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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>COLINS-</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Interactive Possibilities</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Oleksii Kudryk</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Oleg Bisikalo</string-name>
          <email>obisikalo@gmail.com</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Yuliia Oleksii</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Serhii Radio</string-name>
          <email>radio@donnu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Vasyl֦ʹ Stus Donetsk National University</institution>
          ,
          <addr-line>600 richchya street, 21, Vinnytsya, Vinnytsʹka oblastʹ, 21000</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Vinnitsa National Technical University</institution>
          ,
          <addr-line>Khmelʹnytsʹke sh., 95, Vinnytsya, Vinnytsʹka oblastʹ, 21000</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2021</year>
      </pub-date>
      <volume>5</volume>
      <fpage>22</fpage>
      <lpage>23</lpage>
      <abstract>
        <p>convenience. Urusov's crystal energy theory of isomorphous substitutions carried out in our intelligent information system (IIS) was used to calculate mixing energies (interaction parameters) and critical decomposition temperatures (stability temperatures) of solid solutions. Diagram of the thermodynamic stability of solid solutions is built that makes it possible to predict the thermodynamic stability of solid solutions. IIS provides interactive features for user The present results can be useful in choosing the ratio of components in “mixed” matrices, the amount of activator in luminescent, laser, and other practically important materials, as well as in matrices for immobilization of toxic and radioactive waste Intelligent information system, phase stability, mathematical 0392 (S. Radio)</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>model, interactive</p>
    </sec>
    <sec id="sec-2">
      <title>1. Introduction, formulation problem in general</title>
      <p>
        The problem of isomorphic substitutions of atoms in crystals attracts the interest of researchers due
to the fact that most new inorganic materials for phosphors, lasers [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], scintillators, photocatalysts [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ],
LEDs [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], etc. is created on the basis of solid solutions, which allows you to purposefully influence
their properties. "Mixed" solid solutions, which contain, in addition to the activator, several other
cations [
        <xref ref-type="bibr" rid="ref4 ref5">4-5</xref>
        ]. However, it is not always taken into account that solid solutions synthesized at high
temperatures are prone to decomposition on cooling and can uncontrollably change the phase
composition and properties. Therefore, before the synthesis and study of their properties, it is desirable
to evaluate the displacement limits and thermodynamic stability of solid solutions.
      </p>
      <p>
        It is known that some solid solutions of rare earth elements (REE) with a zircon structure can be
used as luminescent materials for optoelectronics (production of displays, LEDs, etc.), biomedicine and
other industries [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. They may include several REEs that are part of both the matrix and the activator
[
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. However, state diagrams, as well as the limits of component substitutions in REE solid solutions
are insufficiently studied, which limits the possibility of choosing the compositions of solid solutions
of appropriate systems to study their luminescent properties and further practical application.
Apparently, the latter is due to the high cost of REE compounds [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]. This forces researchers studying
luminescent properties to choose the composition of matrices and activators, either by analogy with
related systems, or by trial and error.
      </p>
      <p>You can add information about the boundaries of substitutions in two ways:
1. By experimental studies of the dependence of the boundaries of substitutions on the composition.
This requires the cost of expensive reagents, equipment and significantly increases the duration of
Radio)</p>
      <p>
        2021 Copyright for this paper by its authors.
research. Since the number of the above systems of solid solutions exceeds one hundred, experimental
studies can take many years. In addition, they can be performed only in a limited range of temperatures
due to the difficulty of achieving equilibrium at both low and high temperatures [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ].
      </p>
      <p>
        2. Forecasting the boundaries of substitutions by calculation methods that do not require large
expenditures of money and time [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
      </p>
      <p>To conduct research in the second direction requires the creation of a model, methods and
technological means for predicting the boundaries of substitutions by the crystal chemical method in
systems with isostructural components in the approximation of regular solutions. It is proposed to
combine a set of appropriate models, methods and technological means in the form of an intelligent
information system (IIS) for predicting the phase stability of solid solutions. The main task of IIS is the
automated determination of the mixing energy of the components Q, the knowledge of which allows
the Becker equation, setting the decay temperature (stability) Tr to calculate the equilibrium
composition of the solid solution "x", or to calculate Tr for a given "x". It should also be borne in mind
that material scientists, who should be the main users of IIS, when calculating the mixing energy by the
method of V. Urusov may have difficulty in choosing the initial parameters. We are talking, for
example, about choosing the degree of ionicity, coordination number, interatomic distances, and so on.
Therefore, all initial parameters for each component must be entered in the IIS knowledge base. It is
also important that the IIS provides a natural language interface with the database in order to speed up
user decision-making.</p>
      <p>The object of research is the processes of forecasting the phase stability of solid solutions and
building an intelligent information system to automate such forecasting.</p>
      <p>The subject of the research are models and knowledge bases of IIS, as well as technological tools
for building IIS: Oracle Application Express (programming languages javascript, html, pl / sql) and pl
/ sql developer (programming language pl / sql).</p>
    </sec>
    <sec id="sec-3">
      <title>2. Formulation of the purpose of the article</title>
      <p>The aim of the work is to increase the accuracy and speed of predicting the phase stability of solid
solutions based on the development of models based on knowledge and technological shell convenient
for the work of IIS.</p>
      <p>To achieve the higher goal, it is necessary to provide the following characteristics of the IIS, which
provides:
• High accuracy of forecasting results;
• convenience and ease of use of IIS;
• built-in IIS interactive capabilities for user interaction;
• allow simultaneous work with an unlimited number of users;
• lack of rigid binding to specific hardware and software;
• light scalability system;
• high level of security.</p>
    </sec>
    <sec id="sec-4">
      <title>3. Model of phase stability of solid solutions</title>
      <p>
        The main task in calculating the limits of substitutions and thermodynamic stability of solid solutions
using the crystal energy method VS Urusov [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] is the definition of the mixing energy Q (interaction
parameter). In the General case, the mixing energy according to VS Urusov consists of three
contributions due to the difference in the size of the substituting structural units or interatomic distances
in the components (QR), the difference in the degree of ionicity of the chemical bond (Qε) and the
difference in their crystal structures (ΔHII–I/x1), where ΔHII–I enthalpy of the polymorphic transition
from the structure of the component it replaces to the structure of the one it replaces:
      </p>
      <p>Q = QR + Qε + ΔHII–I/x1.</p>
      <p>
        In this paper, the substitution of REEs in isostructural groups of systems is studied. Therefore, the
third term in the above equation is zero. The second term of the equation according to must be taken
into account in cases where the dimensional factor is large enough, and the difference in the
electronegativity of the substitute ions is greater than 0.4; or a difference in the degree of ionicity of the
chemical bond in the components of the systems greater than 0.05. Taking into account the difference
in the size of the structural units to be replaced and the differences in the degrees of ionicity of the
chemical bond in the components, the mixing energy will be [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]:
      </p>
      <p>Q = QR + Qε = Сmnzmzx(ΔR/R1)2 + 1390mzmzxα(Δε)2/(2R1), kJ / mol,
where:</p>
      <p>
        C is an empirical parameter calculated from the expression C = 20 (2Δχ + 1) [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] by the magnitude
of the difference in electronegativity Δχ (EN) of cations and anion;
      </p>
      <p>
        m is the number of structural units in the compounds in the pseudobinary approximation of the
components;
n is the coordination number of the substituting structural unit in the pseudobinary approximation;
zm, zx - charge modules of structural units (Ln3 + and YO43–);
R is the interatomic distance of the cation - the central atom of the oxoanion;
R1 is the smaller interatomic distance;
α is the reduced Madelung constant calculated by the Templeton formula;
Δε - differences in the degrees of ionicity of the chemical bond in the components, calculated by the
difference in electronegativity (EN) of REE and anion cations, taken from [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. The choice of scale [
        <xref ref-type="bibr" rid="ref12 ref13">12,
13</xref>
        ], in contrast to the scales of other authors, was due to the fact that the values of EN change in it at
regular intervals, increasing in the series Ce3 + - Eu3 + from 1,348 to 1,433 and Gd3 + - Yb3 + from 1,386
to 1,479 with a sharp drop in transitions Eu3 + - Gd3 + from 1,433 to 1,386 and Yb3 + - Lu3 + from 1,479
to 1,431, which is due to the structure of their electronic shells REE;
      </p>
      <p>ΔR/R1 - the relative difference in the size of the structural units to be replaced (dimensional
parameter).</p>
      <p>The crystal chemical method of quantitative theory of isomorphic substitutions was first developed
and tested on the example of systems formed by binary compounds - alkali metal halides. This was due
to the existing theoretical developments of previous generations of scientists, as well as a large number
of results of experimental studies on diagrams of states, substitution boundaries, structures,
