10/2/2023 0 Comments Entropy of mixing![]() 22 experimentally showed that the configurational entropy may not be enough to explain the stability of NiCrCoMnFe HEAs. 22, 23, 24 For example, using the Hume–Rothery rules as a guide, Otto et al. However, more recently, it has been shown that the contributions of configurational entropy might only be a part of a bigger picture, and it may not be the only quantity to be considered while explaining the stability of HEAs. 16, 21 It has been argued that increasing the number of elements significantly increases the configurational entropy, and leads to phase stability. High Δ S conf has been perceived to be the main reason for the stability of a single phase solid solution in HEAs. Thus, due to a shallow Δ H mix and an unusually high Δ S conf, the magnitude of entropy contributions can be potentially equal to that of enthalpy in HEAs, thereby making entropy an equally important thermodynamic quantity in phase stability. In addition, due to the random distribution of multiple elements, the configurational entropy (Δ S conf) is higher in HEAs than in the ordered alloys, which further contributes to the HEA phase stability. The shallow Δ H mix in HEAs is in contrast to a deep Δ H mix in the ordered alloys or intermetallics. 16, 18 The stability of a single-phase HEA is due to a relatively shallow negative Δ H mix 19, 20 among the constituting elements which prevents phase separation and formation of a second sub-phase. Despite the random distribution of atoms, HEAs are structurally ordered forming simple face centered cubic (fcc) and body centered cubic (bcc) crystal structures. HEAs are materials that contain random distribution of multiple elements, conventionally five or more, in approximately equal concentrations in a single-phase solid solution. However, in the past decade, with the development of high entropy alloys (HEAs), 16, 17 it is gradually becoming evident that Δ S mix might be equally important in the phase stability predictions. 3, 4, 10, 11, 12, 13, 14, 15 The contribution of Δ S mix has often been considered less important, largely due to its relatively smaller size compared to Δ H mix, particularly in the prediction of ordered structures. In the same vein, Δ S mix contributions have also been included in the calculations, albeit selectively including Δ S mix has shown to improve the accuracy of the predicted thermodynamic quantities, such as the order–disorder phase transformation temperature and miscibility gap temperature. 1, 2, 3, 4, 5, 6, 7, 8, 9 These methods have relied on analyzing Δ H mix in identifying stable metal alloys. ![]() Theoretical advancements in alloy theory over the past three decades have enabled computational prediction of correct ordered phases and ground-state crystal structures. Conventionally, Δ H mix has been perceived as the dominant quantity, where a strongly negative Δ H mix indicates formation of a stable solid solution and a positive Δ H mix indicates unmixing. The phase stability of an alloy is guided by Gibbs free energy (Δ G mix) that comprises of enthalpy (Δ H mix) and entropy (Δ S mix) of mixing. We suggest that including entropic contributions are critical in the development of theoretical framework for the computational prediction of stable, single-phase high entropy alloys that have shallow mixing enthalpies, unlike ordered intermetallics. As a result, even those systems that have negative mixing enthalpy can show phase instability, revealed as a miscibility gap conversely, systems with positive mixing enthalpy can be phase stable due to entropic contributions. The configurational and vibrational entropies can either destabilize or can collectively contribute to stabilize the solid solutions. We show that the contribution of electronic entropy is very small compared to the vibrational and configurational entropies, and does not play a significant role in the phase stability of alloys. In the overall vision of designing high entropy alloys, in this work, using density functional theory calculations, we elucidate the contributions of various entropies, i.e., vibrational, electronic and configurational towards the phase stability of binary alloys. As a result, the phase stability of these alloys is equally dependent on enthalpy and entropy of mixing and understanding the individual contribution of thermodynamic properties is critical. These alloys generally have shallow enthalpy of mixing which makes the entropy contributions of similar magnitude. High entropy alloys contain multiple elements in large proportions that make them prone to phase separation.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |