journal article·2018-12

Thermodynamics of solid Sn and Pb Sn liquid mixtures using molecular dynamics simulations

S. Alireza Etesami, Michael I. Baskes, Mohamed Laradji, Ebrahim Asadi

Acta Materialia· Volume 161
Publisher page

Abstract

Abstract We present a new set of modified embedded-atom method parameters for the Pb Sn system that describes many 0 K and high temperature properties including melting point, elastic constants, and enthalpy of mixing for solid and liquid Pb Sn alloys in agreement with experiments. Then, we calculate the phase diagram of the Sn-rich side of Pb Sn alloys utilizing a hybrid Molecular Dynamics/Monte Carlo simulation that agrees with experimental solidus and liquidus curves as well as stability of α-Sn and β-Sn. In addition, we present structure factors of Pb Sn liquid alloys as well as temperature-dependent thermal expansion coefficients and heat capacity. Our simulations show that the ratios of the heights of the second and third peaks over the first peak for Pb Sn liquid mixtures are maximum at Pb-0.6Sn concentration.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Electronic Packaging and Soldering Technologies · Thermodynamic and Structural Properties of Metals and Alloys · Surface and Thin Film Phenomena

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (84)

Show source-provided references
1. Effect of Ni solute on grain boundary diffusivity and structure of βSn10.1016/j.commatsci.2014.05.008 ↗
2. β -Sn grain-boundary structure and self-diffusivity via molecular dynamics simulations10.1103/PhysRevB.81.134111 ↗
3. Effect of Cu and Ag solute segregation on βSn grain boundary diffusivity10.1063/1.3606421 ↗
4. Thermodynamic and mechanical properties of copper precipitates in α -iron from atomistic simulations10.1103/PhysRevB.88.024116 ↗
5. Atomistic and continuum modeling of dendritic solidification10.1016/S0927-796X(03)00036-6 ↗
6. On the quantification of phase-field crystals model for computational simulations of solidification in metals10.1016/j.commatsci.2016.11.042 ↗
7. “A review of quantitative phase-field crystal modeling of solid–liquid structures10.1007/s11837-014-1232-4 ↗
8. The dependence of ostwald ripening kinetics on particle volume fraction10.1016/0001-6160(79)90041-5 ↗
9. The theory of Ostwald ripening10.1007/BF01017860 ↗
10. New computational method in the theory of spinodal decomposition10.1103/PhysRevA.11.1417 ↗
11. Kinetics of strain-induced morphological transformation in cubic alloys with a miscibility gap10.1016/0956-7151(93)90359-Z ↗
12. Dynamics of late-stage phase separation: a test of theory10.1103/PhysRevLett.82.2725 ↗
13. The development of spatial correlations during Ostwald ripening: a test of theory10.1016/S1359-6454(00)00036-7 ↗
14. Snyder · 2001
15. Self-similar coarsening: a test of theory10.1016/j.actamat.2015.08.036 ↗
16. Measurement and analysis of grain boundary grooving by volume diffusion10.1016/0022-0248(91)90061-9 ↗
17. Wetting behavior and mechanical properties of Sn-Zn and Sn-Pb solder alloys10.1007/s11664-009-0888-y ↗
18. Annotated tin whisker bibliography and anthology10.1109/TEPM.2005.847440 ↗
19. Density and surface tension of the Pb-Sn liquid alloys10.1007/s11669-001-0051-9 ↗
20. Accelerated growth of tin whiskers10.1016/0001-6160(54)90053-X ↗
21. Identification of whisker grain in Sn coatings by analyzing crystallographic micro-texture using electron back-scatter diffraction10.1016/j.actamat.2017.05.063 ↗
22. Phase equilibria and the related properties of Sn-Ag-Cu based Pb-free solder alloys10.1007/s11664-000-0004-9 ↗
23. K. Zeng and K. N. Tu, “Six cases of reliability study of Pb-free solder joints in electronic packaging technology.”
24. Microstructure and mechanical properties of Pb-free solder alloys for low-cost electronic assembly: a review10.1007/BF02651361 ↗
25. Modified embedded-atom potentials for cubic materials and impurities10.1103/PhysRevB.46.2727 ↗
26. Application of the embedded-atom method to covalent materials: a semiempirical potential for silicon10.1103/PhysRevLett.59.2666 ↗
27. Semiempirical atomic potentials for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb based on first and second nearest-neighbor modified embedded atom method10.1103/PhysRevB.68.144112 ↗
28. Second nearest-neighbor modified embedded atom method potentials for bcc transition metals10.1103/PhysRevB.64.184102 ↗
29. Modified embedded atom potentials for HCP metals10.1088/0965-0393/2/1/011 ↗
30. Equilibrium and thermodynamic properties of grey, white, and liquid tin10.1103/PhysRevLett.79.2482 ↗
31. Molecular dynamics for near melting temperatures simulations of metals using modified embedded-atom method10.1016/j.jpcs.2017.09.001 ↗
