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Phase composition of multicomponent aluminum bronzes criteria-based evaluation (Part 1. Supersaturated copper α-matrix and phase composition of Cu–Al–X system multicomponent bronzes stability criteria)

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Parent Category: 2026

Category: Content №4 2026

Created on 24 August 2026

Last Updated on 24 August 2026

Published on 30 November -0001

Written by Т. V. Kimstach, K. І. Uzlov, G. G. Shvachych, О. P. Bilyi, S. I. Repyakh.

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Authors:

Т. V. Kimstach, orcid.org/0000-0002-8993-201X, Ukrainian State University of Science and Technologies, Dnipro, Ukraine; Iron and Steel Institute of Z. I. Nekrasov National Academy of Sciences of Ukraine, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

K. І. Uzlov, orcid.org/0000-0003-0744-9890, Ukrainian State University of Science and Technologies, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

G. G. Shvachych, orcid.org/0000-0002-9439-5511, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

О. P. Bilyi, orcid.org/0000-0003-1234-5404, Ukrainian State University of Science and Technologies, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

S. I. Repyakh*, orcid.org/0000-0003-0203-4135, Ukrainian State University of Science and Technologies, Dnipro, Ukraine, e-mail:  This email address is being protected from spambots. You need JavaScript enabled to view it.

* Corresponding author e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

повний текст / full article

Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2026, (4): 053 - 067

https://doi.org/10.33271/nvngu/2026-4/053

Abstract:

Purpose. To establish structurally reliable and thermodynamically justified criteria for assessing alloys supersaturated copper α-matrix stability and predicting the phase composition of multicomponent bronzes formed under crystallization and subsequent cooling non-equilibrium conditions.

Methodology. Methodology is based on thermodynamic analysis, structural-parametric approach and experimental data generalization combination. Copper matrix condition was estimated by parameter  (theoretically required and actual Cu content ratio). Thermodynamic analysis was performed within Gibbs energy minimization framework, taking into account small deviations and components with  activities connection. Structural and mechanical properties were evaluated using K_R criterion.

Findings. To assess in multicomponent bronzes single-phase state fixing or losing conditions, concentration parameter  has been proposed, which characterizes the conditions for solid solution non-equilibrium stability loss under casting conditions. It has been shown that at   1 conditions for secondary phase’s formation arise. K_R criterion has been proposed to assess structural and mechanical properties. It has been proven that  and K_R joint using provides “composition-stability-structure-properties” relationship for multicomponent aluminum bronzes comprehensive description.

Originality. For the first time, quantitatively consistent system has been established of correlations between supersaturation parameter , compositional criterion K_R and structural parameter  ‒ Cu–Al–Si–Mn–Sn system bronzes secondary phases volume fraction, which are formed under non-equilibrium conditions of solidification and in solid state subsequent cooling and are inherent in castings manufactured using foundry sand and metal molds.

Practical value. Using indicator () and criterion (K_R), proposed in the work, will allow increasing Cu–Al–Si–Mn–Sn system bronzes phase composition and properties predicting accuracy when changing their alloying elements concentrations. to reduce the time spent and resources during new alloys development or known bronze grades composition optimization by building regression and predictive models for managing their phase composition and properties. A parameter and criterion have been developed, along with an approach to creating new alloys and improving the existing alloys, their analysis, etc.

Keywords: bronze, structure, parameter, criterion, thermodynamics, solubility, aluminum, tin, phase composition

References.

1. Popov, S., Frolova, L., Rebrov, O., Naumenko, Y., Postupna, О., Zubko, V., & Shvets, P. (2022). Increasing the mechanical properties of structural cast iron for machine-building parts by combined Mn–Al alloying. EUREKA: Physics and Engineering, (1), 118-130. https://doi.org/10.21303/2461-4262.2022.002243

2. Barrenengoa, J., Loizaga, A., De la Fuente, E., Niklas, A., & Fernández-Calvo, A. I. (2010). Optimisation of the mechanical properties of AlSi₇Mg alloys cast in sand moulds. Revista de Metalurgia, 46(Extra), 64-70. https://doi.org/10.3989/revmetalmadrid.06xiipms

3. Selivorstov, V., Dotsenko, Y., & Borodianskiy, K. (2017). Influence of Low-Frequency Vibration and Modification on Solidification and Mechanical Properties of Al-Si Casting Alloy. Materials, 10(5), 560. https://doi.org/10.3390/ma10050560

4. Cardoso-Legorreta, E., Arenas Flores, A., & García, F. L. (2014). Effect of Mechanical Vibration during the Solidification Process of an Aluminium Alloy A356. Advanced Materials Research, 976, 14-18. https://doi.org/10.4028/www.scientific.net/amr.976.14

