Activation Volume For Diffusion Research Articles

Testing in-situ apatite Lu–Hf dating in polymetamorphic mafic rocks: a case study from Palaeoproterozoic southern Australia

In mafic systems where primary mineral assemblages have witnessed moderate- to high-temperature hydrous overprinting and deformation, little is known about the retentivity of the Lu–Hf isotopic system in apatite. This study presents apatite laser-ablation Lu–Hf and U–Pb geochronology, zircon geochronology, and detailed petrological information from polymetamorphic mafic intrusions located in the central-western Gawler Craton in southern Australia, which records an extensive tectonometamorphic history spanning the Neoarchaean to the Mesoproterozoic. Zircon records magmatic crystallisation ages of c. 2479–2467 Ma, coinciding with the onset of the c. 2475–2410 Ma granulite-facies Sleafordian Orogeny. The amphibole-dominant hydrous assemblages which extensively overprint the primary magmatic assemblages are hypothesised to post-date the Sleafordian Orogeny. The Lu–Hf and U–Pb isotopic systems in apatite are used to test this hypothesis, with both isotopic systems recording significantly younger ages correlating with the c. 1730–1690 Ma Kimban Orogeny and the c. 1590–1575 Ma Hiltaba magmatic event, respectively. While the early Mesoproterozoic apatite U–Pb ages are attributed to thermal re-equilibration, the older Lu–Hf ages are interpreted to reflect re-equilibration facilitated primarily by dissolution-reprecipitation, but also thermally activated volume diffusion. The mechanisms of Lu–Hf isotopic resetting are distinguished based on microscale textures and trace element abundances in apatite and the integration of apatite-amphibole textural relationships and temperatures determined from the Ti content in amphibole. More broadly, the results indicate that at low to moderate temperatures, apatite hosted in mafic rocks is susceptible to complete recrystallisation in rocks that have weak to moderate foliations. In contrast, at higher temperatures in the absence of strain, the Lu–Hf system in apatite is comparatively robust. Ultimately, the findings from this study advance our understanding of the complex role that both metamorphism and deformation play on the ability of mafic-hosted apatite to retain primary Lu–Hf isotopic signatures.

Diffusion of chromium in β-Ti under high pressure

Abstract It is shown that Arrhenius plots of diffusion coefficients of Cr in β-Ti can be represented under each pressure by two straight lines which are fitted in the temperature regions above and below about 1390 K. The activation enthalpies for high temperature are 167 kJ/mol under 0.1 MPa and 191 kJ/mol under 2.1 GPa, and those for low temperature are 147 kJ/mol under 0.1 MPa and 153 kJ/mol under 2.1 GPa. The ratios of activation volumes for impurity diffusion to the molar matrix volume are in the range of 0.38 to 0.45. When the phonon-softening model is applied, the activation enthalpy for the impurity diffusion in the absence of any phonon-induced lattice instabilities is 226 kJ/mol under 0.1 MPa and increases with pressure. Its pressure dependence indicates that the activation volume for the diffusion with no assistance from phonons is 66% of the molar matrix volume, and this result agrees with the activation volume for the diffusion in “normal” bcc metals.

Low‐temperature thermochronology of francolite: Insights into timing of Dead Sea Transform motion

AbstractCambrian siliciclastic sequences along the Dead Sea Transform (DST) margin in southern Israel and southern Jordan host both detrital fluorapatite [D‐apatite] and U‐rich authigenic carbonate‐fluorapatite (francolite) [A‐apatite]. D‐apatite and underlying Neoproterozoic basement apatite yield fission‐track (FT) data reflecting Palaeozoic–Mesozoic sedimentary cycles and epeirogenic events, and dispersed (U–Th–Sm)/He (AHe) ages. A‐apatite, which may partially or completely replace D‐apatite, yields an early Miocene FT age suggesting formation by fracturing, hydrothermal fluid ascent and intra‐strata recrystallisation, linked to early DST motion. The DST, separating the African and Arabian plates, records ~105 km of sinistral strike‐slip displacement, but became more transtensional post‐5 Ma. Helium diffusion measurements on A‐apatite are consistent with thermally activated volume diffusion, indicating Tc ~52 to 56 ± 10°C (cooling rate 10°C/Ma). A‐apatite AHe data record Pliocene cooling (~35 to 40°C) during the transtensional phase of movement. This suggests that timing of important milestones in DST motion can be discerned using A‐apatite low‐temperature thermochronology data alone.

