Revisiting The Phase Diagram of Au – Cu Alloy at Nanoscales

Abstract

Au – Cu nanoparticles are widely used as catalysts in different chemical reactions. Since knowing the phase diagram of nano-alloys is crucial for effective design of nano-catalysts, there have been many efforts to predict the size effect on the phase diagram of the Au – Cu system. However, reported results are inconsistent and sometimes contradictory. In this work, a CALPHAD type thermodynamic model was applied to recalculate the phase diagram of Au – Cu binary alloy nanoparticles at different sizes. The results show that decreasing particle size decreases liquidus and solidus temperatures as well as the congruent melting point. It was also found that by reduction of the particle size, the composition of the congruent alloy shifts towards the Au – rich side of the phase diagram.

Keywords

• Size effect
• alloy nanoparticle
• Au – Cu alloy
• phase diagram
• CALPHAD method

References

1. X. Liu, A. Wang, T. Zhang, D. S. Su, and C. Y. Mou, “Au-Cu alloy nanoparticles supported on silica gel as catalyst for CO oxidation: Effects of Au/Cu ratios,” Catal. Today, 160, 103–108, 2011.
2. M. K. Birhanu et al., “Electrocatalytic reduction of carbon dioxide on gold–copper bimetallic nanoparticles: Effects of surface composition on selectivity,” Electrochim. Acta, 356, 136756, 2020.
3. W. Li, A. Wang, X. Liu, and T. Zhang, “Silica-supported Au-Cu alloy nanoparticles as an efficient catalyst for selective oxidation of alcohols,” Appl. Catal. A Gen., 433–434, 146–151, 2012.
4. M. Hajfathalian et al., “Photocatalytic Enhancements to the Reduction of 4-Nitrophenol by Resonantly Excited Triangular Gold-Copper Nanostructures,” J. Phys. Chem. C, 119, 17308–17315, 2015.
5. R. Biswas, S. Singh, I. Ahmed, R. A. Patil, Y. R. Ma, and K. K. Haldar, “Rational Design of Bimetallic Au/Cu Nanostructure: An Efficient Catalyst for Methanol Oxidation,” ChemNanoMat, 7, 158–164, 2021.
6. H. M. Lu and X. K. Meng, “Theoretical model to calculate catalytic activation energies of platinum nanoparticles of different sizes and shapes,” J. Phys. Chem. C, 114, 1534–1538, 2010.
7. N. Zhao, Y. Q. He, and C. C. Yang, “A new approach to construct bulk and size-dependent continuous binary solution phase diagrams of alloys,” RSC Adv., 5, 96323–96327, 2015.
8. T. Tanaka and S. Hara, “Thermodynamic evaluation of binary phase diagrams of small particle systems,” zeitschrift fur Met., 92, 467–472, 2001.

