H. Hofmeister Max Planck Institute of Microstructure Physics Halle, Germany Forty Years Study of Fivefold Twinned Structures in Small Particles and Thin Films Multiple twinning in crystalline solids forming quintuples of twins is known since 1957 (Segall). It ever has attracted the attention not only of crystal growth and crystallography research, but also of cluster physics, physical chemistry, surface science, thin films and materials research. This review gives a comprehensive record of four decades work on fivefold twinned structures (frequently named ‘multi- ply twinned structures’) in small particles and thin films. After introducing crystallographic aspects of fivefold twinning, an historical review reports on beginning and spread out of the exploration as well as its broad extension to various fields, techniques and materials. The main issues of fivefold twinned structures, i.e. materials and processes involved, formation mechanisms, and stability and lattice de- fects, respectively, are treated in detail and illustrated by various examples. Accompanied by an almost complete list of references this review may not only make available results and experience of previous work in a greater context, but also stimulate future studies on this phenomenon. 1. Introduction 1.1 Crystallographic characteristics Twinning is widespread in crystalline materials of various origin and nature. The phe- nomenon of twinning was described in many textbooks and review papers (for a descrip- tion of the crystallographic fundamentals of twinning see Koch). Multiple twinning, at first instance, denotes repeated twin formation which also includes multiples of parallel matrix/twin lamellae as they are known e.g. from martensitic transformed materials. Since decades, however, the term ‘multiply twinned particles’ (usually abbreviated as MTP’s) mostly was applied to repeated twinning on alternate coplanar twin planes in small particles so as to form circular arranged twins which exhibit at least one axis of fivefold symmetry. Herewithin ‘MTP’ will be used only for particles the shape and struc- ture of which correspond to the originally applied meaning, otherwise, e.g. for thin film objects, the term ‘fivefold twinned structures’ will be used. Preferrentially, face centered cubic (fcc) or diamond cubic (dc) crystals, respectively, hav- ing a low twin boundary energy, contribute to the family of fivefold twinned structures, but any other crystal with coplanar twin planes enclosing an angle of about 2p/5 could do as well. The peculiarities of fivefold twinned structure may be described as follows: 1. they are composed of tetrahedral subunits joined together on adjacent bounding faces; 2. these bounding faces are first order twin planes (mirror planes) of the respective crys- tal, i.e. the subunits are joined along twin boundaries; 3. the subunits contain one pair of coplanar twin planes enclosing an angle of about 2p=5 (i.e. 70.53 for fcc and dc crystals) which allows circular arrangement of subunits around axes of fivefold symmetry. Cryst. Res. Technol. 33 1998 1 3 –– 25
Transcript
H. Hofmeister
Max Planck Institute of Microstructure Physics Halle, Germany
Forty Years Study of Fivefold TwinnedStructures in Small Particles and Thin Films
Multiple twinning in crystalline solids forming quintuples of twins is known since 1957 (Segall). Itever has attracted the attention not only of crystal growth and crystallography research, but also ofcluster physics, physical chemistry, surface science, thin films and materials research. This review givesa comprehensive record of four decades work on fivefold twinned structures (frequently named `multi-ply twinned structures') in small particles and thin films. After introducing crystallographic aspects offivefold twinning, an historical review reports on beginning and spread out of the exploration as well asits broad extension to various fields, techniques and materials. The main issues of fivefold twinnedstructures, i.e. materials and processes involved, formation mechanisms, and stability and lattice de-fects, respectively, are treated in detail and illustrated by various examples. Accompanied by an almostcomplete list of references this review may not only make available results and experience of previouswork in a greater context, but also stimulate future studies on this phenomenon.
1. Introduction
1.1 Crystallographic characteristics
Twinning is widespread in crystalline materials of various origin and nature. The phe-nomenon of twinning was described in many textbooks and review papers (for a descrip-tion of the crystallographic fundamentals of twinning see Koch). Multiple twinning, atfirst instance, denotes repeated twin formation which also includes multiples of parallelmatrix/twin lamellae as they are known e.g. from martensitic transformed materials.Since decades, however, the term `multiply twinned particles' (usually abbreviated asMTP's) mostly was applied to repeated twinning on alternate coplanar twin planes insmall particles so as to form circular arranged twins which exhibit at least one axis offivefold symmetry. Herewithin `MTP' will be used only for particles the shape and struc-ture of which correspond to the originally applied meaning, otherwise, e.g. for thin filmobjects, the term `fivefold twinned structures' will be used.
Preferrentially, face centered cubic (fcc) or diamond cubic (dc) crystals, respectively, hav-ing a low twin boundary energy, contribute to the family of fivefold twinned structures, butany other crystal with coplanar twin planes enclosing an angle of about 2p/5 could do aswell. The peculiarities of fivefold twinned structure may be described as follows:1. they are composed of tetrahedral subunits joined together on adjacent bounding
faces;2. these bounding faces are first order twin planes (mirror planes) of the respective crys-
tal, i.e. the subunits are joined along twin boundaries;3. the subunits contain one pair of coplanar twin planes enclosing an angle of about 2p=5
(i.e. 70.53� for fcc and dc crystals) which allows circular arrangement of subunitsaround axes of fivefold symmetry.
Cryst. Res. Technol. 33 1998 1 3±±25
In principal, two types of multiply twinned particles may be formed according to theabove construction scheme: i. a decahedron (pentagonal bipyramid) which consists offive tetrahedral subunits sharing one fivefold axis (point group symmetry D5h) and isbounded by 10 triangular faces; ii. an icosahedron with six fivefold axes composed of 20tetrahedra sharing one common point at the centre (point group symmetry Ih) which isbounded by 20 triangular faces. Composition and habit of decahedron and icosahedronare shown in Fig. 1. As tetrahedral subunits of regular fcc or dc lattice, respectively,cannot form a complete space filling structure there remains an angular misfit (resultinge.g. in a gap of. 7.35� for the decahedron) which is not considered in the drawings.Obviously, the fivefold axes occuring in such materials are only of pseudo-fivefold sym-metry.
With respect to a crystalline substrate (or matrix), there are three possible high sym-metry orientations for both types of figures. Decahedra may be situated i. with theirfivefold axis perpendicular to the substrate plane (`fivefold orientation', regular penta-gon profile), ii. with one tetrahedral bounding face resting on the substrate (`face orien-tation', contracted pentagon profile), and iii. with one outer edge resting on the sub-strate and the fivefold axis parallel to the substrate plane (`edge orientation', rhombicprofile), respectively. In accordance, icosahedra may be situated i. with their fivefoldaxis perpendicular to the substrate plane (`fivefold orientation', decagon profile), ii. withone tetrahedral bounding face resting on the substrate (`face orientation', regular hexa-gon profile), and iii. with one edge resting on the substrate and two fivefold axes paral-lel to the substrate plane (`edge orientation', elongated hexagon profile), respectively.
Since at least in the case of MTP's the surface plays an essential role it is worth tomention here the peculiarities of their surface structure. Different from single crystallineparticles the common growth form of which is the cuboctahedron for most of the materi-
4 Hofmeister: Fivefold Twinned Structure
Fig. 1. Shape and composition of multiply twinned particles. (a) decahedron (pentagonal bipyramid), made up offive tetrahedral units with one fivefold axis, bounded by 10 triangular faces; (b) icosahedron, made up of 20tetrahedral units meeting in a common point at the centre, bounded by 20 triangular faces.
als concerned, MTP's are bounded by triangular faces of the same type only. This is anoctahedron face (i.e. f111g for fcc and dc crystals) which because of the surface energyanisotropy common to most of the materials concerned is favoured as compared to cubeor dodecahedron faces. This way MTP's by minimizing their surface energy approximatea spherical shape which is most effectively in the case of icosahedra.
1.2 Aims and scope of this survey
Within 40 years a huge amount of work has been done in various directions of this fieldand it is no easy task even to mention all of them exhaustively. After having been con-cerned with the subject under consideration the last 15 of these 40 years it is theauthors experience that more frequently the communication of new experimental find-ings rather than the fundamental work have been lost in the jungle of literature,although the former mostly initiated and fertilized the latter. Therefore it is the aim ofthis survey to trace back this experimental work almost completely to the beginning 40years ago and to give record of the various directions evolved from the first tiny commu-nication.
27 years after the start of this story fivefold symmetry was ready to have quite an-other break-through with the disclosure of icosahedral quasicrystals and related phasesand with the invention of quasilattices to describe these structures basing on local icosa-hedral packing of atoms contained in tetrahedrally close-packed and related phases ofintermetallic compounds. Although, there are from a structural point of view certainrelations, e.g. of decagonally twinned crystalline approximant phases, we will not touchthis field since this quite another story. We will also not go into detail with the worksolely devoted to structure and stability of clusters with non-crystallographic packing ofatoms from a theoretical point of view. Acordingly, we will not mention explicitely thedetailed work concerned with model calculations of electron microscopy image contrastsof fivefold twinned structures only.
Instead, after presenting i. a historical review, we will go into detail with ii. materialsat which fivefold twinned structures may occur and processes of fabrication from whichsuch structures may result, iii. mechanisms of formation of fivefold twinned structures,and iv. stability of and lattice defects in such materials. Since the field of fivefoldtwinned structures is a very broad and complex one ranging from cluster physics andcrystal growth to surface science, physical chemistry and thin film research, some of thereview articles published previously will be referred in the summary.
2. Historical review
2.1 Beginning and spread out of the exploration
Already in 1931, in his paper ``Die Symmetriegruppen der amorphen und mesomorphenPhasen'' in Z. Kristallogr. vol 79, Hermann established the possibility of textures withfivefold symmetry. It was 26 years later, i.e. as early as 1957, that Segall1) for the firsttime reported the observation of fivefold twinned structures. Grains of pentagonal pyra-midal shape in rolled sheets of Cu (OFHC) were made recognizable by thermal etchingin vacuum. The second experimental proof of fivefold twinned structures was by
Cryst. Res. Technol. 33 (1998) 1 5
1) The Baillieu Laboratory, Metallurgy School, University of Melbourne
Melmed, Hayward in 1959 who not only observed Ni, Fe and Pt whiskers of pentago-nal shape grown from the vapour phase on W substrates, but also gave a model consist-ing effectively of five fcc twins with only slight lattice distortions. Just the third paperon this subject entitled ``A dense non-crystallographic packing of equal spheres'' byMackay presented in 1962 for the first time a hard sphere model of multilayer icosahe-dra. Mackay gave a description of icosahedra as made up of 20 tetrahedra, discussedtheir characteristics, calculated the density of hard sphere closed shell icoshedra and alsodemonstrated a mechanism of transition to the fcc structure (cuboctahedron).
Also in 1962 Schl�otterer2) reported the third experimental proof of such structuresfrom fivefold twinned pyramidal grains of Ni grown by electrodeposition on Cu. Oneyear later Wentorf described hundred micrometer sized fivefold twinned crystallites ofsynthetic diamond with indications of a small angle grain boundary accommodating theangular misfit. In 1964 five papers with new experimental findings were published.Faust, John reported on Si and Ge fivefold twinned grains grown from the melt. Skill-man, Berry found fivefold twinned particles of AgBr grown from solution. Ogburnet al.3) communicated the observation of pentagonal dendrites of Cu grown from thevapour phase. Schwoebel4) reported pentagonal pyramids of Au grown in fivefold ori-entation on Au(110) and Au(100) surfaces which possibly resulted from impurities coat-ing the substrates, and Gedwill et al. obtained fivefold twinned grains of pyramidalshape in the deposition of Co by hydrogen reduction of CoBr2, respectively. Similarily,De Blois5) found in 1965 in a study on the deposition of Ni by hydrogen reduction ofNiBr2 the formation of pentagonally shaped whiskers. In the same year Bagley6) pro-posed a model of fivefold twinned structures made up of five twinned tetrahedra theorthorhombic lattice of which is only slightly deviating from the fcc crystal lattice. In1966 Downs, Braun found fivefold twinned grains in the plating of Ni by thermaldecomposition of Ni(CO)4 (carbonyl process). Also in 1966 Millman et al. gave a strik-ing example of fivefold symmetry, also present in the organic world, by communicatingtheir observation of a pentagonal aggregation of virus particles the fascination of whichis the direct evidence of its structural characteristics.
In spite of having introduced broad experimental evidence of the phenomenon, cor-rect nomenclature, astonishing clear models and already reasonable insight in forma-tion mechanisms, respectively, these studies remained almost unnoticed until in 1966the discovery of decahedral and icosahedral particles of Au formed in the early stagesof epitaxial growth on alkali halide and mica substrates caused a revival of interest.These studies started nearly simultaneously from three different groups in Japan, Aus-tralia and France (Ino 19667), Allpress, Sanders 19678), and Gillet, Gillet19669). Extended availability as well as improved capabilities of electron microscopesat this time favoured progress of comparable work and focussing on fivefold twinnedstructures as the subject of research (Kimoto, Nishida: Ag and Au particles by gas
6 Hofmeister: Fivefold Twinned Structure
2) see also Schl�otterer 19643) see also Smit et al. 19684) see also Schwoebel 19665) see also De Blois 19666) see also Bagley 19707) see also Ino, Ogawa 19668) see also Allpress et al. 19669) see also Gillet, Gillet 1969
phase evaporation in argon atmosphere, Ino, Ogawa 1967: Au on NaCl with firstexplanation of the structure of rhombic MTP's, Nohara et al.: Cu, Pd and Ag onmica). By the first successful imaging of lattice plane fringes of small particles in 1968(Komoda) a new quality of insight in the structural characteristics of fivefold twinnedstructures was achieved.
