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Shape variations and anisotropic growth of multiply twinnednanoparticles
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 dis-play nearly regular polyhedron shape variety together withstrongly anisotropic shape variations due to growth pro-cesses are reviewed with regard to their unique shape evo-lution based on the specific formation modes as well as onthe particular structure of twin-related subunits. The re-view includes (i) the shape variations due to growth bystacking of tetrahedral subunits, (ii) the role of growthconditions in the shape evolution of multiply twinned na-noparticles, and (iii) the modes of twin-based anisotropicgrowth including branching growth and unidirectionalgrowth. The particular structures are introduced makinguse of electron microscopy structural characterization ofmultiply twinned metal nanoparticles as well as some non-metal examples, and instructive models of the various con-figurations.
1. Introduction
1.1 Shape evolution of nanoparticles –the role of twinning
Nanoparticles with strong shape anisotropy, like rod orplatelet shapes, attract large attention because of their in-teresting physical properties. For single crystalline parti-cles there is a lot of methods to achieve strongly anisotro-pic growth (see, e.g., [1–5]). Sources of anisotropicgrowth may be either the position within the growth envir-onment which can lead to anisotropic shape of crystalliteshaving equivalent faces, or differences in growth rate ofcrystallites bounded by different faces where the growthrate ratio is depending on temperature and supersaturation.In view of more complex routes of synthesis anisotropicgrowth of one-dimensional nanostructures may occur, forexample, as unidirectional axial growth due to inhibitionof radial growth. Such growth techniques may be classi-fied as seed-mediated, template-directed, or defect-mediated growth, respectively [5].
Quite different, but not less remarkable shape variationscan be found for multiply twinned particles (MTPs) withnon-crystallographic pseudo-fivefold rotation axes, thatmeans particles with decahedron and icosahedron shape[6, 7], respectively. Cyclic fivefold twinning is a wide-spread habit of nanoparticles [7], found not only in syn-thetic materials as reported for the first time in 1957 [8],but also in crystallite compounds of natural origin, datingback as early as 1831 [9]. For the sake of clarity weshould consider all these twins as being due to pseudo-pentagonal 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 oftetrahedron-shaped subunits arranged around fivefold rota-tion axes has experimentally been observed. The shapevariations of multiple twins with nearly regular polyhe-dron shape can mostly be explained by different growthrates of the bounding faces of their subunits, if they donot exhibit tetrahedron, but cuboctahedron shape. Thenstar decahedron, prism, facet, and cube decahedron, re-spectively, may occur as corresponding growth forms.
At particles with decahedron shape a strongly anisotropicshape evolution may proceed by preferred growth along oneor some reentrant edges of the outer bounds of twin planesor along the fivefold junction. While the former results inradial growth in one or some directions, the latter is equiva-lent to unidirectional axial growth due to an inhibition of anyradial growth. The rod shape formed thereupon correspondsto a pentagonal prism with pentagonal pyramids at the rodtips [11]. At particles with icosahedron shape strongly aniso-tropic shape evolution is mainly observed via preferred at-tachment of tetrahedron-shaped subunits along a fivefoldaxis, through which stacks of pentagonal antiprisms withpentagonal pyramids at the rod tips may form [12].
The above mentioned shape variations as well as exam-ples of strongly anisotropic growth of MTPs shall be in-troduced by means of electron microscopy findings of ourown work including various collaborations, as well assome work reported in the literature, and shall be illus-trated by appropriate models. The materials involvedcomprise noble metals and semiconductors, as well as mole-cule crystals and even a silicate mineral. Besides a shortintroduction of composition and appearance of multiplytwinned particles, this review contains considerations of
528 Z. Kristallogr. 224 (2009) 528–538 / DOI 10.1524/zkri.2009.1034
# by Oldenbourg Wissenschaftsverlag, Munchen
* e-mail: [email protected]
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shape variations due to growth by stacking of tetrahedrasubunits, shape variations due to growth rate changes, andthe anisotropic growth of both kinds of MTPs, respectively.
