Z. Kristallogr. 224 (2009) 528–538 / DOI 10.1524/zkri.2009.1034
# by Oldenbourg Wissenschaftsverlag, München
Shape variations and anisotropic growth of multiply twinned
nanoparticles
Herbert Hofmeister*
Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany
Received May 27, 2008; accepted September 21, 2009
Electron microscopy / Crystal morphology /
Shape evolution / Multiple twinning / Pseudofivefold rotation /
Anisotropic growth
Abstract. Cyclic multiple twins as nanoobjects that display nearly regular polyhedron shape variety together with
strongly anisotropic shape variations due to growth processes are reviewed with regard to their unique shape evolution based on the specific formation modes as well as on
the particular structure of twin-related subunits. The review includes (i) the shape variations due to growth by
stacking of tetrahedral subunits, (ii) the role of growth
conditions in the shape evolution of multiply twinned nanoparticles, and (iii) the modes of twin-based anisotropic
growth including branching growth and unidirectional
growth. The particular structures are introduced making
use of electron microscopy structural characterization of
multiply twinned metal nanoparticles as well as some nonmetal examples, and instructive models of the various configurations.
1. Introduction
1.1 Shape evolution of nanoparticles –
the role of twinning
Nanoparticles with strong shape anisotropy, like rod or
platelet shapes, attract large attention because of their interesting physical properties. For single crystalline particles there is a lot of methods to achieve strongly anisotropic growth (see, e.g., [1–5]). Sources of anisotropic
growth may be either the position within the growth environment which can lead to anisotropic shape of crystallites
having equivalent faces, or differences in growth rate of
crystallites bounded by different faces where the growth
rate ratio is depending on temperature and supersaturation.
In view of more complex routes of synthesis anisotropic
growth of one-dimensional nanostructures may occur, for
example, as unidirectional axial growth due to inhibition
of radial growth. Such growth techniques may be classified as seed-mediated, template-directed, or defectmediated growth, respectively [5].
* e-mail: [email protected]
Quite different, but not less remarkable shape variations
can be found for multiply twinned particles (MTPs) with
non-crystallographic pseudo-fivefold rotation axes, that
means particles with decahedron and icosahedron shape
[6, 7], respectively. Cyclic fivefold twinning is a widespread habit of nanoparticles [7], found not only in synthetic materials as reported for the first time in 1957 [8],
but also in crystallite compounds of natural origin, dating
back as early as 1831 [9]. For the sake of clarity we
should consider all these twins as being due to pseudopentagonal metrical features of the corresponding lattice.
Thus they actually are pseudo-fivefold rotation twins [10].
Besides the classical processes of nucleation and growth,
at MTPs also shape evolution by successive stacking of
tetrahedron-shaped subunits arranged around fivefold rotation axes has experimentally been observed. The shape
variations of multiple twins with nearly regular polyhedron shape can mostly be explained by different growth
rates of the bounding faces of their subunits, if they do
not exhibit tetrahedron, but cuboctahedron shape. Then
star decahedron, prism, facet, and cube decahedron, respectively, may occur as corresponding growth forms.
At particles with decahedron shape a strongly anisotropic
shape evolution may proceed by preferred growth along one
or some reentrant edges of the outer bounds of twin planes
or along the fivefold junction. While the former results in
radial growth in one or some directions, the latter is equivalent to unidirectional axial growth due to an inhibition of any
radial growth. The rod shape formed thereupon corresponds
to a pentagonal prism with pentagonal pyramids at the rod
tips [11]. At particles with icosahedron shape strongly anisotropic shape evolution is mainly observed via preferred attachment of tetrahedron-shaped subunits along a fivefold
axis, through which stacks of pentagonal antiprisms with
pentagonal pyramids at the rod tips may form [12].
The above mentioned shape variations as well as examples of strongly anisotropic growth of MTPs shall be introduced by means of electron microscopy findings of our
own work including various collaborations, as well as
some work reported in the literature, and shall be illustrated by appropriate models. The materials involved
comprise noble metals and semiconductors, as well as molecule crystals and even a silicate mineral. Besides a short
introduction of composition and appearance of multiply
twinned particles, this review contains considerations of
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Fig. 1. Schematic representation of a decahedron (left) and an icosahedron (right) composed of regular tetrahedra arranged around fivefold axes.
shape variations due to growth by stacking of tetrahedra
subunits, shape variations due to growth rate changes, and
the anisotropic growth of both kinds of MTPs, respectively.
1.2 Composition and appearance of multiply
twinned particles of regular polyhedron shape
Multiply twinned particles consist of several subunits, that
means they are composed in such a way that subunits of
equal shape of regular tetrahedra are twin-related to each
other resulting in polyhedra of unique morphology and
unusual symmetry [7] as can be seen in the schematic
representation given in Fig. 1. The one on the left hand
side (Fig. 1a) is a decahedron, that means an equal edge
length pentagonal bipyramid, containing 5 tetrahedra in
contact twin orientation to each other stacked around one
fivefold axis that is marked by a dotted line. The other
one (Fig. 1b) is an icosahedron, that means an equal edge
length, pentagonal antiprism pyramid-capped on both
sides, containing 20 tetrahedra, also in contact twin orientation to each other, stacked around six fivefold axes
which are marked by dotted lines. Their mode of appearance depends on the orientation with respect to a supporting substrate or a surrounding matrix – four high symmetry orientations are known for both of the twin polyhedra
[7] which are shown in Fig. 2 (decahedron) and Fig. 3
(icosahedron) where the indices refer to the directions
[110] of a fivefold twin junction, [112] of a twin bound-
Fig. 3. Schematic drawing of the appearance of icosahedra in high
symmetry orientations on a substrate.
ary, or (001) of a tetrahedron subunit parallel to the viewing direction, or to the direction [111] of a bounding face
of a subunit perpendicular to the viewing direction. The
resulting particle images have rhombic, pentagonal or hexagonal contour of various style.
2. Shape variations due to growth by stacking
of tetrahedral subunits
Previous to any shape variation of the multiply twinned
polyhedra, elementary steps of shape evolution occur via
a
b
Fig. 2. Schematic drawing of the appearance of decahedra in high
symmetry orientations on a substrate.
Fig. 4. Successive stacking of tetrahedra via repeated twinning during
growth illustrated by (a) schematic drawing, and (b) TEM images,
adapted with permission from [14], in bright-field (upper row), and
dark-field (lower row) mode of one, two, and three subunits.
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Shape and growth of multiply twinned nanoparticles
H. Hofmeister
Fig. 5. Contact twin-related assembling of 5 tetrahedron subunits to
form a decahedron.
assembling of tetrahedra subunits by repeated twinning
during growth. This successive stacking of subunits easily
results in the formation of decahedra, and icosahedra, respectively [13–15], as it is demonstrated in Figs. 4 and 5
for decahedra and in Figs. 6 and 7 for icosahedra. The
experimental observation of the first steps shown in
Fig. 4b includes transmission electron microscopy (TEM)
images in bright-field (upper row) and in dark-field (lower
row) mode of an unattached tetrahedron in (001) orientation (left) as well as particles containing one and two
twins attached to a parent subunit (centre and right) as it
is schematically sketched in Fig. 4a [14]. In principle, the
assembling of five individual tetrahedra so as to form a
decahedron as indicated by Fig. 5 cannot be excluded.
The process of subunits assembling obviously does not
stop with creating decahedra, but continued stacking of
subunits towards creation of icosahedra via intermediates
containing eight and twelf tetrahedra as it is schematically drawn in Fig. 6 has been observed. Almost halficosahedral particles obtained by physical vapour deposition (PVD) have repeatedly been reported as intermediate
a
c
b
Fig. 7. SEM images of silver particles from solution growth (Gao
et al., adapted with permission from [15]) demonstrating intermediate
stages (incomplete MTPs) formed upon successive stacking of tetrahedra.
stage of the successive stacking of twinned subunits
[14–18].
An experimental example of Gao et al. [15] from the
solution growth of silver particles studied by scanning
electron microscopy (SEM) is presented in Fig. 7 where a
number of incomplete MTPs, including a three tetrahedra
precursor of a decahedron and a 15 tetrahedra precursor of
an icosahedron, are marked by arrows. Another route to
icosahedra is modelled in Fig. 8 where a decahedron (left)
is added to a pentagonal antiprism (centre) composed of
ten twinned tetrahedra so as to create an intermediate
stage (right) that needs another five subunits of a decahedron to end up with an icosahedron. The assembling of
multiply twinned particles from tetrahedra subunits step by
step implies that under certain conditions for the materials
involved the tetrahedron may be a possible growth shape,
at least during growth twinning at the nanometre scale.
Usually, such materials have cubic crystal symmetry
which can be grown into cubic, cuboctahedral, and octahedral shape, respectively, depending on the growth conditions. As will be demonstrated below, the latter modes of
shape may occur for the subunits of completed multiply
twinned particles whose structure is governed by twinning
during the initial stage of spontaneous nucleation.
d
Fig. 6. Continuation of successive stacking of tetrahedra beyond the
decahedron (a). Intermediate stages of 8 subunits (b) and 12 subunits
(c) complement one another to an icosahedron (d).
Fig. 8. Alternative route to the assembly of an icosahedron via attaching a tetrahedron-based pentagonal antiprism to a decahedron leaving
space for another decahedron in mirror symmetry to the first one.
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530
3. Shape variations due to growth rate changes
The shape evolution from the octahedral to the cubic form
of crystals involves intermediate forms like the truncated
octahedron, the cuboctahedron, and the truncated cube.
Their outline is determined by the ratio of cube faces to
octahedron faces growth rates v100/v111
[3] or more compffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
mon by the growth parameter a ¼ 3v100=v111 [19].
Subunits of general cuboctahedral shape are thought to
result from progressive and symmetrical removal of the
corners of both starting polyhedra that are exposed to variations of the growth conditions. Consequently, distinct
shape variations of MTPs originating from multiple twin
formation at the initial stage of growth may evolve upon
suitably controlling the growth conditions, which increases
the number of varieties of nearly regular polyhedron particle shape. The growth parameter a is determined by conditions like the precursor concentration and the substrate
temperature applied during growth. Since the shape of single crystals can be easily correlated to this parameter, at
least in the range 1 a 3, we have chosen four specific values of a corrresponding to characteristic stages of
shape evolution [3, 7, 19]. These are the octahedron obtained for a ¼ 3, the truncated octahedron for a ¼ 2, the
cuboctahedron for a ¼ 1.5, and the cube for a ¼ 1.
3.1 Evolution of the decahedron morphology
According to the above mentioned values of a and the
corresponding single crystal shape unique examples of
MTP shape occur which are shown for the decahedron in
Fig. 9. Different from the regular decahedron composed of
five regular tetrahedra being bounded by equilateral triangular faces of type {111} only (see 1.2), now the particle
morphology is subdivided and contains bounding faces of
different type and size [19–22]. The evolution of the
nearly regular polyhedron shape variety of decahedra contains, starting from a perfect octahedron shape of subunits,
(i) a star decahedron that exhibits 5 peripheral reentrant
edge configurations (Fig. 9a), (ii) a facet decahedron obtained by truncation of the outer tips of the star decahedron so as to display {100} faces (Fig. 9b), (iii) a prism
decahedron resulting from increased truncation where the
a
b
c
d
Fig. 9. Evolution of decahedron morphology with growth parameter
affecting the subunit shape: (a) octahedron; (b) truncated octahedron;
(c) cuboctahedron; (d) cube.
a
b
Fig. 10. TEM images of a PVD grown palladium decahedron with its
twin junction oriented parallel to the electron beam: (a) in brightfield; and (b) in dark-field mode [23].