5. Dotsenko, G. V., & Selyverstov, V. Yu. (2012). Features of solidification casting of aluminum alloys with increasing pressure and modification. Eastern-European Journal of Enterprise Technologies, 1(5(55)), 18-22. https://doi.org/10.15587/1729-4061.2012.3378

6. Laws, K. J., Crosby, C., Sridhar, A., Conway, P., Koloadin, L. S., Zhao, M., Aron-Dine, S., & Bassman, L. C. (2015). High entropy brasses and bronzes – Microstructure, phase evolution and properties. Journal of Alloys and Compounds, 650, 949-961. https://doi.org/10.1016/j.jallcom.2015.07.285

7. Guo, S., & Liu, C. T. (2011). Phase stability in high entropy alloys: Formation of solid-solution phase or amorphous phase. Progress in Natural Science: Materials International, 21(6), 433-446. https://doi.org/10.1016/s1002-0071(12)60080-x

8. Gudivada, G., & Pandey, A. K. (2023). Recent developments in nickel-based superalloys for gas turbine applications: Review. Journal of Alloys and Compounds, 171128. https://doi.org/10.1016/j.jallcom.2023.171128

9. Wee, S., Kim, K., Park, K., & Seok, C. (2021). Study on Creep Damage of Ni-Based Superalloy Caused by Variable Load Conditions at Elevated Temperatures. Materials, 14(22), 6971. https://doi.org/10.3390/ma14226971

10.      Deshmukh, A. A., & Ranganathan, R. (2024). Recent advances in modelling structure-property correlations in high-entropy alloys. Journal of Materials Science & Technology. https://doi.org/10.1016/j.jmst.2024.03.027

11.      Okamoto, H., Schlesinger, M. E., & Mueller, E. M. (Eds.). (2016). Alloy Phase Diagrams. ASM International. https://doi.org/10.31399/asm.hb.v03.9781627081634

12.      Mizutani, U. (2012). Hume-Rothery rules for structurally complex alloy phases. MRS Bulletin, 37(2), 169. https://doi.org/10.1557/mrs.2012.45

13.      Zhang, Y., Mao, Z., Han, Q., Li, Y., Li, M., Du, S., Chai, Z., & Huang, Q. (2020). The role of Hume-Rothery’s rules play in the MAX phases formability. Materialia, 12, 100810. https://doi.org/10.1016/
j.mtla.2020.100810

14.      Poletti, M. G., & Battezzati, L. (2014). Electronic and thermodynamic criteria for the occurrence of high entropy alloys in metallic systems. Acta Materialia, 75, 297-306. https://doi.org/10.1016/j.actamat.2014.04.033

15.      Mizutani, U., & Sato, H. (2017). The Physics of the Hume-Rothery Electron Coогncentration Rule. Crystals, 7(1), 9. https://doi.org/10.3390/cryst7010009

16.      He, Q. F., Ye, Y. F., & Yang, Y. (2017). Formation of Random Solid Solution in Multicomponent Alloys: from Hume-Rothery Rules to Entropic Stabilization. Journal of Phase Equilibria and Diffusion, 38(4), 416-425. https://doi.org/10.1007/s11669-017-0560-9

17.      Ji, X. (2015). Relative effect of electronegativity on formation of high entropy alloys. International Journal of Cast Metals Research, 28(4), 229-233. https://doi.org/10.1179/1743133615y.0000000004

18.      Mizutani, U., Inukai, M., & Sato, H. (2010). Hume-Rothery stabilisation mechanism and d-states-mediated Fermi surface–Brillouin zone interactions in structurally complex metallic alloys. Philosophical Magazine, 91(19-21), 2536-2542. https://doi.org/10.1080/14786435.2010.508758

19.      Wu, H. (2022). A review on the Cahn–Hilliard equation: Classical results and recent advances in dynamic boundary conditions. Electronic Research Archive, 30(6), 2204-2229. https://doi.org/10.3934/era.2022143

20.      Zhou, J., Zhong, J., Chen, L., Zhang, L., Du, Y., Liu, Z.-K., & Mayrhofer, P. H. (2017). Phase equilibria, thermodynamics and microstructure simulation of metastable spinodal decomposition in c–Ti1−xAl_xN coatings. Calphad, 56, 92-101. https://doi.org/10.1016/j.calphad.2016.12.006

21.      Takeuchi, A., & Inoue, A. (2010). Mixing enthalpy of liquid phase calculated by miedema’s scheme and approximated with sub-regular solution model for assessing forming ability of amorphous and glassy alloys. Intermetallics, 18(9), 1779-1789. https://doi.org/10.1016/j.intermet.2010.06.003

22.      Kattner, U. R. (2016). The CALPHAD method and its role in material and process development. Tecnologia em Metalurgia Materiais e Mineração, 13(1), 3-15. https://doi.org/10.4322/2176-1523.1059

