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Thermodynamics
Published in Harshad K. D. H. Bhadeshia, Theory of Transformations in Steels, 2021
For an ideal solution, the entropy of mixing is given by Equation 2.33 with mB=mA=1. There is no enthalpy of mixing since there is no change in energy when bonds between like atoms are broken to create those between unlike atoms. This is why the atoms are randomly distributed in the solution. The molar free energy of mixing is therefore: ΔGM=NakT[(1−x)ln{1−x}+xln{x}].
Solid Solutions
Published in Bankim Chandra Ray, Rajesh Kumar Prusty, Deepak Nayak, Phase Transformations and Heat Treatments of Steels, 2020
Bankim Chandra Ray, Rajesh Kumar Prusty, Deepak Nayak
Enthalpy is the measure of the heat/internal energy change during any reaction/solution/transformation. In case of a solid solution, there may be release of heat or absorption of heat or no change in heat due to the mixing process. For an ideal solution, the net change in enthalpy should be 0, i.e., ΔHmix = 0. However for nonideal solutions, (i) ΔHmix<0, which indicates an exothermic reaction or heat is evolved during the reaction, or (ii) ΔHmix>0, which indicates an endothermic reaction or heat is absorbed during the reaction. Enthalpy of mixing depends on the likeliness of an atom toward similar kind of atoms or dissimilar atoms. In an alloy system of A and B, there may exist three different kinds of bonds, A–A, B–B, and A–B as shown in Figure 4.2.
Alloy thermodynamics and phase diagrams
Published in Gregory N. Haidemenopoulos, Physical Metallurgy, 2018
Case 1: HAB<HAA+HBB2 or Ω < 0. In this case the A − B bonds are more preferable than the A − A or B − B bonds, since the energy of the A − B bond is lower than the mean energy of the A − A and B − B bonds, favoring the formation of a solid solution. The enthalpy of mixing (excess term) is negative. The ⋄Hm curve is parabolic due to the XAXB term. The ⋄Hm, ⋄Sm and ⋄Gm curves are shown in Figure 4.5a for a certain temperature. The free energy of mixing ⋄Gm is negative for all compositions and mixing is therefore thermodynamically feasible. The solid solution exhibits complete solid solubility at this temperature.
Design of a nickel–cobalt based eutectic high entropy alloy (NiCo)1.7AlCrFe with hierarchical microstructural length scales
Published in Philosophical Magazine, 2023
R.J. Vikram, Khushbu Dash, Shanmukha Kiran Aramanda, Satyam Suwas
When the enthalpy of mixing (ΔHmix, a negative interaction parameter) is low, and the atomic size difference is small, single-phase solid solutions are preferred (low misfit). Specifically, for single-phase solid solution, the formation energy and size difference lies in the range of −15 kJ/mol < ΔHmix < 5 kJ/mol and 0 < δ < 5, respectively [19]. If the atoms in the constituents start repelling each other, it represents a positive interaction parameter, which can widen the miscibility gap in the phase diagram even further. During casting, if δ>8 and ΔHmix < −15 kJ, HEAs can form metallic glass, as stated by Inoue [20]. As a result, the two-parameter (ΔHmix vs. δ) approach, as shown in Tables 2 and 3, provides a deeper understanding of alloy design than the one-parameter (ΔSmix) approach. Guo et al. [9] also introduced the concept of the VEC parameter, which extends the Hume-Rothery rule applied to a multi-component system. Table 3 lists the critical parameters of HEA alloy design for the present study. The abbreviation ri, rj, ci, cj stands for the atomic radius and concentration of ith and jth element in the alloy system.