{100} faces contact each other (Fig. 9c), and (iv) a cube
decahedron corresponding to a perfect cube shape of subunits, where no {111} faces remain (Fig. 9d). The prism
decahedron model, also named “Ino decahedron” [20] and
the facet decahedron model, also named “Marks decahedron” [21] have been introduced to take account of the
necessary energy balance, mainly between surface and
strain energy of these particles. Together with that of the
regular decahedron, these decahedral particle shapes have
been most frequently observed experimentally. From the
experimental TEM images of a palladium decahedron, obtained by PVD on potassium iodide substrate, shown in
bright-field and in dark-field mode in Figs. 10a and 10b
one can clearly recognize its compact morphology [23].
Remarkably, the most earliest report on an object that
exhibits multiply twinned configuration and decahedral
shape is by G. Rose from 1831 [9] and it features, as can
be seen from Fig. 11a, the subdivided morphology of a
facet decahedron of gold which has been found near Boicza, Romania. Another early example of natural origin [24]
is the copper decahedron shown in Fig. 11b that exhibits
peripheral reentrant edge configurations like a star decahedron, but no tips at the outer end of the subunits. Additionally, this particle displays a dimple at the emergence
point of the fivefold twin junction, that means a concave
vertex surrounded by five {111} facets. This morphological feature must not be considered as a characteristic of
copper decahedra or decahedra of natural origin. There are
also examples in the literature that describe a copper MTP
of natural origin having clearly star decahedron shape
without such central dimple [25], as well as diamond star
decahedra of natural and of synthetic origin that just display this particular habit [26, 27]. The shape of the decahedron shown in Fig. 11b can be explained by assuming a
truncated tetrahedron shape of its subunits. As illustrated
by Fig. 12, stacking of such truncated tetrahedra, also
known as Friauf polyhedra, easily enables to construct
decahedra and even icosahedra [28] that exhibit both, twin
junction dimpling and twin boundary grooving. Occasionally, a certain anisotropy of decahedral MTPs may occur
because of non-uniform development of such features
within the subunits of a particle as it is observed at the
C60 star decahedron obtained by aerosol synthesis [29].
That is illustrated by the high resolution electron microscopy (HREM) image shown in Fig. 13. Experimental evi-
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531
Shape and growth of multiply twinned nanoparticles
H. Hofmeister
a
b
Fig. 11. Early findings of multiply
twinned crystallites of decahedral
shape: (a) facet decahedron of gold
(1831 [9]), and (b) nearly star-like decahedron of copper (1882 [24]).
mixture of choline chloride and urea as solvent that has
been reported to result in star decahedra [30] whose tips
are distinctly sharper than those bounded by octahedron
faces as considered above. The free faces forming each tip
are of the highly stepped {331} type resulting in a tip
angle of 26.6 instead of 70.53 as expected for {111}
faces. Obviously, this morphology is due to branching
growth (discussed below in sect. 4.1) proceeding in direction of the apex of the octahedral subunits.
a
b
Fig. 12. Assembling of 5 truncated tetrahedron subunits to form a decahedron that exhibits twin junction dimples and twin boundary grooves.
dence of fabrication of a cube decahedron without any
{111} faces is rarely found, but for values of the growth
parameter slightly above a ¼ 1 reentrant grooving at the
twin boundary sections between {111} faces occurs as it
is schematically shown in Fig. 14a for a ¼ 1.16 [19]. This
leads to additional cube faces at the expense of the still
remaining octahedron faces.
Another direction of shape evolution is opened by the
solution synthesis of gold nanoparticles using an eutectic
3.2 Evolution of the icosahedron morphology
The evolution of the nearly regular polyhedron shape variety of multiply twinned icosahedra is illustrated by Figs.
14b and 15. Changes of the subunit outline due to growth
parameter variation produce different types of deviation
from the regular icosahedron having a compact, nearly
spherical shape. For subunits of octahedral shape the corresponding icosahedron is bounded by corner-connected,
equilateral triangular faces of {111} type which always
surround a pit, that means a concave pentagonal vertex
consisting of {111} faces. As can be seen in Fig. 15a all
these pits are corner-connected to each other. Smaller pits
or dimples of the same geometry occur for subunits of
truncated octahedron shape where the peripheral {111}
faces now have hexagonal outline (Fig. 15b). A cuboctahedral subunit shape results in the morphology of a regular
icosahedron not to be distinguished from that composed of
tetrahedral subunits (see Fig. 15c). For values of the
growth parameter a ¼ 1.5 twin boundary grooving occurs,
as it is shown in Fig. 14b, whereby cube faces additionally
appear at the expense of the diminishing octahedron faces.
