Theoretical calculation of the melting curve of Cu-Zr binary alloys

Gunawardana, K. G.S.H.; Wilson, S. R.; Mendelev, M. I.; Song, Xueyu

doi:10.1103/PhysRevE.90.052403

Title: Theoretical calculation of the melting curve of Cu-Zr binary alloys

Journal Article · Fri Nov 14 04:00:00 UTC 2014 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI: https://doi.org/10.1103/PhysRevE.90.052403 · OSTI ID:1226913

Gunawardana, K. G.S.H. ^[1]; Wilson, S. R. ^[1]; Mendelev, M. I. ^[1]; Song, Xueyu ^[2]

Ames Lab. and Iowa State Univ., Ames, IA (United States)
Ames Lab. and Iowa State Univ., Ames, IA (United States). Dept. of Chemistry

Helmholtz free energies of the dominant binary crystalline solids found in the Cu-Zr system at high temperatures close to the melting curve are calculated. This theoretical approach combines fundamental measure density functional theory (applied to the hard-sphere reference system) and a perturbative approach to include the attractive interactions. The studied crystalline solids are Cu(fcc), Cu₅₁Zr₁₄(β), CuZr(B₂), CuZr₂(C11b), Zr(hcp), and Zr(bcc). The calculated Helmholtz free energies of crystalline solids are in good agreement with results from molecular-dynamics (MD) simulations. Using the same perturbation approach, the liquid phase free energies are calculated as a function of composition and temperature, from which the melting curve of the entire composition range of this system can be obtained. Phase diagrams are determined in this way for two leading embedded atom method potentials, and the results are compared with experimental data. Furthermore, theoretical melting temperatures are compared both with experimental values and with values obtained directly from MD simulations at several compositions.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Ames Laboratory (AMES), Ames, IA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-07CH11358

OSTI ID:: 1226913

Report Number(s):: IS--J-8553

Journal Information:: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics Journal Issue: 5 Vol. 90; ISSN 1539-3755; ISSN PLEEE8

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (65)

