Shape Variations and Anisotropic Growth of Multiply Twinned

This article is protected by German copyright law. You may copy and distribute this article for your personal use only. Other use is only allowed with written permission by the copyright holder. 10.1524/zkri.2009.1034 DOI by Oldenbourg Wissenschaftsverlag, Mu¨nchen (2009) 528–538 / # 224 Quite different, but not less remarkable shape variations At particles with decahedron shape a strongly anisotropic The above mentioned shape variations as well as exam- Z. Kristallogr. can be foundnon-crystallographic for multiply pseudo-fivefold twinnedmeans particles rotation particles (MTPs) axes, with[6, with decahedron 7], that and respectively.spread Cyclic icosahedron habit of fivefold shape thetic nanoparticles twinning materials [7], is as foundbut reported a also not for wide- in only theback crystallite in first compounds as syn- time of in earlyshould natural 1957 consider origin, as [8], dating all 1831pentagonal these metrical [9]. twins features ForThus as of they the being actually the sake areBesides due corresponding pseudo-fivefold the to of lattice. rotation classical pseudo- twins clarityat processes [10]. MTPs we of also nucleationtetrahedron-shaped shape and subunits arranged growth, evolutiontion around by fivefold axes successive rota- has stackingvariations of experimentally of multiple beendron twins shape observed. can with Therates mostly nearly shape of be regular thenot explained bounding polyhe- exhibit by faces differentstar tetrahedron, of growth decahedron, their but subunits, prism,spectively, cuboctahedron may if facet, occur shape. they as and Then corresponding do growth cube forms. decahedron,shape evolution re- may proceed byor preferred some growth reentrant along one edgesor of along the the outer boundsradial fivefold growth of junction. in twin While one planes orlent the to some former unidirectional directions, axial results the growthradial due latter in to growth. is an The equiva- inhibition rod of shapeto any formed a thereupon pentagonal corresponds prismtips [11]. with At pentagonal particles with pyramidstropic icosahedron at shape shape strongly the evolution aniso- rod istachment mainly of observed tetrahedron-shaped viaaxis, preferred subunits through at- along whichpentagonal a stacks pyramids at fivefold of the rod pentagonal tips may form antiprisms [12]. with ples of stronglytroduced anisotropic by growth means of ofown electron MTPs work microscopy shall findingssome including be of work in- our various reportedtrated collaborations, in by as thecomprise literature, noble well appropriate metals and and as semiconductors,cule models. shall as well crystals be as The mole- and illus- introduction even materials of a silicate composition involved twinned mineral. and particles, Besides appearance this a of review short contains multiply considerations of – , [1–5]). Sources of anisotropic e.g. * Cyclic multiple twins as nanoobjects that dis- * e-mail: [email protected] Nanoparticles withplatelet strong shapes, shape attract anisotropy,teresting large like physical attention because properties. rodcles of there For or is their single apic in- crystalline lot of growth parti- methods to (see, achieve strongly anisotro- 1. Introduction 1.1 Shape evolution of nanoparticles growth may be eitheronment the which position can within leadhaving the to growth equivalent envir- anisotropic faces, shapecrystallites or of bounded differences crystallites byrate in ratio different growth is faces rate dependingIn where on of view temperature the of andgrowth growth supersaturation. more of complex one-dimensional routesexample, nanostructures of as may synthesis unidirectional occur,of anisotropic axial for radial growth growth.fied due Such to growth as inhibition techniquesmediated growth, may respectively seed-mediated, be [5]. classi- template-directed, or defect- the role of twinning Abstract. Received May 27, 2008; accepted September 21, 2009 Electron microscopy / Crystal morphologyShape / evolution / Multiple twinning / Pseudofivefold rotationAnisotropic / growth play nearly regular polyhedronstrongly shape anisotropic variety together shapecesses with are variations reviewed due withlution to regard based to on growth their thethe pro- unique specific formation shape particular modes evo- structureview as well includes of as (i) on twin-relatedstacking the subunits. of shape The tetrahedralconditions variations re- in subunits, due the (ii)noparticles, to shape and evolution growth the of (iii) by rolegrowth