1.2 Composition and appearance of multiplytwinned particles of regular polyhedron shape
Multiply twinned particles consist of several subunits, thatmeans they are composed in such a way that subunits ofequal shape of regular tetrahedra are twin-related to eachother resulting in polyhedra of unique morphology andunusual symmetry [7] as can be seen in the schematicrepresentation given in Fig. 1. The one on the left handside (Fig. 1a) is a decahedron, that means an equal edgelength pentagonal bipyramid, containing 5 tetrahedra incontact twin orientation to each other stacked around onefivefold axis that is marked by a dotted line. The otherone (Fig. 1b) is an icosahedron, that means an equal edgelength, pentagonal antiprism pyramid-capped on bothsides, containing 20 tetrahedra, also in contact twin orien-tation to each other, stacked around six fivefold axeswhich are marked by dotted lines. Their mode of appear-ance depends on the orientation with respect to a support-ing substrate or a surrounding matrix – four high symme-try 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-
ary, or (001) of a tetrahedron subunit parallel to the view-ing direction, or to the direction [111] of a bounding faceof a subunit perpendicular to the viewing direction. Theresulting particle images have rhombic, pentagonal or hex-agonal contour of various style.
2. Shape variations due to growth by stackingof tetrahedral subunits
Previous to any shape variation of the multiply twinnedpolyhedra, elementary steps of shape evolution occur via
Shape and growth of multiply twinned nanoparticles 529
Fig. 1. Schematic representation of a decahedron (left) and an icosahe-dron (right) composed of regular tetrahedra arranged around fivefold axes.
Fig. 2. Schematic drawing of the appearance of decahedra in highsymmetry orientations on a substrate.
Fig. 3. Schematic drawing of the appearance of icosahedra in highsymmetry orientations on a substrate.
a�
b�Fig. 4. Successive stacking of tetrahedra via repeated twinning duringgrowth illustrated by (a) schematic drawing, and (b) TEM images,adapted with permission from [14], in bright-field (upper row), anddark-field (lower row) mode of one, two, and three subunits.
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assembling of tetrahedra subunits by repeated twinningduring growth. This successive stacking of subunits easilyresults in the formation of decahedra, and icosahedra, re-spectively [13–15], as it is demonstrated in Figs. 4 and 5for decahedra and in Figs. 6 and 7 for icosahedra. Theexperimental observation of the first steps shown inFig. 4b includes transmission electron microscopy (TEM)images in bright-field (upper row) and in dark-field (lowerrow) mode of an unattached tetrahedron in (001) orienta-tion (left) as well as particles containing one and twotwins attached to a parent subunit (centre and right) as itis schematically sketched in Fig. 4a [14]. In principle, theassembling of five individual tetrahedra so as to form adecahedron as indicated by Fig. 5 cannot be excluded.The process of subunits assembling obviously does notstop with creating decahedra, but continued stacking ofsubunits towards creation of icosahedra via intermediatescontaining eight and twelf tetrahedra as it is schemati-cally drawn in Fig. 6 has been observed. Almost half-icosahedral particles obtained by physical vapour deposi-tion (PVD) have repeatedly been reported as intermediate
stage of the successive stacking of twinned subunits[14–18].
An experimental example of Gao et al. [15] from thesolution growth of silver particles studied by scanningelectron microscopy (SEM) is presented in Fig. 7 where anumber of incomplete MTPs, including a three tetrahedraprecursor of a decahedron and a 15 tetrahedra precursor ofan icosahedron, are marked by arrows. Another route toicosahedra is modelled in Fig. 8 where a decahedron (left)is added to a pentagonal antiprism (centre) composed often twinned tetrahedra so as to create an intermediatestage (right) that needs another five subunits of a decahe-dron to end up with an icosahedron. The assembling ofmultiply twinned particles from tetrahedra subunits step bystep implies that under certain conditions for the materialsinvolved the tetrahedron may be a possible growth shape,at least during growth twinning at the nanometre scale.Usually, such materials have cubic crystal symmetrywhich can be grown into cubic, cuboctahedral, and octahe-dral shape, respectively, depending on the growth condi-tions. As will be demonstrated below, the latter modes ofshape may occur for the subunits of completed multiplytwinned particles whose structure is governed by twinningduring the initial stage of spontaneous nucleation.