Diffusion of helium in FCT zircon

To gain a better quantitative understanding of zircon (U-Th)/He ages and evaluate the applicability of zircon (U-Th)/ He dating, the diffusion characteristics, He diffusion kinetics, helium partial retention zone (HePRZ), closure temperature, and (U-Th)/He ages were investigated using high-precision laboratory step heating experiments based on the thermally activated diffusion process. The ln(D/a2) in Fish Canyon Tuff (FCT) zircons determined from laboratory step heating experiments was negatively correlated with reciprocal temperature, as expected for thermally activated volume diffusion. The zircon activation energies ranged from 144 to 184 kJ mol−1 with a mean of 169±12 kJ mol−1. The closure temperatures ranged from 144 to 216°C (a cooling rate of 10°C Ma−1 and an effective grain radius of 38–60 μm) with an average of 176±18°C. The calculated closure temperature increased with increasing cooling rate, yielding an average zircon He closure temperature of ~136°C at a slow cooling rate of 0.1°C Ma−1, whereas the closure value was ~199°C at a cooling rate of 100°C Ma−1. The closure temperature increased with the equivalent spherical radius assuming a constant cooling rate. The He ages from FCT zircons were negligibly affected by grain size because of the rapid cooling. He preserved in the zircon was sensitive to temperature and holding time, and the temperature range for zircon HePRZ gradually decreased with increasing holding time. The (U-Th)/He ages from 26 FCT zircons yielded an algorithmic mean of 28.3±0.3 Ma (S.E.) and a geometric mean of 28.4±0.3 Ma (S.E.), consistent with the ages of 28.4±1.9 Ma reported by other laboratories. The FCT zircons were characterized by rapid cooling, young (U-Th)/He ages with good reproducibility, and low alpha doses. Weak correlations between the He ages and effective uranium (eU) concentrations from the FCT zircons indicated radiation damage did not significantly affect He diffusivity.

Effect of pressure on closure temperature of a trace element in cooling petrological systems

Closure temperature is important to many diffusion-related problems involving cooling. The classic model of Dodson and its modifications for cooling petrological systems are formulated at constant pressure. Many petrologic processes involve changes in both temperature and pressure. The effect of changing pressure on diffusional loss in cooling petrological systems has not been considered in Dodson’s model. During upwelling, the decompression rate is related to the cooling rate through the slope of the upwelling path. Simple analytical expressions for the average or mean closure temperature and closure pressure in cooling-upwelling mono-mineralic and bi-mineralic systems are obtained by noting that both temperature and pressure decrease as a function of time along the upwelling path. These pressure-adjusted equations are nearly identical to closure temperature equations for isobaric cases if one replaces the activation energy and pre-exponential factor for diffusion in the isobaric formulations by the path-dependent activation energy and pre-exponential factor. The latter also depend on the slope of the upwelling path. The competing effects between pressure and temperature on diffusion during upwelling result in reductions in the effective activation enthalpy for diffusion and exchange enthalpy for partitioning, which in turn leads to systematic deviations in closure temperatures from cases of constant pressure. For systems with large activation volume for diffusion, it may be possible to deduce upwelling path and upwelling rate from closure temperatures and closure pressures of selected elements. Examples of closure temperature and closure pressure for REE diffusion in garnet and clinopyroxene and in garnet–clinopyroxene aggregates are presented and discussed in the context of the minor’s rule and the REE-in-garnet–clinopyroxene thermobarometer. Closure temperatures for middle-to-heavy REE in garnet–clinopyroxene aggregates are controlled primarily by diffusion in clinopyroxene unless the modal abundance of garnet is very small or the effective grain size of clinopyroxene is considerably smaller than that of garnet.

