Free Energy of Mixing for Polymer Solutions

2004 ◽  
Vol 37 (9) ◽  
pp. 3475-3486 ◽  
Author(s):  
Takao Yamamoto ◽  
Takayuki Narita ◽  
Masahiro Nobe ◽  
Toshiaki Dobashi
Keyword(s):  
Free Energy ◽  
Polymer Solutions ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

Higher Order Conditional Probabilities and Thermodynamics of Binary Molten Alloys

1997 ◽  
Vol 11 (02n03) ◽  
pp. 93-106 ◽  
Author(s):  
O. Akinlade
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Cluster Model ◽  
Excess Free Energy ◽  
Higher Order ◽  
Thermodynamic Quantities ◽  
Equiatomic Composition ◽  
Conditional Probabilities ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

The recently introduced four atom cluster model is used to obtain higher order conditional probabilities that describe the atomic correlations in some molten binary alloys. Although the excess free energy of mixing for all the systems studied are almost symmetrical about the equiatomic composition, most other thermodynamic quantities are not and thus, the study enables us to explain the subtle differences in their physical characteristics required to describe the mechanism of the observed strong heterocoordination in Au–Zn or homocoordination in Cu–Ni within the same framework. More importantly, we obtain all calculated quantities for the whole concentration range thus complimenting experimental evidence.

Diffusion-Induced Grain Boundary Migration and Role of Defects

1993 ◽  
Vol 319 ◽  
Author(s):  
T.K. Chaki
Keyword(s):  
Free Energy ◽  
Grain Boundary ◽  
Boundary Migration ◽  
Solute Concentration ◽  
Grain Boundary Migration ◽  
Thermally Activated ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Liquid Film Migration ◽  
Lattice Diffusivity

AbstractA model is presented to explain various aspects of diffusion-induced grain boundary migration (DIGM). The driving energies of DIGM are identified as the free energy of mixing and the interface free energy, the former being predominant in most cases of DIGM. The grain boundary migrates due to thermally activated motion of atoms across the interface under the influence of the driving energies. An expression for the velocity of migration is derived. It is shown that this depends parabolically on the solute concentration, in agreement with experimental observations in the case of liquid film migration (LFM), which is analogous to DIGM. Furthermore, the velocity is proportional to lattice diffusivity ahead of the boundary. Recent results of enhancement of DIGM by ion bombardment is explained by radiation-enhanced lattice diffusivity due to introduction of point defects by the ions. The model also explains that diffusion-induced recrystallization (DIR) is due to a free energy decrease associated with the transformation from the amorphous phase in the grain boundary layer to the crystalline phase.

Dolomite Decomposition to (Ca,Mg)O Solid Solutions: An X-Ray Diffraction Study.Part II.

1984 ◽  
Vol 39 (10) ◽  
pp. 981-985 ◽  
Author(s):  
G. Spinolo ◽  
U. Anselmi Tamburini
Keyword(s):  
Free Energy ◽  
Low Temperatures ◽  
Particle Sizes ◽  
Diffusional Process ◽  
X Ray Diffraction ◽  
High Iron Content ◽  
X Ray ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Low Pressures

Abstract The full decomposition of dolomites with low and high iron content at low temperatures and low pressures is discussed with reference to the free energy of mixing of the ternary system Ca. Fe, Mg/O. The actual products of the primary step are a couple of rock salt structured oxides close to the spinodal compositions and with very small particle sizes. A subsequent diffusional process can produce large crystallites with equilibrium compositions, but it is effective only when either a low-iron dolomite is used as starting material or higher temperatures are employed.

Calculation on the Free Energy of Mixing of some Silane Systems

2011 ◽  
Vol 391-392 ◽  
pp. 1017-1021
Author(s):  
Ru Zhang ◽  
Yan Fen Wu ◽  
Ping Hu
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Activity Coefficients ◽  
Influence Factors ◽  
Critical Parameters ◽  
Model Parameters ◽  
Free Energies ◽  
Wilson Model ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

Six binary silane systems were chosen to calculate the activity coefficients (γ) and free energies of mixing (ΔGm). These systems included: methyldichlorosilane + methyltrichlorosilane, methyldichlorosilane + methylvinyldichlorosilane, methyldichlorosilane + toluene, methyltrichlorosilane + methylvinyldichlorosilane, methyltrichlorosilane + toluene, methylvinyldichlorosilane + toluene. Based on the Antoine constants, critical parameters of the pure components and Wilson model parameters, γ and ΔGmwere calculated. The influence factors of these thermodynamic properties were also discussed.

Calculation of Darken Stability Functions of Al-In and Bi-Zn Binary Liquid Alloys

2021 ◽  
Vol 14 (2) ◽  
pp. 111-116
Keyword(s):  
Free Energy ◽  
Activity Ratio ◽  
Binary Alloys ◽  
Concentration Fluctuation ◽  
Nearest Neighbour ◽  
Stability Function ◽  
Energy Of Mixing ◽  
Neighbour Shell ◽  
Free Energy Of Mixing ◽  
The Ideal

Abstract: The thermodynamic model based on clustering of two atoms is considered with the view to obtain the concentration-concentration fluctuation, Scc(0) and the darken stability function. The thermodynamic properties of these alloys were evaluated based on clustering of two atoms (A & B) or (B & A). Each system has the view of obtaining concentration-concentration fluctuation, Scc(0) enumerating the low-order atomic correlation in the nearest neighbour shell of liquid binary alloys. The highlights of reciprocals of Scc(0) of these alloys were noted . The values of Scc(0) for Al-In alloy throughout the entire concentration were positive and higher for activity ratio and lower than the ideal solution values for free energy of mixing at specific Al composition. The values of darken stability function of Al-In alloy fall below the ideal darken stability function for activity ratio and free energy of mixing . The indication of the reciprocal of Scc(0) for all the alloys is in support of homocoordination / heterocoordination in the nearest neighbour shell. The Scc(0) and darken stability function of Bi-Zn binary alloys were noted with fluctuations. Keywords: Concentration-concentration fluctuation, Darken stability function, Ordering energy.

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