530 H. Hofmeister
Fig. 5. Contact twin-related assembling of 5 tetrahedron subunits toform a decahedron.
a� b�
c� d�
Fig. 6. Continuation of successive stacking of tetrahedra beyond thedecahedron (a). Intermediate stages of 8 subunits (b) and 12 subunits(c) complement one another to an icosahedron (d).
Fig. 7. SEM images of silver particles from solution growth (Gaoet al., adapted with permission from [15]) demonstrating intermediatestages (incomplete MTPs) formed upon successive stacking of tetra-hedra.
Fig. 8. Alternative route to the assembly of an icosahedron via attach-ing a tetrahedron-based pentagonal antiprism to a decahedron leavingspace for another decahedron in mirror symmetry to the first one.
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3. Shape variations due to growth rate changes
The shape evolution from the octahedral to the cubic formof crystals involves intermediate forms like the truncatedoctahedron, the cuboctahedron, and the truncated cube.Their outline is determined by the ratio of cube faces tooctahedron faces growth rates v100/v111 [3] or more com-mon by the growth parameter a ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3v100=v111
p[19].
Subunits of general cuboctahedral shape are thought toresult from progressive and symmetrical removal of thecorners of both starting polyhedra that are exposed to vari-ations of the growth conditions. Consequently, distinctshape variations of MTPs originating from multiple twinformation at the initial stage of growth may evolve uponsuitably controlling the growth conditions, which increasesthe number of varieties of nearly regular polyhedron parti-cle shape. The growth parameter a is determined by con-ditions like the precursor concentration and the substratetemperature applied during growth. Since the shape of sin-gle crystals can be easily correlated to this parameter, atleast in the range 1 � a � 3, we have chosen four speci-fic values of a corrresponding to characteristic stages ofshape evolution [3, 7, 19]. These are the octahedron ob-tained for a ¼ 3, the truncated octahedron for a ¼ 2, thecuboctahedron 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 thecorresponding single crystal shape unique examples ofMTP shape occur which are shown for the decahedron inFig. 9. Different from the regular decahedron composed offive regular tetrahedra being bounded by equilateral trian-gular faces of type {111} only (see 1.2), now the particlemorphology is subdivided and contains bounding faces ofdifferent type and size [19–22]. The evolution of thenearly regular polyhedron shape variety of decahedra con-tains, starting from a perfect octahedron shape of subunits,(i) a star decahedron that exhibits 5 peripheral reentrantedge configurations (Fig. 9a), (ii) a facet decahedron ob-tained by truncation of the outer tips of the star decahe-dron so as to display {100} faces (Fig. 9b), (iii) a prismdecahedron resulting from increased truncation where the
{100} faces contact each other (Fig. 9c), and (iv) a cubedecahedron corresponding to a perfect cube shape of sub-units, where no {111} faces remain (Fig. 9d). The prismdecahedron model, also named “Ino decahedron” [20] andthe facet decahedron model, also named “Marks decahe-dron” [21] have been introduced to take account of thenecessary energy balance, mainly between surface andstrain energy of these particles. Together with that of theregular decahedron, these decahedral particle shapes havebeen most frequently observed experimentally. From theexperimental TEM images of a palladium decahedron, ob-tained by PVD on potassium iodide substrate, shown inbright-field and in dark-field mode in Figs. 10a and 10bone can clearly recognize its compact morphology [23].