Finally, the multiply twinned icosahedron for a ¼ 1
a
Fig. 13. HREM image of a slightly modified star decahedron of C60,
adapted with permission from [29], by cyclic twinning of subunits of
nearly octahedral shape.
b
Fig. 14. Schematic drawing of (a) a decahedron, and (b) an icosahedron which exhibit reentrant grooving at twin boundary sections between {111} faces for a growth parameter value slightly above 1.
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532
4. Strongly anisotropic growth of multiply
twinned particles
4.1 Branching growth
a
b
c
d
Fig. 15. Evolution of icosahedron morphology with growth parameter
affecting the subunit shape: (a) octahedron; (b) truncated octahedron;
(c) cuboctahedron; (d) cube.
(Fig. 15d) can be described as regular icosahedron whose
triangular bounding faces are capped by fitting pyramids
such that an all-cube-face star polyhedron results.
Besides regular icosahedra experimental observations
of the shape evolution with growth parameter mainly include examples that exhibit dimples of various size at the
emergence of twin junctions as it is shown in Fig. 16 for
boron suboxide particles [31], as well as twin boundary
grooving of varying extent [27, 32]. Regular icosahedra
can often be found in particle ensembles of transition metals [33] while icosahedra with dimples and grooves at the
surface frequently occur for diamond and boron suboxide
nanoparticles fabricated, for example, by chemical vapour
deposition, acetylen flame synthesis, and high pressure
melt synthesis, respectively [27, 31, 32]. Only one report
has been given up to now on icosahedra having a starry
shape where Burt et al. [34] propose a model of these
gold particles obtained by solution growth which consists
of trigonal pyramids capping the corresponding faces of a
regular icosahedron. However, the additional assumption
that these pyramids have tetrahedral shape and are
bounded by {111} surfaces requires not only capping tetrahedra situated in twin relation with respect to their base
tetrahedron, but it also excludes to consider this starshaped polyhedron as being due to growth conditions favouring a cube face-bounded polyhedron. This will be discussed in more detail in the next section.
Branching growth as directional crystallization along the
apex directions of a polyhedral crystal is induced by concentration effects in a concentric diffusion field formed
around the growing crystal [3]. Similar to the case of single crystalline particles various branched morphologies
can be found in multiply twinned particles with and without including the twin boundaries. Silicon precipitates
grown in Al––Si melt or fabricated by laser processing of
corresponding alloy materials have been reported to exhibit a branched structure where the branches extend like
fingers from the twin boundary corners and proceed
straightaway with these boundaries [35, 36]. Such twin
finger decahedra have been observed also for gold and
platinum nanoparticles fabricated by solution synthesis
[37–39]. As an example Fig. 17 shows a TEM image of a
twin finger decahedron of gold [38] together with the
schematic drawing of two model subunits containing indented trigonal faces surrounding a concave edge from
which the configuration of the MTP may be imagined.
The excessive growth along the twin boundaries is thought
to result from unfavourable growth conditions at the periphery of tetrahedral subunits. Branching growth also is
observed for single crystalline metal particles formed in
the above mentioned solution routes of synthesis [37–39].
Another situation is met with the different geometry of
star decahedra which already exhibit distinctly protruding
apexes. Under certain conditions of growth star decahedra
formed by chemical vapour deposition in boron nitride
platelets [40, 41] may tend to develop a fivefold branched
morphology as it has been observed for relatively high
deposition temperature and relatively low total gas pressure [42]. Here the branching does not extend from the
twin boundaries emergence points, but it proceeds from
the star tips of the subunits, so as to replace the tips by
finger-like protrusions. Quite accordingly, the spiky icosahedron mentioned above [34] could be understood in
terms of branching growth starting at the tips of a star
icosahedron. It may be recognized from the TEM image
b
a
Fig. 16. SEM images of boron suboxide icosahedral particles, adapted
with permission from [31], which exhibit dimples of various size at
the emergence points of twin junctions.
