The metastable phase diagram of the Blume–Emery–Griffiths model in addition to the equilibrium phase diagram

2000 ◽  
Vol 113 (13) ◽  
pp. 5407 ◽  
Author(s):  
Mustafa Keskin ◽  
Cesur Ekiz
Keyword(s):  
Phase Diagram ◽  
Metastable Phase ◽  
Equilibrium Phase ◽  
Equilibrium Phase Diagram ◽  
Metastable Phase Diagram

THE METASTABLE PHASE DIAGRAM OF THE BLUME–EMERY–GRIFFITHS MODEL IN ADDITION TO THE EQUILIBRIUM PHASE DIAGRAM USING THE PAIR APPROXIMATION

2005 ◽  
Vol 19 (10) ◽  
pp. 1741-1755 ◽  
Author(s):  
AHMET ERDİNÇ ◽  
MUSTAFA KESKİN
Keyword(s):  
Phase Diagram ◽  
Metastable Phase ◽  
Equilibrium Phase ◽  
Equilibrium Phase Diagram ◽  
Order Parameters ◽  
Second Order ◽  
Pair Approximation ◽  
Variation Method ◽  
Metastable Phase Diagram ◽  
Phase Boundaries

As a continuation of our previously published work, the metastable phase diagram of the Blume–Emery–Griffiths model with the arbitrary bilinear (J), biquadratic (K) and crystal field interaction (D) is presented in addition to the equilibrium phase diagram in (T/K, J/K) and (T/K, D/K) plane by using the pair approximation of the cluster variation method on a body centered cubic lattice. We also calculate the phase transitions for the unstable branches of order parameters. The calculated first- and second-order phase boundaries of the unstable branches of the order parameters are superimposed on the equilibrium phase diagram and metastable phase diagram. It is found that the metastable phase diagram and the first- and second-order phase boundaries for unstable branches of order parameters always exist at low temperatures, which are consistent with the experimental and theoretical works.

scholarly journals DFT-CEF Approach for the Thermodynamic Properties and Volume of Stable and Metastable Al–Ni Compounds

Metals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1142
Author(s):  
Silvana Tumminello ◽  
Mauro Palumbo ◽  
Jörg Koßmann ◽  
Thomas Hammerschmidt ◽  
Paula R. Alonso ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Thermodynamic Properties ◽  
Dft Calculations ◽  
Density Functional ◽  
Metastable Phase ◽  
Equilibrium Phase ◽  
Configurational Entropy ◽  
Equilibrium Phase Diagram ◽  
Metastable Phases ◽  
Stability Range

The Al–Ni system has been intensively studied both experimentally and theoretically. Previous first-principles calculations based on density-functional theory (DFT) typically investigate the stable phases of this system in their experimental stoichiometry. In this work, we present DFT calculations for the Al–Ni system that cover stable and metastable phases across the whole composition range for each phase. The considered metastable phases are relevant for applications as they are observed in engineering alloys based on Al–Ni. To model the Gibbs energies of solid phases of the Al–Ni system, we combine our DFT calculations with the compound energy formalism (CEF) that takes the Bragg–Williams–Gorsky approximation for the configurational entropy. Our results indicate that the majority of the investigated configurations have negative energy of formation with respect to Al fcc and Ni fcc. The calculated molar volumes for all investigated phases show negative deviations from Zen’s law. The thermodynamic properties at finite temperatures of individual phases allow one to predict the configurational contributions to the Gibbs energy. By applying a fully predictive approach without excess parameters, an acceptable topology of the DFT-based equilibrium phase diagram is obtained at low and intermediate temperatures. Further contributions can be added to improve the predictability of the method, such as phonons or going beyond the Bragg–Williams–Gorsky approximation that overestimates the stability range of the ordered phases. This is clearly demonstrated in the fcc order/disorder predicted metastable phase diagram.

Intermetallic Formation in the Aluminum–Copper System

2003 ◽  
Vol 10 (04) ◽  
pp. 677-683 ◽  
Author(s):  
E. B. Hannech ◽  
N. Lamoudi ◽  
N. Benslim ◽  
B. Makhloufi
Keyword(s):  
Electron Microscopy ◽  
Phase Diagram ◽  
Solid Solution ◽  
Intermetallic Layer ◽  
Equilibrium Phase ◽  
Equilibrium Phase Diagram ◽  
Diffusion Couples ◽  
Intermetallic Formation ◽  
Parabolic Law ◽  
Scanning Electron

Intermetallic formation at 425°C in the aluminum–copper system has been studied by scanning electron microscopy using welded diffusion couples. Several Al–Cu phases predicted by the equilibrium phase diagram of the elements and voids taking place in the diffusion zone have been detected in the couples. The predominant phases were found to be Al 2 Cu 3 and the solid solution of Al in Cu, α. The growth of the intermetallic layer obeyed the parabolic law.

Equilibrium phase diagram of polystyrene and 8CB

1999 ◽  
Vol 37 (15) ◽  
pp. 1841-1848 ◽  
Author(s):  
Farida Benmouna ◽  
Abdelylah Daoudi ◽  
Fr�d�rick Roussel ◽  
Jean-Marc Buisine ◽  
Xavier Coqueret ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Equilibrium Phase ◽  
Equilibrium Phase Diagram

Metastable Phase Diagram of Nanocrystalline ZrO2−Sc2O3 Solid Solutions

2009 ◽  
Vol 113 (43) ◽  
pp. 18661-18666 ◽  
Author(s):  
Paula M. Abdala ◽  
Aldo F. Craievich ◽  
Marcia C. A. Fantini ◽  
Marcia L. A. Temperini ◽  
Diego G. Lamas
Keyword(s):  
Phase Diagram ◽  
Solid Solutions ◽  
Metastable Phase ◽  
Metastable Phase Diagram

scholarly journals Formation of Intermediate Phases and Supersaturated Solid Solution in Al-Cu System during Diffusion

2018 ◽  
Vol 383 ◽  
pp. 31-35 ◽  
Author(s):  
Alexey Rodin ◽  
Nataliya Goreslavets
Keyword(s):  
Phase Diagram ◽  
Solid Solution ◽  
High Temperature ◽  
Chemical Composition ◽  
Low Temperature ◽  
Supersaturated Solid Solution ◽  
Diffusion Processes ◽  
Equilibrium Phase ◽  
Equilibrium Phase Diagram ◽  
Intermediate Phases

The study of diffusion processes in the aluminum - copper system was carried out at the temperature 350 and 520 °C. Special attention was paid on the chemical composition of the system near Al/Cu interface. It was determined that the intermediate phases in the system, corresponding to the equilibrium phase diagram, were not formed at low temperature. At high temperature the intermediate phases forms starting with Cu - rich phases. In both cases supersaturated solid solution of copper in aluminum could be observed near the interface.

scholarly journals Equilibrium Phase Diagram of the Zn–Ag Alloy

2018 ◽  
Vol 20 (3) ◽  
pp. 72-84
Author(s):  
Alexey Korolev ◽  
◽  
Gennagy Maltsev ◽  
Konstantin Timofeev ◽  
Vladimir Lobanov ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Equilibrium Phase ◽  
Equilibrium Phase Diagram

scholarly journals Metastable phases and macroheterogeneous composites

2021 ◽  
Vol 29 (1) ◽  
pp. 65-68
Author(s):  
O. V. Sukhova
Keyword(s):  
Phase Diagram ◽  
Composite Materials ◽  
Abrasive Wear ◽  
Metastable Phase ◽  
Interfacial Reactions ◽  
Metastable Phases ◽  
Metastable Phase Diagram ◽  
Rapid Dissolution ◽  
Strong Adhesion ◽  
Stable And Metastable Phases

The way to control the interfacial reactions that processes during infiltration of macroheterogeneous composite materials is suggested. The idea is to combine the stable and metastable phases in the filler’s structure which dissolves at a different rate in the molten binder. To prove this approach, the structure and gas-abrasive wear of macroheterogeneous composite materials with Cu–20Ni–20Mn binder reinforced by Fe–(9.0–10.0)B–(0.01-0.2)C filler (in wt. %) cooled at 10–20 K/s or 103–104 K/s are studied. It is shown that the wear resistance of the investigated composite materials can be enhanced by accelerating interfacial reactions between the filler and the molten binder. Therefore, the composite materials produced from a rapidly cooled Fe–B–C filler show a higher resistance to gas-abrasive wear due to formation of Fe–Fe2(B,C) metastable eutectics in its structure. This eutectics crystallizes under metastable phase diagram due to the suppression of stable Fe2(B,C) phase formation and saturation of the rest of liquid by iron in the filler cooled at 103–104 K/s. As a result of rapid dissolution of the eutectics in the molten binder during infiltration, the strong adhesion at the interfaces of the composite materials is achieved which prevents the filler from spalling out under the impacts of abrasive.

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