Remarkably, the most earliest report on an object thatexhibits multiply twinned configuration and decahedralshape is by G. Rose from 1831 [9] and it features, as canbe seen from Fig. 11a, the subdivided morphology of afacet decahedron of gold which has been found near Boic-za, Romania. Another early example of natural origin [24]is the copper decahedron shown in Fig. 11b that exhibitsperipheral reentrant edge configurations like a star decahe-dron, but no tips at the outer end of the subunits. Addi-tionally, this particle displays a dimple at the emergencepoint of the fivefold twin junction, that means a concavevertex surrounded by five {111} facets. This morphologi-cal feature must not be considered as a characteristic ofcopper decahedra or decahedra of natural origin. There arealso examples in the literature that describe a copper MTPof natural origin having clearly star decahedron shapewithout such central dimple [25], as well as diamond stardecahedra of natural and of synthetic origin that just dis-play this particular habit [26, 27]. The shape of the deca-hedron shown in Fig. 11b can be explained by assuming atruncated tetrahedron shape of its subunits. As illustratedby Fig. 12, stacking of such truncated tetrahedra, alsoknown as Friauf polyhedra, easily enables to constructdecahedra and even icosahedra [28] that exhibit both, twinjunction dimpling and twin boundary grooving. Occasion-ally, a certain anisotropy of decahedral MTPs may occurbecause of non-uniform development of such featureswithin the subunits of a particle as it is observed at theC60 star decahedron obtained by aerosol synthesis [29].That is illustrated by the high resolution electron micro-scopy (HREM) image shown in Fig. 13. Experimental evi-
Shape and growth of multiply twinned nanoparticles 531
a� b�
c� d�
Fig. 9. Evolution of decahedron morphology with growth parameteraffecting 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 itstwin junction oriented parallel to the electron beam: (a) in bright-field; and (b) in dark-field mode [23].
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dence of fabrication of a cube decahedron without any{111} faces is rarely found, but for values of the growthparameter slightly above a ¼ 1 reentrant grooving at thetwin boundary sections between {111} faces occurs as itis schematically shown in Fig. 14a for a ¼ 1.16 [19]. Thisleads to additional cube faces at the expense of the stillremaining octahedron faces.
Another direction of shape evolution is opened by thesolution synthesis of gold nanoparticles using an eutectic
mixture of choline chloride and urea as solvent that hasbeen reported to result in star decahedra [30] whose tipsare distinctly sharper than those bounded by octahedronfaces as considered above. The free faces forming each tipare of the highly stepped {331} type resulting in a tipangle of 26.6� instead of 70.53� as expected for {111}faces. Obviously, this morphology is due to branchinggrowth (discussed below in sect. 4.1) proceeding in direc-tion of the apex of the octahedral subunits.
3.2 Evolution of the icosahedron morphology
The evolution of the nearly regular polyhedron shape vari-ety of multiply twinned icosahedra is illustrated by Figs.14b and 15. Changes of the subunit outline due to growthparameter variation produce different types of deviationfrom the regular icosahedron having a compact, nearlyspherical shape. For subunits of octahedral shape the cor-responding icosahedron is bounded by corner-connected,equilateral triangular faces of {111} type which alwayssurround a pit, that means a concave pentagonal vertexconsisting of {111} faces. As can be seen in Fig. 15a allthese pits are corner-connected to each other. Smaller pitsor dimples of the same geometry occur for subunits oftruncated octahedron shape where the peripheral {111}faces now have hexagonal outline (Fig. 15b). A cuboctahe-dral subunit shape results in the morphology of a regularicosahedron not to be distinguished from that composed oftetrahedral subunits (see Fig. 15c). For values of thegrowth parameter a ¼ 1.5 twin boundary grooving occurs,as it is shown in Fig. 14b, whereby cube faces additionallyappear at the expense of the diminishing octahedron faces.Finally, the multiply twinned icosahedron for a ¼ 1
532 H. Hofmeister
a� b�
Fig. 11. Early findings of multiplytwinned crystallites of decahedralshape: (a) facet decahedron of gold(1831 [9]), and (b) nearly star-like deca-hedron of copper (1882 [24]).
a� b�Fig. 12. Assembling of 5 truncated tetrahedron subunits to form a deca-hedron that exhibits twin junction dimples and twin boundary grooves.
