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
.