multiply the twinned of modes including na- growth ofgrowth. branching twin-based The anisotropic growth particularuse structures of and electron aremultiply unidirectional twinned microscopy introduced metal structural nanoparticles making metal as examples, characterization well and as of instructivefigurations. some models non- of the various con- Max Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany Herbert Hofmeister Shape variations and anisotropicnanoparticles growth of multiply twinned 528 This article is protected by German copyright law. You may copy and distribute this article for your personal use only. Other use is only allowed with written permission by the copyright holder. b a 529 b) TEM images, ) schematic drawing, and ( a Schematic drawing of the appearance of icosahedra in high Successive stacking of tetrahedra via repeated twinning during adapted with permissiondark-field from (lower row) [14], mode in of one, bright-field two, (upper and row), three subunits. and ary, or (001) ofing a direction, tetrahedron or subunitof to parallel the a to direction subunit theresulting [111] view- perpendicular particle of images a to haveagonal bounding the rhombic, contour face pentagonal viewing of or various direction. hex- style. The Fig. 4. 2. Shape variationsof due tetrahedral to subunits growth by stacking Previous to anypolyhedra, shape elementary variation steps of of the shape evolution multiply occur twinned via growth illustrated by ( Fig. 3. symmetry orientations on a substrate. Schematic drawing of the appearance of decahedra in high Schematic representation of a decahedron (left) and an icosahe- Fig. 2. symmetry orientations on a substrate. 1.2 Composition andtwinned appearance particles of of multiply regular polyhedron shape Multiply twinned particles consistmeans of they several are subunits,equal composed that shape in of suchother regular a resulting tetrahedra way are that inunusual twin-related subunits polyhedra symmetry of to of [7]representation each unique given as in morphology canside Fig. (Fig. be and 1. 1a) seen Thelength is one in a pentagonal on decahedron, the bipyramid,contact the that schematic twin containing means left orientation an 5fivefold hand to equal axis each tetrahedra edge other that in one stacked is (Fig. around 1b) marked one islength, by an icosahedron, a pentagonal that dottedsides, means containing antiprism line. an 20 The equal tetrahedra,tation pyramid-capped edge other also to in on contactwhich each twin are both orien- other, markedance by stacked depends dotted on lines. around theing Their orientation substrate six mode with or of fivefold respect atry appear- surrounding to orientations axes matrix a are support- –[7] known four for which high both are(icosahedron) symme- of the shown where twin in[110] the polyhedra of Fig. indices 2 a fivefold (decahedron) refer twin and to junction, Fig. [112] the 3 of directions a twin bound- shape variations duesubunits, to shape variations growth duethe by anisotropic to stacking growth growth of of both rate kinds changes, tetrahedra of and MTPs, respectively. Fig. 1. dron (right) composed of regular tetrahedra arranged around fivefold axes. Shape and growth of multiply twinned nanoparticles This article is protected by German copyright law. You may copy and distribute this article for your personal use only. Other use is only allowed with written permission by the copyright holder. H. Hofmeister . [15] from the et al SEM images of silver particles from solution growth (Gao Alternative route to the assembly of an icosahedron via attach- ., adapted with permission from [15]) demonstrating intermediate An experimental example of Gao stage of[14–18]. the successive stackingsolution of growth twinnedelectron of microscopy subunits silver (SEM)number is particles presented of studied in incompleteprecursor Fig. MTPs, by 7 of including where a scanning a decahedron a an and three icosahedron, a tetrahedra 15 areicosahedra tetrahedra marked is precursor modelled of by inis arrows. Fig. added 8 Another to where routeten a a to decahedron twinned pentagonal (left) stage antiprism tetrahedra (right) (centre) so that composeddron needs as of another to to five endmultiply subunits create up twinned of particles with a an fromstep decahe- an tetrahedra intermediate implies subunits icosahedron. that step The underinvolved by the certain assembling conditions tetrahedron of forat may the be least materials a duringUsually, possible growth growth such shape, twinningwhich at can materials be the grown havedral