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首页> 外文期刊>Physical review >Interfaces in ferroelastics: Fringing fields, microstructure, and size and shape effects
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Interfaces in ferroelastics: Fringing fields, microstructure, and size and shape effects

机译：铁弹性体中的界面：边缘场，微观结构以及尺寸和形状效应

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摘要

We develop a strain-based approach to study the transformation of a finite martensite domain within an austenite host matrix. Analytical and numerical solutions are obtained for the fringing fields in the austenite and in the martensite and we test how well the stress and strain matching conditions are obeyed at the habit planes. We investigate the scaling of the energy of the fringing fields and show how simulations on relaxed micro-structures corroborate the 1/|k_y| behavior for the energy in Fourier space. Our results show that the functional form F=F_0 + aL_1ξ+bLL_1/ξ for the total elastic energy provides an excellent fit to the numerical simulations, thus demonstrating that ξ～ L~(1/2), where ξ is the twin width for a martensite region L × L_1 with length of the habit plane L_1 and where aL_1ξ, bLL_1/ξ, and F_0 are the energies of the decaying strain field at the habit plane, twin-boundary energy, and energy of a single martensite variant, respectively. However, the result is only true for sufficiently large L and we provide insight into the breakdown of the ξ ～ L~(1/2) scaling at the nanoscale. Our approach allows us to investigate the effect of varying the finite distance between habit planes, L, and our key finding is that there is a minimum length, L~(min), for the nucleation of the twinned martensite structure which depends on temperature. As the temperature is lowered, L~(min) decreases, and at temperatures close to the stability limit of the austenite phase a lattice martensite structure in which the parent and product phases spatially alternate in a checker-board pattern is stable in a narrow region of the temperature versus L phase diagram. Such patterns have been seen at the nanoscale in lithium-based perovskites and inorganic spinels, as well as in coherent decomposition of precipitates in Co-Pt alloys. Finally, we show how the nature of the fringing fields due to an inclusion within an austenite matrix sensitively depends on its shape, size, and orientation and determines whether twinning or lattice martensite are the stable structures.
机译：我们开发了一种基于应变的方法来研究奥氏体宿主矩阵内有限马氏体域的转变。获得了奥氏体和马氏体中的边缘场的解析和数值解，我们测试了在习惯平面上如何满足应力和应变匹配条件。我们研究边缘场能量的标度，并显示如何在松弛的微结构上进行仿真来证实1 / | k_y |。在傅立叶空间中的能量行为。我们的结果表明，总弹性能的函数形式F = F_0 +aL_1ξ+ bLL_1 /ξ为数值模拟提供了很好的拟合，因此证明ξ〜L〜（1/2），其中ξ是马氏体区域L×L_1，其具有习惯平面L_1的长度，其中aL_1ξ，bLL_1 /ξ和F_0分别是习惯平面处的衰减应变场的能量，双边界能量和单个马氏体变体的能量。但是，该结果仅对于足够大的L是正确的，并且我们提供了ξ〜L〜（1/2）尺度在纳米尺度上的分解的见解。我们的方法使我们能够研究改变习惯平面L之间的有限距离的影响，我们的主要发现是孪晶马氏体结构的成核存在最小长度L〜（min），这取决于温度。随着温度降低，L〜（min）降低，并且在接近奥氏体相稳定性极限的温度下，晶格马氏体结构的母体相和产物相在棋盘形图案中在空间上交替，在狭窄的区域内是稳定的温度与L相图的关系。在锂基钙钛矿和无机尖晶石中，以及在Co-Pt合金中沉淀物的连贯分解中，都可以在纳米级观察到这种模式。最后，我们说明了由于奥氏体基体中包含的边缘场的性质如何敏感地取决于其形状，大小和方向，并确定孪晶或晶格马氏体是稳定的结构。

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  • 来源
    《Physical review》 |2009年第21期|214117.1-214117.22|共22页
  • 作者

    Marcel Porta; Teresa Castan; Pol Lloveras; Turab Lookman; Avadh Saxena; Subodh R. Shenoy;

  • 作者单位

    Departament d'Estructura i Constituents de la Materia and Institut de Nanociencia i Nanotecnologia, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Catalonia, Spain Department of Materials Science and Engineering, University of Toronto, Toronto, Canada M5S 3E4;

    Departament d'Estructura i Constituents de la Materia and lnstitut de Nanociencia i Nanotecnologia, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Catalonia, Spain;

    Departament d'Estructura i Constituents de la Materia and lnstitut de Nanociencia i Nanotecnologia, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Catalonia, Spain;

    Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Materials Science and Engineering, University of Toronto, Toronto, Canada M5S 3E4;

    Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA;

    School of Physics, University of Hyderabad, Hyderabad 500046, India;

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  • 正文语种 eng
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  • 关键词

    martensitic transformations; structural transitions in nanoscale materials; defects and impurities in crystals; microstructure; solid surfaces and solid-solid interfaces: structure and energetics;

    机译：马氏体转变;纳米级材料的结构转变;晶体中的缺陷和杂质;微观结构固体表面和固体-固体界面：结构和能量学;

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