diffusion obstacles and opportunities in petrochronology many of the approaches in petrochronology are rooted in the assumption of equilibrium diffusion is an expression of disequilibrium the movement of mass in response to chemical potential gradients and isotopes in response to isotopic gradients it is extremely important that we be aware of how the effects of diffusion can place obstacles across our path towards petrochronologic enlightenment conversely the effects of diffusion also provide opportunities for understanding rates processes and conditions experienced by rocks the enormity of the field does not permit us to provide a comprehensive review of either the mathematics of diffusion or quantitative data that have been obtained relevant to the interpretation of diffusive processes in rocks and minerals many resources cover these topics including rimg volume 72 diffusion in minerals and melts zhang and cherniak 2010 and several textbooks crank 1975 glicksman 2000 particularly relevant to the discussion of petrochronology are summaries of the theory and controls on diffusion brady and cherniak 2010 zhang 2010 as well as diffusion rates in feldspar cherniak 2010a accessory minerals cherniak 2010b garnet ganguly 2010 mica pyroxene and amphibole cherniak and dimanov 2010 and melts zhang and ni 2010 zhang et al 2010 rather than duplicate that material our goal is to explore the obstacles and opportunities presented by the effects of diffusion as they inform the rates of petrologic processes to achieve this goal we emphasize key principles and illustrative examples quantitative interpretation of the effects of diffusion assumes predictability of numerous factors that may affect chemical or isotopic transport including temperature initial and boundary conditions water and oxygen fugacities activities of other components multiple mechanisms of diffusion and crystal chemistry coupling of the substitution of elements into different crystallographic sites additionally the extraction of meaningful ages durations of events and temperatures requires

microchemical and sr isotopic investigation of zoned k feldspar megacrysts insights into the petrogenesis of a granitic system and disequilibrium crystal growth k feldspar megacrysts kfm are used to investigate the magmatic evolution of the 7ma monte capanne mc monzogranite elba italy dissolution and regrowth of kfm during magma mixing or mingling events produce indented resorption surfaces associated with high ba contents diffusion calculations demonstrate that kfm chemical zoning is primary core to rim variations in ba rb sr li and p support magma mixing i e high ba and p and low rb sr at rims but more complex variations require other mechanisms in particular we show that disequilibrium growth related to variations in diffusion rates in the melt may have occurred as a result of thermal disturbance following influx of mafic magma in the magma chamber initial 87 sr 86 sr ratios isr obtained by microdrilling decrease from core to rim inner core analyses define a mixing trend extending towards a high isr rb sr melt component whereas the outer cores and rims display a more restricted range of isr but a larger range of rb sr lower isr at the rim of one megacryst suggests mixing with high k calc alkaline mantle derived volcanics of similar age on capraia trace element and isotopic profiles suggest 1 early megacryst growth in magmas contaminated by crust and refreshed by high isr silicic melts as seen in the inner cores and 2 later recharge with mafic magmas as seen in the outer cores followed by 3 crystal fractionation with possible interaction with hydrothermal fluids as seen in the rim the model is compatible with the field occurrence of mafic enclaves and xenoliths

a study of strontium diffusion in k feldspar na k feldspar and anorthite using rutherford backscattering spectroscopy abstract sr chemical diffusion has been measured in orthoclase anorthoclase and anorthite under dry 1 atm conditions a strontium oxide aluminosilicate powder mixture was used as the source material with rutherford backscattering spectroscopy rbs used to measure diffusion profiles over the temperature range 725 1075 c the following arrhenius relations were obtained orthoclase normal to 001 d 5 97 10 0 0060 0 0030exp 67900 1600rtcm 2 s 1 measurements of diffusion perpendicular to 010 and 100 indicate little diffusional anisotropy in orthoclase anorthoclase normal to 010 d 4 51 10 1 358 5 6exp 89100 4800rt cm 2 s 1 normal to 001 d 2 25 10 2 1615 31exp 89300 4600rt cm 2 s 1 anorthite normal to 010 d 3 85 10 2 0 380 0 0039 exp 78800 5400rt cm 2 s 1 the correlation of sr uptake with a reduction of k and ca in orthoclase and anorthite respectively indicates that sr is exchanging with these species nuclear reaction analysis nra measurements of al in orthoclase suggests that the coupled exchange sr 2 al 3 k 1 si 4 is taking place as expected sr closure temperatures for feldspars calculated with the above parameters are relatively high compared to those of some other minerals e g biotite muscovite apatite however closure temperatures of feldspars may be significantly depressed if they are exsolved or twinned leading to small effective diffusion lengths feldspar crystals of millimeter size should retain 87 sr 86 sr ratios except when subjected to thermal events of extreme temperature or duration

