红鲍珍珠层中文石晶体取向模型的理论表征
Theoretical characterization of a model of aragonite crystal orientation in red abalone nacre
摘要：
珍珠层，通常被称为珍珠母，是一种显著的生物矿物，在红鲍鱼中由400 nm厚的文石晶体片层组成，文石晶体片层被有机基质片限制，文石片层的$(001)$晶轴取向为与层平面的法线成$\pm$ 12度以内。最近的实验表明，这种取向秩序的发展超过了几十层的距离，从棱柱形的边界，珍珠层的形成开始。我们以前的模拟模型，其中的顺序发展，因为差分片剂的增长速度（定向片剂增长速度比错位的）产量模式的片剂同意定性和定量的实验测量。本文提出了一个分析处理这个模型，重点是如何动态发展和最终的程度的秩序依赖于模型参数。动力学方程的概率分布管理片剂的方向介绍其形式可以确定从对称性的考虑，并为实质性的分析进展可以取得。数值模拟进行相关的参数在解析理论中的微观生长模型。分析理论表明，动力学机制是能够实现更高程度的秩序比天真的估计将表明。
英文摘要：
Nacre, commonly known as mother-of-pearl, is a remarkable biomineral that in red abalone consists of layers of 400-nm thick aragonite crystalline tablets confined by organic matrix sheets, with the $(001)$ crystal axes of the aragonite tablets oriented to within $\pm$ 12 degrees from the normal to the layer planes. Recent experiments demonstrate that this orientational order develops over a distance of tens of layers from the prismatic boundary at which nacre formation begins. Our previous simulations of a model in which the order develops because of differential tablet growth rates (oriented tablets growing faster than misoriented ones) yield patterns of tablets that agree qualitatively and quantitatively with the experimental measurements. This paper presents an analytical treatment of this model, focusing on how the dynamical development and eventual degree of order depend on model parameters. Dynamical equations for the probability distributions governing tablet orientations are introduced whose form can be determined from symmetry considerations and for which substantial analytic progress can be made. Numerical simulations are performed to relate the parameters used in the analytic theory to those in the microscopic growth model. The analytic theory demonstrates that the dynamical mechanism is able to achieve a much higher degree of order than naive estimates would indicate.
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