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https://doi.org/10.29013/AJT-22-3.4-35-43
Soliev L., Jumaev M. T., Nizomov I. M., Makhmadov Kh.R., Olimdzonova N. V., Muzafarova D. V., Tajik State Pedagogical University named after Sadriddin Aini, Dushanbe, Tajikistan
FORMATION OF INVARIANTE QUILIBRIA IN MULTICOMPONENT SYSTEMS AND DETERMINATION OF SOLID PHASE CRYSTALLIZATION PATHWAY
Abstract. The structure of a phase complex of the six-component mutual system of Na, K, Mg, Ca||SO4, Cl-H2O at 50 °C in the anhydrite (CaSO4) crystallizationregion is studied by translation method. The variants of the formation of invariantequilibria (invariantfields) at transition from the five to the six component state and possibleways for solid phasecrystallization with anhydrite (CaSO4) participation are shown.
Keywords: multicomponent systems, translation methud, phase complex, geometric images.
Introduction the method for five-and more component systems,
Laws, determining the structure of the phase according to the authors, the resultsobtained will be complex (phase equilibria) of multicomponent sys- unreliable. In addition, it is impossible to construct tems, are a theoretical basis for the creation of op- a phaseequilibrium diagram of the studiedsystem on timal processing conditions of polymineral natural the basis of the obtaineddata. and complex technical raw materials. Experimental Objects and methods
establishment of the seregularitiesrequiresconsider- Kurnakovwrote N. S. the following about the na-able material and time costs. There are also problems ture of diagrams of multicomponentsystems: "... any in displaying the establishedpatterns in the form of diagram of multicomponentsystem can be considered state diagrams (phase equilibrium diagrams) of the as formed from the diagram of systems with smaller system using the geometricfigures of the real three- number of components, complicated by introduction dimensional space [1], identification of solid phases- ofnew components or otherconditions ofequilibrium, because of their diversity. The methodsdeveloped for and characteristicelements of more simple diagram the study of multicomponentsystems [2] have limit- do not disappear, but only take anothergeometrical edapplication. For example, the method of determin- image...". [8; 9]. Ya. G. Goroshchenkohavingtheoret-ingphaseassociations of "marine" system of Na, K, icallygrounded N. S. Kurnakov'sideas in addition to Mg, Ca||SO4, Cl-H2O at 25 °C developed by the au- the two known basicprinciples of physicochemicala-thors [3-7], based on minimizing the Gibbs energy, nalysis (principles of correspondence and continuity) can satisfactorilydetermine the possible phase asso- proposed the third one, the principle of compatibil-ciations in the four-component systems. When using ity of geometricalimages of pi (n+1) component sys-
tems in one diagram [10; 11]. Based on the principle of compatibility we have developed the translation-method [12] to predict the phaseequilibria in mul-ticomponentsystemsfollowed by the construction of their phase complex diagrams (phaseequilibria). The translationmethod is recognized by specialists as one of universal methods for investigations of multicom-ponentsystems [2] and has beenextensivelytested in the study of five-component and fragmented six-component systems [13-19].
The experience of application of translation method for investigation of fragments of six component system Na, K, Mg, Ca||SO4, Cl-H2O [19] has shown the different nature of geometricalimages-formation in multicomponentsystems. For example, the study of formationconditions of nonvariantequi-libria in the five-component system of NaCl-KCl-MgCl2-CaCl2-H2O at 25 °C [20] demonstrated that increasing the component systempromotes the appearance of additional nonvariantpointformation, which is accompanied by the formation of «qua-
sitots» havingdefinite size. The study of sylvinum-fragmentmethod of six-component system of Na, K, Mg, Ca||SO4, Cl-H2O at 50 °C [21] has shown that monovariantcurves can form both at translation of nonvariantpoints of five-component systems to six-component composition level and for binding of nonvariantpoints at this component level.
Results and their discussion
In the presentpaper, we considered the pos-siblevariants of the formation of diovariantfields (diovariantequilibria) of the six-component system Na, K, Mg, Ca|SO4, Cl-H2O at 50 °C in the anhydrite (CaSO4) crystallization domain established by translation. The six-component system under study includes 6 five-component systems in 4 of which anhydrite is an equilibriumphase at 50 °C. The list and phasecomposition of precipitation of nonvariantpoints of the system Na, K, Mg, Ca||SO4, Cl-H2O at 50 °C in the area of crystallization of anhydrite (CaSO4) which weretaken from [19; 22] are given in (table 1).
