Abstract
The investigation of phase equilibria in nanosystems has become one of the new trends in chemical thermodynamics. For binary alloys with limited mutual solubilities, a reduction of the system’s volume can be accompanied by significant changes of solubilities and the appearance of unusual metastable phases. To comprehend the structural characteristics and the thermodynamical stability of nanoalloys and to improve their performance, a knowledge of their phase equilibria, that considers their size and shape dependence, is critically needed. Due to the fact that experimental investigations are extremely challenging to perform at the nanoscale, useful predictions can be provided by nanothermodynamical simulations. In this paper, size- and shape-dependent phase equilibria in core-shell nanoparticles of the Pb5(VO4)3Cl–Pb5(PO4)3Cl stratifying solid solution are calculated. Those compounds are subjects of biochemistry and geochemistry, known as natural minerals vanadinite and pyromorphite. In a core-shell structure, two heterogeneous states are possible. At the nanoscale, one of them is metastable and the size- and shape-dependent properties of co-existing phases are different in each state. The shape of each phase is modeled by its shape coefficient which is equal to the ratio between surface areas of the phase and the sphere of the same volume. The thermodynamical stability of heterogeneous states depends on shape coefficients of both phases. The geometrical properties of core-shell-nanoparticles are also determined by using the fractal geometry.
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References
Magnin, Y., Zappelli, A., Amara, H., Ducastelle, F., Bichara, C.: Size dependent phase diagrams of nickel-carbon nanoparticles. Phys. Rev. Lett. 115(20), 205502–205506 (2015)
Dahan, Y., Makov, G., Shneck, R.Z.: Nanometric size-dependent phase diagram of Bi-Sn. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 53, 136–145 (2016)
Park, J., Lee, J.: Phase diagram reassessment of Ag-Au system including size effect. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 32(1), 135–141 (2008)
Monji, F., Jabbareh, M.A.: Thermodynamic model for prediction of binary alloy nanoparticle phase diagram including size effect. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 58, 1–5 (2017)
Fedoseev, V.B., Shishulin, A.V., Titaeva, E.K., Fedoseeva, E.N.: On the possibility on the formation of NaCl-KCl solid-solution crystal from an aqueous solution at room temperature in small-volume systems. Phys. Solid State 58(10), 2095–2100 (2016)
Shishulin, A.V., Fedoseev, V.B.: Size effect in the phase separation of Cr-W solid solutions. Inorg. Mater. 54(6), 546–549 (2018)
Straumal, B., Baretzky, B., Mazilkin, A., Protasova, S., Myatiev, A., Straumal, P.: Increase of Mn solubility with decreasing grain size in ZnO. J. Eur. Ceram. Soc. 29(10), 1963–1970 (2009)
Ghasemi, M., Zanolli, Z., Stankovski, M., Johansson, J.: Size- and shape-dependent phase diagram of In-Sb nano-alloys. Nanoscale 7, 17387–17396 (2015)
Cui, M., Lu, H., Jiang, H., Cao, Z., Meng, X.: Phase diagram of continuous binary nanoalloys: size, shape and segregation effects. Sci. Rep. 7, 1–10 (2017)
Guisbiers, G., Mendoza-Cruz, R., Bazán-Díaz, L., Velázquez-Salazar, J.J., Mendoza-Pérez, R., Robledo-Torres, J., et al.: Electrum, the gold–silver alloy, from the bulk scale to the nanoscale: synthesis, properties, and segregation rules. ASC Nano 10(1), 188–198 (2015)
Guisbiers, G., Mendoza-Pérez, R., Bazán-Díaz, L., Mendoza-Cruz, R., Velázquez-Salazar, J.J., Yakamán, M.J.: Size and shape effects on the phase diagrams of nickel-based bimetallic nanoalloys. J. Phys. Chem. 121(12), 6930–6939 (2017)
Guisbiers, G., Khanal, S., Ruis-Zepeda, F., Roque de la Puente, J., Yakamán, M.J.: Cu-Ni nano-alloy: mixed, core-shell or janus nano-particle. Nanoscale 24(6), 14630–14635 (2014)
