The standard model of equation 3 su ff ers from fundamental problems on deeper

The standard model of equation 3 su ff ers from

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The standard model of equation (3) su ff ers from fundamental problems on deeper inspection. First, ˙ ε for vacancy-assisted di ff usion of Mg in Al is many orders of magnitude smaller than experimentally derived values. With H b = 1 . 19 eV and ν 0 = 3 . 8 × 10 13 s 1 (ref. 18), ˙ ε at 300 K for c 0 = 2 . 5% (using W = 0 . 08 eV and Ω = 0 . 00063, see below) is 4 × 10 11 s 1 , a discrepancy of 10 6 with experiments. Pipe di ff usion along the dislocation core 19 or other recent models 20,21 do not rectify this discrepancy. Second, the strength of a fully formed solute cloud is also much too large, 500–5,000 MPa (refs 1,5,22,23), and the binding energy formally diverges 1 . Our finite-size simulations here confirm the previous literature, with strengths 300 MPa and binding energies of 50 eV. Third, there is only very weak theoretical justification for the leap from equation (1) to (2) (ref. 8). Fourth, equations (2) and (3) assume that strength is an additive quantity, which is not generally true. Thus, no existing models are predictive at the materials level, and so a quantitatively accurate understanding of the mechanisms of DSA in Al–Mg does not yet exist. Here, we demonstrate that the mechanism of DSA and nSRS on experimentally measured strain rate and stress scales is the single- atomic jump of solutes directly across the slip plane, from the compression to the tension side, in the core of the dislocation. This ‘cross-core’ di ff usion mechanism is outside the scope of continuum models, has a strong thermodynamic driving force due to the large enthalpy di ff erence between solutes on either side of the slip plane in the core, has an activation enthalpy much lower than in the bulk 19 , leads to an additive strengthening in the form of equations (2) and (3), but with n = 1, and connects the parameters in equations (2) and (3) with fundamental solute–dislocation interactions. Moreover, using literature material parameters for Al–Mg, this mechanism has strengths of 10–20 MPa, binding energies of 1–2 eV, and quantitatively agrees with the experiments on Al–Mg over a range of concentrations and temperatures 16,24,25 . Our new picture of the DSA and nSRS phenomena quantitatively addresses all the issues sidestepped in previous models and puts the phenomenon and the widely used equation (3) on a firm theoretical materials science foundation. The new model also points towards quantitative multiscale modelling for the design of new alloy systems via first-principles computations of solute/dislocation-core interaction and di ff usion enthalpies. Figure 1 shows the binding energy E s ( x i , y i ) between a single substitutional Mg at in-plane position ( x i , y i ) and an edge dislocation ( b = 2 . 851 ˚ A) at the origin, computed by molecular statics 19,26 (see the Methods section) the energy is independent of the z coordinate. Across a core interaction region of width w 7 .
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