Ab initio simulations of molten Ni alloys

Christopher Woodward; Mark Asta; Dallas R. Trinkle; James Lill; Stefano Angioletti-Uberti

doi:10.1063/1.3437644

Ab initio simulations of molten Ni alloys

Christopher Woodward, Mark Asta, Dallas R. Trinkle, James Lill, Stefano Angioletti-Uberti

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Abstract

Convective instabilities responsible for misoriented grains in directionally solidified turbine airfoils are produced by variations in liquid-metal density with composition and temperature across the solidification zone. Here, fundamental properties of molten Ni-based alloys, required for modeling these instabilities, are calculated using ab initio molecular dynamics simulations. Equations of state are derived from constant number-volume- temperature ensembles at 1830 and 1750 K for elemental, binary (Ni-X, X=Al, W, Re, and Ta) and ternary (Ni-Al-X, X=W, Re, and Ta) Ni alloys. Calculated molar volumes agree to within 0.6%-1.8% of available measurements. Predictions are used to investigate the range of accuracy of a parameterization of molar volumes with composition and temperature based on measurements of binary alloys. Structural analysis reveals a pronounced tendency for icosahedral short-range order for Ni-W and Ni-Re alloys and the calculations provide estimates of diffusion rates and their dependence on compositions and temperature.

Original language	English (US)
Article number	113522
Journal	Journal of Applied Physics
Volume	107
Issue number	11
DOIs	https://doi.org/10.1063/1.3437644
State	Published - Jun 1 2010

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Physics and Astronomy(all)

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10.1063/1.3437644

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@article{f6e04377c959459d9a5bba12f72c99fc,

title = "Ab initio simulations of molten Ni alloys",

abstract = "Convective instabilities responsible for misoriented grains in directionally solidified turbine airfoils are produced by variations in liquid-metal density with composition and temperature across the solidification zone. Here, fundamental properties of molten Ni-based alloys, required for modeling these instabilities, are calculated using ab initio molecular dynamics simulations. Equations of state are derived from constant number-volume- temperature ensembles at 1830 and 1750 K for elemental, binary (Ni-X, X=Al, W, Re, and Ta) and ternary (Ni-Al-X, X=W, Re, and Ta) Ni alloys. Calculated molar volumes agree to within 0.6%-1.8% of available measurements. Predictions are used to investigate the range of accuracy of a parameterization of molar volumes with composition and temperature based on measurements of binary alloys. Structural analysis reveals a pronounced tendency for icosahedral short-range order for Ni-W and Ni-Re alloys and the calculations provide estimates of diffusion rates and their dependence on compositions and temperature.",

author = "Christopher Woodward and Mark Asta and Trinkle, {Dallas R.} and James Lill and Stefano Angioletti-Uberti",

note = "Funding Information: This research was supported in part by a grant of computer time from the DoD High Performance Computing Modernization Program at the Air Force Research Laboratory DoD Supercomputing Research Center (AFRL-DSRC). MA and DRT were supported in part with a grant from the Air Force Office of Scientific Research under the Materials Engineering for Affordable New Systems (MEANS-II) program. The authors gratefully acknowledge insightful discussions with T. Pollock, P. Voorhees, O. Senkov, and S.H. Davis, and the technical assistance provided by S. Kajihara at the AFRL-DSRC. FIG. 1. Calculated AIMD mean-square displacements of solvent (left) and solute (right) species for elemental Ni and binary Ni–X ( X = Al , W, Re, and Ta) alloys at 1830 K. Deviations in the “random walk” from the long-time linear diffusion relation, ⟨ | r ( t ) − r ( 0 ) | 2 ⟩ = 6 D t , are shown as filled areas for each species. The results shown here are from the lowest pressure simulations at these chemistries. The diffusion constants (d) in Table I are derived from the slopes of the mean-square displacement curves at several volumes interpolated to zero pressure. Self diffusion of Ni decreases with solute additions with Al producing the smallest effect and W the largest. The relative solute diffusion in these liquid Ni–X metals follows the same trends of the respective solvent diffusion. FIG. 2. Radial distribution functions calculated from AIMD simulations for elemental Ni and binary Ni–X ( X = Al , W, and Re) alloys at T = 1830 K . The results shown here are from the lowest pressure simulations at these chemistries. The three plots show results, from left to right, for solvent–solvent (Ni–Ni), solvent–solute (Ni–X), and solute–solute (X–X) pairs. FIG. 3. CNA of pure Ni, Ni 473 Re 27 , and Ni 473 W 27 at 1830 K. The combined analysis shows the presence of similar short-range order in the three samples, with almost no dependence on composition. Icosahedral and bcc type ordering are found to be the most abundant. FIG. 4. Angle distribution function P ( θ ) at 1830 K for pure Ni, Ni 473 Re 27 , and Ni 473 W 27 . For perfect icosahedric or bcc like structures the two main peaks are expected to be around 60° and 108°, in our samples distortions due to the liquid nature shift the peaks to lower values. The angle distribution for all three cases of the Ni-centered data fall on essentially the same line, and there is a slight shift to lower angles for the W centered distribution relative to the rest of the data. FIG. 5. Graphic representation of the equation of state calculations for liquid metal Ni 400 Al 100 alloy at 1830 K. Representative AIMD calculations of pressure as a function of simulation time for four volumes (left) with a horizontal line indicating time-averaged values. The volume at these pressures, with error bars, (right) are fit to a quadratic polynomial, with results of this least-squares fit shown in inset. Interpolating to the zero pressure volume produces the predicted equilibrium volume the bulk modulus and its derivative for a given composition and temperature. Error bars and estimated uncertainties are based on standard uncertainty analysis. FIG. 6. Comparison of molar volumes calculated with AIMD simulations and estimated using the Mukai parameterization. Data in perfect agreement would fall on the line representing a slope of one, the dashed line indicates where the two results differ by 2%. The outliers are compositions that fall outside the composition ranges included in the fit of the Mukai model. FIG. 7. Variation in molar volumes at 1750 K for ternary and binary alloys calculated using AIMD simulations and estimated using the Mukai parameterization. The figure on the left shows compositions spanning the ternary triangle (see inset). Results are linear in composition with deviations from linearity of less than 0.8%. The Mukai model results for Ni 473 Ta 27 are the exception producing deviations from linearity of approximately 3%. The figure on the right shows binary Ni–X ( X = W and Re) compositions up to Ni – 20 X at . % which is outside the range of the Mukai reference measurements. The Mukai Ni–W molar volumes show significant deviations from linearity, which is not predicted by the AIMD simulations. Similar, though far more dramatic deviations are observed for Ni–Ta alloys in this range of composition. FIG. 8. The variation in molar volume with temperature for elemental Ni and Ni 473 Al 27 calculated using N V T and N P T ensembles. The coefficient of thermal expansion ( β = V − 1 d V / d T ) , calculated from a linear fit to each data set, are shown adjacent to each curve. The two methods for deriving the molar volume are within numerical error of the respective calculations, producing slopes, and β that are also within numerical error. Table I. Calculated diffusion parameters ( 10 − 5 cm 2 / s ) and activation volumes for binary Ni alloys at 1830 K. Values for D are the result of a linear fit of the diffusion parameters found for the three or more calculations used to determine the equilibrium volume. The fit produces D at zero pressure and its the first derivative which is used to define the activation volume, V a = − k B T d ( ln D ) / d P . Errors, in parentheses, are derived using standard propagation of errors based on the statistical error estimates from the raw data and represent estimated 95% confidence intervals on the last digit. Composition Solvent (Ni) Solute (X) Cell Alloy D(Ni) V a ( Ni ) D(X) V a ( X ) Ni 500 Ni 5.3(3) 1.3(3) Ni 473 Re 27 Ni–5.4Re 5.0(2) 1.3(2) 3.6(4) 0.3(5) Ni 473 Ta 27 Ni–5.4Ta 4.6(1) 1.3(2) 3.7(3) 0.5(4) Ni 473 W 27 Ni–5.4W 4.2(2) 1.3(2) 3.6(4) 0.9(6) Ni 400 Al 100 Ni–20Al 3.4(4) 1.2(2) 3.5(3) 2.3(4) Ni 400 Re 100 Ni–20Re 3.2(2) 0.9(2) 2.3(2) 0.8(3) Ni 400 Ta 100 Ni–20Ta 3.5(1) 1.2(2) 2.9(2) 0.9(4) Ni 400 W 100 Ni–20W 3.2(1) 1.1(2) 2.5(3) 1.1(2) Table II. Calculated atomic volumes ( cm 3 / mole ) and volumetric thermal expansion coefficients ( 10 − 5 K − 1 ) for molten Ni alloys at 1750 and 1830 K. The numbers in parentheses represent estimated 95% confidence intervals on the last digit. The calculated (AIMD) results are compared with the predictions of the parameterized model due to Mukai et al. 10 For the Ni–Ta alloys Mukai fit to compositions in the dilute limit ( < 3.5 at . % ) making it inappropriate to extrapolate to high solute concentrations. Composition T = 1750 K T = 1830 K AIMD Mukai AIMD Mukai V β V β V β V β Al 500 12.80(2) 12.0 12.91(3) 10.9 Ni 500 7.57(1) 7.10 7.4597 18.6 7.62(1) 6.71 7.5724 18.6 Ni 400 Al 100 7.88(1) 7.33 7.7628 13.9 7.94(1) 5.55 7.8492 13.8 Ni 473 W 27 7.66(1) 6.61 7.5534 16.3 7.70(1) 5.74 7.6520 16.1 Ni 400 W 100 7.94(1) 6.38 6.5192 155. 7.98(1) 6.44 7.3294 138. Ni 473 Re 27 7.65(1) 7.37 7.4940 26.0 7.69(1) 7.00 7.6499 25.5 Ni 400 Re 100 7.91(1) 6.84 7.5869 44.9 7.93(1) 6.25 7.8593 43.3 Ni 473 Ta 27 7.70(1) 7.28 7.3310 29.7 7.75(1) 6.26 7.5053 29.0 Ni 400 Ta 100 8.14(1) 10.5 ⋯ 8.18(1) 9.09 ⋯ Ni 436 Al 50 W 14 7.77(1) 7.52 7.6920 12.0 7.80(1) 6.18 7.7655 11.8 Ni 436 Al 50 Re 14 7.75(1) 7.62 7.6291 20.0 7.80(1) 9.10 7.7510 19.7 Ni 436 Al 50 Ta 14 7.79(1) 7.74 7.6911 10.4 7.84(1) 7.29 7.7553 10.4 Table III. Partial molar volumes at infinite dilution. Chemistry T = 1750 K T = 1850 K Solute PMV AIMD Mukai AIMD Mukai W V ¯ W ∞ / V Ni 1.25 1.55 1.24 1.33 Re V ¯ Re ∞ / V Ni 1.22 1.08 1.20 1.19 Ta V ¯ Ta ∞ / V Ni 1.38 2.13 1.37 1.61 ",

