to get a little further into the weeds on that one, there are really two definitions of eutectic. the first is theoretical, and has to do with the physical chemistry of an ideal piece of bulk material in an ideal environment. the second is empirical, and like most things, reifies the theoretical assumptions and finds that life is just more complicated than those scientist pinheads could possibly imagine.
FIRST: the ideal theoretical definition
let us consider a single "grain" of the material in a vacuum with an instantaneous and perfect model of the effects of power exerted on the bulk material.
let's go over that sentence again. by "a single grain of material", i mean that the bulk material (imagine a block of solder) is a single continuous uninterrupted lattice (linear algebraic and not abstract algebraic) of the component molecules of the alloy. for simplicity, let's just imagine a single cube where each edge of the cube is a bond between constituent molecules.
now let's put that cube of metal in space. ta-da! it's in space.
ok, by ideal model of power, what i mean is that, when you use energy to heat the block of metal, every part of the block is always at the same temperature. (more clearly, the entropy of each constituent structure is equal at all times). if you heat any bit, you heat all the bits and v.v.
so with many unrealistic assumptions established, we define a eutectic substance to be one for which that single piece of material of ours releases all its bonds at exactly the same time when it reaches the single "melting temperature". so our lead/tin alloy, for example, goes from being a block of lead/tin hybrid material to a pot of lead and tin liquids floating around the instant it hits its melting temperature.
THE SECOND: empirical definition
in practice, we just want to know if the alloy is _indistinguishable_ from an alloy that is eutectic. that is, can we, with the best of our current technology, measure the difference in melting points of the constituent parts of the alloy?
to see why this is a tricky and important distinction, let's step back for a second and look at this block of material again and start blowing away our theoretical assumptions. first, in practice a single piece of bulk material is effectively NEVER a single "grain" of uninterrupted structure. in fact, that is the the crux of material science. if all materials just kind of formed their perfect ideal shapes when you shoved all the atoms together, we wouldn't need all these fancy carbon fibers, fiber fibers, silk fibers, and super comfortable fleec... ok, sorry, it's cold here.
anyway, so in actuality, if you take an imaging device like an "x-ray" imager and shoot a bunch of high energy high frequency little energy thingamabobs at a piece of steel, what you're actually going to see is a random pattern of solid material that looks well structured, and between these will be some form of misshapen solid and finally, there will be bits of "void", that is, empty space. so you can just cross this assumption off the list with prejudice.
next, energy takes time to do work, and hence, material properties like temperature take time to propagate through a piece of bulk solid. in fact, it's a double whammy, since we learned above that the solid isn't even a completely uniform solid! so the energy expended is doing more work in the solid regions and less work in the voided regions. oof!
finally, we're not in space (but i wish we were
), so there will be the competing effects of atmospheric gases cooling the outside of the material, the potential for things like gas and water to have gotten into the material lattices and be filling the voids, etc.
SO, in practice, the useful measure of whether a material is eutectic or not is whether we can successfully observe a point in the material's phase change behavior in which we see liquidus of one constituent of the alloy but solidus of another. we can look at this behavior using a few tools. one is called a differential scanning calorimeter. another neat one is called electron energy loss or energy-dispersive spectroscopy (two closely related methods actually). the way to think about all of these is that you're looking for the number of atomic units of each constituent metal of the alloy at every step of the phase change. a perfect eutectic material will always measure out to the constituent ratios of the alloy at all points in the melting process. however, there is wiggle room in our ability to measure, which is reflected in the word "always". replace "always" with "as quickly as we can measure it", and you have a good empirical definition.
basically, if we can't identify a point at which we have more of one constituent metal melted than the others, we empirically say that the material is euctetic.
OK, out of the weeds! aren't you happy?
there are a number of effective eutectic and actually eutectic tin alloys out there, but they generally have high silver content, which makes them significantly more expensive. they also have issues with material creep over time due to mechanical disruption, and some other stuff. however, as a hobbyist, there really isn't any reason to forgo the lead in your solder. you're making a handful of parts, not shipping millions of parts around the world. use the easiest/cheapest and most practical solder possible. that happens to be 63/37 sn/pb. it's theoretically and practically eutectic, has a low, safer melting point, and is pretty darned cheap. the result is workhorse solder that's easy to work with and builds one's confidence.
and that's how a lot of science turns into a gut decision about money.