rates of hydrothermal cooling of new oceanic upper crust derived from lithium geospeedometry episodic emplacement and cooling of lavas and dikes at mid ocean ridges leads to large fluctuations in hydrothermal fluxes and biological activity however the processes operating beneath the seafloor during these transient events such as permeability creation and dike cooling are poorly understood we have developed a new approach to determine the cooling rate of the sheeted dike complex based on the extent of diffusion of lithium from plagioclase into clinopyroxene during cooling we have calibrated this li geospeedometer using new high temperature experiments to determine both the temperature dependence of the partitioning of li between plagioclase and clinopyroxene and the diffusion coefficient for li in clinopyroxene application of this method to lavas and dikes from odp hole 504b shows that cooling rates vary dramatically with depth in the upper oceanic crust extremely rapid cooling rates 450 c hr 1 in the upper part of the sheeted dike complex are sufficient to power hydrothermal megaplume formation within the overlying water column

the little ice age and medieval warm period in the sargasso sea sea surface temperature sst salinity and flux of terrigenous material oscillated on millennial time scales in the pleistocene north atlantic but there are few records of holocene variability because of high rates of sediment accumulation holocene oscillations are well documented in the northern sargasso sea results from a radiocarbondated box core show that sst was approximately 1 degree c cooler than today approximately 400 years ago the little ice age and 1700 years ago and approximately 1 degree c warmer than today 1000 years ago the medieval warm period thus at least some of the warming since the little ice age appears to be part of a natural oscillation 39 refs 4 figs 1 tab

sr and pb isotope micro analysis of plagioclase crystals from skye lavas an insight into open system processes in a flood basalt province crystals in many magmatic rocks are heterogeneous in terms of their isotope composition detailed crystal isotope stratigraphy cis studies have shown that crystals act as reliable recorders of their magma source composition and of the pathways of magma interaction and successfully identify the end members involved in magmatic systems in this paper we have analysed cores and rims and single plagioclase crystals from samples of the skye volcanic centre part of the british palaeogene igneous province the isotope analyses reveal that plagioclase crystals from different volcanic samples through thelava succession in skye skye main lava series preshal more basalts and big feldspar lavas have larger sr and pb isotopic ranges than the isotopic ranges found in hundreds of whole rock analyses the large sr and pb isotopic variation in plagioclase crystals in skye is due to variable degrees of crustal contamination of the parental magmas during fractional crystallization and during the ascent of such magmas to the surface the isotope variation of plagioclase crystals in the early lavas skye main lava series reflects assimilation fractional crystallization processes dominated by the lower crust whereas plagioclase crystals from later erupted magmas big feldspar lavas and preshal more basalts show assimilation of upper crust superimposed on previous lower crustal contamination processes the variability in sr and pb isotopes documented in different crystals within the same rocks shows that the crystals have been aggregated in magmas from different sites of storage and differentiation during the ascent of the magmas to the surface

the role of hydrogen in promoting alsi interdiffusion in albite naalsi3o8 at high pressures the rate of al si disorder in dry low albite is greatly enhanced at high pressures this enhancement takes place in ap t regime where the presence of water would induce melting none was observed the experimental work was carried out in piston cylinder apparatus using nacl pressure medium modification of the experimental conditions to avoid production of hydrogen by dissociation of moisture in the pressure medium as well as to capture hydrogen with fe2o3 and zno indicates that hydrogen is the active agent in promoting al si diffusion at high pressures in naalsi3o8 a mechanism involving transient oh groups that stimulate coordinations greater than 4 simultaneously breaking alo and sio network bonds is proposed

diffusion of a multi species component and its role in oxygen and water transport in silicates an important but poorly understood factor that affects diffusion rates is the role of speciation during diffusion of a multi species component the diffusion of such a component is complicated by the different diffusion coefficient of each species and the interconversion reactions among the species these complexities can be treated by a diffusion equation that incorporates the diffusive fluxes of all species contributing to the concentration of the component the effects of speciation on the diffusion of the component can be investigated experimentally in some simple cases by measuring concentration profiles of all species developed during diffusion experiments or by studying some of their other consequences experimental data on water diffusion in rhyolitic glasses indicate that although dissolved water is present as two species h 2o molecules and oh groups molecular h 2o is the dominant diffusing species at very low to high water concentrations this explains the apparently complex behavior of water diffusion experimental data on oxygen diffusion in some silicates using 18 o tracers in the form of h 2 18 o are consistent with the idea that 18 o transport is dominated by diffusion of h 2o molecules even at lower water contents ppm or less this explains why oxygen transport depends on the presence of water and generally depends on water fugacity linearly for this mode of oxygen transport there is a simple theoretical relationship between the effective total oxygen diffusion coefficient and the total water diffusion coefficient that is a function of only the water concentration of the silicate at low water content this relationship appears to describe quantitatively the existing data over a wide range in water contents and diffusion coefficients in several phases

