Skip to main content
Log in

Closure temperature in cooling geochronological and petrological systems

  • Published:
Contributions to Mineralogy and Petrology Aims and scope Submit manuscript


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 T c.

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  • Amirkhanov, K. I., Brandt, S. B., Bartnitsky, E. N.: Radiogenic argon in minerals and its migration. Ann. N.Y. Acad. Sci. 91 (2), 235–275 (1961).

    Google Scholar 

  • Armstrong, R. L.: K-Ar dating of plutonic and volcanic rocks in orogenic belts. In: Potassium-argon dating, O. A. Schaeffer, J. Zähringer, eds., p. 117–133. Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  • Armstrong, R. L., Jäger, E., Eberhardt, P.: A comparison of K-Ar and Rb-Sr ages on Alpine biotites. Earth Planet. Sci. Lett. 1, 13–19 (1966).

    Google Scholar 

  • Carslaw, H. S., Jaeger, J. C.: Conduction of heat in solids. Oxford: Clarendon Press 1959.

    Google Scholar 

  • Crank, J.: Mathematics of diffusion. Oxford: Clarendon Press 1956.

    Google Scholar 

  • Damon, P. E.: A theory of “real” K-Ar clocks. Eclogae Geol. Helv. 53, 69–76 (1970).

    Google Scholar 

  • Fleischer, R. L.., Price, P. B., Walker, R. M.: Identification of Pu244 fission tracks and the cooling of the parent body of the Toluca meteorite. Geochim. Cosmochim. Acta. 32, 21–31 (1968).

    Google Scholar 

  • Gentner, W., Goebel, K., Präg, R.: Argonbestimmungen an Kalium-Mineralien. III. Vergleichende Messungen nach der Kalium-Argon-und Uran-Helium-Methode. Geochim. Cosmochim. Acta. 5, 124–134 (1954).

    Google Scholar 

  • Goldstein, J. I., Short, J. M.: Cooling rates of 27 iron and stony-iron meteorites. Geochim. Cosmochim. Acta. 31, 1001–1023 (1967).

    Google Scholar 

  • Hanson, G. N., Gast, P. W.: Kinetic studies in contact metamorphic zones. Geochim. Cosmochim. Acta 31, 1119–1153 (1967).

    Google Scholar 

  • Harper, C. T.: The geological intepretation of potassium-argon ages of metamorphic rocks from the Scottish Caledonides. Scot. J. Geol. 3, 46–66 (1967).

    Google Scholar 

  • Hart, S. R.: The petrology and isotopic-mineral age relations of a contact zone in the Front Range, Colorado. J. Geol. 72, 493–525 (1964).

    Google Scholar 

  • Hartree, D. R.: Numerical analysis. Oxford: Clarendon Press 1958.

    Google Scholar 

  • Hofmann, A. W., Giletti, B. J.: Diffusion of geochronologically important nuclides under hydrothermal conditions. Eclogae Geol. Helv. 63, 141–150 (1970).

    Google Scholar 

  • Jäger, E.: Rb-Sr age determination on minerals and rocks from the Alps. Sci. Terre 10, 395–406 (1965).

    Google Scholar 

  • Jäger, E., Niggli, E., Wenk, E.: Rb-Sr Alters-Bestimmungen an Glimmern der Zentralalpen. Beitr. Geol. Karte Schweiz, N.F. 134 Lieferung (1967).

  • Jahnke-Emde: Funktionentafeln. Leipzig: Teubner (1933).

    Google Scholar 

  • Wagner, G. A., Reimer, G. M.: Fission track tectonics: the tectonic interpretation of fission track apatite ages. Earth Planet. Sci. Lett. 14, 263–268 (1972).

    Google Scholar 

  • Wood, J. A.: The cooling rate and parent planets of several iron meteorites. Icarus 3, 429–459 (1964).

    Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

About this article

Cite this article

Dodson, M.H. Closure temperature in cooling geochronological and petrological systems. Contr. Mineral. and Petrol. 40, 259–274 (1973).

Download citation

  • Received:

  • Issue Date:

  • DOI: