![]() ![]() ![]() As the metal to non-metal ratio is varied in the discussion pertaining to Fig. The contribution to the configurational entropy term stems from the metal sublattice only as the contribution from the non-metal sublattice is zero for all here considered examples. In the following discussion, only compounds with five equimolar metallic components in addition to only one non-metal component are considered. All of the aforementioned ceramic compounds, namely, MN, MO 2, and M 2B 14, can be viewed as an assemblage of metal and non-metal sublattices. 20 for the calculation of the mixing entropy -per formula unit-any of the above-mentioned ceramic compounds containing five different metals would result in a mixing entropy of 1.61 R as indicated by the red line in Fig. Let us consider the magnitude of the configurational entropy of ceramic compounds with different metal to non-metal rations, namely, metal nitrides with the stoichiometry MN, metal oxides with the stoichiometry MO 2, and metal borides with the stoichiometry of M 2B 14. (7) is employed to calculate a five component, equimolar alloy, then the molar configurational entropy is 1.61 R. This includes the treatment of material systems with sublattices-for example, intermetallics-which can be described based on the compound energy formalism as proposed by Hillert in 2001. These excess terms enable often a reasonable approximation by correcting the incorrect ideal solution description in the configurational entropy term. Tomlin and Kaloshkin 18 stated as “… in real practically important metallic systems, strong interactions between components always win the battle with chaos, decreasing entropy.” I concur with this assessment and want to add that in CALPHAD modelling, the influence of these strong interactions is contained in the excess terms of Gibbs energy and/or enthalpy and/or entropy. (6) results in a correct assessment of the configurational entropy. Hence, ideal solutions-even in metallic systems-are the exception to the rule, 18 and only for these exceptions to the rule, Eq. 17 Miracle and Senkov 7 argue convincingly that the fraction of ideal solutions obtained in the solid state will be even smaller than 4%. Miracle and Senkov 7 cite an investigation of the mixing enthalpies by Takeuchi and Inoue of 1176 binary liquid solutions, where only 4% of the probed binary metallic systems fulfill the requirements of ideal solutions. In an ideal solid state mixture of A–B, the probabilities of populating a certain lattice site is equal for A and B, and hence, substituting Eq. (6) is only valid for purely random mixing scenarios. It must be kept in mind that this is for the case, where there is no energetically favored bond between or among the particles of the system.” 16 Gaskell underlines with this statement that Eq. Gaskell states in the chapter “The statistical interpretation of entropy” on page 101 “The increase in entropy of the system arises from the increase in configurational entropy. Equation (6) is utilized to describe the mixture of ideal gases 15-the textbook scenario for an ideal mixture-and by Gaskell and Laughlin 16 to introduce ideal solutions in the solid state. In an ideal solution, the mixing enthalpy is per definition zero. In chemical thermodynamics, such mixing scenarios are referred to as ideal solutions. (3), only purely random mixing scenarios can be described. 9 At this point, it is evident that with w, as defined in Eq. This equation was utilized by Yeh 9 to compute the change in molar configurational entropy of HEAs and to define HEAs in terms of a critical-or threshold-entropy value. ![]()
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