Nonvariant Points Research Articles

Phase complex of a NaCl—KCl—SrCl2—Sr(NO3)2 four-component system and the physicochemical properties of a eutectic mixture

Tree of phases and crystallization were plotted via a priori prediction, and the coordinates (composition) of a nonvariant point of a NaCl-KCl-SrCl2-Sr(NO3)2 four-component system were determined according to calculations and experimental data. The promise of the method for determining the coordinates of nonvariant points in multicomponent systems was confirmed experimentally. The dependence of density and electroconductivity vs. temperature was studied. The volume dilation of a melt was calculated up to the maximum operating temperature.

Modeling of deep-seated high-alumina parageneses on the basis of the stability fields of corundum- and spinel-normative assemblages of the system CaO–MgO–Al 2O 3–SiO 2

To elaborate physicochemical models for the origin of crystalline rocks, experimental studies of the field of high-alumina assemblages of the system CaO–MgO–Al 2O 3–SiO 2 were carried out at 10–30 kbar and 1250–1535 °C. We have determined the phase relations between the melt (L) and An, Sp, Cpx, Cor, and Ga, the slope of the rays of the monovariant reactions An + Sp = Cpx + Cor + (Ga) and L = Cpx +Ga + Cor + Sp, the position of the nonvariant point (An, Sp, Cpx, Cor, Ga, L), and the compositions of phases participating in these reactions. Based on a topological analysis of the studied segment of the system CaO–MgO–Al 2O 3–SiO 2, we have substantiated that “eclogitization” must follow the reaction Opx + An + Sp = Cpx + Ga. A fundamental continuous series of eutectic monovariant equilibria was observed: L = Cpx + Opx + Fo + An, L = Cpx + Opx + An + Sp, L = Cpx (+ Ga) + An + Sp, and L = Cpx + Cor (+ Ga) + An. A change in the melt composition in this series of eutectic reactions depending on pressure must reflect the most likely magma genesis trend in nature. Comparision of the composition fields in which the above series of reactions is observed with the composition fields of the rocks of magmatic formations showed that this series is most similar to the alkali-earth series of rocks. The mineralogical compositions of cumulates and phenocrysts found in the effusive and dike varieties of these rocks correspond to unique sets of subsolidus phase associations and individual subsolidus phases crystallizing in this fundamental eutectic series.

Heterogenization of supercritical fluids and nonvariant critical equilibria in ternary systems with one volatile component (for water-salt systems as examples)

The phase equilibria in ternary systems with one volatile component and a homogeneous supercritical fluid (SCF) region in one of the binary subsystems (with two critical end-points p and Q) were analyzed. Heterogenization of SCFs, extending from the 2d′ boundary subsystem into a ternary system, starts with monovariant critical phenomena in saturated solutions (l1 = l2-s) or (g = l−s), which pass through the extremal parameters of the temperature or composition to form special critical equilibria such as double critical end-points DCEs (l1 = l2-s, g = l-s, l1 = l2-g) or double homogeneous points DHPs (l1 = l2-s ↔ g = l-s). Ternary nonvariant critical points (l1 = l2 = g, l1 = l2-g-s, and l1 = g-l2-s) appear at the intersections of the monovariant critical and noncritical curves.

Thermodynamic calculations of phase equilibria in the neodymium-barium-copper-oxygen system at O2 pressures of 0.21 and 1 bar

The analytic equations for the Gibbs energy of Nd-Ba-Cu-O system phases obtained earlier were used to calculate the phase diagrams of the Ba0.5Cu0.5O-Nd0.5Cu0.5O section at oxygen partial pressures of 0.21 and 1 bar. For p(O2)= 0.21 bar, the coordinates of the nonvariant system points, the projection of the liquidus surface, and the phase diagram of the Nd1 + xBa2 − xCu3O6 + z compound in the subsolidus region were determined.

Phase equilibria in the neodymium-barium-copper-oxygen system at low oxygen pressures

The analytic equations for the Gibbs energies of Nd-Ba-Cu-O system phases obtained earlier were used to calculate the (1/2)BaCuO2-(1/2)NdCuO2 section of the phase diagram at oxygen partial pressures of 0.01 and 0.001 bar. For p(O2) = 0.01 bar, the coordinates of the nonvariant points of the Nd-Ba-Cu-O system were determined, and the phase diagrams of the (1/8)Ba3Cu5O8-NdO1.5 and (1/4)BaCu3O4-(1/4)BaNd3O5.5 systems were calculated.

