One more peculiarity of high-temperature phase equilibria in nanoparticles of the Crx-W1-x heavy pseudo-alloy
A.V. Shishulin, A.V. Shishulina
R.E. Alekseev Nizhny Novgorod State Technical University
DOI: 10.26456/pcascnn/2025.17.328
Short communication
Abstract: Thanks to a unique set of physicochemical properties, nanoparticle-fabricated heavy tungsten pseudo-alloys with ultrafine-grained structures, manufactured using modern powder metallurgy methods, have become a subject of increased interest among researchers. In this study, within a thermodynamic approach, the features of the equilibrium phase composition of spherical Crx-W1-x nanoparticles of various diameters with different Cr fractions and a core-shell structure have been simulated in the temperature range between the liquidus and solidus. Examples of the dependencies of the equilibrium compositions of solid and liquid phases on the particle diameter have been obtained; it has been demonstrated that these dependencies significantly differ depending on the relative arrangement of solid and liquid phases within the core-shell structure. The results are complemented by an analysis of the effect of the initial composition, which consists in a dependence not only of the volume fraction of coexisting phases but also of their composition on the initial chromium content in a particle. To visualize some of these effects, some specific θ-diagrams have been applied, being previously suggested by the authors. A thermodynamic interpretation of the observed effects is presented based on three possible mechanisms for reducing the free energy of the system.
Keywords: nanoparticles, chemical thermodynamics, liquidus, solidus, core-shell structure, tungsten, chromium
- Alexander V. Shishulin – Ph. D., Associate Professor, R.E. Alekseev Nizhny Novgorod State Technical University
- Anna V. Shishulina – Ph. D., Associate Professor, R.E. Alekseev Nizhny Novgorod State Technical University
For citation:
Shishulin A.V., Shishulina A.V. O eshche odnoj osobennosti vysokotemperaturnykh fazovykh ravnovesij v nanochastitsakh tyazhelogo psevdosplava Crx-W1-x [One more peculiarity of high-temperature phase equilibria in nanoparticles of the Crx-W1-x heavy pseudo-alloy], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2025, issue 17, pp. 328-338. DOI: 10.26456/pcascnn/2025.17.328. ⎘
Full article (in Russian): download PDF file
References:
1. Vilémová M., Illková K., Lukáš F. et al. Microstructure and phase stability of W-Cr alloy prepared by spark plasma sintering,
Fusion Engineering and Design, 2018, vol. 127, pp. 173-178. DOI: 10.1016/j.fusengdes.2018.01.012.
2. Hou Q.-Q., Huang K., Luo L.-M. et al. Microstructure and its high temperature oxidation behavior in W-Cr alloys prepared by spark plasma sintering, Materialia, 2019, vol. 6, art. no. 100332, 8 p. DOI: 10.1016/j.mtla.2019.100332.
3. Cordero Z.C., Carpenter R.R., Schuh C.A., Schuster B.E. Sub-scale ballistic testing of an ultrafine grained tungsten alloy into concrete targets, International Journal of Impact Engineering, 2016, vol. 91, pp. 1-5. DOI: 10.1016/j.ijimpeng.2015.11.013.
4. Chookajorn T., Park M., Schuh C.A. Duplex nanocrystalline alloys: entropic nanostructure stabilization and a case study on W-Cr, Journal of Materials Research, 2015, vol. 30, issue 2, pp. 151-162. DOI: 10.1557/jmr.2014.385.
5. Bose A., Schuh C.A., Tobia J.C. et al. Traditional and additive manufacturing of a new tungsten heavy alloy alternative, International Journal of Refractory Metals and Hard Materials, 2018, vol. 73, pp. 22-28. DOI: 10.1016/j.ijrmhm.2018.01.019.
6. Knowles A.J., Cheng T.Y.S., Ma K. et al. Spinodally reinforced W-Cr fusion armour, Applied Materials Today, 2024, vol. 41, art. no. 102430, 7 p. DOI: 10.1016/j.apmt.2024.102430.