thermodynamics and other characteristics of these compounds. Formulated by VS Urus's rule of
assistance allowed us to move to the characteristics of the size factor - from the relative difference in
the size of structural units (tabular radii of ions), which are replaced by the difference in interatomic
distances cation-anion. The latter were determined experimentally with greater accuracy and included
not only the size of the structural units to be replaced, but also the total structural units. Later, the
method was extended to systems formed by ternary compounds that contain complex anions isolated
from each other, which can be considered as separate structural units, and the compounds themselves
are called pseudobinary. Unlike alkali metal halides, pseudobinary compounds have been studied to a
much lesser extent, which in many cases complicates the determination of the dimensional parameter
due to the limited amount of structural data.</p>
      <p>
        According to [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ], in the case of using the crystal chemical method, for systems of solid solutions
of compounds with a tetrahedral anion, the following options can be selected to calculate the size
parameter ΔR/R as a relative difference:
1. Experimentally found interatomic distances cation-central atom of the complex anion
components of the systems
      </p>
      <p>(RLn1 ••• V - RLn2 ••• V) / (RLn2 ••• V).
r.</p>
      <p>Hereinafter, the interatomic distances are denoted by the letter R, the ionic radii will be denoted by
2. Sums of experimentally found interatomic distances of cation-oxygen and central oxygen-atom
components of systems</p>
      <p>[(RLn1-O + RV-O) - (RLn2-O + RV-O)] / (RLn2-O + RV-O).
3. The sum of the interatomic distances cation-oxygen and the central oxygen atom, calculated
from the values of ionic radii</p>
      <p>[(RLn1 + rO) + (rV + rO) - (rLn2 + rO) - (rV + rO)] / [(rLn2 + rO) + (rV + rO)].
4. Cubic roots from the volumes of elementary cells (V):</p>
      <p>(V11/3 - V21/3) / V21/3.</p>
      <p>Of the presented options, the first was used as a basis for deriving the basic equation of the crystal
chemical method of calculating the substitution limits in binary systems of alkali metal halides.
Therefore, it should be used primarily when testing the method on pseudobinary compounds. The
disadvantage of this option is the small number in the reference and periodic literature of the distances
cation-central atom, even for pseudobinary compounds, the structure of which is known. While the
initial data for the calculation of the other three options for most cases are in the literature.</p>
      <p>Thus, the critical decay temperatures in solid solution systems with a tetrahedral anion, as expected,
are most accurately determined when calculating the first option for selecting a dimensional parameter
(the inaccuracy is approximately 1%). In the absence of data on distances Ln ••• V the accuracy of
calculations should be higher when calculating the second option (inaccuracy 2%). Quite high accuracy
is achieved when calculating the fourth option (inaccuracy 1.9). The use of the third option can be
recommended only in the absence of the possibility of calculation of other options for an approximate
estimate of the critical decomposition temperature.</p>
      <p>The obtained results can be useful in predicting the limits of isomorphic substitutions,
thermodynamic and phase stability of solid solutions, in cases where experimental studies are difficult
due to the radioactive or toxic properties of the compounds.</p>
      <p>
        If the values of the dimensional parameters are less than 0.1, according to the recommendation [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ],
the values of the critical decay temperatures of solid solutions are calculated in the approximation of
regular solutions by the expression:
      </p>
      <p>Tkr = Q/2kN,
where k is the Boltzmann constant,</p>
      <p>N is the Avogadro number.</p>
      <p>
        The decay temperature Tr was set at a given substitution limit x or the substitution limit x at the
decomposition temperature using Becker's equation [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]:
      </p>
      <p>– (1 – 2 x) / ln[x/(1 – x)] = kN ×Tр/Q.</p>
      <p>
        According to the graphical dependences, as in [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ], it is possible to estimate the decay temperature
of limited series of solid solutions by setting the substitution limit, or to estimate the substitution limit
of one REE to another by setting the decay temperature. In the second case, the point of intersection of
the isotherm drawn from a given decay temperature with the vertical drawn from the REE number
allows to determine the composition interval in which the substitution boundary is located, and the
interpolation between the two nearest curves gives the substitution boundary. The limit of substitution
can be clarified by constructing for a particular system the dependence of the decomposition
temperatures calculated by the Becker equation on the composition, which in the approximation of
regular solutions will be almost symmetric.
