the ASTM grain-size number
The ASTM grain-size number is a single tidy number, usually written G, that captures how fine or coarse a metal's grains are. Fine grains get a big G, coarse grains a small G. It is a way to turn 'the grains look pretty small' into a repeatable value that two labs on opposite sides of the world will agree on.
The definition is N = 2^(G-1), where N is the number of grains you count per square inch when you look at the polished, etched surface at 100x magnification. So G = 1 means 1 grain per square inch at 100x; G = 8 means 2^7 = 128; each step up in G doubles the grain count and shrinks the grains. Because the relation is a power of two, a small change in G is a big change in grain size — going from G = 5 to G = 8 packs eight times as many grains into the same area.
Grain size is one of the few structural knobs that raises strength AND toughness together at room temperature: by the Hall-Petch relationship, finer grains (higher G) give higher yield strength because grain boundaries block dislocations. So a spec sheet demanding 'ASTM grain size 7 or finer' is really demanding a minimum strength and a clean, controlled heat treatment. The honest caveat: fine grains help at room temperature but HURT at high temperature, where grain boundaries slide and creep — turbine blades go the opposite way, toward huge grains or single crystals.
A micrograph at 100x shows about 64 grains per square inch. Solving 64 = 2^(G-1) gives G-1 = 6, so G = 7 — a moderately fine grain that meets a typical 'ASTM 5 or finer' requirement.
N = 2^(G-1) grains per square inch at 100x: each step up in G doubles the count.
A higher G (finer grain) means higher room-temperature strength via Hall-Petch — but the same fine grain is a liability at high temperature, where grain-boundary sliding drives creep. There is no single 'best' grain size, only the best for the service temperature.