into nanometre cubic, shape, cubic scale. cuboctahedral, respectively, andtions. depending octahe- crystal As on willshape the symmetry be growth demonstrated may below, condi- occurtwinned the for particles latter whose the modes structureduring subunits of the is of initial governed stage completed by of twinning multiply spontaneous nucleation. Fig. 8. ing a tetrahedron-based pentagonalspace for antiprism another to decahedron a in decahedron mirror leaving symmetry to the first one. Fig. 7. et al stages (incomplete MTPs)hedra. formed upon successive stacking of tetra- d b b) and 12 subunits d). c a ). Intermediate stages of 8 subunits ( a Contact twin-related assembling of 5 tetrahedron subunits to Continuation of successive stacking of tetrahedra beyond the ) complement one another to an icosahedron ( c ( Fig. 6. decahedron ( form a decahedron. assembling ofduring tetrahedra growth. subunits This successiveresults by stacking in repeated of the subunitsspectively twinning formation easily [13–15], of as decahedra,for it and decahedra is icosahedra, demonstrated andexperimental re- in in Figs. observation Figs. 4Fig. and 6 4b of 5 includes and theimages transmission 7 in electron for first bright-field microscopy (upper icosahedra.row) (TEM) row) steps mode The and of in showntion an dark-field unattached (lower (left) in tetrahedrontwins as in attached well (001) to orienta- is as a schematically parent particles sketched subunitassembling in containing (centre Fig. of one and 4a five right) [14].decahedron and individual as In as two tetrahedra principle, it The the indicated so process as by to ofstop Fig. 5 form subunits with a cannot assembling creatingsubunits be obviously towards decahedra, creation does excluded. butcontaining of not continued eight icosahedra stacking andcally via of intermediates twelf drawn tetrahedraicosahedral in particles as Fig. 6 obtained ittion by has (PVD) is physical have been schemati- vapour repeatedly observed. deposi- been Almost reported as half- intermediate Fig. 5. 530 This article is protected by German copyright law. You may copy and distribute this article for your personal use only. Other use is only allowed with written permission by the copyright holder. 531 ) in bright- a b b) in dark-field mode [23]. TEM images of a PVD grown palladium decahedron with its Remarkably, the most earliest report on an object that a {100} faces contactdecahedron each corresponding other to (Fig.units, a 9c), perfect where and cube no (iv)decahedron shape {111} a model, of faces also cube sub- named remainthe “Ino (Fig. facet 9d). decahedron” decahedron [20]dron” The model, and prism [21] also havenecessary named been “Marks energy introduced decahe- strain balance, to energy take mainly ofregular account these between decahedron, particles. of these surface Together the been decahedral with and most particle that frequently shapes ofexperimental have TEM the observed images experimentally. oftained From a by palladium the PVD decahedron,bright-field ob- on and potassium inone iodide dark-field can mode clearly substrate, recognize in shown its Figs. in compact morphology 10aexhibits [23]. and 10b multiplyshape twinned is by configuration G.be and Rose seen from decahedral from 1831facet [9] decahedron Fig. 11a, of and gold itza, the which features, Romania. has subdivided as Another been can morphology earlyis found example near the of of Boic- copper a naturalperipheral decahedron origin reentrant [24] shown edge in configurationsdron, like Fig. but 11b a no star thattionally, tips decahe- exhibits this at particle thepoint displays outer of a end thevertex dimple of fivefold surrounded at twin the by the junction, subunits.cal five that emergence Addi- {111} feature means facets. must acopper This not decahedra concave morphologi- or be decahedraalso considered of examples natural as in origin. the aof There literature characteristic are natural that of describewithout origin a such copper having central MTP decahedra dimple clearly of [25], as star naturalplay well and decahedron this as of particular diamond shape synthetichedron habit star origin shown [26, that in 27]. Fig. justtruncated The 11b dis- tetrahedron shape can be of shapeby explained the of by deca- Fig. its assuming 12, a subunits.known stacking As as illustrated ofdecahedra Friauf and such polyhedra, even icosahedrajunction truncated easily [28] dimpling that tetrahedra, enables and exhibitally, twin to both, also a boundary twin construct grooving. certainbecause Occasion- anisotropy of of decahedralwithin non-uniform MTPs the may development subunitsC60 occur of of star a decahedron suchThat particle obtained is as features by illustrated itscopy aerosol by is (HREM) image synthesis the observed shown [29]. high at in resolution Fig. the 13. electron Experimental micro- evi- Fig. 10. twin junction orientedfield; and parallel ( to the electron beam: ( [19]. 