Daniel Schauries

Effect of orientation on ion track formation in apatite and zircon

Abstract Fission track (FT) thermochornology is essentially based on empirical fits to annealing data of FTs revealed by chemical etching, because, until now, unetched, latent FTs could not be examined analytically at the atomic-scale. The major challenge to such an analysis has been the random orientation of FTs and their extremely small diameters. Here we use high-energy ions (2.2 GeV Au or 80 MeV Xe) to simulate FT formation along specific crystallographic orientations. By combining results from transmission electron microscopy (TEM) of single tracks and small-angle X-ray scattering (SAXS) for millions of tracks, a precise picture of track morphology as a function of orientation is obtained. High-resolution analysis reveals that orientation affects the shape of tracks in apatite and zircon through the preferential creation of damage along directions with highest atomic density. However, track radius does not depend on orientation, contradicting previous reports. Independent of track orientation, track radii, as measured at each point along the entire length of 80 MeV Xe ion tracks in apatite, can be understood using the thermal spike model of Szenes. Thus, the well-known track annealing anisotropy of apatite is not due to track radius anisotropy. The combination of ion-irradiations with TEM and SAXS analysis provides a unique opportunity to understand and model track formation and annealing under various geologic conditions.

Temperature dependence of ion track formation in quartz and apatite

Ion tracks were created in natural quartz and fluorapatite from Durango, Mexico, by irradiation with 2.2 GeV Au ions at elevated temperatures of up to 913 K. The track radii were analysed using small-angle X-ray scattering, revealing an increase in the ion track radius of approximately 0.1 nm per 100 K increase in irradiation temperature. Molecular dynamics simulations and thermal spike calculations are in good agreement with these values and indicate that the increase in track radii at elevated irradiation temperatures is due to a lower energy required to reach melting of the material. The post-irradiation annealing behaviour studied for apatite remained unchanged.

Orientation dependent annealing kinetics of ion tracks in c-SiO2

The structure and thermal response of amorphous ion tracks formed along the [112¯0], [101¯0], and [0001]-directions in crystalline quartz have been investigated using small angle x-ray scattering. The radii of the ion tracks vary by about 5% (0.3 nm) for tracks along different crystallographic directions. Molecular dynamics simulations reproduce this anisotropy along the [101¯0] and [0001] directions and suggest that differences in thermal conductivity along these directions are partly responsible for this observation. Using in situ annealing, tracks along the [101¯0] and [0001] directions were shown to recrystallize during thermal annealing around 960–1020 °C with activations energies around 6 eV, while those along the [112¯0]-direction already disappeared at 640 °C with a significantly lower activation energy around 3–4 eV.

Morphology of ion irradiation induced nano-porous structures in Ge and Si1−xGex alloys

Crystalline Ge and Si1−xGex alloys (x = 0.83, 0.77) of (100) orientation were implanted with 140 keV Ge− ions at fluences between 5 × 10 15 to 3 × 10 17 ions/cm2, and at temperatures between 23 °C and 200 °C. The energy deposition of the ions leads to the formation of porous structures consisting of columnar pores separated by narrow sidewalls. Their sizes were characterized with transmission electron microscopy, scanning electron microscopy, and small angle x-ray scattering. We show that the pore radius does not depend significantly on the ion fluence above 5 × 10 15 ions/cm2, i.e., when the pores have already developed, yet the pore depth increases from 31 to 516 nm with increasing fluence. The sidewall thickness increases slightly with increasing Si content, while both the pore radius and the sidewall thickness increase at elevated implantation temperatures.

Nanoscale density variations induced by high energy heavy ions in amorphous silicon nitride and silicon dioxide

The cylindrical nanoscale density variations resulting from the interaction of 185 MeV and 2.2 GeV Au ions with 1.0 μm thick amorphous SiN x :H and SiO x :H layers are determined using small angle x-ray scattering measurements. The resulting density profiles resembles an under-dense core surrounded by an over-dense shell with a smooth transition between the two regions, consistent with molecular-dynamics simulations. For amorphous SiN x :H, the density variations show a radius of 4.2 nm with a relative density change three times larger than the value determined for amorphous SiO x :H, with a radius of 5.5 nm. Complementary infrared spectroscopy measurements exhibit a damage cross-section comparable to the core dimensions. The morphology of the density variations results from freezing in the local viscous flow arising from the non-uniform temperature profile in the radial direction of the ion path. The concomitant drop in viscosity mediated by the thermal conductivity appears to be the main driving force rather than the presence of a density anomaly.

