Information Entropy of Liquid Metals

Gao, M. C.; Widom, M.

doi:10.1021/acs.jpcb.7b10723

Title: Information Entropy of Liquid Metals

Abstract

Correlations reduce the configurational entropies of liquids below their ideal gas limits. By means of first-principles molecular dynamics simulations, we obtain accurate pair correlation functions of liquid metals, then subtract the mutual information content of these correlations from the ideal gas entropies to predict the absolute entropies over a broad range of temperatures. We apply this method to liquid aluminum and copper and demonstrate good agreement with experimental measurements; then, we apply it to predict the entropy of a liquid aluminum–copper alloy. In conclusion, corrections due to electronic entropy and many-body correlations are discussed.

Authors:

Gao, M. C. ^[1];

^[2]

National Energy Technology Lab. (NETL), Albany, OR (United States); AECOM, Albany, OR (United States)
Carnegie Mellon Univ., Pittsburgh, PA (United States)

Publication Date:: Tue Feb 20 00:00:00 EST 2018

Research Org.:: National Energy Technology Lab. (NETL), Albany, OR (United States)

Sponsoring Org.:: USDOE Office of Fossil Energy (FE)

OSTI Identifier:: 1478391

Grant/Contract Number:: SC0014506; FE0004000

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Physical Chemistry. B, Condensed Matter, Materials, Surfaces, Interfaces and Biophysical Chemistry

Additional Journal Information:: Journal Volume: 122; Journal Issue: 13; Journal ID: ISSN 1520-6106

Publisher:: American Chemical Society

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats


                    Gao, M. C., and Widom, M. Information Entropy of Liquid Metals.  United States: N. p., 2018. 
Web.  doi:10.1021/acs.jpcb.7b10723.

Copy to clipboard


                    Gao, M. C., & Widom, M. Information Entropy of Liquid Metals.  United States.  https://doi.org/10.1021/acs.jpcb.7b10723

Copy to clipboard


                    Gao, M. C., and Widom, M. Tue .  
"Information Entropy of Liquid Metals".  United States.  https://doi.org/10.1021/acs.jpcb.7b10723.  https://www.osti.gov/servlets/purl/1478391.

Copy to clipboard


                    
@article{osti_1478391,

  title        = {Information Entropy of Liquid Metals},

  author       = {Gao, M. C. and Widom, M.},

  abstractNote = {Correlations reduce the configurational entropies of liquids below their ideal gas limits. By means of first-principles molecular dynamics simulations, we obtain accurate pair correlation functions of liquid metals, then subtract the mutual information content of these correlations from the ideal gas entropies to predict the absolute entropies over a broad range of temperatures. We apply this method to liquid aluminum and copper and demonstrate good agreement with experimental measurements; then, we apply it to predict the entropy of a liquid aluminum–copper alloy. In conclusion, corrections due to electronic entropy and many-body correlations are discussed.},

  doi          = {10.1021/acs.jpcb.7b10723},

  journal      = {Journal of Physical Chemistry. B, Condensed Matter, Materials, Surfaces, Interfaces and Biophysical Chemistry},

  number       = 13,

  volume       = 122,

  place        = {United States},

  year         = {Tue Feb 20 00:00:00 EST 2018},

  month        = {Tue Feb 20 00:00:00 EST 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1021/acs.jpcb.7b10723

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 18 works

Citation information provided by
Web of Science

Figures / Tables:

Figure 1: (a) Radial distribution function g(r) of liquid Al at T=1000 K. (b) Contributions to the entropy of liquid Al integrated from r = 0 up to R.

All figures and tables (5 total)

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

A Mathematical Theory of Communication
journal, July 1948

Shannon, C. E.
Bell System Technical Journal, Vol. 27, Issue 3
DOI: 10.1002/j.1538-7305.1948.tb01338.x

Information Theory and Statistical Mechanics
journal, May 1957

Jaynes, E. T.
Physical Review, Vol. 106, Issue 4
DOI: 10.1103/PhysRev.106.620

Quantum Statistics of Almost Classical Assemblies
journal, July 1933

Kirkwood, John G.
Physical Review, Vol. 44, Issue 1
DOI: 10.1103/PhysRev.44.31

Quantum Statistics of Almost Classical Assemblies
journal, January 1934

Kirkwood, John G.
Physical Review, Vol. 45, Issue 2
DOI: 10.1103/PhysRev.45.116

Microcanonical Ensemble in Quantum Statistical Mechanics
journal, October 1965

Griffiths, Robert B.
Journal of Mathematical Physics, Vol. 6, Issue 10
DOI: 10.1063/1.1704681

Direct entropy calculation from computer simulation of liquids
journal, October 1989