2, the and the ¼ 1. a a v111 ¼ = a b d ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3v100 b) truncated octahedron; p is determined by con- ¼ a a 3, we have chosen four speci- ) octahedron; ( a 1.5, and the cube for a ¼ a d) cube. corrresponding to characteristic stages of 3, the truncated octahedron for a ¼ c a a Evolution of decahedron morphology with growth parameter ) cuboctahedron; ( c ( affecting the subunit shape: ( Fig. 9. According to the above mentioned values of 3.1 Evolution of the decahedron morphology corresponding singleMTP crystal shape shape occurFig. which unique 9. are Different shown examples fromfive for the of regular the regular tetrahedra decahedron decahedrongular being composed in faces of bounded of bymorphology type equilateral is {111} trian- subdivided onlydifferent and (see contains 1.2), type bounding nownearly the faces and regular particle of size polyhedron shapetains, [19–22]. variety starting of from The a decahedra(i) perfect con- a evolution octahedron shape star ofedge of decahedron configurations subunits, the that (Fig.tained 9a), exhibits by (ii) 5 truncation adron peripheral of facet so reentrant the decahedron as outerdecahedron ob- to tips resulting display of from {100} the increased faces star truncation (Fig. 9b), where decahe- (iii) the a prism The shape evolution fromof the crystals octahedral involves tooctahedron, the intermediate cubic the forms form likeTheir cuboctahedron, the outline and truncated isoctahedron the determined faces growth by truncated rates themon cube. v100/v111 ratio [3] by or of more the cube com- growth faces to parameter 3. Shape variations due to growth rate changes Shape and growth of multiply twinned nanoparticles Subunits of generalresult cuboctahedral from progressive shapecorners of and are both symmetrical starting thoughtations polyhedra removal to that of are ofshape exposed the the to variations vari- growth offormation MTPs conditions. at originating Consequently, thesuitably from initial distinct controlling multiple stage the twin growth ofthe conditions, growth number which of may increases varietiescle evolve of shape. upon nearly The regular growth polyhedron parameter parti- ditions like thetemperature precursor applied during concentration growth.gle and Since crystals the the shape can substrate least of be in sin- easily the range correlated 1 to this parameter, at fic values of shape evolution [3,tained 7, for 19]. These are the octahedron ob- cuboctahedron for This article is protected by German copyright law. You may copy and distribute this article for your personal use only. Other use is only allowed with written permission by the copyright holder. 1 b ¼ a H. Hofmeister b) an icosahe- b) nearly star-like deca- as expected for {111} ) facet decahedron of gold Early findings of multiply a ) a decahedron, and ( a (1831 [9]), and ( hedron of copper (1882 [24]). Fig. 11. twinnedshape: crystallites ( of decahedral 1.5 twin boundary grooving occurs, a ¼ b a instead of 70.53 Schematic drawing of ( dron which exhibittween reentrant {111} grooving faces at for a twin growth boundary parameter sections value slightly be- above 1. faces. Obviously, thisgrowth (discussed morphology below intion is of sect. the due 4.1) apex proceeding to of in the direc- branching octahedral subunits. Fig. 14. 3.2 Evolution of the icosahedron morphology The evolution of theety nearly of regular multiply polyhedron14b shape twinned and vari- icosahedra 15. Changes isparameter of illustrated variation the by subunit producefrom Figs. outline different the due to typesspherical regular growth shape. of icosahedron For deviation responding having subunits of icosahedron a octahedral isequilateral compact, shape bounded the triangular nearly by cor- facessurround corner-connected, of a {111} pit,consisting of that type {111} means whichthese faces. a always pits As are concave canor corner-connected be pentagonal to dimples seen vertex each of intruncated other. Fig. Smaller the 15a octahedron pits same all faces shape now geometry where have occur hexagonaldral the outline for subunit (Fig. peripheral 15b). subunits shape Aicosahedron {111} results of cuboctahe- not in to the betetrahedral