Constitutional and structural studies of the intermetallic phase, ZrCu Carvalho, E. M.; Harris, I. R. Journal of Materials Science, Vol. 15, Issue 5 https://doi.org/10.1007/BF00551811	journal	May 1980
Bulk amorphous metal—An emerging engineering material Johnson, W. L. JOM, Vol. 54, Issue 3 https://doi.org/10.1007/BF02822619	journal	March 2002
Constitutional and structural studies of the intermetallic phase, ZrCu Carvalho, E. M.; Harris, I. R. Journal of Materials Science, Vol. 15, Issue 5 https://doi.org/10.1007/bf00551811	journal	May 1980
Bulk amorphous metal—An emerging engineering material Johnson, W. L. JOM, Vol. 54, Issue 3 https://doi.org/10.1007/bf02822619	journal	March 2002
Freezing of simple liquid metals Denton, A. R.; Kahl, G.; Hafner, J. Journal of Non-Crystalline Solids, Vol. 250-252 https://doi.org/10.1016/S0022-3093(99)00108-8	journal	August 1999
Fundamental measure theory and dimensional interpolation for the hard spheres fluid Tarazona, Pedro Physica A: Statistical Mechanics and its Applications, Vol. 306 https://doi.org/10.1016/S0378-4371(02)00501-0	journal	April 2002
Stabilization of metallic supercooled liquid and bulk amorphous alloys Inoue, Akihisa Acta Materialia, Vol. 48, Issue 1 https://doi.org/10.1016/S1359-6454(99)00300-6	journal	January 2000
Phase stability for the Cu–Zr system: First-principles, experiments and solution-based modeling Zhou, S. H.; Napolitano, R. E. Acta Materialia, Vol. 58, Issue 6 https://doi.org/10.1016/j.actamat.2009.12.004	journal	April 2010
Bulk metallic glasses Wang, W. H.; Dong, C.; Shek, C. H. Materials Science and Engineering: R: Reports, Vol. 44, Issue 2-3 https://doi.org/10.1016/j.mser.2004.03.001	journal	June 2004
Freezing of simple liquid metals Denton, A. R.; Kahl, G.; Hafner, J. Journal of Non-Crystalline Solids, Vol. 250-252 https://doi.org/10.1016/s0022-3093(99)00108-8	journal	August 1999
Fundamental measure theory and dimensional interpolation for the hard spheres fluid Tarazona, Pedro Physica A: Statistical Mechanics and its Applications, Vol. 306 https://doi.org/10.1016/s0378-4371(02)00501-0	journal	April 2002
Stabilization of metallic supercooled liquid and bulk amorphous alloys Inoue, Akihisa Acta Materialia, Vol. 48, Issue 1 https://doi.org/10.1016/s1359-6454(99)00300-6	journal	January 2000
Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids Weeks, John D.; Chandler, David; Andersen, Hans C. The Journal of Chemical Physics, Vol. 54, Issue 12 https://doi.org/10.1063/1.1674820	journal	June 1971
Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres Mansoori, G. A.; Carnahan, N. F.; Starling, K. E. The Journal of Chemical Physics, Vol. 54, Issue 4 https://doi.org/10.1063/1.1675048	journal	February 1971
Bulk metallic glass formation in the binary Cu–Zr system Wang, D.; Li, Y.; Sun, B. B. Applied Physics Letters, Vol. 84, Issue 20 https://doi.org/10.1063/1.1751219	journal	May 2004
Fundamental measure density functional theory studies on the freezing of binary hard-sphere and Lennard-Jones mixtures Warshavsky, Vadim B.; Song, Xueyu The Journal of Chemical Physics, Vol. 129, Issue 3 https://doi.org/10.1063/1.2953329	journal	July 2008
A perturbation theory of classical equilibrium fluids Kang, Hong Seok; Lee, Choong Sik; Ree, Taikyue The Journal of Chemical Physics, Vol. 82, Issue 1 https://doi.org/10.1063/1.448762	journal	January 1985
Free‐energy model for the inhomogeneous hard‐sphere fluid: ‘‘Closure’’ relation between generating functionals for ‘‘direct’’ and ‘‘cavity’’ distribution functions Rosenfeld, Yaakov The Journal of Chemical Physics, Vol. 93, Issue 6 https://doi.org/10.1063/1.458712	journal	September 1990
Development of suitable interatomic potentials for simulation of liquid and amorphous Cu–Zr alloys Mendelev, M. I.; Kramer, M. J.; Ott, R. T. Philosophical Magazine, Vol. 89, Issue 11 https://doi.org/10.1080/14786430902832773	journal	April 2009
A blip-function calculation of the structure of liquid binary alloys Kahl, G.; Hafner, J. Journal of Physics F: Metal Physics, Vol. 15, Issue 8 https://doi.org/10.1088/0305-4608/15/8/003	journal	August 1985
Bulk metallic glasses Schneider, Susanne Journal of Physics: Condensed Matter, Vol. 13, Issue 34 https://doi.org/10.1088/0953-8984/13/34/316	journal	August 2001
Fundamental measure theory for hard-sphere mixtures revisited: the White Bear version Roth, R.; Evans, R.; Lang, A. Journal of Physics: Condensed Matter, Vol. 14, Issue 46 https://doi.org/10.1088/0953-8984/14/46/313	journal	November 2002