Baranyai, Andras; Evans, Denis J.
Physical Review A, Vol. 40, Issue 7
DOI: 10.1103/PhysRevA.40.3817

Expression in Terms of Molecular Distribution Functions for the Entropy Density in an Infinite System
journal, December 1958

Nettleton, R. E.; Green, M. S.
The Journal of Chemical Physics, Vol. 29, Issue 6
DOI: 10.1063/1.1744724

Entropy and Molecular Correlation Functions in Open Systems. I. Derivation
journal, September 1971

Raveché, Harold J.
The Journal of Chemical Physics, Vol. 55, Issue 5
DOI: 10.1063/1.1676399

Entropy and Molecular Correlation Functions in Open Systems. II Two‐ and Three‐Body Correlations
journal, September 1971

Mountain, Raymond D.; Raveché, Harold J.
The Journal of Chemical Physics, Vol. 55, Issue 5
DOI: 10.1063/1.1676400

From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999

Kresse, G.; Joubert, D.
Physical Review B, Vol. 59, Issue 3, p. 1758-1775
DOI: 10.1103/PhysRevB.59.1758

Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
journal, April 2008

Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gábor I.
Physical Review Letters, Vol. 100, Issue 13
DOI: 10.1103/PhysRevLett.100.136406

Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics
journal, November 2013

Jakse, Noel; Pasturel, Alain
Scientific Reports, Vol. 3, Issue 1
DOI: 10.1038/srep03135

Thermodynamic potentials and distribution functions: II. The HNC equation as an optimized superposition approximation
journal, February 1990

Hernando, J. A.
Molecular Physics, Vol. 69, Issue 2
DOI: 10.1080/00268979000100221

Calculation of the entropy of binary hard sphere mixtures from pair correlation functions
journal, August 1992

Laird, Brian B.; Haymet, A. D. J.
The Journal of Chemical Physics, Vol. 97, Issue 3
DOI: 10.1063/1.463103

Entropy and Diffuse Scattering: Comparison of NbTiVZr and CrMoNbV
journal, September 2015

Widom, Michael
Metallurgical and Materials Transactions A, Vol. 47, Issue 7
DOI: 10.1007/s11661-015-3095-x

Calculation of the entropy from multiparticle correlation functions
journal, April 1992

Laird, Brian B.; Haymet, A. D. J.
Physical Review A, Vol. 45, Issue 8
DOI: 10.1103/PhysRevA.45.5680

Test of the Universal Scaling Law for the Diffusion Coefficient in Liquid Metals
journal, July 2000

Hoyt, J. J.; Asta, Mark; Sadigh, Babak
Physical Review Letters, Vol. 85, Issue 3
DOI: 10.1103/PhysRevLett.85.594

Dependence of solid–liquid interface free energy on liquid structure
journal, July 2014

Wilson, S. R.; Mendelev, M. I.
Modelling and Simulation in Materials Science and Engineering, Vol. 22, Issue 6
DOI: 10.1088/0965-0393/22/6/065004

On the role of density fluctuations in the entropy of a fluid
journal, August 1987

Wallace, Duane C.
The Journal of Chemical Physics, Vol. 87, Issue 4
DOI: 10.1063/1.453158

Excess Entropy, Diffusion Coefficient, Viscosity Coefficient and Surface Tension of Liquid Simple Metals from Diffraction Data
journal, January 2002

Yokoyama, Isao; Tsuchiya, Shusaku
MATERIALS TRANSACTIONS, Vol. 43, Issue 1
DOI: 10.2320/matertrans.43.67

Recent progress in understanding high temperature dynamical properties and fragility in metallic liquids, and their connection with atomic structure
journal, July 2017

Gangopadhyay, A. K.; Kelton, K. F.
Journal of Materials Research, Vol. 32, Issue 14
DOI: 10.1557/jmr.2017.253

A universal scaling law for atomic diffusion in condensed matter
journal, May 1996

Dzugutov, Mikhail
Nature, Vol. 381, Issue 6578
DOI: 10.1038/381137a0

Assessing the performance of recent density functionals for bulk solids
journal, April 2009

Csonka, Gábor I.; Perdew, John P.; Ruzsinszky, Adrienn
Physical Review B, Vol. 79, Issue 15
DOI: 10.1103/PhysRevB.79.155107

The free energy of the crystal-melt interface from the radial distribution function—further calculations
journal, April 1972

Ewing, R. H.
Philosophical Magazine, Vol. 25, Issue 4
DOI: 10.1080/14786437208229303

A universal scaling law for atomic diffusion in condensed matter
journal, May 1996

