( 26 ), presenting a hexagonal two-dimensional
(2D) projection composed of four {111} and
two {200} planes (Fig. 1A). During this process,
the Au NPs moved and aggregated. The decom-
position of the surfactant led us to make the
assumption that the type does not affect the
mechanisms for this system ( 26 ). To understand
the relation between the two grains, we used
the degree of fit (S)todefinethegrainbound-
ary (GB) based on coincident site lattice theory,
whereSis the ratio of the total number of sites
to coincidence sites ( 27 ). During aggregation,
NPs specifically underwent OA along the {111}
planes, forming either interface-free single
crystals (Fig. 1A) orS3 twin structures (Fig. 1B),
similar to Au and iron oxide particle OA pro-
cesses previously reported in liquid phases
( 21 , 28 ). In addition, multiple twin interfaces
often formed. For example, repeated OA pro-
cesses induced both parallel (Fig. 1C) and three
types of crossed-twin interfaces (Fig. 1, D to F).
AsecondtwinboundaryS 32 formed when a
twinned crystal (with the firstS 31 )underwent
OA with another single crystal, resulting in
two types of concave surfaces with angles of
~94° ({111}+{200} surfaces) (Figs. 1, D and E,
and 2, A and B) and ~150° (two {111} surfaces)
(Fig. 1F). The angle between twoS3s was
either ~109° (Fig. 1D) or ~70° (Fig. 1, E and F).
In addition, we often observed twinning and
detwinning processes through the slipping of
atoms in {111} planes by 61 ½ 112 —that is, partial
dislocation slipping with a Burgers vector (b)of
1
6 ½^112 (fig. S3).
Mechanism 1: Formation of 5-FT by
forming and decomposing high-energy
grain boundaries
The angle of ~70° between twoS3s (Fig. 1, E
and F) provided the possibility of 5-FT forma-
tion, in which the theoretical angle between
S3s is 70.53°. The two types of concave surfaces
with angles of ~98° (Fig. 1E) and ~150° (Fig. 1F)
lead to two mechanisms for the 5-FT formation.At the 89.9° concave surface (Fig. 2B and
movieS1,thesameOAprocessasshownin
Fig. 1E), adjacent atoms migrated to this high-
energy surface because of the small curvature
radius (Fig. 2C and movie S1) ( 29 ), forming a
new high-energyS9, identified by the 39° angle
between {111} planes in regions I and IV (Fig.
2Candfig.S4,AtoC).TheGBenergy(EGB)
ofS9is~542mJ/m^2 ( 30 ), which is high com-
pared with the ~17.5 mJ/m^2 EGBofS3( 31 ).
Because of this highEGB,S9subsequentlyde-
composed into a stableS3(thethirdS 33 )and
anewhigh-energyS27 (EGB~560mJ/m^2 )( 30 ),
identified by the 32° angle between the {111}
planes in regions I and IV (Fig. 2D and fig. S4,
DtoF).TheS9 decomposition follows the
dissociation theory of the coincidence site lat-
tice [S(A/B)↔SA+SBorS(A × B)↔SA+
SB] ( 32 ). As atoms further filled the concave
surface through either particle aggregation
(Fig. 2, C and D) or surface atom diffusion (fig.
S5), stacking faults formed in region IV, re-
sulting in aS27 between stacking faults and
{200}Iplanes in region I [S27-(200)I](Fig.2E).
This unstableS27-(200)Ievolved into a dif-
ferentS27 between (111)IVand the region I
[S27-(111)IV] with the disappearance of stack-
ing faults (Fig. 2F and movie S1), resulting in
an oscillation between them (Figs. 2, E to G,
and 3). After three consecutive 64-s oscillation
cycles (Fig. 2, D to H; fig. S6; and movie S1),
twin lamellae—previously termed a zero-strain
twin (ZST)—that exhibit localized strain, but
possessstrainfieldsthatsumtozerointhe
surrounding crystal lattice, nucleated at the
twin pole alongS27 (Figs. 2H and 4) ( 33 , 34 ).
TheS27 immediately decomposed into the
fourth and fifth twin boundaries (S 34 andS 35 )
within 0.2 s and formed a 5-FT (Fig. 2I), cor-
responding toS 27 →S 34 +S 35 + 7.35° (S81 =
S 35 + 7.35°). The misfit angle of 7.35° between
the twin planes after 5-FT formation is ac-
commodatedbylatticestrainintwinunits
( 30 ), and the lattice strain can also be relaxed
through surface adjustment, such as forming
a truncated (Marks) decahedron (fig. S7) ( 35 ).
The evolution betweenS27-(200)IandS27-
(111)IVwas accompanied by an oscillation of the
anglea(betweenS27 andS 32 )(Figs.2,EtoG,
and 3, A to D). The theoreticalais 125.3° and
148.4° forS27-(200)IandS27(111)IV, respective-
ly, which leads to a large angle misfit of 23.1°
between (200)Iand (111)IV(Fig.3C).Duringthis
process, the angle misfit was mainly accom-
modated by either stacking faults in region IV
or lattice deformation in region I. In a perfect
Au crystal, the angle (b) between {111} planes is
70.53°. With stacking faults (a~130°)(Fig.3A),
the lattice deformed slightly in region I, withbI
of 72.5°. When the stacking faults disappeared
(a~ 150°), the lattice in region I deformed fur-
ther, withbIof ~74° (Fig. 3E), to compensate the
lattice mismatch. Region III was also affected
during the oscillatory evolution ofS27, withSonget al.,Science 367 ,40–45 (2020) 3 January 2020 3of6
Fig. 4. Decomposition ofS27 through ZST formingS 34 andS 35 .(AandB) Enlarged high-resolution
TEM images of twin pole regions of the NP at 76.8 and 80.6 s, respectively, showing the formation of a ZST
near the twin pole. (C) Schematics of the ZST. (D) MD simulation (model 1) with {111} surfaces. (EtoH)ZST
nucleation onS27 and growth in region I at 800 K. (I) Enlarged black-box area in (G). (J) Energy profile
of the NP during decomposition ofS27.
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