Physical Background of Ion Tracks

When energetic ions pass through solids, they dissipate their energy into the target. The resulting energy loss can be divided into two main regimes. The first is nuclear energy loss, which displaces atoms by elastic collisions between the ion and the nuclei. This process typically dominates for heavy ions with kinetic energies around and below 1 MeV. The second type of interaction, the electronic energy loss, occurs mainly between the ions and the electrons of the target and is the primary type of energy loss for ion energies above 10 MeV (so-called swift heavy ions). Additional energy losses can result from repulsive decay of excited states, track potential, and exciting of vibrational states in molecular solids. Radiation emitted from the particle and nuclear reactions can also dissipate energy, although this is only relevant at energies higher than those within the present work.

Ion Track Formation Under Ambient Conditions

This chapter presents the experimental results on the influence of the parameters of the ion irradiation on the resulting ion tracks as well as the physical parameters of the irradiated materials. The results contribute towards the further understanding of the fundamental processes of ion track formation. With the primary focus of this work on ion tracks in minerals and an increased understanding of fission tracks, the materials investigated were natural apatite and quartz. Apatite is among the most common materials used for fission track dating [1], while quartz has a simple and well-understood structure, allowing to run a series of simulations on track formation under different conditions [2].

Track Formation Under Temperature and Pressure

This chapter discusses the influence of two external ion irradiation parameters on ion track formation: temperature and pressure. In natural environments where fission tracks are generated, both parameters can be significantly elevated compared with ambient conditions. This particularly applies to fission tracks formed several thousand metres below the earth’s surface, which are relevant for oil and gas exploration (Augustine et al., in Proceedings, Thirty-First Workshop on Geothermal Reservoir Engineering, 2006, [1]). The majority of irradiation experiments that simulate fission tracks, however, are conducted under ambient conditions for practical reasons. Lang et al. have investigated track formation under high temperature (\(250\,^{\circ }\hbox {C}\)) and in the presence of elevated pressure (0.75 GPa), by irradiating zircon within a heatable high-pressure cell (Lang et al., in Earth Planet Sci Lett 274, 355–358, 2008, [2]). The track sizes were measured with TEM and indicate a small, positive correlation between track cross-section and a simultaneous increase in temperature and pressure during track formation. The present work systematically investigates the influences of temperature and pressure independently in quartz and apatite. The results are explained by using existing models for track formation.

X-Ray Characterisation Techniques

The present chapter discusses the theory of X-rays characterisation methods in material science, based on the interaction of X-rays with matter through absorption and scattering. In particular, the theoretical aspects of X-ray diffraction and scattering are introduced and the concepts of small angle X-ray scattering (SAXS) are explained. As the main characterisation technique used in this work, focus is set on the application of this technique on cylindrical ion tracks and the analysis of the SAXS patterns to extract their size and density profile.

Thermal Annealing of Ion Tracks

At ambient temperatures, ion tracks in minerals are known to be stable and fairly constant in size. Even over geological timescales, in the range of hundreds of million years, only small reductions in length occur [1]. This changes dramatically when the tracks are exposed to elevated temperatures, leading to a recrystallisation of the damaged structure and a shrinkage in track size (i.e. length and radius). This process is extremely temperature-dependent, with a full recovery and disappearance of all tracks at 170–200 \(^{\circ }\)C over geological timescales of 10\(^{6}\) years [2]. When annealed at 350–400 \(^{\circ }\)C, however, a duration of less than 1 hr is sufficient to fully erase all tracks [3]. This is a result of the rate of recrystallization being typically associated with an exponential dependence of the diffusion rate of the displaced atoms incorporated in the ion tracks on temperature.