32. Two-phase solid-liquid coexistence of Ni, Cu, and Al by molecular dynamics simulations using the modified embedded-atom method10.1016/j.actamat.2014.12.010 ↗
33. The anisotropy of hexagonal close-packed and liquid interface free energy using molecular dynamics simulations based on modified embedded-atom method10.1016/j.actamat.2016.01.043 ↗
34. Phase-field crystal model for Fe connected to MEAM molecular dynamics simulations10.1007/s11837-013-0845-3 ↗
35. Structural and dynamic properties of liquid tin from a new modified embedded-atom method force field10.1103/PhysRevB.95.064202 ↗
36. “First-principle and molecular dynamics calculations for physical properties of Ni–Sn alloy system10.1016/j.commatsci.2014.11.031 ↗
37. Fast parallel algorithms for short-range molecular dynamics10.1006/jcph.1995.1039 ↗
38. “Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool10.1088/0965-0393/18/1/015012 ↗
39. “http://ovito.org/”.
40. “Two-phase solid–liquid coexistence of Ni, Cu, and Al by molecular dynamics simulations using the modified embedded-atom method10.1016/j.actamat.2014.12.010 ↗
41. Second nearest-neighbor modified embedded-atom-method potential10.1103/PhysRevB.62.8564 ↗
42. Quantitative modeling of the equilibration of two-phase solid-liquid Fe by atomistic simulations on diffusive time scales10.1103/PhysRevB.91.024105 ↗
43. Universal features of the equation of state of metals10.1103/PhysRevB.29.2963 ↗
44. “A deformation–fluctuation hybrid method for fast evaluation of elastic constants with many-body potentials10.1016/j.cpc.2011.09.006 ↗
45. Kittel · 1996
46. Simmons · 1971
47. Barrett · 1966
48. Gale · 2003
49. Equilibrium properties and the phase transition of grey and white tin10.1103/PhysRevB.23.1576 ↗
50. “High pressure melting curve of tin measured using an internal resistive heating technique to 45 GPa10.1063/1.4730968 ↗
51. SGTE data for pure elements10.1016/0364-5916(91)90030-N ↗
52. The elastic constants for single-crystal lead and indium from room temperature to the melting point10.1016/0022-3697(77)90159-7 ↗
53. Elastic constants of β tin from 4.2°K to 300°K10.1103/PhysRev.120.1658 ↗
54. Frenkel · 2001
55. Structure parameters and structure sensitive properties of Sn0.739Pb0.261 melt10.1134/S0869864311010136 ↗
56. Free-energy calculations and the melting point of Al10.1103/PhysRevB.46.21 ↗
57. “Numerical evaluation of the exact phase diagram of an empirical Hamiltonian: embedded atom model for the Au-Ni system10.1103/PhysRevB.66.054201 ↗
58. Phase diagram of an empirical potential: the case of Fe-Cu10.1103/PhysRevB.68.214205 ↗
59. Efficient free-energy calculations by the simulation of nonequilibrium processes10.1109/5992.841802 ↗
60. Polymorphic transitions in single crystals: a new molecular dynamics method10.1063/1.328693 ↗
61. Nonequilibrium free-energy calculation of solids using LAMMPS10.1016/j.commatsci.2015.10.050 ↗
62. Einstein crystal as a reference system in free energy estimation using adiabatic switching10.1103/PhysRevE.53.465 ↗
63. Touloukian · 1970
64. SGTE data for pure elements10.1016/0364-5916(91)90030-N ↗
65. “XRD study of the kinetics of β ↔ α transformations in tin10.1080/14786435.2013.820381 ↗
66. E.A · 1992
67. Thermochemical Properties of Inorganic Substances. Berlin: Springer-Verlag, 1973.
68. Harrison · 1989
69. Waseda · 1980
70. Modified embedded-atom method interatomic potentials for the Fe–Nb and Fe–Ti binary systems10.1016/j.scriptamat.2008.05.007 ↗
71. The modified embedded-atom method interatomic potentials and recent progress in atomistic simulations10.1016/j.calphad.2010.10.007 ↗
72. The lattice spacings of lead-rich substitutional solid solutions10.1107/S0365110X54001600 ↗
73. The lattice spacings of binary tin-rich alloys10.1088/0370-1301/67/10/301 ↗
74. “Thermodynamics of the lead–tin system10.1021/j150577a031 ↗
75. The heat of formation of α-PbSn alloys10.1016/0001-6160(58)90176-7 ↗
76. A new high temperature reaction calorimeter: the heats of mixing of liquid lead–tin alloys10.1021/j150524a020 ↗
77. Scalable parallel Monte Carlo algorithm for atomistic simulations of precipitation in alloys10.1103/PhysRevB.85.184203 ↗
78. “An embedded-atom potential for the Cu–Ag system10.1088/0965-0393/14/5/002 ↗
79. Viscosity and density of liquid lead-tin and antimony-cadmium alloys10.1007/BF03398346 ↗
80. The lead-tin system of alloys re-examined by an electrical resistance method10.1039/tf9282400209 ↗
81. The solubility of lead in tin
82. Ab initio-aided CALPHAD thermodynamic modeling of the Sn-Pb binary system under current stressing10.1038/srep02731 ↗
83. Short-range order and dynamics of atoms in liquid gallium10.1134/S1063776115110072 ↗
84. Cooling rate dependence of solidification for liquid aluminium: a large-scale molecular dynamics simulation study10.1039/C6CP02172G ↗