distinguished morphology from of subunits that agrowth composed (see parameter regular of Fig.as 15c). it is For shownappear in at values Fig. the 14b, expense wherebyFinally, of of cube the faces the the additionally diminishing octahedron multiply faces. twinned icosahedron for mixture of cholinebeen chloride reported and toare urea result distinctly as in sharper solvent starfaces as that than decahedra considered [30] has those above.are whose The bounded of free tips by faces theangle octahedron forming highly each of tip stepped 26.6 {331} type resulting in a tip , b 60 1.16 [19]. This ¼ a a 1 reentrant grooving at the ¼ a a HREM image of a slightly modified star decahedron of C Assembling of 5 truncated tetrahedron subunits to form a deca- Another direction of shape evolution is opened by the Fig. 13. dence of fabrication{111} faces of is aparameter rarely cube slightly found, above but decahedron for without values any of the growth Fig. 12. hedron that exhibits twin junction dimples and twin boundary grooves. 532 adapted with permission fromnearly octahedral [29], shape. by cyclic twinning of subunits of twin boundary sectionsis between schematically {111} shown in faces Fig. occurs 14a as for it solution synthesis of gold nanoparticles using an eutectic leads to additionalremaining cube octahedron faces. faces at the expense of the still This article is protected by German copyright law. You may copy and distribute this article for your personal use only. Other use is only allowed with written permission by the copyright holder. b 533 ) together with sche- a a b) to be joined along a twin plane HREM image of a finger decahedron of gold from solution Another situation is met with the different geometry of matic drawing offaces surrounding two a model concave(arrowed) edge subunits and ( to containingunits. be indented completed trigonal accordingly by three matching sub- Fig. 17. synthesis, adapted with permission from [38], ( 4. Strongly anisotropictwinned growth particles of multiply 4.1 Branching growth Branching growth asapex directional directions of crystallizationcentration a along polyhedral effects the crystal inaround is the induced a growing by concentric crystalgle con- [3]. diffusion crystalline Similar field tocan particles the be formed case found various in ofout multiply sin- branched including twinned morphologies particlesgrown the with in and Al––Si twin melt with- corresponding or boundaries. alloy fabricated materials Silicon bybit have laser been a precipitates processing reported branched of fingers to structure exhi- from wherestraightaway the the with branches twin thesefinger extend boundaries decahedra boundary like [35, haveplatinum corners been 36]. nanoparticles and observed Such[37–39]. fabricated also twin proceed As an by fortwin example gold Fig. solution finger 17 and shows synthesis schematic decahedron a drawing TEM of image ofdented gold of two a trigonal [38] model faceswhich subunits together the surrounding containing with configuration in- aThe the excessive of concave growth along the edgeto the MTP twin result from boundaries from may isriphery unfavourable thought be of growth imagined. tetrahedralobserved conditions subunits. at for Branching the singlethe growth pe- above crystalline also mentioned metal solution is routes particles of formed synthesisstar [37–39]. in decahedra whichapexes. already Under exhibit certain distinctlyformed conditions protruding of by growthplatelets chemical star [40, decahedra vapour 41] may depositionmorphology tend as in to develop it borondeposition a has temperature nitride fivefold branched and beensure relatively observed [42]. low for Heretwin total the relatively boundaries gas branching high emergencethe pres- does points, star not tips butfinger-like extend of it protrusions. from the Quite proceeds the subunits,hedron accordingly, from the so mentioned spiky as icosa- terms to above of replace [34] the branchingicosahedron. tips could growth It by starting may be be at understood recognized the from in tips the of TEM a image star b d b) truncated octahedron; ) octahedron; ( a . [34] propose a model of these et al d) cube. c a Evolution of icosahedron morphology with growth parameter SEM images of boron suboxide icosahedral particles, adapted Besides regular icosahedra experimental observations ) cuboctahedron; ( c ( Fig. 16. with permission fromthe [31], emergence which points of exhibit twin dimples junctions. of various size at of the shapeclude evolution examples with that growthemergence exhibit parameter of dimples twin of mainlyboron various junctions in- size suboxide as at it particlesgrooving the is [31], of shown as in varyingcan well Fig. often extent 16 as be [27, for foundals twin in 32]. [33] boundary particle while Regular ensembles icosahedrasurface of icosahedra with frequently transition dimples met- occurnanoparticles and for grooves fabricated, diamond at for and the deposition, example, boron by suboxide acetylen chemicalmelt flame vapour synthesis, synthesis, respectivelyhas [27, and been 31, high given 32].shape up pressure Only where to one now Burt report on icosahedra having a starry (Fig. 15d) can betriangular described bounding as facessuch regular are that icosahedron an capped whose all-cube-face by star polyhedron fitting results. pyramids Fig. 15. affecting the subunit shape: ( Shape and growth of multiply twinned nanoparticles gold particles obtainedof by trigonal solution pyramids growthregular capping which the icosahedron. consists corresponding However,that faces the of a these additionalbounded assumption by pyramids {111}rahedra surfaces have situated requires in not tetrahedraltetrahedron, twin only relation capping but shape with tet- shaped respect it and polyhedron to also their asvouring are base being excludes a due cube to face-bounded tocussed polyhedron. growth in consider This more conditions will this detail fa- be in dis- star- the next section. This article is protected by German copyright law. You may copy and distribute this article for your personal use only. Other use is only allowed with written permission by the copyright holder. b d H. Hofmeister d) by additional trans- ) a prism decahedron, a ) and ( c a c Elongated decahedral structures as formed by preferred Pentagonal prismatic needle of gold of about 2 mm length b) a star decahedron, as well as ( formation of the prism faces to pyramid faces. the rod tips. Pentagonalhave rods been and needlesshown reported of as natural an rather origin exampleadditional of early twin 1877 species [44] forpyramid in of shape Fig. rhombic gold. 19 on prism carriestip The the and some obviously pentagonal trigonal needle does prism bi- expected not stem. for The display decahedral needle fiveshape structures, {111} and but faces faceszohedron. has corresponding as Two to a being different a more growthdirected half spiky modes pentagonal growth are trape- junction. known of One for decahedra simply the hedral consists along particle in their an havingschematically elongation fivefold regular drawn of for or twin a thein modified deca- prism Fig. shape and the 20a as{100} star and and it decahedron {111} b. is prism The faces to other periodically exhibits stepped faces a modification of and ( Fig. 20. growth along the fivefold twin junction of ( Zeitschr. f. Kryst. u. Min. I Bd. Taf. II. Fig. 19. with two kinds of secondary growths from a natural deposite [44]. . article [34] it can be et al TEM image of a star-like icosahedral particle of gold, 4.2.1 Elongated decahedral structures Elongated decahedral structuresby simply axial may growthtwin of be junction, a achieved provided prismor a decahedron some along distinct kindcant its of growth radial surface fivefold rate growth. modification The anisotropy sponds will rod to shape prevent a formed signifi- pentagonal thereupon prism corre- with pentagonal pyramids at 4.2 Unidirectional growth One-dimensional nanostructureswires like are mostly nanorods obtainedassisted, or by and/or template-directed, nano- seed-mediated surfactant- fine the processes growth that tofor one either the dimension or con- adsorptionor act of twin-induced as reactant growth favourable based sites molecules.aries on Defect-mediated the and effectgrowth of fivefold twin rates bound- twin ateven junctions low allow precursor totures. promoter-free concentration The enable [5, formation elongation of 43] reasonable direational of multiply may twinned growth such particlescesses proceeds by nanostruc- for uni- via decahedra and distinctly icosahedra, respectively. different pro- concluded that there istetrahedra no twin forming boundarycapping between the pyramids. the icosahedron base That means,ticles and the appear spikes like their making stara respective the polyhedra kind par- most of probably branchingcrystalline result growth particles that from obtained also in is the observed same for synthesis. single adapted with permissionthan expected from for [34], aing cube growth. whose icosahedron tips so as appear being more affected by spiky branch- in Fig. 18 thatcle the obviously pyramids appear cappingments more this icosahedral pointed of parti- than adron expexted cube as for capping seg- shownimages the in presented faces Fig. in of 15d. the a Furthermore, Burt regular from icosahe- dark-field Fig. 18. 