Phase complex of the system Na,Ca||SO4,CO3,HCO3-H2O at 100 ºC 71 D O I: 1 0. 15 82 6/ ch im te ch .2 02 0. 7. 2. 04 Soliev L., Jumaev M. T. Chimica Techno Acta. 2020. Vol. 7, no. 2. P. 71–80. ISSN 2409–5613 Soliev L., Jumaev M. T. Tajik State Pedagogical University named after S. Ayni 121 Prospect Rudaki, Dushanbe, 734003, Tajikistan e-mail: Soliev.lutfullo@yandex.com, Jumaev_m@bk.ru Phase complex of the system Na,Ca||SO4,CO3,HCO3–H2O at 100 °C The article discusses the results of determining the possible phase equilibria in geometric images of a five-component reciprocal water-salt system of sulfates, carbonates, sodium bicarbonates and calcium at 100 °C with subsequent con- struction of its phase complex diagram. The laws that determine the structure of the phase complex diagram of this system are needed to be obtained for the production of scientific data used both as a reference material and also to cre- ate the optimal conditions for the recycling of liquid waste industrial production of aluminum-containing sulfate carbonate and bicarbonate salts of sodium and calcium. It was established that the system under study at 100 °C is character- ized by the presence of 31 divariant double saturation fields, 25 monovariant trisaturation curves and 14 invariant points. Keywords: translation method; phase complex diagram; geometric images Received: 17.04.2020. Accepted: 22.06.2020. Published: 30.06.2020. © Soliev L., Jumaev M. T., 2020 Introduction The phase diagrams for the com- plex systems are not only of scientific inter- est, but also necessary for creating opti- mal conditions for the galurgic processing of natural mineral raw materials and in- dustrial wastes containing sulfates, carbon- ates, sodium and calcium bicarbonates [1]. The  Na,Ca||SO4,CO3,HCO3-H2O system has not been studied yet at 100 °C. Earlier we studied phase equilibria in this system by the translation method at temperatures of 0 and 50 °C [2, 3]. Methods We have deduced phase equilibria in  the  Na,Ca||SO4,CO3,HCO3–H2O sys- tem at 100 °C using translation methods [4, 5] which follows from the  principle of  compatibility of  structural elements of n and n + 1 component systems in one diagram [6, 7]. According to the transla- tion method, the  addition of  one more component to  the  n-component system and its transition to the n + 1 component state is  accompanied by  transformation of the geometric image of the n-component system. The transformed geometric images are translated to the n + 1 level according to their topological property in accordance with the Gibbs phase rule, forming corre- spondent geometric images (fields, curves, points) in  the  n  +  1 component system. The application of translation methods for predicting and constructing phase diagram 72 for multicomponent water-salt systems was considered in more details in our previous work [4]. Earlier this method was success- fully used for other multicomponent sys- tems [8, 9]. T h e   f i v e - c o m p o n e n t s y s t e m Na,Ca||SO4,CO3,HCO3-H2O can be rep- resented as  a  combination of  the  fol- low ing four comp onent systems: Na2SO4–Na2CO3–NaHCO3–H2O, CaSO4– CaCO3–Ca(HCO3)2–H2O, Na,Ca||SO4,CO3, – H 2 O , N a , C a | | S O 4 , H C O 3 – H 2 O , Na,Ca||CO3,HCO3–H2O. The phase equi- libria of  invariant points in  these four- component systems were studied earlier by the method of the multiple solubility [1, 10] and by the translational method [11– 15]. Coexisted