Opening and resetting temperatures in heating geochronological systems

Abstract

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, $$ T_{\text{op}} = \frac{E}{{R{\kern 1pt} \,\ln \left( {\frac{{A_{\text{op}} \tau D_{0} }}{{a^{2} }}} \right)}}\;{\text{and}}\;T_{\text{rs}} = \frac{E}{{R{\kern 1pt} \,\ln \left( {\frac{{A_{\text{rs}} \tau D_{0} }}{{a^{2} }}} \right)}}, $$ 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 τ the heating time constant, related to the heating rate by $$ \tau = RT_{\text{op}}^{2}/E{\kern 1pt}({\text{d}}T/{\text{d}}t)_{{T_{\text{op}} }} =RT_{\text{rs}}^{2}/E{\kern 1pt} ({\rm d}{{T}}/{\rm d}{{t}})_{{T_{\text{rs}} }}.$$ 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 × 105, 5.07 × 104 and 1.27 × 104 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.