Elastic and Plastic Deformation in Binary Alloy Crystallization

该奖项由材料研究和数学科学部门共同资助，隶属于NSF范围内的数学科学优先领域。 本文提出了一种用于研究纯材料结晶过程中弹性行为的相场晶体模型。 这是通过对扩散时间和原子长度尺度上的质量密度进行建模来实现的。 PFC的方法自然结合了弹性和塑性变形，多晶取向和自由表面，并用于研究晶界能，液相外延生长和纳米晶体固体的屈服强度。 原始工作中没有包括的一个成分是浓度，这一点特别重要，因为大多数材料至少含有两种元素，元素的相对浓度会显著影响非平衡过程和所得微观结构。 此外，由于所有元素具有不同的晶格结构和尺寸，因此弹性和塑性变形受到浓度的强烈影响。 拟议的研究的目标是开发一个计算有效的模型的微观结构的形成和稳定的二元合金结晶现象，并使用该模型来研究技术上的重要应用，如枝晶生长，共晶结晶和液相外延生长二元合金。 该模型将通过为每个元素引入密度场，构建这些场的适当自由能泛函F，并假设动力学是耗散的并被驱动以使F最小化来开发。 PI在构建此类模型方面拥有丰富的经验，并与其他人合作开发了共晶凝固、驱动电荷密度波、多晶结晶和渗吸模型。 为了这项研究的目的，PI已经开发了一个初步的二元合金结晶模型，包括弹性和塑性变形。 该模型将PFC方法与共晶凝固模型相结合。 初步计算表明，该初步模型采用了通用的功能，共晶相图和许多典型的模式中观察到的非平衡现象，如枝晶和共晶微晶与层状结构。 除了这些标准特征之外，该模型还包括上述原始PFC模型中包含的所有弹性行为，并且设计为可以容易地调整晶格和弹性常数的浓度依赖性。 虽然该初步模型可能需要微调，但这些初步计算表明PI很有可能实现本项目的主要目标。这项研究将对基础科学和应用科学产生广泛的影响。 本科生将参与项目。%该奖项由材料研究和数学科学部门共同资助，隶属于NSF范围内的数学科学优先领域。 提出了一个新的二元合金微观组织演化模型，该模型还包括了合金的弹性和塑性行为随相对浓度的变化。 这项研究将对基础科学和应用科学产生广泛的影响。 本科生将参与项目。*

This award is co-funded by the Divisions of Materials Research and Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area. A phase field crystal (PFC) model has been developed to study elastic behavior in the crystallization of pure materials. This was achieved by modeling the mass density on diffusive time and atomic length scales. The PFC approach naturally incorporates elastic and plastic deformations, multiple crystal orientations and free surfaces and was used to study grain boundary energy, liquid phase epitaxial growth and the yield strength of nano-crystalline solids. One ingredient not included in the original work was concentration which is particularly important since most materials contain at least two elements and the relative concentration of the elements can significantly impact the non-equilibrium processes and resulting microstructures. In addition, since all elements have different lattice structures and sizes, elastic and plastic deformations are strongly influenced by concentration. The goal of the proposed research is to develop a computationally efficient model of microstructure formation and stability in binary alloy crystallization phenomena and to use this model to study technologically important applications such as dendritic growth, eutectic crystallization and liquid phase epitaxial growth in binary alloys. The model will be developed by introducing a density field for each element, constructing an appropriate free energy functional F of these fields and assuming the dynamics are dissipative and driven to minimize F. The PI has extensive experience in constructing such models and has developed, in collaboration with others, models of eutectic solidification, driven charge density waves, polymorphic crystallization and imbibition. For the purposes of this research the PI has developed a preliminary model of binary alloy crystallization that includes elastic and plastic deformation. This model combines the PFC approach with a model of eutectic solidification. Initial calculations indicate that this preliminary model incorporates the generic features of a eutectic phase diagram and many of the typical patterns observed in non-equilibrium phenomena such as dendrites and eutectic crystallites with lamellar structures. In addition to these standard features the model includes all the elastic behavior incorporated in the original PFC model discussed above and was designed so that the concentration dependence of the lattice and elastic constants can be easily adjusted. While this preliminary model may need to be fine tuned, these initial calculations indicate a high likelihood that the PI will accomplish the primary goals of this project. The research will have broad impact on both fundamental and applied science. Undergraduate students will be involved in the projects.%%% This award is co-funded by the Divisions of Materials Research and Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area. A new model has been developed to describe microstructural evolution of binary alloys that also includes their elastic and plastic behavior as a function of their relative concentration. The research will have broad impact on both fundamental and applied science. Undergraduate students will be involved in the projects.***