Contributions to Mineralogy and Petrology

, Volume 40, Issue 3, pp 259–274 | Cite as

Closure temperature in cooling geochronological and petrological systems

  • Martin H. Dodson


Closure temperature (T c ) of a geochronological system may be defined as its temperature at the time corresponding to its apparent age. For thermally activated diffusion (D=D o e −E/RT it is given by
$$T_c = R/[E ln (A \tau D_0 /a^2 )]$$
(i) in which R is the gas constant, E the activation energy, τ the time constant with which the diffusion coefficient D diminishes, a is a characteristic diffusion size, and A a numerical constant depending on geometry and decay constant of parent. The time constant τ is related to cooling rate by
$$\tau = R/(Ed T^{ - 1} /dt) = - RT^2 /(Ed T/dt).$$
(ii) Eq. (i) is exact only if T−1 increases linearly with time, but in practice a good approximation is obtained by relating τ to the slope of the cooling curve at Tc.

If the decay of parent is very slow, compared with the cooling time constant, A is 55, 27, or 8.7 for volume diffusion from a sphere, cylinder or plane sheet respectively. Where the decay of parent is relatively fast, A takes lower values. Closure temperatures of 280–300° C are calculated for Rb-Sr dates on Alpine biotites from measured diffusion parameters, assuming a grain size of the order 0.5 mm.

The temperature recorded by a “frozen” chemical system, in which a solid phase in contact with a large reservoir has cooled slowly from high temperatures, is formally identical with geochronological closure temperature.


Activation Energy Cooling Curve Decay Constant Chemical System Cooling Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Martin H. Dodson
    • 1
  1. 1.Department of Earth SciencesThe UniversityLeeds

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