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Journal articles on the topic 'Ternary Diagrams'

Author: Grafiati

Published: 4 June 2025

Last updated: 23 June 2025

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1

Setel, A., M. Sebesan, B. Gabriela, A. Craciun Cornel, and R. Sebesan. "Physico-chemical characterization of geothermal water from wells 1704 Săcuieni and 752 Săcuieni in north-western Romania with ternary diagrams." International Review of Applied Sciences and Engineering 1, no. 1-2 (2010): 31–34. http://dx.doi.org/10.1556/irase.1.2010.1-2.5.

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Abstract In this paper presents ternary diagrams for geothermal waters from two wells in Săcuieni: ternary diagram Na-K-Mg, ternary diagram Cl-SO4-HCO3 and calculation model, which allows location of geothermal fluids in these diagrams. Classification of geothermal water with the two diagrams, involving knowledge of their chemical composition. Thus, it was the chemical composition of geothermal water coming from drillings: 1704 Săcuieni and 752 Săcuieni, situated in Bihor county. Location of geothermal water on the two diagrams we will establish the type of water, depending to the presence in their content of major anions and cations, what is of great importance for use in various purposes of the geothermal fluids.

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2

Winnefeld, Frank, and Barbara Lothenbach. "Phase equilibria in the system Ca₄Al₆O₁₂SO₄ – Ca₂SiO₄ – CaSO₄ – H₂O referring to the hydration of calcium sulfoaluminate cements." RILEM Technical Letters 1 (April 18, 2016): 10. http://dx.doi.org/10.21809/rilemtechlett.2016.5.

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This paper presents thermodynamic calculations of the stable hydrate assemblages in calcium sulfoaluminate cements containing different amounts of ye’elemite, calcium sulfate and belite. The ternary diagrams developed in this paper can be used directly to assess the long-term composition of such calcium sulfoaluminate cements containing belite. The phase diagram was validated using experimental data from literature. The ternary diagrams developed can be used to read out directly the stable hydrate assemblage of calcium sulfoaluminate cements containing belite based on their initial composition.

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3

Winnefeld, Frank, and Barbara Lothenbach. "Phase equilibria in the system Ca₄Al₆O₁₂SO₄ – Ca₂SiO₄ – CaSO₄ – H₂O referring to the hydration of calcium sulfoaluminate cements." RILEM Technical Letters 1 (April 18, 2016): 10. http://dx.doi.org/10.21809/rilemtechlett.v1.5.

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This paper presents thermodynamic calculations of the stable hydrate assemblages in calcium sulfoaluminate cements containing different amounts of ye’elemite, calcium sulfate and belite. The ternary diagrams developed in this paper can be used directly to assess the long-term composition of such calcium sulfoaluminate cements containing belite. The phase diagram was validated using experimental data from literature. The ternary diagrams developed can be used to read out directly the stable hydrate assemblage of calcium sulfoaluminate cements containing belite based on their initial composition.

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4

Zhuang, Dian Xiang, Ming Xie, Lin Jing Liu, et al. "Recent Research on Ternary Phase Diagram of Gold Alloy." Advanced Materials Research 834-836 (October 2013): 323–29. http://dx.doi.org/10.4028/www.scientific.net/amr.834-836.323.

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phase diagram is known as Maps of Materials Science. However, the existing precious metal phase diagrams are far from able to meet the needs of the development of the precious metal materials science and technology. In this paper, the recent research achievements of Au-Ag-Y ternary phase diagram by experimental method and Au-Pd-Zr ternary phase diagram by multi-phase equilibrium thermodynamic calculation software were introduced.

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5

Wang, Ji-Tao, Yong-Zhong Wan, David Wei Zhang, Zhi-Jie Liu, and Zhong-Qiang Huang. "Calculated phase diagrams for activated low pressure diamond growth from C–H, C–O, and C–H–O systems." Journal of Materials Research 12, no. 12 (1997): 3250–53. http://dx.doi.org/10.1557/jmr.1997.0426.

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Three-dimensional temperature (T)–pressure (P)–composition (X) phase diagrams of binary carbon-hydrogen (C–H) and carbon-oxygen (C–O) systems for activated low pressure diamond growth have been calculated. Based on an approximation of linear combination between C–H and C–O systems, a projective ternary carbonhydrogen-oxygen (C–H–O) phase diagram has also been obtained. There is always a diamond growth region in each of these phase diagrams. Once a supply of external activating energy stops, the diamond growth region will not exist. Nearly all of the reliable experimental data reported in the literature drop into the possible diamond growth region of the calculated projective ternary C–H–O phase diagram under the conditions of 0.01–100 kPa and above 700 K.

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6

Valyashko, V. M. "Derivation of complete phase diagrams for ternary systems with immiscibility phenomena and solid–fluid equilibria." Pure and Applied Chemistry 74, no. 10 (2002): 1871–84. http://dx.doi.org/10.1351/pac200274101871.

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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.

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7

Yang, Hui Min, Liang Shun Luo, Mei Hui Song, Hai Qun Qi, Chun Yan Wang, and Chuang Yang. "Calculation of Aluminum Equivalent Based on Thermo-Calc Software in Ti-Al-Nb Ternary System." Materials Science Forum 788 (April 2014): 144–49. http://dx.doi.org/10.4028/www.scientific.net/msf.788.144.

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Ti-Al-Nb ternary phase diagrams were calculated by Thermo-Calc software. The analysis of the calculated vertical sections of Ti-Al-Nb phase diagram indicated that when Nb content is fixed at 5at.% and Al content is lower than 52.3at.%, the primary phase would be β phase during solidification. With 10 at.%Nb and Al content lower than 55.8at.%, or with 15 at.%Nb and Al content lower than 56.9at.%, the primary phase would be β phase. The vertical sections of Ti-Al-Nb ternary phase diagram were further simplified into pseudo-Ti-Al binary phase diagram. According to the pseudo-Ti-Al diagram, the expression of the aluminum equivalent was obtained in Ti-Al-5Nb ternary alloys.

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8

Pan, Zhu, Yong Du, and Baiyun Huang. "Experimental investigation and thermodynamic calculation in the Al–Be–Si ternary system." International Journal of Materials Research 96, no. 11 (2005): 1301–7. http://dx.doi.org/10.1515/ijmr-2005-0227.

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Abstract A thermodynamic optimization for the Be– Si system has been performed using the CALPHAD (CALculation of PHAse Diagrams) technique applied to newly measured phase diagram data. The description for this binary system is then combined with the thermodynamic parameters in the Al –Be and Al –Si systems to synthesize a thermodynamic description for the Al –Be –Si ternary system. To verify the reliability of the extrapolated ternary phase diagrams, 11 decisive ternary alloys are prepared by are melting Al, Be and Si pieces and annealing at 530 °C for 8 days. Water-quenched samples are analyzed using differential thermal analysis (DTA), X-ray diffraction (XRD), optical microscopy, and scanning electron microscopy with energy dispersive X-ray (SEM/EDX) techniques. The calculated isopleths at 94 wt.% Al, 88 wt.% Al, 50 at.% Al, and 2 wt.% Be are compared with the experimental data from the present work and the literature. The comparisons show that no ternary interaction parameter is needed for the ther-modynamic description of this ternary system. The liquidus projection and reaction scheme are also presented.

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9

Shcherbakova, Nataliya, Vincent Gerbaud, and Kevin Roger. "Using the Intrinsic Geometry of Binodal Curves to Simplify the Computation of Ternary Liquid–Liquid Phase Diagrams." Entropy 25, no. 9 (2023): 1329. http://dx.doi.org/10.3390/e25091329.

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Phase diagrams are powerful tools to understand the multi-scale behaviour of complex systems. Yet, their determination requires in practice both experiments and computations, which quickly becomes a daunting task. Here, we propose a geometrical approach to simplify the numerical computation of liquid–liquid ternary phase diagrams. We show that using the intrinsic geometry of the binodal curve, it is possible to formulate the problem as a simple set of ordinary differential equations in an extended 4D space. Consequently, if the thermodynamic potential, such as Gibbs free energy, is known from an experimental data set, the whole phase diagram, including the spinodal curve, can be easily computed. We showcase this approach on four ternary liquid–liquid diagrams, with different topological properties, using a modified Flory–Huggins model. We demonstrate that our method leads to similar or better results comparing those obtained with other methods, but with a much simpler procedure. Acknowledging and using the intrinsic geometry of phase diagrams thus appears as a promising way to further develop the computation of multiphase diagrams.

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10

Vergara, Diego, Manuel Pablo Rubio, and Miguel Lorenzo. "New Virtual Application for Improving the Students' Understanding of Ternary Phase Diagrams." Key Engineering Materials 572 (September 2013): 578–81. http://dx.doi.org/10.4028/www.scientific.net/kem.572.578.

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Students consider spatial visualization as one of the major difficulties at which they had to face in engineering studies. Most of them think that any effort leading to improve the understanding of such problem is welcomed. Taking this into account, an interactive application is developed in this paper in order to overcome the difficulties that engineering students traditionally find with regard to the visualization of ternary phase diagrams. To develop the didactic application diverse commercial software were used: (i) 3DStudioMax for designing the ternary equilibrium diagram and (ii) Quest3D for giving the tool a more intuitive and easy to use character. The result is a 3D virtual application which students can use for interacting in real time with a ternary diagram, e.g. changing point of view, rotating view, observing hidden zones of the diagram by applying transparency option, exploding view phases, cutting the diagram revealing isothermal sections and so on.

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11

Lutsyk, V. I., V. P. Vorob'eva, and Anna Zelenaya. "Reference Book on the Oxide Systems Space Diagrams as a Tool for Data Mining." Solid State Phenomena 230 (June 2015): 51–54. http://dx.doi.org/10.4028/www.scientific.net/ssp.230.51.

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The Reference Book of Ternary Oxide Systems phase diagrams computer models is presented. Its computer models of T-x-y diagrams give a possibility to calculate the mass balances at any temperature, to observe crystallization history and the process of microstructure forming at different crystallization stages. The investigation of concentration fields with the different phase constituents on the T-x-y diagram projection by means of its computer model is considered. Phase diagram of CaO-SiO2-Al2O3system is used as an example.

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12

Perkowski, Marek A., Malgorzata Chrzanowska-Jeske, Andisheh Sarabi, and Ingo Schäfer. "Multi-Level Logic Synthesis Based on Kronecker Decision Diagrams and Boolean Ternary Decision Diagrams for Incompletely Specified Functions." VLSI Design 3, no. 3-4 (1995): 301–13. http://dx.doi.org/10.1155/1995/24594.

