Confined Track Length Research Articles

Tectonic controls on ore deposit exhumation and preservation: A case study of the Handan-Xingtai iron-skarn district

Despite the growing concern regarding post-mineralization thermo-tectonic processes in recent years, the relative roles in exhuming and preserving ore deposits remain highly controversial. This study presents new apatite fission track and (U-Th)/He data from the Xishimen iron skarn deposit in the Handan-Xingtai district, central North China Craton. Apatite fission track dating yielded central ages ranging from 88 ± 18 Ma to 125 ± 9 Ma, with mean confined track lengths varying between 11.9 ± 0.4 μm and 13.3 ± 0.2 μm. Integrated apatite (U-Th)/He dating provided ages of 42.5 ± 0.8 Ma to 48.1 ± 3.3 Ma. Our new data, combined with previous zircon U-Pb and potassium-bearing mineral 40Ar/39Ar ages, revealed three cooling episodes: very rapid cooling (100–140 °C/Ma) at ca. 130–120 Ma, a protracted slow cooling period (0.2–0.4 °C/Ma) at ca. 120–50 Ma, and moderate cooling (0.8–1.0 °C/Ma) since ca. 50 Ma. The initial rapid cooling phase was primarily attributed to post-magmatic thermal equilibration following the shallow emplacement of the Xishimen deposit. The subsequent cooling phases were controlled by uplift and exhumation processes. Our thermal models indicate an estimated total unroofing thickness of < 3 km, which is shallower than the emplacement depth of the ore deposit (3–5 km). This suggests significant potential for mineral exploration. Furthermore, a comprehensive review of preservation mechanisms for various ore deposits underscores the significant role of tectonics in both exhuming and preserving ore bodies.

Extensional exhumation of cratons: insights from the Early Cretaceous Rio Negro–Juruena belt (Amazonian Craton, Colombia)

Abstract. This study presents results from apatite fission track (AFT) thermochronology to investigate the thermal history and exhumation dynamics of the Rio Negro–Juruena basement, situated within the western Guiana Shield of the Amazonian Craton. AFT dating and associated thermal history modeling in South America has largely been restricted to the plate's margins (e.g., Andean active margin, Brazilian passive margin, and others). Our paper reports on low-temperature thermochronological data from the internal part of the western Guiana Shield for the first time. This area is part of a vast cratonic lithosphere that is generally thought to be stable and little influenced by Mesozoic and Cenozoic tectonics. Our data, however, show AFT central ages ranging from 79.1 ± 3.2 to 177.1 ± 14.8 Ma, with mean confined track lengths of ca. 12 µm. Contrary to what might be expected of stable cratonic shields, inverse thermal history modeling indicates a rapid basement cooling event in the early Cretaceous. This cooling is interpreted as a significant exhumation event of the basement that was likely driven by the coeval extensional tectonics associated with back-arc rifts in the Llanos and Putumayo–Oriente–Maranon basins. The extensional tectonics facilitated both basement uplift and subsidence of the adjoining basins, increasing erosional dynamics and consequent exhumation of the basement rocks. The tectonic setting shifted in the late Cretaceous from extensional to contractional, resulting in reduced subsidence of the basins and consequential diminishing cooling rates of the Guiana Shield basement. Throughout the Cenozoic, only gradual, slow subsidence occurred in the study area due to regional flexure linked to the Andean orogeny. Comparative analysis with low-temperature thermochronology data from other west Gondwana cratonic segments highlights that exhumation episodes are highly controlled by tectonic inheritance, lithospheric strength, and proximity to rift zones. This study underscores the complex interplay between tectonic events and the response of cratonic lithosphere over geological timescales and highlights extensional settings as an important geological context for craton exhumation.