Phase diagram of the system KF-K2TaF7-Ta2O5

The phase diagrams of the binary system Ta2O5-K2TaF7 and the ternary system KF-Ta2O5-K2TaF7 were determined using the thermal analysis method. The system Ta2O5-K2TaF7 was measured up to 25 mol% of Ta2O5. Eutectic point is estimated to be at \( x_{Ta_2 O_5 } \)=0.14 and t=601°C. Crystallization of K2TaF7, K2Ta2O3F6 and a new phase was identified. The new phase shows isomorphism with K3Nb2F11O. In the ternary system four nonvariant equilibria points at 3 mol% of Ta2O5, 72 mol% of KF and 25 mol% of K2TaF7 at 715(1)°C; 6 mol% of Ta2O5, 44 mol% of KF and 50 mol% of K2TaF7 at 603(2)°C; 1 mol% of Ta2O5, 22 mol% of KF and 77 mol% of K2TaF7 at 704(1)°C and 8 mol% of Ta2O5, 8 mol% of KF and 84 mol% of K2TaF7 at 580(1)°C were proposed. Crystallization fields of KF, K2TaF7, K3TaF8, K3TaOF6, K4Ta2OF12 and K2Ta2O3F6 were considered.

Thermodynamic description of phases in the neodymium-barium-copper-oxygen system

The available experimental data were used to construct thermodynamic models of Nd-Ba-Cu-O system phases. The coordinates of the nonvariant points of this system were determined, and the phase diagram for the Nd1 + x Ba2 − x Cu3O6 + z (x = 10−4) compound was calculated.

Fluid phase diagrams of ternary systems with one volatile component and immiscibility in two of the constituent binary mixturesPresented at the International Bunsen Discussion Meeting of the Deutsche Bunsen-Gesellschaft für Physikalische Chemie, Walberberg, Germany, 19–22 August, 2001.

Four types of fluid phase diagram where the critical curves and immiscibility regions are not intersected by crystallization surfaces are selected as the main types of fluid phase behavior in binary mixtures. These types are used as a starting point for the systematic classification of the main types of binary complete phase diagram, describing any equilibria with liquid, gas and solid phases over a wide range of temperatures and pressures, by the method of continuous topological transformation. This method and the classification of binary phase diagrams, containing the boundary version phase diagrams with ternary nonvariant points, are used as a quasi-binary approach to derive the main types of fluid phase behavior for ternary mixtures with one volatile component and immiscibility in two of the constituent binary subsystems. In such ternary systems there are six classes distinguished by the types of fluid phase behavior in the binary subsystems. A wide variety of ternary fluid phase diagrams, obtained either by a transformation of the topological types or by changing the location of nonvariant points without transformation of topological types, is discussed.

Derivation of complete phase diagrams for ternary systems with immiscibility phenomena and solid–fluid equilibria

Abstract Four main types of binary fluid-phase diagrams and available experimental data on binary systems are used as a starting point for derivation of the systematic classification of binary complete phase diagrams by the method of continuous topological transformations. This method and the classification of binary phase diagrams, containing the boundary versions of phase diagrams with ternary nonvariant points, are applied to derive the main types of fluid and complete phase diagrams for ternary systems with one volatile component and immiscibility phenomena in two constituent binary subsystems. The results gained from this analysis of derived fluid and complete phase diagrams of ternary systems are represented.

High-pressure phase behavior of binary systems of heptadecane and octadecane with carbon dioxide or ethane.

Phase behavior of four binary systems of heptadecane and octadecane with CO2 and ethane was investigated in the temperature range from 270 to 320 K and pressures up to 30 MPa. The observed phase boundaries correspond to the three-phase coexisting lines with some nonvariant points of quadruple points and critical endpoints. Phase density inversion between two liquid phase was also observed in the n-alkanes with CO2 systems. The phase density inversion points form a straight line in the pressure–temperature diagram regardless of the carbon number of the n-alkanes. In the homologous series of n-alkane + CO2 systems, the “odd-even effect” of carbon numbers of n-alkanes has been observed in the relation of the triple point of n-alkane and the quadruple point.

