Melting point-general chemistry
This is discussed pretty thoroughly in materials engineering textbooks when melting and freezing of (mostly) metals in general is considered. A good reference is Gaskell’s “Introduction to thermodynamics of materials”. But you will find helpful explnations to fill in the gaps of what uou know by reading up on undercooling in Wikipedia etc. Feezing and melting are related.

And if you read my answer to highest melting point materials, I mention some related issues. 

One issue is that you cannot consider materials as “pure” or “impure”: a pure material of any amount large enough to test is in practice almost impossible to make. In fact any real world material is impure once you consider a large enough scale: which is on the order of anything bigger than (say) millions of atoms. You cannot actually make a “pure” material of appreciable size, but can only approach it once you get larger than a relatively small size of sample. In addition, a lot of materials have only been made as thin coatings, or as individual small crystals. And their behaviour is not the same as larger amounts of what you might think is the same material. A single crystal behaves very differently from a polycrystalline mass, and the surface of any material is very different from its interior, so a thin film is dominated by surface effects, as are very fine particles. 

So you are looking at degrees of impurity, in terms of orders of magnitude. And the general effect of purity level is not linear but more like exponential in terms of its effect on material behaviour.

A related concept is to look at the theoretical strength of a material. From a theoretical point, a pure and defect free material would be incredibly strong, but in practice this is impossible to achieve, you can only approach it.