Dzugutov, Mikhail
Nature, Vol. 381, Issue 6578
DOI: 10.1038/381137a0

Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics
journal, November 2013

Jakse, Noel; Pasturel, Alain
Scientific Reports, Vol. 3, Issue 1
DOI: 10.1038/srep03135

Three-particle contribution to the configurational entropy of simple fluids
journal, July 1990

Baranyai, András; Evans, Denis J.
Physical Review A, Vol. 42, Issue 2
DOI: 10.1103/physreva.42.849

Works referencing / citing this record:

Mutual information does not detect growing correlations in the propensity of a model molecular liquid
journal, January 2019

Tripodo, Antonio; Giuntoli, Andrea; Malvaldi, Marco
Soft Matter, Vol. 15, Issue 34
DOI: 10.1039/c9sm01143a

Modeling the structure and thermodynamics of high-entropy alloys
journal, July 2018

Widom, Michael
Journal of Materials Research, Vol. 33, Issue 19
DOI: 10.1557/jmr.2018.222

Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

Similar Records in DOE PAGES and OSTI.GOV collections:

Ab initio free energies of liquid metal alloys: Application to the phase diagrams of Li-Na and K-Na

Journal Article Huang, Yang ; Widom, Michael ; Gao, Michael C. - Physical Review Materials

Comparison of free energies between different phases and different compositions underlies the prediction of alloy phase diagrams. To allow direct comparison, consistent reference points for the energies or enthalpies are required, and the entropy must be placed on an absolute scale, yielding absolute free energies. Here we derive absolute free energies of liquids from ab-initio molecular dynamics (AIMD) by combining the directly simulated enthalpies with an entropy derived from simulated densities and pair correlation functions. Additionally, as an example of the power of this method we calculate the phase diagrams of two binary alkali metal alloys, Li-Na and K-Na, revealingmore »« less
https://doi.org/10.1103/physrevmaterials.6.013802

Full Text Available
Tailoring magnetic behavior of CoFeMnNiX (X = Al, Cr, Ga, and Sn) high entropy alloys by metal doping

Journal Article Zuo, Tingting ; Gao, Michael C. ; Ouyang, Lizhi ; ... - Acta Materialia

Magnetic materials with excellent performances are desired for functional applications. Based on the high-entropy effect, a system of CoFeMnNiX (X = Al, Cr, Ga, and Sn) magnetic alloys are designed and investigated. The dramatic change in phase structures from face-centered-cubic (FCC) to ordered body-centered-cubic (BCC) phases, caused by adding Al, Ga, and Sn in CoFeMnNiX alloys, originates from the potent short-range chemical order in the liquid state predicted by ab initio molecular dynamics (AIMD) simulations. This phase transition leads to the significant enhancement of the saturation magnetization (M_s), e.g., the CoFeMnNiAl alloy has M_s of 147.86 Am²/kg. In conclusion, first-principlesmore »« less
Cited by 149
https://doi.org/10.1016/j.actamat.2017.03.013

Full Text Available
First-principles prediction of high-entropy-alloy stability

Journal Article Feng, Rui ; Liaw, Peter K. ; Gao, Michael C. ; ... - npj Computational Materials

High entropy alloys (HEAs) are multicomponent compounds whose high configurational entropy allows them to solidify into a single phase, with a simple crystal lattice structure. Some HEAs exhibit desirable properties, such as high specific strength, ductility, and corrosion resistance, while challenging the scientist to make confident predictions in the face of multiple competing phases. We demonstrate phase stability in the multicomponent alloy system of Cr–Mo–Nb–V, for which some of its binary subsystems are subject to phase separation and complex intermetallic-phase formation. Our first-principles calculation of free energy predicts that the configurational entropy stabilizes a single body-centered cubic (BCC) phase frommore »« less
Cited by 62
https://doi.org/10.1038/s41524-017-0049-4

Full Text Available
Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions

Journal Article Nicholson, Donald M. ; Gao, C. Y. ; McDonnell, Marshall T. ; ... - Entropy

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson’s theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs–Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pairmore »« less
https://doi.org/10.3390/e23020234

Full Text Available
Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements

Journal Article Huang, Yang ; Widom, Michael - Entropy

The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the N-body distribution of atomic displacements, ρ_N. We calculate the information-theoretic entropy from the expectation value of lnρ_N. At a first level of approximation, treating individual atomic displacements independently, our method may be applied using Debye–Waller B-factors, allowing diffraction experiments to obtain an upper bound on the thermodynamic entropy. At the next level of approximation we correct the overestimation through inclusion of displacement covariances. Wemore »« less
https://doi.org/10.3390/e24050618

Similar Records

Title: Information Entropy of Liquid Metals

Abstract

Citation Formats

Figures / Tables:

