Statistical modelling of thermal annealing of fission tracks in apatite

We develop an improved methodology for modelling the relationship between mean track length, temperature, and time in fission track annealing experiments. We consider “fanning Arrhenius” models, in which contours of constant mean length on an Arrhenius plot are straight lines meeting at a common point. Features of our approach are explicit use of subject matter knowledge, treating mean length as the response variable, modelling of the mean-variance relationship with two components of variance, improved modelling of the control sample, and using information from experiments in which no tracks are seen.

This approach overcomes several weaknesses in previous models and provides a robust six parameter model that is widely applicable. Estimation is via direct maximum likelihood which can be implemented using a standard numerical optimisation package. Because the model is highly nonlinear, some reparameterisations are needed to achieve stable estimation and calculation of precisions. Experience suggests that precisions are more convincingly estimated from profile log-likelihood functions than from the information matrix.

We apply our method to the B-5 and Sr fluorapatite data of Crowley et al. (1991) and obtain well-fitting models in both cases. For the B-5 fluorapatite, our model exhibits less fanning than that of Crowley et al. (1991), although fitted mean values above 12 μm are fairly similar. However, predictions can be different, particularly for heavy annealing at geological time scales, where our model is less retentive. In addition, the refined error structure of our model results in tighter prediction errors, and has components of error that are easier to verify or modify. For the Sr fluorapatite, our fitted model for mean lengths does not differ greatly from that of Crowley et al. (1991), but our error structure is quite different.     

Thermal annealing characteristics of fission tracks in natural zircons of different ages

Fission track (FT) thermochronometry using zircon has widely been applied to the resolution of a variety of geologic problems, for which the understanding of FT annealing behaviour is essential. Thermal annealing experiments were conducted on FTs in natural zircons having different ages (ranging from ~0.6 to ~70 Ma) and radiation damage levels. We measured horizontal confined track lengths on nine zircon concentrates separated from rapidly cooled volcanic rocks, after 1 hr annealing at 400–700°C. As the annealing temperature increases, the observed tracks show a consistent and systematic length reduction in all samples, and the mean track lengths are hardly distinguishable among the nine samples for the same annealing step. Our results suggest that the thermal annealing characteristics at laboratory time‐scale are concordant among the zircons, regardless of their ages, and that identical annealing kinetics may work for Late Mesozoic to Cenozoic zircons.     

Annealing studies of fission tracks in allanite

The annealing characteristics of fission tracks in allanite have been studied. All the tracks in the mineral fade at 720° C for one hour heating. The activation energy of allanite ranges from 1.4 to 3.4 eV.     

A natural long‐term annealing experiment for the zircon fission track system in the Songpan‐Garzê flysch,China

Application of the zircon fission track (FT) method to derive reliable cooling histories requires that rocks have undergone temperatures sufficient to reach full resetting prior to cooling. Zircons commonly show significant variation in accumulated radiation damage and therefore FT annealing behaviour. Twenty‐eight samples of mainly anchizonal to lowermost greenschist facies Triassic sandstones from the Songpan‐Garzê flysch, China, were evaluated for their FT annealing status. Literature data suggest a heating period in the range of 100 myr duration. Our results define a temperature range for partial FT annealing of 270–350°C (based on illite crystallinity data), higher than the proposed range for radiation‐damaged zircons. We suggest that the long residence at high temperature has led to annealing of relevant parts of radiation damage along with FT annealing, so that even for long durations of FT annealing, full resetting requires temperatures in the range of greenschist facies conditions typical for zero‐damage zircons.     

Survey of garnets for fossil fission tracks

Andradites and spessartines contain enough uranium to make these minerals interesting for fission track dating. Almandines and pyropes usually are not favourable.     

Etching of fission tracks in monazite: An experimental study

This study reports a range of etching and annealing experiments to establish the optimum conditions for the etching of fission tracks in monazite. The previously reported concentrated (12 M) HCl etchant at 90°C was found to cause grain loss from epoxy mounts and high degrees of grain corrosion, as did much longer etching times at lower temperatures. Using implanted ²⁵²Cf semi‐tracks, a series of experiments were performed on internal prismatic faces of monazite‐(Ce) crystals from the Palaeozoic Harcourt Granodiorite (Victoria, Australia) using an alternative 6 M HCl etchant, also at 90°C. Step‐etch results show optimal etching at 60–90 min. Further, an isothermal annealing experiment illustrated that the degree of annealing that can be expected during etching at 90°C under laboratory time scales is negligible. The etching rate between grains is not uniform, with a correlation demonstrated between over‐etched grains and high U and Th concentrations.     

