Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Direct evaluation of the phase diagrams of dense multicomponent plasmas by integration of the Clapeyron equations

Abstract

Accurate phase diagrams of multicomponent plasmas are required for the modeling of dense stellar plasmas, such as those found in the cores of white dwarf stars and the crusts of neutron stars. Those phase diagrams have been computed using a variety of standard techniques, which suffer from physical and computational limitations. Here we present an efficient and accurate method that overcomes the drawbacks of previously used approaches. In particular, finite-size effects are avoided as each phase is calculated separately; the plasma electrons and volume changes are explicitly taken into account; and arbitrary analytic fits to simulation data as well as particle insertions are avoided. Furthermore, no simulations at “uninteresting” state conditions, i.e., away from the phase coexistence curves, are required, which improves the efficiency of the technique. The method consists of an adaptation of the so-called Gibbs-Duhem integration approach to electron-ion plasmas, where the coexistence curve is determined by direct numerical integration of its underlying Clapeyron equation. The thermodynamics properties of the coexisting phases are evaluated separately using Monte Carlo simulations in the isobaric semigrand canonical ensemble (NPT Δ μ). We describe this Monte Carlo-based Clapeyron integration method, including its basic physical and numerical principles, our extension to electron-ion plasmas,more » and our numerical implementation. We illustrate its applicability and benefits with the calculation of the melting curve of dense carbon-oxygen plasmas under conditions relevant for the cores of white dwarf stars and provide analytic fits to implement this new melting curve in white dwarf models. While this work focuses on the liquid-solid phase boundary of dense two-component plasmas, a wider range of physical systems and phase boundaries are within the scope of the Clapeyron integration method, which had until now only been applied to simple model systems of neutral particles.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1825416
Report Number(s):
LA-UR-21-20287
Journal ID: ISSN 2470-0045; TRN: US2215799
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 103; Journal Issue: 4; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Blouin, Simon, and Daligault, Jerome Olivier. Direct evaluation of the phase diagrams of dense multicomponent plasmas by integration of the Clapeyron equations. United States: N. p., 2021. Web. doi:10.1103/physreve.103.043204.
Copy to clipboard
Blouin, Simon, & Daligault, Jerome Olivier. Direct evaluation of the phase diagrams of dense multicomponent plasmas by integration of the Clapeyron equations. United States. https://doi.org/10.1103/physreve.103.043204
Copy to clipboard
Blouin, Simon, and Daligault, Jerome Olivier. Thu . "Direct evaluation of the phase diagrams of dense multicomponent plasmas by integration of the Clapeyron equations". United States. https://doi.org/10.1103/physreve.103.043204. https://www.osti.gov/servlets/purl/1825416.
Copy to clipboard
@article{osti_1825416,
title = {Direct evaluation of the phase diagrams of dense multicomponent plasmas by integration of the Clapeyron equations},
author = {Blouin, Simon and Daligault, Jerome Olivier},
abstractNote = {Accurate phase diagrams of multicomponent plasmas are required for the modeling of dense stellar plasmas, such as those found in the cores of white dwarf stars and the crusts of neutron stars. Those phase diagrams have been computed using a variety of standard techniques, which suffer from physical and computational limitations. Here we present an efficient and accurate method that overcomes the drawbacks of previously used approaches. In particular, finite-size effects are avoided as each phase is calculated separately; the plasma electrons and volume changes are explicitly taken into account; and arbitrary analytic fits to simulation data as well as particle insertions are avoided. Furthermore, no simulations at “uninteresting” state conditions, i.e., away from the phase coexistence curves, are required, which improves the efficiency of the technique. The method consists of an adaptation of the so-called Gibbs-Duhem integration approach to electron-ion plasmas, where the coexistence curve is determined by direct numerical integration of its underlying Clapeyron equation. The thermodynamics properties of the coexisting phases are evaluated separately using Monte Carlo simulations in the isobaric semigrand canonical ensemble (NPT Δ μ). We describe this Monte Carlo-based Clapeyron integration method, including its basic physical and numerical principles, our extension to electron-ion plasmas, and our numerical implementation. We illustrate its applicability and benefits with the calculation of the melting curve of dense carbon-oxygen plasmas under conditions relevant for the cores of white dwarf stars and provide analytic fits to implement this new melting curve in white dwarf models. While this work focuses on the liquid-solid phase boundary of dense two-component plasmas, a wider range of physical systems and phase boundaries are within the scope of the Clapeyron integration method, which had until now only been applied to simple model systems of neutral particles.},
doi = {10.1103/physreve.103.043204},
journal = {Physical Review E},
number = 4,
volume = 103,
place = {United States},
year = {Thu Apr 15 00:00:00 EDT 2021},
month = {Thu Apr 15 00:00:00 EDT 2021}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/physreve.103.043204
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Melting of the Wigner crystal at finite temperature
journal, August 1987