Diffusion in Quasi-Crystalline Alloys

In this Chapter, we review knowledge about diffusion in quasi-crystalline alloys (quasicrystals). In Section 1 we first remind the reader of some major aspects of the quasi-crystalline state and in Section 2 we introduce phase diagrams with quasi-crystalline phases, for which detailed diffusion studies are available. We mention in Section 3 the more common experimental methods for diffusion studies. The diffusive motion of atoms in quasi-crystalline alloys can be studied by the same techniques used for crystalline metallic alloys and intermetallics – measurements of radiotracer diffusion and diffusion of stable isotopes and solute atoms by SIMS profiling. The best-studied quasi-crystalline alloys are icosahedral AlPdMn, icosahedral ZnMgRE (RE = rare earth metal), and decagonal AlNiCo. The major diffusion results for these quasicrystals are reviewed in Sections 4, 5, and 6. Section 7 is devoted to the pressure dependence of diffusion in quasicrystals and to a comparison of the activation volumes with those of crystalline metals. Positron annihilation studies are also mentioned, which together with activation volumes for diffusion strongly favour a vacancy mechanism in quasicrystals. The major results and conclusions are summarized in Section 8.

Variable helium diffusion characteristics in fluorite

Precise analysis of the diffusion characteristics of helium in fluorite is crucial for establishing the new fluorite (U–Th–Sm)/He thermochronometer (FHe), which potentially provides a powerful tool for dating ore deposits unsuitable for the application of conventional geochronometers. Incremental helium outgassing experiments performed on fluorites derived from a spectrum of geological environments suggest a thermally activated volume diffusion mechanism. The diffusion behaviour is highly variable and the parameters range between logD0/a2=0.30±0.27–7.27±0.46s−1 and Ea=96±3.5–182±3.8kJ/mol. Despite the fact that the CaF2 content of natural fluorites in most cases exceeds 99 weight percent, the closure temperature (Tc) of the fluorite (U–Th–Sm)/He thermochronometer as calculated from these diffusion parameters varies between 46±14°C and 169±9°C, considering a 125μm fragment size. Here we establish that minor substitutions of calcium by rare earth elements and yttrium (REE+Y) and related charge compensation by sodium, fluorine, oxygen and/or vacancies in the fluorite crystal lattice have a significant impact on the diffusivity of helium in the mineral. With increasing REE+Y concentrations F vacancies are reduced and key diffusion pathways are narrowed. Consequently, a higher closure temperature is to be expected. An empirical case study confirms this variability: two fluorite samples from the same deposit (Horni Krupka, Czech Republic) with ca. 170°C and ca. 43°C Tc yield highly different (U–Th–Sm)/He ages of 290±10Ma and 79±10Ma, respectively. Accordingly, the fluorite sample with the high Tc could have quantitatively retained helium since the formation of the fluorite-bearing ores in the Permian, despite subsequent Mesozoic burial and associated regional hydrothermal heating. In contrast, the fluorite with the low Tc yields a Late Cretaceous age close to the apatite fission track (AFT) and apatite (U–Th)/He ages (AHe) from the same locality. Remarkably, thermal modelling of FHe yields comparable results to the well-established modelling based on AFT and AHe.

