Geospeedometry

Geospeedometry is the science of measuring the timescales and/or temperatures of thermal events in the history of a metamorphic or igneous rock using diffusion profiles of elements within individual minerals. "Geospeedometry" refers to the speed, or timescale, of thermal events in geologic materials. The term first appeared in the literature in 1983; prior thermochronometric studies focused on diffusion of iron and magnesium in olivine provided the foundation for the field. Geospeedometry has since developed rapidly as further studies have experimentally calibrated the diffusivity of elements in various minerals.

Geospeedometry is the science of measuring the timescales and/or temperatures of thermal events in the history of a metamorphic or igneous rock using diffusion profiles of elements within individual minerals. "Geospeedometry" refers to the speed, or timescale, of thermal events in geologic materials. The term first appeared in the literature in 1983; prior thermochronometric studies focused on diffusion of iron and magnesium in olivine provided the foundation for the field. Geospeedometry has since developed rapidly as further studies have experimentally calibrated the diffusivity of elements in various minerals. {\operatorname{\partial}\!C\over\operatorname{\partial}\!t} = {{\operatorname{\partial}}\over{\operatorname{\partial}\!x}}\left(D {\operatorname{\partial}\!C\over\operatorname{\partial}\!x} \right) where D is the diffusion coefficient, or diffusivity (m 2 s −1 ) of the element in the medium x is the position (length) t is time C is the concentration of the element; C(x,t) is a function dependent on both length and time. For a one-dimensional interface at x = 0 with a fixed concentration C 0 , C \left(x,t \right)=C_0 \mathrm{erfc} \left( \frac{x}{2\sqrt{Dt}}\right) where erfc is the complementary error function. The diffusivity of an element in a medium is given by the temperature-dependent Arrhenius equation D = D_0 e^{-E_A/RT} where D 0 is the maximum diffusivity at infinite temperature; also known as the pre-exponential factor (m 2 s −1 ) E A is the activation energy for diffusivity (J mol −1 ) R is the gas constant (J mol −1 K −1 ) T is absolute temperature (K) Given an experimentally determined D 0 for a given element in a given substance, an empirical diffusion profile can be used to calculate the peak temperature or duration of a thermal pulse experienced by the substance. In cases of varying temperature (e.g. during cooling) D becomes a function of time and the simple analytical solution may no longer be applicable. ==References==

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