Thermodynamic Calculation of Phase Diagram in the Bi-In-Sb Ternary System

Cui, Yujie; Ishihara, Satoru; Liu, Xing Jun; Ohnuma, Ikuo; Kainuma, Ryosuke; Ohtani, Hiroshi; Ishida, K.

doi:10.2320/matertrans.43.1879

Cited by 32 publications

(14 citation statements)

References 16 publications

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“…23) However, it was found that the (In) solid solution is stable at the Bi-rich portion in the temperature range from 100 to 125 C based on Chevalier's parameters, which is obviously unreasonable although there is no direct experimental information. A modification of the parameters was carried out by the present authors 24) Evaluation of the thermodynamic properties in the Ag-Bi system was preformed by Karakaya and Thompson,25) and a thermodynamic description of this binary system was conducted by Kattner and Boettinger. 26) Recently Ohtani et al reported a set of the parameters, including the matastable phases hcp and Ag 3 Sn, on the basis of the thermodynamic assessment of the Sn-Ag-Bi ternary system.…”

Section: Calculation Of Binary Systemmentioning

confidence: 99%

Thermodynamic Calculations of Phase Equilibria, Surface Tension and Viscosity in the In-Ag-X (X=Bi, Sb) System

et al. 2004

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The phase equilibria of the In-Ag-Bi and In-Ag-Sb systems were determined by differential scanning calorimetry (DSC) and electron probe microanalysis (EPMA). Thermodynamic calculations of these systems were also carried out by taking the experimental results into account. The Gibbs energies of the liquid and solid solution phases are described on the basis of the sub-regular solution model, and that of the intermetallic compounds are based on the two-sublattice model. A consistent set of thermodynamic parameters was optimized for describing the Gibbs energy of each phase, which leads to a good fit between calculated and experimental results. In addition, the surface tension and viscosity of liquid phase were calculated on the basis of the thermodynamic parameters obtained in the present assessment.

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Section: Calculation Of Binary Systemmentioning

confidence: 99%

Thermodynamic Calculations of Phase Equilibria, Surface Tension and Viscosity in the In-Ag-X (X=Bi, Sb) System

et al. 2004

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“…Three constitutive binary systems have been investigated extensively in recent years by many research groups [16][17][18][19][20][21]. However, in case of Ag-Bi and Bi-In binaries these investigations have not resulted in any changes of phase diagrams.…”

Section: Literature Datamentioning

confidence: 99%

The influence of chemical composition on microstructure, hardness and electrical conductivity of Ag-Bi-In alloys at 100 °C

Ćosović

Minić²,

Premović³

et al. 2017

Metall Mater Eng

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Considering possible applications and scarceness of literature data, Ag-Bi-In system was investigated in terms of microstructure, mechanical and electrical properties of ternary alloys from an isothermal section at 100 °C. Based on the experimentally obtained results hardness and electrical conductivity of all ternary alloys from the ternary Ag-Bi-In system at 100 °C were predicted. In addition, the selected isothermal section was further thermodynamically assessed and experimentally studied using scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS), X-ray powder diffraction (XRD) analysis and light optical microscopy (LOM). Phase transition temperatures of alloys with overall compositions along vertical sections x(Ag)=0.5 as well as liquidus temperatures were experimentally determined by DTA. The experimentally obtained results were compared with literature data and with the results of thermodynamic calculation of phase equilibria based on CALPHAD method and corrected data for Ag-In binary system. Calculated liquidus projection, invariant equilibria and phase diagram of the Ag-Bi-In ternary system are presented as well.

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“…One-dimensional oscillator model for 4-component solders This one-dimensional oscillator model is a simple equation that successfully elucidates numerous phenomena; it has been used to theoretically deduce the molar specific heat of solids regardless of material, which explains Dulong-Petit's Law, [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] theoretically analyze the atomic dynamics of crystals, [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] conduct behavioral analyses of elastic waves of cubic systems, deduce the Bragg-Williams Model, [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] etc. For this reason, this one-dimensional oscillator model was used to derive a theoretical formula of non-equilibrium thermal dynamics for 4-component lead-free solder.…”

Section: 2mentioning

confidence: 99%

“…On the one hand, there are the K-T 12,13) and G-L Theory 12,13) that deal with target materials on the atomic level, while on the other hand is the so-called method of ''calculation of phase diagram (CALPHAD)'' that makes phase diagrams using calculations based on an applicable statistical thermodynamic model. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] In the case of phase diagrams of some multiple-component alloys, it was difficult to obtain accurate experimental data that repeatedly fit with calculation data. Accordingly, in order to promote developments of higher temperature lead-free solders, it was necessary to develop a new method of thermodynamic analysis that included the non-equlibrium sate of lead-free solder.…”

Section: Introductionmentioning

confidence: 99%

“…Even today, its realization has been difficult because of the extensive time and manpower required. [4][5][6][7][8] For this reason, theoretical studies have been recently promoted and developed [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] . On the one hand, there are the K-T 12,13) and G-L Theory 12,13) that deal with target materials on the atomic level, while on the other hand is the so-called method of ''calculation of phase diagram (CALPHAD)'' that makes phase diagrams using calculations based on an applicable statistical thermodynamic model.…”

Section: Introductionmentioning

confidence: 99%

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Non-Equilibrium Thermodynamic Theory of 4-Component Lead-Free Solder

et al. 2009

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We investigated non-equilibrium thermodynamic theories for 4-component lead-free solders based on classical thermodynamics using one-dimensional oscillator model to obtain their specific heat and the coefficient of linear thermal expansion.We analyzed In and Sn reactions in SnAgBiIn solder as a representative lead-free material and experimentally obtained an N c factor for expressing the state of non-equilibrium from the formation of metallic compounds. It was considered that the state of equilibrium did not occur experimentally, and that metallic compounds InSn 4 formed in some parts of the 2-component eutectic solder. We then built a theory as onedimensional oscillator model by approximating this N c factor, as a representation of the non-equilibrium behavior of high temperature lead-free solder. Using this model representing the non-equilibrium state, the correlation between specific heat and coefficient of linear thermal expansion was derived theoretically, which was found to be linear in mathematical studies. In fact, it was learned that experimental results of this correlation also tended to be linear. This suggested that the derived non-equilibrium theory was practically useful, moreover other thermodynamic characteristics could be analyzed by this non-equilibrium thermodynamic theory using one-dimensional oscillator model.

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Thermodynamic Calculation of Phase Diagram in the Bi-In-Sb Ternary System

Cited by 32 publications

References 16 publications

Thermodynamic Calculations of Phase Equilibria, Surface Tension and Viscosity in the In-Ag-X (X=Bi, Sb) System

Thermodynamic Calculations of Phase Equilibria, Surface Tension and Viscosity in the In-Ag-X (X=Bi, Sb) System

The influence of chemical composition on microstructure, hardness and electrical conductivity of Ag-Bi-In alloys at 100 °C

Non-Equilibrium Thermodynamic Theory of 4-Component Lead-Free Solder

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