362 | Nature | Vol 577 | 16 January 2020
Article
regular Mn 3 O 4 lattice (also see Supplementary Fig. 9). On the other
hand, lower values are observed for the nanocrystals without islands,
which can be attributed to the distribution of tensile and compressive
strains induced along Mn 3 O 4 [220] and [004], respectively, owing to
the gap closing.
The local strain distribution is reflected in the electron diffraction
patterns and powder XRD data through a reasonably uniform grain con-
figuration in the nanocrystals (Fig. 3e, Supplementary Figs. 9, 10). The
GB areas and gap angles are almost identical for all the GBs, implying
that the residual stresses associated with the gap closing between two
grains near each GB are almost the same. At a given residual stress, an
island appears to have less normal strain per plane than a CL according
to the strain field mapping. The Mn 3 O 4 (112) XRD peak for the CoMn-CL
nanocrystals is broader than that for the CoMn-CL+I nanocrystals at a
similar Mn content, which indicates a higher proportion of nonuniform
deformation due to the smaller volume or the absence of islands. Such
uniformity in the GB structure provides a valuable opportunity to inves-
tigate the properties of strained GB structures, which are otherwise
hard to achieve. For instance, one can obtain the correlation between
the microscopic defect structures and the ensemble properties.
When the gap closes, we observe not only normal strain and the
accompanying Poisson effect, but also shear strain and rotation of
unit cells at the GBs due to the high elastic anisotropy of orthotropic
Mn 3 O 422. The more accurate strain tensor measurement^23 , which is of
the order of 0.5 nm, shows that the normal strain and the rotation are
the principal deformation components (Fig. 4 , Supplementary Fig. 11;
see Supplementary Methods for the algorithm). In both the nanocrys-
tals with and without islands, the aspect ratios of the unit cells at the
GBs are close to unity. Furthermore, the sizes of the unit cells increase
with increasing distance from the Co 3 O 4 /Mn 3 O 4 interface, with very
similar values are for unit cells at the same distance. Interestingly, the
Mn 3 O 4 shell accommodates a large 3D strain (~8% for each axis) per
GB without producing any dislocations. The value is quite large com-
pared to that of decahedral Au nanoparticles—another material well
known to exhibit GBs within nanocrystals^14. Moreover, GBs in the form
of disclinations could also be created in the core/shell nanocrystals
of other material combinations, such as Fe 3 O 4 /Mn 3 O4, Mn 3 O 4 /Co 3 O4,
Fe 3 O 4 /Co 3 O 4 and Pd/Au, via geometric misfit strain (Supplementary
Figs. 12–15, Supplementary Discussion).
Thin films in 2D SK growth mode often exhibit periodic ripple pat-
terns along with island formation, which is mainly attributed to the
epitaxial strain^9 ,^24. Pre-patterned substrates with ordered pit arrays
and stripes are used for directing the island growth and ordering^25.
In our demonstration of the 3D analogy of the SK growth, each of the
well-defined polyhedral nanocrystals (that is, the core) acts as a pre-
patterned substrate. Consequently, a thin film (that is, the shell) grows
with a strain field patterned along the sharp edges owing to the geo-
metric misfit strain in addition to the epitaxial strain. This 3D network
of strains also organizes the grains into a 3D superlattice^26. Given that
the self-organization of lattice domains in 2D epitaxial thin films has
been a key element for various physical phenomena, this utilization
of geometric misfit strains in 3D shell growth could facilitate the engi-
neering of the properties of nanocrystalline materials for improved
applications, such as in mechanics, catalysis and dielectrics^27 –^30.Online content
Any methods, additional references, Nature Research reporting sum-
maries, source data, extended data, supplementary information,
acknowledgements, peer review information; details of author con-
tributions and competing interests; and statements of data and code
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5 nm2 nmad–4 6 16% –4 6 16% –2.3 0 2.3
Strain, Strain, Rotation, T5 nm15
10
5
Strain, 0(%)15
10
5
Strain, 0(%)unit cells–8 –4 0 4 8
Distance from corner
(unit cells)Distance from corner
(unit cells)Distance from corner
(unit cells)Distance from corner
(unit cells)Corner–8 –4 0 4 8Aspect ratio1.11.00.9
–8 –4 0 4 8 Unit-cell area (nm–8 –4 0 4 82 )
0.750.700.65Mn 3 O 4 Co 3 O 4Mn 3 O 4beCo 3 O 4Mn 3 O 4Mn 3 O 4 a 2 Co 3 O 4Mn 3 O 4 cMn 3 O 4 a 2 Co 3 O 4Mn 3 O 4 cc5 nmFig. 4 | Strain tensor measurements of Co 3 O 4 /Mn 3 O 4 nanocrystal. a, HA ADF-
STEM image of the nanocrystal. b, Map of displacement based on the atomic
position of Co 3 O 4. c, Infinitesimal strains and rotation in the x and y directions
and rotation of the unit cell. d, Line traces (coloured lines) and unit cells (white
rectangles) showing the change in aspect ratio and volume of the unit cells.
e, Infinitesimal strains in the x and y directions, aspect ratio and unit cell area
over the line traces shown in d.