero-flux planes and transient chemical solitary waves in garnet

Diffusion profiles in minerals are increasingly used to determine the duration of geological events. For this purpose, the distinction between growth and diffusion zoning is critical; it requires the understanding of complex features associated with multicomponent diffusion. Seed-overgrowth interdiffusion experiments carried out in the range 1,050–1,250°C at 1.3 GPa have been designed to quantify and better understand Fe–Mg–Ca interdiffusion in garnet. Some of the diffusion profiles measured by analytical transmission electron microscope show characteristic features of multicomponent diffusion such as uphill diffusion, chemical solitary waves, zero-flux planes and complex diffusion paths. We implemented three different methods to calculate the interdiffusion coefficients of the D matrix from the experimental penetration curves and determined that with Ca as the dependent component, the crossed coefficients of the D matrix are negative. Experiments and numerical simulations indicate that: (1) uphill diffusion in garnet can be observed indifferently on the three components Fe, Mg and Ca, (2) it takes the form of complementary depletion/repletion waves and (3) chemical waves occur preferentially on initially flat concentration profiles. Derived D matrices are used to simulate the fate of chemical waves in time, in finite crystals. These examples show that the flow of atoms in multicomponent systems is not necessarily unidirectional for all components; it can change both in space along the diffusion profile and in time. Moving zero-flux planes in finite crystals are transitory features that allow flux reversals of atoms in the diffusion zone. Interdiffusion coefficients of the D matrices are also analyzed in terms of eigenvalues and eigenvectors. This analysis and the experimental results show that depending on the composition of the diffusion couple, (1) the shape of chemical waves and diffusion paths changes; (2) the width of the diffusion zone for each component may or may not be identical; and (3) the width of diffusion calculated at a given D and duration may greatly vary. D matrices were retrieved from thirteen sets of diffusion profiles. Data were cast in Arrhenius relations. Linear regressions of the data yield activation energies equal to 368, 148, 394, 152 kJ mol⁻¹ at 1 bar and frequency factors D_o equal to 2.37 × 10⁻⁶, −4.46 × 10⁻¹⁶, −1.31 × 10⁻⁵, 9.85 × 10⁻¹⁵ m² s⁻¹ for [(D)\tilde]_FeFe^Ca \tilde{D}_{FeFe}^{Ca} , [(D)\tilde]_FeMg^Ca \tilde{D}_{FeMg}^{Ca} , [(D)\tilde]_MgFe^Ca \tilde{D}_{MgFe}^{Ca} , [(D)\tilde]_MgMg^Ca \tilde{D}_{MgMg}^{Ca} , respectively. These values can be used to calculate interdiffusion coefficients in Fe–Mg–Ca garnets and determine the duration of geological events in high temperature metamorphic or magmatic garnets.     

Disequilibrium for Ca during growth of pelitic garnet

Compositional zoning in hundreds of almandine-rich garnets in amphibolite by facies micaceous quartzites from the Picuris Range, north-central New Mexico USA, indicates that although Mn, Mg and Fe achieve chemical equilibrium at hand-sample scale during garnet growth, Ca does not. Instead, Ca concentrations at the surface of growing garnets appear to depend strongly on kinetic factors that govern the local chemical environment, yielding disequilibrium for Ca at scales larger than the region immediately surrounding an individual porphyroblast. Detailed zoning profiles were obtained for 371 garnet crystals in a small volume of a single sample of garnetiferous quartzite, and core analyses were made of 97 additional crystals. Each analysis was made on a section that passed precisely through the morphological centre of the crystal, located by means of 3-D imagery from computed X-ray tomography. The data reveal strong correlations between crystal size and concentrations of Mn, Mg and Fe (but not Ca) in garnet cores; a relationship between crystal size and isolation; rigorous cross-correlations among concentrations of Mn, Mg and Fe (but not Ca); and systematic variations in Ca concentrations as a function of crystal size and core composition that are anomalous in comparison to the behaviour of the other divalent cations. We interpret these observations as the result of thermally accelerated diffusion-controlled garnet growth, in circumstances that promoted rapid intergranular diffusion and thus rock-wide equilibration of Mn, Mg and Fe, but that prevented equilibration at similar scale for Ca because of its more sluggish intergranular diffusion. The anomalous behaviour of Ca is made evident in these garnets by the presence of sharp spikes in Ca concentration, which are demonstrably not a consequence of any simultaneous rock-wide event, such as a change in pressure, temperature, or some other intensive parameter. Instead, Ca concentrations probably reflect the local extent of reaction in the immediate vicinity of each porphyroblast. To the degree that such kinetic factors introduce departures from chemical equilibrium for Ca, thermobarometric estimates that involve grossular contents of pelitic garnet will be in error.