Late Cretaceous exhumation of the Little Belt Mountains and regional development of the Helena salient, west-central Montana, USA

The timing of deformation within and adjacent to the Helena salient of west-central Montana is poorly constrained relative to other segments of the Sevier fold-and-thrust belt. This study presents low-temperature thermochronology data from the Little Belt Mountains, a basement-cored Laramide uplift that is juxtaposed with the leading edge of the salient. We analyzed eight samples of Paleoproterozoic basement for apatite fission-track (AFT) and zircon (U-Th)/He (ZHe) thermochronology. Four samples yielded AFT ages ranging from ca. 80 Ma to 73 Ma and associated long, unimodal confined track lengths, indicating rapid cooling and exhumation of Little Belt Mountains basement during the Late Cretaceous. The other four samples are characterized by younger AFT ages (ca. 55 Ma), which suggest a combination of prolonged residence in the apatite partial annealing zone and postexhumation magmatic reheating. In total, 20 new ZHe dates range from ca. 236 Ma to 28 Ma and show a correlation between date and effective uranium. Forward model results for ZHe data are consistent with upper-crustal residence during the Proterozoic followed by Phanerozoic burial and rapid Late Cretaceous cooling. Cross sections across the Little Belt Mountains display the geometry of the Volcano Valley fault zone, an array of down-to-the-south Proterozoic normal faults that profoundly influenced the development of the Cordilleran thrust belt. Our new constraints from the Little Belt Mountains when integrated with published kinematic constraints from the Helena salient reveal significant out-of-sequence deformation in this portion of the thrust belt between ca. 80 Ma and 55 Ma. A kinematic model is proposed that involves Late Cretaceous (ca. 80 Ma) exploitation of rheologically incompetent units at the base of the Belt Supergroup within the Helena Embayment, facilitating early exhumation in the Little Belt Mountains. Our new data and synthesis are consistent with previous interpretations in which an inherited stratigraphic and structural architecture of Proterozoic ancestry was the predominant control on the development of the Helena salient during Cretaceous−early Eocene time.

A grain-by-grain comparison of apatite fission-track analysis by LA-ICP-MS and the External Detector Method

Laser-ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) is increasingly used in fission-track analysis to determine the uranium content of host mineral specimens, particularly apatite. Fission-track dating by LA-ICP-MS (LAFT) has several advantages over the conventional External Detector Method (EDM), particularly in terms of sample turn-around times and the fact that neutron irradiations and the handling of radioactive materials are no longer necessary, while providing a similar level of in-situ information about parent nuclide (238U) concentrations. In addition, it facilitates the simultaneous measurement of multiple isotopes for double or triple-dating approaches or compositional characterisation. While it is often implicitly assumed that the EDM and LAFT fission-track dating approaches produce equivalent results, this assertion has yet to be adequately tested. We present an extensive dataset of apatite fission track results from 17 samples representing a large range of fission-track ages (∼0–2 Ga), 238U concentrations (0.14–410 ppm) and thermal histories that were analysed grain-by-grain using both techniques in order to investigate whether they yield concordant results during routine fission-track analysis.Apart from a few outliers, our data show that 238U concentrations measured by the EDM and LAFT techniques yield indistinguishable results across at least three orders of magnitude when a similar calibration system against rapidly cooled standards (e.g., Durango) is used. Comparison of single grain pooled and central ages reveals that LAFT ages are within error of EDM ages for apatite fission track standards such as Fish Canyon Tuff or Durango, as well as for a range of other samples whose shorter mean confined track lengths (<13 μm) and broader track distributions indicate they experienced more complex cooling histories. The most important conclusion here is that both the conventional EDM and LAFT methods can be expected to yield identical results for the breadth of ages, 238U concentrations, and underlying thermal histories commonly found in real world apatites.Importantly, the aggregate empirical calibrations for EDM and LAFT mask an underlying assumption that the mean etchable range of fission fragments is a constant having the mean value observed for spontaneous tracks in age standards such as the Durango apatite. Given that this assumption is known to be false in the great majority of samples, it is our view that empirically derived EDM and LAFT fission-track ages are best considered as model ages and that there should be greater clarity about the assumptions involved in their calculation.

