Uranium–lead dating, abbreviated U–Pb dating, is one of the oldest and most refined of the radiometric dating schemes. It can be used to date rocks that formed and crystallised from about 1 million years to over 4.5 billion years ago with routine precisions in the 0.1–1 percent range. The method is usually applied to zircon. This mineral incorporates uranium and thorium atoms into its crystal structure, but strongly rejects lead when forming. As a result, newly-formed zircon crystals will contain no lead, meaning that any lead found in the mineral is radiogenic. Since the exact rate at which uranium decays into lead is known, the current ratio of lead to uranium in a sample of the mineral can be used to reliably determine its age. The method relies on two separate decay chains, the uranium series from 238U to 206Pb, with a half-life of 4.47 billion years and the actinium series from 235U to 207Pb, with a half-life of 710 million years. Decay routes Uranium decays to lead via a series of alpha and beta decays, in which 238U and its daughter nuclides undergo a total of eight alpha and six beta decays, whereas 235U and its daughters only experience seven alpha and four beta decays. The existence of two 'parallel' uranium–lead decay routes (238U to 206Pb and 235U to 207Pb) leads to multiple feasible dating techniques within the overall U–Pb system. The term U–Pb dating normally implies the coupled use of both decay schemes in the 'concordia diagram' (see below). However, use of a single decay scheme (usually 238U to 206Pb) leads to the U–Pb isochron dating method, analogous to the rubidium–strontium dating method. Finally, ages can also be determined from the U–Pb system by analysis of Pb isotope ratios alone. This is termed the lead–lead dating method. Clair Cameron Patterson, an American geochemist who pioneered studies of uranium–lead radiometric dating methods, used it to obtain one of the earliest estimates of the age of the Earth. Mineralogy Although zircon (ZrSiO4) is most commonly used, other minerals such as monazite (see: monazite geochronology), titanite, and baddeleyite can also be used. Where crystals such as zircon with uranium and thorium inclusions cannot be obtained, uranium–lead dating techniques have also been applied to other minerals such as calcite / aragonite and other carbonate minerals. These types of minerals often produce lower-precision ages than igneous and metamorphic minerals traditionally used for age