Clathrate formation in binary aqueous systems with CH2Cl2, CHCl3 and CCl4 at high pressures

P,T,X phase diagrams of the CH2Cl2-H2O, the CHCl3-H2O and the CCl4-H2) systems have been studied by DTA in the pressure range 10−3 to 5.0 kbar. Under pressure the cubic structure II (CS-II) hydrates forming in all the systems are replaced by hydrates with the composition M·7.3 H2O whose stoichiometry and positive dT/dP values of melting lead us to believe that they are CS-I hydrates. In the CH2Cl2 and CHCl3 systems the nonvariant point coordinates of the hydrate transformationQ 2 h (l1h17h7l2, where l1 and l2 are liquid phases abundant in water and hydrate former, respectively, h17 and h7 are hydrates with hydrate numbers 17 and 7, respectively) areP = 0.6 kbar, T = −1.5°C andP =2.65 kbar,T = −10.5°C, respectively. In the CCl4 system the 4-phaseQ 3 h point (l1h17h7s, where ‘s’ is crystalline CCl4) has coordinatesP = 0.75 kbar and T = 0.4°C. The main obstacle of the present study, the very slow achievement of equilibrium, has been eliminated by adding small amounts (0.25% by mass) of surfactants followed by ultrasonic mixing. We have shown that this accelerates the achievement of equilibrium without changing its position.

Phase behavior of binary mixtures of indole or quinoxaline with CO 2, C 2H 4, C 2H 6, and CHF 3 in the critical region

Phase behavior of eight binary mixtures consisting of indole or quinoxaline as the first component and CO 2, C 2H 4, C 2H 6, or CHF 3 as the second component was investigated around the critical point of the light component in the temperature range from 280 to 350 K and pressures up to 30 MPa. These systems show three kinds of phase diagrams. The observed phase boundaries correspond to the three-phase coexisting lines (i.e., liquid-liquid-gas, solid-liquid-liquid, and solid-liquid-gas) and the critical lines (i.e., liquid=liquid and liquid=gas). Some nonvariant points for binary mixtures are also obtained. These include a quadruple point where four phases (solid-liquid-liquid-gas) coexist in equilibrium, and critical end points where two fluid phases are critically identical in the presence of another phase.

Phase equilibrium, glass-forming, properties and structure of glasses in the TeO2-B2O3 system

Phase equilibrium, glass-forming, properties and structure of the glasses in the TeO2-B2O3 system have been investigated. The phase diagram is a simple eutectic-like type without any compound formation. A wide region of stable phase separation has been established. A monotectic temperature at 934 K and nonvariant point at 73.6% TeO2 has been determined. The temperature dependence of the stable phase separation in the system has been studied. Some properties (density, transformation temperature, softening point, coefficient of thermal expansion, hardness, absorption in the UV and VIS region) of the tellurite borate glasses have been investigated. A structural interpretation of the glasses, on the basis of B11 NMR spectra was undertaken and two coordination states of boron atoms have been established. A simple model of two tellurium-boron-oxygen building units is presented.

Phase diagrams of thE CaF 2- (Y, Ln) F 3 svstems I. Experimental

The phase diagrams of the CaF 2- (Y, Ln) F 3 systems, where Ln is any one of the lanthanides except Pm and Eu, were studied by thermal and X-ray phase analysis methods. The investigations were made from 800 (600)°C up to the melting temperature. The oxygen concentration of the specimens was checked after thermal treatment. For the systems with Ln = Ce, Pr, Tb, Ho, Tm and Lu the fusibility data have been obtained for the first time. Phases with the following structure types are present in the systems investigated: (a) solid solutions Ca 1− x (Y, Ln) x F 2+ x with the fluorite structure type, which undergo ordering in the systems with Ln = HoLu, Y; (b) non-stoichiometric phases (Y, Ln) 1− y Ca y F 3− y with the tysonite (LaF 3) structure type, which undergo ordering in the systems with Ln = TbLu, Y; (c) solid solutions with the α-UO 3 structure type, based on α modifications (Y, Ln) F 3 (Ln = ErLu); and (d) modifications (Y, Ln) F 3 (Ln = GdLu) of the β-YF 3 type. Successive transitions, from solid solutions of the components of the system to the berthollide phases and the stoichiometric compound, were found for phases with the tysonite structure type. The maxima on fusion curves of non-stoichiometric phases were noticed in Sm, Gd, Tb, Ho and Er for Ca 1− x - (Y, Ln) x F 2− x and for Ln = PrLu in (Y, Ln) 1− y Ca y F 3− y . The coordinates of non-variant points for equilibria of the liquid-solid type and also the equations describing the dependence of the lattice parameters of nonstoichiometric phases on the composition are given for the systems investigated.