fingerprinting feldspar phenocrysts using crystal isotopic composition stratigraphy implications for crystal transfer and magma mingling in s type granites microsampling of cm scale feldspar crystals within an s type granite from the lachlan fold belt of southeastern australia has revealed complex internal sr and nd isotopic variations the observed isotopic zonations are in part interpreted as recording feldspar crystallisation in a dynamically mixing magma system the isotopic composition of which was varying in response to the influx of more mafic and isotopically more mantle like magmas the latter stages of which are now represented in modified form by microgranular enclaves similar core to rim isotopic variations in feldspar megacrysts from a microgranular enclave and the adjacent host granite strongly suggest megacrysts in the enclave were transferred from the granitic magma during crystallisation feldspar rims have higher 87sr 86sri and lower nd i than adjacent whole rock analyses but match those of mineral separates from the surrounding enclave matrix this suggests that the final stages of megacryst growth occurred in the presence of a component that had previously interacted with a high 87sr 86sr low nd i component such as metasedimentary wall rocks isotopic heterogeneities are also presererved within different mineral phases in the enclave matrix suggesting that differing phases grew at differing stages of equilibration between the enclave magma and its host granitic magma our results reveal major isotopic heterogeneities on a single crystal and also inter mineral scale in a pluton which shows well constrained evidence for magma mingling these results indicate the suitability of feldspars as recorders of isotopic change in magmatic systems even those which have cooled slowly in the plutonic environment and suggest that much heterogeneity in plutonic systems may be overlooked on a whole rock scale

amphibole clinopyroxene and plagioclase melt partitioning of trace and economic metals in halogen bearing rhyodacitic melts

strontium diffusion kinetics in plagioclase feldspars abstract a pronounced systematic variation by a factor of 104 in strontium tracer diffusion kinetics has been measured in four feldspar specimens that span the range of plagioclase compositions the experiments were carried out in air using isotopically enriched 86sr and analyzed with an ion microprobe the arrhenius relations for strontium diffusion are plagioclase ab d 0 m 2 s q kj g atom sr temperature range c albite 98 1 05e 279 550 1080 oligoclase 73 7 4e 7 261 750 1100 labradorite 36 1 1e 6 295 800 1300 anorthite 4 5 7e 9 267 900 1300 no difference was found within the measurement uncertainty between these results and those for albite under hydrothermal conditions at one kbar 100 mpa strontium diffusion rates parallel to and normal to the albite twin lamellae are the same there is no effect on the strontium diffusion rate in albite between an oxygen partial pressure of 0 2 bar air and 10 19 bar graphite buffer a relation is developed that permits calculation of the strontium diffusion arrhenius parameters for any normal plagioclase composition the large variation in diffusion rate with composition has a major effect on the ease of strontium isotope exchange at high temperatures between plagioclases and coexisting phases in rocks which may prove useful in determining thermal histories

magma mixing recharge and eruption histories recorded in plagioclase phenocrysts from el chichon volcano mexico operative throughout the 200 ky history of the el chichon magma consistent core to rim decreases of sr sr ratios and coincident system increases in sr concentrations in plagioclase phenocrysts of varying size 1 cm to 2 mm are reported from samples of the 1982 and pre 1982 200 ka eruptions of el chichon volcano maximum sr sr ratios of 0 7054 significantly higher than the wholerock isotopic ratios 0 7040 0 7045 are found in the cores

pb isotopic zoning of k feldspar megacrysts determined by laser ablation multi collector icp ms insights into granite petrogenesis this study investigates pb isotopic zoning in magmatic k feldspar megacrysts from the monte capanne pluton elba italy using laser ablation multi collector icpms the studied crystals provide an ideal opportunity to use in situ techniques to assess the extent of open system processes and better characterize the components involved in the genesis of complex magma systems earlier investigations of the pluton identified the importance of magma mixing between mantle and crustal derived magmas the investigated k feldspar megacrysts exhibit strong zoning in 207pb 206pb and 208pb 206pb correlated with lead elemental variations we interpret these variations as reflecting growth zoning as opposed to secondary diffusive exchange despite a great variety of zoning patterns we were able to correlate different events of megacryst growth reflecting crystallization in a dynamic magma system our two step model includes 1 growth of a granitic magma chamber by addition of low 208pb 206pb magma to a high 208pb 206pb magma contaminated with crustal material i e the megacryst cores and 2 recharge by mantle derived magma i e the megacryst rims we interpret the thorogenic nature of the megacryst rims to reflect the mantle derived component involved in the mixing process taking account of other data from the tuscan magmatic province the mantle source is inferred to have been metasomatized by continental material during subduction tims sr isotopic data from microdrilled cores in one megacryst provides general support for the model but show that the two isotopic systems are decoupled