      </p>
      <p>
        The novelty of the proposed mathematical model, in comparison with the basic model of Urusov in
the approximation of regular solutions, is that when calculating the empirical parameter C takes into
account the contribution of the electronegativity of each lanthanide. This contribution is taken into
account by the product of the substitution limit and the electronegativity of the corresponding lanthanide
[
        <xref ref-type="bibr" rid="ref16">16</xref>
        ].
      </p>
      <p>Therefore, a more accurate expression of the calculation of the empirical parameter C:</p>
      <p>
        C = 20 (2[χ(Ln1)∙(1-x)]-[χ(Ln2)∙x] + 1),
since the substitution limit of the substituent lanthanide is x, and the amount of substituted lanthanide
is 1, respectively [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ].
      </p>
      <p>Therefore, the calculation of the empirical parameter C is more accurate because it immediately
takes into account the specific limit of substitutions and, accordingly, increases the accuracy of the
calculation of the mixing energy. As a result, for each individual solid solution system with the specified
substitution limit, the exact rather than the total critical decomposition temperature can be calculated.
Therefore, it is proposed to put the obtained model (1) in the basis of the knowledge base of the
projected IIS.</p>
    </sec>
    <sec id="sec-5">
      <title>4. Ensuring the interactivity of the intelligent information system</title>
      <p>
        One of the manifestations of intellectual behavior is the ability of the system to transmit information
about its internal state and current needs. This ability is possessed not only by man and the artificial
systems created by him, but also by representatives of the higher animal world, who lead mainly a
collective way of life [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ].
      </p>
      <p>Known artificial systems generate only symbolic messages about the state of their own functioning,
mainly in the following cases [19, 20]:
• in case of incorrect user actions (in most systems);
• to control significant system parameters (operating systems, databases and knowledge, security
systems);
• in order to explain the obtained results (expert systems, automatic proof of theorems);
• to obtain intermediate data in the process of debugging algorithms and software products
(programming systems);</p>
      <p>• to signal dangerous situations (banking and security systems, support for communication services,
computer games, etc.).</p>
      <p>It is clear that only in the first and last case it is a limited internal need of the system to report outward
information about the occurrence of problems in performing clearly defined functions. There are no
formal statements in the literature about the generation of such messages in relation to one of the
possible needs of an open system that meet the complex criteria for the functioning of this system. The
approach to the formalization of the figurative meaning of natural language constructions (NLC),
proposed in [21], allows to solve such a problem and, thus, to obtain a model of adequate functioning
of IIS.</p>
      <p>Consider an IIS that exchanges information with the outside world through image streams. Internal
criteria for the functioning of the system, which characterize the principle of minimizing energy costs,
also have a figurative nature, as they depend on the previous history of the accumulation of
combinations of external images in the form of a chain of events. If we present emotions in the form of
the images closest to them, then the problem is to formalize the procedures for the following messages
of the system:
1. definition of the "emotional state" of IIS in the form of an ensemble of images (AO);
2. the need for external verification of the solution obtained by the system of one of the
semantically dependent problems, which belongs to the model of cognitive activity;
3. obtaining the system's requirements for the external environment, for example, in the case of
applying the cognitive criterion, the system should indicate that it is unclear which images still
require additional definition;
4. alarm about "abnormal situations" in the operation of the system.</p>
      <p>Let's solve the problem of generating 4 types of messages in the development of the proposed
approach to determining the meaning of NLC by modeling the image processing of textual information.
