Nanocomposites and nanomaterials
Prediction of Substitution Limits and Thermodynamic Stability for Y1–xLnxF3 (Ln = Sm–Lu) Nanosized Materials

Get’man E.I.1, Oleksii Yu.A.1, Ardanova L.I.2,*, Radio S.V.1,*

1 Vasyl' Stus Donetsk National University, Vinnytsia, 21027 Ukraine
2 Minnesota State University, Mankato, Minnesota, 56001 USA
* e-mail: radio@donnu.edu.ua, lyudmyla.stackpool@mnsu.edu
Recently the trifluorides of rare-earth elements (REE) attract more attention from researchers in various fields of science and technology, such as optoelectronic devices, phosphors, lasers, and others. The studies on their application in the form of nanomaterials in medicine as optical 3D devices, probes for visualization of biological objects, for intracellular labels or measurements, and immunoassays have become relevant. In many cases, not individual compounds but solid solutions whose properties can be controlled based on the composition are being used.
However, the physicochemical foundations for the synthesis of solid solutions such as state diagrams and the solubility regions are much less studied than the dependencies of the composition-physical properties. There are practically no data on substitution limits and stability regions of solid solutions. 
Using V. Urusov’s crystal-chemical model, in the approximation of regular solutions, the mixing energies (interaction parameters), critical temperatures of decomposition (stability), and substitution limits were calculated for 10 systems Y1–xLnxF3 solid solutions, where Ln = Sm–Lu. It was established that the mixing energies and critical decomposition temperatures of solid solutions first decrease in the series of Sm–Er, then increase in the series Er–Lu trifluoride systems as the REE atomic number increases. It was shown that the total mixing energy is determined mainly by the difference in the sizes of the substituting structural units and to a lesser extent by the difference in the degrees of ionicity of the chemical bond of the systems’ components. The presented diagram of thermodynamic stability for systems Y1–xLnxF3, Ln = Sm–Lu makes it possible to visually evaluate not only the thermodynamic stability, instability, and metastability of the solid solutions in a wide range of compositions and temperatures but also the substitution limits for limited series of solid solutions for a given decomposition temperature, or the temperature of their decomposition according to the given substitution limit.
Using the Becker equation, the decomposition temperatures (Td) of solid solutions in the Y1–xLnxF3, Ln = Sm–Lu systems were calculated for the composition range 1.0 > x > 0 with a step size, x = 0.05. According to calculations, the Td of solid solutions of the YF3–LnF3, Ln = Sm–Lu systems are in the interval 51 K–685 K.