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RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 61 No. 4 2016 STABLE TRIANGLE (LiF) CrO phases of the system was obtained, which consists of five stable tetrahedra LiFKIK CrO CrO CrO CrO KI, separated by four stable triangles LiFKIK CrO , and LiFLi CrO The table gives the full description of the chemical interaction in the quaternary reciprocal system Li,K||F,I,CrO . The table presents the material bal- ance equations with account for occurring chemical reactions and also describes the conditions imposed on the amounts of components of the initial composi- tion for them to form the products of their interaction, i.e., for the initial composition to move to one of the above stable simplexes as a result of the indicated reac- tions. To find the amounts of the products of the chemical interaction in the sample consisting of com- ponents of the system and determine the chemical transformations in it from the data in the table, it is necessary to: (1) determine the stable simplex to which the inter- action products belong based on the amounts of the initial components in the mixture using algebraic expressions for their coefficients, and (2) calculate the amounts of the reaction products (using the corresponding material balance equation) and the amounts of the reactants according to the Unfolded pattern of the faceting elements of the quaternary reciprocal system Li,K||F,I,CrO 849 414 414 849 675 531 523 239 343 464 CrO 464 849 384 540 494 E 490 490 735 764 CrO 973 764 543 e 543 681 RUSSIAN JOURNAL OF INORGANIC CH EMISTRY Vol. 61 No. 4 2016 BURCHAKOV et al. Fig. 2. Schematic of the composition prism of the system Li,K||F,I,CrO FCrO CrO LiKCrO CrO identified stable simplex from the amounts of the ini- tial components (a, b, c, d, e, f). To obtain the data in the table, we proposed to use the material balance equation in the general form CrO CrO CrO4(1) CrO + mLiKCrO FCrO The left side of Eq. (1) characterizes the set of the initial components in the mixture, and its right side describes both the initial components and the prod- ucts. The following elementary reactions occur in the system: CrO CrO CrO CrO CrO CrO = 2rLiKCrO CrO FCrO To solve the material balance equation with account for occurring chemical reactions, a system of linear equations for each component of the system was written. The equality condition was taken to be the constancy of the amounts of the unreacted substances: (7) Each stable simplex has its own solution of the sys- tem of Eqs. (7). In the system of Eqs. (7), the coeffi- cients characterizing the amounts of the reaction products that do not form this simplex are taken as zeros. The solution is the coefficients for the reaction products for Eq. (1) and the coefficients of the equa- tions of chemical transformations for Eqs. (2)(6), which are expressed in terms of the coefficients for the initial substances in Eq. (1): a, b, c, d, e, f. Figure 3 presents the linear tree of phases as a set of stable triangles and tetrahedra. In this work, we detected a regularity that, with increasing content of the component that is contained only in the terminal stable element of the linear tree of phases (in this case, this is KF or LiI) in comparison with the contents of the other initial substances in the mixture, the prod- ucts of the chemical transformations form successive elements of the tree of phases. =++ = =+ = =++ =+ 234 LiF:gaoq LiI:hbop LiCrO:icqrp KF:jdoqs KI:keop KCrO:lfpr2sq DLiKCrO:m2r