Tests of MacPherson-Srolovitz Grain Growth in Metallic Polycrystals

技术：蜂窝结构，从肥皂泡或其他泡沫到多晶体中的晶体颗粒，随着时间的推移往往会变粗。粗化指的是一些细胞生长，而另一些细胞收缩和消失。了解任何细胞结构中的这一过程有助于控制它并为特定的需求和应用量身定做。在两个维度上，20世纪50年代著名的冯·诺伊曼-穆林斯计算用细胞的三个点(细胞有两个邻居的点)的数量来表示细胞面积的变化率。直到2007年，麦克弗森和斯罗洛维茨发表了一个d维推广，在三维中还没有类似的公式。MacPherson和Srolovitz的计算用简单的几何量给出了细胞体积的变化率：颗粒大小(平均宽度)和包围颗粒的三重线的总长度。然而，将这一计算应用于多晶体中的颗粒生长是有些可疑的，因为它假设所有边界都具有相同的性质。不幸的是，对于性质取决于五个介观参数的晶体到晶体界面来说，情况并非如此。所以问题是，理论结果能帮助我们理解真实材料中的生长吗？可以把它作为开发更复杂模型的起点吗？这些都是基本的科学问题，对现实世界的材料有直接影响。制造具有理想性能的材料需要控制晶粒度和晶界类型分布。要获得对这些属性的预测控制，需要一个详细的、经过验证的模型。与理论发展同步的是X射线衍射显微镜(XDM)的发展，XDM是一种非破坏性、高能、同步辐射x射线技术，可以测量大块多晶体中大量晶体颗粒的位置、形状和取向。非破坏性意味着可以绘制出一组颗粒，对样品进行退火以允许生长，并重新绘制相同体积的材料以确定变化。在微米级分辨率范围内，测量得到每个晶界的类型和颗粒的几何形状。XDM测量将从高纯度铝多晶开始，它应该近似于MacPherson-Srolovitz理论的假设，并继续使用更复杂(不纯和更各向异性)的材料。目标是确定该理论是否适用，以及即使在不能很好地满足假设的情况下，它作为起点是否有用。非技术性：执行非破坏性3D微结构测量的能力将在材料科学中产生广泛影响。颗粒生长测量将展示先进光子源(APS)的微结构映射能力，并将有助于吸引大量用户使用过去五年开发的专用设施。该设施将包括产生显微镜输出所需的硬件、软件和计算能力。使用该设施的结果和其他测量将有助于约束和/或验证材料对包括热处理、机械和化学处理在内的各种加工处理的理论和计算机模拟。这项技术可以用来研究任何晶体材料。物理学、材料科学和工程专业的研究生和本科生将在一个跨学科的环境中工作，该环境横跨基础材料问题、X射线科学和应用技术。他们将在CMU和APS的一个大型、活跃的微结构社区内工作。

TECHNICAL: Cellular structures, ranging from soap bubbles or other froths to crystalline grains in polycrystals, tend to coarsen over time. Coarsening refers to the fact that some cells grow while others shrink and disappear. Understanding this process in any cellular structure contributes to controlling it and tailoring it for particular needs and applications. In two dimensions, the famous 1950s von Neumann-Mullins calculation expresses the rate of change of the area of a cell in terms of the number of its triple points (points where the cell has two neighbors). Until 2007, when MacPherson and Srolovitz published a d-dimensional generalization, there was no analogous formula in three dimensions. The MacPherson and Srolovitz calculation gives the rate of change of a cell volume in terms of simple geometrical quantities: the grain size (the mean width) and the total length of triple lines bounding the grain. However, applying this calculation to grain growth in polycrystals is somewhat suspect since it assumes that all boundaries have the same properties. Unfortunately, this is not true for crystal-to-crystal interfaces where properties depend on five mesoscopic parameters. So the question is, does the theoretical result help us understand growth in real materials? Can it be taken as a starting point from which to develop more complex models? These are basic scientific questions with direct implications for real world materials. Making materials with desirable properties requires control over grain size and grain boundary type distributions. Gaining predictive control over these properties requires a detailed, verified model. Contemporaneous with theoretical developments is the development of x-ray diffraction microscopy (XDM), a non-destructive, high energy, synchrotron x-ray technique that measures the location, shape, and orientation of large numbers of crystalline grains inside bulk polycrystals. Being non-destructive means that an ensemble of grains can be mapped, the sample annealed to allow growth, and the same volume of material re-mapped to determine changes. Within micron scale resolution limits, the measurements yield the types of each grain boundary and the geometry of grains. XDM measurements will begin with a high purity aluminum polycrystal that should approximate assumptions of the MacPherson-Srolovitz theory and continue with more complicated (impure and more anisotropic) materials. The objective is to determine whether the theory is applicable and whether it is useful as a starting point even when the assumptions are not well met. NON-TECHNICAL: The ability to perform non-destructive 3D microstructure measurements will have a broad impact in the materials sciences. Grain growth measurements will demonstrate the capabilities of microstructure mapping at the Advanced Photon Source (APS) and will help attract a community of users to the dedicated facility that has been developed over the past five years. The facility will include hardware and the software and computational power necessary to generate microscope output. Results and other measurements using the facility will help to constrain and/or validate theories and computer simulations of materials response to a variety of processing treatments including thermal, mechanical, and chemical. The technique can be used to study any crystal-based materials. Graduate and undergraduate students in Physics and Materials Science and Engineering will work in an interdisciplinary environment that cuts across fundamental materials issues, x-ray science, and applications technology. They will work within a large, active microstructure-community at CMU and at APS.