mineral chemistry of muses c regio inferred from analysis of dust particles collected from the first and second touchdown sites on asteroid itokawa the mineralogy and mineral chemistry of itokawa dust particles captured during the first and second touchdowns on the muses c regio were characterized by synchrotron radiation x ray diffraction and field emission electron microprobe analysis olivine and low and high ca pyroxene plagioclase and merrillite compositions of the first touchdown particles are similar to those of the second touchdown particles the two touchdown sites are separated by approximately 100 meters and therefore the similarity suggests that muses c regio is covered with dust particles of uniform mineral chemistry of ll chondrites quantitative compositional properties of 48 dust particles including both first and second touchdown samples indicate that dust particles of muses c regio have experienced prolonged thermal metamorphism but they are not fully equilibrated in terms of chemical composition this suggests that muses c particles were heated in a single asteroid at different temperatures during slow cooling from a peak temperature of approximately 800 c chemical compositions of plagioclase and k feldspar seem to have been modified ab and or contents changed during cooling but an did not this compositional modification is reproduced by a numerical simulation that modeled the cooling process of a 50 km sized itokawa parent asteroid after cooling some particles have been heavily impacted and heated which resulted in heterogeneous distributions of na and k within plagioclase crystals impact induced chemical modification of plagioclase was verified by a comparison to a shock vein in the kilabo ll6 ordinary chondrite where na k distributions of plagioclase have been disturbed

coupled caal nasi diffusion in plagioclase feldspar experiments and applications to cooling rate speedometry abstract the rate of caal nasi interdiffusion in plagioclase feldspar was determined under 1 atm anhydrous conditions over the temperature range 1400 to 1000 c in calcic plagioclase an80 81 by homogenizing coherent exsolution lamellae the dependence of the average interdiffusion coefficient on temperature is given by the expression d 10 99 cm 2 sec exp 123 4 kcal mol rt t in k this value is for diffusion perpendicular to the 03 1 interface of the lamellae caal nasi interdiffusion is 4 to 5 orders of magnitude slower than oxygen diffusion in the temperature range 1400 to 1200 c and possibly 10 orders of magnitude slower at subsolidus temperatures the large differences in diffusion rates explain the apparent contradiction posed by the plagioclases of large layered intrusions e g the skaergaard which retain delicate ca na compositional zoning profiles on the micron scale but have undergone complete oxygen isotopic exchange with heated meteoric groundwater from the surrounding wall rocks caal nasi diffusion is slow the closure temperature is high within the solidus liquidus interval and ca na zoning is preserved oxygen diffusion is faster the closure temperature is lower 350 400 c and the feldspars exchange oxygen with the low temperature hydrothermal fluids the complex micron scale oscillatory zones in plagioclase can also be used as cooling rate speedometers for volcanic and plutonic plagioclase cooling histories typical of large mafic intrusions e g the stillwater are slow begin at high initial temperatures 1200 c and result in homogenization of oscillatory zones on the scale of 10 microns the oscillatory zones found in the plagioclase of granodioritic plutons are preserved because cooling is initiated at a lower temperature 1000 c limiting diffusion to submicron length scales despite the slow cooling rate of the intrusion

ree diffusion in calcite chemical diffusion of four rare earth elements la nd dy and yb has been measured in natural calcite under anhydrous conditions using rare earth carbonate powders as the source of diffusants experiments were run in sealed silica capsules along with finely ground calcite to ensure stability of the single crystal samples during diffusion anneals rutherford backscattering spectroscopy rbs was used to measure diffusion profiles the following arrhenius relations were obtained over the temperature range 600 850 c dla 2 6 10 14 exp 147 14 kj mol 1 rt m2 s 1 dnd 2 4 10 14 exp 150 13 kj mol 1 rt m2 s 1 ddy 2 9 10 14 exp 145 25 kj mol 1 rt m2 s 1 dyb 3 9 10 12 exp 186 23 kj mol 1 rt m2 s 1 in contrast to previous findings for refractory silicates e g zircon differences in transport rates among the ree are not pronounced over the range of temperature conditions investigated in this study diffusion of the ree is significantly slower than diffusion of the divalent cations sr and pb and slower than transport of ca and c at temperatures above 650 c fine scale zoning and isotopic and ree chemical signatures may be retained in calcites under many conditions if diffusion is the dominant process affecting alteration

rb and sr diffusion in alkali feldspars with implications for cooling histories of rocks volume diffusion of sr and rb have been measured in orthoclase feldspar as well as sr diffusion in albite using isotope exchange hydrothermal solutions and analysis by ion microprobe for water pressures of 1000 bars the kinetics of diffusion parallel to the c axis are given by the arrhenius relations strontium transport in the or is isotropic to within a factor of four the measurements use a new procedure in which only the elements in question are present in the starting fluid cooling rates of igneous rocks can now be determined from closure temperatures material balance and the rb sr dating method based on the departures of the mineral data from the whole rock isochron for cooling rates less than approximately 100 c my

