A simple model of oscillatory zoning in magmatic plagioclase: Development of an isothermal undercooling model
A simple model of oscillatory zoning in magmatic plagioclase: Development of an isothermal undercooling model
复制标题
DOI：
10.2138/am.2007.2236
复制
发表时间：
2007-07
影响因子：
3.1
通讯作者：
Akira Tsune;A. Toramaru
中科院分区：
文献类型：
--
作者：
Akira Tsune;A. Toramaru
根据Sibley等（1976）的模型，晶体表面在光滑和粗糙状态之间的交替转换导致生长速度的急剧变化和随后的振荡环带（OZ）的发展。本文发展了Sibley等模型的等温过冷机制，并计算了OZ的振幅和波长，以检验Sibley等模型的正确性。我们假设生长速度取决于晶体表面的粗糙度。粗糙度表示为表面积的函数，并且发现由于开关，生长速度变化两倍。我们还假设，当达到稳态或当生长和扩散速度平衡时，表面状态发生变化。假设扩散层的厚度是固定的，模拟扩散反应，我们确定发生切换的浓度。基于这些数学考虑，我们模拟了OZ的生长。结果表明，计算的振幅和波长的大小与自然界中的观测值一致。
Abstract According to the model of Sibley et al. (1976), the alternate switching of the crystal surface between smooth and rough states results in a drastic change in the growth velocity and the subsequent development of oscillatory zoning (OZ). In the present paper, we develop the isothermal undercooling mechanism of the Sibley et al. model and calculate the magnitudes of the amplitude and wavelength of OZ to check the validity of the Sibley et al. model. We assume that the growth velocity depends on the roughness of the crystal surface. The roughness is expressed as a function of the surface area, and it is found that the growth velocity varies twice due to the switching. We also assume that the surface states change when steady states are achieved or when the growth and diffusion velocities are balanced. Simulating the diffusion-reaction on the supposition that the thickness of the diffusion layer is fixed, we determine the concentrations at which the switching takes place. We simulate the OZ growth based on these mathematical considerations. The results show that the magnitudes of the calculated amplitude and wavelength agree with those observed in nature.