Abstract
The size effects on the composition of coexisting phases, the interfacial layer between them, and the interfacial tension in a binary system composed of a matrix and the monodispersed particles of arbitrary (including nanoscale) size are described in the context of a Gibbs method for dispersed systems. Obtaining the relevant relationships has allowed plotting the size-dependent phase state diagrams for a Cr–Ti system with a point of equal concentrations with a minimum. The coefficients of size composition of the nanoparticles and the matrix, as well as those of interfacial tension under the isobaric and isothermal conditions, are calculated at different degree of dispersion. The calculated data coincide with the experimental ones.
Similar content being viewed by others
References
B. Sonderegger, J. Holzer, and E. Kozeschnik, Mater. Sci. Forum 638–642, 2730 (2010).
H. Aaronson, M. Enomoto, and J. K. Lee, Mechanisms of Diffusional Phase Transformations in Metals and Alloys (CRC, Taylor and Francis Group, Boca Raton, 2010).
D. Fors and G. Wahnström, J. Appl. Phys. 109, 113709 (2011).
P. E. L’vov and V. V. Svetukhin, Phys. Solid State 55, 2374 (2013).
M. A. Shebzukhova and A. A. Shebzukhov, Bull. Russ. Acad. Sci.: Phys. 80, 718 (2016).
P. E. L’vov, V. V. Svetukhin, and A. V. Obukhov, Phys. Solid State 53, 421 (2011).
A. I. Rusanov, Lectures on Surface Thermodynamics (Lan’, St. Petersburg, 2013) [in Russian].
Nanoscience and Nanotechnologies. Encyclopedy of Life Support Systems (Yunesko, EOLSS, Magistr-Press, Moscow, 2010) [in Russian].
V. K. Grigorovich, High-Temperature Strength and State Diagram (Metallurgiya, Moscow, 1969) [in Russian].
A. I. Rusanov, Phase Equilibria and Surface Phenomena (Khimiya, Leningrad, 1967) [in Russian].
M. A. Shebzukhova and A. A. Shebzukhov, Phys. Solid State 59, 1395 (2017).
T. V. Bykov and A. K. Shchekin, Inorg. Mater. 35, 641 (1999).
L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams: With Special Reference to Refractory Metals (Academic, New York, 1970).
M. A. Shebzukhova and A. A. Shebzukhov, Bull. Russ. Acad. Sci.: Phys. 76, 773 (2012).
Z. A. Shebzukhov, M. A. Shebzukhova, and A. A. Shebzukhov, Poverkhnost’, No. 11, 102 (2009).
Z. A. Shebzukhov, M. A. Shebzukhova, and A. A. Shebzukhov, Poverkhnost’, No. 12, 94 (2009).
M. Hansen and K. Anderko, Structure of Binary Alloys (McGraw-Hill, New York, 1958; Metallurgizdat, Moscow, 1962), Vol. 2.
Q. Jiang and H. M. Li, Surf. Sci. Rep. 63, 427 (2008).
S. V. Stankus, Preprint No. 247-91 (Novosibirsk,1991).
M. N. Magomedov, Study of Interatomic Interaction, Vacance Formation and Self-Diffusion in Crystals (Fizmatlit, Moscow, 2010) [in Russian].
W. Vogelsberger and G. Marx, Z. Phys. Chem. 257, 580 (1976).
Physical Encyclopedic Dictionary (Sov. Entsiklopediya, Moscow, 1966), Vol. 5, no. 187, p. 380.
V. B. Kogan, Heterogeneous Equilibria (Khimiya, Leningrad, 1968) [in Russian].
M. A. Shebzukhova and A. A. Shebzukhov, Bull. Russ. Acad. Sci.: Phys. 73, 928 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.A. Shebzukhova, A.A. Shebzukhov, 2018, published in Fizika Tverdogo Tela, 2018, Vol. 60, No. 1, pp. 180–186.
Rights and permissions
About this article
Cite this article
Shebzukhova, M.A., Shebzukhov, A.A. Phase diagram and interfacial characteristics in a binary system. Phys. Solid State 60, 183–190 (2018). https://doi.org/10.1134/S1063783418010225
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063783418010225