pb diffusion in zircon abstract chemical diffusion of ti under anhydrous conditions at 1 atm and under fluid present elevated pressure 1 1 1 2 gpa conditions has been measured in natural zircon the source of diffusant for 1 atm experiments was a zro2 tio2 zircon mixture with experiments run in crimped pt capsules diffusion experiments done in the presence of h2o co2 fluid were run in a piston cylinder apparatus using a source of ground tio2 zrsio4 and sio2 with oxalic acid added to produce h2o co2 vapor and partially melt the solid source material yielding an assemblage of rutile zircon melt vapor nuclear reaction analysis nra with the resonant nuclear reaction 48ti p 49v was used to measure diffusion profiles for both sets of experiments the following arrhenius parameters were obtained for ti diffusion normal to cover the temperature range 1350 1550 c at 1 atm d ti 3 33 10 2 exp 754 56 kj mol 1 r t m 2 s 1 ti diffusivities were found to be similar for experiments run under fluid present conditions a fit to all of the data yields the arrhenius relation d 1 34 102 exp 741 46 kj mol 1 rt m2 s 1 these data suggest that zircon should be extremely retentive of ti chemical signatures indicating that the recently developed ti in zircon crystallization geothermometer watson e b harrison t m 2005 zircon thermometer reveals minimum melting conditions on earliest earth science 308 841 844 will be quite robust in preserving temperatures of zircon crystallization titanium diffuses somewhat faster in zircon than larger tetravalent cations u th and hf but considerably more slowly than pb the ree and oxygen hence ti crystallization temperatures may be retained under circumstances when radiometric ages or other types of geochemical information are lost

alkali diffusion in plagioclase feldspar tracer diffusion kinetics at 1 atm pressure under dry conditions using 6li 41k and 87rb in four plagioclase feldspars have been determined diffusion profiles were measured using an ion microprobe sims the arrhenius parameters and 2 uncertainties for li k and rb respectively in albite are pre exponential factor log do 3 8 1 0 3 4 1 4 and 5 8 3 8 in m2 s and activation energies 146 14 296 30 and 283 85 kj mol the diffusion rate of k in albite at 700 c and 100 mpa water pressure equals that at 1 atm dry suggesting that diffusion of k is not dependent on water fugacity between 0 004 and 100 mpa the k diffusion rate depends on plagioclase anorthite content and is approximately 20 times slower in labradorite than albite li diffusion rates in albite and anorthite are identical a linear relation between log d for the alkalis measured and their ionic radius squared permits an estimate of cs diffusion kinetics diffusion rates are isotropic or nearly so in albite

three dimensional gravity or magnetic constrained depth inversion with lateral and vertical variation of contrast depth mapping inversion of gravity or magnetic fields generally assumes that anomalies originate from a main density or magnetization contrast interface this particular inversion takes into account inhomogeneous density or magnetization distributions reflecting sediment compaction and basement heterogeneities above the interface the density can be approximated by an exponential function and below it an intrabasement contrast map can be used the inversion also integrates local depth constraints from wells or seismic data as well as general constraints set on the geometry and the contrast of the interface after field transformations spectral analysis and con straints help to define a starting model characterized mainly by the interface mean depth and the mean parameter contrast between the two media the depth adjustment is completed iteratively under constraints using a space domain formulation derived from the bouguer slab approximation the interface model effect is computed in the wavenumber domain a model data example shows the accuracy of the inversion and illustrates the role of the constraints in a field example of a basin area where constraints can be derived from numerous well data successive inversions of gravity data result in an isodepth map of the basement the compatibility of the map with local depth constraints from wells is obtained by taking into account density heterogeneities related to known lithologic variations in the basement