Several Problems in Low-Temperature Thermal History Modeling

Thermal history modeling based on low-temperature thermochronological data is widely used in the study of geology. Despite its common applications, several problems remain easy to ignore yet should not be overlooked in the execution of such models. This paper describes four key problems of thermal history modeling, namely, (1) is the best-fit thermal history the best? (2) Is the date constraint box a suitable constraint? (3) Does the bimodal distribution of the apatite fission track confined track length absolutely correspond to the cooling reheating model? (4) Is the whole thermal history path credible? Counterexamples are then provided to stress the importance of accounting for these problems in the application of thermal history modeling. Acknowledging the uncertainty and considering the geological constraints are recommended to improve the accuracy of thermal history models. Moreover, thermal historical intervals with high credibility and strong constraint ability are recommended to interpret the selected geological phenomenon.

Short communication: Experimental factors affecting fission-track counts in apatite

Abstract. The tools for interpreting fission-track data are evolving apace, but, even so, the outcomes cannot be better than the data. Recent studies showed that track etching and observation affect confined-track length measurements. We investigated the effects of grain orientation, polishing, etching and observation on fission-track counts in apatite. Our findings throw light on the phenomena that affect the track counts and hence the sample ages, whilst raising the question: what counts as an etched surface track? This is pertinent to manual and automatic track counts and to designing training strategies for neural networks. Counting prism faces and using the ζ calibration for age calculation are assumed to deal with most etching- and counting-related factors. However, prism faces are not unproblematic for counting, and other surface orientations are not unusable. Our results suggest that a reinvestigation of the etching properties of different apatite faces could increase the range useful for dating and lift a significant restriction for provenance studies.

Confined fission-track revelation in apatite: how it works and why it matters

Abstract. We present a new model for the etching and revelation of confined fission tracks in apatite based on variable along-track etching velocity, vT(x). Insights from step-etching experiments and theoretical energy loss rates of fission fragments suggest two end-member etching structures: constant-core, with a central zone of constant etching rate that then falls off toward track tips; and linear, in which etching rates fall linearly from the midpoint to the tips. From these, we construct a characterization of confined track revelation that encompasses all relevant processes, including penetration and widening of semi-tracks etching in from the polished grain surface, intersection with and expansion of confined tracks, and analyst selection of which tracks to measure and which to bypass. Both etching structures are able to fit step-etching data from five sets of paired experiments of fossil tracks and unannealed and annealed induced tracks in Durango apatite, supporting the correctness of our approach and providing a series of insights into the theory and practice of fission-track thermochronology. Etching rates for annealed induced tracks are much faster than those for unannealed induced and spontaneous tracks, impacting the relative efficiency of both confined track length and density measurements and suggesting that high-temperature laboratory annealing may induce a transformation in track cores that does not occur at geological conditions of partial annealing. The model quantifies how variation in analyst selection criteria, summarized as the ratio of along-track to bulk etching velocity at the etched track tip (vT/vB), likely plays a first-order role in the reproducibility of confined length measurements. It also accounts for and provides an estimate of the large proportion of tracks that are intersected but not measured, and it shows how length biasing is likely to be an insufficient basis for predicting the relative probability of detection of different track populations. The vT(x) model provides an approach to optimizing etching conditions, linking track length measurements across etching protocols, and discerning new information on the underlying structure of fission tracks.

Burial and Exhumation History of the Lujing Uranium Ore Field, Zhuguangshan Complex, South China: Evidence from Low-Temperature Thermochronology