Statistical thermodynamics of polydisperse fluids
journal, April 1984

  • Briano, J. G.; Glandt, E. D.
  • The Journal of Chemical Physics, Vol. 80, Issue 7
  • DOI: 10.1063/1.447087

Numerical simulation of strongly coupled binary ionic plasmas
journal, October 1996

Electron–Ion Scattering in Dense Multi-Component Plasmas: Application to the Outer Crust of an Accreting Neutron star
journal, September 2009

Phase separation in hydrogen-helium mixtures at Mbar pressures
journal, January 2009

  • Morales, M. A.; Schwegler, E.; Ceperley, D.
  • Proceedings of the National Academy of Sciences, Vol. 106, Issue 5
  • DOI: 10.1073/pnas.0812581106

Phase diagram of Yukawa systems near the one‐component‐plasma limit revisited
journal, November 1996

  • Hamaguchi, S.; Farouki, R. T.; Dubin, D. H. E.
  • The Journal of Chemical Physics, Vol. 105, Issue 17
  • DOI: 10.1063/1.472802

22 Ne Phase Separation as a Solution to the Ultramassive White Dwarf Cooling Anomaly
journal, April 2021

  • Blouin, Simon; Daligault, Jérôme; Saumon, Didier
  • The Astrophysical Journal Letters, Vol. 911, Issue 1
  • DOI: 10.3847/2041-8213/abf14b

Crystallization of classical multicomponent plasmas
journal, March 2010

The Lennard-Jones equation of state revisited
journal, February 1993

Error estimates on averages of correlated data
journal, July 1989

  • Flyvbjerg, H.; Petersen, H. G.
  • The Journal of Chemical Physics, Vol. 91, Issue 1
  • DOI: 10.1063/1.457480

A Eutectic in Carbon-Oxygen White Dwarfs ?
journal, March 1980

The Principles of Chemical Equilibrium
book, January 1981

Crystallization of Carbon-Oxygen Mixtures in White Dwarf Stars
journal, June 2010

Equation of state of the one-component plasma derived from precision Monte Carlo calculations
journal, January 1990

  • Stringfellow, Guy S.; DeWitt, Hugh E.; Slattery, W. L.
  • Physical Review A, Vol. 41, Issue 2
  • DOI: 10.1103/PhysRevA.41.1105

Direct molecular dynamics simulation of liquid-solid phase equilibria for two-component plasmas
journal, June 2012

Equation of state of fully ionized electron-ion plasmas. II. Extension to relativistic densities and to the solid phase
journal, December 2000

Thermodynamic and structural properties of model systems at solid-fluid coexistence: I. Fcc and bcc soft spheres
journal, May 1995

Universal scaling in complex (dusty) plasmas
journal, July 2002

Effects of Fe/C phase separation on the ages of white dwarfs
journal, March 1992

  • Xu, Z. W.; van Horn, H. M.
  • The Astrophysical Journal, Vol. 387
  • DOI: 10.1086/171115

Triple point of Yukawa systems
journal, October 1997

Direct evaluation of phase coexistence by molecular simulation via integration along the saturation line
journal, March 1993

  • Kofke, David A.
  • The Journal of Chemical Physics, Vol. 98, Issue 5
  • DOI: 10.1063/1.465023

Ewald sums for Yukawa potentials
journal, December 2000

  • Salin, Gwenaël; Caillol, Jean-Michel
  • The Journal of Chemical Physics, Vol. 113, Issue 23
  • DOI: 10.1063/1.1326477

Core crystallization and pile-up in the cooling sequence of evolving white dwarfs
journal, January 2019

  • Tremblay, Pier-Emmanuel; Fontaine, Gilles; Fusillo, Nicola Pietro Gentile
  • Nature, Vol. 565, Issue 7738
  • DOI: 10.1038/s41586-018-0791-x

Monte Carlo simulations of complete phase diagrams for binary Lennard–Jones mixtures
journal, June 2001

