a substitutional solid solution

This is the more intuitive of the two ways to make a solid solution. Picture a checkerboard where every square holds a red piece; now swap a few of the red pieces for blue ones, keeping them on the exact same squares. The blue pieces have substituted for red ones on the regular grid. In a substitutional solid solution the solute atoms do exactly that — they replace host atoms directly on their lattice sites, sitting where a host atom would have sat.

For this to work well, the guest atom has to be a reasonably good stand-in for the host — similar in size, structure, and chemistry. That is precisely what the Hume-Rothery rules spell out: roughly, the atomic radii must be within about 15 percent of each other, the two pure metals should share the same crystal structure, and their electronegativities and valences should be close. When all these are satisfied, as with copper and nickel (radii 0.128 and 0.125 nm, both FCC), the two elements dissolve in each other completely, across the whole range from 0 to 100 percent.

Substitutional solutions are the backbone of most engineering alloys. Brass is zinc substituting into copper; bronze is tin in copper; the nickel and chromium in stainless steel and superalloys sit substitutionally in the iron or nickel lattice. Because the substituting atom is a slightly different size, it puts a local strain field around itself, and that strain is what pins gliding dislocations and strengthens the metal — the mechanism called solid-solution strengthening.