Skip to main content
Log in

Merging of Solidus and Liquidus Curves in Copper–Nickel Nanophase Diagram due to Segregation

  • Original Contribution
  • Published:
Journal of The Institution of Engineers (India): Series D Aims and scope Submit manuscript

Abstract

Phase diagram was predicted for Cu–Ni nanoalloy system using regular solution considering various models with and without segregation. Phase diagrams for nanoparticles are affected by the melting point of nanoparticles, and various models are available to predict the melting point for nanoparticles. Hence, choosing the right model helps in accurate nanophase diagram predictions. Three models are considered to predict the melting point of nanoparticles and phase diagrams. Thermodynamic model, enthalpy and entropy model and crystal structure models were compared for their melting points and phase diagram predictions. These three models were then compared with experimental results carried out by Sopousek et al. for a 26 nm particle size. It was found that for a 11.1 Wt% Ni nanoalloy, thermodynamic model accurately predicts the phase diagram with an error of 0.09% compared to enthalpy and entropy model. Thermodynamic model is also known as the surface-phonon instability model which considers various factors like surface phonons, atoms and intrinsic defects in the nanoparticle and hence accurately predicts the melting point and the phase diagram. Further segregation effects were also considered, and for the first time, a comparison between three models is reported which shows significant merging of solidus and liquidus curves in thermodynamic model and enthalpy and entropy model using William–Nason’s model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. W.A. Jesser, G.J. Shiflet, G.L. Allen, J.L. Crawford, Equilibrium phase diagrams of isolated nano-phases. Mater. Res. Innov. (1999). https://doi.org/10.1007/s100190050087

    Article  Google Scholar 

  2. N. Saunders, A.P. Miodownik, Evaluation of glass forming ability in binary and ternary metallic alloy systems—an application of thermodynamic phase diagram calculations. Mater. Sci. Technol. (2014). https://doi.org/10.1179/mst.1988.4.9.768

    Article  Google Scholar 

  3. H.J. Seifert, H.L. Lukas, F. Aldinger, Development of Si–B–C–N ceramics supported by phase diagrams and thermochemistry. Ber. Der Bunsenges. Für Phys. Chem. (2012). https://doi.org/10.1002/bbpc.19981020942

    Article  Google Scholar 

  4. N.A. Pertsev, A.G. Zembilgotov, A.K. Tagantsev, Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films. Phys. Rev. Lett. (1998). https://doi.org/10.1103/physrevlett.80.1988

    Article  Google Scholar 

  5. R. Klenk, T. Walter, H.W. Schock, D. Cahen, A model for the successful growth of polycrystalline films of CuInSe2 by multisource physical vacuum evaporation. Adv. Mater. (1993). https://doi.org/10.1002/adma.19930050209

    Article  Google Scholar 

  6. G. Inden, The role of magnetism in the calculation of phase diagrams. Phys B+C (1981). https://doi.org/10.1016/0378-4363(81)91004-4

    Article  Google Scholar 

  7. D. Li, L. Liu, Y. Zhang, C. Ye, X. Ren, Y. Yang et al., Phase diagram calculation of high chromium cast irons and influence of its chemical composition. Mater. Des. (2009). https://doi.org/10.1016/j.matdes.2008.04.061

    Article  Google Scholar 

  8. A. San-Miguel, Nanomaterials under high-pressure. Chem. Soc. Rev. (2006). https://doi.org/10.1039/b517779k

    Article  Google Scholar 

  9. V. Bobnar, Z. Kutnjak, R. Pirc, A. Levstik, Electric-field-temperature phase diagram of the relaxor ferroelectric lanthanum-modified lead zirconate titanate. Phys. Rev. B Condens. Matter Mater. Phys. (1999). https://doi.org/10.1103/physrevb.60.6420

    Article  Google Scholar 

  10. M. Wautelet, On the shape dependence of the melting temperature of small particles. Phys. Lett. Sect. Gen. Solid State Phys. 246, 341–342 (1998). https://doi.org/10.1016/S0375-9601(98)00538-6

    Article  Google Scholar 

  11. M. Wautelet, J.P. Dauchot, M. Hecq, On the phase diagram of non-spherical nanoparticles. J. Phys. Condens. Matter (2003). https://doi.org/10.1088/0953-8984/15/21/313

    Article  Google Scholar 

  12. R. Vallée, M. Wautelet, J.P. Dauchot, M. Hecq, Size and segregation effects on the phase diagrams of nanoparticles of binary systems. Nanotechnology (2001). https://doi.org/10.1088/0957-4484/12/1/312

    Article  Google Scholar 

  13. M. Wautelet, J.P. Dauchot, M. Hecq, Size effects on the phase diagrams of nanoparticles of various shapes. Mater. Sci. Eng. C (2003). https://doi.org/10.1016/s0928-4931(02)00266-7

    Article  Google Scholar 

  14. P.G. Bruce, B. Scrosati, J. Tarascon, Lithium batteries nanomaterials for rechargeable lithium batteries. Angew. Chem. Int. Ed. (2008). https://doi.org/10.1002/anie.200702505

    Article  Google Scholar 

  15. X. Chen, S.S. Mao, Titanium dioxide nanomaterials: synthesis, properties, modifications and applications. Chem. Rev. (2007). https://doi.org/10.1021/cr0500535

    Article  Google Scholar 

  16. G. Guisbiers, S. Mejia-Rosales, S. Khanal, F. Ruiz-Zepeda, R.L. Whetten, M. José-Yacaman, Gold-copper nano-alloy, “tumbaga”, in the era of nano: phase diagram and segregation. Nano Lett. (2014). https://doi.org/10.1021/nl503584q

    Article  Google Scholar 

  17. E. Sutter, P. Sutter, Phase diagram of nanoscale alloy particles used for vapor–liquid–solid growth of semiconductor nanowires. Nano Lett. (2008). https://doi.org/10.1021/nl0719630

    Article  Google Scholar 

  18. M. Asadikiya, H. Sabarou, M. Chen, Y. Zhong, Phase diagram for a nano-yttria-stabilized zirconia system. RSC Adv. (2016). https://doi.org/10.1039/c5ra24330k

    Article  Google Scholar 

  19. T. Ivas, A.N. Grundy, E. Povoden-Karadeniz, L.J. Gauckler, Phase diagram of CeO 2CoO for nano-sized powders. CALPHAD Comput. Coupling Phase Diagr. Thermochem. (2012). https://doi.org/10.1016/j.calphad.2011.10.005

    Article  Google Scholar 

  20. H.L. Lukas, S.G. Fries, B. Sundman, Computational thermodynamics: the CALPHAD method (Cambridge University Press, Cambridge, 2007). https://doi.org/10.1017/cbo9780511804137

    Book  MATH  Google Scholar 

  21. Z.K. Liu, First-principles calculations and CALPHAD modeling of thermodynamics. J. Phase Equilibria Diffus. (2009). https://doi.org/10.1007/s11669-009-9570-6

    Article  Google Scholar 

  22. B. Sundman, J. Ågren, A regular solution model for phases with several components and sublattices, suitable for computer applications. J. Phys. Chem. Solids (1981). https://doi.org/10.1016/0022-3697(81)90144-x

    Article  Google Scholar 

  23. A. van de Walle, G. Ceder, Automating first-principles phase diagram calculations. J. Phase Equilibria (2002). https://doi.org/10.1361/105497102770331596

    Article  Google Scholar 

  24. G. Ouyang, X. Tan, C.X. Wang, G.W. Yang, Solid solubility limit in alloying nanoparticles. Nanotechnology 1, 2–3 (2006). https://doi.org/10.1088/0957-4484/17/16/042

    Article  Google Scholar 

  25. M. Cui, H. Lu, H. Jiang, Z. Cao, X. Meng, Phase diagram of continuous binary nanoalloys: size, shape, and segregation effects. Sci. Rep. (2017). https://doi.org/10.1038/srep41990

    Article  Google Scholar 

  26. G. Guisbiers, R. Mendoza-Cruz, L. Bazán-Díaz, J.J. Velázquez-Salazar, R. Mendoza-Perez, J.A. Robledo-Torres et al., Electrum, the gold-silver alloy, from the bulk scale to the nanoscale: synthesis, properties, and segregation rules. ACS Nano (2016). https://doi.org/10.1021/acsnano.5b05755

    Article  Google Scholar 

  27. G. Guisbiers, S. Khanal, F. Ruiz-Zepeda, J. Roque De La Puente, M. José-Yacaman, Cu–Ni nano-alloy: mixed, core-shell or Janus nano-particle? Nanoscale 6, 14630–14635 (2014). https://doi.org/10.1039/c4nr05739b

    Article  Google Scholar 

  28. S.H. Overbury, P.A. Bertrand, G.A. Somorjai, The surface composition of binary systems. Prediction of surface phase diagrams of solid solutions. Chem. Rev. (1975). https://doi.org/10.1021/cr60297a001

    Article  Google Scholar 

  29. S. an Mey, Thermodynamic re-evaluation of the CuNi system. CALPHAD (1992). https://doi.org/10.1016/0364-5916(92)90022-p

    Article  Google Scholar 

  30. A. Christensen, P. Stoltze, J.K. Norskov, Size dependence of phase separation in small bimetallic clusters. J. Phys. Condens. Matter (1995). https://doi.org/10.1088/0953-8984/7/6/008

    Article  Google Scholar 

  31. J. Lee, J. Park, T. Tanaka, Effects of interaction parameters and melting points of pure metals on the phase diagrams of the binary alloy nanoparticle systems: a classical approach based on the regular solution model. CALPHAD Comput. Coupling Phase Diagr. Thermochem. (2009). https://doi.org/10.1016/j.calphad.2008.11.001

    Article  Google Scholar 

  32. J. Park, J. Lee, Phase diagram reassessment of Ag–Au system including size effect. CALPHAD Comput. Coupling Phase Diagr. Thermochem. (2008). https://doi.org/10.1016/j.calphad.2007.07.004

    Article  Google Scholar 

  33. M. Wautelet, J.P. Dauchot, M. Hecq, Phase diagrams of small particles of binary systems: a theoretical approach. Nanotechnology (2000). https://doi.org/10.1088/0957-4484/11/1/302

    Article  Google Scholar 

  34. J. Ross, R.P. Andres, Melting temperature of small clusters. Surf. Sci. (1981). https://doi.org/10.1016/0039-6028(81)90175-8

    Article  Google Scholar 

  35. M. Wautelet, Estimation of the variation of the melting temperature with the size of small particles, on the basis of a surface-phonon instability model. J. Phys. D Appl. Phys. (1991). https://doi.org/10.1088/0022-3727/24/3/017

    Article  Google Scholar 

  36. P. Puri, V. Yang, Effect of particle size on melting of aluminum at nano scales. J. Phys. Chem. C (2007). https://doi.org/10.1021/jp0724774

    Article  Google Scholar 

  37. R.J.C. Brown, R.F.C. Brown, Melting point and molecular symmetry. J. Chem. Educ. (2009). https://doi.org/10.1021/ed077p724

    Article  Google Scholar 

  38. J. Sun, S.L. Simon, The melting behavior of aluminum nanoparticles. Thermochim. Acta (2007). https://doi.org/10.1016/j.tca.2007.07.007

    Article  Google Scholar 

  39. M. Schmidt, R. Kusche, B. Von Issendorff, H. Haberland, Irregular variations in the melting point of size-selected atomic clusters. Nature (1998). https://doi.org/10.1038/30415

    Article  Google Scholar 

  40. Q. Jiang, S. Zhang, M. Zhao, Size-dependent melting point of noble metals. Mater. Chem. Phys. (2003). https://doi.org/10.1016/s0254-0584(03)00201-3

    Article  Google Scholar 

  41. M. Wautelet, A.S. Shirinyan, Thermodynamics: nano vs. macro. Pure Appl. Chem. (2009). https://doi.org/10.1351/pac-con-08-07-04

    Article  Google Scholar 

  42. G. Guisbiers, G. Abudukelimu, Influence of nanomorphology on the melting and catalytic properties of convex polyhedral nanoparticles. J. Nanoparticle Res. (2013). https://doi.org/10.1007/s11051-013-1431-x

    Article  Google Scholar 

  43. H.M. Lu, F.Q. Han, X.K. Meng, Size-dependent thermodynamic properties of metallic nanowires. J. Phys. Chem. B. (2008). https://doi.org/10.1021/jp802888t

    Article  Google Scholar 

  44. K.K. Nanda, S.N. Sahu, S.N. Behera, Liquid-drop model for the size-dependent melting of low-dimensional systems. Phys. Rev. A Mol. Opt. Phys. (2002). https://doi.org/10.1103/physreva.66.013208

    Article  Google Scholar 

  45. A.S. Shirinyan, M. Wautelet, Phase separation in nanoparticles. Nanotechnology (2004). https://doi.org/10.1088/0957-4484/15/12/004

    Article  Google Scholar 

  46. Q. Jiang, H.X. Shi, M. Zhao, Melting thermodynamics of organic nanocrystals. J. Chem. Phys. (1999). https://doi.org/10.1063/1.479489

    Article  Google Scholar 

  47. G. Guisbiers, L. Buchaillot, Modeling the melting enthalpy of nanomaterials. J. Phys. Chem. C (2009). https://doi.org/10.1021/jp809338t

