Opening and resetting temperatures in heating geochronological systems

We present a theoretical model for diffusive daughter isotope loss in radiochronological systems with increasing temperature. It complements previous thermochronological models, which focused on cooling, and allows for testing opening and resetting of radiochronometers during heating. The opening and resetting temperatures are, respectively, T-op = E/R ln(A(op)tau D-0/a(2)) and T-rs = E/R ln(A(rs)tau D-0/a(2)), where R is the gas constant, E and D-0 are the activation energy and the pre-exponential factor of the Arrhenius law for diffusion of the daughter isotope, a the half-size of the system ( radius for sphere and cylinder and half-thickness for plane sheet) and tau the heating time constant, related to the heating rate by tau = RTop2/E(dT/dt)T-op = RTrs2/E(dT/dt)T-rs. For opening and resetting thresholds corresponding to 1 and 99% loss of daughter isotope, respectively, the retention parameters for sphere, cylinder and plane sheet geometries are A(op) = 1.14 x 10(5), 5.07 x 10(4) and 1.27 x 10(4) and A(rs) = 2.40, 1.37 and 0.561. According to this model, the opening and resetting temperatures are significantly different for most radiochronometers and are, respectively, lower and higher than the closure temperature.