Modeling dike cooling time to obtain plagioclase growth rate

Finite element modeling indicates that the cooling/crystallization time interval for a diabase porphyry dike, 12.2 meters thick, intruded into lower Paleozoic limestones in the Shenandoah Valley of Virginia, was from 5.5 to 8 years. The limestone does not show contact metamorphism, yet fine grained chilled margins exist locally in the dike. In the model we assumed an ambient limestone temperature of 100 degrees Celsius and a depth of 1 kilometer at the time of intrusion, and magma liquidus and solidus temperatures of 1100 and 600 degrees respectively. The wide range between the highest and lowest thermal diffusivities for limestone as obtained from published tables accounts for the range in the cooling time span above. The latent heat of crystallization was modeled over the cooling interval and added approximately 15 percent to the cooling time of the dike. The groundmass (GM) plagioclase crystals show a linear crystal size distribution which would suggest a constant growth rate as a first approximation. Since the largest GM plagioclase was 0.08 cm, this would indicate a plagioclase growth rate from 0.317 E -9 to .46 E -9. This rate is faster than that reported for plagioclase in Makaopuhi lava lake (E -11) but within the range of other reported plagioclase growth rates (E-8 to E -11) .