Fig. 13. HREM image of a slightly modified star decahedron of C60,adapted with permission from [29], by cyclic twinning of subunits ofnearly octahedral shape.
a� b�Fig. 14. Schematic drawing of (a) a decahedron, and (b) an icosahe-dron which exhibit reentrant grooving at twin boundary sections be-tween {111} faces for a growth parameter value slightly above 1.
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(Fig. 15d) can be described as regular icosahedron whosetriangular bounding faces are capped by fitting pyramidssuch that an all-cube-face star polyhedron results.
Besides regular icosahedra experimental observationsof the shape evolution with growth parameter mainly in-clude examples that exhibit dimples of various size at theemergence of twin junctions as it is shown in Fig. 16 forboron suboxide particles [31], as well as twin boundarygrooving of varying extent [27, 32]. Regular icosahedracan often be found in particle ensembles of transition met-als [33] while icosahedra with dimples and grooves at thesurface frequently occur for diamond and boron suboxidenanoparticles fabricated, for example, by chemical vapourdeposition, acetylen flame synthesis, and high pressuremelt synthesis, respectively [27, 31, 32]. Only one reporthas been given up to now on icosahedra having a starryshape where Burt et al. [34] propose a model of thesegold particles obtained by solution growth which consistsof trigonal pyramids capping the corresponding faces of aregular icosahedron. However, the additional assumptionthat these pyramids have tetrahedral shape and arebounded by {111} surfaces requires not only capping tet-rahedra situated in twin relation with respect to their basetetrahedron, but it also excludes to consider this star-shaped polyhedron as being due to growth conditions fa-vouring a cube face-bounded polyhedron. This will be dis-cussed in more detail in the next section.
4. Strongly anisotropic growth of multiplytwinned particles
4.1 Branching growth
Branching growth as directional crystallization along theapex directions of a polyhedral crystal is induced by con-centration effects in a concentric diffusion field formedaround the growing crystal [3]. Similar to the case of sin-gle crystalline particles various branched morphologiescan be found in multiply twinned particles with and with-out including the twin boundaries. Silicon precipitatesgrown in Al––Si melt or fabricated by laser processing ofcorresponding alloy materials have been reported to exhi-bit a branched structure where the branches extend likefingers from the twin boundary corners and proceedstraightaway with these boundaries [35, 36]. Such twinfinger decahedra have been observed also for gold andplatinum nanoparticles fabricated by solution synthesis[37–39]. As an example Fig. 17 shows a TEM image of atwin finger decahedron of gold [38] together with theschematic drawing of two model subunits containing in-dented trigonal faces surrounding a concave edge fromwhich the configuration of the MTP may be imagined.The excessive growth along the twin boundaries is thoughtto result from unfavourable growth conditions at the pe-riphery of tetrahedral subunits. Branching growth also isobserved for single crystalline metal particles formed inthe above mentioned solution routes of synthesis [37–39].
Another situation is met with the different geometry ofstar decahedra which already exhibit distinctly protrudingapexes. Under certain conditions of growth star decahedraformed by chemical vapour deposition in boron nitrideplatelets [40, 41] may tend to develop a fivefold branchedmorphology as it has been observed for relatively highdeposition temperature and relatively low total gas pres-sure [42]. Here the branching does not extend from thetwin boundaries emergence points, but it proceeds fromthe star tips of the subunits, so as to replace the tips byfinger-like protrusions. Quite accordingly, the spiky icosa-hedron mentioned above [34] could be understood interms of branching growth starting at the tips of a staricosahedron. It may be recognized from the TEM image
Shape and growth of multiply twinned nanoparticles 533
a� b�
c� d�
Fig. 15. Evolution of icosahedron morphology with growth parameteraffecting the subunit shape: (a) octahedron; (b) truncated octahedron;(c) cuboctahedron; (d) cube.
Fig. 16. SEM images of boron suboxide icosahedral particles, adaptedwith permission from [31], which exhibit dimples of various size atthe emergence points of twin junctions.
b�
a�Fig. 17. HREM image of a finger decahedron of gold from solutionsynthesis, adapted with permission from [38], (a) together with sche-matic drawing of two model subunits containing indented trigonalfaces surrounding a concave edge (b) to be joined along a twin plane(arrowed) and to be completed accordingly by three matching sub-units.
