菊花石生长几何模型
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国家自然科学基金资助项目(49602030)


The Geometric Growth Model of the Chrysanthemum Stone
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    摘要:

    通过与DLA模型类比,建立起一个菊花石生长几何模型,分析了菊花石生长过程中的“间距分叉”现象及花瓣间距H的演变规律及速率,并对比分析了菊花石实际形貌与生长模型形态的异同和原因。

    Abstract:

    The growth model of the chrysanthemum stone occurring in Qixia Formation of South China has been studied in this paper. The chrysanthemum stone is composed of celestite, and formed by a core and many petals. The core consists of grain aggregate and the petals are of radial arrangement. Through a comparison with the Diffusion_Limited Aggregation (DLA) model, the authors have established a growth model of the chrysanthemum stone. Due to the resistance of the mud media to the crystal growth and the control role of the crystal structure, there is no branching in the growth model of the chrysanthemum stone, which is different from things of the DLA model. Nevertheless, there exists“branch_between”in the growth model which forms more and more crystal columns, like the branching in the DLA model. As the crystalline substance (SrSO4) moves toward and condenses at the center, and the mud media are pushed outward, the concentration of SrSO4gradually decreases from the center outwards. Hence, the formation of the“branch_between”phenomenon becomes more difficult, and the H (the interval of the crystal columns at the moment of“branch_between”) becomes increasingly larger from the center outwards. There is a critical value H0during the change of H. When H H0, the petals are formed. H0is the key to form the boundary of the core and the petal. The change rate of H, defined asβ, determines the morphological parameterσ(length of petal/diameter of core). Based on the model, one can obtain the relationshipσ≈β-0·5. ln the real morphology of the chrysanthemum stone, H0≈ 0·5mm , which is independent of the occurrence place. However,σis related to the occurrence place. This indicates that the change rate of H(β)depends on the occurrence place. In addition to the“branch_between”and the evolution of H, there must exist“geometric superseding”in the growth of the chrysanthemum stone, because all the petals have the same crystal form: {011}.

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赵珊茸,谭 劲,王文魁, 1998. 菊花石生长几何模型[J]. 岩石矿物学杂志, 17(4):345~351.
Zhao Shanrong, Tan Jin, Wang Wenkui, 1998. The Geometric Growth Model of the Chrysanthemum Stone[J]. Acta Petrologica et Mineralogica, 17(4): 345~351.

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