Microdomain Structures in Polyelectrolyte Systems: Calculation of the Phase Diagrams by Direct Minimization of the Free Energy

1994 ◽  
Vol 27 (15) ◽  
pp. 4220-4230 ◽  
Author(s):  
Irina A. Nyrkova ◽  
Alexei R. Khokhlov ◽  
Masao Doi
Keyword(s):  
Free Energy ◽  
Phase Diagrams ◽  
Direct Minimization

Phase diagrams

2021 ◽  
pp. 19-29
Author(s):  
Adrian P Sutton
Keyword(s):  
Free Energy ◽  
Phase Diagrams ◽  
Binary Systems ◽  
Full Range ◽  
Phase Rule ◽  
Intermediate Phases ◽  
Ordered Alloys ◽  
Regions Of Stability ◽  
Liquid States

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.

Thermodynamic modelling of acidic collagenous solutions: from free energy contributions to phase diagrams

Soft Matter ◽  
2019 ◽  
Vol 15 (8) ◽  
pp. 1833-1846 ◽  
Author(s):  
Sayyed Ahmad Khadem ◽  
Alejandro D. Rey
Keyword(s):  
Free Energy ◽  
Phase Diagrams ◽  
Thermodynamic Modelling

Tropocollagen is considered one of the main precursors in the fabrication of collagen-based biomaterials.

Phase diagrams of Ni2+xMn1-xGa Heusler alloys from Hubbard Hamiltonian with account of Jahn-Teller effect

2011 ◽  
Vol 1310 ◽  
Author(s):  
Mikhail A. Zagrebin ◽  
Vasiliy D. Buchelnikov ◽  
Sergey V. Taskaev ◽  
Natal’ya Yu. Fedulova
Keyword(s):  
Phase Diagram ◽  
Free Energy ◽  
Phase Transitions ◽  
Phase Diagrams ◽  
Density Of States ◽  
Heusler Alloys ◽  
Teller Effect ◽  
Hubbard Hamiltonian ◽  
Jahn Teller ◽  
Jahn Teller Effect

ABSTRACTIn this work a microscopic Hamiltonian is investigated using the Hubbard model for a ferromagnet with two degenerate bands, taking into account the Jahn-Teller effect. A macroscopic free energy is obtained from the microscopic Hubbard Hamiltonian. All free energy coefficients depend on microscopic parameters: temperature T and composition x. As a result of analytical minimization of free energy, phase diagrams are numerically constructed. It is shown that at certain values of parameters on the phase diagrams there are thermodynamic paths which correspond to experimentally observed sequences of phase transitions. Using density of states spectra for different compositions x the T-x phase diagram is numerically constructed. This phase diagram can theoretically explain experimentally observed behavior of the temperatures of phase transitions.

Phase Diagrams and the Multiple Valued Free Energy

1972 ◽  
Vol 5 (6) ◽  
pp. 255-262
Author(s):  
O Stormark
Keyword(s):  
Free Energy ◽  
Phase Diagrams

Calculation of Gallium-Arsenic-Metal Phase Diagrams

1990 ◽  
Vol 204 ◽  
Author(s):  
James D. Scofield ◽  
J. E. Davison ◽  
S. R. Smith
Keyword(s):  
Free Energy ◽  
Phase Diagrams ◽  
Ternary Alloy ◽  
Regular Solution ◽  
Alloy System ◽  
Energy Functions ◽  
Solid Phases ◽  
Solution Parameters ◽  
Liquid And Solid Phases ◽  
Alloy Systems

ABSTRACTContact metallizations for space-based GaAs solar cells must survive at high temperatures for several minutes. Which metallizations will survive can be predicted by properly calculated phase diagrams instead of performing hundreds of reactions. A method for calculating the ternary temperature constitution phase diagrams Is briefly explained and the phase diagrams are calculated for two Ga-As-X alloy systems. The free energy functions of the liquid and solid phases are approximated by the regular solution theory. The phase diagrams of the three binary alloy systems which form the boundaries of the ternary alloy system are utilized to calculate the binary regular solution parameters. The free energy functions for the ternary liquid and solid phases are expressed In terms of the binary regular solution parameters. The temperature and composition of the liquidus and solidus boundaries for the ternary alloy systems are calculated from these free energy functions. Calculated results are presented for the Ga-As-Ag and the Ga-As-Ge systems.

scholarly journals Free energy of solid solutions and phase diagrams via quasiharmonic lattice dynamics

2001 ◽  
Vol 63 (9) ◽  
Author(s):  
N. L. Allan ◽  
G. D. Barrera ◽  
R. M. Fracchia ◽  
M. Yu. Lavrentiev ◽  
M. B. Taylor ◽  
...  
Keyword(s):  
Free Energy ◽  
Phase Diagrams ◽  
Solid Solutions ◽  
Lattice Dynamics
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