Natural processes driven by heat flow can be understood using quantitative reconstruction of the thermal history of accessory and common minerals that were formed or modified in these processes. Thermochronology assumes that isotopes are lost from minerals by thermally-activated volume diffusion, and forms the basis of many studies of the thermal evolution of the crust. However, some studies challenge this assumption and suggest that the mechanisms controlling isotope transport in minerals over geological time-scales are dominated by aqueous fluid flow within mineral pathways. Here, we test these contrasting hypotheses by inverse modelling apatite uranium–lead (U–Pb) dates to produce theoretical t–T solutions assuming Pb was lost by volume diffusion. These solutions are compared with independent geological constraints and intra-grain apatite U–Pb dates, which demonstrate that volume diffusion governed the displacement of Pb. This confirmation, combined with an inverse-modeling procedure that permits reheating and cooling paths to be distinguished between ∼375 and 570 °C, provides geologists with a unique tool for investigating the high-temperature thermal evolution of accessory minerals using the U–Pb method

K-feldspar is a common detrital mineral in sandstones. It contains little U or Th, and hence the common Pb isotope composition of unaltered K-feldspar is that of the source rock. Pb isotope variations in igneous and metamorphic crustal rocks define broad spatial patterns that make the Pb signature of detrital K-feldspar grains a useful provenance tool. However, it is unclear how robust this signal is, and to what extent it can be modified by weathering, transport, burial diagenesis, and/or exposure to hydrothermal fluids. This study reports an evaluation of the technique, using two granite–arkose pairs (from Helmsdale, northern Scotland, and Shap, northwest England) where the composition of the detrital grains can be compared to feldspars in the granite from which they were derived. The results of this test have informed a pilot study using the Pb isotope composition of detrital K-feldspar in Upper Carboniferous fluvial sedimentary rocks of northern England to constrain the sediment routing. Pb isotope compositions have been measured using an in situ high-resolution single-grain technique that can distinguish original composition, heterogeneity, and subsequent alteration within individual sand grains. The results for the granite–arkose pairs show that the common Pb isotope signature of the detrital K-feldspar grains matches the in situ feldspars in the source granites. The signal is independent of grain size (medium-grained sand to granules), but alteration along a paleo-regolith at Helmsdale has resulted in perturbations in Pb composition and an increase in the errors on the analyses. The application of the technique to arkosic Carboniferous (Serpukhovian–Bashkirian) Millstone Grit Group sandstones in the Pennine Basin reveals two discrete populations of K-feldspars that cannot be distinguished petrographically. Matching of the compositions to potential sourcelands to the north and northeast of the basin suggest a far-traveled (> 500 km) source of K-feldspar from the Archean–Paleoproterozoic Lewisian rocks of northwest Scotland or their extension to the north, but also an equally important proximal source emanating from the Southern Uplands Belt of Scotland in what would have been the lower part of the hinterland drainage basin of the Millstone Grit.