DKFCrO:n2s. RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 61 No. 4 2016 STABLE TRIANGLE (LiF) CrO Table Stable simplex Amounts of initial substances, mol Material balance equation and equations of occurring chemical reactions FCrO �d b + 1.5c + 0.5fa(LiF) CrO CrO + (d b 1.5c 0.5f)(KF) FCrO CrO CrO CrO FCrO FCrO d = b + 1.5c + 0.5fa(LiF) CrO CrO FCrO CrO CrO CrO FCrO CrO FCrO d b + 1.5c + 0.5f CrO CrO = (a + b + c)(LiF) + (b + c + e)(KI) + (f 2d + CrO FCrO CrO CrO CrO FCrO CrO d = b + ca(LiF) CrO CrO CrO CrO CrO CrO LiKCrO CrO CrO CrO + (2b + 2c 2d)LiKCrO : (d b)Li CrO CrO CrO CrO 2(b + c d)LiKCrO CrO LiKCrO CrO CrO = (a + d)(LiF) + (b + e)(KI) + (f 2b c + 2d) CrO + (2b + 2c 2d)LiKCrO + d(KF) : (b d)(LiI) CrO CrO CrO CrO 2(b + c d)LiKCrO RUSSIAN JOURNAL OF INORGANIC CH EMISTRY Vol. 61 No. 4 2016 BURCHAKOV et al. LiFKILiKCrO CrO CrO + (c + f)LiKCrO : (d b)Li CrO CrO CrO CrO 2(d b + f)LiKCrO CrO CrO + (c + f)LiKCrO + d(KF) : (b d)(LiI) CrO CrO CrO CrO 2(d b + f)LiKCrO CrO LiKCrO CrO CrO CrO + (2d 2b + 2f)LiKCrO : (d b)Li CrO CrO CrO CrO 2(d b + f)LiKCrO CrO LiKCrO CrO CrO CrO + (2d 2b + 2f)LiKCrO + d(KF) = d(LiF) : (b d)(LiI) CrO CrO CrO CrO 2(d b + f)LiKCrO CrO d = b fa(LiF) CrO CrO CrO CrO CrO CrO d b fa(LiF) CrO CrO CrO + d(KF) = d(LiF) CrO CrO Stable simplex Amounts of initial substances, mol Material balance equation and equations of occurring chemical reactions Table (Contd.) RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 61 No. 4 2016 STABLE TRIANGLE (LiF) CrO EXPERIMENTAL In this work, we for the first time experimentally studied phase equilibria in the quasi-ternary system CrO , which is the stable triangle of the quaternary reciprocal system Li,K||F,I,CrO (Fig. 4). The experimental studies were carried out by differen- tial thermal analysis according to a standard procedure [21, 22]. All the compositions in this work are expressed as equivalent percentages. In the primary crystallization field of lithium fluo- ride, we chose and experimentally studied the poly- thermal section AB , the Tx diagram of which is shown in Fig. 5. From this section, we found the ratio between potassium iodide and lithium chromate in the quasi-ternary eutectic E 392, and also the composi- tion and temperature of the point in the monovariant monotectic curve describing the equilibrium L LiF. The coordinates of this point allowed one to more accurately construct a geometric model of the phase complex and determine the point of the minimum of the monotectic equilibrium M 760, which charac- terizes the composition with the minimum tempera- ture at which phase separation of liquids in the system is possible. Fig. 3. Effect of the concentrations of the initial components, lithiu m iodide or potassium fluoride, in the mixture on the forma- tion of a linear tree of phases of the system Li,K||F,I,CrO equiv % equiv % ()2]100% ()2]+ [K2CrO ()2] 0.5[Li2CrO 2CrO ()2] [Li2CrO ()2] [(KF)2] 1.5[Li CrO 2CrO ()2] [K2CrO ()2] + 0.5[Li2CrO 2CrO ()2] + [Li2CrO ()2] + 1.5[Li CrO 2CrO 100% CrO CrO CrO LiKCrO LiKCrO LiKCrO CrO CrO CrO FCrO FCrO FCrO RUSSIAN JOURNAL OF INORGANIC CH EMISTRY Vol. 61 No. 4 2016 BURCHAKOV et al. Composition triangle of the quasi-ternary system (LiF) CrO 849 675 681 e415 CrO e464 Fig. 5. diagram of the polythermal section AB of the system (LiF) CrO L CrO CrO Composition, equiv % CrO CrO (90%) RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 61 No. 4 2016 STABLE TRIANGLE (LiF) CrO Figure 6 presents the Tx diagram of the polyther- mal section LiFC, which enabled one to determine