short-range order

Short-range order is the neighborhood, not the city. Even in a chaotic-looking glass or a liquid, each atom is still choosy about its immediate neighbors, how many there are and how far away they sit. Short-range order is this local regularity: a well-defined arrangement of an atom's nearest (and maybe next-nearest) neighbors, even when there is no repeating pattern over long distances.

Concretely, atoms are not point particles that can overlap; each has a size and prefers certain bond lengths and angles, so its first shell of neighbors sits at a fairly definite distance. In silica glass every silicon is surrounded by four oxygens in a tetrahedron, with a silicon-oxygen distance of about 1.6 angstrom, sharp short-range order, even though a few atoms out the network wanders and never repeats. We measure this with the radial distribution function (RDF), which shows a sharp first peak (well-defined nearest neighbors) that blurs out at larger distances.

Short-range order is why amorphous does not mean random. It explains why glasses have definite densities and specific chemistry, and why liquids and glasses still diffract (into broad halos, positioned by the nearest-neighbor distance). Between pure short-range and full long-range order lies medium-range order, partial organization over a few nanometers, which is important in real glasses. Caveat: short-range order alone cannot give sharp diffraction spots; only long-range order does that.