7. Sdobnyakov N.Yu., Kolosov A.Yu, Bogdanov S.S. Modelirovaniye protsessov koalestsentsii i spekaniya v mono- i bimetallichenkikh nanosistemakh [Simulation of the processes of coalescence and sintering in mono-and bimetallic nanosystems]. Tver, Tver State University Publ., 2021, 168 p. (In Russian). DOI: 10.26456/skb.2021.168.
8. Gryaznov M.Yu, Shotin S.V. et al. Titanium alloys scaffolds for medical application produced by additive technologies: a review, Russian Journal of Biomechanics, 2024, vol. 28, issue 4, pp. 12-33. DOI: 10.15593/RZhBiomeh/2024.4.01.
9. Shishulin A.V., Potapov A.A., Shishulina A.V. Fractal nanoparticles of phase-separating solid solutions: nanoscale effects on phase equilibria, thermal conductivity, thermoelectric performance, Springer Proceedings in Complexity, ed. by C.H. Skiadas, Y. Dimotikalis, Cham, Springer, 2022, pp. 421-432. DOI: 10.1007/978-3-030-96964-6_30.
10. Sdobnyakov N.Yu. Modelirovanie strukturnykh prevrascheniy v odnokomponentnykh i mnogokomponentnykh metallicheskikh nanosistemakh [Simulation of structural transformations in monokomponent and multicomponent metal nanosystems]. Tver, Tver State University Publ., 2025, 408 p. (In Russian). DOI: 10.26456/sny.2025.408.
11. Savina K.G., Veselov A.D., Grigoryev R.E. et al. Strukturnye prevrascheniya v binarnykh nanochastistakh Ti-V: razmernyj effect i effect izmeneniya sostava [Structural transformations in binary Ti-V nanopartivles: size effect and effect of composition change], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostructur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2024, issue 16, pp. 532-542. DOI: 10.26456/pcascnn/2024.16.532 (In Russian).
12. Shishulin A.V., Shishulina A.V. Nekotorye osobennosti vysokotemperaturnykh fazovykh ravnovesij v nanochastitsakh sistemy Six-Ge1-x [Several peculiarities of high-temperature phase equilibria in nanoparticles of the Six-Ge1-x system], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostructur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2019, issue 11, pp. 268-276. DOI: 10.26456/pcascnn/2019.11.268 (In Russian).
13. Shishulin A.V., Shishulina A.V., Kuptsov A.V. Osobennosti fazovykh ravnovesij «zhidkost’ – tverdoe telo» v nanochastitsakh sistemy Six-Ge1-x pri razlichnom vzaimnom raspolozhenii faz [Peculiarities of «liquid – solid» phase equilibria in Six-Ge1-x nanoparticles for various mutual arrangement of phases], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostructur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2024, issue 16, pp. 437-447. DOI: 10.26456/pcascnn/2024.16.437 (In Russian).
14. Shishulin A.V., Fedoseev V.B., Shishulina A.V. Melting behavior of fractal-shaped nanoparticles (the example of Si-Ge system), Technical Physics, 2019, vol. 64, issue 9, pp. 1343-1349. DOI: 10.1134/S1063784219090172.
15. Shishulin A.V., Potapov A.A., Shishulina A.V. The initial composition as an additional parameter determining the melting behaviour of nanoparticles (a case study on Six-Ge1-x alloys), Eurasian Physical Technical Journal, 2021, vol. 18, issue 4(38), pp. 5-13. DOI: 10.31489/2021No4/5-13.
16. Sdobnyakov N.Yu, Kolosov A.Yu, Sokolov D.N. et al. Kompleksnyj podkhod k modelirovaniyu plavleniya i kristallizatsii v pyatikomponentnykh metallicheskikh nanochastitsakh: molekulyarnaya dinamika i metod Monte- Karlo [Complex approach to the simulation of melting and crystallization in five-component metallic nanoparticles: molecular dynamics and the Monte Carlo method], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2023, issue 15, pp. 589-601. DOI: 10.26456/pcascnn/2023.15.589 (in Russian).
17. Shishulin A.V. Termodinamicheskie zakonomernosti vliyaniya na fazovye ravnovesiya sostava i morfologii granits razdela malykh ob"emov binarnykh organicheskikh rasslaivayushchikhsya system [How do the composition of a binary organic phase-separating system and the morphology of its interface boundaries influence on the phase equilibria: a thermodynamical analysis], Cand. chem. sci. diss.: 1.4.4. Nizhny Novgorod, N.I. Lobachevsky Nizhny Novgorod State University, 2023, 126 p. (In Russian).
18. Magomedov M.N. O zavisimosti fazovoy diagrammy splava zamescheniya ot razmera i formy nanokristalla [On the dependence of the phase diagram of a substitution alloy on the size and shape of a nanocrystal], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2017, issue 9, pp. 291-300. DOI: 10.26456/pcascnn/2017.9.291. (in Russian).
19. Samsonov V.M., Demenkov D.E., Karacharov V.I., Bembel’ A.G. Fluctuation approach to the problem of thermodynamics’ applicability to nanoparticles, Bulletin of the Russian Academy of Sciences: Physics, 2011, vol. 75, issue 8, pp. 1073-1077. DOI: 10.3103/S106287381108034X.
20. Shishulin A.V., Fedoseev V.B. Size effect in the phase separation of Cr-W solid solutions, Inorganic Materials, 2018, vol. 54, issue 6, pp. 546-549. DOI: 10.1134/S0020168518050114.
21. Shishulin A.V., Fedoseev V.B. Effect of initial composition on the liquid-solid phase transition in Cr-W alloy nanoparticles, Inorganic Materials, 2019, vol. 55, issue 1, pp. 14-18. DOI: 10.1134/S0020168519010138.
22. Shishulin A.V., Shishulina A.V. Ravnovensnyj fazovyj sostav i vzaimnaya rastvorimost’ komponentov v nanochastitsakh fraktal’noj formy tyazhelogo psevdosplava W-Cr [Equilibrium phase composition and mutual solubility in fractal nanoparticles of the W-Cr heavy pseudo-alloy], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostructur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2019, issue 11, pp. 380-388. DOI: 10.26456/pcascnn/2019.11.380 (in Russian).
23. Shishulin A.V., Shishulina A.V. Vliyanie iskhodnogo sostava na fazovye ravnovesiya pri tverdofaznom rasslaivanii v nanochastitsakh binarnykh splavov (na primere sistemy W-Cr) [Influence of the initial composition on the phase equilibria in the case of the solid phase separation in binary alloy nanoparticles (exemplifying on the W-Cr system)], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2023, issue 15, pp. 299-307. DOI: 10.26456/pcascnn/2023.15.299 (In Russian).
24. Shishulin A.V., Potapov A.A., Shishulina A.V. Fractal nanoparticles of phase-separating solid solutions: morphology-dependent phase equilibria in tungsten heavy pseudo-alloys, Eurasian Physical Technical Journal, 2023, vol. 20, issue 4(46), pp. 125-132. DOI: 10.31489/2023no4/125-132.
25. Touloukian Y.S., Kirby R.K. et al. Thermal expansion: metallic elements and alloys, Thermophysical properties of matter, vol. 12, New York, IFI/Plenum, 1975, 500 p.
26. hishulin A.V., Fedoseev V.B. On some peculiarities of stratification of liquid solutions within pores of fractal shape, Journal of Molecular Liquids, 2019, vol. 278, pp. 363-367. DOI: 10.1016/j.molliq.2019.01.050.
27. Shishulin A.V., Fedoseev V.B. Stratifying polymer solutions in microsized pores: phase transitions induced by deformation of a porous material, Technical Physics, 2020, vol. 65, issue 3, pp. 340-346. DOI: 10.1134/S1063784220030238.
28. Shirinyan A., Wilde G., Bilogorodskyy Y. Solidification loops in the phase diagrams of nanoscale alloy particles: from a specific example towards a general vision, Journal of Materials Science, 2018, vol. 53, issue 4, pp. 2859-2879. DOI: 10.1007/s10853-017-1697-y.
29. Fedoseev V.B. Ravnovesnaya konfiguratsiya yanus-chastits pri uslovii kompensatsii sil poverkhnostnogo natyazheniya [Equilibrium configuration of janus-particles on condition of the compensation of surface-tension forces], Pisma v Zhurnal Tekhnicheskoi Fiziki [Technical Physics Letters], 2025, vol. 51, issue 6, pp. 22-25. (In Russian).