equilibrium solid phases inside the invariant four-component sys- tems are listed in Table 1. Phase composi- tion of these non-variant points was used to predict the phase equilibria and for con- struction of phase complex of the studied system by the translation method. In Table 1 and further E denotes the in- variant point, where the upper index indi- cates its multiplicity (the number of sys- tem’s component), and the  lower index indicates its serial number. The following notations for solid phases that were formed in the system were used: Te — tenaedite, Na2SO4; CaG  — calcium hydrocarbonat, Ca(HCO3)2; Gp — gypsum, CaSO4·2H2O; Nk — nakhcolite, NaHCO3; Pr — gayluscite, Na2CO3·CaCO3·2H2O; Cc — calcite CaCO3; Na·1 — Na2CO3; Ber — berkeite, 2Na2SO4·Na2CO3; Table 1 Phase composition of precipitates for the non-variant points in the Na,Ca||SO4,CO3,HCO3-H2O system at 100 °C at the four-component composition level Invariant points Solid phase equilibrium Invariant points Solid phase equilibrium Na2SO4-Na2CO3-NaHCO3-H2O system Na,Ca||SO4,CO3-H2O system E1 4 Te+Nk+3Na·C E10 4 Te+Br+Gb E2 4 Br+Na·1+Tr E11 4 5Ca·Na·3+Gp+Cc E3 4 Te+Br+Tr E12 4 Br+Na·1+Pr E4 4 Te+Tr+3Na·C E13 4 Gb+5Ca·Na·3+Br System CaSO4-CaCO3-Ca(HCO3)2-H2O E14 4 Pr+Cc+5Ca·Na·3 E5 4 Gp+Cc+CaG E15 4 Br+Pr+5Ca·Na·3 Na,Ca||SO4,HCO3-H2O system Na,Ca||CO3,HCO3–H2O system E6 4 Nk+Te+Gb E16 4 Na·1+Tr+Pr E7 4 Gp+5Ca·Na·3+CaG E17 4 Pr+Cc+CaG E8 4 Nk+CaG+Gb E18 4 Nk+3Na·C+CaG E9 4 Gb+CaG+5Ca·Na·3 E19 4 Tr+3Na·C+Pr E20 4 Pr+3Na·C+CaG 73 Tr — trona, Na2CO3·NaHCO3·2H2O; 3Na·C — 3NaHCO3·Na2CO3; Gb — glauberit, Na2SO4·CaSO4; 5Ca·Na·3 – 5CaSO4·Na2SO4·3H2O. Results and discussion Based on the  data listed in  Table  1 the  phase diagram (phase complex) for the  Na,Ca||SO4,CO3,HCO3-H2O system was constructed at  100  °C at  the  level of four component composition of the salt part, which is shown in the figure as pro- jection of tetrahedral faces. A  unification of  the  salt part of the phase diagram (combining of identical crystallization fields of various constitu- ent four-component systems), we obtain a schematic diagram for the phase equi- libria in the Na,Ca||SO4, CO3,HCO3-H2O Fig. 1. Projection of the salt part of the phase diagram for the Na,Ca||SO4,CO3,HCO3–H2O system at 100 °C at level of the four-component composition 74 system at 100 °C at the level of four-com- ponents, which is shown in the Fig. 2. The constructed diagram contains geo- metric images (invariant points, multi-var- iant curves, divariant fields) correspondent to the various states of the system under study as  a  function of  its composition at the level of four component composition. The phase compositions of the quadruple invariants are listed in Table 1. The phase compositions of  the  precipitation for the divariant fields are shown in the figure. The phase composition for the monovari- ant curves connecting quadruple invariant are presented as follows: Е1 4 Е4 4 = Te + 3Na·C; Е1 4 Е6 4 = Nk + Te; Е1 4 Е18 4 = Nk + 3Na·C; Е2 4 Е3 4 = Ber + Tr; Е2 4 Е12 4 = Ber + Na·1; Е2 4 Е16 4 = Tr + Na·1; Е3 4 Е4 4 = Te + Tr; Е3 4 Е10 4 = Te + Ber; Е4 4 Е19 4 = Tr + 3Na·C; Е5 4 Е7 4 = CaG + Gp; Е5 4 Е11 4 = Gp + Cc; Е5 4 Е17 4 = Cc + CaG; Е6 4 Е8 4 = Nk + Gb; Е6 4 Е10 4 = Te + Gb; Е7 4 Е9 4 = CaG + 5Ca·Na·3; Fig. 2. The schematic diagram of phase equilibrium in the Na,Ca||SO4,CO3,HCO3-H2O system at 100 °C at the level of four-component composition, constructed by the translation method 75 Е7 4 Е11 4 = Gp + 5Ca·Na·3; Е8 4 Е9 4 = CaG + Gb; Е8 4 Е18 4 = CaG + Nk; Е9 4 Е13 4 = 5Ca·Na·3 + Gb; Е10 4 Е13 4 = Gb + Ber; Е11 4 Е14 4 = Gp + 5Ca·Na·3; Е12 4 Е15 4 = Ber + Pr; Е12 4 Е16 4 = Na·1 + Pr; Е13 4 Е15 4 = Ber + 5Ca·Na·3; Е14 4 Е15 4 = Cc + 5Ca·Na·3; Е14 4 Е17 4 = Cc + Pr; Е16 4 Е19 4 = Tr + Pr; Е17 4 Е20 4 = Pr + CaG; Е18 4 Е20 4 = 3Na·C + CaG; Е18 4 Е20 4 = 3Na·C + Pr. Through and one-way translation pro- cedure [4] of invariant points from the level of four component composition to the lev- el of  five-component composition leads to the formation of the following invariant points: E1 4 + E6 4 E1 5 = Nk + Te + 3Na·C + Gb; E2 4 + E12 4 + E16 4 E2 5 = Ber + Na·1 + Tr + Pr; E3 4 + E10 4 E3 5 = Te + Ber + Tr + Gb; E4 4 + E19 4 E4 5 = Te + Tr + 3Na·C + Pr; E5 4 + E7 4 + E11 4 E5 5 = Gp + Cc + CaG + 5Ca·Na·3; E8 4 + E18 4 E6 5 = Nk + CaG + Gb + 3Na·C; E9 4 + E13 4 E7 5 = Gb + CaG + 5Ca·Na·3 + Ber; E14 4 + E17 4 E8 5 = Pr + Cc + 5Ca·Na·3 + CaG; E15 4 + CaG E9 5 = Ber + Pr + 5Ca·Na·3 + CaG; E20 4 + Gb E10 5 = Pr + 3Na·C + CaG + Gb; The  analysis of  phase equilibria in  the  Na,Ca||SO4,CO3,HCO3-H2O sys- tem at 25 °C based on the obtained data at the level of five-component composition shows that the crystallization fields formed during the  translation of  monovariant curves of level four-component composi- tion with their characteristic equilibrium solid phases, namely Tr+Pr, Pr+CaG, 3Na·C+Pr, Ber+Pr, Gb+Ber and CaG+Gb, do not closed for their closure by the “in- termediate” translation [4] method: E11 5 = Te + 3Na·C + Gb + Pr; E12 5 = Gb + Ber + Tr + CaG; E13 5 = Tr + Pr + Ber + Te; E14 5 = Pr + CaG + 5Ca·Na·3 + Gb The  displaced chart of  phase balance in  the  Na,Ca||SO4,CO3,HCO3-H2O sys- tem at 100 °C the level of four-component system has been constructed taking into account all types of translations (Fig. 3). Bold lines indicate monovariant level curves of the five-component composition. These lines connected five various invariant points; they are characterized by the fol- lowing phase composition of the precipi- tates: E1 5 E6 5 = Nk + 3Na·C + Gb; E1 5 E11 5 = Te + 3Na·C + Gb; E2 5 E12 5 = Ber+ Pr + Tr; E3 5 E13 5 = Ber+ Te + Tr; E4 5 E11 5 = Te + Pr + 3Na·C; E5 5 E8 5 = Cc + 5Ca·Na·3 + CaG; E6 5 E10 5 = CaG + Gb + 3Na·C; E7 5 E9 5 = CaG + 5Ca·Na·3 + Ber; E7 5 E12 5 = Gb + Ber + CaG; E8 5 E9 5 = Pr + CaG + 5Ca·Na·3; E9 5 E14 5 = Pr + CaG + 5Ca·Na·3; E10 5 E11 5 = Pr + 3Na·C + Gb; E10 5 E14 5 = Pr + CaG + Gb. Table  2 demonstrates the  sol- id phase equilibrium and contour of  the  divariant sodium-based system Na,Ca||SO4,CO3,HCO3-H2O at  100 °C. Among 31 divariant fields that charac- terized the  studied system at  100 °C, 30 fields are formed as a result of translation 76 of monovariant curves at the level of four- component composition to  the  level of five-component composition and one more field with equilibrium solid phas- es Gb+3Na·C was obtained as  a  result of the contouring of five invariant points and monovariant curves. The  thin solid lines in  Figure 3 indi- cate the  monovariant curves at  the  lev- el of  four-component composition. The  equilibrium solid phases that are correspondent to these curves were pre- sented above. Dash lines with arrows (in  Table  2) indicate monovariant curves at  the  level of five-component composition, They are formed as a result of translation therefore the  equilibrium phases corresponded to these monovariant curves are identical to the equilibrium solid