A Bayesian approach to calibrating apatite fission track annealing models for laboratory and geological timescales

We present a new approach for modelling annealing of fission tracks in apatite, aiming to address various problems with existing models. We cast the model in a fully Bayesian context, which allows us explicitly to deal with data and parameter uncertainties and correlations, and also to deal with the predictive uncertainties. We focus on a well-known annealing algorithm [Laslett, G.M., Green, P.F., Duddy, I.R., Gleadow. A.J.W., 1987. Thermal annealing of fission tracks in apatite. 2. A quantitative-analysis. Chem. Geol., 65 (1), 1-13], and build a hierachical Bayesian model to incorporate both laboratory and geological timescale data as direct constraints. Relative to the original model calibration, we find a better (in terms of likelihood) model conditioned just on the reported laboratory data. We then include the uncertainty on the temperatures recorded during the laboratory annealing experiments. We again find a better model, but the predictive uncertainty when extrapolated to geological timescales is increased due to the uncertainty on the laboratory temperatures. Finally, we explictly include a data set [Vrolijk, P., Donelick, R.A., Quenq, J., Cloos. M., 1992. Testing models of fission track annealing in apatite in a simple thermal setting: site 800, leg 129. In: Larson, R., Lancelet, Y. (Eds.), Proceedings of the Ocean Drilling Program, Scientific Results, vol. 129, pp. 169-176] which provides low-temperature geological timescale constraints for the model calibration. When combined with the laboratory data, we find a model which satisfies both the low-temperature and high-temperature geological timescale benchmarks, although the fit to the original laboratory data is degraded. However, when extrapolated to geological timescales, this combined model significantly reduces the well-known rapid recent cooling artifact found in many published thermal models for geological samples.     

A comparative study of the modelling of cement hydration and cement-rock laboratory experiments

The use of cement and concrete as fracture grouting or as tunnel seals in a geological disposal facility for radioactive wastes creates potential issues concerning chemical reactivity. From a long-term safety perspective, it is desirable to be able model these interactions and changes quantitatively. The ‘Long-term Cement Studies’ (LCS) project was formulated with an emphasis on in situ field experiments with more realistic boundary conditions and longer time scales compared with former experiments. As part of the project programme, a modelling inter-comparison has been conducted, involving the modelling of two experiments describing cement hydration on one hand and cement-rock reaction on the other, with teams representing the NDA (UK), Posiva (Finland), and JAEA (Japan).This modelling exercise showed that the dominant reaction pathways in the two experiments are fairly well understood and are consistent between the different modelling teams, although significant differences existed amongst the precise parameterisation (e.g. reactive surface areas, dependences of rate upon pH, types of secondary minerals), and in some instances, processes (e.g. partition of alkali elements between solids and liquid during cement hydration; kinetic models of cement hydration). It was not conclusive if certain processes such as surface complexation (preferred by some modellers, but not by others) played a role in the cement-rock experiment or not. These processes appear to be more relevant at early times in the experiment and the evolution at longer timescales was not affected. The observed permeability profile with time could not be matched. The fact that no secondary minerals could be observed and that the precipitated mass calculated during the simulations is minor might suggest that the permeability reduction does not have a chemical origin, although a small amount of precipitates at pore throats could have a large impact on permeability.The modelling exercises showed that there is an interest in keeping the numerical models as simple as possible and trying to obtain a reasonable fit with a minimum of processes, minerals and parameters. However, up-scaling processes and model parameterisation to the timescales appropriate to repository safety assessment are of considerable concern. Future modelling exercises of this type should focus on a suitable natural or industrial analogue that might aid assessing mineral-fluid reactions at these longer timescales.     

Improved zircon fission-track annealing model based on reevaluation of annealing data

The thermal recovery (annealing) of mineral structure modified by the passage of fission fragments has long been studied by the etching technique. In minerals like apatite and zircon, the annealing kinetics are fairly well constrained from the hour to the million-year timescale and have been described by empirical and semi-empirical equations. On the other hand, laboratory experiments, in which ion beams interact with minerals and synthetic ceramics, have shown that there is a threshold temperature beyond which thermal recovery impedes ion-induced amorphization. In this work, it is assumed that this behavior can be extended to the annealing of fission tracks in minerals. It is proposed that there is a threshold temperature, T ₀, beyond which fission tracks are erased within a time t ₀, which is independent of the current state of lattice deformation. This implies that iso-annealing curves should converge to a fanning point in the Arrhenius pseudo-space (ln t vs. 1/T). Based on the proposed hypothesis, and laboratory and geological data, annealing equations are reevaluated. The geological timescale estimations of a model arising from this study are discussed through the calculation of partial annealing zone and closure temperature, and comparison with geological sample constraints found in literature. It is shown that the predictions given by this model are closer to field data on closure temperature and partial annealing zone than predictions given by previous models.     

