Determining phase transition using potential energy distribution and surface energy of Pd nanoparticles

Maryam Azadeh; Movaffaq Kateb; Pirooz Marashi

doi:10.1016/j.commatsci.2019.109187

Determining phase transition using potential energy distribution and surface energy of Pd nanoparticles

Maryam Azadeh, Movaffaq Kateb, Pirooz Marashi^*

^*Corresponding author for this work

Reykjavik University

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Molecular dynamics simulation is employed to understand the thermodynamic behavior of cuboctahedron (cub) and icosahedron (ico) nanoparticles with 2–20 number of shells (55–28,741 atoms). The embedded atom method was used to describe the interatomic potential. Conventional melting criteria such as potential energy and specific heat capacity (C_p) caloric curves as well as structure analysis by radial distribution function (G(r)) and common neighbor analysis (CNA) were utilized simultaneously to provide a comprehensive picture of the melting process. It is shown that the potential energy distribution and surface energy (γ_p) proposed here are holding several advantages over previous criteria. In particular, potential energy distribution can distinguish between interior and surface atoms and even corner, edge and plane atoms at the surface. While G(r) and CNA are not surface sensitive methods and cannot distinguish between surface melting and an allotropic transition. It is also shown that allotropic change appears more clearly in C_p and γ_p rather than potential energy. However, determining accurate C_p requires enough sampling to be averaged. Finally, a few issues in the current methods for determining γ_p were discussed and a simple method based on available models was proposed which, independent of estimation of the surface area, predicts the correct temperature and size-dependent trend in agreement with Guggenheim-Katayama and Tolman's models, respectively.

Original language	English
Article number	109187
Journal	Computational Materials Science
Volume	170
DOIs	https://doi.org/10.1016/j.commatsci.2019.109187
Publication status	Published - Dec 2019

Bibliographical note

Funding Information:
The Authors would like to thank Dr. Ebrahim Tayyebi and professor Hamid Modarress from Physical Chemistry groups respectively at University of Iceland and Amirkabir University of Technology for sharing their expertise in the surface energy calculation. This work is partially supported by University of Iceland Research Fund .

Funding Information:
The Authors would like to thank Dr. Ebrahim Tayyebi and professor Hamid Modarress from Physical Chemistry groups respectively at University of Iceland and Amirkabir University of Technology for sharing their expertise in the surface energy calculation. This work is partially supported by University of Iceland Research Fund.

Publisher Copyright:
© 2019 Elsevier B.V.

Other keywords

Allotropic transition
Melting
Nanoparticle
Potential energy distribution
Surface energy

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10.1016/j.commatsci.2019.109187

Cite this

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title = "Determining phase transition using potential energy distribution and surface energy of Pd nanoparticles",

abstract = "Molecular dynamics simulation is employed to understand the thermodynamic behavior of cuboctahedron (cub) and icosahedron (ico) nanoparticles with 2–20 number of shells (55–28,741 atoms). The embedded atom method was used to describe the interatomic potential. Conventional melting criteria such as potential energy and specific heat capacity (Cp) caloric curves as well as structure analysis by radial distribution function (G(r)) and common neighbor analysis (CNA) were utilized simultaneously to provide a comprehensive picture of the melting process. It is shown that the potential energy distribution and surface energy (γp) proposed here are holding several advantages over previous criteria. In particular, potential energy distribution can distinguish between interior and surface atoms and even corner, edge and plane atoms at the surface. While G(r) and CNA are not surface sensitive methods and cannot distinguish between surface melting and an allotropic transition. It is also shown that allotropic change appears more clearly in Cp and γp rather than potential energy. However, determining accurate Cp requires enough sampling to be averaged. Finally, a few issues in the current methods for determining γp were discussed and a simple method based on available models was proposed which, independent of estimation of the surface area, predicts the correct temperature and size-dependent trend in agreement with Guggenheim-Katayama and Tolman's models, respectively.",