    Article  Google Scholar 

  48. M. Singh, S. Lara, S. Tlali, Effects of size and shape on the specific heat, melting entropy and enthalpy of nanomaterials. J. Taibah Univ. Sci. (2016). https://doi.org/10.1016/j.jtusci.2016.09.011

    Article  Google Scholar 

  49. W. Qi, Nanoscopic thermodynamics. Acc. Chem. Res. (2016). https://doi.org/10.1021/acs.accounts.6b00205

    Article  Google Scholar 

  50. L.H. Liang, D. Liu, Q. Jiang, Size-dependent continuous binary solution phase diagram. Nanotechnology (2003). https://doi.org/10.1088/0957-4484/14/4/306

    Article  Google Scholar 

  51. G. Li, Q. Wang, D. Li, X. Lü, J. He, Size and composition effects on the melting of bimetallic Cu–Ni clusters studied via molecular dynamics simulation. Mater. Chem. Phys. (2009). https://doi.org/10.1016/j.matchemphys.2008.10.031

    Article  Google Scholar 

  52. H. Liao, A. Fisher, Z.J. Xu, Surface segregation in bimetallic nanoparticles: a critical issue in electrocatalyst engineering. Small (2015). https://doi.org/10.1002/smll.201403380

    Article  Google Scholar 

  53. B.N. Wanjala, J. Luo, B. Fang, D. Mott, C.J. Zhong, Gold-platinum nanoparticles: alloying and phase segregation. J. Mater. Chem. (2011). https://doi.org/10.1039/c0jm02682d

    Article  Google Scholar 

  54. L. Deng, W. Hu, H. Deng, S. Xiao, Surface segregation and structural features of bimetallic Au–Pt nanoparticles. J. Phys. Chem. C (2010). https://doi.org/10.1021/jp100194p

    Article  Google Scholar 

  55. L. Peng, E. Ringe, R.P. Van Duyne, L.D. Marks, Segregation in bimetallic nanoparticles. Phys. Chem. Chem. Phys. (2015). https://doi.org/10.1039/c5cp01492a

    Article  Google Scholar 

  56. D.R. Gaskell, Introduction to the thermodynamics of materials (CRC Press, Hoboken, 1994). https://doi.org/10.1115/1.2901487

    Book  Google Scholar 

  57. J. Sopousek, J. Vrestal, J. Pinkas, P. Broz, J. Bursik, A. Styskalik et al., Cu–Ni nanoalloy phase diagram—prediction and experiment. CALPHAD Comput. Coupling Phase Diagr. Thermochem. (2014). https://doi.org/10.1016/j.calphad.2013.11.004

    Article  Google Scholar 

  58. T.T. Li, C. He, W.X. Zhang, M. Cheng, Structural and melting properties of Cu–Ni clusters: a simulation study. J. Alloys Compd. (2018). https://doi.org/10.1016/j.jallcom.2018.04.145

    Article  Google Scholar 

  59. J. Pinkas, J. Sopoušek, P. Brož, V. Vykoukal, J. Buršík, J. Vřešťál, Synthesis, structure, stability and phase diagrams of selected bimetallic silver- and nickel-based nanoparticles. CALPHAD Comput. Coupling Phase Diagr. Thermochem. (2019). https://doi.org/10.1016/j.calphad.2018.11.013

    Article  Google Scholar 

  60. F.L. Williams, D. Nason, Binary alloy surface compositions from bulk alloy thermodynamic data. Surf. Sci. (1974). https://doi.org/10.1016/0039-6028(74)90177-0

    Article  Google Scholar 

Download references

Acknowledgements

The authors thankfully acknowledge the financial support provided by the Institution of Engineers (India) (Project ID RDDR2017014) for carrying out research and development work in this subject. The authors would like to express deepest gratitude to late| Dr. B.N.V.Subrahmanya, Smt. B.V.Seetha, Shri M Narasimhan, Shri B.K.Ramesh, Shri B.V.Venkatasubrahmanya and all the other trustees and management, Principal and HOD (Department of Mechanical Engineering) of Jyothy Charitable trust and CIIRC for their immense support in all aspects. The authors also thank Visvesvaraya Technological University, Belgaum, and the management team and Principal of PES Institute of Technology and Siddaganga Institute of Technology for their assistance.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H. R. Aniruddha Ram.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ram, H.R.A., Venkatesh, K., Gopalakrishna, K. et al. Merging of Solidus and Liquidus Curves in Copper–Nickel Nanophase Diagram due to Segregation. J. Inst. Eng. India Ser. D 100, 243–253 (2019). https://doi.org/10.1007/s40033-019-00192-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40033-019-00192-3

Keywords

Navigation