Thermochronology of extensional orogenic collapse in the deep crust of Zealandia

The exhumed Fiordland sector of Zealandia offers a deep-crustal view into the life cycle of a Cordilleran-type orogen from final magmatic construction to extensional orogenic collapse. We integrate U-Pb thermochronologic data from metamorphic zircon and titanite with structural observations from >2000 km 2 of central Fiordland to document the tempo and thermal evolution of the lower crust during the tectonic transition from arc construction and crustal thickening to crustal thinning and extensional collapse. Data reveal that garnet granulite facies metamorphism and partial melting in the lower crust partially overlapped with crustal thickening and batholith construction during emplacement of the Western Fiordland Orthogneiss (WFO) from 118 to 115 Ma. Metamorphic zircons in metasedimentary rocks yield 206 Pb/ 238 U (sensitive high-resolution ion microprobe–reverse geometry) dates of 116.3–112.0 Ma. Titanite laser ablation split stream inductively coupled plasma–mass spectrometry chronology from the same rocks yielded complex results, with relict Paleozoic 206 Pb/ 238 U dates preserved at the margins of the WFO. Within extensional shear zones that developed in the thermal aureole of the WFO, titanite dates range from 116.2 to 107.6 Ma and have zirconium-in-titanite temperatures of ∼900–750 °C. A minor population of metamorphic zircon rims and titanites in the Doubtful Sound region yield younger dates of 105.6–102.3 Ma with corresponding temperatures of 740–730 °C. Many samples record Cretaceous overdispersed dates with 5–10 m.y. ranges. Core-rim traverses and grain maps show complex chemical and temporal variations that cannot easily be attributed to thermally activated volume diffusion or simple core-rim crystallization. We interpret these Cretaceous titanites not as cooling ages, but rather as recording protracted growth and/or crystallization or recrystallization in response to fluid flow, deformation, and/or metamorphic reactions during the transition from garnet granulite to upper amphibolite facies metamorphism. We propose a thermotectonic model that integrates our results with structural observations. Our data reveal a clear tectonic break at 108–106 Ma that marks a change in processes deep within the arc. Prior to this break, arc construction processes dominated and involved (1) emplacement of mafic to intermediate magmas of the Malaspina and Misty plutons from 118 to 115 Ma, (2) contractional deformation at the roof of the Misty pluton in the Caswell Sound fold-thrust belt from 117 to 113 Ma, and (3) eclogite to garnet granulite facies metamorphism and partial melting over >8 m.y. from 116 to 108 Ma. These processes were accompanied by complex patterns of lower crustal flow involving both horizontal and vertical displacements. After this interval, extensional orogenic collapse initiated along upper amphibolite facies shear zones in the Doubtful Sound shear zone at 108–106 Ma. Zircon and titanite growth and/or crystallization or recrystallization at this time clearly link upper amphibolite facies metamorphism to mylonitic fabrics in shear zones. Our observations are significant in that they reveal the persistence of a hot and weak lower crust for ≥15 m.y. following arc magmatism in central Fiordland. We propose that the existence of a thermally weakened lower crust within the Median Batholith was a key factor in controlling the transition from crustal thickening to crustal thinning and extensional orogenic collapse of the Zealandia Cordillera.

Accounting for long alpha-particle stopping distances in (U–Th–Sm)/He geochronology: 3D modeling of diffusion, zoning, implantation, and abrasion

In apatite (U–Th)/He thermochronology the helium distribution in a crystal is a function of the simultaneous processes of radiogenic production, thermally activated volume diffusion and the ejection of He caused by long alpha stopping distances. These processes are further complicated by zonation of U, Th and Sm within the grain and implantation of 4He from neighboring U–Th–Sm bearing minerals. We use a refined version of the 3D Monte Carlo diffusion code of Gautheron and Tassan-Got (2010) to simulate the interplay between ejection and diffusion with or without zonation, ejection and abrasion for a suite of thermal histories. We examine the phenomenon of over-correction produced by the alpha ejection correction parameter (FT or FZAC for homogeneous or heterogeneous eU repartition) by comparing the raw (measured) and FT- or FZAC-corrected ages for a number of scenarios to the ejection-free age (AEF), which we define as the age that would be obtained if alpha ejection had not occurred, or equivalently if the stopping distance was zero. We show that the use of FT- or FZAC-corrected ages generally reproduces the ejection-free age to within typical (U–Th)/He uncertainties (±8%), even for zoned apatites. We then quantify the effect of alpha implantation on (U–Th)/He ages, showing that implantation from a single external source with modest relative U or Th enrichment can generate as much as 50% excess He. For more extreme cases where an apatite is surrounded by multiple external sources the measured age can be >300% of that determined from an isolated crystal. While abrasion of the outer 20–25μm can significantly reduce the age dispersion for rapidly cooled samples, slowly cooled samples can still retain 10–30% excess He. The removal of the rim of the crystal reduces the thermal information from very low temperatures (<40°C), and introduces additional technical complications and biases, and should therefore be used with caution. Overall we demonstrate that although zonation and implantation may not be routinely determined, we now have the 3D modeling capability to fully investigate and constrain the causes of age dispersion within a sample, leading to significant improvement in our ability to interpret (U–Th)/He data.

