Every article or text I've read on crystallization states that it works by taking advantage primarily of differences in solubilities, but I've also been told that it can purify compounds with equivalent solubilities if one is present in a greater quantity.
For instance, if there is a solution of 90% Compound A, and 10% Compound B, both with equal solubilities, a crystallization would supposedly purify it. But how? I've been told that, if say, 20% of the product was left behind in the solution, then it would consist of equal ratio of Compound A and Compound B, causing the formed crystals to be almost pure Compound A (saying a 1:1 ratio of A:B gets left behind). I was told that this ratio that gets left behind in the solution depends on the relative solubilities of the compounds, and not the quantity that which they were present.
Is this accurate? How does this work exactly? I've read dozens of articles on crystallization and none of them seem to explain this sort of instance well, yet it seems very widely used in preparative chemistry.