Fig. 17. HREM image of a finger decahedron of gold from solution
synthesis, adapted with permission from [38], (a) together with schematic drawing of two model subunits containing indented trigonal
faces surrounding a concave edge (b) to be joined along a twin plane
(arrowed) and to be completed accordingly by three matching subunits.
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533
Shape and growth of multiply twinned nanoparticles
H. Hofmeister
Zeitschr. f. Kryst. u. Min. I Bd.
Fig. 18. TEM image of a star-like icosahedral particle of gold,
adapted with permission from [34], whose tips appear more spiky
than expected for a cube icosahedron so as being affected by branching growth.
in Fig. 18 that the pyramids capping this icosahedral particle obviously appear more pointed than expexted for segments of a cube capping the faces of a regular icosahedron as shown in Fig. 15d. Furthermore, from dark-field
images presented in the Burt et al. article [34] it can be
concluded that there is no twin boundary between the base
tetrahedra forming the icosahedron and their respective
capping pyramids. That means, the spikes making the particles appear like star polyhedra most probably result from
a kind of branching growth that also is observed for single
crystalline particles obtained in the same synthesis.
4.2 Unidirectional growth
One-dimensional nanostructures like nanorods or nanowires are mostly obtained by template-directed, surfactantassisted, and/or seed-mediated processes that either confine the growth to one dimension or act as favourable sites
for the adsorption of reactant molecules. Defect-mediated
or twin-induced growth based on the effect of twin boundaries and fivefold twin junctions to enable reasonable
growth rates at low precursor concentration [5, 43] may
even allow promoter-free formation of such nanostructures. The elongation of multiply twinned particles by unidireational growth proceeds via distinctly different processes for decahedra and icosahedra, respectively.
Taf. II.
Fig. 19. Pentagonal prismatic needle of gold of about 2 mm length
with two kinds of secondary growths from a natural deposite [44].
the rod tips. Pentagonal rods and needles of natural origin
have been reported rather early for gold. The needle
shown as an example of 1877 [44] in Fig. 19 carries some
additional twin species of rhombic prism and trigonal bipyramid shape on the pentagonal prism stem. The needle
tip obviously does not display five {111} faces as being
expected for decahedral structures, but has a more spiky
shape and faces corresponding to a half pentagonal trapezohedron. Two different growth modes are known for the
directed growth of decahedra along their fivefold twin
junction. One simply consists in an elongation of a decahedral particle having regular or modified shape as it is
schematically drawn for the prism and the star decahedron
in Fig. 20a and b. The other exhibits a modification of
{100} and {111} prism faces to periodically stepped faces
a
b
4.2.1 Elongated decahedral structures
Elongated decahedral structures simply may be achieved
by axial growth of a prism decahedron along its fivefold
twin junction, provided a distinct growth rate anisotropy
or some kind of surface modification will prevent significant radial growth. The rod shape formed thereupon corresponds to a pentagonal prism with pentagonal pyramids at
c
d
Fig. 20. Elongated decahedral structures as formed by preferred
growth along the fivefold twin junction of (a) a prism decahedron,
and (b) a star decahedron, as well as (c) and (d) by additional transformation of the prism faces to pyramid faces.
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534
a
b
Fig. 21. SEM image of a boron suboxide nanowire grown via solid
state chemical reaction, adapted with permission from [45], the starshaped cross-section of which is indicated by the dotted line (a), and
corresponding model in cross-section view with the twin planes arrowed (b). T1 to T5 mark the five twinned subunits of the nanowire.
so as to result in oblong pentagonal bipyramid shapes as it
is drawn in Fig. 20c and d.