A Mathematical Theory of Communication journal, July 1948

Information Theory and Statistical Mechanics journal, May 1957

Quantum Statistics of Almost Classical Assemblies journal, July 1933

Quantum Statistics of Almost Classical Assemblies journal, January 1934

Microcanonical Ensemble in Quantum Statistical Mechanics journal, October 1965

Direct entropy calculation from computer simulation of liquids journal, October 1989

Expression in Terms of Molecular Distribution Functions for the Entropy Density in an Infinite System journal, December 1958

Entropy and Molecular Correlation Functions in Open Systems. I. Derivation journal, September 1971

Entropy and Molecular Correlation Functions in Open Systems. II Two‐ and Three‐Body Correlations journal, September 1971

From ultrasoft pseudopotentials to the projector augmented-wave method journal, January 1999

Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces journal, April 2008

Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics journal, November 2013

Thermodynamic potentials and distribution functions: II. The HNC equation as an optimized superposition approximation journal, February 1990

Calculation of the entropy of binary hard sphere mixtures from pair correlation functions journal, August 1992

Entropy and Diffuse Scattering: Comparison of NbTiVZr and CrMoNbV journal, September 2015

Calculation of the entropy from multiparticle correlation functions journal, April 1992

Test of the Universal Scaling Law for the Diffusion Coefficient in Liquid Metals journal, July 2000

Dependence of solid–liquid interface free energy on liquid structure journal, July 2014

On the role of density fluctuations in the entropy of a fluid journal, August 1987

Excess Entropy, Diffusion Coefficient, Viscosity Coefficient and Surface Tension of Liquid Simple Metals from Diffraction Data journal, January 2002

Recent progress in understanding high temperature dynamical properties and fragility in metallic liquids, and their connection with atomic structure journal, July 2017

A universal scaling law for atomic diffusion in condensed matter journal, May 1996

Assessing the performance of recent density functionals for bulk solids journal, April 2009

The free energy of the crystal-melt interface from the radial distribution function—further calculations journal, April 1972

A universal scaling law for atomic diffusion in condensed matter journal, May 1996

Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics journal, November 2013

Three-particle contribution to the configurational entropy of simple fluids journal, July 1990

Mutual information does not detect growing correlations in the propensity of a model molecular liquid journal, January 2019

Modeling the structure and thermodynamics of high-entropy alloys journal, July 2018

A Mathematical Theory of Communication
journal, July 1948

Information Theory and Statistical Mechanics
journal, May 1957

Quantum Statistics of Almost Classical Assemblies
journal, July 1933

Quantum Statistics of Almost Classical Assemblies
journal, January 1934

Microcanonical Ensemble in Quantum Statistical Mechanics
journal, October 1965

Direct entropy calculation from computer simulation of liquids
journal, October 1989

Expression in Terms of Molecular Distribution Functions for the Entropy Density in an Infinite System
journal, December 1958

Entropy and Molecular Correlation Functions in Open Systems. I. Derivation
journal, September 1971

Entropy and Molecular Correlation Functions in Open Systems. II Two‐ and Three‐Body Correlations
journal, September 1971

From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999

Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
journal, April 2008

Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics
journal, November 2013

Thermodynamic potentials and distribution functions: II. The HNC equation as an optimized superposition approximation
journal, February 1990

Calculation of the entropy of binary hard sphere mixtures from pair correlation functions
journal, August 1992

Entropy and Diffuse Scattering: Comparison of NbTiVZr and CrMoNbV
journal, September 2015

Calculation of the entropy from multiparticle correlation functions
journal, April 1992

Test of the Universal Scaling Law for the Diffusion Coefficient in Liquid Metals
journal, July 2000

Dependence of solid–liquid interface free energy on liquid structure
journal, July 2014

On the role of density fluctuations in the entropy of a fluid
journal, August 1987

Excess Entropy, Diffusion Coefficient, Viscosity Coefficient and Surface Tension of Liquid Simple Metals from Diffraction Data
journal, January 2002

Recent progress in understanding high temperature dynamical properties and fragility in metallic liquids, and their connection with atomic structure
journal, July 2017

A universal scaling law for atomic diffusion in condensed matter
journal, May 1996

Assessing the performance of recent density functionals for bulk solids
journal, April 2009

The free energy of the crystal-melt interface from the radial distribution function—further calculations
journal, April 1972

A universal scaling law for atomic diffusion in condensed matter
journal, May 1996

Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics
journal, November 2013

Three-particle contribution to the configurational entropy of simple fluids
journal, July 1990

Mutual information does not detect growing correlations in the propensity of a model molecular liquid
journal, January 2019

Modeling the structure and thermodynamics of high-entropy alloys
journal, July 2018