Table 1. - Phase composition of the precipitation of the nonvariantpoints of the system Na, K, Mg, Ca||SO4, Cl-H2O at 50 °C in the area of crystallization of anhydrite (CaSO4)
Nonvariant points Phase composition of precipitation Nonvariant points Phase composition of deposits system
System Na2SO4-K2SO4-MgSO4-CaSO4-H2O E 5 E56 An+Ac+Cc+Lev
An+Ac+Pg+Sc E 5 E57 An+Ki+Lev+Sk
V An+As+Gb+Gz E 5 58 An+Ga+Ki+Lev
V An+Gz+Pg+Ps System K, Mg, Ca SO4, Cl-H2O
V An+Gz+As+Pg E 5 E62 An+Pg+Ps+Ci
System Na, K, Ca SO, Cl-HO E 5 E64 An+Gf+Kr+Ci
E 5 41 An+Ga+Gb+Gz E 5 E65 An+Bi+Kr+Tx
E 5 42 An+Gz+Pg+Ci E 5 E66 An+Gf+Tx+Ca-2
E 5 45 An+Ga+Gf+Ci E 5 E67 An+Ki+La+Cc
E 5 E46 An+Ga+Gf+Ca-2 E 5 E68 An+Bi+Ki+Kr
E 5 47 An+Ga+Gz+Ci E 5 70 An+Pg+La+Cr
System Na, M g, Ca SO4, Cl-H2O E 5 71 An+Gf+Kr+Tx
E 5 48 An+Ga+Bi+Tx E 5 73 An+Kai+Kr+Ci
E 5 49 An+Ga+Tx+Ca-2 E 5 75 An+Kai+Ki+La
E 5 50 An+As+Ga+Lev E 5 E76 An+Kai+Ki+Kr
E 5 51 An+As+Ga+Gb E 5 77 An+Kai+Cn+Cy
E 5 54 An+B+Ga+Ki E 5 78 An+Kai+La+Pg
In (Table) 1 and below, E is the designation of a nonvariantpoint, where its upper indexindicates the multiplicity of the point (system component), and the lowerindexindicates the ordinal number of the point. For convenience, the ordinal numbers of the points are preserved as in [19, 22]. The following notation of the equilibrium solid phases is accepted [23, 24]: An - anhydrite (CaSO4); As - as-trachanite (Na2SO4-MgSO4-4H2O); Bi - bischofite (MgCl2-6H2O); Ga - halite (NaCl); Gb - glau-
berite (Na2SO4-CaSO4); Gz - glaserite (3K2SO4--Na2SO4); Gf - hydrophilite (KCl-CaCl2); Kai - kainite (KCl-MgSO4-3H2O); Ki - kiser-ite (MgSO4-H2O); Cr - carnallite (lKCl-MgCl2--6H2O); La - langbeinite (K2SO4-2MgSO4); Lev-leveite (Na2SO4-MgSO4-2,5H2O); Pg - polyhalite (K2SO4-MgSO4-2CaSO4-2H2O); Ps - pentasolite (K2SO4-5CaSO4-H2O); Si - sylvin (KCl); Sk - saky-ite (MgSO4-6Hi2O); Tx - tachhydrite (2MgCl2--CaCl2-12H2O); Ca-2 - CaCl2-2H2O.
Ein5— E^ —I
Figure 1. Composition of the phase complex diagram of the 50 °C isotherm of the system Na, K, Mg, Ca||SO4, Cl-H2O at the five-component composition in the anhydrite (CaSO4) crystallizationregion, constructed by the translation method
Drawingcorresponding (according to Gibbs rule of phases) monovariantcurvesbetweenfive-pointnonvariantpoints we obtain a phase complex diagram of the system Na, IK, Mg, Ca||SO4, Cl-H2O at 50 °C in the area of crystallization of anhydrite (CaSO4) at five-component composition. Such diagram is shown in (Fig. 1) where the five nonvariantpoints, monovariantcurves and di-variantfieldscontaininganhydrite (CaSO4) as one of equilibrium solid phases and mutual location of thesegeometricalimages are shown.
