Question

A eutectic systemis a mixture of substances which has a lower melting point than any of it's components. For example salt to melt ice. Also, a eutectic has the right mixture of components so that it freezes all at once (the liquidus and solidus temperatures are the same). It seems that the eutectic effect generally grows stronger when we mix three components instead of two. For example in a magma chamber. If we blend more and more components, how much further can we take this effect? Could we have room temperature inorganic halide salts? An alloy with over a dozen metals liquid below -100C? This is a quite broad question, and I will try to keep at a reasonably high level. Undoubtedly there are specific systems (more below) that will have unusual features that differ from this outline. Lets look solely at the liquid phases of mixtures. To zeroth order, one treats a random (unordered) phase as an ideal gas - no atom-to-atom interaction (attractive or repulsive) contributing to the enthalpy, and the entropy comes from random mixing of the A and B atoms. This entropy term ends up being -RT(xAlnxA+xBlnxB) with xA+xB=1and is a maximum when xA=xB=1/2. The first order treatment of solutions adds an enthalpy of mixing term Ω, the heat of mixing. This comes from considering the energetics of A-A, B-B, and A-B interactions. So, the adjustment to the enthalpy takes on the form ΔHmix=xAxBΩ If the A-B interactions are stronger than the A-A and B-B interactions, the heat of mixing is negative and eutectic may form. A positive heat of mixing leads to miscibility gaps. Again, the enthalpy of mixing takes on a maximum atxA=xB=1/2for a regular solution, being0.25Ω. Now, real alloys tend to be non-ideal and non-regular, but lets stay up at 30,000 feet for now. An extension of the entropy of mixing to ternary solutions is straightforward, looking like -RT(xAlnxA+xBlnxB+xClnxC) withxA+xB+xC=1, and is a maximum when all compositions are1/3. The enthalpy term gets a bit trickier, since you have to consider A-A, B-B, C-C, A-B, A-C, B-C, as well as A-B-C interactions. So one can write: ΔHmix=xAxBΩAB+xAxCΩAC+xBxCΩBC+xAxBxCΩABC As you add more components to the mixture, you need to add more interaction terms. OK, where are we now? First, the entropy term increases (is increasing negative) as the number of components in the solution increases. For 2 components, the natural log terms come to−0.69, for a ternary it is−1.09, and for 10 components in equal proportions it is−2.30. Not too surprising, the more components the higher the possible entropy. On the enthalpy side, things look pretty good as well initially. Lets ignore the ternary interaction terms like ΩABC. Still one is left with more interaction terms that could add up to something. If ΩAB=ΩAC=ΩBC(and all are negative) then the enthalpy of mixing is 13Ω, which is larger than the enthalpy of mixing of the binary solution. As the number of components increases, one goes from0.25for a binary to0.33for a ternary to0.45for a 10-component system. Wow, we win on both counts! Well, except that it would be highly unlikely that ΩAB=ΩAC=ΩBC(and even less likely as the number of components increases). If the A-B term is more negative than A-C or B-C, then the lowest enthalpy of mixing is found away from the equal 1/3 compositions, so the entropy term is no longer minimized. If the D-E term in a 5-component system is highly positive, that skews things even worse. As one example, lets look a bit at the Galinstan alloy mentioned in comments. In the Ga-In system, modeling (Ch. Li et al, J. Phase Equilibria 21(4) 357 (2000)) indicates that the enthalpy of mixing term is actually positive - the Ga-In (small) eutectic is driven mainly by the entropy term. For Ga-Sn (Bhupendra Kumar et al., Metals 2021 (11) 1363), the mixing term is also positive. Again, the small eutectic is from the entropy. For In-Sn (X.J. Liu et al., J. Electronic Materials 30(9) 1093 (2001)), the enthalpy term is indeed negative, but fairly small. Why does Galinstan melt so low? Well, it is mostly gallium so melts pretty low already, the Ga-In and Ga-Sn eutectics are way over by Ga to begin with, so a bit of both helps add more entropy, and the In-Sn negative enthalpy of mixing adds to that effect. Could there be better systems? Perhaps, but all the stars have to align with respect to the enthalpy of mixing terms. Added mostly as a comment, but a paper hot off the press (Journal of Phase Equilibria and Diffusion) might be interesting. The point is to try and use the Calphad method to rapidly find possible eutectic points in a quaternary system. To quote the abstract: In

multicomponent systems, finding eutectic points can be
challenging due to the complexity of the systems...

Answer 1

The melting point is when solid and liquid phases of a substance are in equilibrium, and preventing heat exchange maintains this equilibrium. Solutions form through solvation, with enthalpy and increased entropy (ΔS > 0) favoring dissolution.

Step-by-step explanation:

The melting point of a substance is the temperature at which its solid and liquid phases are in equilibrium. If we prevent heat from entering or escaping a melting mixture, the solid and liquid will remain in equilibrium, as seen in a mixture of ice and water in a thermos.

Similarly, a solution is a physical process where one substance, the solute, dissolves into another, the solvent, forming a homogenous mixture. Solvation, or hydration when water is the solvent, involves solute particles being surrounded by solvent molecules. The process is accompanied by an overall enthalpy change, ΔHsoln, and an increase in entropy, which measures the system's disorder and favors dissolution.

The addition of more components into a mixture increases its entropy, as more different particle types result in more orientations, interactions, and microstates. The entropy is greater for mixtures than for pure substances, and when solids dissolve in liquids, dissolving typically results in increased entropy.

The dissolution process often involves an increase in entropy (ΔS > 0) and can be affected by the enthalpy change, which can be exothermic (ΔH < 0) or endothermic based on the nature of solute-solvent interactions.