Predicting the solid state phase diagram for glass-forming alloys of copper and zirconium Tang, C.; Harrowell, Peter Journal of Physics: Condensed Matter, Vol. 24, Issue 24 https://doi.org/10.1088/0953-8984/24/24/245102	journal	May 2012
Perturbation Theory of Fluids at High Temperatures Henderson, D.; Barker, J. A. Physical Review A, Vol. 1, Issue 4 https://doi.org/10.1103/PhysRevA.1.1266	journal	April 1970
Weighted-density-functional and simulation studies of the bcc hard-sphere solid Curtin, W. A.; Runge, K. Physical Review A, Vol. 35, Issue 11 https://doi.org/10.1103/PhysRevA.35.4755	journal	June 1987
Relationship between the Hard-Sphere Fluid and Fluids with Realistic Repulsive Forces Andersen, Hans C.; Weeks, John D.; Chandler, David Physical Review A, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevA.4.1597	journal	October 1971
Nonperturbative density-functional theories of classical nonuniform systems Lutsko, James F.; Baus, Marc Physical Review A, Vol. 41, Issue 12 https://doi.org/10.1103/PhysRevA.41.6647	journal	June 1990
Application of the embedded-atom method to liquid transition metals Foiles, S. M. Physical Review B, Vol. 32, Issue 6 https://doi.org/10.1103/PhysRevB.32.3409	journal	September 1985
Accurate method to calculate liquid and solid free energies for embedded atom potentials Song, Xueyu; Morris, James R. Physical Review B, Vol. 67, Issue 9 https://doi.org/10.1103/PhysRevB.67.092203	journal	March 2003
Relationship between structure, dynamics, and mechanical properties in metallic glass-forming alloys Cheng, Y. Q.; Sheng, H. W.; Ma, E. Physical Review B, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevB.78.014207	journal	July 2008
Phase diagrams of binary alloys calculated from a density functional theory Warshavsky, Vadim B.; Song, Xueyu Physical Review B, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevB.79.014101	journal	January 2009
Theoretical approach to the correlations of a classical crystal Rascón, C.; Mederos, L.; Navascués, G. Physical Review E, Vol. 54, Issue 2 https://doi.org/10.1103/PhysRevE.54.1261	journal	August 1996
Fundamental-measure free-energy density functional for hard spheres: Dimensional crossover and freezing Rosenfeld, Y.; Schmidt, M.; Löwen, H. Physical Review E, Vol. 55, Issue 4 https://doi.org/10.1103/PhysRevE.55.4245	journal	April 1997
Calculations of free energies in liquid and solid phases: Fundamental measure density-functional approach Warshavsky, Vadim B.; Song, Xueyu Physical Review E, Vol. 69, Issue 6 https://doi.org/10.1103/PhysRevE.69.061113	journal	June 2004
Properties of non-fcc hard-sphere solids predicted by density functional theory Lutsko, James F. Physical Review E, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevE.74.021121	journal	August 2006
Theoretical studies of the correlations in moderately asymmetric binary hard-sphere solid mixtures Warshavsky, Vadim B.; Song, Xueyu Physical Review E, Vol. 77, Issue 5 https://doi.org/10.1103/PhysRevE.77.051106	journal	May 2008
Perturbation theory of solid-liquid interfacial free energies of bcc metals Warshavsky, Vadim B.; Song, Xueyu Physical Review E, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevE.86.031602	journal	September 2012
Atomic Level Structure in Multicomponent Bulk Metallic Glass Cheng, Y. Q.; Ma, E.; Sheng, H. W. Physical Review Letters, Vol. 102, Issue 24 https://doi.org/10.1103/PhysRevLett.102.245501	journal	June 2009
Free-energy model for the inhomogeneous hard-sphere fluid mixture and density-functional theory of freezing Rosenfeld, Yaakov Physical Review Letters, Vol. 63, Issue 9 https://doi.org/10.1103/PhysRevLett.63.980	journal	August 1989
Perturbation Theory for Classical Solids Rascón, C.; Mederos, L.; Navascués, G. Physical Review Letters, Vol. 77, Issue 11 https://doi.org/10.1103/PhysRevLett.77.2249	journal	September 1996
Density Functional for Hard Sphere Crystals: A Fundamental Measure Approach Tarazona, P. Physical Review Letters, Vol. 84, Issue 4 https://doi.org/10.1103/PhysRevLett.84.694	journal	January 2000
Theoretical Evidence for a Dense Fluid Precursor to Crystallization Lutsko, James F.; Nicolis, Grégoire Physical Review Letters, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRevLett.96.046102	journal	February 2006
Perturbation Theory of Fluids at High Temperatures Henderson, D.; Barker, J. A. Physical Review A, Vol. 1, Issue 4 https://doi.org/10.1103/physreva.1.1266	journal	April 1970
Weighted-density-functional and simulation studies of the bcc hard-sphere solid Curtin, W. A.; Runge, K. Physical Review A, Vol. 35, Issue 11 https://doi.org/10.1103/physreva.35.4755	journal	June 1987