diffusion in mineral geochronometers present and absent abstract in solid state physics and materials science fick s law diffusion is a well established process in earth sciences laboratory experiments on garnet olivine and other anhydrous minerals do document the intra grain element concentration gradients that follow the functional form required by fick s law natural gradients in minerals have rarely been analyzed with the necessary spatial resolution reports of actual observations of diffusion profiles of element concentrations are rare in the literature and diffusion profiles of isotope ratios in minerals used for geochronology are absent an in depth re examination of recent and older literature suggests that isotope transport in minerals is instead often dominated by fluid mediated retrogression reactions imaging microtextures by cathodoluminescence or back scattered electron maps provides ubiquitous evidence of patchy or dendritic replacement structures which correspond to multiple growth stages in zircon monazite muscovite biotite k feldspar etc the u pb k ar and rb sr systems in these partly retrogressed minerals show isotopic inheritance that survived the retrograde reactions at least in part in close correspondence with the petrologic relicts depending on the relative rates of the petrological processes relevant for isotope transport geochronometers can be grouped in two classes class i thermochronometers are those for which the diffusivity of a given radiogenic isotope is faster than the rate of dissolution and or reprecipitation and class ii hygrochronometers are those for which aqueous dissolution reprecipitation is the faster process all of the abovementioned geochronometers for which patchy dendritic textures formed by diachronous mineral generations and isotopic inheritance were observed must be assigned to class ii class ii samples in petrologic equilibrium can but need not record purely thermal diffusion of daughter isotopes the isotope record of class ii minerals in petrologic disequilibrium being controlled by inheritance and retrogression reactions depends chiefly on the reaction promoting factors water activity and strain the dependence of class ii mineral ages on thermal diffusion is subordinate and never unique

ca diffusion in k feldspar abstract diffusion of ca has been characterized in natural k feldspar under dry 1 atm conditions using a 44ca tracer polished sections of feldspar were surrounded by source powders in pt capsules and annealed in air or with solid buffers to buffer at nno or iw one hydrous experiment was conducted in a piston cylinder device at 800 c and 1 gpa in all cases the source of diffusant was pre synthesized anorthitic powder doped with 44ca prepared sample capsules were held at run conditions for times ranging from a few hours to a few months at temperatures from 750 to 1050 c the 44ca distributions in the feldspars were profiled by rutherford backscattering spectrometry rbs the following arrhenius relation is obtained for ca diffusion in k feldspar for diffusion normal to 001 d 3 91 10 9 exp 276 41 kj mol rt m2 sec 1 diffusivities normal to 010 appear similar suggesting little anisotropy for ca diffusion diffusion coefficients for experiments buffered at nno and iw agree within experimental uncertainty with those for experiments run in air indicating little dependence of ca diffusion on oxygen fugacity under the investigated range of conditions on the basis of the single high pressure experiment neither pressure nor the presence of h2o appear to affect ca diffusion ca diffusion in k feldspar is slower than the diffusivities of the larger divalent cations sr and pb and also slower than ca diffusion in plagioclase which may be attributable to the large size mismatch of ca in the k feldspar structure ca diffusion is 7 8 orders of magnitude slower than ar diffusion in k feldspar indicating that k feldspars will be much more retentive of ca chemical signatures than of ar as an example 1 mm diameter feldspar grains will experience 50 ar loss in 1500 years at 500 c while ca loss of only 1 would require 100 million years at this temperature

mapping of crustal discontinuities by wavelength filtering of the gravity field1 a statistical technique based on the concept of a 1d energy density spectrum of the observed gravity field has been used to compute ensemble average depths to various horizons containing causative sources of random geometric shape size density etc the plot of the logarithm of the energy of the observed bouguer anomaly versus the angular frequency can be approximated over a certain frequency band by a linear segment whose slope is related to an average ensemble depth around which a random distribution of numerous anomalous sources exists suitable matched filters based on the computed values of intercepts and slopes of several linear segments approximating the spectrum have been used to deconvolve the gravity effects associated with the causative sources occurring around their respective mean depths the individual deconvolved gravity effects thus separated out have been modelled using the sin x x method by assuming a fluctuating interface between two formations the applicability of the present method has been assessed using two observed bouguer anomaly profiles one from ujjain to mahan and the other from jhansi to mandla where deep seismic sounding dss results are available the proposed geological crustal models along these two profiles exhibit reasonably good agreement with those obtained from dss results a geologically plausible model of the crust in a virgin region has been presented along a bouguer anomaly profile from jaipur to raipur the following main conclusions have been drawn from the present analysis 1 the depths to the moho and archaean basement interfaces fluctuate between 33 2 and 36 8 km and between 4 6 and 7 0 km respectively 2 the narmada son lineament nsl does not coincide exactly with the moho upwarp beneath it however this offset is greater in the eastern part of the nsl rather than in the western part 3 the development of the satpura horst structure is due to a rise in the moho interface in a compressional regime 4 the intrabasement feature depth from 5 to 12 km represents a hybrid massif possibly formed due to an admixture of sialic and simatic crust under a tensional regime in the ujjain mahan section

