Numerical models of P-T, time and grain-size controls on Ar diffusion in biotite: an aide to interpreting 40Ar/39Ar ages

40Ar/39Ar dating of biotite is used extensively to determine the timing of cooling and exhumation in metamorphic terranes. 40Ar/39Ar age interpretations commonly assume that 40Ar diffuses out of biotite through temperature-dependent volume diffusion, and therefore that the age represents the time at which biotite cooled through the nominal closure temperature. Several processes or scenarios affect the reliability of the interpretation of 40Ar/39Ar ages as representing the timing of cooling through a nominal closure temperature, including incomplete re-setting of Ar systematics, incorporation of excess Ar, crystal defects acting as Ar traps or fast-pathways, or fluid-present recrystallization/dissolution. We present a series of numerical diffusion model results that show the percentage of radiogenic Ar that should theoretically be retained in biotite with different grain radii residing for various periods over a range of P–T conditions in a perfect open system that loses Ar via volume diffusion alone. A second set of models demonstrate the effects of crustal residence temperatures, residence timescales, and subsequent cooling rates, on ‘perfect open system’ biotite 40Ar/39Ar age and intra-grain Ar distributions. The model results are useful for constraining cooling and exhumation histories from 40Ar/39Ar biotite data in a variety of metamorphic settings. They also provide baseline data for biotite Ar retention, 40Ar/39Ar ages and intra-grain age distributions that would theoretically be produced from volume diffusion acting alone. Consequently, the models can help evaluate the plausibility of alternative scenarios that may have affected biotite 40Ar/39Ar ages, including extraneous Ar contamination or Ar loss via processes other than diffusion. In conjunction with well-constrained petrogenetic histories, numerical diffusion models are a powerful tool for interpreting 40Ar/39Ar biotite ages, especially when linked with intra-grain 40Ar/39Ar age profiles.