The Zhuguangshan complex hosts the main uranium production area in South China. We report (U-Th)/He and fission track thermochronological data from Triassic–Jurassic mineralized and non-mineralized granites and overlying Cambrian and Cretaceous sandstone units from the Lujing uranium ore field (LUOF) to constrain the upper crustal tectono-thermal evolution of the central Zhuguangshan complex. Two Cambrian sandstones yield reproducible zircon (U-Th)/He (ZHe) ages of 133–106 Ma and low effective uranium (eU) content (270–776 ppm). One Upper Cretaceous sandstone and seven Mesozoic granites are characterized by significant variability in ZHe ages (154–83 Ma and 167–36 Ma, respectively), which show a negative relationship with eU content (244–1098 ppm and 402–4615 ppm), suggesting that the observed age dispersion can be attributed to the effect of radiation damage accumulation on 4He diffusion. Correspondence between ZHe ages from sandstones and granites indicates that surrounding sedimentary rocks and igneous intrusions supplied sediment to the Cretaceous–Paleogene Fengzhou Basin lying adjacent to the LUOF. The concordance of apatite fission track (AFT) central ages (61–54 Ma) and unimodal distributions of confined track lengths of five samples from different rock units suggest that both sandstone and granite samples experienced a similar cooling history throughout the entire apatite partial annealing zone (~110–60 °C). Apatite (U-Th-Sm)/He (AHe) ages from six non-mineralized samples range from 67 to 19 Ma, with no apparent correlation to eU content (2–78 ppm). Thermal history modeling of data suggests that the LUOF experienced relatively rapid Early Cretaceous cooling. In most samples, this was followed by the latest Early Cretaceous–Late Cretaceous reheating and subsequent latest Late Cretaceous–Recent cooling to surface temperatures. This history is considered as a response to the transmission of far-field stresses, involving alternating periods of regional compression and extension, related to paleo-Pacific plate subduction and subsequent rollback followed by Late Paleogene–Recent India–Asia collision and associated uplift and eastward extrusion of the Tibetan Plateau. Thermal history models are consistent with the Fengzhou Basin having been significantly more extensive in the Late Cretaceous–Early Paleogene, covering much of the LUOF. Uranium ore bodies which may have formed prior to the Late Cretaceous may have been eroded by as much as ~1.2 to 4.8 km during the latest Late Cretaceous–Recent denudation.

A quantitative description of fission-track etching in apatite

Abstract We measured the apatite etch rate νR in 5.5 M HNO3 at 21 °C as a function of orientation. Results for Durango apatite evidence that νR varies by a factor &amp;gt;5 with angle to the c-axis. Our measurements also provided track etch rates νT and surface etch rates νS. However, these cannot be combined for calculating track etching or counting efficiencies. By inserting the measured etch rates in a recent model, we calculate the geometries and dimensions of surface tracks in different apatite faces. The proposed model must be recalibrated for different etching protocols and adapted for other minerals. We submit that the new model justifies reviewing track counting efficiencies based on the existing (νB-νT) etch model. We anticipate that this will have an effect on practical aspects of fission track dating. Single-track step-etch data show that the confined track lengths increase with etch time at a decreasing average rate νL that differs from the track etch rate νT and the apatite etch rate νR. Both νT and νL exhibit large track-to-track differences that produce irreducible length variation related to the latent-track structure resulting from formation and annealing. Step etching and track width measurements are effective for reducing or eliminating procedure-related artifacts from track length data, and so for accessing more fundamental track properties.

Detrital Thermochronology Reveals Major Middle Miocene Exhumation of the Eastern Flank ofthe Andes That Predates the PampeanFlat Slab (33°–33.5°S)

AbstractThe Cordón del Plata and Cordón del Portillo (32.6°–33.8°S) are the portions of the Frontal Cordillera that straddle the transition zone between the Pampean flat‐slab subduction segment to the north and the normal subduction segment to the south. A complete understanding of how the Frontal Cordillera developed is necessary in order to evaluate different tectonic models for the Andes along with their relation to subduction dynamics and contractional upper‐crustal deformation. Detrital apatite fission track thermochronology of modern river sediments that drain the eastern and western slopes of the Cordón del Plata and the northern Cordón del Portillo provides constraints on regional exhumation histories. AFT data from each catchment typically contain multiple age peaks, but all have a prominent 15.3–17 Ma age peak. One catchment, the Las Tunas River has a unimodal distribution at 17.0 ± 1.1 Ma, with a confined track length distribution indicative of rapid cooling at that time. These results, combined with provenance analysis in the adjacent Cacheuta Basin, indicate significant early to middle Miocene (~16 Ma) exhumation in the Cordón del Plata and the northern sector of the Cordón del Portillo. Exhumation related to rock uplift occurred prior to the ~11 Ma onset of a flat slab geometry at these latitudes, but immediately after the main east vergent contractional event in the adjacent Principal Cordillera. Such Frontal Cordillera exhumation fits in an eastward, youngest to the foreland sequence of deformation of the different morphostructural Andean units at ~33°–34°S, arguing against the recently proposed west vergent orogenic system at these latitudes.