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in Fig. 18 that the pyramids capping this icosahedral parti-cle obviously appear more pointed than expexted for seg-ments of a cube capping the faces of a regular icosahe-dron as shown in Fig. 15d. Furthermore, from dark-fieldimages presented in the Burt et al. article [34] it can beconcluded that there is no twin boundary between the basetetrahedra forming the icosahedron and their respectivecapping pyramids. That means, the spikes making the par-ticles appear like star polyhedra most probably result froma kind of branching growth that also is observed for singlecrystalline particles obtained in the same synthesis.
4.2 Unidirectional growth
One-dimensional nanostructures like nanorods or nano-wires are mostly obtained by template-directed, surfactant-assisted, and/or seed-mediated processes that either con-fine the growth to one dimension or act as favourable sitesfor the adsorption of reactant molecules. Defect-mediatedor twin-induced growth based on the effect of twin bound-aries and fivefold twin junctions to enable reasonablegrowth rates at low precursor concentration [5, 43] mayeven allow promoter-free formation of such nanostruc-tures. The elongation of multiply twinned particles by uni-direational growth proceeds via distinctly different pro-cesses for decahedra and icosahedra, respectively.
4.2.1 Elongated decahedral structures
Elongated decahedral structures simply may be achievedby axial growth of a prism decahedron along its fivefoldtwin junction, provided a distinct growth rate anisotropyor some kind of surface modification will prevent signifi-cant radial growth. The rod shape formed thereupon corre-sponds to a pentagonal prism with pentagonal pyramids at
the rod tips. Pentagonal rods and needles of natural originhave been reported rather early for gold. The needleshown as an example of 1877 [44] in Fig. 19 carries someadditional twin species of rhombic prism and trigonal bi-pyramid shape on the pentagonal prism stem. The needletip obviously does not display five {111} faces as beingexpected for decahedral structures, but has a more spikyshape and faces corresponding to a half pentagonal trape-zohedron. Two different growth modes are known for thedirected growth of decahedra along their fivefold twinjunction. One simply consists in an elongation of a deca-hedral particle having regular or modified shape as it isschematically drawn for the prism and the star decahedronin Fig. 20a and b. The other exhibits a modification of{100} and {111} prism faces to periodically stepped faces
534 H. Hofmeister
Fig. 18. TEM image of a star-like icosahedral particle of gold,adapted with permission from [34], whose tips appear more spikythan expected for a cube icosahedron so as being affected by branch-ing growth.
Fig. 19. Pentagonal prismatic needle of gold of about 2 mm lengthwith two kinds of secondary growths from a natural deposite [44].
a� b�
c� d�Fig. 20. Elongated decahedral structures as formed by preferredgrowth along the fivefold twin junction of (a) a prism decahedron,and (b) a star decahedron, as well as (c) and (d) by additional trans-formation of the prism faces to pyramid faces.
Zeitschr. f. Kryst. u. Min. I Bd. Taf. II.
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so as to result in oblong pentagonal bipyramid shapes as itis drawn in Fig. 20c and d.
Figure 21 illustrates outline and geometry of a boronsuboxide nanowire that is supposed to result from a stardecahedron by directed growth along the twin junction ina solid state reaction [45]. Although this image is notmuch convincing because of the rounded tips of the star-shaped cross-section, the multiple twinned structure isconfirmed by selected area electron diffraction. The corre-sponding structural model in Fig. 21b features the atomicnature of the terminating surfaces and twin planes (ar-rowed). The boron suboxid structure (rhombohedral, spacegroup 166) with a dihedral angle of 71.8� between twoadjacent twin planes appears to be well suited for the crea-tion of cyclic twinned configurations. Quite similar twin-ning, that means prisms with striking five-pointed, star-shaped cross section, has been observed in pentagonite, anatural calcium vanadium silicate mineral [46]. The spe-cial geometry of the pentagonite crystal structure (orthor-hombic, space group 36) with a dihedral angle of 72.7between two adjacent twin planes readily permits fivefoldcyclic twinning. An example for pentagonal rods grownfrom a prism decahedron [11, 46–48] is shown in Fig. 22.The structural characterization by high resolution electronmicroscopy of the silver nanorods grown by inert-gas ag-gregation technique [11] makes use of their 36� rotationalperiodicity. Distinctly different image contrast appearanceis obtained for rotating the rod by 18� from a base-orienta-tion where the electron beam hits perpendicular to a prismface (see, for example, the hatched area in the schematicdrawing, Fig. 22b) to a side-orientation where the electronbeam runs parallel to a prism face.