As can be seen from (Fig. 1), the invariantfields are contoured with different numbers of nonvariantpoints and monovariantcurves. Obviously, the greater the number of nonvariantpoints and monovariant-curvesinvolved in the contouring of the divariant-fields, the more significant are the parts of the system under study occupied by thesefields. For example, 10 nonvariantpoints and 10 monovariantcurves take part in contouring of a diovariantfield with equilibrium solid phases An+Ci (Fig. 1) and 7 nonvariantpoints and 7 monovariantcurves take part in contouring of a diovariantfield with equilibrium solid phases An+Ci:
This indicates that the first invariantfield in the givenconditionsoccupies a largerpart of the system than the secon dinvariant field.
The invariant fields with equilibrium solid phasesAn+Ps, An+Gb and An+Ca.2 are contoured by three five-valuednonvariantpoints and the same number of monovariant curves:
This indicates that they separatelyoccupy a much At transition of system from a five-component lev-
smallerpart of the investigate dsystem under the el on a six-component level (for example, by addition
givenconditions than the divariantfields with equi- ofthe sixth component in any of four five-component
librium solid phasesAn+Ga and An+Si. systemswhere one of equilibriumphases is anhydrite),
transformation of geometricalimages of five-component systems with their subsequenttranslation (transfer) to a level of six-component compositionoccurs. Further the translatedgeometricalimagesparticipate in formation of elements of a structure diagram of researchedsystem at a six-component level [19; 22].
In accordance with the principle of compatibility [10; 11], combining the geometrical images of the five and six component levels of the system Na, K, Mg, Ca|SO4, Cl-H2O at 50 °C in the anhydrite (CaSO4) crystallization area, we obtain its combined diagram of the phase complex (Fig. 2).
Figure 2. Structure of the combined diagram of the phase complex of the 50 °C isotherm at the level of five-six-component composition in the anhydrite (CaSO4) crystallization area by the translationmethod
Such combined diagram of the phase complex reflects the interrelation between all geometrical images of the five- and six-component levels of the system under study in the considered conditions. For example, in (Fig. 2), the thin solid lines represent the monovariant curves of the five-component composition level (they run between the five non-variant points). The dotted lines are the monovariant level curves of the six-component composition. They are formed by the translation of the five-not-variant points to the level of the six-component composition, and the arrow points to the direction of translation. The bold solid lines are also monovariant curves of the six-component composition level. They run between the six-component non-variant points. The six-valued nonvariant points are formed by interrupting (following Gibbs' phase rule) the monovariant level curves of the six-component composition.
The analysis of the joint diagram of the system Na, K, Mg, Ca||SO4, Cl-H2O at 50 °C in the anhydrite (CaSO4) crystallisation range [19; 22] demonstrates that it is characterised by the following number of geometricalpatterns at the five component (A) and six component (B) compositions under given-conditions (Table 2).
Table 2.- Number of geometricalpatterns of the system Na, K, Mg, Ca||SO4, Cl-H2O at 50 °C in the area of crystallisation of anhydrite (CaSO4) at levels of five (A) and six (B) componentsdetermined by method of translation
Geometricimages System ^mponents
A B
Non-variant points 30 22
Monovariant curves 44 58
Divariant fields 18 47
The conditions for the formation of geometrici-mages of the system under study in the given system are discussed in detail in [19; 22]. In this paper, according to the task, we will considerexamples of the formation of the invariantfields (invariantequilibria) and the possibility of determining the crystallization-
path of the solid phases by their structure. A more detailedanalysis of constructedcombined diagram of phasecomplexes of the system Na, K, Mg, Ca|SO4, Cl-H2O at 50 °C in anhydrite (CaSO4) crystallisation area is considered in [19; 22].
The formation of diadivariantfields on the level of six component composition is realized in two ways. The first way is related to translation of the mon-ovariantcurves of the five-component composition level to the level of the six-component composition. The secondway is related to contouring of the sys-temsurface with six nonvariantpoints and monovari-antcurvespassingbetween them.
The invariant fields formed by translation of the monovariantcurves of the five-component composition level to the level of the six-component composition (Fig. 2) can be contoured by
a) Five-not-variantpoints - monovariantcurves-formed by translation of five-not-variantpoints -six-not-variantpointspassingbetween them. For instance:
b) five-not-variantpoints - monovariantcurves-passingbetweenthem - monovariantcurvesformed by translation of five-not-variantpoints - six-not-variantpoints - monovariantcurvespassingbetween them. For example:
Analysis of the phase complex diagram of the system Na, K, Mg, Ca||SO4, Cl-H2O at 50 °C in the anhydrite (CaSO4) crystallization region shows that three (3) diwariant fields are for medalong the secondpath and they have the following contours
(Fig. 2):
Principles of formation of geometricalimages, in particular of the invariantfields, have not only scientific-theoretical value for understanding of regularitiesde-terminingstructures of diagrams of multicomponent chemical systems, but also are extremelyimportant for the solution of practicalproblems, in particular at establishment of possibleways of crystallization of solid phases. For example, if a figurative point of an anhydrite (CaSO4) fragmentcomposition of a system under study at 500C in the beginning of iso-thermalevaporation is located on the invariantfield
E11 '5 An+Gz+ÏV Pu ^ E/ An+Gz+Ps
Ea5 "" "Àn+Cz+Ps+Sr ,
then two options are possible (according to the number of monovariantcurves of the six-component composition level, which outline this field) further-crystallizationpath: a) towardsmonovariantcurve E511^E63, uponreaching which Pg (polyhalite) crystallizes as the fourthequilibrium solid phase and; b) towardsmonovariantcurve E542 ->E63, uponreach-ing which Si (sylvin) crystallizes as the fourthequi-librium solid phase. Further the crystallizationpath ends at nonvariantpoint E36 with equilibrium solid phases An+Gz+Pg+Ci+Ps.
Finding the figurative point of the mixturecom-position on the invariantfield
E,iiAo+Ci+EsH^> Ati*Gz*Pg+Si E,/ An+G?-+Pg
Lii6S An+Àcb+Gz"ri['■+ Pg " Bj6
There are fouroptions for the fourth equilibrium solid phase crystallizationpath (accord-
ing to the number of monovariant curves of the six-component composition level). Further the crystallizationpathwill end at one of the three six nonvarian tpoints. For example, when the crystalli-zationpathreaches the E115 ^ E36 monovariantcurve, the quadruple equilibrium solid phase will be Ps (pentasol) and crystallization will terminate at the E36 nonvariantpoint with equilibrium solid phases An+Gz+Pg+Ps+Ci. At achievement of a crystallizationpath of monovariantcurve E165 ^E69 the quaternary equilibrium solid phase will be As (as-trachanite) and the crystallization will terminate at nonvariant point E96 with equilibrium solid phases An+Ac+Ga+Gz+Pg.
When the crystallization pathreaches the monovariantcurves E36 ~~ Eiy6 , E'j6 E106 itsfur-thermovementdepends on the process of saturation of the solution with the fifthequilibriumsolidphase. For example, if reaching the path of crystallization of monovariantcurve E36 — Kin6 solution satura-tionprocess is accompanied by increasing of solution concentrationdue to pentasol (Ps), then the crystallization pathwill be directedtowards nonvariant sixth point E36, uponreaching which equilibrium solid phases will be An+Gz+Pg+Ps+Cs. If upon achievement of the path of crystallization of monovariantcurve E16 — E[ofi) the process ofsolutionsatura-tion is accompanied by increasing of solution concentration due to halite (Ga), the path of crystal-lizationwill be directedtowardsnonvariantsixthpoint E106, upon achievement of whichequilibriumsolid-phaseswill be An + Ga + Gz + Pg + Ci. In the same-wayfurthercrystallizationpaths can be determined on the monovariantcurve E96... ~ E106.
References:
1. Anosov V. Ya., Ozerova M. I., Fialkov Yu. Ya. Major Methods of Physicocemical Analysis. (Nauka, Moscow); 1976.- 504 p. [in Russian].
2. Goroshenko Ya. G., Soliev L. The main trends in the methodology of physical and chemical analysis of complex and multicomponent systems. Russ. J Inorg Chem.- 32(7). 1987.- P. 1676-81.
3. Pitser K. S., Kim J. Termodynamcs of electrolytes 1V. Activity and osmotic coefficients for mixed electrolytes. Journal American Chemical Soctarey.- 96(18). 1974.- P. 5701-07.
4. Wood J. R. Termodynamica of brine-Salt egailibria the systems NaCl-KCl-MgCl2-CaCl2-H2O at 25 °C. Geochim at Cosmochim Acta.- 39(8). 1975.- P. 1147-63.
5. Harviec E., Weare J. H. The prediction of miniral Soliblities natural water the Na-K-Mg-Ca-Cl-SO4-H2O system from Geochem at CosmochimActa.- 44(7). 1980.- P. 981-97.
6. Eugster H. P., Harvie C. F., Weare J. H. The prediction of mineral solubilities natural water the Na-K-Mg-Ca-Cl-SO4-H2O system from zero to high concentration at 250C. Geochem at Cosmochim Acta.- 44(9). 1980.- P. 1335-47.
7. Harvie C. F., Eugster H. P., Weare J. H. Mineral equilibrium in a six-components seawater system Na-K-Mg-Ca-Cl-SO4-H2O at 25 °C II compositions of the soluroted solutions. Geochem at Cosmochim Acta.- 46(9). 1982.- P. 1603-18.
8. Kurnakov N. S. Some questions of the theory of phesical and chemical analysis. Reports of the USSR Academy of Scenses.- 25(5). 1939.- P. 38487. [Russian].
9. Kurnakov N. S. The introduction to Physicochemical Analysis. Izd-vo Akad. Nauk USSR.- Moscow / Leningrad. 1940. [Russian].
10. Goroshenko Ya. G. Physicochemical Analysis of Homogeneous and Heterogeneous Systems. - Kiev: Naukova Dumka; 1978. [Russian].
11. Goroshenko Ya. G. The Center ofMass Method for Multicomponent Systems Imaging.- Kiev: Naukova Dumka;1982. [Russian].
12. Soliev L. Prediction of structure of multicomponent water-salt systems phase equilibria diagram by means of translation method. VINITI № 8990-B87, 1987.- 28 p. Russian.
13. Soliev L. Phase Equlibria in the Na, K, Mg, Ca||SO4, Cl-H2O System at 25 °C in the Region of Glaubarite Crystallization. Rus J Phys Chem.-77(3). 2003.- P. 351-54.
14. Soliev L. Phase Equlibria in the Na, K, Mg, Ca||SO4, Cl-H2O System at 50 °C in the Crystalliza-tionGlazirite (3K2SO4-Na2SO4). Rus J Phys Chem.- 87(9). 2013.- P. 1442-47. DOI: 10.1134/ S0036024413090227
15. Tursunbadalov Sh., Soliev L. Phase Eguilibria in the quinery Na, K //SO4, CO3, HCO3-H2O system at 75 °C. Journal of Solution Chemistry.- 44(8). 2015.- P. 1626-39. DOI: 10.1007/s10953-015-0368-3.
16. Tursunbadalov Sh., Soliev L. Phas Equilibria in multicomponent water-salt system. Journal of chemical engineering data.- 61(7). 2016.- P. 2209-20. DOI: 10.2021/acs.jced.5b00875.
17. Tursunbadalov Sh., Soliev L. Determination of phase Equilibria and construction of comprehensive phase Diagram for the Quinery Na, K, // SO4, CO3, HCO3-H2O system at 25 °C. Journal of chemical engineering data.- 62. 2017.- P. 698-03. DOI: 10.2021/acs.jced.6b00739.
18. Soliev L., Jumaev M. T. Phase complex of the system Na, Ca||SO4, CO3, HCO3-H2O at 100 °C. Chemica Techno Acta.- 7(2). 2020.- P. 192-98. DOI: 10.15826/chimtech.2020.7.2.04
19. Soliev L. Prediction of Phase Equilibria in Multinary Marine-Type Systems by the Translation Method, Book 3. Dushanbe: Er-Graph; 2019.- 232 p. Russian.
20. Soliev L. Invariant Equlibria in Multicomponent Systems. Russ J Inorg Chem.- 64(7). 2019.- P. 894-98. DOI: 10.1134/S0036023619070167
21. Soliev L. Monovariant Equlibria in Multinary Systems. Russ J Inorg Chem.- 65(2). 2020.- P. 212-16. DOI: 10.1134/S0036023620020187
22. Soliev L. Phase Equilibria in the Na, K, Mg, Ca||SO4, Cl-H2O system at 50 °C in the Angidrite criystal-lization. Russ J Inorg Chem.- 56(10). 2011.- P. 1659-65. DOI: 10.1134/S0036023611100238
23. Reference book on experimental data for solubility in multicomponent water-salt systems. - Vol. I., Books. 1-2. - Saint-Petersburg: Khimizdat, 2003.- 1152 p. Russian.
24. Reference book on experimental data for solubility in multicomponent water-salt systems.- Vol. II., Books. 1-2. - Saint-Petersburg: Khimizdat, 2004.- 1247 p. Russian.
