Elastic and Plastic Deformation in Binary Alloy Crystallization

该奖项由材料研究部和数学科学部共同资助，隶属于美国国家科学基金会数学科学优先领域。为了研究纯材料结晶过程中的弹性行为，建立了相场晶体（PFC）模型。这是通过在扩散时间和原子长度尺度上模拟质量密度来实现的。PFC方法自然地结合了弹塑性变形、多晶向和自由表面，并用于研究纳米晶体固体的晶界能、液相外延生长和屈服强度。原始工作中没有包括的一个因素是浓度，这是特别重要的，因为大多数材料包含至少两种元素，元素的相对浓度可以显著影响非平衡过程和由此产生的微观结构。此外，由于所有元素具有不同的晶格结构和尺寸，因此弹塑性变形受到浓度的强烈影响。提出的研究目标是建立一个计算效率高的二元合金结晶现象的微观结构形成和稳定性模型，并利用该模型研究二元合金中枝晶生长、共晶结晶和液相外延生长等技术上重要的应用。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函数F，并假设动力学是耗散的，并且驱动到最小F来开发。PI在构建此类模型方面具有丰富的经验，并与他人合作开发了共晶凝固、驱动电荷密度波、多晶结晶和吸胀模型。为了本研究的目的，PI开发了一个包括弹性和塑性变形的二元合金结晶的初步模型。该模型结合了PFC方法和共晶凝固模型。初步计算表明，该初步模型结合了共晶相图的一般特征和许多在非平衡现象中观察到的典型模式，如具有片层结构的枝晶和共晶。除了这些标准特征外，该模型还包括上述原始PFC模型中包含的所有弹性行为，并且设计得使晶格常数和弹性常数的浓度依赖性可以很容易地调整。虽然这个初步模型可能需要进行微调，但这些初始计算表明PI很有可能实现这个项目的主要目标。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。该奖项由材料研究部和数学科学部共同资助，隶属于美国国家科学基金会数学科学优先领域。建立了一种新的模型来描述二元合金的微观组织演变，包括它们的弹性和塑性行为作为它们相对浓度的函数。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.***