Variation of illite/muscovite 40Ar/39Ar age spectra during progressive low-grade metamorphism: an example from the US Cordillera

40Ar/39Ar step-heating data were collected from micron to submicron grain-sizes of correlative illite- and muscovite-rich Cambrian pelitic rocks from the western United States that range in metamorphic grade from the shallow diagenetic zone (zeolite facies) to the epizone (greenschist facies). With increasing metamorphic grade, maximum ages from 40Ar/39Ar release spectra decrease, as do total gas ages and retention ages. Previous studies have explained similar results as arising dominantly or entirely from the dissolution of detrital muscovite and precipitation/recrystallization of neo-formed illite. While recognizing the importance of these processes in evaluating our results, we suggest that the inverse correlation between apparent age and metamorphic grade is controlled, primarily, by thermally activated volume diffusion, analogous to the decrease in apparent ages with depth observed for many thermochronometers in borehole experiments. Our results suggest that complete resetting of the illite/muscovite Ar thermochronometer occurs between the high anchizone and epizone, or at roughly 300 °C. This empirical result is in agreement with previous calculations based on muscovite diffusion parameters, which indicate that muscovite grains with radii of 0.05–2 μm should have closure temperatures between 250 and 350 °C. At high anchizone conditions, we observe a reversal in the age/grain-size relationship (the finest grain-size produces the oldest apparent age), which may mark the stage in prograde subgreenschist facies metamorphism of pelitic rocks at which neo-formed illite/muscovite crystallites typically surpass the size of detrital muscovite grains. It is also approximately the stage at which neo-formed illite/muscovite crystallites develop sufficient Ar retentivity to produce geologically meaningful 40Ar/39Ar ages. Results from our sampling transect of Cambrian strata establish a framework for interpreting illite/muscovite 40Ar/39Ar age spectra at different stages of low-grade metamorphism and also illuminate the transformation of illite to muscovite. At Frenchman Mtn., NV, where the Cambrian Bright Angel Formation is at zeolite facies conditions, illite/muscovite 40Ar/39Ar data suggest a detrital muscovite component with an apparent age ≥967 Ma. The correlative Carrara Fm. is at anchizone conditions in the Panamint and Resting Spring Ranges of eastern California, and in these locations, illite/muscovite 40Ar/39Ar data suggest an early Permian episode of subgreenschist facies metamorphism. The same type of data from equivalent strata at epizone conditions (greenschist facies) in the footwall of the Bullfrog/Fluorspar Canyon detachment in southern Nevada reveals a period of slow-to-moderate Late Cretaceous cooling.

