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Some Thermodynamic Considerations for Phase Equilibria and Transformations
Published in D. R. F. West, N. Saunders, Ternary Phase Diagrams in Materials Science, 2020
When one or two components of a ternary phase system are low molecular weight polymers, or an organic solvent is involved, then the entropy of mixing term has greater significance. Features can then emerge similar those encountered in metallic or ceramic systems. For example, a polymer system with an UCST, is represented by part of the polystyrene-cyclohexane system. (Figure 2.10). This system also illustrates the important feature of the dependence of the critical temperature on the molecular weight of the polystyrene; there is an increase in the UCST with increase in molecular weight. A further feature of this particular system is that, as the temperature is raised sufficiently above the UCST, the association between the polymer chains and the solvent molecules is lost. The chains then aggregate, leading again to a region of phase separation, in this case with a LCST.
Thermal Distribution of Electrons, Holes, and Ions in Solids
Published in Juan Bisquert, The Physics of Solar Energy Conversion, 2020
The entropy in Equation 5.8 is configurational entropy of the system that arises from the random distribution of nonidentical particles. In physical chemistry, it is known as the entropy of mixing. From the expression of the entropy, we obtain the configurational part of the chemical potential ζn=−T∂Sn∂n=kBTln(nNc−n)
Thermodynamics
Published in Harshad K. D. H. Bhadeshia, Theory of Transformations in Steels, 2021
The regular solution model assumes a random distribution of atoms even though the enthalpy of mixing is not zero, whereas in reality a random solution is only expected at high temperatures when the entropy term overwhelms any tendency for ordering or clustering of atoms. It follows that the configurational entropy of mixing should therefore vary with the temperature. The quasichemical solution model has a better treatment of configurational entropy which accounts for a non-random distribution of atoms. The model is so-called because it has a mass-action equation that has similarity to chemical reactions [100]. However, the presentation below follows derivations by Christian [101] and Lupis [97].
Microstructural evolution and mechanical properties of AlCrFeNiCoC high entropy alloy produced via spark plasma sintering
Published in Powder Metallurgy, 2019
Armin Emamifar, Behzad Sadeghi, Pasquale Cavaliere, Hosein Ziaei
For the multi-component system, is the average value of the alloy system. Based on the total electronegativity of HEA alloy whether attractive or repulsive, could be negative or positive. If , it means that the effect of the mixing entropy is greater than that of the enthalpy of mixing at the melting temperature, consequently solid solution phase with high entropy forms. Therefore, −T is the predominant factor leading to the decreasing of the Gibbs free energy of the system. Since the formation of disordered phases such as random solid solution as well as clustering and ordering phases are reflected the mixing entropy and mixing enthalpy, respectively, thus it is expected that in the understudy system, the formation of solid-solution phases should be much easier than the formation of intermetallic compounds. On the other hands, it well known that the mixing enthalpy of mixture of the atomic pairs is highly negative while aluminium and carbon are two significant consistent in order to negative enthalpy of mixing in this HEA. In this situation, it is expected that the alloy shows a strong tendency for ordering or clustering[27]. It is clear that the portion corresponding to the mixing entropy for the Al0.5CrFeNiCo0.3C0.2 HEA is more than the portion corresponding to the mixing enthalpy. Accordingly, the formation of the Al0.5CrFeNiCo0.3C0.2 HEA solid solution could be more related to its high mixing entropy.
Structure and stability of δ-UZr2 phase in U-50 wt% Zr alloy
Published in Philosophical Magazine, 2022
The instability of the δ-phase at 0 K, owing to the positive energy of formation at 0 K, indicates that in the phase diagram the existence of the δ-UZr2 phase field might vanish gradually with lowering the temperature. It has recently been shown that the contribution from entropy of mixing, comprising of configurational entropy (ΔSconf), vibrational entropy (ΔSvib) and electronic contribution (ΔSelec) to entropy, plays a decisive role in determining the phase stability, especially when the absolute value of the energy of formation is near to zero (when expressed in eV/atom) [31]. Usually, |ΔSelec| < |ΔSvib| << |ΔSconf| and ΔSconf always tends to stabilise a phase with its positive value; however, the ΔSvib can stabilise a compound with positive enthalpy of formation or can destabilise a compound with a negative enthalpy of formation. Such indecisive role of the vibrational entropy is more critical when the enthalpy of formation is within −0.05 to +0.05 eV/atom; from ref. [29], it appears that calculated values of enthalpy of formation of UZr2 phase fall within this critical range. With increasing temperature, the term –TΔSmix becomes more negative and might counteract the positive enthalpy of formation in stabilising a phase with positive enthalpy of formation. In the case of a random solid solution, the lattice positions are usually well defined though the local atomic environment varies around a given atomic species; however, in the UZr2 phase, the EXAFS analysis shows not only extremely high local variations in terms of atomic environment but also a large numbers of symmetrically nonequivalent lattice sites (manifested by the variations of near-neighbour distances in comparison to that of an ordered lattice) owing to the spatial distribution of incomplete lattice collapse of various degrees of the parent bcc phase. It can, therefore, be expected that the configurational entropy contributes in a major way to the Gibbs free energy of mixing in stabilising this phase at a finite temperature.