Systematics in the fission track annealing of minerals

A linear relationship exists between annealing temperatures and activation energies of fission tracks for different minerals. The temperature and activation energy needed to erase 50% of the tracks in minerals depend on the lattice energy per mole. These relationships make possible predictions about the stability of tracks in silicates, provided their chemical composition is known or a few isochronal annealing data are available.     

Denudation of the Côte d'Ivoire-Ghana transform continental margin from apatite fission tracks

Apatite fission track analysis of samples from the shoulder (marginal ridge) of the Côte d'Ivoire-Ghana transform continental margin reveal a cooling of the margin between 85 and 65 Ma for the central and eastern parts of the ridge. All samples were heated in situ during sedimentary burial with a temperature >120 °C, except for two samples located in the eastern part which were heated between 105 and 120 °C. For the first time, age/depth diagram along a transform margin shows a shape involving erosion starting at the bottom of the continental slope, then stepping backwards towards the edge of the slope. This retrogressive erosion can result from the deepening of the lithospheric plate sliding along the transform margin, from thick continental crust to thin continental crust, and finally to oceanic crust. This process could be at the origin of the shoulder uplift by flexural response to the important crustal discharge (>2 km).     

班公湖- 怒江缝合带东段八宿地区花岗岩体差异性隆升：来自锆石和磷灰石裂变径迹证据

班公湖- 怒江缝合带为青藏高原内部分隔羌塘和拉萨两地块的构造边界,是研究青藏高原构造演化的重要窗口之一。该缝合带自西向东分为西段（班公湖至改则）、中段（安多至东巧）和东段（丁青至怒江）,其中东段的研究程度较低。本次以东段八宿县郭庆乡一条花岗岩高程剖面为研究对象,采用激光剥蚀电感耦合等离子体质谱仪（LA- ICPMS）法对锆石和磷灰石开展裂变径迹测试。花岗岩锆石U- Pb年龄为~180 Ma,指示其结晶时代为早侏罗世。锆石和磷灰石裂变径迹年龄分别为180～130 Ma、86～61 Ma,对应的年龄- 海拔曲线分别为负斜率和正斜率。QTQt模拟显示花岗岩高程剖面顶部在130～60 Ma时剥蚀冷却速率快,中部在130～40 Ma时剥蚀冷却速率居中,而底部在~130 Ma之后一直保持最低的剥蚀冷却速率。这种差异性隆升源自班公湖- 怒江缝合带东段的南向俯冲板片断离早于北向俯冲板片断离。     

A borehole investigation of zircon radiation damage annealing

This contribution reports Raman radiation damage measurements of zircons from the Kontinentale Tiefbohrung, on the western border of the Bohemian Massif. The mean wavenumbers (ω₃) and widths (Γ₃) of the ν₃(SiO₄) Raman band are constant down to 3 km, decrease (ω₃) resp. increase (Γ₃) between 3 and 5 km, and are again constant between 5 and 7 km. Uniform high Γ₃ values associated with ω₃ values close to those of undamaged zircon between 5 and 7 km are interpreted as due to residual damage predating the exhumation of the Bohemian Massif. A superimposed post‐exhumation signal indicates full damage retention down to 3 km depth, partial annealing between 3 and 5 km, and zero retention at greater depth. An attempt to calculate radiation damage ages gives results of a meaningful order of magnitude but also exposes difficulties associated with dating basement samples with complex damage accumulation and annealing histories.     

Modelling the formation of fission tracks in apatite minerals using molecular dynamics simulations

We introduce a simple method to simulate the “ion explosion spike” mechanism of fission track formation within the framework of classical molecular dynamics. The method is applied to six apatite compositions and the resulting tracks are compared with each other as well as with the damage produced by another mechanism—the “Displacement spike”. In contrast to experimentally observed tracks, the radii of simulated tracks are not dependent on their direction in the crystal. Since the simulations model accurately the elastic response of apatites, this suggests that the experimentally observed difference in track radii for tracks along different crystal directions is not entirely caused by anisotropy in the elasticity of apatite. We suggest that anisotropy in the interactions between the electric fields of fission fragments and the crystal ions is a major factor in the final radii of fission tracks. In fluorapatite, the simulations also reveal the formation of small clusters of fluorite-like material in the core of the fission track, a phenomenon which has yet to be confirmed experimentally.