year = "2010",

month = jun,

day = "1",

doi = "10.1063/1.3437644",

language = "English (US)",

volume = "107",

journal = "Journal of Applied Physics",

issn = "0021-8979",

publisher = "American Institute of Physics Publising LLC",

number = "11",

}

TY - JOUR

T1 - Ab initio simulations of molten Ni alloys

AU - Woodward, Christopher

AU - Asta, Mark

AU - Trinkle, Dallas R.

AU - Lill, James

AU - Angioletti-Uberti, Stefano

N1 - Funding Information: This research was supported in part by a grant of computer time from the DoD High Performance Computing Modernization Program at the Air Force Research Laboratory DoD Supercomputing Research Center (AFRL-DSRC). MA and DRT were supported in part with a grant from the Air Force Office of Scientific Research under the Materials Engineering for Affordable New Systems (MEANS-II) program. The authors gratefully acknowledge insightful discussions with T. Pollock, P. Voorhees, O. Senkov, and S.H. Davis, and the technical assistance provided by S. Kajihara at the AFRL-DSRC. FIG. 1. Calculated AIMD mean-square displacements of solvent (left) and solute (right) species for elemental Ni and binary Ni–X ( X = Al , W, Re, and Ta) alloys at 1830 K. Deviations in the “random walk” from the long-time linear diffusion relation, ⟨ | r ( t ) − r ( 0 ) | 2 ⟩ = 6 D t , are shown as filled areas for each species. The results shown here are from the lowest pressure simulations at these chemistries. The diffusion constants (d) in Table I are derived from the slopes of the mean-square displacement curves at several volumes interpolated to zero pressure. Self diffusion of Ni decreases with solute additions with Al producing the smallest effect and W the largest. The relative solute diffusion in these liquid Ni–X metals follows the same trends of the respective solvent diffusion. FIG. 2. Radial distribution functions calculated from AIMD simulations for elemental Ni and binary Ni–X ( X = Al , W, and Re) alloys at T = 1830 K . The results shown here are from the lowest pressure simulations at these chemistries. The three plots show results, from left to right, for solvent–solvent (Ni–Ni), solvent–solute (Ni–X), and solute–solute (X–X) pairs. FIG. 3. CNA of pure Ni, Ni 473 Re 27 , and Ni 473 W 27 at 1830 K. The combined analysis shows the presence of similar short-range order in the three samples, with almost no dependence on composition. Icosahedral and bcc type ordering are found to be the most abundant. FIG. 4. Angle distribution function P ( θ ) at 1830 K for pure Ni, Ni 473 Re 27 , and Ni 473 W 27 . For perfect icosahedric or bcc like structures the two main peaks are expected to be around 60° and 108°, in our samples distortions due to the liquid nature shift the peaks to lower values. The angle distribution for all three cases of the Ni-centered data fall on essentially the same line, and there is a slight shift to lower angles for the W centered distribution relative to the rest of the data. FIG. 5. Graphic representation of the equation of state calculations for liquid metal Ni 400 Al 100 alloy at 1830 K. Representative AIMD calculations of pressure as a function of simulation time for four volumes (left) with a horizontal line indicating time-averaged values. The volume at these pressures, with error bars, (right) are fit to a quadratic polynomial, with results of this least-squares fit shown in inset. Interpolating to the zero pressure volume produces the predicted equilibrium volume the bulk modulus and its derivative for a given composition and temperature. Error bars and estimated uncertainties are based on standard uncertainty analysis. FIG. 6. Comparison of molar volumes calculated with AIMD simulations and estimated using the Mukai parameterization. Data in perfect agreement would fall on the line representing a slope of one, the dashed line indicates where the two results differ by 2%. The outliers are compositions that fall outside