Second the mechanism has implications for solute drag creep at higher

Second the mechanism has implications for solute drag

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Second, the mechanism has implications for solute-drag creep at higher temperatures and low stresses. Third, the mechanism can be included in 3D discrete dislocation simulations that include dislocation junction creation and annihilation, bowing, forest hardening and pile-ups 27–30 . In summary, the cross-core model provides a physical justification of a widely used phenomenological model for DSA, shows that the DSA behaviour depends on only a limited number of fundamental material parameters and makes accurate predictions for the strength and strain-rate parameters in application to Al–Mg. All of the key material parameters can be computed with higher fidelity via quantum-mechanical calculations of solute–dislocation configurations. The present model and methods therefore provide the framework within which first-principles data for Al or other face-centred-cubic metal alloys containing a range of elemental solute additions can be used to predict dynamic strain ageing phenomena. METHODS We study Al alloyed with Mg as a substitutional solute using well calibrated embedded-atom-method potentials for the Al, Mg and Al/Mg interactions 31–33 . We model a straight edge dislocation with line direction along ˆ z and b = 2 . 85 ˚ A along ˆ x , as in previous analyses 1,3–16,22,23 , in a simulation cell of size X = 114 ˚ A, Y = 91 . 8 ˚ A, Z = ξ = 113 . 4 ˚ A that is periodic in X and Z (refs 26,34). This dislocation disassociates approximately into two partial dislocations, separated by a stacking fault of width 15 ˚ A. This width is slightly larger than expected in real Al, but scales out of the calculations of strengthening. The width is independent of Mg concentration in the core in the concentration range relevant here ( < 10%; ref. 26). We appropriately choose the segment length, important for total energies, as ξ ( Adb 3 / 2 / Wc 1 / 2 0 ) 2 / 3 , where A is the line tension and d 10–20 ˚ A is an e ff ective range of dislocation/solute interactions; segments smaller than ξ remain straight 35,36 . We computed our Mg migration enthalpies using the ridge–saddle method 37 . These calculations and those in ref. 19 include full relaxation of the simulation cell during the search for the transition state. We carried out the kMC simulations as follows. In a simulation cell containing an initial random distribution of c 0 = 5 at.% Mg atoms, we place the dislocation at a location denoted x = 0, where Mg concentration fluctuations pin the dislocation with initial strengths in the range τ s0 45–90 MPa (ref. 26). We apply a small initial stress of τ 0 = 15 MPa. We then model di ff usion of Mg atoms by a vacancy mechanism, by successive exchanges of Mg with neighbouring Al atoms, following the standard kMC methodology 38 . Because only very few site-to-site cross-core activation enthalpies have been computed previously and obtaining them all is a daunting task, and to illustrate the e ff ects of both cross-core di ff usion and the traditional bulk solute di ff usion within one simulation, we use the bulk activation enthalpy H b
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