To this end, we will use the capabilities of the mathematical apparatus, which is designed to implement
the conceptual foundations of figurative meaning, taking into account the architecture of the knowledge
base of the system [21].</p>
      <p>1. To determine the "emotional state" of the system, we will rely on the model of the mechanism of
random access memory [22], according to which the IIS in each clock cycle is updated ensemble of
images. At the same time, images from RAM fall into the block of emotions, the task of which is to
direct the focus of attention to one of these images based on the evaluation of the connections of the
images that make up the vector of emotions. Formally, this means determining the binary code of the
image in focus Focus – Bi and the weight of the image in focus Focus – Weight, which is the largest of
all AO images.</p>
      <p>To solve this problem, we will include the most emotionally colored images in the Vector-Set
emotion vector. Then the vector of emotions of each image of AO is determined on the basis of the
operation Evaluate – Vector, as a result of which we obtain formal signs of focus of focus Focus – Bi
and Focus – Weight. Finally, the message about the "emotional state" of the system will be considered
a function - the formal dependence of the change of focus Focus – Bi on the model time t</p>
      <p>Focus  Bi  Fe (t) .</p>
      <p>The proposed approach does not preclude the continuous display of the entire composition of the
ensemble of images of RAM, which will take the form of a description (protocol) of internal events that
occur in the IIS right now.</p>
      <p>2. Suppose that the IIS implies the need for external verification or "reinforcement" according to IIS
Pavlov obtained by the system of solving one of the tasks of cognitive activity. We will assume that the
result of such a solution is the emergence of a new paradigmatic relationship, and the formal sign is an
increase in the amount of meaning in the system, for example, for a synonymous relationship according
to [22]. It is clear that the tasks of cognitive activity can have a complex hierarchical structure [21], but
for the elementary component of cognitive activity we take the creation of a new paradigmatic
relationship. Then the purpose of generating a message to verify the solution of the problem of cognitive
activity is to confirm the truth of the new paradigmatic relationship. Leaving aside the planning and
initialization of cognitive tasks, we will formally present such a message for synonymy with the help
of
 Pcij | Pcij  Pc  If  Synonim ,</p>
      <p>Pc</p>
      <p>Ses Se ij Synonim Ses ,
where If – Synonim is a predicate that requires external confirmation; Synonym - the function of
increasing the overall meaning of the system by adding a synonymous link.</p>
      <p>The task is to execute the Synonim-Plus operator, which increases the meaning of the IIS due to the
verification of the synonymous connection - if external confirmation of the synonymy is received (the
predicate If-Synonim is true), the Synonim operator is executed:</p>
      <p>Synonim  Plus :: ([If  Synonim] Synonim, E) ,
where E is an empty operator. The graph diagram of the Synonim – Plus operator is shown in Figure 1:</p>
      <p>Synonim-Plus

If-Synonim</p>
      <p>If</p>
      <p>
Synonim</p>
      <p>E</p>
      <p>The proposed approach can be applied in the process of dialogue with IIS, during which there is a
natural initialization of cognitive tasks and figurative search for a species. In this case, predicates like
If-Synonym can be considered true by default until the "teacher", as the other side of the dialogue,
"corrects" the system error in solving the corresponding partial problem of cognitive activity.</p>
      <p>3. In contrast to messages about the "emotional state", the IIS is able to generate requirements for
the external environment due to the continuous analysis of the state of the internal cognitive space of
associative pairs in the form of a graph. One of the criteria for the functioning of the system can be
applied, for example, the maximum increase in the total amount of IIS meaning as a model of the
dominant motive of "pure" intellectual activity.</p>
      <p>In what follows, we will consider the total amount of meaning of IIS as a cognitive criterion. Then
the general task of cognitive activity is interpreted in the form</p>
      <p>Ses  max | Gz</p>
      <p>To solve problem (14), the IIS can initiate a dialogue with an external "teacher", for example, to
indicate which images (graph vertices) require additional definition. To this end, it is proposed to cluster
the vertices of the graph by topological parameters and the value of meaning. The division of vertices
into clusters can be carried out on the basis of one of the known methods [23, 24], or with the help of a
specialized algorithm, which additionally initiates a dialogue with an external "teacher".</p>
      <p>Consider the algorithm Question – Out, for which the average values are pre-determined and:
''
[Step 1] nm'in  ni / 2 , nmin  ni / 2 , Semin  Sei , Minimum  Bi  1.