9. R. Vallée, M. Wautelet, J. P. Dauchot, and M. Hecq, “Size and segregation effects on the phase diagrams of nanoparticles of binary systems,” Nanotechnology, 12, 68–74, 2001.
10. G. Guisbiers, S. Mejia-Rosales, S. Khanal, F. Ruiz-Zepeda, R. L. Whetten, and M. José-Yacaman, “Gold-copper nano-alloy, " tumbaga ", in the era of nano: Phase diagram and segregation,” Nano Lett., 14, 6718–6726, 2014.
11. M. Cui, H. Lu, H. Jiang, Z. Cao, and X. Meng, “Phase Diagram of Continuous Binary Nanoalloys: Size, Shape, and Segregation Effects,” Sci. Rep., 7, 1–10, 2017.
12. A. P. Chernyshev, “The influence of the size effect on the transition of Au-Cu alloy nanoparticles to the dynamic amorphous state,” Mater. Today Proc., 25, 370–372, 2020.
13. H. R. Martínez-Muñoz and S. Mejía-Rosales, “The AuCu Phase Diagram at the Nano Scale: A Molecular Dynamics Approach,” J. Clust. Sci., doi: https://doi.org/10.1007/s10876-021-02015-6
14. M. Z. Chu et al., “Melting and phase diagram of Au-Cu alloy at nanoscale,” J. Alloys Compd., 891, 162029, 2021.
15. J. Park and J. Lee, “Phase diagram reassessment of Ag–Au system including size effect,” Calphad, 32, 135–141, Mar. 2008.
16. G. Garzel, J. Janczak-rusch, and L. Zabdyr, “Reassessment of the Ag – Cu phase diagram for nanosystems including particle size and shape effect,” CALPHAD Comput. Coupling Phase Diagrams Thermochem., 36, 52–56, 2012.
17. F. Monji and M. A. Jabbareh, “Thermodynamic model for prediction of binary alloy nanoparticle phase diagram including size dependent surface tension effect,” Calphad Comput. Coupling Phase Diagrams Thermochem., 58, 1–5, 2017.
18. M. A. Jabbareh and F. Monji, “Thermodynamic modeling of Ag – Cu nanoalloy phase diagram,” Calphad, 60, 208–213, 2018.
19. M. Z. Chu et al., “Thermodynamic reassessment of the Ag–Cu phase diagram at nano-scale,” Calphad, 72, 102233, 2021.
20. N. Sunders and A. P. Miodownik, CALPHAD ( Calculation of Phase Diagrams ): A Comprehensive Guide. Pergamon, 1998.
21. W. H. Qi, M. P. Wang, and Q. H. Liu, “Shape factor of nonspherical nanoparticles,” J. Mater. Sci., 40, 2737–2739, 2005.
22. J. A. V Butler, “The thermodynamics of the surfaces of solutions,” Proc. R. Soc. A, 135, 348–375, 1932.
23. S. Xiong, W. Qi, Y. Cheng, B. Huang, M. Wang, and Y. Li, “Modeling size effects on the surface free energy of metallic nanoparticles and nanocavities,” Phys. Chem. Chem. Phys., 13, 10648–10651, 2011.
24. A. Delsante, “SGTE data for pure elements” Calphad, 15, 317–425, 1991.
25. J. Sopousek et al., “Cu – Ni nanoalloy phase diagram – Prediction and experiment,” CALPHAD Comput. Coupling Phase Diagrams Thermochem., 45, 33–39, 2014.
26. B. Sundman, S. G. Fries, and W. A. Oates, “A thermodynamic assessment of the Au-Cu system,” Calphad, 22, 335–354, 1988.
27. K. K. Nanda, S. N. Sahu, and S. N. Behera, “Liquid-drop model for the size-dependent melting of low-dimensional systems,” Phys. Rev. A, 66, 013208, 2002.
28. J. M. McDavid and S. C. Fain, “Segregation at CuAu alloy surfaces,” Surf. Sci., 52, 161–173, 1975.
29. F. M. Takrrori and A. H. Ayyad, “Surface energy of metal alloy nanoparticles,” Appl. Surf. Sci., 401, 65–68, 2017. M. A. Jabbareh, “Size, shape and temperature dependent surface energy of binary alloy nanoparticles,” Appl. Surf. Sci., 426, 1094–1099, 2017.
30. C.-H. Huang, H. P. Wang, J.-E. Chang, and E. M. Eyring, “Synthesis of nanosize-controllable copper and its alloys in carbon shells,” Chem. Commun., 2, 4663–4465, 2009.
31. S. Delsante et al., “Synthesis and thermodynamics of Ag–Cu nanoparticles,” Phys. Chem. Chem. Phys., 17, 28387–28393, 2015.
32. G. Guisbiers, “Advances in thermodynamic modelling of nanoparticles,” Adv. Phys. X, 4, 1668299, 2019.
33. P. Buffat and J. P. Borel, “Size effect on the melting temperature of gold particles,” Phys. Rev. A, 13, 2287–2298, 1976.
34. Z. Cui, B. Ji, Q. Fu, H. Duan, Y. Xue, and Z. Li, “Research on size dependent integral melting thermodynamic properties of Cu nanoparticles,” J. Chem. Thermodyn., 149, 106148, 2020.
35. F. Delogu, “Structural and energetic properties of unsupported Cu nanoparticles from room temperature to the melting point: Molecular dynamics simulations,” Phys. Rev. B - Condens. Matter Mater. Phys., 72, 205418, 2005.
36. G. Guisbiers, “Review on the analytical models describing melting at the nanoscale,” J. Nanosci. Lett., 2, 8–18, 2012.
37. S. S. Kim, “Thermodynamic modeling of the CeO 2 – CoO nano-phase diagram,” J. Alloys Compd., 588, 697–704, 2014.