At particles with decahedron shape anisotropic growthalso may proceed, in addition to the preferred growthalong the fivefold twin junction, by preferred growthalong a reentrant edge at the outer bounds of one of thetwin planes. Thus unidirectional radial growth is combinedwith axial growth so as to create plates of asymmetricstructure as it is demonstrated in Fig. 23 by an example ofgold from solution synthesis [49]. The twin boundary ex-tended this way is marked by hatching in the schematicdrawing of Fig. 23b. Another type of deviation from thepyramid capped pentagonal prism shape of multiplytwinned rods is reported for copper rods grown by metal-lorganic chemical vapour deposition [50] where the radial
prism edges uniformly increase during growth leading to abaseball bat-like shape. An opposite way of modificationof decahedron-based multiply twinned rods consists in auniform decrease of the radial prism edges during growthleading to an oblong pentagonal bipyramid shape as it hasbeen reported for the Ag(+)-assisted solution synthesis ofgold nanostructures [51–55]. Apparently, the {100} prismfaces of pentagonal rods have been replaced by periodi-cally stepped faces like {11n}. An example is given inFig. 24 where the schematic representation points to a cer-tain rounding effect at the tips of these particles. Even
Shape and growth of multiply twinned nanoparticles 535
a� b�
Fig. 21. SEM image of a boron suboxide nanowire grown via solidstate chemical reaction, adapted with permission from [45], the star-shaped cross-section of which is indicated by the dotted line (a), andcorresponding model in cross-section view with the twin planes ar-rowed (b). T1 to T5 mark the five twinned subunits of the nanowire.
a�
b�
Fig. 22. HREM image of a pentagonal nanorod of silver (a) grownby inert gas aggregation, adapted with permission from [11], recordedwith the electron beam perpendicular to one of the prism faces, indi-cated by the hatched area in the schematic drawing (b).
a�
b�
Fig. 23. SEM image of gold particles (a) formed in a polyol-assistedsolution synthesis, adapted with permission from [49], where one ex-hibits, in addition to growth along the twin junction, preferred growthalong a twin boundary marked by hatching in the corresponding mod-el (b).
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more complicated structures have been observed very re-cently in the seed-mediated synthesis of gold nanocrystalswhich exhibit in addition to this oblong pentagonal bipyr-amid shape also a star-shaped cross-section [56] as sche-matically drawn in Fig. 20d. Likewise, molybdenum nano-trees have been formed in ambient air using atmospheric-pressure microplasma [57] where branching growth alongthe twin boundaries in combination with preferred growthalong the twin junction produces a fivefold-twinned star-shaped cross-section with gaps between branches andtwigs inclined upwards to the stem by about 30� whichexhibit increasing extension from the base to the tip.
4.2.2 Elongated icosahedral structures
Icosahedron-based structures do not by far show as muchtendency for anisotropic growth as it is observed for deca-hedral particles. One of the main reasons should be theirminimal surface energy because of the only slight differ-ence to a nearly spherical shape. Another one is the highlyuniform configuration. From a central point shared by 20tetrahedral subunits fivefold twin junctions extend in 12directions around which 30 twin boundaries are grouped.Nevertheless, there are two exceptions which favour aniso-
tropic growth variations also for icosahedra. One is givenby a certain probability of uniaxial growth along one ofthe twin junctions as it is drawn schematically in Fig. 25.In principle this may be understood as a transition froman icosahedral to a decahedral structure and the resultingparticle configuration is readily obtained by adding a pyr-amid-capped pentagonal rod to an incomplete icosahedronof 15 subunits consisting of a decahedron plus a pentago-nal antiprism.
