S 34 andS 35 , forming 5-FT (Fig. 6, C and D)
by means of mechanism 1. At a ~149° concave
surface induced through OA (Fig. 6, E and
F), 5-FT formed through partial dislocation
slipping—that is, by means of mechanism 2
(Fig. 6, F and G).
On the basis of most observations of Pd and
Pt 5-FTs, the sizes of twin units are one to
three layers of {111} planes (Fig. 6 and fig. S20),
which is smaller than that of Au 5-FTs (4 to
10 layers) (Fig. 2I and figs. S15 and S17). During
themechanism1process,wedidnotobservea
ZST (composed of three layers of {111} planes).
AZSTmayormaynotformdependingonthe
size of twin units. The average particle size of
the initial Pt and Pd NPs was ~2.7 nm (figs. S21
and S22), which is only slightly smaller than
that of the Au NPs (~3 nm) (fig. S1). Therefore,
the small twin units are unlikely to be attrib-
utable to the initial Pd or Pt particle size. For
example, by means of mechanism 1, after the
OA of two ~3-nm Pt NPs (Fig. 6, I and J), the
twin pole of the resulting 5-FT is near the sur-
face, with small twin units of two to three layers
of {111} planes (Fig. 6, K and L). Another Pt
example shows small twin units with one to
two layers of {111} planes by means of mech-
anism 2 (Fig. 6, I to L and M to P). On the other
hand, because of the higher twin-fault energy,
more energy is required to form twin inter-
faces for Pt and Pd than Au, resulting in small
twin units. For the same reason, few 5-FTs in
Pt, which has the highest twin-fault energy,
were reported previously ( 38 ). Many other fac-
tors may affect the stability of 5-FTs, such as
particle morphologies, external environments,
and surface absorbents ( 38 ). Large 5-FTs with
high twin-fault energies may form under dif-
ferent conditions.
In total, we observed 57 (Au), 33 (Pd), and 57
(Pt) OA processes and ~26% (Au), ~15% (Pd),
and ~9% (Pt) of them led to 5-FTs by means of
mechanism 1 or 2, indicating that the two 5-FT
formation mechanisms are applicable for var-
ious metal systems.Discussion and outlook
Our findings reveal that OA processes lead to
multiply twinned structures, among which
two types of concave surfaces lead to 5-FTsthrough two well-defined and reproducible
mechanisms. In mechanism 1, when OA leads
to a ~94° concave surface with a small radius
of curvature, OA provides a path to create
behavior that is far from equilibrium. A large
strain quickly accumulates while the surface
energy is minimized through atomic surface
diffusion to the curved surface, resulting in
lattice deformation and high-energy grain
boundaries (Fig. 3). To release this high strain
energy, a small twin forms through slipping
on three consecutive {111} planes, which does
not create extra strain in the nearby lattice or
require high energy—there is zero net strain.
Continuous nucleation and growth of this
twin structure releases the strain, eventually
forming a 5-FT.
In mechanism 2, after surface diffusion at
~150° concave surfaces, OA only creates a
smallS9 (Fig. 5C) because of the large radius
of curvature, and the crystal lattice is less de-
formed than in mechanism 1. Consequently,
asymmetrical 5-FTs form through partial dis-
location slipping of only a few layers of {111}
planes because further slipping creates extra
strain energy in the lattice because of large
interfaces. By contrast, in mechanism 1 a highly
strained lattice is already formed through sur-
face diffusion after the OA event. The forma-
tion of 5-FTs within the bulk of the particle
(with large interfaces) results in a reduction of
strain. Similar processes of mechanisms 1 and
2 are also found in high twin-fault energy sys-
tems, such as Pd and Pt, but result in smaller
twin units.
Multiply twinned structures, including
5-FTs, have attracted increased interest owing
to their distinct properties ( 6 , 7 )andhavebeen
widely used in mechanical engineering ( 9 ),
optics ( 11 ), and catalysis ( 12 ). OA events have
been recognized as a common pathway for
crystal growth and occur widely in diverse
systems, including oxides, metals, semicon-
ductors, organics, and biomineral phases ( 1 – 5 ).
Therefore, what we learned from our observa-
tion may generalize to a wide range of mate-
rials and enable the formation of multiply
twinned structures besides 5-FTs, such as the
formation of multiply twinned iron oxide in
solution ( 21 ), depending on specific crystal
structureandthenatureoftwinboundaries
in each system. Our findings place disparate
systems into the context of well-developed
theories for multiple-twin-formation mecha-
nisms, provide a guide for interpreting and
controlling twinned crystal structures and
morphologies, and hopefully will result in
advances in materials design and synthesis
for diverse applications.REFERENCES AND NOTES- N. Daneu, H. Schmid, A. Rečnik, W. Mader,Am. Mineral. 92 ,
1789 – 1799 (2007). - V.Šrot, A. Rečnik, C. Scheu, S.Šturm, B. Mirtič,Am. Mineral.
88 , 1809–1816 (2003).
Songet al.,Science 367 ,40–45 (2020) 3 January 2020 5of6
Fig. 6. Examples of formation of 5-FTs in Pd and Pt NPs by means of mechanisms 1 and 2.(Ato
D) Formation process of mechanism 1 in Pd NPs. (EtoH) Formation process of mechanism 2 in Pd NPs.
(ItoL) Formation process of mechanism 1in Pt NPs. (MtoP) Formation process of mechanism 2 in Pt NPs.
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