[Step 2] Open a loop on each i-th vertex of the graph Gz .</p>
      <p>[Step 3] If (ni'  nm'in )  (ni''  nm''in )  (Sei  Semin ) , then nm'in  ni' , nm''in  ni'' , Semin  Sei ,
Minimum  Bi  i .</p>
      <p>[Step 4] Index cycle i is closed.
[Step 5] Output (as a question object) an image with a number Minimum-Bi.</p>
      <p>We will assume that the number of new connections to support the "weakest" image will be
maximum. Then adding each new syntagmatic connection to the system increases the meaning
parameter of the system</p>
      <p>Ses  Ses   0,5
which is the ultimate goal of the Question – Out algorithm and figurative search of the species InsZX
.</p>
      <p>4. Partition of vertices of the graph G z on clusters provides the ability to generate signals to the
outside of various "abnormal situations" in the work, depending on the specifics and subject area of IIS.
If we do not take into account the dynamic characteristics of the system in real time, then the "abnormal
situation" in the narrow sense will mean the case of defining a new cluster based on a set of information
about the graph G z ,that has changed over time.</p>
      <p>As a result of an "abnormal situation", for example, in speech activity there is a possibility to give a
name to a new cluster, which will lead to a new paradigmatic relationship such as separate-general Pch
between all images of the cluster and increase the overall meaning of IIS. Therefore, the task is formally
reduced to:
• detection of the fact of the emergence of a new cluster of images;
• notification of the external "teacher" about the composition of the new cluster;
• receiving in response the number of the vertex of the graph Gz , the corresponding image of which
is determined by the name of the new cluster.</p>
      <p>Whether or not the cluster image-name is part of a cluster, in this approach, the amount of added IIS
meaning depends on the number of syntagmatic connections combined in this way.
Therefore, on the basis of the offered approach to an estimation of figurative sense of NLC formal
methods of generation of 4 types of messages of IIS on types of figurative search are received InsZX
and InsZY The message about the "emotional state" of the system is interpreted as a reflection of the
functional dependence of the change of focus Focus-Bi on the model time. The message about the
solution of one of the tasks of cognitive activity is reduced to the operator, which increases the overall
meaning of IIS due to the external verification of the corresponding paradigmatic connection.
Generation of requirements to the external environment is implemented in the form of the Question –
Out algorithm, which is based on the search of the vertices of the graph Gz finds the "weakest" Minimum
– Bi image, which differs in the smallest values of topological parameters ni' and ni'' and the meaning
of meaning Sei . The signal about the "abnormal situation" is reduced to the appearance with the
participation of the "teacher" of a paradigmatic relationship of the type separate-common between the
images of the discovered new cluster and an increase in the total number Ses sense of IIS.</p>
      <p>Let us consider an example of helping materials specialists, who should be the main users of IIS,
when calculating the mixing energy by the method of V. Urusov may have difficulty in choosing the
initial parameters. We are talking, for example, about choosing the degree of ionicity, coordination
number, interatomic distances, and so on. In Figure 2 shown the ontology of the concepts of the subject
area, which is proposed to form the basis of the interactive interaction between the user and the IIS
knowledge base.</p>
      <p>With the help of such a basic ontology, it is possible to further expand the network of concepts in
the subject area, using the analysis of both texts and the results of interaction between users and IIS.