phases of the in- variant points of the corresponding qua- ternary systems. Fig. 3. Combined diagram of phase equilibria (phase complex) for the Na,Ca||SO4,CO3,HCO3–H2O system at 100 °C at the level of four-component composition constructed by the translation method 77 Table 2 Equilibrium solid phases and contours of the divariante fields in the Na,Ca||SO4,CO3,HCO3-H2O system Equilibrium solid phases of fields Field contours in the diagram (Fig. 3) Equilibrium solid phases of fields Field contours in the diagram (Fig. 3) 3Na·C+Nk E1 4 E1 5 E18 4 E6 5 CaG+5Ca·Na·3 E7 4 E5 5 E1 5 E9 4 E2 5 E2 5 Nk+Te E1 4 E1 5 E6 4 CaG+Gb E8 4 E6 5 E14 5 E9 4 E7 5 E12 5 Te+3Na·C E1 4 E1 5 E4 4 E4 5 E11 5 CaG+Nk E8 4 E6 5 E18 4 Na·1+Tr E2 4 E2 5 E6 4 5Ca·Na·3+Gb E9 4 E7 5 E13 4 Na·+Ber E2 4 E2 5 E12 4 Gb+Ber E10 4 E3 5 E12 5 E13 4 E7 5 CaG+Gp E2 4 E2 5 E13 5 E3 4 E3 5 Gp+5Ca·Na·3 E11 4 E5 5 E14 4 E8 5 Te+Ber E3 4 E3 5 E10 4 Na·1+Pr E12 4 E2 5 E16 4 Te+Tr E3 4 E3 5 E13 5 E4 4 E4 5 Ber+5Ca·Na·3 E13 4 E7 5 E15 4 E9 5 78 Equilibrium solid phases of fields Field contours in the diagram (Fig. 3) Equilibrium solid phases of fields Field contours in the diagram (Fig. 3) Tr+3Na·C E4 4 E4 5 E19 4 Ber+Pr E12 4 E2 5 E13 5 E4 5 E1 5 E15 4 E9 5 E14 5 E10 5 Cc+CaG E5 4 E5 5 E17 4 E8 5 Cc+5Ca·Na·3 E14 4 E8 5 E15 4 E9 5 Gp+Cc E5 4 E5 5 E11 4 Pr+Cc E14 4 E8 5 E17 4 CaG+Gp E5 4 E5 5 E7 4 Tr+Pr E16 4 E2 5 E13 5 E19 4 E4 5 Te+Gb E6 4 E1 5 E11 5 E4 5 E10 4 E3 5 E13 5 Pr+CaG E17 4 E8 5 E9 5 E20 4 E10 5 E14 5 Nk+Gb E6 4 E1 5 E8 4 E6 5 3Na·C+CaG E18 4 E8 5 E20 4 E10 5 5Ca·Na·3 E7 4 E5 5 E11 4 3Na·C+Pr E19 4 E4 5 E11 5 E1 5 E20 4 E10 5 E14 5 E6 5 Gb+3Na·C E6 5 E10 5 E1 5 E11 5 End of table 2 79 Conclusions The  translation method applied for the  Na,Ca||SO4,CO3,HCO3-H2O system at  100 °C while transforming the  phase equilibria from the level of four-compo- nent (A) to the level of five-component (B) reveals following changes in the numbers of geometric patterns: Component level A  B Invariant point 20 14 Monovariant curves 30 33 Divariant fields 13 31 The decrease in the number of invari- ant points from 20 at  the  level of  four- component composition to 14 at the level of  five-component composition is  due to  the  mutual combination (from math- ematical approach) of quadruple invariant points, or mutual intersection of  mono- variant curves (within the  graphical ap- proach) formed during the transformation and subsequent translation of these quad- ruple invariant points to the level of five- component composition and the formation of quintuple invariant points. The increase in the number of monovariant curves from 30 at the level of four-component compo- sition up to 33 at the level of five-compo- nent composition is due to the fact that 20 of them are formed as a result of transla- tion and quadruple invariant points, and another 13 connected five invariant points. The raise of components’ number by unity from four to five leads to the increase of di- variant fields’ number from 13 at the level of  four-component composition to  31 at  the  level of  five-component composi- tion. It was shown that 30 of  them were formed in a course of translation procedure of monovariant curves of the level of four- component composition and one more was obtained as a result of the surface contour- ing in the system with five invariant points and monovariant curves connecting these points. References 1. 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