Noble gas diffusion mechanism in lunar soil simulant grains: Results from 4He+ implantation and extraction experiments

Experiments on ion implantation were performed in order to better characterize diffusion of noble gases in lunar soil. 4He+ at 50 keV with 5×1016 ions/cm2 was implanted into lunar simulants and crystal ilmenite. Helium in the samples was released by stepwise heating experiments. Based on the data, we calculated the helium diffusion coefficient and activation energy. Lunar simulants display similar 4He release patterns in curve shape as lunar soil, but release temperatures are a little lower. This is probably a consequence of long-term diffusion after implantation in lunar soil grains. Variation of activation energy was identified in the Arrhenius plots of lunar simulants and Panzhihua (攀枝花) ilmenite. We conclude that noble gas release in lunar soil cannot be described as simple thermally activated volume diffusion. Variation of diffusion parameters could be attributed to physical transformation during high temperature. Radiation damage probably impedes helium diffusion. However, bubble radius growth during heating does not correlate with activation energy variation. Activation energy of Panzhihua ilmenite is 57.935 kJ/mol. The experimental results confirm that ilmenite is more retentive for noble gas than other lunar materials.

A computational study of ionic vacancies and diffusion in MgSiO 3 perovskite and post-perovskite

We have performed first-principles simulations within density functional theory to investigate the effects of pressure on the formation of defects (ionic vacancies) and ionic diffusion in the perovskite (pv) and post-perovskite (ppv) phases of MgSiO 3. Our results show that the predicted formation enthalpies of three Schottky (MgO, SiO 2 and MgSiO 3) defects are similar between the two phases at high pressures (100 to 150 GPa) with MgO Schottky defect being the most favorable. However, the calculated activation enthalpies and activation volumes of diffusion are shown to differ substantially between them. In particular, the activation enthalpies for Mg and Si diffusion in ppv are smaller than the corresponding values for pv, for example, by factors of 2.2 and 3.4, respectively, at 120 GPa, whereas the O migration enthalpy of ppv is only slightly larger than that of pv. The easy migration paths of the cations in ppv are shown to take place along the 〈100〉 direction in which Si–O octahedra share the edges. Visualization of the simulation data reveals that the vacancy defects and migrating ions induce substantial distortions in the atomic and electronic structures around them. It is suggested that diffusion is equally easy for all three species in ppv and is likely to occur through extrinsic processes near the bottom of the lower mantle.

Structure modification of rapidly solidified Al–11 wt% Si alloy by the addition of 2 wt% Fe

An investigation of the structure formation of as-cast Al–11 wt% Si (AlSi11) and Al–11 wt% Si–2 wt% Fe (AlSi11Fe2) rapidly solidified (RS) ribbons is performed. Ribbon samples are examined in detail using Auger electron spectroscopy (AES) and transmission electron microscopy (TEM). A nanoscale thickness layer of Si-precipitations, at both Al-grains boundary and oxide/Al-matrix interface, is found to be characteristic for “pure” AlSi11 ribbons. For Fe-doped ribbons, this layer comprises Fe-containing phase also, which appears to possess amorphous nature and is situated between the Si-grains and Al-matrix. A possible mechanism of altering the thermally activated volume diffusion of elements, due to the effect of Fe on the structure modification, is speculated based on the obtained results.

Diffusion of Co in Zr＿46.75Ti＿8.25Cu＿7.5Ni＿10Be＿27.5 bulk metallic glass in supercooled liquid region under high pressure

Diffusion of Co in Zr＿46.75Ti＿8.25Cu＿7.5Ni＿10Be＿27.5 bulk metallic glass under high pressure is investigated in supercooled liquid regio n by ion implantation combined with secondary ion mass spectroscopy.Before impla ntation of Co atoms,the amorphous samples were annealed and relaxed in supercool ed liquid region.Diffusion coefficients of Co at 603K in the relaxed samples are found to increase with increasing pressure.And the activation volume for diffus ion is obtained to be -1.236Ω,where Ω is the mean atomic volume of the alloy.The result shows that diffusion of Co in this case is in an interstitial way.