Such hybrid multiply twinned structures have been re-ported for gold and silver particles to result from coales-cence processes [58], and for FePt particles owing to alack in stability during the growth [59]. For the latter ex-ample Fig. 26 shows a HREM image together with an im-age contrast simulation according to a model sketched inFig. 25. In both cases there is achieved only a limited ex-tent of anisotropic growth. Another way to overcome theanisotropy restraint is the directed growth of icosahedralstructures by preferred stacking of tetrahedral subunitsalong one fivefold twin junction that has been experimen-tally observed in metal particles grown on crystalline sub-strates via PVD [12, 16, 58]. As it may be deduced fromthe schematically drawing in Fig. 27 it needs a certain
536 H. Hofmeister
a� b�Fig. 24. TEM image of gold nanoparticles by Ag(+)-assisted solutionsynthesis, adapted with permission from [53], including particles ofoblong pentagonal bipyramid shape (a) as schematically drawn in (b).
a�
b�Fig. 25. Transition from icosahedral to decahedral structure by uniax-ial growth along one fivefold twin junction which can be thought as apentagonal rod supplemented to an incomplete icosahedron consistingof a decahedron plus a pentagonal antiprism.
Fig. 26. HREM image (a) and image contrast calculation (b) of aFePt particle obtained by inert gas condensation that exhibits an ico-sahedral-decahedral hybrid structure, adapted with permission from[57].
a�
b�
Fig. 27. Schematic repreesentation of the directed growth of icosahe-dral structures by preferred stacking of tetrahedral subunits along onefivefold twin junction that can be described as linear assembling ofpentagonal bipyramids and pentagonal antiprisms.
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growth configuration being in favour of attaching tetrahe-dral subunits so as to create pentagonal antiprisms andpentagonal bipyramids along one of the twin junctionspresent in an icosahedral particle. The resulting structurecould be named double icosahedron or twin icosahedron.Appropriate growth configurations are met with straightsurface steps of substrate crystals that provide preferredsites of accomodation of vapour species so as to promotegrowth and coalescence of particles along the step line.Figure 28a shows a HREM image of such a double icosa-hedron gold particle consisting of two icosahedra in twinposition that share one common decahedron as sketchedschematically in Fig. 28b [12]. From Fig. 27 one may re-cognize that the particle morphology corresponds to a pen-tagonal bi-antiprism pyramid-capped on both sides. Contin-uation of such template-directed growth should lead torod-like particles as shown in Fig. 28c having multi-anti-prism surface morphology.
5. Summary
An overview is given on the considerable number ofweakly as well as strongly anisotropic forms of nanoparti-cle shape resulting from cyclic pseudo-fivefold twinningas constitutive building principle. Besides the shape varia-tions due to growth stacking of tetrahedral subunits thisoverview includes the nearly regular polyhedron shapevariations due to growth rate changes and the strongly ani-sotropic growth of multiply twinned particles occurring asbranching growth, or as unidirectional growth, respec-tively. Generally, the weakly anisotropic shape evolutionas well as the strongly anisotropic growth of decahedralparticles appear more rich in variety as those of icosahe-dral particles. It is worthwile to point out that for a certainclass of materials multiple twinning represents a reason-able means to approach the issue of one-dimensional na-nostructures.
Acknowledgments. The author would like to thank all colleaguesclose and far who made available to him results related to the subjectof multiply twinned particles in the course of nearly three decades ofconsideration.
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a�b�
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Fig. 28. HREM image of a double icosahedron gold particle (a) oncrystalline substrate, adapted with permission from [12], consisting oftwo icosahedra in twin position which share one common decahe-dron as sketched schematically in (b). Continuation of this directedgrowth leads to rod-like particles with multi-antiprism morphology asshown in (c).
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