=Paper=
{{Paper
|id=Vol-3126/paper49
|storemode=property
|title=Information System to Forecasting the Stadiness of Ree Ooss Solid Solutions for Environmental Monitoring
|pdfUrl=https://ceur-ws.org/Vol-3126/paper49.pdf
|volume=Vol-3126
|authors=Oleksii Kudryk,Oleg Bisikalo,Yuliia Oleksii,Eugeni Get’man
}}
==Information System to Forecasting the Stadiness of Ree Ooss Solid Solutions for Environmental Monitoring==
<pdf width="1500px">https://ceur-ws.org/Vol-3126/paper49.pdf</pdf>
<pre>
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 <x <1 at temperatures above the
leads to the formation of a solid solution, we can      critical one (2060 – 1400 K; Table 1, Fig. 1);
estimate the temperature of spontaneous                 when the temperature depression to the range
hardening and the area of metasteadiness in the         between Tcr and ~1173 K, they become
system.                                                 thermodynamically unstable and can decay. At
    It was previously established (Table 3) that the    T < 1173 K, solid solutions will not decay, i.e.
temperature during the synthesis of solid solutions
of Sc2 – xErxSiO5 OOS as a part of the preparation
spontaneous hardening will occur, and they will
become metastable.
    In the systems containing REE from Erbium to
Lutetium, the maximum temperatures of
disintegration (1010 – 650 K) are lower than the
spontaneous quenching temperature (~1173 K),
unlimited solid solutions do not decay upon
cooling, and remain stable at temperatures higher
than critical one and metastable at temperatures
lower than critical one.
    The difference between the critical
temperature for a system containing Holmium
(1150 K) and the temperature of spontaneous             Figure 2: Dependence of the calculated
quenching (~1173 K) is less than the calculation        temperatures of disintegration of solid solutions
error (± 100 K [17]); therefore, it is difficult to     for the system (Sc1 – xLux)[(SiO4)0.5O0.5] (■) on the
forecast disintegration of an unlimited solid           molar fraction of Lutetium, and experimental
solution in this system.                                data on the synthesis temperatures (●) for the
    Likewise, limited solid solutions with x = 0.01,    compositions with x = 0.25, 0.4, and 0.50 [12]
0.03, 0.05, 0.10, and 0.20 in the areas above the
curves a, b, c, d, and e, respectively, are
thermodynamically stable (Fig. 1), in the areas
below the curves they are unstable and can decay,
while at T < 1173 K they are metastable.
    Notwithstanding        there    are    numerous
publications, which study the laser properties of
Scandium OOS, doped with, for example, 0.5 at%
of Holmium [3], 1 at% of Neodymium [9, 27],
4 at% of Thulium [7], 5 at% of Ytterbium [28]
and others, and some papers on the properties of
“hybrid” OOS Y(Lu,Sc)2SiO5 [2], (Sc0.5Y0.5)2SiO5
[8, 10], (Sc0.2Y0.8)2SiO5 [11], there is practically
no data on the limits of isomorphic replacements        Figure 3: Dependence of the calculated
in the corresponding systems. This, of course,
                                                        temperatures of disintegration of solid solutions
makes it difficult to assess the reliability of our
                                                        for the system (Sc1 – xLux)[(SiO4)0.5O0.5] (■) on the
calculations. But, they do not contradict the
experimental data obtained previously for               molar fraction of Lutetium, and experimental
Lu2 – xScxSiO5 and ErxSc2 – xSiO5 solid solutions.      data on the synthesis temperatures (●) for the
For example, in the Lu2 – xScxSiO5 system, a            compositions with x = 0.25, 0.4, and 0.50 [12]
mixture of Lu2O3, Sc2O3 and SiO2 was calcined to
synthesize solid solutions for compositions with
x = 0.5, 0.8, 1.0 at a temperature of 1670 K [12],      3. Conclusions
i.e. in the area of continuous series of solid
solutions, which are thermodynamically stable                   The crystal-chemical approach in the
according to the results of our calculation (Fig. 2).   approximation of regular solutions was used to
    In [13], the ErxSc2 – xSiO5 solid solutions were    calculate the interaction parameters Emix of solid
received      by     calcination     of    atomized     solutions      based      on    Scandium        OOS
multinanolayer films in the temperature range           (Sc1 – xLnx)[(SiO4)0.5O0.5], modified with REEs
1173 – 1373 K; i.e. also in the area of continuous      with x = 0.01, 0.03, 0.05, 0.10, 0.20, and 0.5. With
series of solid solutions above the disintegration      an increase in the number of the rare earth
curve calculated by us (Fig. 3).                        element, the calculated mixing energies and
                                                        critical temperatures of disintegration of solid
                                                        solutions become smaller, which is due by the
                                                        decrease in the ionic radii of REE in the series
                                                        from Lanthanum to Ytterbium.
    The diagram of thermodynamic steadiness               working on the research topics “Identification of
makes it possible to evaluate not only the                hidden dependencies in online social networks
steadiness of (Sc1 – xLnx)[(SiO4)0.5O0.5] solid           based on methods of fuzzy logic and
solutions in a wide range of compositions and             computational linguistics” and “Information and
temperatures, but also to forecast for some solid         communication technologies for solving
solutions the replacement limits at a given               semantic-dependent problems” of the Department
disintegration temperature, or the disintegration         of Automation and Intelligent Information
temperature at a given replacement limit.                 Technologies of Vinnytsia National Technical
    In the systems (Sc1 – xLnx)[(SiO4)0.5O0.5] with       University (Ukraine, Vinnytsia).
Ln = Tb, Dy, and Y, unlimited solid solutions are             The authors are especially appreciative to the
thermodynamically stable at temperatures above            staff of the Department of Automation and
critical one (2060 – 1400 K), and if the                  Intelligent Information Technologies, personally
temperature depression to the range between               to the head of the Department, Doctor of
critical temperature and ~1173 K, the solutions           Technical Sciences, prof. Roman N. Kvyetnyy
become thermodynamically unstable and can                 also personally to the professor of the Department
decay. At a temperature of T < 1173 K, solid              of Computer Science and Information
solutions will not decay, since they become               Technology, Vasyl’ Stus Donetsk National
metastable. In the systems containing REE from            University, Doctor of Technical Sciences, prof.
Erbium to Lutetium, where the critical                    Sergiy D. Shtovba for consultations on theoretical
temperatures of disintegration are vastly lower           and applied aspects of the research.
(1010 – 650 K) than the temperature of
spontaneous quenching (~1173 K), unlimited                5. References
solid solutions do not decay upon cooling, and
they remain stable at temperatures higher than
                                                          [1]    Yu.D. Zavartsev, A.I. Zagumennyi , Yu.L.
critical one and metastable at temperatures lower
                                                                Kalachev,      S.A.       Kutovoi,      V.A.
than Tcr.
    The calculation results obtained do not                     Mikhailov, I.A. Shcherbakov, Study of
                                                                Tm:Sc2SiO5 laser pumped into the 3H6 – 3F4
contradict the experimental data obtained
previously for (Sc1 – xLux)[(SiO4)0.5O0.5] and                  transition of Tm3+ ions. Quantum Electron,
(Sc1 – xErx)[(SiO4)0.5O0.5 ] solid solutions, since the         2013, volume 43(11), pp. 989 – 993.
temperatures of their synthesis are in the limits         [2]   A. Denoyer, Études optiques de nouveaux
attributed by us to thermodynamically stable ones.              matériaux laser: des orthosilicates dopes à
    Materials based on such solid solutions have                l’ytterbium Yb:Y(Lu,Sc)2SiO5. Thesis,
budding       prospects       in    optical     remote          Université de Sherbrooke, Sherbrooke,
                                                                Québec, 2007.
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solid solutions of different structural types” of the           volume 7(5), p. 434.
Department of Inorganic, Organic and Analytical           [5]   X. Yang , B. Yao , Y. Ding , X. Li , G. Aka ,
Chemistry, Vasyl’ Stus Donetsk National                         L. Zheng , J. Xu, Spectral properties and
University (Ukraine, Vinnytsia). The authors are                laser performance of Ho:Sc2SiO5 crystal at
grateful to the staff of this department and                    room temperature. Opt. Express, 2013,
personally to the lecturer of the Department of                 volume 21(26), pp. 32566 – 32571.
Inorganic, Organic and Analytical Chemistry               [6]   L. Zheng, L. Su , J. Xu, Growth and
PhD, Associate Professor, Serhii V. Radio for                   Characterization of Ytterbium Doped
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