磷灰石裂变径迹退火影响因素研究进展

磷灰石裂变径迹退火是一个繁杂的化学动力学过程,清楚地了解其退火的影响因素对于该技术的应用十分重要。文章概述了磷灰石裂变径迹退火动力学模型的发展史,并结合以往对其退火影响因素的研究,将磷灰石裂变径迹退火影响因素分为自身和外部环境两方面：自身影响因素包括化学成分、晶体结构、径迹长度与半径、径迹与结晶轴的方位关系,其中化学成分对退火起到主导作用;外部环境影响中,温度是主导因素,压力和蚀刻条件的改变也会影响退火。研究成果有利于完善磷灰石裂变径迹的实验室退火模型,提高其作为热历史记录器的精度。     

Hydromechanical modelling of the SEALEX experiments

Numerical modelling of coupled physical processes in bentonite–sand mixtures under the geological conditions is significant for designing and constructing sealing systems in deep underground repositories for highly radioactive nuclear waste. Within the framework of DECOVALEX 2015, Task A, this work presents the model validation of OpenGeoSys by numerical modelling of coupled hydromechanical (HM) processes in bentonite–sand mixtures. Parameters used in the HM model were determined by modelling the laboratory tests of the sealing experiment (SEALEX). Afterwards these parameters were applied for the modelling of a small-scale mock-up test considering the influence of technological gap and incidental fail of the seal in the sealing system. In order to investigate the availability of employing these HM parameters and numerical models directly to field predictions, the modelling results and measured data of an in situ SEALEX experiment were analysed comparatively. The modelling results reproduced well the main features in HM behaviour of the compacted bentonite–sand mixture, which denotes that the adopted HM models and parameters are adequate for describing the HM processes in the sealing system. It is necessary to take the elastoplastic behaviour and evolution of the permeability of bentonite–sand mixtures into account when using the adopted models to reproduce the HM processes of a sealing system.     

Statistical treatment of experimental errors in the fission track dating method

The major stochastic elements in the fission track dating method are (i) the number of spontaneous fission tracks (N _s ) in a sample, and (ii) the number of induced tracks (N _i ) observed when the sample is irradiated with neutrons. The foundations for the statistical uncertainty in these measures are of two kinds: (i) there exists a definite probability of uranium fission by means of natural decay and by neutron activation, and (ii) within a crystal the distribution of uranium is not uniform and perhaps follows something like a Poisson law. In any event, the natural logarithm of the ratio (N _s /N _i ) is proportional to age. A plausible statistical fission track dating model should, therefore, start by considering the joint distribution of N _s and N _i . In this paper a joint bivariate normal model is described which allows the rigorous definition of the probability distributions of N_s, N _i , the ratio N _s /N _i , and age itself. A general computer program (FISSION) has been developed to perform all the necessary computations. By accounting for the correlation between N _s and N _i , the statistical model here ascribes smaller standard errors to N _s /N _i (and therefore age) than do previous methods. In addition, the error associated with neutron flux is a significant factor in the age relationships and has been incorporated into the model.     

柴达木盆地新生界碎屑锆石FT年龄对蚀源区的约束

柴达木盆地新生界碎屑锆石裂变径迹年龄的研究表明, 沉积物主要蚀源区是遭受海西-印支运动影响的盆地周缘山地, 燕山运动仅在柴西阿尔金山有所表现。揭示出蚀源区发生过多次的(热) 构造运动, 在柴北缘有5次( ～284.5 Ma、～263.6 Ma、～243.6 Ma、～221.6 Ma和～199.8 Ma) , 而在柴西则有6次( ～344.2 Ma、～275.2 Ma、～244.9 - 246.8 Ma、～210 - 220.3 Ma、～186.9 - 195.7 Ma和～162.9 Ma) , 说明青藏高原北部在前新生代具有多阶段、同步整体隆升特点。进入新生代, 柴达木盆地及其周缘山带构造活动具有强-弱-强的特征。     

Metamictisation of natural zircon: accumulation versus thermal annealing of radioactivity-induced damage

Annealing of the radiation damage generated in !-decay events is a common phenomenon in natural zircons. We have studied relationships between radiation damage, age and radionuclide content of natural zircons on a micro-scale. The degree of metamictisation was estimated by means of confocal laser-Raman spectroscopic measurements. Raman band broadening in well-ordered to moderately metamict zircons that have not experienced significant healing of the radiation damage since the time of their growth, shows a nearly linear dependence on the !-fluence. This dependence is proposed as a calibration line for examining unknown zircons in order to consider complete or incomplete damage storage, which may contribute to the understanding of the low-T thermal history of their host rocks. Seven examples for the application are presented. Radiation damage may anneal heterogeneously, with preferred re-ordering in more damaged micro-areas. Results suggest that single point defects do not anneal continuously over geologic periods of time but are, in contrast, a comparably stable type of radiation damage. In contrast to recrystallisation processes, structural recovery due to simple thermal annealing is not necessarily connected with loss of radiogenic Pb. The most prominent example for this are concordant zircons from Sri Lanka. Although they are excellent standards for U-Pb dating, Sri Lankan zircons should not be used as standards for structural radiation damage. The experimental work is completed by Monte Carlo simulations of !-decay events in zircon.