cation diffusion in feldspars feldspars are among the most common minerals in the earth s crust and are found in a variety of rock types diffusion in feldspars has been studied for well over half a century with rosenqvist s 1949 measurements of ra and pb diffusion among the earliest published works major efforts in measuring diffusion in feldspars primarily of the alkali elements were undertaken in the early 1970s with the work of bailey 1971 lin and yund 1972 petrovic 1972 foland 1974 giletti et al 1974 and kasper 1975 many of these early studies used bulk exchange techniques rather than direct depth profiling or employed methods of limited depth resolution such as serial sectioning these methods while state of the art for their time impose several limitations including a range of measurement restricted to relatively fast diffusivities and the difficulty of distinguishing the effects on measured chemical or isotopic compositions that may be a result of diffusional fast paths surface reaction and or other artifacts from those contributions due solely to volume diffusion development of high resolution depth profiling techniques such as sims and rbs have permitted measurement of much smaller diffusivities for a broader range of elements and reduced some of the uncertainties characteristic of bulk exchange methods feldspar diffusion data have been previously summarized in yund 1983 and smith and brown 1988 and were included in brady s 1995 compilation of diffusion data for silicate minerals since the publication of these works there have been numerous diffusion studies of feldspars encompassing a range of compositions in alkali feldspars and across the plagioclase series these have included measurements of diffusion of major elements na k ca ba oxygen and silicon as well as na k and caal nasi interdiffusion diffusion of noble gases and diffusion of minor and trace elements including fe mg sr

silicon self diffusion in single crystal natural quartz and feldspar abstract silicon diffusion was measured in natural quartz and anorthitic feldspar under dry low pressure 0 1 mpa conditions using a 30 si tracer sources of diffusant consisted of 30 si enriched silica powder for experiments on quartz and microcrystalline 30 si doped synthetic feldspar of composition comparable to the feldspar specimens distributions of 30 si were measured with rutherford backscattering spectrometry and nuclear reaction analysis using the reaction 30 si p 31 p the following arrhenius relations were obtained for anneals at 1 atm in air for quartz transport normal to c d qtz c 7 97 10 6 exp 447 31 kj mol 1 rt m 2 s 1 transport parallel to c d qtz c 6 40 10 6 exp 443 22 kj mol 1 rt m 2 s 1 for anorthitic feldspar an 93 d an 3 79 10 7 exp 465 50 kj mol 1 rt m 2 s 1 the few successful experiments on diffusion in plagioclase of more albitic compositions an 67 and an 23 reveal si diffusivities a few orders of magnitude faster than that in the anorthite the results for these feldspars bracket the determination of caal nasi interdiffusion under dry conditions by grove et al geochim cosmochim acta 48 1984 2113 2121 suggesting that the rate limiting process is indeed si diffusion si diffusion in quartz under more reducing conditions nno is slightly slower by about half an order of magnitude than diffusion in samples annealed in air this is consistent with observations made in studies of synthetic quartz bejina and jaoul phys earth planet inter 50 1988 240 250

lead diffusion in apatite and zircon using ion implantation and rutherford backscattering techniques abstract ion implantation was used to introduce pb into the minerals zircon and apatite diffusion profiles were obtained using rutherford backscattering and the results were fitted with a model to determine the diffusion coefficients this approach is both simple and useful in studying diffusion over a temperature range of geologic interest without inordinate annealing times results for apatite over the temperature range 600 900 c are in good agreement with earlier results obtained for higher temperatures watson et al 1985 and are described by the following arrhenius law d 1 27 10 4 cm 2 s 1 exp 54 6 1 7 kcl mol 1 rt this suggests that radiation damage induced by ion implantation has little effect on pb diffusion in this case due to rapid annealing of induced damage at low temperatures the activation energy stated above is somewhat smaller than that previously determined 70 kcal mol 1 reflecting the larger range in 1 t sampled by the present results closure temperatures calculated with these diffusion parameters are in good agreement with those inferred from geochronologic data diffusion coefficients for pb in zircon determined in this study are greater than those obtained from a single experimental measurement and estimates of pb diffusion based on geochronologic data and u pb zoning in natural zircons the differing results for zircon and apatite obtained in this study appear to be related to each mineral s ability to anneal the radiation damage induced by ion implantation

magma recharge contamination and residence times revealed by in situ laser ablation isotopic analysis of feldspar in volcanic rocks we illustrate a rapid and effective method for determining variations in 87sr 86sr across single plagioclase feldspar crystals using laser ablation interfaced to a multicollector inductively coupled plasma source mass spectrometer the speed of analysis proves to be a particular advantage permitting representative populations of crystals to be characterized or enabling reconnaissance analysis of rocks to test for mineral scale isotopic heterogeneity our results from magmatic crystals in lavas from el chichon volcano confirm trends previously obtained by the more time consuming microdrilling method for the first time with confidence the laser data allow us to associate abrupt changes in 87sr 86sr with distinct petrographic discontinuities such as dissolution surfaces in the crystal because the isotopic variations within crystals would be expected to equilibrate diffusively with time the width over which abrupt changes in 87sr 86sr occur can also be used to constrain timescales at which the crystal has been held at magmatic temperatures

diffusion and fluid interaction in itrongay pegmatite madagascar evidence from in situ 40ar 39ar dating of gem quality alkali feldspar and u pb dating of protogenetic apatite inclusions alkali feldspar 40ar 39ar and apatite upb geochronological studies have typically invoked two mechanisms to account for apparent loss of radiogenic 40ar and 206 208pb some studies have suggested that the radiogenic isotopes were lost by volume diffusion and used these dates to constrain temporal variations of rock temperatures others have argued that the radiogenic isotopes were lost due to interaction with fluids and related these dates to chemical alteration these two end member interpretations have fundamentally different implications for tectonic models derived from geochronological data and therefore it is important to reliably identify the principal mechanism for loss of radiogenic isotopes here we revisit the mechanisms of 40ar loss in the famous gem quality alkali feldspar from the itrongay pegmatite in madagascar previous studies have suggested that volume diffusion is the dominant mechanism of 40ar loss providing key evidence to support the use of 40ar 39ar dating of alkali feldspar for thermochronology we attempted to verify these results by obtaining time temperature paths from petrologically characterised cogenetic feldspar and apatite from the itrongay pegmatite and comparing them with each other however our results suggest that only a minor component in the variability of 40ar 39ar dates of itrongay feldspar is related to the diffusive loss of 40ar and that this loss was not compatible with the majority of previously proposed models which hinders quantitative interpretations the crystal studied here grew in five episodes related to the influx initially of co existing dense sio2 rich solution and co2 dominated fluid the first and supposedly the following two episodes and subsequently of h2o rich fluid supposedly the final two episodes much greater component in the variability of the acquired 40ar 39ar dates is interpreted to reflect the differences in the ages of these growth episodes which we estimate to span from 477 ma to 176 ma the first four episodes apatite inclusions in this crystal are interpreted to be xenocrysts derived from the country rocks of the itrongay pegmatite these yield older upb dates than the estimated age of their host feldspar and have apparently experienced diffusive loss of 206 207pb prior to entrapment our 40ar 39ar results indicate that there is a lack of unambiguous evidence for diffusive loss of 40ar from alkali feldspar that can be readily interpreted for thermochronological purposes however in situ 40ar 39ar dating of alkali feldspar appears to be a promising tool for tracking fluid flow events in the earth s crust whose applicability is not restricted to sedimentary rocks our upb results corroborate previous suggestions that upb dating of apatite can be used for thermochronology

gravity inversion of basement relief constrained by the knowledge of depth at isolated points we present an interpretation method for the gravity anomaly of an arbitrary interface separating two homogeneous media it consists essentially of a downward continuation of the observed anomaly and the division of the continued anomaly by a scale factor involving the density contrast between the media the knowledge of the interface depth at isolated points is used to estimate the depth d1 of the shallowest point of the interface the density contrast between the two media and the coefficients c1 and c2 of a first order polynomial representing a linear trend to be removed from data the solutions are stabilized by introducing a damping parameter in the computation of the downward continued anomaly by the equivalent layer method different from other interface mapping methods using gravity data the proposed method 1 takes into account the presence of an undesirable linear trend in data 2 requires just intervals for both rather than the knowledge of its true value and coefficients c1 and c2

mg diffusion in anorthite implications for the formation of early solar system planetesimals we have measured the self diffusion coefficients of mg ca and sr in anorthitic plagioclase in order to assess the potential of mg isotopic heterogeneities in early solar system planetesimals to survive thermal metamorphism diffusion couples were constructed from polished single crystals of natural anorthite and synthetic isotopically enriched anorthite glass couples were annealed at atmospheric pressure and 1200 1400 c and isotopic concentration profiles were measured with an ion microprobe the results show that mg diffusion in anorthite is surprisingly fast with d mg being over 2 orders of magnitude greater than d sr this indicates that the diffusion coefficient of mg in anorthite cannot be approximated with that for sr mg diffusion in the c direction is also slightly faster than in the b direction while ca and sr diffusion appear to be isotropic the results provide important constraints on the thermochronological history of anorthite bearing mineral assemblages that preserve radiogenic 26 mg excesses in a planetesimal heated by the decay of 26 al the temperature at any point depends on the planetesimal size time of formation thermal conductivity and depth within the planetesimal given sufficient heating 26 mg heterogeneities produced by the in situ decay of 26 al in ca al rich inclusions cais and chondrules will be erased by diffusive equilibration using the self diffusion coefficient for mg in anorthite measured in this study we show that the common occurrence of 26 mg excesses in these inclusions requires that they must be stored in small 15 km bodies or the outermost rims of larger bodies for the first 1 2 million years of the solar system s history for early formed bodies larger than 15 km most of the mass will have been heated sufficiently for any radiogenic 26 mg to have been diffusively homogenized in the mg rich planetary environment