the composition and temperature of the quasi-ternary eutecic E 392: (392 C, 4% LiF, 9.6% KI, 86.4% CrO RESULTS AND DISCUSSION A 3D computer model of the phase complex of the system (LiF) CrO was constructed in coordinates based on the experimental data, in the KOMPAS-3D v.13 environment [23]. The calcula- tions were performed using the MO Excel software. The constructed model is a set of local spaces (or sol- ids in terms of computer modeling of geometric objects) responsible for a certain type of phase equilib- rium in the system (Fig. 7). For the ternary system, by identifying lines of inter- section of horizontal planes with surfaces of the model, we constructed isotherms of the liquidus sur- face (Fig. 8) and a series of isothermal sections (Fig. 9). Analysis of the series of isothermal sections showed that, at a temperature below 832 C (temperature of invariant monotectic equilibrium in the quasi-binary system LiFKI), in the system, along with the two- phase phase separation region L + L L + LiF, three-phase region L + L + LiF forms. With decreas- ing temperature, one of the sides of the tie-line trian- gle of the three-phase region approaches the mini- mum point M 760 of monovariant monotectic equilibrium in the system; in addition, the region of the coexistence of the liquid and solid phases of LiF increases, and simultaneously the region of phase sep- aration of liquids decreases. At a temperature below C, the limited solubility of liquids in the system vanishes, and the heterogeneity region L + LiF increases. With a further decrease in temperature, in the system, two-phase regions L + KI and L + (/)- CrO and three-phase regions L + LiF + KI, L + CrO , and L + KI + (/)-Li CrO form and grow, and the regions L and L + LiF decrease. Fig. 6. diagram of the polythermal sect ion LiFC of the system (LiF) CrO CrO CrO Composition, equiv % 849 849 10% (KI) CrO 90% Li CrO RUSSIAN JOURNAL OF INORGANIC CH EMISTRY Vol. 61 No. 4 2016 BURCHAKOV et al. Phase spaces of the system (LiF) CrO 681 e675 CrO CrO CrO CrO 464 CrO CrO Composition triangle of the system (LiF) (KI) CrO with isotherms of the liquidus surface. 849 675 681 E392 e415 CrO 464 775 750 725 675 575 875 900 RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 61 No. 4 2016 STABLE TRIANGLE (LiF) CrO ACKNOWLEDGMENTS This work was performed within the framework of the 2014 State Assignment for the Samara State Technical University, Samara, Russia (project code no. 1285). REFERENCES 1.N. Lidorenko, G. Muchnik, and S. Trushevskii, Nauka Zhizn, No. 3, 19 (1974). 2.Yu. K. Delimarskii, Chemistry of Ionic Melts (Naukova dumka, Kiev, 1980) [in Russian]. 3.D. U. Smagulov, Doctoral Dissertation in Technical Sciences, http://www.dissercat.com/ 4.www.chem.msu.su/cgi-bin/tkv.pl?show=welcom.html Thermal Constants of Substances: Handbook , Issue X, part 1: Tables of Accepted Values: Li, Na , Ed. by V.P.Glushko (VINITI, Moscow, 1981) [in Russian]. Isothermal sections of the system (LiF) CrO CrO CrO CrO 849 681485 CrO 849 681485 CrO 849 681485 = 675 CrO 849 681485 CrO 849 681485 CrO 849 681485 e 675 RUSSIAN JOURNAL OF INORGANIC CH EMISTRY Vol. 61 No. 4 2016 BURCHAKOV et al. Thermal Constants of Substances: Handbook , Issue X, part 2: Tables of Accepted Values: K, Rb, Cs, Fr , Ed. by V. P. Glushko (VINITI, Moscow, 1981) [in Russian]. 7.J. M. Sangster and A. D. Pelton, J. Phys. Chem. Ref. Data , 509 (1987). 8.Z. A. Mateiko and G. A. Bukhalova, Zh. Neorg. Khim. , 1649 (1959). 9.I. N. 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