Collection of scientific works Nanosystems, nanomaterials, nanotechnologies
Year 2026 Volume 24, Issue 1
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E. I. GET'MAN1, O. Yu. MARIICHAK1, L. I. ARDANOVA2, and S. V. RADIO1

1Vasyl' Stus Donetsk National University, 21, 600-Richchia Str., UA-21021 Vinnytsia, Ukraine
2Minnesota State University, 228, Wiecking Center, 56001 Mankato, Minnesota, USA

Prediction of the Thermodynamic Stability and Limits of Isomorphous Substitutions in Solid Solutions Y1-xLnxPO4, Where Ln = Gd–Lu, Sc

123–139 (2026)

PACS numbers: 64.75. Ef, 64.75.Jk, 64.75.Nx, 81.30.Dz, 81.30.Mh, 82.33.Pt, 82.60.L

Received 11 August, 2025; in revised form, 18 August, 2025

Using V. S. Urusov's crystal-energy theory of isomorphous miscibility, the mixing energies (interaction parameters), critical decomposition (stability) temperatures, and limits of isomorphous substitutions are calculated, as well as the thermodynamic stability regions of zircon-type orthophosphate solid solutions with the composition Y1-xLnxPO4, where Ln-lanthanides or Sc. The contributions to the mixing energy arising from differences in the sizes of the substitutional structural units and from differences in the nature of the chemical bonding of the system components are characterized. A thermodynamic-stability diagram of solid solutions and the corresponding decomposition domes are presented, enabling graphical prediction of the decomposition temperatures of solid solutions for given substitution limits, or the equilibrium substitution limits for a given temperature and thermodynamic-stability region. The results do not contradict the experimental data reported in the literature. They may be helpful in the search for compositions of mixed matrices and activators for new luminescent, laser, and other materials based on Y1-xLnxPO4 (Ln= Gd-Lu, Sc) solid solutions, including nanomaterials.

KEY WORDS: solid solutions, lanthanides, yttrium, scandium, orthophosphates, isomorphous substitutions, mixing energy, thermodynamic stability, substitution limits

DOI: https://doi.org/10.15407/nnn.24.01.0123

Citation:
E. I. Get'man, O. Yu. Mariichak, L. I. Ardanova, and S. V. Radio, Prediction of the Thermodynamic Stability and Limits of Isomorphous Substitutions in Solid Solutions Y1-xLnxPO4, Where Ln = Gd–Lu, Sc, Nanosistemi, Nanomateriali, Nanotehnologii, 24, No. 1: 123–139 (2026); https://doi.org/10.15407/nnn.24.01.0123

Funding / Acknowledgments:
This research was carried out with the support of the Ministry of Education and Science of Ukraine within the framework of the priority areas of scientific development of the accredited research direction 'Natural and Mathematical Sciences' at Vasyl' Stus Donetsk National University.

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