the other hand, the concentration of carbon-14 falls off so steeply that the age of relatively young remains can be determined precisely to within a few decades. Closure temperature The closure temperature or blocking temperature represents the temperature below which the mineral is a closed system for the studied isotopes. If a material that selectively rejects the daughter nuclide is heated above this temperature, any daughter nuclides that have been accumulated over time will be lost through diffusion, resetting the isotopic "clock" to zero. As the mineral cools, the crystal structure begins to form and diffusion of isotopes is less easy. At a certain temperature, the crystal structure has formed sufficiently to prevent diffusion of isotopes. Thus an igneous or metamorphic rock or melt, which is slowly cooling, does not begin to exhibit measurable radioactive decay until it cools below the closure temperature. The age that can be calculated by radiometric dating is thus the time at which the rock or mineral cooled to closure temperature. This temperature varies for every mineral and isotopic system, so a system can be closed for one mineral but open for another. Dating of different minerals and/or isotope systems (with differing closure temperatures) within the same rock can therefore enable the tracking of the thermal history of the rock in question with time, and thus the history of metamorphic events may become known in detail. These temperatures are experimentally determined in the lab by artificially resetting sample minerals using a high-temperature furnace. This field is known as thermochronology or thermochronometry. The age equation The mathematical expression that relates radioactive decay to geologic time is where is age of the sample, is number of atoms of the radiogenic daughter isotope in the sample, is number of atoms of the daughter isotope in the original or initial composition, is number of atoms of the parent isotope in the sample at time (the present), given by , and is the decay constant of the parent isotope, equal to the inverse of the radioactive half-life of the parent isotope times the natural logarithm of 2. The equation is most conveniently expressed in terms of the measured quantity N(t) rather than the constant initial value No. To calculate the age, it is assumed that the system is closed (neither parent nor daughter isotopes have been lost from system), D0 must be either negligible or can be accurately estimated, λ