Is Low‐Temperature Fission‐Track Annealing in Apatite a Thermally Controlled Process?

AbstractWe report a new series of experiments to explore the phenomenon of low‐temperature annealing of fission tracks in apatite that feature a number of improvements over previous work. Grain mounts were preirradiated using 252Cf to increase confined track detection and allow briefer thermal neutron irradiation. We coirradiated and etched four apatite varieties (Durango, Fish Canyon, Renfrew, and Tioga) over five time steps equally spaced from 3.66 to 15 ln(s). A length standard was coetched with all experiments to ensure that subtle differences are within detection limits. Finally, we used a standard etching protocol, allowing the data to be comodeled with extensive high‐temperature data sets and recent analyses of induced tracks that underwent ambient‐temperature annealing over year‐to‐decade time scales. Ambient‐temperature annealing occurs at two different rates, with faster annealing at early stages that decreases to a slower rate that converges with empirical fanning linear or curvilinear models. The nature of this decrease varies among the apatite species examined, but no patterns could be determined. The fitted models make geological time‐scale predictions consistent with those based on high‐temperature data only and also make predictions consistent with reasonable inferred low‐temperature histories for all four apatite varieties. The empirical fanning curvilinear equation encompasses low‐temperature annealing at month‐to‐decade time scales, but low‐temperature annealing at shorter time scales may occur by a distinct mechanism. We consider but rule out annealing by radiation from short‐lived activated isotopes. We also reconsider the notion of the initial track length, and the appropriate length for normalizing confined track length measurements.

Late Paleozoic Exhumation of the West Junggar Mountains, NW China

AbstractThe Tianshan and Altai mountain belts dominate the present‐day topography of central Asia and are major constituents of the Central Asian Orogenic Belt. These mountain belts have been extensively studied using low‐temperature thermochronology to understand their uplift and exhumation history. In comparison, few studies have focused on the spatial extent and timing of intracontinental deformation in the intervening ranges, such as the West Junggar Mountains. Apatite fission track (AFT) and apatite U‐Pb dating of igneous samples from the West Junggar Mountains reveals AFT central ages ranging from latest Carboniferous to Middle Jurassic and mean confined track lengths between 14.1 and 12.0 µm, which are negatively correlating to AFT central ages. Apatite U‐Pb dating produced mid‐Carboniferous‐early Permian ages within uncertainty of zircon U‐Pb crystallization ages, indicating cooling to below ∼450–550 °C immediately following emplacement. Thermal history modeling of our AFT data combined with published (U‐Th)/He data predicts rapid cooling to &lt;60 °C during the early‐middle Permian (285–260 Ma), followed by slower cooling rates during the Mesozoic‐Cenozoic. The rapid cooling event coincides with (1) the timing of major basinward thrusting in the Junggar Basin adjacent to the study area and (2) exhumation in the Chinese Altai to the north. In contrast to previous studies, our results imply that the West Junggar Mountains do not record significant exhumation during the Mesozoic‐Cenozoic. This suggests that Mesozoic deformation of the Central Asian Orogenic Belt was less pervasive and widespread than previously assumed.

Thermochronological insights into the thermotectonic evolution of Mishmi hills across the Dibang Valley, NE Himalayan Syntaxis

Eastern Himalayan Syntaxis (EHS) that forms the northeastern termination of the Himalaya consists of three broad zones; Namche Barwa massif, Siang antiform and Mishmi Hills. The present work provides new in-situ apatite fission track (AFT), zircon (U-Th)/He (ZHe) and 40Ar/39Ar multi-thermochronometric ages across the Dibang valley in the Mishmi hills. The study constrains the structure, emplacement time of major thrusts and initiation of Lesser Himalayan Duplex (LHD). Biotite 40Ar/39Ar ages of the Lohit batholith suggest late Oligocene cooling. ZHe ages indicate late Miocene (~8–9 Ma) foreland directed duplex initiation in the Dibang valley. The AFT cooling ages (~5–3 Ma) suggest LHD continued into Mid Pliocene. Confined track lengths and thermal modelling indicate that the northeastern samples from the study area underwent a phase of rapid exhumation around 10 Ma, followed by slow cooling. It is in contrast to the south-western samples from the Dibang valley that have cooled and uplifted rapidly only after around 4 Ma, due to accelerated phase of LHD. Our 3D thermo-kinematic modelling of the data indicates less mass removal around Hunli than other parts of Dibang valley. The result is in contrast to previously estimated ~16 km uplift near Hunli and mass removal. AFT ages from the Hunli window indicate that the region witnessed modest uplift of ~4–5 km since ca. 4 Ma. Brittle duplexing of the lower LHS at Hunli and Mayodia caused the warping of the overlying litho-units. Hunli duplex alone accommodated ~86% of the total shortening.

Phanerozoic cooling history of Archean/Paleoproterozoic basement in the southern Espinhaço Range, southeastern Brazil, through apatite fission-track analysis

Apatite fission track thermochronology of basement rocks from the southern Espinhaço Range and Quadrilátero Ferrífero in southeastern Brazil unravels the tectonic history of this portion of the Brazilian Shield. The study area encompasses an Archean and Paleoproterozoic granitoid-gneiss basement, in the southern border of the São Francisco Craton, and an Archean to Paleo-Mesoproterozoic sedimentary cover. Apatite fission track ages (AFT) vary from 187 ± 18 to 91.8 ± 7.3 Ma and horizontal confined track lengths vary from 9.62 ± 1.81 μm to 12.85 ± 1.35 μm. Thermal history modeling shows an accelerated cooling episode starting in the Upper Devonian to Early Permian. After this event, quiescence lasted from 115 to 170 Ma. Apatite samples lack evidence of far-field effects from rifting and opening of the South Atlantic Ocean, and also evidence from alkaline and basaltic magmatism emplacement during Mesozoic-Cenozoic. The AFT thermochronometer remained undisturbed during Transminas mafic dyke swarm intrusion. Finally, the last cooling event in the Espinhaço Range-Quadrilátero Ferrífero basement records ascension to surface temperatures due to epeirogeny after new configurations of the Nazca, South American and African plates. A climatic origin for the ascension is supported by accentuated erosion rates, even though a weathering-prone phase is registered in weathering profiles.

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

AbstractFission 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.

New insights into the Gondwana breakup at the Southern South America by apatite fission-track analyses

Abstract. Apatite fission-track (AFT) analyses, applied to Southern Brazil and Uruguay samples, was employed aiming to understand the low temperature history of the Dom Feliciano Belt Segment. The Dom Feliciano Belt formed during the Neoproterozoic to Early Paleozoic, linked to the Brasiliano/Pan-African Orogeny. Twenty-four samples were dated, and confined track lengths of twenty samples were measured. The spatial distribution of ages shows three domains with different evolution cut by shear zones and, or suture zones in the Dom Feliciano Belt. The Western Domain exhibits AFT ages &gt; 250 Ma (Permian to Devonian) while the Eastern Domain shows AFT ages &lt; 230 Ma (Paleogene to Triassic). In the Central Domain, the AFT ages range from ∼196 to 130 Ma (Jurassic to Early Cretaceous). The thermal modeling in the domains revealed a complex evolution, with cooling and reheating phases, and a denudation of ∼2600 m. The AFT ages clearly postdate the Gondwanide, Paraná-Etendeka and Rio Grande Cone exhumation history of the Dom Feliciano Belt.

Standardless fission-track ages of the IUGS age standards

Standardless fission-track ages for four zircon, two titanite and three apatite age standards, most of them recommended by the Fission Track Working Group of the IUGS Subcommission on Geochronology, were redetermined. The age calculations used the decay constant for spontaneous fission of 238U (λf = (8.5 ± 0.1) 10−17 a−1) recommended by the IUPAC, the ratio of etchable to latent track length in both the dated minerals (zircon, titanite and apatite) and mica detectors and the 187 track counts with the external-detector and population methods. We found the resulting standardless fission-track ages are in line with results from more recent high precision geochronology including zircon U-Pb dating. These results confirm that standardless fission-track dating of zircon, titanite and apatite with the external-detector method is feasible, as well as dating of apatite with the population method, and that ζ-calibration can be based on the zircon U-Pb ages of the current standard samples. On the other hand, there is no room for an age correction for partial annealing of the fossil tracks based on their mean confined-track lengths of the apatite, titanite and zircon age standards.

