Growth of multilayered polycrystalline reaction rims in the MgO–SiO2 system, part II: modelling
Growth of multilayered polycrystalline reaction rims in the MgO–SiO2 system, part II: modelling
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MgO-SiO2 系统中多层多晶反应环的生长，第二部分：建模
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发表时间：
2011
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通讯作者：
W. Heinrich
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作者：
E. Gardes;W. Heinrich
这篇文章的第一部分（gard<s:1>等人在《矿物汽油贡献》，2010年）报道了长方石和石英单晶之间的多晶森林长辉石-顽辉石双层和长辉石单层之间的时间和温度依赖实验生长。双层和单层均表现出生长速率随时间减小和晶粒粗化的趋势。本文提出了一种晶界扩散与晶粒粗化耦合的层生长模型来解释层生长速率的下降。结果表明，层的生长规律为（Δx）2∝t1−1/n，其中Δx为层厚度，n为晶粒粗化指数。结果表明，组分输运主要通过晶界扩散发生，体积扩散的作用可以忽略不计。假设有效晶界宽度为1 nm，推导出MgO晶界扩散的Arrhenius定律：在长辉石中，log Dgb,0Fo (m2/s) =−2.71±1.03,EgbFo = 329±30 kJ/mol；在顽辉石中，log Dgb,0En (m2/s) = 0.13±1.31,EgbEn = 417±38 kJ/mol。不同的活化能是导致顽火辉石/forsterite厚度比随温度变化的主要原因。我们表明，如果假设恒定的体扩散率来模拟晶界扩散控制的边缘生长，则会引入显著的偏差，从而可能产生超过100 kJ/mol的活化能差异。因此，在模拟层状反应区时考虑晶粒粗化是很重要的，因为它们通常是多晶的，并受晶界输运的控制。
Part I of this contribution (Gardés et al. in Contrib Mineral Petrol, 2010) reported time- and temperature-dependent experimental growth of polycrystalline forsterite-enstatite double layers between single crystals of periclase and quartz, and enstatite single layers between forsterite and quartz. Both double and single layers displayed growth rates decreasing with time and pronounced grain coarsening. Here, a model is presented for the growth of the layers that couples grain boundary diffusion and grain coarsening to interpret the drop of the growth rates. It results that the growth of the layers is such that (Δx)2 ∝ t1−1/n, where Δx is the layer thickness and n the grain coarsening exponent, as experimentally observed. It is shown that component transport occurs mainly by grain boundary diffusion and that the contribution of volume diffusion is negligible. Assuming a value of 1 nm for the effective grain boundary width, the following Arrhenius laws for MgO grain boundary diffusion are derived: log Dgb,0Fo (m2/s) = −2.71 ± 1.03 and EgbFo = 329 ± 30 kJ/mol in forsterite and log Dgb,0En (m2/s) = 0.13 ± 1.31 and EgbEn = 417 ± 38 kJ/mol in enstatite. The different activation energies are responsible for the changes in the enstatite/forsterite thickness ratio with varying temperature. We show that significant biases are introduced if grain boundary diffusion-controlled rim growth is modelled assuming constant bulk diffusivities so that differences in activation energies of more than 100 kJ/mol may arise. It is thus important to consider grain coarsening when modelling layered reaction zones because they are usually polycrystalline and controlled by grain boundary transport.