You are correct with your scepticism about the sometimes observed confusion between these terms in the context of HEAs and MEAs.

In metallurgy and generally in materials science, the stability of solid metallic solutions is governed by a complex interplay of thermodynamic factors when in equilibrium. Two key concepts in this context are configurational entropy (mixing entropy) and Gibbs free energy, which both indeed play crucial roles in stabilizing metallic solutions.

The configurational entropy, or mixing entropy, refers to the entropy change associated with the random arrangement of different atomic species in a solution, as described the partition function (Zustandssumme), i.e. the total multitude of states the atoms can be placed relative to each other. More of these possible arrangement lead to high mixing entropy. Essentially, this term thus quantifies the positional disorder introduced when different elements are mixed together in an alloy. For instance, in a binary alloy system with two elements, the configurational entropy increases as the atoms of these elements are mixed more randomly. The greater the randomness or disorder, the higher the entropy. This concept is indeed particularly significant in the formation of massive solid solutions high-entropy alloys (HEAs and MEAs), which are characterized by having multiple principal elements mixed in nearly equal proportions (in its original definition, which however is not always pertinent), resulting in an assumed high configurational entropy.

In stark contrast the term Gibbs free energy is a thermodynamic potential form that measures the maximum reversible work a system can perform at constant temperature and pressure. It serves as a comprehensive indicator of a system's stability, where a process or reaction is spontaneous if it leads to a decrease in Gibbs free energy. In metallic solutions, the free energy of mixing combines contributions from both enthalpy AND entropy to determine the overall stability of a material (i.e. it is inded NOT the entropy but Delta G that matters). The interplay between these factors dictates whether the alloy will form a stable solution or separate into different phases.

The stability of solid metallic solutions thus hinges ONLY on minimizing Gibbs free energy (all in equilibrium of course). High configurational entropy is only one of the factors that can promote stability by increasing the disorder within the alloy, thereby reducing the free energy. This reduction is crucial for maintaining a stable solution, especially in alloys with multiple elements. However, the enthalpy of mixing also plays a significant role as you correctly elude to. The enthalpy of mixing is the heat absorbed or released when different atoms mix (related to their bond strength). If the interactions between unlike atoms (those of different elements) are more favorable than those between like atoms (those of the same element), the enthalpy of mixing is negative, further stabilizing the solution by lowering Gibbs free energy. Conversely, if the interactions between unlike atoms are less favorable, the enthalpy of mixing is positive, potentially destabilizing the solution by increasing Gibbs free energy.

You are therefore indeed correct that enthalpy contributions also significantly affect the phase behavior and stability of metallic alloys. Depending on whether the enthalpy of mixing is positive or negative, various scenarios can arise. If the enthalpy of mixing is negative and sufficiently large, the alloy forms a completely miscible solid solution across all compositions, as the attractive interactions between different atoms dominate. A small positive enthalpy of mixing can result in partial solubility, where the alloy exhibits miscibility gaps, leading to phase separation at certain compositions and temperatures. A large positive enthalpy of mixing leads to immiscibility, causing the elements to segregate and form distinct phases rather than a solid solution. Additionally, alloys can exhibit ordered structures at lower temperatures and disordered solid solutions at higher temperatures. This transition is driven by the competition between the enthalpic preference for ordering and the entropic gain from disordering.

It must also be noted (and s sometimes overlooked in this field) that - apart from configurational entropy terms - also other types of entropy can influence the stability of metallic solutions. Vibrational entropy, associated with atomic vibrations in the lattice (use e g Debye theory), increases with temperature and can affect phase stability. High vibrational entropy can stabilize certain phases at elevated temperatures. Electronic entropy arises from the distribution of electrons among energy levels. It is generally small compared to configurational and vibrational entropy but can be significant in materials with complex electronic structures. Magnetic entropy, relevant in alloys with magnetic elements, is related to the alignment of magnetic moments and can influence phase stability, particularly in magnetic transitions.

The stability of solid metallic solutions thus indeed results from the intricate balance between configurational entropy and Gibbs free energy, with significant contributions from enthalpy and other forms of entropy. High configurational entropy favors stability by increasing disorder and lowering free energy. The enthalpy of mixing, depending on its sign and magnitude, can either promote or hinder the formation of stable solutions. A thorough understanding of these thermodynamic principles is essential for designing advanced materials with desired properties and stability.

I attach some papers where I also tried to disentangle these contributions a bit, trying to show that the design of HEAs (and related) is indeed NOT a single facetted (mixing entropy-focussed) thermodynamic task.

Good luck!

Yes! it is possible to develop a purely simple solid solution with high entropy. Based on the second law of thermodynamics, high mixing entropy usaually promote elements random distribution. However, when the system exists mixing heat (mixing enthalpy not zero), the biased interaction among the alloying elements can be introduced, thus, exhibing mixing enthalpy drive phase formation mechanisms. As a result, the local chemical ordering or chemical fluctuation formed. That is to say, mixing enthalpy is a key indicator for quantifying the chemical affinity among atoms. An ideal random solid solution can be achieved when the mixing enthalpy is nearly zero. With the decrease in mixing enthalpy (negative mixing enthalpy), by adding negative mixing enthalpy elements, the alloy system is expected to exhibit more chemical affinity heterogeneities, such as chemical affinity fluctuation, short-range order, medium-range order and others. As a result, the ideal solution (near zero enthalpies) is broken and forming a regular solution.

Recently studies show that with the decrease of mixing enthalpy, the degree of local chemical ordering can be enhanced, forming the negative mixing enthalpy solid solution. As thus, compared with ideal solid solution (near zero enthalpies), multi-level chemical affinity heterostructure, such as local chemical fluctuation, and short/medium-range ordering, can be induced in mixing enthalpy solid solution alloys, endowing their high strength like to intermetallic compounds and high ductility akin to solid solution. Therefore, it could possibly open a research field of negative-enthalpy solid solutions with improved strength and ductility

Some papers are attached.

Good luck