He diffusion and (U–Th)/He thermochronometry of zircon: initial results from Fish Canyon Tuff and Gold Butte

To evaluate the potential of (U–Th)/He geochronometry and thermochronometry of zircon, we measured He diffusion characteristics in zircons from a range of quickly and slowly cooled samples, (U–Th)/He ages of zircons from the quickly cooled Fish Canyon Tuff, and age-paleodepth relationships for samples from 15 to 18 km thick crustal section of the Gold Butte block, Nevada. (U–Th)/He ages of zircons from the Fish Canyon Tuff are consistent with accepted ages for this tuff, indicating that the method can provide accurate ages for quickly cooled samples. Temperature-dependent He release from zircon is not consistent with thermally activated volume diffusion from a single domain. Instead, in most samples apparent He diffusivity decreases and activation energy ( E a) increases as cycled step-heating experiments proceed. This pattern may indicate a range of diffusion domains with distinct sizes and possibly other characteristics. Alternatively, it may be the result of ongoing annealing of radiation damage during the experiment. From these data, we tentatively suggest that the minimum E a for He diffusion in zircon is about 44 kcal/mol, and the minimum closure temperature ( T c, for a cooling rate of 10 °C/myr) is about 190 °C. Age–paleodepth relationships from the Gold Butte block suggest that the base of the zircon He partial retention zone is at pre-exhumation depths of about 9.5–11 km. Together with constraints from other thermochronometers and a geothermal gradient derived from them in this location, the age–depth profile suggests a He T c of about 200 °C for zircon, in reasonable agreement with our interpretation of the laboratory measurements. A major unresolved question is how and when radiation damage effects become significant for He loss from this mineral.

Helium diffusion and (U–Th)/He thermochronometry of titanite

We have explored the diffusivity characteristics of radiogenic He in titanite (sphene) and have developed analytical techniques for (U–Th)/He dating of this mineral. Results of incremental He outgassing experiments performed on titanites from a variety of geological environments suggest a thermally activated volume diffusion mechanism with an activation energy of 44.6 ± 3.4 (2σ) kcal/mol and a frequency factor of ∼60 cm 2/s. Diffusivity is highly linearly correlated with the inverse square of the grain size, indicating that the He diffusion domain in titanite is the crystal itself. For typical titanite grains of 200- to 800-μm minimum dimension, the He closure temperature is in the range 191 to 218°C (for a cooling rate of 10°C/Myr). There is no indication in the titanites we studied that radiation damage plays a major role in He diffusion. (U–Th)/He ages of titanites from quickly cooled rocks yield ages (with ∼5–8% 1 σ reproducibility) that are concordant with known ages, and (U-Th)/He ages of titanites from slowly cooled rocks are consistent with independently established cooling paths, supporting the closure temperature estimates. These experiments suggest that titanite (U–Th)/He ages may be useful for constraining cooling histories at temperatures near the lower limit of those accessed by feldspar 40Ar/ 39Ar dating but higher than apatite fission track or (U-Th)/He dating.

Temperature dependence of diffusion and structural defects in a molecular-dynamics model of amorphous Ni 81B 19

The temperature dependence of atomic diffusion and the distribution of interatomic voids in Ni 81B 19 is studied by molecular-dynamics (MD) simulations, at temperatures less than and greater than the glass transition temperature. The voids can be classified according to the number of surrounding atoms and, for each class, the void volumes are log-normally distributed. This type of distribution is also observed in crystalline fcc Ni and Ni 3B models at room temperature. With increasing temperature, the number of larger voids increases, because of the thermal expansion and as a result of the coalescence of smaller voids. Voids with a volume larger than the activation volume for diffusion are considered to be defects. The defect concentration at room temperature is ≈10 −5 and shows an Arrhenian temperature dependence. This classification of the interatomic empty space leads to a plausible identification of sites in the structure that act as diffusion catalysts.

