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Accurate determination of the Gibbs energy of Cu–Zr melts using the thermodynamic integration method in Monte Carlo simulations
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10.1063/1.3624530
/content/aip/journal/jcp/135/8/10.1063/1.3624530
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/8/10.1063/1.3624530

Figures

Image of FIG. 1.
FIG. 1.

Partial RDF of Cu50Zr50(liq.) at 1800 K and 1500 K. The solid lines represent the MCS results of the present study; the circles (T = 1800 K) and the triangles (T = 1500 K) are the results obtained by Ref. 57.

Image of FIG. 2.
FIG. 2.

Atomic density as a function of temperature for different Cu1–x Zr x melts. The solid lines represent the experimental results of Ref. 40 for Cu–Zr melts, the assessment of Ref. 90 for pure Cu(liq.), and the experimental results of Ref. 91 for pure Zr(liq.), respectively. The symbols represent: open circles = MCS of the present work, stars = experimental data of Ref. 92, filled diamonds = experimental data of Ref. 43. The dashed line represents the lowest eutectic temperature of the Cu–Zr system: Cu10Zr7(s) + CuZr(s) →Liquid.

Image of FIG. 3.
FIG. 3.

Atomic density as a function of the molar fraction of Zr for Cu–Zr: (a) liquid alloys. The solid line represents the exponential regression of the data of Ref. 40 (T = 1473 K). The open circles are the atomic densities obtained by MCS (T = 1500 K); (b) amorphous alloys (T = 300 K). The solid line represents the exponential regression of the data of Ref. 41. The symbols represent: open circles = MCS of the present study, stars = experimental data of Ref. 36, square = experimental data of Ref. 51.

Image of FIG. 4.
FIG. 4.

Evolution of the isothermal bulk modulus of Cu–Zr melts as a function of temperature. The solid line represents a linear regression of the MD simulation results of Ref. 43 for a Cu64.5Zr35.5 liquid alloy. The open circles represent the MCS of the present work for the Cu64.5Zr35.5 melt. The filled circles are the MCS results obtained for pure Cu(liq.); the half-filled circles are the MCS results for pure Zr(liq.).

Image of FIG. 5.
FIG. 5.

Total RDF of (a) Cu64Zr36, Cu57Zr43, Cu50Zr50, and Cu30Zr70 liquid alloys. The filled circles represent the experimental data of Ref. 49 obtained at 1223 K, the hall-filled (1540 K) and open circles (1450 K) are the data of Ref. 45; The hall-filled (1400 K) and open triangles (1300 K) are the data of Ref. 50. Solid lines represent our NPT-MCS results. (b) Cu64.5Zr35.5 amorphous alloy. The thick line represents the amorphous alloy obtained by NPT-MCS for an infinite quenching rate with T 0 = 1200 K and T F = 800 K followed by an equilibrium cooling to 300 K. The thin line represents the amorphous alloy obtained by equilibrating a bcc structure at room temperature using NPT-MCS. Experimental data of Ref. 44 (squares), Ref. 41 (triangles), and Ref. 39 (circles) are also presented in this figure.

Image of FIG. 6.
FIG. 6.

Comparison between partial RDF for NVT-MCS of the present work (solid lines) and NVT-AIMD (dashed lines) calculated by Ref. 56 for Cu28Zr72(a), Cu46Zr54(b), Cu64Zr36(c), and Cu80Zr20(d) melts at 1500 K.

Image of FIG. 7.
FIG. 7.

Simulation results for the integrand in the TI method for X Zr equals to (a) 0, (b) 0.2, (c) 0.5, (d) 0.8, and (e) 1 at 1800 K. The solid lines represent the spline interpolation performed for each composition.

Image of FIG. 8.
FIG. 8.

Comparison between the MCS (circles) and the calculated thermodynamic properties obtained using the MQMPA (solid lines) of Cu–Zr(liq.) at 1800 K (a) pair fractions, (b) enthalpy of mixing, and (c) entropy of mixing.

Image of FIG. 9.
FIG. 9.

Comparison between predicted (solid line) activity of copper at 1499 K in Cu–Zr melts and experimental data of Ref. 8 (circles, T = 1499 K) and Ref. 13 (triangles, T = 1473 K).

Image of FIG. 10.
FIG. 10.

This figure presents the various entropy contributions (dashed lines) and the resulting total entropy of mixing (solid line) calculated from the hard sphere mixture theory. The circles represent the entropy of mixing obtained from the TI method. The effect of the electronic contribution using the Sommerfeld model is also clearly presented in this figure.

Image of FIG. 11.
FIG. 11.

The solid line presents the fitted curve of as a function of X Zr used in Eq. (20) to reproduce the entropy of mixing at 1800 K obtained from the TI method. The diamonds represent the experimental data of Ref. 100 obtained for Cu–Zr amorphous alloys, while the triangle symbol represents the experimental value for pure amorphous Zr determined by Ref. 101. The value of for pure Cu was estimated from the work of Ref. 100.

Tables

Generic image for table
Table I.

Thermal expansion of Cu–Zr liquid and amorphous alloys with α V = cte.

Generic image for table
Table II.

Summary of the first-nearest-neighbor coordination numbers in Cu1–x Zr x melts.

Generic image for table
Table III.

Summary of the results obtained in NPT/NVT simulations and the thermodynamic functions calculated from the TI method at 1800 K.

Generic image for table
Table IV.

Optimized thermodynamic parameters of the MQMPA model for the Cu–Zr liquid phase.

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/content/aip/journal/jcp/135/8/10.1063/1.3624530
2011-08-23
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Accurate determination of the Gibbs energy of Cu–Zr melts using the thermodynamic integration method in Monte Carlo simulations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/8/10.1063/1.3624530
10.1063/1.3624530
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