After practical testing of the considered formal methods for generating 4 types of messages, the
development of the proposed approach is possible in the direction of increasing the number of types of
chemical reactions.</p>
    </sec>
    <sec id="sec-6">
      <title>5. Software implementation and approbation of IIS</title>
    </sec>
    <sec id="sec-7">
      <title>5.1. Creating an IIS architecture</title>
    </sec>
    <sec id="sec-8">
      <title>Development of database structure</title>
    </sec>
    <sec id="sec-9">
      <title>Confirmation of the adequacy of the mathematical model</title>
      <p>To compare and establish the convergence of the obtained results with the literature data, a system
was chosen La1-xPO4 with the structure of monazite, because it is for her in the literature there are a
sufficient number of experimental values and calculations of the mixing energy.</p>
      <p>To obtain forecast data in the proposed IIS, the user must:
1. Log in to the interface "Existing systems".
2. Choose the structure of the monazite.
3. Select the system La1-xPO4.
4. Select the lanthanide variables Gadolinium (Gd) and Europe (Eu).
5. Select the calculation step (default is 0.01).
6. Click on the "Calculate" button.</p>
      <p>After these actions, IIS calculates based on model (1) and visualizes the graphs of the systems
La1xEuxPO4 and La1-xGdxPO4 which are shown in Figure 3.</p>
      <p>Together with the schedule the user receives the table with calculations of systems La1-xEuxPO4 and
La1-xGdxPO4 which are shown in Figure 4.</p>
      <p>At the top of the table, you can use grouping to see which method was used to calculate the system
and which variable lanthanide was used. The header of the table indicates x, x1, x2, t - decay temperature,
T kritical - critical decomposition temperature, Q - mixing energy.</p>
      <p>To compare the adequacy of the model taking into account the mixing energy at each step and
without taking into account the mixing energy at each step, the calculation was performed, which is
shown in Figure 5. On it you can see and compare the results obtained at each step.</p>
      <p>To demonstrate how accurate the calculations of mixing energy and critical temperature are based
on the scientific result (when calculating the empirical parameter C, the contribution of
electronegativity of each lanthanide is taken into account by the product of the substitution limit and
electronegativity of the corresponding lanthanide). ).</p>
      <p>Figure 5 shows that without taking into account the contribution of electronegativity for each
substitution limit, only the total critical decomposition temperature (430.18474 K) and the total mixing
energy (7147.60549 kJ / mol) are calculated, as a result of which the accuracy of calculations decreases
significantly.</p>
      <p>To calculate the limits of substitutions, decomposition temperatures and assess the stability of
solid solutions, it is necessary to know the parameters of interaction (mixing energy) of solid solutions.
There are several theoretical and experimental methods for determining them. During the period
20072017, they were repeatedly used to calculate the interaction parameters in phosphate systems La1-xPO4
(Ln = Eu, Gd).</p>
      <p>This was due to the fact that solid solutions of these systems are promising matrices for
radioactive waste disposal, surpassing in many respects the aluminophosphate or borosilicate glass
currently in use.</p>
      <p>Table 2 shows the values of the parameters of the interaction of the mixing energy Q, kJ / mol
for systems La1-xEuxPO4 and La1-xGdxPO4 with the structure of monazite, obtained by various authors
and methods for the period 2007-2017, as well as the results obtained using the developed IIS.</p>
      <p>As can be seen from this table, there is a significant variation in the parameters of interaction.