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This paper introduces several new families of decision diagrams for multi-output Boolean functions. The introduced families include several diagrams known from literature (BDDs, FDDs) as subsets. Due to this property, these diagrams can provide a more compact representation of functions than either of the two decision diagrams. Kronecker Decision Diagrams (KDDs) with negated edges are based on three orthogonal expansions (Shannon, Positive Davio, Negative Davio) and are created here for incompletely specified Boolean functions as well. An improved efficient algorithm for the construction of KDD is presented and applied in a mapping program to ATMEL 6000 fine-grain FPGAs. Four other new families of functional decision diagrams are also presented: Pseudo KDDs, Free KDDs, Boolean Ternary DDs, and Boolean Kronecker Ternary DDs. The last two families introduce nodes with three edges and require AND, OR and EXOR gates for circuit realization. There are two variants of each of the last two families: canonical and non-canonical. While the canonical diagrams can be used as efficient general-purpose Boolean function representations, the non-canonical variants are also applicable to incompletely specified functions and create don't cares in the process of the creation of the diagram.. They lead to even more compact circuits in logic synthesis and technology mapping.

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13

Chou, Kuo-Chih, Seetharaman Sridhar, and Uday B. Pal. "Activities and ternary phase diagrams." Calphad 21, no. 4 (1997): 483–95. http://dx.doi.org/10.1016/s0364-5916(98)00006-6.

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14

Gabriel, Armand, and Arthur D. Pelton. "Phase diagram measurements and thermodynamic analysis of the PbCl2–NaCl, PbCl2–KCl, and PbCl2–KCl–NaCl systems." Canadian Journal of Chemistry 63, no. 11 (1985): 3276–82. http://dx.doi.org/10.1139/v85-542.

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The phase diagrams of the PbCl2–NaCl and PbCl2–KCl systems have been measured by the cooling curve technique. In addition, a number of measurements at compositions in the ternary system PbCl2–KCl–NaCl have been made. The binary data have been analysed along with other available thermodynamic data for the binary systems in order to obtain mathematical expressions for the binary thermodynamic properties. Various estimation procedures were then used to calculate the Gibbs energy of the ternary liquid from the binary expressions, and the ternary phase diagram calculated therefrom was compared to the experimental ternary points. In the case of the Conformal Ionic Solution equation, agreement was within 3 °C at all measured points. In the case of two "geometric" estimation techniques, the Kohler and Toop equations, agreement was within 10 °C but could be brought to within 3 °C by the addition of only one small adjustable ternary correction term. The technique of coupled thermodynamic/phase diagram analysis permits a large reduction in the amount of experimental work necessary to measure the ternary diagram. In addition, the ternary thermodynamic expressions developed can be used to calculate all thermodynamic properties of the ternary liquid.

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15

Chen, Qing, Jiping She, and Yang Xiao. "Study of Phase Equilibrium of NaBr + KBr + H2O and NaBr + MgBr2 + H2O at 313.15 K." Journal of Chemistry 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/2319635.

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The phase equilibrium for the ternary systems NaBr + KBr + H2O and NaBr + MgBr2 + H2O at 313.15 K was investigated by isothermal solution saturation method. The solubilities of salts and the densities of saturated solutions in these ternary systems were determined by chemical methods, while the equilibrium solid phases were analyzed by Schreinermarker wet residues method. Based on the experimental data, phase diagrams and density versus composition diagrams were plotted. The two ternary systems were type of simple common-saturation and without complex salt and solid solution. There are in all two crystalline regions, two univariant curves, and one invariant point in these phase diagrams of two ternary systems at 313.15 K. The equilibrium solid phases in the ternary system NaBr + KBr + H2O are KBr and NaBr·2H2O, and those in the ternary system NaBr + MgBr2 + H2O are NaBr·2H2O and MgBr2·6H2O.

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16

Adama, K. K., U. P. Onochie, and E. Gbeinzi. "Production, characterization and application of ternary phase diagrams for the purification of biodiesel produced from tropical almond seed oil." Nigerian Journal of Technology 39, no. 4 (2021): 1066–75. http://dx.doi.org/10.4314/njt.v39i4.13.

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This study presents the application of ternary phase diagrams to tropical almond biodiesel components separation and purification at two temperatures. The seed oil was extracted mechanically and alkaline transesterified to produce biodiesel. The oil and biodiesel were characterized using standard methods. Tie lines and binodal solubility curve data were determined using modified cloud point titration procedures. Gas chromatographic method was employed in the analysis of the phase compositions. The mixture of biodiesel, methanol and glycerol were investigated at 20 °C, 30 °C and withdrawal times of 2 to 32 minutes at 2 minutes intervals. Distribution coefficient, K and solvent selectivity, S analysis were performed. Results obtained showed that S > 1 indicating the ability of methanol to promote phase separation and purification. K < 1 implying that there was lower quantities of methanol solubilized in the biodiesel phase. The ternary phase diagrams provided the means of predicting the components distribution. Keywords: Production, Characterization, Tropical Almond Biodiesel, Purification, Ternary Phase Diagram

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17

Igarashi, K., H. Ohtani, and J. Mochinaga. "Phase Diagram of the System LaCl3-CaCl2-NaCl." Zeitschrift für Naturforschung A 42, no. 12 (1987): 1421–24. http://dx.doi.org/10.1515/zna-1987-1212.