Observations on three-dimensional measurement of confined fission track lengths in apatite using digital imagery

We report the results of a comparative study to explore the usefulness of 3D measurements of confined fission track lengths (TINTs) relative to confined track length measurements (dips ≤10°), and evaluate their suitability for thermal history modeling. Confined fission track lengths were measured in 10 annealed Fish Canyon Tuff apatites containing synthetic mixtures of different length components, and two Durango apatites containing spontaneous fission tracks. Measurements were primarily carried out using a digital image-based microscope system, and they were compared to those from a regular optical drawing tube-digitizing tablet setup, and a confocal laser scanning microscope. The results indicate that 3D measurements of confined track lengths are closely comparable to conventional track measurements, and the mean track lengths of inclined (dips > 10°) and (dips ≤10°) confined tracks from the one sample are equivalent within the measurement uncertainty. A strong dip-bias was observed, so that almost all the confined tracks measured were dipping at < 30°, and the great majority (∼70%) were dipping at ≤10°, thereby qualifying as horizontal confined tracks. Our results suggest that a useful increase of more than 40% in sample size can be achieved from including dip-and refraction-corrected 3D track length measurements. Some evidence was seen for a small bias in favor of shorter tracks at higher dip angles but this has very little influence on the mean lengths or length distributions up to the practical limit of dips (∼30°) observed in these measurements. Results obtained using the same measurement system by a single analyst over time and between six different observers in the one laboratory show good reproducibility. These results also agree well with conventional confined track length measurements in the same samples in the second laboratory involved. We conclude that 3D measurements of confined track lengths, including both and inclined tracks, are suitable for use in current fission track annealing models derived from experiments using confined tracks.

Improved output‐feedback second order sliding mode control design with implementation for underactuated slosh‐container system having confined track length

In this study, a new second order sliding mode controller is designed through a novel non-linear sliding surface proposal for a slosh-container system. A linear sliding surface based controller using second order sliding mode is also derived for the comparison purpose. Both the controllers need only output measurements. The super-twisting algorithm is employed to ensure the finite time convergence of system trajectories to a second order sliding set. In sliding phase, the asymptotic stability of the system states to a desired origin is proved by proposing a new Lyapunov function for the system. A slosh-container system representing underactuated interconnected non-linear dynamics is considered. It is shown that how the consideration of limited track length of container affects the stability conditions. To generate a position trajectory for container from the control input signal, a new approach is employed for the implementation purpose. It is demonstrated through simulations and experimental results that the proposed controller based on the novel non-linear sliding surface outperforms the other controller based on the linear surface and it is more suitable on various practical aspects. This also validates the theoretical findings of the study.

Standardless fission-track dating of the Durango apatite age standard

Five dating strategies were used for determining the standardless fission-track age of the Durango apatite. These use the same fossil-track densities but differ in the manner in which the induced-track densities are determined. A conventional age calculation, without correction for experimental factors, gives inconsistent ages with method-related differences >15%. Correcting for these factors brings the ages in line with each other and with the reference age but leaves no room for a partial-annealing correction based on the confined-track lengths. Three further reasons suggest that a length correction is not appropriate. (1) The evidence for length-based corrections is inconclusive. (2) The plateau age of the Durango apatite is consistent with its apparent fission-track age to within 1%. (3) The calculated effective etchable length of the fossil tracks agrees within error with that of the induced tracks; both are further consistent with the measured mean length of confined induced tracks. The circumstance that the (U,Th)/He ages of the accepted and proposed apatite age standards are consistent with their reference ages leaves no margin for a lowered fission-track age resulting from partial annealing, although the case of the Durango apatite itself is inconclusive because of its exceptional crystal size. It is conjectured that the shortening of the fossil tacks in the Durango apatite is due to a lowering of the track etch rate over time. In this case, annealing equations fitted to induced-track data underestimate the extent of confined-track-length reduction in geological samples.