534 This article is protected by German copyright law. You may copy and distribute this article for your personal use only. Other use is only allowed with written permission by the copyright holder. 535 ) grown a b b). ) formed in a polyol-assisted a b HREM image of a pentagonal nanorod of silver ( SEM image of gold particles ( b). a a prism edges uniformly increasebaseball during bat-like growth shape. leadingof to An a decahedron-based opposite multiply wayuniform twinned of decrease rods of modification leading the consists to radial in an prism oblong a been edges pentagonal reported during bipyramid for growth shapegold the as nanostructures Ag(+)-assisted it [51–55]. has solutionfaces Apparently, synthesis of the of {100} pentagonalcally prism rods stepped have facesFig. been 24 like replaced where {11n}. the bytain schematic An periodi- representation rounding example points effect to is at a given cer- the in tips of these particles. Even solution synthesis, adapted withhibits, in permission addition from to [49],along growth a where along twin one the boundary ex- el twin marked ( junction, by hatching preferred in growth the corresponding mod- Fig. 23. Fig. 22. by inert gas aggregation,with adapted the with electron permissioncated beam from by perpendicular [11], the recorded to hatched one area of in the the prism schematic drawing faces, ( indi- b ), and a rotational between two from a base-orienta- a SEM image of a boron suboxide nanowire grown via solid b). T1 to T5 mark the five twinned subunits of the nanowire. At particles with decahedron shape anisotropic growth Figure 21 illustrates outline and geometry of a boron adjacent twin planes appearstion to of be well cyclicning, suited twinned for that configurations. the crea- Quite meansshaped similar cross prisms twin- section, withnatural has striking calcium been observed five-pointed, vanadiumcial in silicate star- geometry pentagonite, mineral of a hombic, [46]. the space The pentagonite crystal spe- groupbetween structure two 36) (orthor- adjacent withcyclic twin a planes twinning. dihedral readily Anfrom permits angle a example fivefold prism of for decahedronThe 72.7 pentagonal [11, structural 46–48] rods characterization ismicroscopy grown by shown of high in the resolution Fig.gregation silver 22. electron technique nanorods [11] grown makes by use inert-gas of ag- their 36 also mayalong proceed, in thealong addition fivefold a to twin reentranttwin edge the planes. junction, at Thus preferred unidirectional the bywith radial growth outer growth axial preferred bounds is growthstructure combined of growth as so one it of as isgold the demonstrated from to in solution Fig. createtended 23 synthesis plates by this [49]. an The of way exampledrawing twin is of asymmetric of boundary marked Fig. ex- pyramid 23b. by Another hatching capped type intwinned of the rods pentagonal deviation is schematic lorganic reported from prism chemical for the vapour copper shape deposition rods [50] grown of where by metal- the multiply radial tion where the electronface beam (see, hits for perpendiculardrawing, example, to Fig. a the 22b) prism to hatchedbeam a area runs side-orientation parallel in where to the a the schematic prism electron face. corresponding model inrowed cross-section ( view with the twin planes ar- so as to resultis in drawn oblong in pentagonal Fig. bipyramid 20c shapes and as d. it suboxide nanowire thatdecahedron is by supposed directed toa growth result along solid the from statemuch twin a convincing junction reaction star because in shaped [45]. of the Although cross-section, roundedconfirmed this tips the by image of selected multiple the areasponding is star- electron twinned structural not diffraction. model structure Thenature in corre- is of Fig. 21b therowed). features The the terminating boron atomic suboxid surfacesgroup structure 166) and (rhombohedral, space with twin a planes dihedral (ar- angle of 71.8 Fig. 21. state chemical reaction,shaped adapted cross-section with of permission which from is [45], indicated by the the star- dotted line ( Shape and growth of multiply twinned nanoparticles periodicity. Distinctly differentis image obtained contrast for rotating appearance the rod by 18 This article is protected by German copyright law. You may copy and distribute this article for your personal use only. Other use is only allowed with written permission by the copyright holder. a b)ofa H. Hofmeister b ) and image contrast calculation ( a HREM image ( Schematic repreesentation of the directed growth of icosahe- Such hybrid multiply twinned structures have been re- FePt particle obtainedsahedral-decahedral by inert hybrid gas structure,[57]. condensation that adapted exhibits with an permission ico- from tropic growth variationsby also a for icosahedra. certainthe One probability twin is of junctions given In as uniaxial it principle growth is this alongan drawn may one icosahedral schematically be of to inparticle understood Fig. a configuration 25. as decahedral is a structureamid-capped readily transition and pentagonal obtained the rod from byof to adding resulting 15 an a incomplete subunits pyr- consisting icosahedronnal antiprism. of a decahedron plus a pentago- ported for goldcence and processes silver particles [58],lack to and in result stability forample from during FePt Fig. coales- the 26 particles growth showsage [59]. owing a contrast HREM For to simulation image theFig. a together according latter 25. with ex- to In an both atent im- cases model of there sketched anisotropic isanisotropy in growth. achieved restraint Another only is way astructures limited to the ex- by overcome directed the along preferred growth one of fivefold stacking icosahedral twintally of junction observed that in tetrahedral has metalstrates been particles via subunits experimen- grown PVD onthe [12, crystalline 16, schematically sub- 58]. drawing As it in may Fig. be 27 deduced it from needs a certain Fig. 27. dral structures by preferredfivefold stacking twin of junction tetrahedralpentagonal that subunits bipyramids can along and pentagonal one be antiprisms. described as linear assembling of Fig. 26. b b). a which b a ) as schematically drawn in ( a TEM image of gold nanoparticles by Ag(+)-assisted solution Transition from icosahedral to decahedral structure by uniax- Fig. 25. ial growth along onepentagonal fivefold rod twin supplemented junction to whichof an a can incomplete decahedron be icosahedron plus thought consisting a as pentagonal a antiprism. more complicated structurescently have in been the observedwhich seed-mediated very exhibit synthesis in of re- amid addition gold to nanocrystals shape this alsomatically oblong a drawn pentagonal star-shaped in bipyr- cross-section Fig.trees 20d. [56] have Likewise, as been molybdenumpressure formed sche- nano- microplasma in ambient [57]the air where twin using branching boundaries atmospheric- growthalong in along combination the with twinshaped preferred junction growth produces cross-sectiontwigs a with fivefold-twinned inclined star- gaps upwards to between the branches stem by and about 30 Fig. 24. synthesis, adapted withoblong permission pentagonal bipyramid from shape [53], ( including particles of 536 4.2.2 Elongated icosahedral structures Icosahedron-based structures dotendency not for by anisotropic far growthhedral show as particles. as it One much isminimal of observed surface for the deca- energy mainence because reasons to of a should nearly theuniform be spherical only configuration. their shape. slight From Anothertetrahedral one a differ- is central subunits the point fivefold highly directions shared twin around by junctions which 20 Nevertheless, 30 extend there twin are in two boundaries 12 exceptions are which grouped. favour aniso- exhibit increasing extension from the base to the tip. 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Continuation of this directed a ). c HREM image of a double icosahedron gold particle ( An overviewweakly is as well given ascle on strongly shape anisotropic the resulting formsas of considerable constitutive from nanoparti- building cyclic number principle.tions pseudo-fivefold Besides due of the twinning to shapeoverview growth varia- includes stackingvariations the of due to tetrahedral nearly growthsotropic subunits rate regular growth changes this of polyhedron and multiplybranching the shape strongly twinned growth, ani- particles occurringtively. or as Generally, as theas weakly unidirectional well anisotropic growth, asparticles shape the appear respec- evolution strongly moredral anisotropic rich particles. growth in It variety is ofclass worthwile as decahedral of to those point materialsable of out multiple means icosahe- that for twinning to anostructures. approach represents certain the a issue reason- of one-dimensional na- 5. 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