Validity of the linear mixing rule for strongly coupled ionic fluids
journal, October 2003

The Potential of White Dwarf Cosmochronology
journal, April 2001

  • Fontaine, G.; Brassard, P.; Bergeron, P.
  • Publications of the Astronomical Society of the Pacific, Vol. 113, Issue 782
  • DOI: 10.1086/319535

Phase separation in the crust of accreting neutron stars
journal, June 2007

Thermal energy of the crystalline one-component plasma from dynamical simulations
journal, June 1993

First-order anharmonic correction to the free energy of a Coulomb crystal in periodic boundary conditions
journal, October 1990

Equilibria between solid, liquid, and vapor phases in binary Lennard–Jones mixtures
journal, March 2002

On the relativistic degenerate electron gas
journal, July 1962

Evolution of crystallizing pure C-12 white dwarfs
journal, September 1975

  • Lamb, D. Q.; van Horn, H. M.
  • The Astrophysical Journal, Vol. 200
  • DOI: 10.1086/153789

Cooling theory of crystallized white dwarfs
journal, October 1994

  • Segretain, L.; Chabrier, G.; Hernanz, M.
  • The Astrophysical Journal, Vol. 434
  • DOI: 10.1086/174766

The Physics of Crystallizing White Dwarfs
journal, August 1997

  • Isern, J.; Mochkovitch, R.; Garcia‐Berro, E.
  • The Astrophysical Journal, Vol. 485, Issue 1
  • DOI: 10.1086/304425

Physics of Iron at Earth's Core Conditions
journal, February 2000

Equations of state and phase diagrams for dense multi-ionic mixture plasmas
journal, August 1993

Coexistence diagrams of mixtures by molecular simulation
journal, August 1994

Direct molecular dynamics simulation of liquid-solid phase equilibria for a three-component plasma
journal, December 2012

Molecular simulation of complete phase diagrams for binary mixtures
journal, July 2001

Thermodynamics of strongly‐coupled Yukawa systems near the one‐component‐plasma limit. II. Molecular dynamics simulations
journal, December 1994

  • Farouki, R. T.; Hamaguchi, S.
  • The Journal of Chemical Physics, Vol. 101, Issue 11
  • DOI: 10.1063/1.467955

Statistical mechanics of dense ionized matter. VII. Equation of state and phase separation of ionic mixtures in a uniform background
journal, November 1977

Freezing transition and phase diagram of dense carbon-oxygen mixtures in white dwarfs
journal, November 1988

  • Ichimaru, Setsuo; Iyetomi, Hiroshi; Ogata, Shuji
  • The Astrophysical Journal, Vol. 334
  • DOI: 10.1086/185303

Critical examination of N dependence in the Monte Carlo calculations for a classical one-component plasma
journal, December 1987

New phase diagrams for dense carbon-oxygen mixtures and white dwarf evolution
journal, December 2011

Effect of pressure on the complete phase behavior of binary mixtures
journal, January 2004

  • Lamm, Monica H.; Hall, Carol K.
  • AIChE Journal, Vol. 50, Issue 1
  • DOI: 10.1002/aic.10020

Monte Carlo simulation of multicomponent equilibria in a semigrand canonical ensemble
journal, August 1988

Toward precision cosmochronology: A new C/O phase diagram for white dwarfs
journal, August 2020

Properties of high-density binary mixtures and the age of the Universe from white dwarf stars
journal, June 1988

  • Garcja-Berro, E.; Hernanz, M.; Isern, J.
  • Nature, Vol. 333, Issue 6174
  • DOI: 10.1038/333642a0

Solid-Fluid Coexistence for Inverse-Power Potentials
journal, January 1995

The Energetics of Crystallizing White Dwarfs Revisited Again
journal, January 2000

  • Isern, J.; Garcia‐Berro, E.; Hernanz, M.
  • The Astrophysical Journal, Vol. 528, Issue 1
  • DOI: 10.1086/308153

Solid–liquid phase equilibrium for binary Lennard-Jones mixtures
journal, June 1999

  • Hitchcock, Monica R.; Hall, Carol K.
  • The Journal of Chemical Physics, Vol. 110, Issue 23
  • DOI: 10.1063/1.479084

Improved equation of state for the classical one-component plasma
journal, June 1980

    Sort by:
    [ × clear filter / sort ]

    Similar Records in DOE PAGES and OSTI.GOV collections: