Phase Diagram Features Associated with Multicritical Points in Alloy Systems

1982 ◽  
Vol 19 ◽  
Author(s):  
Samuel M. Allen ◽  
John W. Cahn

ABSTRACTMany features in the vicinity of critical points in phase diagrams can be illustrated using a Landau type free energy expansion as a power series in one or more order parameters and composition. This simple approach can be used with any solution model. It also predicts limits to metastability, and is useful for understanding mechanisms of phase change. The theory is applied to all the critical points that can occur in binary systems according to a Landau theory: critical consolute points, order-disorder transitions, tricritical points, critical end points, as well as to systems in which two transitions such as chemical and magnetic ordering occur.

1984 ◽  
Vol 62 (3) ◽  
pp. 457-474 ◽  
Author(s):  
A. D. Pelton ◽  
C. W. Bale ◽  
P. L. Lin

Phase diagrams and thermodynamic properties of five additive molten salt ternary systems and nine reciprocal molten salt ternary systems containing the ions Li+, Na+, [Formula: see text], OH− are calculated from the thermodynamic properties of their binary subsystems which were obtained previously by a critical assessment of the thermodynamic data and the phase diagrams in these binary systems. Thermodynamic properties of ternary liquid phases are estimated from the binary properties by means of the Conformal Ionic Solution Theory. The ternary phase diagrams are then calculated from these thermodynamic properties by means of computer programs designed for the purpose. It is found that a ternary phase diagram can generally be calculated in this way with a maximum error about twice that of the maximum error in the binary phase diagrams upon which the calculations are based. If, in addition, some reliable ternary phase diagram measurements are available, these can be used to obtain small ternary correction terms. In this way, ternary phase diagram measurements can be smoothed and the isotherms drawn in a thermodynamically correct way. The thermodynamic approach permits experimental data to be critically assessed in the light of thermodynamic principles and accepted solution models. A critical assessment of error limits on all the calculated ternary diagrams is made, and suggestions as to which composition regions merit further experimental study are given.


2012 ◽  
Vol 101 (5) ◽  
pp. 1843-1851 ◽  
Author(s):  
Pratik Upadhyay ◽  
Ajay K. Dantuluri ◽  
Lokesh Kumar ◽  
Arvind K. Bansal

1993 ◽  
Vol 71 (12) ◽  
pp. 1957-1957 ◽  
Author(s):  
I. Luk’yanchuk ◽  
M. Sigrist ◽  
M. Zhitomirsky

Calphad ◽  
1994 ◽  
Vol 18 (4) ◽  
pp. 387-396 ◽  
Author(s):  
D.O. López ◽  
J. Van Braak ◽  
J.L.L. Tamarit ◽  
H.A.J. Oonk

Author(s):  
Andrew V. Kosyakov ◽  
Ivan N. Nekrylov ◽  
Nikolai Yu. Brezhnev ◽  
Ekaterina N. Malygina ◽  
Alexander Yu. Zavrazhnov

Целью настоящей работы было термографическое исследование T-x диаграммы системы Ga – Se в диапазоне температур от 500 до 1100 °С и в диапазоне составов от 48.0 до 61.5 mol % Se. Методом исследования являлся дифференциальный термический анализ c компьютерной регистрацией данных. Получены свидетельства о наличии ретроградного солидуса фазы g-GaSe со стороны селена (с областью гомогенности в несколько десятых mol % при температурах выше эвтектической) и о независимом существовании близких по составу фаз e-GaSe и g-GaSe. При этом более богатая галлием фаза e-GaSe испытывает перитектический распад с образованием расплава (L2) и g-GaSe. Для темпера-туры предполагаемой перитектической реакции получено значение 921 ±2 °С. Вместе стем, на данном этапе работ не получено никаких данных в пользу существования ожидавшейся (по аналогии с системой Ga – S) высокотемпературной модификации, близкой по составу к сесквиселениду галлия (Ga2S3). Другие результаты, полученные в настоящей работе (характер и температуры плавления промежуточных фаз, температуры эвтектического и монотектического превращений, а также координата эвтектического состава), хорошо согласуются с литературными данными по исследованной системе         ЛИТЕРАТУРА1. Kainzbauer P., Richter K. W., Ipser H. The binary Bi-Rh phase diagram: stable and metastable phases //J. Phase Equilibria and Diffusion, 2018, v. 39(1), pp. 17– 34. DOI: https://doi.org/10.1007/s11669-017-0600-52. Dolyniuk J.-A., Kaseman D. C., Sen S., Zhao J., Osterloh F. E., Kovnir K. mP-BaP3: A new phase froman old binary system // Chem. Eur. J., 2014, v. 20, pp. 10829–10837, DOI: https://doi.org/10.1002/chem.2013050783. Березин С. С., Завражнов А. Ю., Наумов А. В., Некрылов И. Н., Брежнев Н. Ю. Фазовая диаграммасистемы Ga–S в области 48.0–60.7 мол. % S // Конденсированные среды и межфазные границы, 2017,т. 19(3), с. 321–335. DOI: https://doi.org/10.17308/kcmf.2017.19/2084. Волков В. В., Сидей В. И., Наумов А. В., Некрылов И. Н., Брежнев Н. Ю., Малыгина Е. Н., Завражнов А. Ю. Высокотемпературная кубическая модификация сульфида галлия (Xs = 59 мол. %) и Т, х-диаграмма системы Ga – S // Конденсированные среды и межфазные границы, 2019, т. 21(1), с. 37–50.DOI: https://doi.org/10.17308/kcmf.2019.21/7155. Zavrazhnov A., Berezin S., Kosyakov A., Naumov A., Berezina M., Brezhnev N. J. The phase diagramof the Ga–S system in the concentration range of 48.0–60.7 mol % S // Thermal Analysis and Calorimetry,2018, v. 134(1), pp. 483–492. DOI: https://doi.org/10.1007/s10973-018-7124-z6. Okamoto H. Ga–Se (Gallium-Selenium) // J. Phase Equilibria and Diffusion, 2009, v. 30, p. 658. DOI:https://doi.org/10.1007/s11669-009-9601-37. Dieleman J., Sanders F. H. M. Phase diagram of the Ga-Se system // Phillips J. Res., 1982, v. 37(4),pp. 204 – 229.8. Zavrazhnov A. Yu. Turchen D. N., Goncharov Eu. G., Zlomanov V. P. Manometric method for thestudy of P-T-x diagrams // J. Phase Equilibria and Diffusion, 2001, v. 22(4), pp. 482–490. DOI: https://doi.org/10.1361/1054971017703330639. Shtanov V. I, Komov A. A, Tamm M. E., Atrashenko D. V., Zlomanov V. P. Gallium-selenium systemphase diagram and photoluminescence spectra of GaSe crystals // Doklady Akademii nauk SSSR, 1998, v. 361(3),pp. 357–361. (in Russ.)10. Glazov V. M., Pavlova L. M. Semiconductor and metal binary systems. Phase equilibria and chemicalthermodynamics. Springer, 1989, 327 p. DOI: https://doi.org/10.1007/978-1-4684-1680-011. Ider M. Pankajavalli R., Zhuang W. Thermochemistry of the Ga–Se System. J. Solid State Scienceand Techn., 2015, v. 4(5), Q51–Q60 DOI: https://doi.org/10.1149/2.0011507jss12. Zavrazhnov A., Naumov A., Sidey V., Pervov V. Composition control of low-volatile solids throughchemical vapor transport reactions. III. The example of gallium monoselenide: Control of the polytypicstructure, non-stoichiometry and properties // Thermochimica Acta, 2012, v. 527, pp. 118–124. DOI:https://doi.org/10.1016/j.tca.2011.10.012


2021 ◽  
pp. 19-29
Author(s):  
Adrian P Sutton

Temperature-composition phase diagrams are introduced as maps of the regions of stability of binary systems at constant pressure, usually atmospheric pressure at sea level. Their construction is based on minimisation of the Gibbs free energy as a function of composition at a given temperature. The simple case of miscibility in the solid and liquid states over the full range of composition is discussed first. Eutectic and peritectic phase diagrams result from limited miscibility in the solid state. Intermediate phases, or ordered alloys, usually occur in narrow ranges of composition in phase diagrams, and this is also explained in terms of free energy composition curves. Each phase diagram is shown to obey the phase rule discussed in the previous chapter.


1987 ◽  
Vol 42 (12) ◽  
pp. 1421-1424 ◽  
Author(s):  
K. Igarashi ◽  
H. Ohtani ◽  
J. Mochinaga

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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