Entropies in Alloy Design for High-Entropy and Bulk Glassy Alloys

Abstract

High-entropy (H-E) alloys, bulk metallic glasses (BMGs) and high-entropy BMGs (HE-BMGs) were statistically analyzed with the help of a database of ternary amorphous alloys. Thermodynamic quantities corresponding to heat of mixing and atomic size differences were calculated as a function of composition of the multicomponent alloys. Actual calculations were performed for configurational entropy (S config. ) in defining the H-E alloys and mismatch entropy (S  ) normalized with Boltzmann constant (k B ), together with mixing enthalpy (H mix ) based on Miedema's empirical model and Delta parameter () as a corresponding parameter to S  /k B . The comparison between H mix - and H mix -σ B S k diagrams for the ternary amorphous alloys revealed S  /k B ~ ( /22) 2 . The zones S, S′ and B's where H-E alloys with disordered solid solutions, ordered alloys and BMGs are plotted in the H mix - diagram are correlated with the areas in the H mix -S  /k B diagram. The results provide mutual understandings among H-E alloys, BMGs and HE-BMGs.

High-entropy alloys: a critical assessment of their founding principles and future prospects

“…A common approach has been to utilise the empirical rules of Hume-Rothery 144,145 and/or accessible thermodynamic quantities to form parametric criteria for the stability of HEA solid solutions, which are fitted to experimental results. 152,159,163,173,[203][204][205]207,[252][253][254][255][256][257][258][259][260][261][262][263][264][265][266][267] These phase-selection rules for as-cast HEAs were recently reviewed by Wang et al 258 and Guo, 208 and are discussed briefly here.…”

An Insight into Evolution of Light Weight High Entropy Alloys: A Review

“…Some thermodynamic parameters have been used to define the conditions for the formation of BMG or a solid solution in multicomponent alloys such as ∆H mix , ∆S mix and topological parameters like δ [35,36]. Zhang et al [36] have shown that simple solid solutions will form in alloys if −20 ≤ ∆H mix ≤ 5 kJ/mol, 12 ≤ ∆S mix ≤ 17.5 J/K mol, and δ ≤ 6.4%.…”

“…For the considered example, a regular solid solution model has been considered to simplify the calculation for free energy of multi-component HEAs. Therefore, enthalpy of mixing for Al 35 Li 20 Mg 35 Ti 5 Zn 5 alloy with five elements can be determined from Equation (7):…”

“…In such condition, besides just theoretical modeling [35,38,[52][53][54], computational approaches, such as density functional theory (DFT) calculations [55] and ab initio molecular dynamics (AIMD) [56] simulations, can also be used to study phase formation in HEAs. Due to the significant cost and computational time required based on the current technology and among other limitations [17], these approaches are not feasible for designing of HEAs.…”

Alloy Designs of High-Entropy Crystalline and Bulk Glassy Alloys by Evaluating Mixing Enthalpy and Delta Parameter for Quinary to Decimal Equi-Atomic Alloys

“…HE-BMGs are considerably different from conventional H-E alloys in points that former three alloys have larger and negative ¦H mix and larger ¤ values than the latter alloys in zone S. This is due to the facts that the Al 0. 22) with the help of the plots of 6150 ternary amorphous alloys in the ¦H mix ¤ diagram. The statistical analysis revealed that the Al 0.5 TiZrPdCuNi H-E alloy has a set of ¦H mix and ¤ values where the amorphous alloys are less formed in the ¦H mix ¤ diagram, which is similar to zone S for H-E alloys Fig.…”