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Title: A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations

Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. Continuum partial differential equations (PDEs) of atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability, accuracy and robustness of numerical methods to solve these PDEs are sensitive to the particular functional representations of the free energy. In this communication we investigate the influence of different representations of thermodynamic data on phase field computations of diffusion and two-phase reactions in the solid state. First-principles statistical mechanics methods were used to generate realistic free energy data for HCP titanium with interstitially dissolved oxygen. While Redlich-Kister polynomials have formed the mainstay of thermodynamic descriptions of multi-component solids, they require high order terms to fit oscillations in chemical potentials around phase transitions. Here, we demonstrate that high fidelity fits to rapidly fluctuating free energy functions are obtained with spline functions. As a result, spline functions that are many degrees lower than Redlich-Kister polynomials provide equal or superior fits to chemical potential data and, when used in phase field computations, result in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials.
Authors:
 [1] ;  [2] ;  [1] ;  [2] ;  [1] ;  [2] ;  [1]
  1. Univ. of Michigan, Ann Arbor, MI (United States)
  2. Univ. of California, Santa Barbara, CA (United States)
Publication Date:
Grant/Contract Number:
SC0008637
Type:
Accepted Manuscript
Journal Name:
Computational Materials Science
Additional Journal Information:
Journal Volume: 128; Journal ID: ISSN 0927-0256
Publisher:
Elsevier
Research Org:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; free energy; spinodal decomposition; phase transformation
OSTI Identifier:
1332699

Teichert, Gregory H., Gunda, N. S. Harsha, Rudraraju, Shiva, Natarajan, Anirudh Raju, Puchala, Brian, Van der Ven, Anton, and Garikipati, Krishna. A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations. United States: N. p., Web. doi:10.1016/j.commatsci.2016.11.024.
Teichert, Gregory H., Gunda, N. S. Harsha, Rudraraju, Shiva, Natarajan, Anirudh Raju, Puchala, Brian, Van der Ven, Anton, & Garikipati, Krishna. A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations. United States. doi:10.1016/j.commatsci.2016.11.024.
Teichert, Gregory H., Gunda, N. S. Harsha, Rudraraju, Shiva, Natarajan, Anirudh Raju, Puchala, Brian, Van der Ven, Anton, and Garikipati, Krishna. 2016. "A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations". United States. doi:10.1016/j.commatsci.2016.11.024. https://www.osti.gov/servlets/purl/1332699.
@article{osti_1332699,
title = {A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations},
author = {Teichert, Gregory H. and Gunda, N. S. Harsha and Rudraraju, Shiva and Natarajan, Anirudh Raju and Puchala, Brian and Van der Ven, Anton and Garikipati, Krishna},
abstractNote = {Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. Continuum partial differential equations (PDEs) of atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability, accuracy and robustness of numerical methods to solve these PDEs are sensitive to the particular functional representations of the free energy. In this communication we investigate the influence of different representations of thermodynamic data on phase field computations of diffusion and two-phase reactions in the solid state. First-principles statistical mechanics methods were used to generate realistic free energy data for HCP titanium with interstitially dissolved oxygen. While Redlich-Kister polynomials have formed the mainstay of thermodynamic descriptions of multi-component solids, they require high order terms to fit oscillations in chemical potentials around phase transitions. Here, we demonstrate that high fidelity fits to rapidly fluctuating free energy functions are obtained with spline functions. As a result, spline functions that are many degrees lower than Redlich-Kister polynomials provide equal or superior fits to chemical potential data and, when used in phase field computations, result in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials.},
doi = {10.1016/j.commatsci.2016.11.024},
journal = {Computational Materials Science},
number = ,
volume = 128,
place = {United States},
year = {2016},
month = {12}
}