Information System to Forecasting the Steadiness of REE OOSS Solid Solutions for Environmental Monitoring Oleksii Kudryk1, Oleg Bisikalo2, Yuliia Oleksii3 and Eugeni Get’man4 1,2 Vinnitsa National Technical University, Khmelʹnytsʹke sh., 95, Vinnytsya, Vinnytsʹka oblastʹ, 21000, Ukraine 3,4 Vasyl֦ʹ Stus Donetsk National University, 600 richchya street, 21, Vinnytsya, Vinnytsʹka oblastʹ, 21000, Ukraine Abstract V.S. Urusov’s crystal-energy theory of isomorphic replacements accomplished in our information system was used to calculate mixing energies and critical temperatures of disintegration (steadiness) of solid solutions in the systems (Sc1 – xLnx)[(SiO4)0.5O0.5], where Ln is rare-earth elements (REE) of Terbium – Lutetium row, and Yttrium. Steadiness temperatures of some solid solutions at x = 0.01, 0.03, 0.05, 0.10, and 0.20 were established. Based on the given calculation results, a diagram was created to estimate the areas of sustainability of solid solutions and forecast the replacement limits based on the steadiness temperature depending on the obtained replacement limits. The results of the research can be helpful for choosing the ratio of the components in the host materials and the amount of dopant in newly “hybrid” REE OOSs (OOS) (Sc1 – xLnx)[(SiO4)0.5O0.5], where Ln represent REEs of Terbium – Lutetium row, and Yttrium. Keywords 1 Information system, phase steadiness, solid solutions, mathematical modeling, model, OOSs. 1. Introduction Sc2SiO5 — Ln2SiO5 systems [8-11]. The use of “hybrid” Sc and REE OOS is due to the purpose of synthesizing materials with better properties Solid solutions based on Scandium-OOS compared to Ln2SiO5, and which are cheaper Sc2SiO5 are innovational materials for creating compared to Sc2SiO5, since the cost of Sc is higher efficacious lasers for medicine, laser ranging [1], than one of REE. military purposes, metalworking [2], and what is No analysis of physical and chemical important for environmental monitoring [3-5] foundations for the receiving of solid since they have become an attractive research solutions – state diagrams and, in particular, areas topic due to their huge benefits. For example, such of solubility based on the components of the lasers are not dangerous for eye and it has fine Sc2SiO5 and Ln2SiO5 systems – has been carried transparency in the atmosphere, can serve as out, while this result is necessary for choosing the efficient sources in optical measurements, for compound of materials. As far as we know, only example, weather conditions (wind data about the Lu2 – xScxSiO5 [12] and measurement), as well as the determining of the ErxSc2 – xSiO5 [13] systems are available. In [12], concentration of atmospheric atoms. They serve it was reported that three compositions of as host materials, while the triple charged Ln3+ polycrystalline solid solutions with x = 0.5, 0.8, ions, which are contained in small amounts (up to 1.0 at a temperature of 1670 K were obtained, 5 at%), act as dopants. In addition to OOSs while in [13] the synthesis of ErxSc2 – xSiO5 in the containing only Scandium cations in their form of films within the temperature range matrices [6-7], we also studied materials based on 1173 – 1373 K was studied. In [13], it was also “hybrid” OOS with two different cations – Sc and reported that ErxSc2 – xSiO5 films could be used to REEs, which are solid solutions of ISIT 2021: II International Scientific and Practical Conference «Intellectual Systems and Information Technologies», September 13–19, 2021, Odesa, Ukraine EMAIL: kydrikalex@gmail.com (A. 1); obisikalo@gmail.com (A. 2); oleksii.i@donnu.ua (A. 3); gtmn@i.ua (A. 4) ORCID: 0000-0002-0592-6633 (A. 1); 0000-0002-7607-1943 (A. 2)); 0000-0002-7328-6674 (A. 3); 0000-0002-7665-556X (A. 4) ©️ 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) create a light source with high optical gain since their pseudo-binary representation, there are two they have a higher Erbium concentration contributions to the mixing energy, which are compared to Silicon-based materials doped with caused by the difference in the size of the Erbium. Nevertheless, no information on the substituting structural units Eδ and the difference replacement limits in the Lu2 – xScxSiO5 and in the degree of ionicity of the chemical bond Eε: ErxSc2 – xSiO5 systems are available. Emix = Eδ + Eε = Сmnzmzxδ2 + (1) It is very important to determine + 1390mzmzxα(Δε)2/(2D), (kJ/mol), experimentally areas of solubility in the solid where: С is a constant calculated from the phase, which requires expensive equipment, equation C = 20(2Δχ + 1) [18] based on the additional reagents, large energy and time difference in electronegativity χ of Ln3+ cations consumption. This forces researchers who study and anions [19]. The value χ(SO44-), as the properties of “hybrid” REE OOS to choose the recommended [20], was accepted equal to χ(O2- ) composition of host matrix materials and [19]; m is the number of` formula units in the activators either by analogy with similar systems pseudo-binary approximation of components. or by selection method that is trial and error. Since the anionic sublattice of the crystal structure It is often not taken into account that “hybrid” of OOS contains Orthosilicate and Oxide anions REE OOS tend to decay and modification their that are not bonded to the Silicon atom [15], and phase composition and properties upon cooling. the replacement limits are calculated per one mole This can lead to the damage of materials based on of the replaceable ion, the OOS formulas will be them if used in applications. Accordingly, before presented below as a pseudo-binary compound carrying synthesis and studying it, it is Ln[(SiO4)0.5O0.5]; n is the coordination number of recommended to evaluate the steadiness of solid the replaceable structural unit in the pseudo- solutions in the corresponding systems during binary approximation of the structure; zm, zx is the their obtaining and intended use. formal charges of the replaced and general In view of this, the aim of this research is to structural units in the components; δ is a forecast the phase steadiness and replacement dimensional parameter, which for each system is limits in materials based on solid solutions of characterized by the relative difference of cube OOS of Scandium and REEs of roots of unit cell volumes taken from [15, 21-22], Terbium – Lutetium row, and Yttrium. calculated by the formula: Yttrium subgroup REEs and Yttrium were 𝛿 = (𝑉 1/3 𝐿𝑛 – 𝑉 1/3𝑆𝑐 )/𝑉1/3𝑆𝑐 (2) chosen as second cations due to the same structure α is the reduced Madelung constant calculated with Sc2SiO5, as well as the proximity of by the Hoppe formula [23]: (α / n)2 + α; Δε is the crystalline ionic radii of Sc3+ (0.885 Å) and triply difference in the degree of ionicity of the chemical charged cations of Yttrium subgroup REEs and bond in the components of the systems. Yttrium (1.063 – 1.001 Å [14]), which suggests For example, using an information system for the wide presence of isomorphic replacement of forecasting the phase steadiness of solid solutions, Scandium by these REEs. The radii of the Cerium which based on the crystal-energy theory of subgroup REE cations (1.172 – 1.078 Å) vastly isomorphic miscibility, were calculated the differ from the ionic radius of Scandium, and their energies of mixing Emix and critical temperatures OOS are not isostructural with Sc2SiO5 [15], of disintegration Tcr of (Sc1 – xLnx)[(SiO4)0.5O0.5] which, according to the theory of isomorphic solid solutions (where Ln is a REE, Ln = Tb – Lu miscibility [16-18], should vastly limit the and Y). Some initial data and calculation results solubility of components in systems with are summarized in Tables 1, 2 and Fig. 1. The Scandium and REEs of the Table 1 shows that as the number of REE in the Lanthanum – Gadolinium series. Terbium – Lutetium row increases, the contributions of Eδ values to the total mixing 2. Calculation method and results energy become smaller (from 34.5 to 10.8 kJ/mol), which is explained by smaller differences in the size of substitutable structural The main aim in establishing the replacement units – Scandium and REE. limits of solid solutions using the crystal energy method by Urusov [16-18] is to determine the mixing energy Emix. As to components with the same structure of the system and the possibility of Table 1 Sourced data for the calculation of mixing energies and critical temperatures of disintegration of solid solutions (Sc1 – xLnx)[(SiO4)0.5O0.5], Ln = Tb – Lu and Y Ln V, Å3 δ* Eδ, kJ/mol χLn ε Δε Tcr, K Tb 876.80 [21] 0.0535 34.5 1.410 0.708 0.001 2060 Dy 856.57 [15] 0.0453 24.8 1.426 0.706 0.003 1480 Ho 843.04[15] 0.0398 19.1 1.433 0.704 0.005 1150 Er 836.70[15] 0.0372 16.7 1.438 0.703 0.006 1010 Tm 828.59 [15] 0.0338 13.8 1.455 0.699 0.010 860 Yb 824.07 [15] 0.0319 12.3 1.479 0.694 0.015 810 Lu 819.31[15] 0.0299 10.8 1.431 0.705 0.004 650 Sc 749.97 [22] – – 1.415 0.709 – – Y 852.25 [21] 0.0435 22.8 1.340 0.722 0.013 1400 *Note: according to the recommendations in [17-18] and considering the dependence of the interaction parameter on the difference in volumes of the unit cells of components [29], the calculation of the dimensional parameter was carried out according to the volumes of the unit cells Contributions due to different degrees of ionicity of chemical bonds in the components of the Eε systems are substantially smaller (in most cases, two-three times smaller) than in Eδ, and they can be neglected in this case. This agrees with the recommendation not to consider them, provided that Δε ≤ 0.05 [16-18] (in this case, Δε ≤ 0.015). Consequently, it is accepted that Emix = Eδ. Figure 1: The diagram of thermodynamic steadiness of solid solutions in the systems (Sc1 – xLnx)[(SiO4)0.5O0.5], where х = 0.01 (a), 0.03 (b), 0.05 (c), 0.10 (d), 0.20 (e) and 0.50 (f) Table 2 Temperatures of disintegration of (Sc1 – xLnx)[(SiO4)0.5O0.5] solid solutions for х = 0.01, 0.03, 0.05, 0.10, and 0.20 х Tb Dy Ho Er Tm Yb Lu 0.01 880 630 490 430 370 350 280 0.03 1110 800 620 550 469 440 350 0.05 1260 910 700 620 520 490 400 0.10 1500 1080 840 730 620 590 470 0.20 1780 1280 990 870 740 700 560 In all systems, the size parameter (δ) does not temperatures of disintegration on the system exceed 0.1 with its maximum value of 0.0535 composition will be nearly symmetric. Therefore, (Table 1). This, according to [16-18], makes it to calculate Tcr, the following equation was used: possible to use the approximation of regular Tcr = Emix/2kN, (3) solutions when calculating the temperatures of where k is Boltzmann constant, N is the disintegration of solid solutions. In this case, the Avogadro number. In order to calculate the curve showing the dependence of the replacement limits for a given disintegration temperature of a solid solution (Td), or the of multinanolayer films is in the range of disintegration temperature for a given 1173 – 1373 K, while the temperature during the replacement limit [24], the Becker`s equation was synthesis of Gadolinium, Lutetium and Yttrium used [24]: OOS using the solution combustion synthesis – (1 – 2 x) / ln[x/(1 – x)] = RTd/Emix, (4) method is 1273 K, and the temperature during where R is universal gas constant; Emix is a solid-phase synthesis of REE OOS of the mixing energy (or interaction parameter), x is a Terbium – Lutetium row, and Yttrium, using the replacement limit. sol-gel method is in the range of 1173 – 1323 K. As can be seen from the Table 1 and Fig. 1 (curve f), the values of maximum temperatures of Table 3 disintegration, as expected, become smaller as Methods and temperatures for the synthesis of REE number increases. The Becker`s equation REE OOS was also used to calculate the temperatures of Method of Composition Т, К disintegration of solid solutions for the synthesis replacement limits x = 0.01, 0.03, 0.05, 0.10, and 0.20 (Table 2), and to build their dependences Calcination of Sc2 – xErxSiO5 1173 – 1373 (Fig. 1) on the REE number (curves a, b, c, d and multinanolayer e, respectively). The latter can be used to films [13] determine the replacement limit of Scandium for Solution Lu2SiO5:Ce 1273 REE based on a given temperature or calculate the combustion Gd2SiO5:Ce 1273 disintegration temperature based on the synthesis (SCS) Y2SiO5:Ce 1273 replacement limit. In the first case, it is necessary [25] to draw an isotherm from a given temperature to Sol-gel method Y2SiO5 1323 the intersection with the vertical line for this REE. followed by Tb2SiO5 1323 The intersection point makes it possible to calcination Dy2SiO5 1323 estimate the range of x values within which the [26] Ho2SiO5 1273 replacement limit lies. The replacement limit should be defined by interpolating the vertical Er2SiO5 1273 segment between the closest to the intersection Tm2SiO5 1273 point dependencies of the replacement limit on the Yb2SiO5 1223 REE number. In the second case, based on the Lu2SiO5 1173 given composition the point is determined on the vertical line of the REE, and then the horizontal In this way, at a temperature of less than line is drawn until its intersection with the 1173 K, the diffusion rate of structural units is temperature axis. More precise results can be apparently insufficient for the synthesis of REE obtained if using the Becker`s equation. OOS and solid solutions based on them. It is generally known that as the temperature Consequently, it can be assumed that the depression, the movability of the structural units disintegration of solid solutions at temperatures in solid solution becomes smaller due to a below ~1173 K is unlikely to occur, hence, the decrease in the diffusion rate, while the areas of solid solution will be metastable. solubility become narrower [17]. This happens The diagram also makes it possible to evaluate until the diffusion rate becomes so low that the the areas of thermodynamic steadiness of solid decrease in the areas of solubility practically solutions of Scandium OOS and REEs of the ceases, i.e. spontaneous quenching occurs, and Terbium – Lutetium series. In the solid solutions become metastable. If we assume (Sc1 – xLnx)[(SiO4)0.5O0.5] systems with Ln = Tb, that the hardening temperature is close to the Dy, and Y, unlimited solid solutions are minimum temperature at which the interaction of thermodynamically stable in the entire range of the components in the solid phase begins that concentrations 0