Bajaj Saurabh, Haverty Michael G, Arróyave Raymundo, Goddard William A, Shankar Sadasivan
Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, CA 91125, USA.
Nanoscale. 2015 Jun 7;7(21):9868-77. doi: 10.1039/c5nr01535a.
Phase diagrams of multi-component systems are critical for the development and engineering of material alloys for all technological applications. At nano dimensions, surfaces (and interfaces) play a significant role in changing equilibrium thermodynamics and phase stability. In this work, it is shown that these surfaces at small dimensions affect the relative equilibrium thermodynamics of the different phases. The CALPHAD approach for material surfaces (also termed "nano-CALPHAD") is employed to investigate these changes in three binary systems by calculating their phase diagrams at nano dimensions and comparing them with their bulk counterparts. The surface energy contribution, which is the dominant factor in causing these changes, is evaluated using the spherical particle approximation. It is first validated with the Au-Si system for which experimental data on phase stability of spherical nano-sized particles is available, and then extended to calculate phase diagrams of similarly sized particles of Ge-Si and Al-Cu. Additionally, the surface energies of the associated compounds are calculated using DFT, and integrated into the thermodynamic model of the respective binary systems. In this work we found changes in miscibilities, reaction compositions of about 5 at%, and solubility temperatures ranging from 100-200 K for particles of sizes 5 nm, indicating the importance of phase equilibrium analysis at nano dimensions.
多组分体系的相图对于所有技术应用中材料合金的开发和工程设计至关重要。在纳米尺度下，表面（和界面）在改变平衡热力学和相稳定性方面起着重要作用。在这项工作中，研究表明这些小尺寸的表面会影响不同相的相对平衡热力学。采用针对材料表面的CALPHAD方法（也称为“纳米CALPHAD”），通过计算三个二元体系在纳米尺度下的相图并将其与相应的体相相图进行比较，来研究这些变化。使用球形颗粒近似法评估导致这些变化 的主要因素——表面能贡献。首先用有球形纳米尺寸颗粒相稳定性实验数据的Au-Si体系进行验证，然后扩展到计算类似尺寸的Ge-Si和Al-Cu颗粒的相图。此外，使用密度泛函理论（DFT）计算相关化合物的表面能，并将其纳入各自二元体系的热力学模型。在这项工作中，我们发现对于5nm尺寸的颗粒，其混溶性、反应组成变化约5 at%，以及溶解温度在100 - 200 K范围内发生了变化，这表明纳米尺度下相平衡分析的重要性。
