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n-Mg alloys with small additions of Cu[5] and Al-Cu-Mg (a + S) alloys microalloyed with Ag.[2] Evidence[3,4,6] suggests that the RHP is due to the formation of solute-vacancy co-clusters that act as preprecipitate strengthening agents by presenting a diffuse boundary by the pairing (or higher order combinations) of the clustered solute species. This mechanism has been termed ‘‘cluster hardening/strengthening’’ by Ringer et al.[4] and is distinct from the usual inference of the term age hardening that implies the occurrence of precipitation. Contrary to the cluster hardening mechanism, Reich et al.[7] proposed that the RHP was caused by a dislocation-locking interaction, where solutelocked dislocation loops impede the motion of moving dislocations. In this work, we seek to clarify which of these two hardening mechanisms is more likely based on measurements and calculations of the average diffusion distances traveled by the solute atoms during the early stages of age hardening. For a random walk in three dimensions, after time t, the average atom will have advanced a radial distance x from the origin: pffiffiffiffiffiffiffiffi x ¼ 6Dt ½1 where the temperature-dependent term, D, is known as the intrinsic diffusivity or diffusion coefficient with units (m2 s1).[8] It is expressed as D ¼ D0 exp

Age-hardenable aluminum alloys undergo an aging heat treatment in order to achieve desired mechanical properties by, for example, the precipitation of secondphase particles that provide resistance to dislocation motion and cause hardening. Al-Cu-Mg alloys that lie in the a + S phase field and have a medium/low Cu:Mg ratio exhibit a two-stage age-hardening response, separated by a prolonged hardness plateau, upon artificial isothermal aging between 383.15 K and 513.15 K (110 C and 240 C).[1,2] The first stage of hardening is extremely rapid and usually accounts for ~40 to 70 pct of the overall hardness increment within the first 60 seconds of aging (Figure 1), whereas the second hardness increase takes much longer, often many days, depending on the aging temperature.[3,4] This rapid hardening phenomenon (RHP) occurs in Al-1.1Cu-xMg alloys that contain at least 0.5 Mg (at. pct), but not in binary Al-Cu and Al-Mg alloys or, in general, within ternary Al-Cu-Mg alloys with phase compositions in the a + h field (high Cu:Mg ratio), even though they are all age hardenable. The RHP, however, is not completely restricted to the Al-Cu-Mg system and also occurs in

R.K.W. MARCEAU, N. TSAFNAT, D. HALEY, and S.P. RINGER are with the Australian Centre for Microscopy & Microanalysis, The University of Sydney, NSW 2006, Australia. Contact e-mail: [email protected] Manuscript submitted June 10, 2009. Article published online May 26, 2010 METALLURGICAL AND MATERIALS TRANSACTIONS A

Q RT

½2

where the pre-exponential factor D0 is a material constant, Q is the activation energy of substitutional diffusion, R is the universal gas constant (=8.3145 J/ mol K), and T is the absolute temperature in Kelvin.[8] The values for D0 and Q that were used to calculate the diff