the stacking-fault energy
Close-packed crystals are built by stacking flat layers of atoms in a repeating order — FCC follows ABCABC, HCP follows ABAB. A stacking fault is a local slip-up in that order, a place where the sequence stutters (say ABCABCACBC, with one layer out of turn). Making such a fault costs a little energy per unit of its area, because the atoms just across the fault find themselves in a slightly less comfortable neighbourhood. That cost, measured in energy per area (millijoules per square metre), is the stacking-fault energy, written gamma. It is small, but it is one of the most influential small numbers in physical metallurgy.
Why so influential? Because gamma sets how far a perfect dislocation splits into partials. The two partials repel and want to spread apart; the fault ribbon between them costs gamma per unit area and wants to shrink; the equilibrium width goes roughly as 1/gamma. So a LOW stacking-fault energy means a WIDE ribbon of dissociated partials, and a HIGH gamma means the partials huddle so close the dislocation is effectively undissociated. To picture the scale: aluminium has a high gamma near 166 mJ/m^2 (narrow ribbon), copper a moderate 45, and austenitic stainless steel or 70/30 brass a low 20 or less (wide ribbon).
From that one parameter cascades a whole deformation personality. A dissociated screw dislocation must pull its partials back together before it can cross-slip, so low-gamma metals cross-slip with great difficulty: their dislocations glide in flat planar bands, pile up, and work-harden strongly, and they readily deform by mechanical twinning or even transform to martensite (the basis of TWIP and TRIP steels). High-gamma metals cross-slip freely, tangle into three-dimensional cells, recover and creep more easily. So gamma, a subtle quantity you measure by imaging ribbon widths in a TEM or from node geometry, quietly forecasts ductility, hardening rate, and whether a metal twins.
Adding zinc to copper to make brass lowers the stacking-fault energy from copper's ~45 mJ/m^2 toward ~20 mJ/m^2. The ribbon widens (width proportional to 1/gamma), cross-slip is choked off, and the alloy work-hardens far more steeply and twins readily — which is exactly why cartridge brass is so much harder to soften by simple recovery than pure copper.
gamma (mJ/m^2) sets partial separation and hence cross-slip; low gamma means wide ribbons, strong hardening, twinning.
Do not confuse the stacking fault (the planar defect itself) with the stacking-fault energy (the cost per area of making it). The energy is what you tune with alloying, and lowering it does not weaken the metal — it usually makes it harder and more twinning-prone.