Relationship between the Hard-Sphere Fluid and Fluids with Realistic Repulsive Forces Andersen, Hans C.; Weeks, John D.; Chandler, David Physical Review A, Vol. 4, Issue 4 https://doi.org/10.1103/physreva.4.1597	journal	October 1971
Nonperturbative density-functional theories of classical nonuniform systems Lutsko, James F.; Baus, Marc Physical Review A, Vol. 41, Issue 12 https://doi.org/10.1103/physreva.41.6647	journal	June 1990
Application of the embedded-atom method to liquid transition metals Foiles, S. M. Physical Review B, Vol. 32, Issue 6 https://doi.org/10.1103/physrevb.32.3409	journal	September 1985
Accurate method to calculate liquid and solid free energies for embedded atom potentials Song, Xueyu; Morris, James R. Physical Review B, Vol. 67, Issue 9 https://doi.org/10.1103/physrevb.67.092203	journal	March 2003
Relationship between structure, dynamics, and mechanical properties in metallic glass-forming alloys Cheng, Y. Q.; Sheng, H. W.; Ma, E. Physical Review B, Vol. 78, Issue 1 https://doi.org/10.1103/physrevb.78.014207	journal	July 2008
Phase diagrams of binary alloys calculated from a density functional theory Warshavsky, Vadim B.; Song, Xueyu Physical Review B, Vol. 79, Issue 1 https://doi.org/10.1103/physrevb.79.014101	journal	January 2009
Theoretical approach to the correlations of a classical crystal Rascón, C.; Mederos, L.; Navascués, G. Physical Review E, Vol. 54, Issue 2 https://doi.org/10.1103/physreve.54.1261	journal	August 1996
Fundamental-measure free-energy density functional for hard spheres: Dimensional crossover and freezing Rosenfeld, Y.; Schmidt, M.; Löwen, H. Physical Review E, Vol. 55, Issue 4 https://doi.org/10.1103/physreve.55.4245	journal	April 1997
Calculations of free energies in liquid and solid phases: Fundamental measure density-functional approach Warshavsky, Vadim B.; Song, Xueyu Physical Review E, Vol. 69, Issue 6 https://doi.org/10.1103/physreve.69.061113	journal	June 2004
Properties of non-fcc hard-sphere solids predicted by density functional theory Lutsko, James F. Physical Review E, Vol. 74, Issue 2 https://doi.org/10.1103/physreve.74.021121	journal	August 2006
Theoretical studies of the correlations in moderately asymmetric binary hard-sphere solid mixtures Warshavsky, Vadim B.; Song, Xueyu Physical Review E, Vol. 77, Issue 5 https://doi.org/10.1103/physreve.77.051106	journal	May 2008
Perturbation theory of solid-liquid interfacial free energies of bcc metals Warshavsky, Vadim B.; Song, Xueyu Physical Review E, Vol. 86, Issue 3 https://doi.org/10.1103/physreve.86.031602	journal	September 2012
Atomic Level Structure in Multicomponent Bulk Metallic Glass Cheng, Y. Q.; Ma, E.; Sheng, H. W. Physical Review Letters, Vol. 102, Issue 24 https://doi.org/10.1103/physrevlett.102.245501	journal	June 2009
Free-energy model for the inhomogeneous hard-sphere fluid mixture and density-functional theory of freezing Rosenfeld, Yaakov Physical Review Letters, Vol. 63, Issue 9 https://doi.org/10.1103/physrevlett.63.980	journal	August 1989
Perturbation Theory for Classical Solids Rascón, C.; Mederos, L.; Navascués, G. Physical Review Letters, Vol. 77, Issue 11 https://doi.org/10.1103/physrevlett.77.2249	journal	September 1996
Density Functional for Hard Sphere Crystals: A Fundamental Measure Approach Tarazona, P. Physical Review Letters, Vol. 84, Issue 4 https://doi.org/10.1103/physrevlett.84.694	journal	January 2000
Theoretical Evidence for a Dense Fluid Precursor to Crystallization Lutsko, James F.; Nicolis, Grégoire Physical Review Letters, Vol. 96, Issue 4 https://doi.org/10.1103/physrevlett.96.046102	journal	February 2006
Zr ₁₄ Cu ₅₁ and Hf ₁₄ Cu ₅₁ with GdAg _3.6 structure type Gabathuler, J. -P.; White, P.; Parthé, E. Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry, Vol. 31, Issue 2 https://doi.org/10.1107/S0567740875003378	journal	February 1975
Zr ₁₄ Cu ₅₁ and Hf ₁₄ Cu ₅₁ with GdAg _3.6 structure type Gabathuler, J. -P.; White, P.; Parthé, E. Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry, Vol. 31, Issue 2 https://doi.org/10.1107/s0567740875003378	journal	February 1975
Mechanical Behavior of Metallic Glasses: Microscopic Understanding of Strength and Ductility Chen, Mingwei Annual Review of Materials Research, Vol. 38, Issue 1 https://doi.org/10.1146/annurev.matsci.38.060407.130226	journal	August 2008
Formation, Thermal Stability and Mechanical Properties of Cu-Zr and Cu-Hf Binary Glassy Alloy Rods Inoue, Akihisa; Zhang, Wei MATERIALS TRANSACTIONS, Vol. 45, Issue 2 https://doi.org/10.2320/matertrans.45.584	journal	January 2004