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The phase diagram of ternary system LaCl3-CaCl2-NaCl has been constructed from the phase diagrams of the three binary systems and of thirteen quasi-binary systems determined by DTA. For the binaries LaCl3-CaCl2 and CaCl2-NaCl eutectic points were observed at 651 °C , 35.1 mol% LaCl3 and at 508 °C , 49.9 mol% NaCl, respectively. For LaCl3-NaCl, a peritectic point besides the eutectic point at 545 °C , 36.1 mol% LaCl3 was found at 690 °C , 57.5 mol%, which is attributable to the formation of the peritectic compound 3 LaCl3 · NaCl. The phase diagram of the ternary system has a ternary eutetic point and a ternary peritectic point due to 3 LaCl3-NaCl, the form er at 462 °C and 12.1 - 3 9 .7 - 4 8 .2 mol% (LaCl3-CaCl2-NaCl) and the latter at 612 °C and 26.9 - 55.1 - 18.0 mol%.

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18

Li, Yandong, Tongsheng Zhang, Yefeng Feng, Chengjun Liu, and Maofa Jiang. "Liquid Regions of Lanthanum-Bearing Aluminosilicates." Materials 13, no. 2 (2020): 450. http://dx.doi.org/10.3390/ma13020450.

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The Al2O3-SiO2, La2O3-Al2O3, and La2O3-SiO2 binary phase diagrams were estimated by Redlich–Kister expression. La4.67Si3O13 (=La4.67(SiO4)3O) was introduced to improve the existing phase diagrams. The Al2O3-SiO2-La2O3 ternary phase diagram extrapolated by Kohler method was optimized. Then, the liquidus of Al2O3-SiO2-La2O3 system at 1600 °C was compared with Al2O3-SiO2-RE2O3 (RE = Rare Earth Elements) systems and experimental results in other literature. The high temperature experiments were conducted in the tube furnace at 1500 °C. Then the field emission scanning electron microscope (FE-SEM), energy dispersive spectrometer (EDS), and X-ray diffraction (XRD) were employed to verify the calculated liquid region and precipitates phase at 1500 °C. Moreover, the liquidus of binary systems were compared with FactSage results and experiments. The optimized ternary phase diagram shows the relatively reliable region of liquid phase, and it is significant to the seal glass of solid oxide fuel cells and other fields being related to RE containing silicates.

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19

Dong, Jie, Chao Qing Yin, Hong Xu Lu, Zi Xin Zhang, and Qing Hua Zhang. "Morphology Control of Polyimide Fibers by Phase Separation under Different Coagulation Bath Conditions." Materials Science Forum 789 (April 2014): 142–47. http://dx.doi.org/10.4028/www.scientific.net/msf.789.142.

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In order to investigate the effects of the coagulation bath temperature and composition on the formation of polyimide fiber in wet spinning, theoretical ternary phase diagrams of water/NMP/PI system at two coagulation bath temperatures was investigated based on the extended Flory-Huggins theory. The cloud-points data of the system for more dilute PI terpolymer solutions were determined by cloud point titration, and the cloud point data for more concentrated PI terpolymer solutions were calculated by Boom's linearized cloud point curve correlation. The obtained diagrams showed that if the titration process constructed at a higher temperature, the meta-stable two-phase region in the ternary phase diagram increases, which is beneficial for the de-mixing of the filament via nucleation and growth mechanisms, resulting in a homogenous dense structure for PI fiber.

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20

Qiang, Jian-Bing, De-He Wang, Cui-Min Bao, et al. "Formation rule for Al-based ternary quasi-crystals: Example of Al–Ni–Fe decagonal phase." Journal of Materials Research 16, no. 9 (2001): 2653–60. http://dx.doi.org/10.1557/jmr.2001.0364.

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After examining ternary Al-based quasi-crystalline phase diagrams, we pointed out that the presence of e/a-constant and e/a-variant lines is a common phenomenon. Ternary quasi-crystal compositions are located at the crossing point of these lines in ternary phase diagrams. Such an empirical rule can be used to predict the ternary quasi-crystal compositions from binary ones. We applied this rule to the Al–Fe–Ni system and clarified the decagonal phase composition zone. There are two decagonal phases, D-Al72.5Fe14.5Ni13 and D′-Al705Fe12Ni17.5, that correspond respectively to Al–Fe-based and Al–Ni-based decagonal phases in the same ternary system.

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21

Tartas, Jean, and Emile J. Knystautas. "Predicting quasicrystals with quantum structural diagrams." Journal of Materials Research 6, no. 6 (1991): 1219–29. http://dx.doi.org/10.1557/jmr.1991.1219.

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Binary and ternary quasicrystals have been successfully separated by means of quantum structural diagrams in the light of new experimental data, and new potential candidates for the quasicrystalline state are presented. A general and simple classification of alloy systems, consistent with the experimental data, is proposed, which allows predictions of any type of binary and ternary quasicrystals. Quantum coordinates are analyzed and interpreted, and suggestions are given for an improvement of the present method.

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22

Tan, R. R., and S. Bandyopadh. "Trigeneration System: Visualization through Ternary Diagrams." Journal of Applied Sciences 14, no. 13 (2014): 1481–84. http://dx.doi.org/10.3923/jas.2014.1481.1484.

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23

Wennerström, Håkan. "Ternary Phase Diagrams in Surfactant Science." Journal of Dispersion Science and Technology 28, no. 1 (2007): 31–37. http://dx.doi.org/10.1080/01932690600992563.

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24

Karukstis, Kerry K., Sara K. Avrantinis, Stephanie L. Boegeman, et al. "Spectroscopic Determination of Ternary Phase Diagrams." Journal of Chemical Education 77, no. 6 (2000): 701. http://dx.doi.org/10.1021/ed077p701.

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25

Stead, Rebecca J., and Keith Stead. "Phase diagrams for ternary liquid systems." Journal of Chemical Education 67, no. 5 (1990): 385. http://dx.doi.org/10.1021/ed067p385.

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26

McClurg, Richard B. "Taxonomy of Cocrystal Ternary Phase Diagrams." Journal of Chemical & Engineering Data 61, no. 12 (2016): 4313–20. http://dx.doi.org/10.1021/acs.jced.6b00791.

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27

Schultz, Allan, and Y. Austin Chang. "Computer Graphics for Ternary Phase Diagrams." JOM 37, no. 11 (1985): 10–13. http://dx.doi.org/10.1007/bf03258731.

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28

KING, T. A., C. E. GLASS, and R. A. SCHOWENGERDT. "Multispectral Ratio Selection Using Ternary Diagrams." Environmental & Engineering Geoscience xxvii, no. 1 (1990): 93–102. http://dx.doi.org/10.2113/gseegeosci.xxvii.1.93.

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29

Philip, G. M., C. Gregory Skilbeck, and D. F. Watson. "Algebraic dispersion fields on ternary diagrams." Mathematical Geology 19, no. 3 (1987): 171–81. http://dx.doi.org/10.1007/bf00897745.

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30

Watson, G. S. "Confidence regions in ternary diagrams 2." Mathematical Geology 19, no. 4 (1987): 347–48. http://dx.doi.org/10.1007/bf00897844.

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31

Al Badareen, M., I. Kayali, and M. Hanania. "Extraction and Microemulsion of Lupin Protein." Asian Journal of Chemistry 34, no. 11 (2022): 2942–46. http://dx.doi.org/10.14233/ajchem.2022.23923.

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In present study, protein and oil were extracted from sweet and bitter lupin that were used to define the phase behaviour of a three-component system (lupin oil, Tween 80/propylene glycol and water/lupin protein). Ternary phase diagrams were constructed and the optimum area of ternary phase diagrams corresponding to the formation of microemulsions were identified using emulsion titration method. Phase inversion composition method was applied, which involved the spontaneous formation of microemulsion, characterized by visual observation for their phase separation and optical clarity (e.g. transparency and opacity). Generally, o/w microemulsions were formed at a small region of the ternary phase diagrams with a relatively large ratio of water/lupin protein. Some differences between the sweet and bitter lupin diagrams were observed in regions, including bi- and multiphase, liquid crystals, gel and coarse emulsions. The physical characteristics of the microemulsions did not change with different storage temperatures.

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32

Li, Bin, Xinjun Jing, and Junsheng Yuan. "Phase Equilibrium of the Quaternary System LiBr-Li2SO4-KBr-K2SO4-H2O at 308.15 K." Processes 10, no. 5 (2022): 823. http://dx.doi.org/10.3390/pr10050823.

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The phase equilibria of the reciprocal quaternary system LiBr-Li2SO4-KBr-K2SO4-H2O and its ternary sub-systems LiBr-Li2SO4-H2O and KBr-K2SO4-H2O at 308.15 K were studied using the isothermal dissolution equilibrium method. Then, the solubility data of the equilibrium solutions were collected, and the phase diagrams were plotted. The phase diagrams of the ternary sub-systems at 308.15 K were compared with those at other temperatures. This study found that the phase diagram of the LiBr-Li2SO4-H2O system at 308.15 K consisted of an invariant point, two solid-phase crystallization regions of Li2SO4·H2O and LiBr·2H2O, and their corresponding solubility curves. The system generated two hydrated salts, which belonged to the hydrate type I phase diagram. The phase diagram of the KBr-K2SO4-H2O system at 308.15 K consisted of an invariant point, two univariant solubility curves, and two solid-phase crystallization regions of KBr and K2SO4, and no solid solution and double salts were formed. Thus, it belonged to a simple co-saturation type phase diagram. In the LiBr-Li2SO4-KBr-K2SO4-H2O system, K2SO4·Li2SO4 double salt formed at 308.15 K, and the phase diagram consisted of three invariant points, five crystallization regions, and seven univariant solubility curves.

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33

Jiménez-Preciado, Ana Lorena, and Nora Gavira-Durón. "Social Mobility Patterns in the World's Populated Cities Through COVID-19." Revista Mexicana de Economía y Finanzas 16, no. 3 (2021): 1–15. http://dx.doi.org/10.21919/remef.v16i3.675.

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Objective: identify social mobility patterns in the world's most populated cities from the ravaging pandemic of COVID-19 and the confinement and social distancing measures. Method: ternary diagrams to examine the simultaneous movement to different places (grocery, services, parks, workplaces, residence, and transit). Specifically, we use crosshair ternary plots and a Gaussian Kernel Density Estimator (KDE) for ternary density diagrams. Results: for the most part, the mobility reduction was between 40% and 60% in the selected cities. Nevertheless, there were more significant transit cases, but not workplaces or residences, suggesting that the informal market may absorb part of the labor work. Limitations and implications: the main limitation of this analysis is in scaling the data since the mobility statistics represent negative percentages. Main contribution: the work's principal contribution and originality lie in using ternary diagrams, allowing the identification of social mobility patterns in the largest cities and understanding how displacement of populations has changed since COVID-19.

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34

Vadapalli, Ratna Sree, and Sunitha Reddy, M. "Formulation and Evaluation of Self-Micro Emulsifying Drug Delivery System (SMEDDS) of Ticagrelor." Saudi Journal of Medical and Pharmaceutical Sciences 8, no. 11 (2022): 628–43. http://dx.doi.org/10.36348/sjmps.2022.v08i11.001.

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The present work mainly emphasized on the enhancement of solubility of Ticagrelor by developing Self- Micro emulsifying drug delivery system. Ticagrelor is a BCS class IV drug with poor aqueous solubility and permeability. The saturated solubility of Ticagrelor in various oils, surfactants and co-surfactants was determined by using UV-spectroscopy. The excipients were selected based on their maximum solubility and compatibility for Ticagrelor. SMEDDS formulations od Ticagrelor were developed using different oils, surfactants and co-surfactant combinations (4:1 and 3:1). Pseudo ternary phase diagrams were constructed and based on pseudo ternary phase diagrams, Nano emulsification area was evaluated .Formulations were designed based on the pseudo ternary phase diagram using various proportions of oil (Capmul MCM E8 EP), surfactant (Labrasol), co-surfactant (PEG-400). The prepared formulations were selected among them F1 was optimized and carried out for further evaluations like dispersibility test, self-emulsification time ,phase separation and stability test, thermodynamic stability studies, droplet size and zeta potential, invitro drug release studies. The results of present study demonstrate that Ticagrelor SMEDDS can be used as a potential means for improving the solubility of Ticagrelor.

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35

Ermoline, Alexandre, Mirko Schoenitz, and Edward L. Dreizin. "High-temperature phase equilibria in the system Zr–O–N." Journal of Materials Research 21, no. 2 (2006): 320–28. http://dx.doi.org/10.1557/jmr.2006.0062.

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Powders of Zr, ZrO2, and ZrN were mixed and pressed to produce samples with different bulk stoichiometries in the ternary Zr–O–N systems. The samples were laser heated above melting, maintained at a high temperature, and quenched. The processed samples were cross-sectioned and studied using scanning electron microscopy, energy dispersive x-ray spectroscopy, and x-ray diffraction. The results pointed to the location of the ternary invariant point Liquid + Gas + ZrO2 + ZrN on the high-temperature portion of the Zr–ZrO2–ZrN phase diagram. The ternary liquidus in the Zr–O–N system was further constrained based on the comparison of the results obtained in this work with composition histories of zirconium particles burning in air reported earlier. Elemental analysis of nitrogen-rich inclusions found in the samples showed the existence of an extended compositional range for ternary solid Zr–O–N solutions. X-ray diffraction analysis of the quenched samples indicated that these solutions are likely to be derived from the ZrN phase. A preliminary outline of the subsolidus ternary Zr–ZrO2–ZrN phase diagram is constructed based on these findings and the interpretations of the well-known binary Zr–O and Zr–N phase diagrams.

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36

Tokunaga, T., N. Hanaya, Hiroshi Ohtani, and Mitsuhiro Hasebe. "Thermodynamic Analysis of the Fe-Mn-P Ternary Phase Diagram by Combining the First-Principles and CALPHAD Methods." Materials Science Forum 561-565 (October 2007): 1899–902. http://dx.doi.org/10.4028/www.scientific.net/msf.561-565.1899.

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A thermodynamic analysis of the Fe-Mn-P ternary system has been carried out using the CALPHAD method. Among the three binary systems relevant to this ternary phase diagram, the thermodynamic parameters of the Mn-P binary system were evaluated in this study. The enthalpy of formation of the binary phosphides obtained from our first-principles calculations was utilized in the present analysis to compensate for the lack of available experimental data. The thermodynamic descriptions of the Fe-Mn and Fe-P binary systems were taken from previous studies. The phase equilibria in the Fe-Mn-P ternary system were analysed based on the experimental data on the phase boundaries. The calculated phase diagrams are in agreement with the experimental results.

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37

Li, Jia Lian, Shu Liang Wang, Lu Jiang Zhou, Xiao Hong Wang, Yuan Hua Lin, and Xing Jun Liu. "Thermodynamic Study of Ag-Au-Gd, Tb Ternary Systems." Materials Science Forum 814 (March 2015): 313–18. http://dx.doi.org/10.4028/www.scientific.net/msf.814.313.

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The addition of the rare earth elements into the Ag-based filler alloy, which is typical and important, can control and eliminate the negative effect of impurity elements, and furthermore, it improves the spreading property of the Ag-based filler alloy. Phase diagram provides an important direction for materials design of the Ag-based filler alloy. Thus it is necessary to investigate the phase diagrams and construct the thermodynamic database. On the basis of this background, thermodynamic assessments of the Au-Gd, Tb binary systems were carried out by using the CALPHAD (Calculation of Phase Diagrams) method based on the experimental data including thermodynamic properties and phase equilibrium. The Gibbs free energies of the solution phases were described by sub-regular solution models with the Redlich-Kister equation, while all of the intermetallic compounds were described by sub-lattice models. A consistent set of thermodynamic parameters was derived from describing the Gibbs free energies of each solution phase and intermetallic compound. The calculated phase diagram achieved consistency with the available experiments. Then combined with the assessed relevant binary systems, the Ag-Au-Gd, Tb ternary systems have been predicted. The thermodynamic database of these ternary systems has been developed to present the significant information for the design of Ag-based filler alloys.

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38

Yen, Yee-wen, and Sinn-wen Chen. "Phase equilibria of the Ag–Sn–Cu ternary system." Journal of Materials Research 19, no. 8 (2004): 2298–305. http://dx.doi.org/10.1557/jmr.2004.0296.