keywords = "Allotropic transition, Melting, Nanoparticle, Potential energy distribution, Surface energy",

author = "Maryam Azadeh and Movaffaq Kateb and Pirooz Marashi",

note = "Funding Information: The Authors would like to thank Dr. Ebrahim Tayyebi and professor Hamid Modarress from Physical Chemistry groups respectively at University of Iceland and Amirkabir University of Technology for sharing their expertise in the surface energy calculation. This work is partially supported by University of Iceland Research Fund . Funding Information: The Authors would like to thank Dr. Ebrahim Tayyebi and professor Hamid Modarress from Physical Chemistry groups respectively at University of Iceland and Amirkabir University of Technology for sharing their expertise in the surface energy calculation. This work is partially supported by University of Iceland Research Fund. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

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N1 - Funding Information: The Authors would like to thank Dr. Ebrahim Tayyebi and professor Hamid Modarress from Physical Chemistry groups respectively at University of Iceland and Amirkabir University of Technology for sharing their expertise in the surface energy calculation. This work is partially supported by University of Iceland Research Fund . Funding Information: The Authors would like to thank Dr. Ebrahim Tayyebi and professor Hamid Modarress from Physical Chemistry groups respectively at University of Iceland and Amirkabir University of Technology for sharing their expertise in the surface energy calculation. This work is partially supported by University of Iceland Research Fund. Publisher Copyright: © 2019 Elsevier B.V.

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N2 - Molecular dynamics simulation is employed to understand the thermodynamic behavior of cuboctahedron (cub) and icosahedron (ico) nanoparticles with 2–20 number of shells (55–28,741 atoms). The embedded atom method was used to describe the interatomic potential. Conventional melting criteria such as potential energy and specific heat capacity (Cp) caloric curves as well as structure analysis by radial distribution function (G(r)) and common neighbor analysis (CNA) were utilized simultaneously to provide a comprehensive picture of the melting process. It is shown that the potential energy distribution and surface energy (γp) proposed here are holding several advantages over previous criteria. In particular, potential energy distribution can distinguish between interior and surface atoms and even corner, edge and plane atoms at the surface. While G(r) and CNA are not surface sensitive methods and cannot distinguish between surface melting and an allotropic transition. It is also shown that allotropic change appears more clearly in Cp and γp rather than potential energy. However, determining accurate Cp requires enough sampling to be averaged. Finally, a few issues in the current methods for determining γp were discussed and a simple method based on available models was proposed which, independent of estimation of the surface area, predicts the correct temperature and size-dependent trend in agreement with Guggenheim-Katayama and Tolman's models, respectively.

AB - Molecular dynamics simulation is employed to understand the thermodynamic behavior of cuboctahedron (cub) and icosahedron (ico) nanoparticles with 2–20 number of shells (55–28,741 atoms). The embedded atom method was used to describe the interatomic potential. Conventional melting criteria such as potential energy and specific heat capacity (Cp) caloric curves as well as structure analysis by radial distribution function (G(r)) and common neighbor analysis (CNA) were utilized simultaneously to provide a comprehensive picture of the melting process. It is shown that the potential energy distribution and surface energy (γp) proposed here are holding several advantages over previous criteria. In particular, potential energy distribution can distinguish between interior and surface atoms and even corner, edge and plane atoms at the surface. While G(r) and CNA are not surface sensitive methods and cannot distinguish between surface melting and an allotropic transition. It is also shown that allotropic change appears more clearly in Cp and γp rather than potential energy. However, determining accurate Cp requires enough sampling to be averaged. Finally, a few issues in the current methods for determining γp were discussed and a simple method based on available models was proposed which, independent of estimation of the surface area, predicts the correct temperature and size-dependent trend in agreement with Guggenheim-Katayama and Tolman's models, respectively.

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Determining phase transition using potential energy distribution and surface energy of Pd nanoparticles

Abstract

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