Cited By (2)

Minimising oxygen contamination through a liquid copper-aided group IV metal production process Yoo, Bung Uk; Lee, Young Jun; Ri, Vladislav Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-018-35739-z	journal	November 2018
Theoretical prediction of crystallization kinetics of a supercooled Lennard-Jones fluid Gunawardana, K. G. S. H.; Song, Xueyu The Journal of Chemical Physics, Vol. 148, Issue 20 https://doi.org/10.1063/1.5021944	journal	May 2018

Similar Records

Polymorphism and melt in high-pressure tantalum. II. Orthorhombic phases

Journal Article · Thu Oct 11 04:00:00 UTC 2018 · Physical Review B · OSTI ID:1488793

Haskins, Justin B.; Moriarty, John A.

The [alpha]-Zr phase field in the Zr-Sn-O system

Journal Article · Fri Jun 18 04:00:00 UTC 1999 · Scripta Materialia · OSTI ID:6304726

Arico, S F; Gribaudo, L M

Free Energy Calculations of Crystalline Hard Sphere Complexes Using Density Functional Theory

Journal Article · Mon Dec 22 04:00:00 UTC 2014 · Journal of Physical Chemistry. B, Condensed Matter, Materials, Surfaces, Interfaces and Biophysical Chemistry · OSTI ID:1221914

Gunawardana, K. G.S.H.; Song, Xueyu

Related Subjects

36 MATERIALS SCIENCE

Title: Theoretical calculation of the melting curve of Cu-Zr binary alloys

Citation Formats

References (65)

Cited By (2)

Similar Records

Related Subjects