Tovbin, YuK: Lower size boundary for the applicability of thermodynamics. Russ. J. Phys. Chem. A 86(9), 1356–1369 (2012)
Fedoseev, V.B., Potapov, A.A., Shishulin, A.V., Fedoseeva, E.N.: Size and shape effect on the phase transitions in a small system with fractal interphase boundaries. Eurasian Phys. Tech. J 14(1), 18–24 (2017)
Shishulin, A.V., Fedoseev, V.B., Shishulina, A.V.: Environment-dependent phase equilibria in a small volume system in case of decomposition of Bi-Sb solid solutions. Butlerov Commun. 51(7), 31–37 (2017). (In Russian)
Gusev, A.I., Rempel, A.A.: Nanocrystalline Materials. Fizmatlit, Moscow (2000). (In Russian)
Gladkikh, N.T., Dukarov, S.V., Kryshtal, A.P., Larin, V.I., Sukhov, V.N., Bogatyrenko, S.I.: Surface Phenomena and Phase Transitions in Condensed Thin Films. V. N. Karazin Kharkiv National University, Kharkiv (2004). (In Russian)
Alymov, M.I., Shorshorov, MKh: The influence of size factors on the melting temperature and surface tension of ultra-disperse particles. Metally 2, 29–31 (1999). (In Russian)
Rusanov, A.I.: Phase Equilibria and Surface Phenomena. Khimiya, Leningrad (1967). (In Russian)
Gusarov, V.V.: The thermal effect of melting in polycrystalline systems. Thermochim. Acta 256(2), 467–472 (1995)
Betkhtin, A.G.: The Course of Mineralogy. Gosudarstvennoye nauchno-tekhnicheskoye izdatel’stvo po geologii i okhrane nedr, Moscow (1956). (In Russian)
Chernorukov, N.G., Knyazev, A.V., Bulanov, E.N.: Isomorphism and phase diagram of the Pb5(VO4)3Cl–Pb5(PO4)3Cl system. Russ. J. Inorg. Chem. 55(9), 1463–1470 (2010)
Hourlier, D., Perrot, P.: Au-Si and Au-Ge phase diagrams for nanosystems. Mater. Sci. Forum 653, 77–85 (2010)
Rakovan, J.: Growth and surface properties of apatite. Rev. Mineral. Geochem. 48(1), 51–86 (2002)
Lazarev, S.Y.: Assessment of substance properties by the criteria of surface energy, hardness and energy density. Metalloobrabotka 2, 38–42 (2003). (In Russian)
Kalinin, S.V., Gorbachev, D.L., Borisevich, A.Y., Tomashevitch, K.V., Vertegel, A.A., Markworth, A.J., et al.: Evolution of fractal particles in systems with conserved order parameter. Phys. Rev. E 61(2), 1189–1194 (2000)
Katunin, A.: Construction of fractals based on catalan solids. Int. J. Math. Sci. Comput. (IJMSC) 3(4), 1–7 (2017). https://doi.org/10.5815/ijmsc.2017.04.01
Nayak, S.R., Mishra, J.: On calculation of fractal dimension of color images. Int. J. Image Graph. Sig. Process. (IJIGSP) 9(3), 33–40 (2017). https://doi.org/10.5815/ijigsp.2017.03.04
Khemis, K., Lazzouni, S.A., Messadi, M., Loudjedi, S., Bessaid, A.: New algorithm for fractal dimension estimation based on texture measurements: application on breast tissue characterization. Int. J. Image Graph. Sig. Process. (IJIGSP) 8(4), 9–15 (2016). https://doi.org/10.5815/ijigsp.2016.04.02
Fedoseev, V.B., Shishulin, A.V.: Shape effect in layering of solid solutions in small volume: bismuth-antimony alloy. Phys. Solid State 60(7), 1398–1404 (2018)
Acknowledgements
The authors acknowledge the support from the Russian Foundation for Basic Research (RFBR) (project № 18-08-01356). V. B. Fedoseev acknowledges the support from the Russian Science Foundation (project № 15-13-00137–p.).
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Shishulin, A.V., Potapov, A.A., Fedoseev, V.B. (2020). Phase Equilibria in Fractal Core-Shell Nanoparticles of the Pb5(VO4)3Cl–Pb5(PO4)3Cl System: The Influence of Size and Shape. In: Hu, Z., Petoukhov, S., He, M. (eds) Advances in Artificial Systems for Medicine and Education II. AIMEE2018 2018. Advances in Intelligent Systems and Computing, vol 902. Springer, Cham. https://doi.org/10.1007/978-3-030-12082-5_37
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