Supplement Materials for
Interface-dependent nucleation in nanostructured layered composites
Irene J. Beyerlein1a, Jian Wang b, Ruifeng Zhang a
a
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA
b
Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545
USA
1
Phone: 505-665-2231, Irene@lanl.gov
Figure S1. The Thompson tetrahedron providing the relationship and nomenclature for the
Shockley partial dislocation systems in an fcc crystal.
Extension of Equation 5. Equation (5) is a first-order expression. A more refined expression
weights the alignment of a given LD (j) with an ID (i) with the magnitude of the ID (i):
(𝑖)
(𝑖)
(𝑗)
(𝑖)
(𝑖)
(𝑗)
(𝑖)
(𝑖)
(𝑗)
𝐻 𝑖𝑗 = |𝑏⃑𝐼𝑒 |𝑝⟨𝑏⃑𝐼𝑒 ∙ 𝑏⃑𝑃 ⟩ + |𝑏⃑𝐼𝑠 |(1 − 𝑝)⟨𝑏⃑𝐼𝑠 ∙ 𝑏⃑𝑃 ⟩ + |𝑏⃑𝐼𝑁 |⟨𝑏⃑𝐼𝑁 ∙ 𝑏⃑𝑃 ⟩
(S.1)
Estimation of the critical angle c. Orowan’s law for the stress to bow out a dislocation
segment with Burgers vector of value b between two pinning points with spacing L is given by
 = b/L
(S.2)
For room temperature conditions, the shear modulus  is 48 GPa for Cu. For the current model,
let  be the angle between the trace of the glide plane of b on the interface plane and the ID line
(i). Within the ID network, the ID line (i) will intersect another ID array (j) at regular points,
spaced apart. According to the above, the stress required to bow out a Shockley partial
dislocation into Cu between these two intersection points, spaced L = /sin apart, is simply
b//sin. For Cu-Nb interfaces,  ~ 2 nm. Assuming a resolved shear stress limit of 500 MPa
yields a practical limit of 10° for c.
MD simulations. MD simulations are performed to study dislocation nucleation from a Cu-Nb
interface. The bicrystal model of the relaxed interface (Fig. 1) is uniformly strained in increments
of 0.2%. At each increment, the strained system was relaxed until the uniaxial stress condition is
satisfied. Next we apply dynamic quenching MD until the maximum residual force on each
atom becomes less than 5 pN. The site and Burgers vector of the nucleated LD(s) are identified
by disregistry analysis [1]. These simulations are performed at 0 K in order to accentuate the
structure dependence on nucleation. Repeating the simulations at higher temperatures (such as
10 K or 300 K) results in the emission of the same types of lattice dislocations from the same
types of nucleation sites as those observed at 0 K. The thermal fluctuations in the finite
temperature simulations, however, lead to heterogeneous nucleation, wherein not all identical
nucleation sites form a dislocation at the same time. Likewise, when the simulations are carried
out at higher strain rates than presented here or in shock conditions [24], the types of dislocations
nucleated and their nucleation sites do not change. In other words, dislocation systems that were
suppressed (emitted) at lower strain rates were also suppressed (emitted) at higher strain rates.
Table S1. Comparison of MD simulation results of nucleated systems (boldface) with the
proposed nucleation propensity factor 𝜒𝑗 𝛿 𝑗 (assuming p = 0.4) for (a) the KS interface and (b)
the NW interface. The value p = 0.4 is selected not as a fitting parameter but to give more
weight to the screw component since it has a larger influence on in-plane shearing. The data
support Fig. 3.
(a) KS interface
Slip System
̅̅̅̅1)
[1̅21](11
̅̅̅̅1)
[21̅1](11
̅̅̅̅̅
̅̅̅̅1)
[112](11
̅̅̅̅)
[11̅2](111
̅̅̅̅)
[121̅](111
̅̅̅̅̅](111
̅̅̅̅)
[211
[211̅](1̅11̅)
[1̅12](1̅11̅)
̅̅̅̅̅](1̅11̅)
[121
𝑚𝑎𝑥[𝜒𝑗 𝛿 𝑗 ]
j*
x-straining y-straining z-straining
𝛿𝑗
𝛿𝑗
𝛿𝑗
0.157
0.000
0.157
0.157
0.000
0.157
0.000
0.314
0.314
0.471
0.314
0.157
0.393
0.236
0.157
0.314
0.079
0.236
0.393
0.236
0.157
0.471
0.314
0.157
0.314
0.079
0.236
0.248


̅
̅̅
̅̅
̅
̅
̅
̅̅
̅̅̅̅̅
̅̅̅̅1)
[121](111) [112](111) [112](11
𝜒𝑗
0.00
1.19
0.79
1.80
1.08
0.00
0.00
0.00
0.00
(b) NW interface
Slip system
̅̅̅̅1)
[1̅21](11
x-straining
𝛿𝑗
0.157
y-straining
𝛿𝑗
0.000
z-straining
𝛿𝑗
0.157
𝜒𝑗
1.83
̅̅̅̅1)
0.157
0.000
[21̅1](11
0.157
̅̅̅̅̅](11
̅̅̅̅1)
0.000
0.314
[112
0.314
̅̅̅̅)
[11̅2](111
0.471
0.314
0.157
̅
̅
̅
̅
̅
[121](111)
0.393
0.236
0.157
̅̅̅̅̅
̅
̅
̅
̅
[211](111)
0.314
0.079
0.236
[211̅](1̅11̅)
0.393
0.236
0.157
[1̅12](1̅11̅)
0.471
0.314
0.157
̅̅̅̅̅](1̅11̅)
[121
0.314
0.079
0.236
𝑗 𝑗
0.230
𝑚𝑎𝑥[𝜒 𝛿 ]


̅̅̅̅) [11̅2](111
̅̅̅̅) [211
̅̅̅̅̅](111
̅̅̅̅)
j*
[121̅](111
̅
̅
̅
̅
̅
̅
̅̅̅̅̅
̅
j*
[211](111) [112](111) [121](111̅)
1.83
0.00
1.10
1.10
0.732
1.10
1.10
0.732
MD calculations of interface energy changes after nucleation. Upon nucleation, an interfacial
segment forms within the interface. The energetic alterations that result are denoted here by G.
As a basis for comparison, it suffices to associate G with the excess potential energy associated
with introducing an interfacial segment to the relaxed interface at 0 K. For some LDs that can
nucleate from the KS interface, G is calculated using molecular statics methods described in [2]
and summarized in Table S2.
̅̅̅̅)
[121̅](111
Slip system
Energy (eV/nm)
0.34
̅̅̅̅̅](111
̅̅̅̅)
[211
̅̅̅̅1)
[21̅1](11
̅̅̅̅̅](11
̅̅̅̅1)
[112
[211̅](1̅11̅)
[1̅12](1̅11̅)
1.24
0.48
0.34
1.27
1.52
Table S2. Change in formation energy of the interface (eV/nm) due to insertion of different
Shockley partial dislocation segments within the KS interface [2]. Energy is integrated within a
circular area of radius ~ 1 nm from the segment.
References
1.
J. Wang, A. Misra, R. G. Hoagland, and J. P. Hirth, Acta Mater. 60, 1503–1513 (2012).
2.
R. G. Zhang, J. Wang, I. J. Beyerlein, A. Misra, and T. C. Germann, Acta Mater. 60, 2855-
2865 (2012).