Obviously, the most adequate results give average values. They are 8.3 kJ / mol and 13.5 kJ / mol,
respectively La1-xEuxPO4 and La1-xGdxPO4.</p>
      <p>For the system La1-xEuxPO4 the closest value of Q = 6.2 kJ / mol to the average (Q = 8.3 kJ /
mol) was obtained by the method of Ab initio / strain energy. However, this method for the system
La1xGdxPO4 gives a value of Q = 8.6 kJ / mol, which differs significantly from the average (Q = 13.5 kJ /
mol).</p>
      <p>Similarly, the Drop solution method for the system La1-xGdxPO4 received the closest to the
average (Q = 13.5 kJ / mol) value of Q = 11.4 kJ / mol. At the same time for the system La1-xEuxPO4
the same method obtained Q = 2.5 kJ / mol, ie much less than the average (Q = 8.3 kJ / mol). Thus,
none of the above methods can be given a definitive advantage in determining the mixing energy.</p>
      <p>A comparative analysis of the data in table 2 shows that the results obtained by the proposed IIS are
between the results obtained by the method of Ab initio quantum chemical calculations, and the data
obtained by calculation according to the model of regular solid solutions. Therefore, we can assume
that the results obtained by crystal-energy and quantum-chemical methods are consistent, and the results
of IIS are more adequate than the published results for the system La1-xPO4 with the structure of
monazite. In particular, the obtained IIS values of mixing energies for systems La1-xEuxPO4 and
La1xGdxPO4 (10,872 kJ / mol and 10,564 kJ / mol, respectively) closest to the average values of the above
methods (8.7 kJ / mol and 12.97 kJ / mol), ie adequacy for the system La1-xEuxPO4 improved within
3.77% - 46.24%, and for the system La1-xGdxPO4 - within 8.66% - 66.45%.</p>
      <p>The speed of forecasting has increased dramatically (by several orders of magnitude), because the
actual forecasting process is not carried out experimentally (months for conducting and processing an
expensive experiment), but by a calculation method based on the created IIS (hours for data entry).</p>
    </sec>
    <sec id="sec-10">
      <title>6. Conclusions</title>
      <p>This research work is devoted to solving the urgent problem of predicting the phase stability of solid
solutions based on the determination of the limits of substitutions by the crystal chemical method in
systems of solid solutions with isostructural components in the approximation of regular solid solutions.</p>
      <p>In order to solve this problem, the existing knowledge bases and structures of IIS are analyzed and
the requirements to the system designed to solve the research problem are determined.</p>
      <p>To build the knowledge base of IIS, a mathematical model was developed, which, in contrast to the
basic model of VS Urusov (in the approximation of regular solid solutions) is that when calculating the
empirical parameter C, the contribution of electronegativity of each lanthanide is taken into account by
the product of the substitution limit and electronegativity of the corresponding lanthanide, which allows
to calculate accurate rather than total critical decomposition temperature. The adequacy of the model is
proved by comparing the obtained forecasting results with the published results of solving this problem
by known methods.</p>
      <p>By formalizing the natural language flows on the basis of the concepts of language image and
emotional state of the system, it is proposed to lay in the IIS interactive capabilities. The new approach
takes into account quantitative assessments of the figurative meaning of natural language constructions
and allows to obtain formal methods of generating 4 types of IIS messages by types of figurative search.</p>
      <p>The technological implementation of IIS is substantiated - Pl / sql and Oracle APEX programming
environment (Oracle Application Express) were chosen as the programming language for the server
part; HTML hypertext markup language, CSS style language and Javascript language were chosen for
the client part.</p>
      <p>The architecture of the system is offered and programmatically implemented, taking into account its
functionality the physical model of ER database is presented, the IIS interface is developed taking into
account the needs of end users.</p>
      <p>Thus, based on the study and construction of easy-to-operate IIS, the accuracy (compared to the
known published results in the range of 3.77% - 66.45%) of predicting the phase stability of solid
solutions is increased. At the same time, the created IIS allowed to abandon experiments, which
dramatically increased the speed of forecasting by several orders of magnitude.</p>
    </sec>
    <sec id="sec-11">
      <title>7. References</title>
      <p>[19] M. Schlesinger, V. Hlavác, Ten lectures on statistical and structural pattern recognition, Springer</p>
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[20] N. Khairova, S. Petrasova, APS. Gautam, The logical-linguistic model of fact extraction from
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[21] O. Bisikalo, A. Lisovenko, O. Jahumovuch, S. Trachenko, M. Pradivliannyi, System of
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