23.      Gorsse, S., & Senkov, O. (2018). About the Reliability of ­CALPHAD Predictions in Multicomponent Systems. Entropy, 20(12), 899. https://doi.org/10.3390/e20120899

24.      Tolborg, K., Klarbring, J., Ganose, A. M., & Walsh, A. (2022). Free energy predictions for crystal stability and synthesisability. Digital Discovery, 1(5), 586-595. https://doi.org/10.1039/d2dd00050d

25.      Iranshahr, A., Voskov, D. V., & Tchelepi, H. A. (2012). Gibbs energy analysis: Compositional tie-simplex space. Fluid Phase Equilibria, 321, 49-58. https://doi.org/10.1016/j.fluid.2012.02.001

26.      Sasidhar, K. N., & Meka, S. R. (2018). Spinodal decomposition during isothermal gas-solid equilibration – Its effects and implications. Acta Materialia, 161, 266-272. https://doi.org/10.1016/j.actamat.2018.09.039

27.      Zhou, X., Darvishi Kamachali, R., Boyce, B. L., Clark, B. G., Raabe, D., & Thompson, G. B. (2021). Spinodal Decomposition in Nanocrystalline Alloys. Acta Materialia, 215, 117054. https://doi.org/10.1016/j.actamat.2021.117054

28.      Kim, B., Sietsma, J., & Santofimia, M. J. (2019). Theoretical Aspects of Spinodal Decomposition in Fe-C. Metallurgical and Materials Transactions A, 50(3), 1175-1184. https://doi.org/10.1007/s11661-018-5094-1

29.      Rudraraju, S., Van der Ven, A., & Garikipati, K. (2016). Mechanochemical spinodal decomposition: a phenomenological theory of phase transformations in multi-component, crystalline solids. Computational Materials, 2(1). https://doi.org/10.1038/npjcompumats.2016.12

30.      Miracle, D. B., & Senkov, O. N. (2017). A critical review of high entropy alloys and related concepts. Acta Materialia, 122, 448-511. https://doi.org/10.1016/j.actamat.2016.08.081

31.      Troparevsky, M. C., Morris, J. R., Kent, P. R. C., Lupini, A. R., & Stocks, G. M. (2015). Criteria for Predicting the Formation of Single-Phase High-Entropy Alloys. Physical Review X, 5(1). https://doi.org/10.1103/physrevx.5.011041

32.      Yang, Y.-F., Hu, F., Xia, T., Li, R.-H., Bai, J.-Y., Zhu, J.-Q., Xu, J.-Y., & Zhang, G.-F. (2024). High entropy alloys: a review of preparation techniques, properties and industry applications. Journal of Alloys and Compounds, 177691. https://doi.org/10.1016/j.jallcom.2024.177691

33.      Guo, Q., Xu, X., Pei, X., Duan, Z., Liaw, P. K., Hou, H., & Zhao, Y. (2022). Predict the phase formation of high-entropy alloys by compositions. Journal of Materials Research and Technology. https://doi.org/10.1016/j.jmrt.2022.12.143

34.      Peivaste, I., Jossou, E., & Tiamiyu, A. A. (2023). Data-driven analysis and prediction of stable phases for high-entropy alloy design. Scientific Reports, 13(1). https://doi.org/10.1038/s41598-023-50044-0

35.      Morral, J. E., & Chen, S. (2021). Stability of High Entropy Alloys to Spinodal Decomposition. Journal of Phase Equilibria and Diffusion. https://doi.org/10.1007/s11669-021-00915-8

36.      Hart, G. L.W., Mueller, T., Toher, C., & Curtarolo, S. (2021). Machine learning for alloys. Nature Reviews Materials, 6(8), 730-755. https://doi.org/10.1038/s41578-021-00340-w

37.      Hu, M., Tan, Q., Knibbe, R., Xu, M., Jiang, B., Wang, S., Li, X., & Zhang, M.-X. (2023). Recent applications of machine learning in alloy design: A review. Materials Science and Engineering: R: Reports, 155, 100746. https://doi.org/10.1016/j.mser.2023.100746

38.      Yi Wang, W., Li, J., Liu, W., & Liu, Z.-K. (2019). Integrated computational materials engineering for advanced materials: A brief review. Computational Materials Science, 158, 42-48. https://doi.org/10.1016/j.commatsci.2018.11.001

39.      Vecchio, K. S., Dippo, O. F., Kaufmann, K. R., & Liu, X. (2021). High-throughput rapid experimental alloy development (HT-READ). Acta Materialia, 221, 117352. https://doi.org/10.1016/j.actamat.2021.117352

40.      Ma, D., Friák, M., Pezold, J.V., Raabe, D., & Neugebauer, J. (2013). Ab initioidentified design principles of solid-solution strengthening in Al. Science and Technology of Advanced Materials, 14(2), 025001. https://doi.org/10.1088/1468-6996/14/2/025001

