Precipitation hardening, in which small particles inhibit the movement of dislocations to strengthen a metal, has long been used to improve mechanical strength, especially of aluminum alloys. The small size of precipitates and the many possible variants of the orientation relation have made their structural determination difficult. Small precipitates in commercial aluminum-magnesium-silicon alloys play a crucial role in increasing the mechanical strength of these alloys. The composition and structure of the P" phase in an aluminum-magnesium-silicon alloy, which occur as precipitates (typically 4 nanometers by 4 nanometers by 50 nanometers) and are associated with a particularly strong increase in mechanical strength, were determined. Element analysis indicates that the composition is Mg,Si ,.A rough structure model was obtained from exit waves reconstructed from high-resolution electron microscopy images. The structure was refined with electron nanodiffraction data (overall Rvalue of 3.1 percent) with the use of a recently developed least squares refinement procedure in which dynamic diffraction is fully taken into account. P u r e metals are in general rather soft. For L Z example, A1 and Fe have a strength of 40 to 70 MPa, depending o n grain size, stress level (which reflects, among other things, the dislocation densitv), and solutes in the , , , matrix, whereas tool steel has a strength of 800 to 1400 MPa. For common a o~l i c ations, most pure metals are too soft, and for many centuries research has been focused o n methods to increase the strength of metals. T h e methods used to obtain this result can be divided into a few groups, including cold working, solid solution hardening, and precipitation hardening. Cold working and solid solution harden--ing have been used since ancient times. Research o n precipitation hardening started at the beginning of this century with the discovery of Al-Cu alloys and Wilm's research (1) o n the strength of A1-Mg alloys. With precipitation hardening, small amounts of other elements are added that form precipitates during a specified temperature cycle. Commonly used precipitationhardened A1 alloys are the binary systems with C u and Ag and the ternary systems H W Zandbergen is at the National with Mg and Zn (Al-Mg-Zn) and with Mg and Si (Al-Mg-Si). Typically, the alloying agents are present at roughly 0.5 weight %.The common procedure is to bring the allov to a high temoerature so as to dissolve all of the addedYeleme'nts, after which it is cooled quickly to room temperature, thus forming a supersaturated solid solution. When kept at a reasonably low temperature (typically 150' to 250°C for the A1 alloys), the materials increase in strength because of oreci~itation -. L from a supersaturated solid solution. In the case of the Al-Si-Mg alloy, precipitation hardening can triple or quadruple the strength.The strength-time curve shows a maximum at some aging time. Usually, the materials are just slightly underaged, which means that aging (precipitation hardening) is stopped jus...