Self-Diffusion in Bulk Metallic Glasses

AbstractWe have studied self-diffusion in the bulk metallic glasses Zr46.75Ti8.25Cu7.5Ni10Be27.5 and Zr65Cu17.5Ni10A17.5 by means of the radiotracer method. Diffusion of 63Ni has been investigated as a function of temperature in both alloys and also as a function of hydrostatic pressure in Zr46.75Ti8.25Cu7.5Ni10Be27.5. With the isotope 95Zr diffusion studies of the major component Zr were performed in Zr46.75Ti8.25Cu7.5Ni10Be27.5. The diffusivity of 95Zr is much smaller than that of 63Ni. The temperature dependence of 63Ni self-diffusion into Zr46.75Ti8.25Cu7.5Ni10Be27.5 and into Zr65Cu17.5Ni10A17.5 cannot be described by a single set of Arrhenius parameters, breaks in the Arrhenius curves are observed. We attribute the non-linear Arrhenius behaviour to the transition from the glassy to the supercooled liquid state. For the first time activation volumes of diffusion in a supercooled melt have been determined. From the pressure dependence of 63Ni diffusion in Zr46.75Ti8.25Cu7.5 Ni10Be27.5 we get activation volumes around one mean atomic volume favouring a diffusion mechanism via vacancy-like defects.

High-pressure proton NMR study of lateral self-diffusion of phosphatidylcholines in sonicated unilamellar vesicles

Effects of pressure on the lateral diffusion of phospholipid molecules in sonicated pure 1,2-dipalmitoylphosphatidyl-choline (DPPC) and 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) vesicles (15 wt%) in D 2O were examined using the high-pressure proton NMR rotating frame spin-lattice relaxation time ( T 1 π ) method. Proton T 1 ϱ were measured at pressures from 1 bar to 5000 bar and at temperatures of 50°C to 70°C for DPPC and 5°C to 35°C for POPC. The T 1 ϱ −1 values were plotted as a function of the square root of the spin-locking field angular frequency ( ω 1 1 2 ) and the lateral diffusion coefficient ( D) calculated from the slope. Pressure effects on lateral diffusion were observed in the liquid-crystalline (LC) phase. The lateral diffusion coefficient exhibited sharp decreases in response to the various pressure-induced phase transitions encountered. However pressure had little, if any, effect on lateral diffusion in the pressure-induced gel I (GI) phase and pressure-induced interdigitated gel (Gi) phase. The activation volumes for diffusion were calculated from the slopes from plots of ln D versus pressure for both DPPC (37 ml/mol at 50°C, 34 ml/mol at 60°C and 25 ml/mol at 70°C) and POPC (16 ml/mol at 5°C, 9 ml/mol at 20°C and 6 ml/mol at 35°C) sonicated vesicles in the LC phase. The activation energy for diffusion ( E a) was calculated using the slopes from plots of ln D versus the inverse of the temperature ( 1 T ) for both DPPC and POPC in the LC phase (3.5 kcal/mol and 3.9 kcal/mol, respectively) and for both DPPC and POPC in the GI phase (6.0 kcal/mol and 4.4 kcal/mol, respectively). From the lateral diffusion coefficient and line width data pressure-temperature phase diagrams for sonicated pure DPPC and POPC vesicles were constructed. The values of the temperature to pressure equivalence of DPPC (d T m/d P) were estimated to be 22.1°C/kbar for the LC to GI phase transition and 28.6°C/kbar for the GI to Gi phase transition. The value of the temperature to pressure equivalence of POPC for the LC to GI phase transition was estimated to be 19.0°C/kbar.

Pressure dependence of cobalt diffusion in amorphous Fe 39Ni 40B 21

The pressure dependence of cobalt diffusion has been measured in structurally relaxed, melt-spun metallic Fe 39Ni 40B 21 glass. The samples were characterized by X-ray diffraction, electron-microprobe analysis and differential scanning calorimetry. The radio-tracer technique in conjunction with ion-beam sputtering for serial sectioning was employed. Within error margins, no significant pressure dependence of 57Co diffusion was observed. The activation volume of diffusion V act = kT ∂ln D/∂p⊥ T = (−0.1 ± 0.1) Ω , withΩ being the average volume of an atom of the alloy. These results indicate that diffusion of cobalt in FeNiB in the relaxed state is not mediated through quasi-vacancies in thermal equilibrium.