41.      Fu, H., Zhang, H., Wang, C., Yong, W., & Xie, J. (2022). Recent progress in the machine learning-assisted rational design of alloys. International Journal of Minerals, Metallurgy and Materials, 29(4), 635-644. https://doi.org/10.1007/s12613-022-2458-8

42.      Chen, B. (2025). A Comprehensive Review of θ-Series Precipitates in Aluminum Alloys. Materials, 18(23), 5406. https://doi.org/10.3390/ma18235406

43.      Chen, H., Sun, J., Yang, S., Zhang, Y., Tang, K., Zhang, C., Lu, Y., Luo, Q., & Li, Q. (2025). Thermodynamics and kinetics of isothermal precipitation in magnesium alloys. Materials Genome Engineering Advances. https://doi.org/10.1002/mgea.86

44.      Fallah, V., Ofori-Opoku, N., Stolle, J., Provatas, N., & Esmaeili, S. (2013). Simulation of early-stage clustering in ternary metal alloys using the phase-field crystal method. Acta Materialia, 61(10), 3653-3666. https://doi.org/10.1016/j.actamat.2013.02.053

45.      Xu, X., Lv, Y., Hu, M., Xiong, D., Zhang, L., Wang, L., & Lu, W. (2016). Influence of second phases on fatigue crack growth behavior of nickel aluminum bronze. International Journal of Fatigue, 82, 579-587. https://doi.org/10.1016/j.ijfatigue.2015.09.014

46.      Porter, D. A., Easterling, K. E., & Sherif, M. Y. (2021). Phase Transformations in Metals and Alloys. Taylor & Francis Group. https://doi.org/10.1201/9781003011804

47.      Hillert, M. (2012). Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis. Cambridge University Press. https://doi.org/10.1017/CBO9780511812781

48.      Chen, L.-Q. (2019). Chemical potential and Gibbs free energy. MRS Bulletin, 44(7), 520-523. https://doi.org/10.1557/mrs.2019.162

49.      Tajčmanová, L., Podladchikov, Y., Moulas, E., & Khakimova, L. (2021). The choice of a thermodynamic formulation dramatically affects modelled chemical zoning in minerals. Scientific Reports, 11(1). https://doi.org/10.1038/s41598-021-97568-x

50.      Kimstach, T. V., Uzlov, K. I., Bilyi, O. P., & Repyakh, S. I. (2026). Mechanical properties and structure of Cu-Al-Si-Sn-Mn system non-magnetic cast bronzes. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (1), 58-67. https://doi.org/10.33271/nvngu/2026-1/058

51.      Nai, X., Zhao, S., Wang, P., Chen, H., Wang, P., Song, X., Vairis, A., & Li, W. (2024). Solid-state transformation composite filler: A new strategy to strengthen ceramic/metal joint. Materials & Design, 243, 113040. https://doi.org/10.1016/j.matdes.2024.113040

52.      Sun, X., Jie, J., Wang, T., & Li, T. (2020). Precipitate phase transformation behavior, microstructure, and properties of Cu–Cr–Co–Si alloy. Journal of Materials Research, 35(6), 623-632. https://doi.org/10.1557/jmr.2020.31

53.      Kumar, S., Grant, P. S., & O’Reilly, K. A. Q. (2016a). Evolution of Fe Bearing Intermetallics During DC Casting and Homogenization of an Al-Mg-Si Al Alloy. Metallurgical and Materials Transactions A, 47(6), 3000-3014. https://doi.org/10.1007/s11661-016-3451-5

54.      Asghar, Z., Requena, G., & Boller, E. (2011). Three-dimensional rigid multiphase networks providing high-temperature strength to cast AlSi₁₀Cu₅Ni_1-2 piston alloys. Acta Materialia, 59(16), 6420-6432. https://doi.org/10.1016/j.actamat.2011.07.006

55.      Bugelnig, K., Germann, H., Steffens, T., Sket, F., Adrien, J., Maire, E., Boller, E., & Requena, G. (2018). Revealing the Effect of Local Connectivity of Rigid Phases during Deformation at High Temperature of Cast AlSi12Cu4Ni(2,3)Mg Alloys. Materials, 11(8), 1300. https://doi.org/10.3390/ma11081300

56.      Wang, C. Y., Cepeda-Jiménez, C. M., & Pérez-Prado, M. T. (2020). Dislocation-particle interactions in magnesium alloys. Acta Materialia, 194, 190-206. https://doi.org/10.1016/j.actamat.2020.04.055

57.      Monnet, G., Naamane, S., & Devincre, B. (2011). Orowan strengthening at low temperatures in bcc materials studied by dislocation dynamics simulations. Acta Materialia, 59(2), 451-461. https://doi.org/10.1016/j.actamat.2010.09.039

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