Fundamental studies of 75S (1st Report)

As one of the fundamental studies on 75S, the investigation has been made on the phase diagrams of the systems Al-Zn-Cu, Al-Zn-Mg and Al-Zn-Mg-Cu (especially in the range of Al-Zn side). The diagrams have been obtained by means of inverse-rate thermal analysis, electric resistance measurement, X-ray analysis and microscopic observation.The reactions appeared in these diagrams are summed up as follows:1) In the phase diagram of the system Al-Zn-Cu four non-variant points are observed.2) In the phase diagram of the system Al-Zn-Mg six non-variant points are observed.3) The Al side of the system Al-Zn-Mg-Cu is divided into three ranges by the pseudo-ternary systems of Al-ω-CuAl2 and Al-ω-S, and in these ranges no quarternary intermetallic compound appears.In the ranges of Al-ω-CuAl2-S and Al-ω-S-T-β eight ternary eutectic, two quarternary eutectic and one peritecto-ternary eutectic reactions are observed.

75Sの基礎的研究（第1報）Al-Zn-Cu三元系状態図の研究

The author have studied the phase diagram of the system Al-Zn-Cu (especially in the range of Al-Zn side). The diagram obtained by means of inverse rate thermal analysis, electric resistance measurement and microscopic observation is shown in Fig. 10, and four non-variant points are observed in this diagram.(This article is not displayable. Please see full text pdf.)

Cd-Ag-Cu系平衡状態圖

Using 147 kinds of this ternary alloy, the equilibrium diagram has been thoroughly studied chiefly by thermal analysis and microscopic examination. In this ternary system, no ternary compound exists, while 3 binary compounds, Cu2Cd, Cu4Cd3 and CuCd3, 2 Ag-Cd binary solid solutions β and ε and 4 ternary solid solutions, Cu, Ag, δ and η exist. η ternary solid solution is formed by Cu5Cd8 and γ solid solutions. So there exist 9 primary crystallization surfaces and 14 monovariant curves, and along these curves the following reactions take place, Mono-variant reactions:(1) M_??_Cu+Ag, (2) M+Ag_??_β, (3) M_??_β+Cu, (4) M+β_??_η, (5) M_??_Cu+η, (6) M+Cu_??_Cu2Cd, (7) M_??_Cu2Cd+η, (8) M+Cu2Cd_??_Cu4Cd3, (9) M_??_η+Cu4Cd3, (10) M+η_??_δ, (11) M+η_??_CuCd3, (12) M_??_CuCd3+δ, (13) M+δ_??_ε, (14) M_??_Cd+CuCd3. In this ternary system, there exist 5 non-variant points, at which the following reactions take place at temperatures given. Non-variant reactions: (1) M+Ag_??_β+Cu, (712°) (2) M+β_??_η+Cu (620°), (3) M+Cu_??_Cu2Cd+η, (518°), (4) M+Cu2Cd_??_η+Cu4Cd3 (516°), (5) M+η_??_CuCd3+δ (329°), (6) M+δ_??_CuCd3+ε (318°).

Cu-Ni-Si三元全系平衡状態の研究(第3報)

The ternary equilibrium state of the system copper-nickel-silicon relating to liquid was thoroughly investigated by thermal and X-ray analyses as well as microscopic examination, and heterogeneous equilibria were determined by the construction of many sectional diagrams using many specimens. As shown in Fig. 2 (quantitatively drawn) and Fig. 3 (qualitatively drawn) the diagram is very complicated. The binary systems are not formed on the lines Cu-Ni2Si, Cu-Ni5Si2, Cu-NiSi, Cu3Si-Ni2Si, Cu3Si-Ni5Si2 and Cu3Si-NiSi, the last one being liable to be taken for a binary system but clear microscopically that it is not formed on the line; accordingly no binary system does exist in this system. Moreover, the phases appearing in Cu-Si system do not form continuous solid solutions solutions with those in Ni-Si system. The significant points in the diagram are as follows:-there exists a ternary compound ω in the composition range of about 12-15% of Si and about 11-12% of Ni, which is formed by the ternary peritectic reaction L+γ+θ→ω at 859°; the γ phase stated in the 1 st. report of this investigation is formed in the ternary system by the binary peritectic reaction L+γ'+γ. the line of this reaction having a peak of temperature at 954° (the point s3';) and falling from this point to each side rich or poor in silicon. The reactions and the ranges of 13 primary crystals, 26 monovariant curves and 13 non-variant points are given in Tables 1, 2, and 3.4 respectively.