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Phase equilibria of the Ag–Sn–Cu ternary system have been determined experimentally as well as using the calculation of phase diagram (CALPHAD) method. Various Ag–Sn–Cu alloys were prepared to study the isothermal sections of the Ag–Sn–Cu ternary system at 240 and 450 °C. No ternary compounds were found and all the binary compounds had only limited ternary solubility. The ∈1–Cu3Sn phase is a very stable phase. It is in equilibrium with the Ag, ζ–Ag4Sn, ∈2–Ag3Sn, η–Cu6Sn5, and Cu phases at 240 °C, and is in equilibrium with the Ag, ζ, ∈2, L, and δ–Cu4Sn phases at 450 °C. Thermodynamic models of the Ag–Sn–Cu ternary system were developed based on available thermodynamic models of the constituent binary systems without introducing ternary interaction parameters. The isothermal sections at 240 and 450 °C were calculated, and the results were in good agreement with those determined experimentally. In addition to the isothermal sections, stability diagrams of Sn and Cu were calculated as well.

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39

Minic, D., Y. Du, M. Premovic, et al. "Experimental and thermodynamic description of ternary Bi-Cu-Ga system." Journal of Mining and Metallurgy, Section B: Metallurgy 53, no. 3 (2017): 189–201. http://dx.doi.org/10.2298/jmmb170505017m.

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Phase diagram of the Bi-Cu-Ga ternary system has been investigated experimentally with 27 alloys and analytically by using a Calphad method. Thirteen annealed alloys at 200?C were investigated by using scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS), and X-ray powder diffraction (XRD) methods. Temperatures of phase transformation were determined with 14 alloys which are lying along three vertical sections Bi-Cu0.5Ga0.5, Cu-Bi0.5Ga0.5 and Ga-Bi0.5Cu0.5 by using differential thermal analysis (DTA). Based on the experimental result and by using Calphad method, ternary phase diagrams were constructed with a new description of liquidus phase. Calculated phase diagram and experimentally obtained results are in good agreement. Liquidus projection and invariant reaction were calculated by using new thermodynamic parameters for liquidus phase.

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40

Shallcross, David C., and Binh Son Vo. "Ternary Error Diagrams: Graphical Representation of Errors in Ternary System Compositions." Industrial & Engineering Chemistry Research 44, no. 11 (2005): 4139–41. http://dx.doi.org/10.1021/ie050039i.

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41

Ohtani, Hiroshi, N. Hanaya, and Mitsuhiro Hasebe. "Thermodynamic Analysis of Steels by Incorporating First-Principles Calculations into the CALPHAD Approach." Materials Science Forum 539-543 (March 2007): 2413–18. http://dx.doi.org/10.4028/www.scientific.net/msf.539-543.2413.

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A thermodynamic analysis of the Fe−M−P (M = Nb, Ti) ternary system has been performed by combining first-principles calculations with the CALPHAD approach. Because of the lack of experimental information available, thermodynamic properties of orthorhombic anti-PbCl2-type FeMP were evaluated using the Full Potential Linearized Augmented Plane Wave method, and the estimated values were introduced into a CALPHAD-type thermodynamic analysis. Applying this procedure, the phase diagrams of the Fe−M−P ternary phase diagrams whose contents are uncertain so far were calculated with a high degree of probability. Phase diagrams for high-purity ferritic stainless steels obtained following the same procedure are also presented.

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42

Kim, Young Hoon, Yu Chul Kim, Dong-Jin Jang, et al. "Development of 20(S)-Protopanaxadiol-Loaded SNEDDS Preconcentrate Using Comprehensive Phase Diagram for the Enhanced Dissolution and Oral Bioavailability." Pharmaceutics 12, no. 4 (2020): 362. http://dx.doi.org/10.3390/pharmaceutics12040362.

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In this study, we aimed to develop a 20(S)-protopanaxadiol (PPD)-loaded self-nanoemulsifying drug delivery system (SNEDDS) preconcentrate (PSP) using comprehensive ternary phase diagrams for enhanced solubility, physical stability, dissolution, and bioavailability. Capmul MCM C8 and Capryol 90 were selected as the oil phase owing to the high solubility of PPD in these vehicles (>15%, w/w). Novel comprehensive ternary phase diagrams composed of selected oil, surfactant, and PPD were constructed, and the solubility of PPD and particle size of vehicle was indicated on them for the effective determination of PSP. PSPs were confirmed via particle size distribution, physical stability, and scanning electron microscope (SEM) with the dispersion of water. The optimized PSP (CAPRYOL90/Kolliphor EL/PPD = 54/36/10, weight%) obtained from the six possible comprehensive ternary phase diagrams showed a uniform nanoemulsion with the particle size of 125.07 ± 12.56 nm without any PPD precipitation. The PSP showed a dissolution rate of 94.69 ± 2.51% in 60 min at pH 1.2, whereas raw PPD showed negligible dissolution. In oral pharmacokinetic studies, the PSP group showed significantly higher Cmax and AUCinf values (by 1.94- and 1.81-fold, respectively) than the raw PPD group (p < 0.05). In conclusion, the PSP formulation with outstanding solubilization, dissolution, and in-vivo oral bioavailability could be suggested using effective and comprehensive ternary phase diagrams.

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43

Ohtake, Naoto, Masanori Hiratsuka, Kazuhiro Kanda, et al. "Properties and Classification of Diamond-Like Carbon Films." Materials 14, no. 2 (2021): 315. http://dx.doi.org/10.3390/ma14020315.

