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Published June 7, 2015 | Erratum + Published + Supplemental Material
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Phase stability in nanoscale material systems: extension from bulk phase diagrams

Abstract

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.

Additional Information

© 2015 The Royal Society of Chemistry. Received 09 Mar 2015, Accepted 15 Apr 2015, First published online 22 Apr 2015. The authors thank Intel Corporation for the specific project definition, and the internship opportunity. The Materials and Process Simulation Center (MSC) at Caltech (with funding from DARPA W31P4Q-13-1-0010), and the Chemical Engineering Cluster at Texas A&M University are acknowledged for providing computing resources useful in conducting the research reported in this work.

Attached Files

Published - c5nr01535a.pdf

Supplemental Material - c5nr01535a1.pdf

Erratum - c5nr90199e_er.pdf

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August 20, 2023
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