Figure 21 illustrates outline and geometry of a boron
suboxide nanowire that is supposed to result from a star
decahedron by directed growth along the twin junction in
a solid state reaction [45]. Although this image is not
much convincing because of the rounded tips of the starshaped cross-section, the multiple twinned structure is
confirmed by selected area electron diffraction. The corresponding structural model in Fig. 21b features the atomic
nature of the terminating surfaces and twin planes (arrowed). The boron suboxid structure (rhombohedral, space
group 166) with a dihedral angle of 71.8 between two
adjacent twin planes appears to be well suited for the creation of cyclic twinned configurations. Quite similar twinning, that means prisms with striking five-pointed, starshaped cross section, has been observed in pentagonite, a
natural calcium vanadium silicate mineral [46]. The special geometry of the pentagonite crystal structure (orthorhombic, space group 36) with a dihedral angle of 72.7
between two adjacent twin planes readily permits fivefold
cyclic twinning. An example for pentagonal rods grown
from a prism decahedron [11, 46–48] is shown in Fig. 22.
The structural characterization by high resolution electron
microscopy of the silver nanorods grown by inert-gas aggregation technique [11] makes use of their 36 rotational
periodicity. Distinctly different image contrast appearance
is obtained for rotating the rod by 18 from a base-orientation where the electron beam hits perpendicular to a prism
face (see, for example, the hatched area in the schematic
drawing, Fig. 22b) to a side-orientation where the electron
beam runs parallel to a prism face.
At particles with decahedron shape anisotropic growth
also may proceed, in addition to the preferred growth
along the fivefold twin junction, by preferred growth
along a reentrant edge at the outer bounds of one of the
twin planes. Thus unidirectional radial growth is combined
with axial growth so as to create plates of asymmetric
structure as it is demonstrated in Fig. 23 by an example of
gold from solution synthesis [49]. The twin boundary extended this way is marked by hatching in the schematic
drawing of Fig. 23b. Another type of deviation from the
pyramid capped pentagonal prism shape of multiply
twinned rods is reported for copper rods grown by metallorganic chemical vapour deposition [50] where the radial
a
b
Fig. 22. HREM image of a pentagonal nanorod of silver (a) grown
by inert gas aggregation, adapted with permission from [11], recorded
with the electron beam perpendicular to one of the prism faces, indicated by the hatched area in the schematic drawing (b).
prism edges uniformly increase during growth leading to a
baseball bat-like shape. An opposite way of modification
of decahedron-based multiply twinned rods consists in a
uniform decrease of the radial prism edges during growth
leading to an oblong pentagonal bipyramid shape as it has
been reported for the Ag(+)-assisted solution synthesis of
gold nanostructures [51–55]. Apparently, the {100} prism
faces of pentagonal rods have been replaced by periodically stepped faces like {11n}. An example is given in
Fig. 24 where the schematic representation points to a certain rounding effect at the tips of these particles. Even
a
b
Fig. 23. SEM image of gold particles (a) formed in a polyol-assisted
solution synthesis, adapted with permission from [49], where one exhibits, in addition to growth along the twin junction, preferred growth
along a twin boundary marked by hatching in the corresponding model (b).
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535
Shape and growth of multiply twinned nanoparticles
H. Hofmeister
a
b
Fig. 24. TEM image of gold nanoparticles by Ag(+)-assisted solution
synthesis, adapted with permission from [53], including particles of
oblong pentagonal bipyramid shape (a) as schematically drawn in (b).
more complicated structures have been observed very recently in the seed-mediated synthesis of gold nanocrystals
which exhibit in addition to this oblong pentagonal bipyramid shape also a star-shaped cross-section [56] as schematically drawn in Fig. 20d. Likewise, molybdenum nanotrees have been formed in ambient air using atmosphericpressure microplasma [57] where branching growth along
the twin boundaries in combination with preferred growth
along the twin junction produces a fivefold-twinned starshaped cross-section with gaps between branches and
twigs inclined upwards to the stem by about 30 which
exhibit increasing extension from the base to the tip.
4.2.2 Elongated icosahedral structures
Icosahedron-based structures do not by far show as much
tendency for anisotropic growth as it is observed for decahedral particles. One of the main reasons should be their
minimal surface energy because of the only slight difference to a nearly spherical shape. Another one is the highly
uniform configuration. From a central point shared by 20
tetrahedral subunits fivefold twin junctions extend in 12
directions around which 30 twin boundaries are grouped.