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Diamond-like carbon (DLC) films have been extensively applied in industries owing to their excellent characteristics such as high hardness. In particular, there is a growing demand for their use as protective films for mechanical parts owing to their excellent wear resistance and low friction coefficient. DLC films have been deposited by various methods and many deviate from the DLC regions present in the ternary diagrams proposed for sp3 covalent carbon, sp2 covalent carbon, and hydrogen. Consequently, redefining the DLC region on ternary diagrams using DLC coatings for mechanical and electrical components is urgently required. Therefore, we investigate the sp3 ratio, hydrogen content, and other properties of 74 types of amorphous carbon films and present the classification of amorphous carbon films, including DLC. We measured the sp3 ratios and hydrogen content using near-edge X-ray absorption fine structure and Rutherford backscattering-elastic recoil detection analysis under unified conditions. Amorphous carbon films were widely found with nonuniform distribution. The number of carbon atoms in the sp3 covalent carbon without bonding with hydrogen and the logarithm of the hydrogen content were inversely proportional. Further, we elucidated the DLC regions on the ternary diagram, classified the amorphous carbon films, and summarized the characteristics and applications of each type of DLC.

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44

Ohtake, Naoto, Masanori Hiratsuka, Kazuhiro Kanda, et al. "Properties and Classification of Diamond-Like Carbon Films." Materials 14, no. 2 (2021): 315. http://dx.doi.org/10.3390/ma14020315.

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Diamond-like carbon (DLC) films have been extensively applied in industries owing to their excellent characteristics such as high hardness. In particular, there is a growing demand for their use as protective films for mechanical parts owing to their excellent wear resistance and low friction coefficient. DLC films have been deposited by various methods and many deviate from the DLC regions present in the ternary diagrams proposed for sp3 covalent carbon, sp2 covalent carbon, and hydrogen. Consequently, redefining the DLC region on ternary diagrams using DLC coatings for mechanical and electrical components is urgently required. Therefore, we investigate the sp3 ratio, hydrogen content, and other properties of 74 types of amorphous carbon films and present the classification of amorphous carbon films, including DLC. We measured the sp3 ratios and hydrogen content using near-edge X-ray absorption fine structure and Rutherford backscattering-elastic recoil detection analysis under unified conditions. Amorphous carbon films were widely found with nonuniform distribution. The number of carbon atoms in the sp3 covalent carbon without bonding with hydrogen and the logarithm of the hydrogen content were inversely proportional. Further, we elucidated the DLC regions on the ternary diagram, classified the amorphous carbon films, and summarized the characteristics and applications of each type of DLC.

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45

Hu, B., Y. Du, J. J. Yuan, Z. F. Liu, and Q. P. Wang. "Thermodynamic reassessment of the Mn-Ni-Si system." Journal of Mining and Metallurgy, Section B: Metallurgy 51, no. 2 (2015): 125–32. http://dx.doi.org/10.2298/jmmb141002015h.

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Iased on the new experimental data available in the literature, the Mn-Ni-Si system has been reassessed using the CALPHAD (CALculation of PHAse Diagram) approach. Compared with the previous modeling, the ?8 and ?12 ternary phases were treated as the same phase according to the new experimental data. The Mn3Si phase was described with two sublattice model (Mn, Ni)3(Si)1. The reported new ternary phase ? was not considered in the present work. Comprehensive comparisons between the calculated and measured phase diagrams showed that a set of thermodynamic parameters of the Mn-Ni-Si system obtained in this work was more accurate than the previous one.

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46

Liu, H. K., S. X. Dou, M. Ionescu, Z. B. Shao, K. R. Liu, and L. Q. Liu. "Equilibrium phase diagrams in the system CuO–PbO–Ag." Journal of Materials Research 10, no. 11 (1995): 2933–37. http://dx.doi.org/10.1557/jmr.1995.2933.

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Silver has played a critical role for the fabrication of metal/high temperature superconductor composites. Phase equilibrium and microstructure in the ternary PbO-CuO-Ag system have been investigated using differential thermal analysis (DTA), thermogravimetry (TG), scanning electron microscope (SEM), and x-ray diffraction (XRD) techniques. Composition versus temperature diagrams have been established for these systems in air. In the ternary CuO-PbO-Ag system, there is a eutectic reaction CuO + PbO + Ag = L at 750 °C and a composition of 12.04 mol % Ag, 16.35 mol % CuO, and 72.62 mol % PbO. Two immiscible regions near the two binary tie lines PbO-Ag and CuO-Ag were detected. No binary or ternary compound was detected in these systems. SEM and EDS results confirm the presence of two liquid phases and the eutectic point

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47

Pratap, A. P., and D. N. Bhowmick. "Pseudo Ternary Diagrams of Pesticide Microemulsion Systems." Tenside Surfactants Detergents 41, no. 2 (2004): 78–82. http://dx.doi.org/10.3139/113.100211.

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Dujmović, Jozo, and Carl Herder. "Visualization of Java workloads using ternary diagrams." ACM SIGSOFT Software Engineering Notes 29, no. 1 (2004): 261–65. http://dx.doi.org/10.1145/974043.974085.

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Clare, B. W., G. T. Hefter, and P. E. Kloeden. "The representation of ternary liquid composition diagrams." Journal of Chemical Education 62, no. 8 (1985): 680. http://dx.doi.org/10.1021/ed062p680.

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50

Teubner, Max. "Fluctuations and phase diagrams in ternary mixtures." Journal of Chemical Physics 94, no. 6 (1991): 4490–94. http://dx.doi.org/10.1063/1.460739.

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