the composition ranges included in the fit of the Mukai model. FIG. 7. Variation in molar volumes at 1750 K for ternary and binary alloys calculated using AIMD simulations and estimated using the Mukai parameterization. The figure on the left shows compositions spanning the ternary triangle (see inset). Results are linear in composition with deviations from linearity of less than 0.8%. The Mukai model results for Ni 473 Ta 27 are the exception producing deviations from linearity of approximately 3%. The figure on the right shows binary Ni–X ( X = W and Re) compositions up to Ni – 20 X at . % which is outside the range of the Mukai reference measurements. The Mukai Ni–W molar volumes show significant deviations from linearity, which is not predicted by the AIMD simulations. Similar, though far more dramatic deviations are observed for Ni–Ta alloys in this range of composition. FIG. 8. The variation in molar volume with temperature for elemental Ni and Ni 473 Al 27 calculated using N V T and N P T ensembles. The coefficient of thermal expansion ( β = V − 1 d V / d T ) , calculated from a linear fit to each data set, are shown adjacent to each curve. The two methods for deriving the molar volume are within numerical error of the respective calculations, producing slopes, and β that are also within numerical error. Table I. Calculated diffusion parameters ( 10 − 5 cm 2 / s ) and activation volumes for binary Ni alloys at 1830 K. Values for D are the result of a linear fit of the diffusion parameters found for the three or more calculations used to determine the equilibrium volume. The fit produces D at zero pressure and its the first derivative which is used to define the activation volume, V a = − k B T d ( ln D ) / d P . Errors, in parentheses, are derived using standard propagation of errors based on the statistical error estimates from the raw data and represent estimated 95% confidence intervals on the last digit. Composition Solvent (Ni) Solute (X) Cell Alloy D(Ni) V a ( Ni ) D(X) V a ( X ) Ni 500 Ni 5.3(3) 1.3(3) Ni 473 Re 27 Ni–5.4Re 5.0(2) 1.3(2) 3.6(4) 0.3(5) Ni 473 Ta 27 Ni–5.4Ta 4.6(1) 1.3(2) 3.7(3) 0.5(4) Ni 473 W 27 Ni–5.4W 4.2(2) 1.3(2) 3.6(4) 0.9(6) Ni 400 Al 100 Ni–20Al 3.4(4) 1.2(2) 3.5(3) 2.3(4) Ni 400 Re 100 Ni–20Re 3.2(2) 0.9(2) 2.3(2) 0.8(3) Ni 400 Ta 100 Ni–20Ta 3.5(1) 1.2(2) 2.9(2) 0.9(4) Ni 400 W 100 Ni–20W 3.2(1) 1.1(2) 2.5(3) 1.1(2) Table II. Calculated atomic volumes ( cm 3 / mole ) and volumetric thermal expansion coefficients ( 10 − 5 K − 1 ) for molten Ni alloys at 1750 and 1830 K. The numbers in parentheses represent estimated 95% confidence intervals on the last digit. The calculated (AIMD) results are compared with the predictions of the parameterized model due to Mukai et al. 10 For the Ni–Ta alloys Mukai fit to compositions in the dilute limit ( < 3.5 at . % ) making it inappropriate to extrapolate to high solute concentrations. Composition T = 1750 K T = 1830 K AIMD Mukai AIMD Mukai V β V β V β V β Al 500 12.80(2) 12.0 12.91(3) 10.9 Ni 500 7.57(1) 7.10 7.4597 18.6 7.62(1) 6.71 7.5724 18.6 Ni 400 Al 100 7.88(1) 7.33 7.7628 13.9 7.94(1) 5.55 7.8492 13.8 Ni 473 W 27 7.66(1) 6.61 7.5534 16.3 7.70(1) 5.74 7.6520 16.1 Ni 400 W 100 7.94(1) 6.38 6.5192 155. 7.98(1) 6.44 7.3294 138. Ni 473 Re 27 7.65(1) 7.37 7.4940 26.0 7.69(1) 7.00 7.6499 25.5 Ni 400 Re 100 7.91(1) 6.84 7.5869 44.9 7.93(1) 6.25 7.8593 43.3 Ni 473 Ta 27 7.70(1) 7.28 7.3310 29.7 7.75(1) 6.26 7.5053 29.0 Ni 400 Ta 100 8.14(1) 10.5 ⋯ 8.18(1) 9.09 ⋯ Ni 436 Al 50 W 14 7.77(1) 7.52 7.6920 12.0 7.80(1) 6.18 7.7655 11.8 Ni 436 Al 50 Re 14 7.75(1) 7.62 7.6291 20.0 7.80(1) 9.10 7.7510 19.7 Ni 436 Al 50 Ta 14 7.79(1) 7.74 7.6911 10.4 7.84(1) 7.29 7.7553 10.4 Table III. Partial molar volumes at infinite dilution. Chemistry T = 1750 K T = 1850 K Solute PMV AIMD Mukai AIMD Mukai W V ¯ W ∞ / V Ni 1.25 1.55 1.24 1.33 Re V ¯ Re ∞ / V Ni 1.22 1.08 1.20 1.19 Ta V ¯ Ta ∞ / V Ni 1.38 2.13 1.37 1.61

