Rate laws in metamorphism |
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| Authors: | George W Fisher |
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| Institution: | Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, U.S.A. |
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| Abstract: | Once a new mineral has nucleated in a metamorphic rock, further growth generally involves three mechanisms, operating simultaneously: (1) diffusion of components; (2) supply of heat needed for chemical reactions; and (3) precipitation on the nucleus. The resulting structure can grow no faster than is permitted by the slowest mechanism, the rate-determining step. During growth, the relative rates of these mechanisms change systematically, so that metamorphic structures pass through a definite sequence of stages, each characterized by a different rate-determining step. Spherical structures tend to pass through three successive stages: (1) an initial reaction-controlled stage, in which growth is linearly proportional to time; (2) an intermediate diffusion-controlled stage, in which growth is proportional to the square root of time; and (3) a final heat-flow-controlled stage, with growth proportional to the cube root of time. Planar reaction zones follow a two-stage sequence beginning with either a reaction-controlled or a heat-flow-controlled stage, both characterized by linear growth laws; and culminating with a diffusion-controlled stage, in which growth is proportional to the square root of time.Estimated values of the kinetic coefficients governing each of these steps suggest that in most metamorphic processes the reaction-controlled stage will end long before the structure is large enough to detect, and that most growth will occur by either a heat-flow-controlled or diffusion-controlled mechanism. Increasing distance between the initial nuclei, increasing grain size, decreasing diffusion coefficients, and increasing heat flow rates all tend to favor diffusion control over heat-flow control. The rate-determining step can be expected to vary both with local and regional changes in these variables; and attempts to delineate domains in which different mechanisms constitute the ratedetermining step may provide valuable insight into the scale on which these parameters vary in metamorphism. |
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