Nevertheless, there are two exceptions which favour aniso-
Fig. 26. HREM image (a) and image contrast calculation (b) of a
FePt particle obtained by inert gas condensation that exhibits an icosahedral-decahedral hybrid structure, adapted with permission from
[57].
tropic growth variations also for icosahedra. One is given
by a certain probability of uniaxial growth along one of
the twin junctions as it is drawn schematically in Fig. 25.
In principle this may be understood as a transition from
an icosahedral to a decahedral structure and the resulting
particle configuration is readily obtained by adding a pyramid-capped pentagonal rod to an incomplete icosahedron
of 15 subunits consisting of a decahedron plus a pentagonal antiprism.
Such hybrid multiply twinned structures have been reported for gold and silver particles to result from coalescence processes [58], and for FePt particles owing to a
lack in stability during the growth [59]. For the latter example Fig. 26 shows a HREM image together with an image contrast simulation according to a model sketched in
Fig. 25. In both cases there is achieved only a limited extent of anisotropic growth. Another way to overcome the
anisotropy restraint is the directed growth of icosahedral
structures by preferred stacking of tetrahedral subunits
along one fivefold twin junction that has been experimentally observed in metal particles grown on crystalline substrates via PVD [12, 16, 58]. As it may be deduced from
the schematically drawing in Fig. 27 it needs a certain
a
a
b
Fig. 25. Transition from icosahedral to decahedral structure by uniaxial growth along one fivefold twin junction which can be thought as a
pentagonal rod supplemented to an incomplete icosahedron consisting
of a decahedron plus a pentagonal antiprism.
b
Fig. 27. Schematic repreesentation of the directed growth of icosahedral structures by preferred stacking of tetrahedral subunits along one
fivefold twin junction that can be described as linear assembling of
pentagonal bipyramids and pentagonal antiprisms.
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536
Acknowledgments. The author would like to thank all colleagues
close and far who made available to him results related to the subject
of multiply twinned particles in the course of nearly three decades of
consideration.
References
b
a
c
Fig. 28. HREM image of a double icosahedron gold particle (a) on
crystalline substrate, adapted with permission from [12], consisting of
two icosahedra in twin position which share one common decahedron as sketched schematically in (b). Continuation of this directed
growth leads to rod-like particles with multi-antiprism morphology as
shown in (c).
growth configuration being in favour of attaching tetrahedral subunits so as to create pentagonal antiprisms and
pentagonal bipyramids along one of the twin junctions
present in an icosahedral particle. The resulting structure
could be named double icosahedron or twin icosahedron.
Appropriate growth configurations are met with straight
surface steps of substrate crystals that provide preferred
sites of accomodation of vapour species so as to promote
growth and coalescence of particles along the step line.
Figure 28a shows a HREM image of such a double icosahedron gold particle consisting of two icosahedra in twin
position that share one common decahedron as sketched
schematically in Fig. 28b [12]. From Fig. 27 one may recognize that the particle morphology corresponds to a pentagonal bi-antiprism pyramid-capped on both sides. Continuation of such template-directed growth should lead to
rod-like particles as shown in Fig. 28c having multi-antiprism surface morphology.
5. Summary
An overview is given on the considerable number of
weakly as well as strongly anisotropic forms of nanoparticle shape resulting from cyclic pseudo-fivefold twinning
as constitutive building principle. Besides the shape variations due to growth stacking of tetrahedral subunits this
overview includes the nearly regular polyhedron shape
variations due to growth rate changes and the strongly anisotropic growth of multiply twinned particles occurring as
branching growth, or as unidirectional growth, respectively. Generally, the weakly anisotropic shape evolution
as well as the strongly anisotropic growth of decahedral
particles appear more rich in variety as those of icosahedral particles. It is worthwile to point out that for a certain
class of materials multiple twinning represents a reasonable means to approach the issue of one-dimensional nanostructures.
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