PY - 2010/6/1

Y1 - 2010/6/1

N2 - Convective instabilities responsible for misoriented grains in directionally solidified turbine airfoils are produced by variations in liquid-metal density with composition and temperature across the solidification zone. Here, fundamental properties of molten Ni-based alloys, required for modeling these instabilities, are calculated using ab initio molecular dynamics simulations. Equations of state are derived from constant number-volume- temperature ensembles at 1830 and 1750 K for elemental, binary (Ni-X, X=Al, W, Re, and Ta) and ternary (Ni-Al-X, X=W, Re, and Ta) Ni alloys. Calculated molar volumes agree to within 0.6%-1.8% of available measurements. Predictions are used to investigate the range of accuracy of a parameterization of molar volumes with composition and temperature based on measurements of binary alloys. Structural analysis reveals a pronounced tendency for icosahedral short-range order for Ni-W and Ni-Re alloys and the calculations provide estimates of diffusion rates and their dependence on compositions and temperature.

AB - Convective instabilities responsible for misoriented grains in directionally solidified turbine airfoils are produced by variations in liquid-metal density with composition and temperature across the solidification zone. Here, fundamental properties of molten Ni-based alloys, required for modeling these instabilities, are calculated using ab initio molecular dynamics simulations. Equations of state are derived from constant number-volume- temperature ensembles at 1830 and 1750 K for elemental, binary (Ni-X, X=Al, W, Re, and Ta) and ternary (Ni-Al-X, X=W, Re, and Ta) Ni alloys. Calculated molar volumes agree to within 0.6%-1.8% of available measurements. Predictions are used to investigate the range of accuracy of a parameterization of molar volumes with composition and temperature based on measurements of binary alloys. Structural analysis reveals a pronounced tendency for icosahedral short-range order for Ni-W and Ni-Re alloys and the calculations provide estimates of diffusion rates and their dependence on compositions and temperature.

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U2 - 10.1063/1.3437644

DO - 10.1063/1.3437644

M3 - Article

AN - SCOPUS:77953648971

SN - 0021-8979

VL - 107

JO - Journal of Applied Physics

JF - Journal of Applied Physics

IS - 11

M1 - 113522

ER -

Ab initio simulations of molten Ni alloys

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