This resulted in new experimental findings and a change of research topics to theessence of multiple twinning. In 1969 Nohara, Imura communicated the observation offivefold twinned Cu crystals of decahedral shape grown by reduction of CuI2. Ogawa,Ino (1969), Fukano, Wayman as well as Allpress, Sanders (1970) published arti-cles on formation, structure and stability of MTP's. In 1971 Mader introduced a nu-cleus model consisting of non-crystallographic packing of atoms to explain the amor-phous-to-crystalline transition including the formation of fivefold twinned structures ingermanium thin films. Ino et al. (1972) achieved for the first time recording of a selectedarea electron diffration pattern (SAED) at 1000 kV acceleration voltage from a singledecahedron of Au in fivefold orientation. The number of 36 papers and communicationswhich appeared within 15 years past the work of Segall is completed by Ogawa, Ino(1972) and Gillet, Gillet (1972) who discussed nucleation and growth as well as for-mation mechanisms of MTP's.
Since then there is a continuous interest in fivefold twinned structures the direction ofwhich is changed from time to time following the favourite issues of thin film researchand materials science. This historical review cannot give a comprehensive record of eachwork done in the field, but will highlight those which introduced new directions and/ortechniques of investigation, new classes of materials, as well as new models and mecha-nisms of formation. Thereby the traces of the most active groups shall be followed.
The number of known processes from which MTP's may evolve was extended byUyeda et al. who studied colloidal Au particles precipitated from gold sols. The class ofmaterials which exhibit MTP's was extended to Fe by Uyeda and by Fukano whofound decahedral particles of Fe grown by gas phase evaporation in inert gas atmo-sphere. Yagi et al. accomplished the first in-situ transmission electron microscopy(TEM) investigation of the growth of Ag and Au particles. They observed that MTP'swere created ab initio by nucleation as well as by successive twinning events and re-ported MTP reforming after coalescence of particles. A first review on various multiplytwinned structures formed by electrodeposition of Ni was given by Digard et al.. Sol-liard et al. confirmed MTP's being the equilibrium shapes of Au particles grown inargon by the inert gas aggregation method and subsequently annealed at enhanced tem-peratures. Growth and formation mechanisms of MTP's were extensively discussed byGillet et al. (1977) who, in contrast to Allpress, Sanders (1967, 1970) stressingsuccessive twin formation, favoured the ab initio nucleation and layer by layer growth ofMTP's. In a detailed study on the formation of small metal particles by inert gas aggre-gation Hayashi et al. confirmed Fe, Co, Ni, Cu, Pd, Ag and Au as materials with tend-ency to multiply twinning. Saito et al.10) communicated the formation of well estab-lished decahedra of Ge grown by gas phase evaporation in argon atmosphere whichshowed pseudo-fivefold symmetry SAED, extended faceting and twin boundary groov-ing, respectively. Fukaya et al. compared various metal deposits on KI substrate and
Cryst. Res. Technol. 33 (1998) 1 7
10) see also Saito
reported the growth of comparably large MTP's of Pd. Pipkin, Davies found smallangle grain boundaries in large decahedral particles of synthetic diamond. ExtendedTEM and crystallographic studies on MTP's of Au grown on NaCl substrate were re-ported by Heinemann et al.11) who utilized sophisticated dark-field imaging techniquesand proposed a body centered orthorhombic structure for decahedral particles and arhombohedral structure for icosahedral particles, respectively, both only slightly deviat-ing from the fcc structure. Ohno, Yamauchi communicated their observation of MTP'sof Mg grown by the gas phase evaporation technique, the up to now only example of ahexagonal close packed crystal with fivefold twinned structure. Marks, Smith (1981)12)opened the era of high level HREM studies on MTP's by applying their 600 kV deviceto Ag and Au particles grown on NaCl and KCl substrates. Hofmeister et al.13) studiedthe growth of MTP's of Au on AgBr substrates by successive twin formation. Gomezet al.14) obtained microdiffraction patterns of icosahedral particles of Au and calculatedsuch patterns according to specific particle models.
2.2 New materials, new aims, new techniques
The next decade of research in this field is characterised by an enormous rise of investi-gations on fivefold twinned structures in thin films mostly of technologically importantmaterials like diamond, semiconductors, and Ni, respectively, and by utilisation of dedi-cated experimental techniques like cluster source equipped molecular beam devices forsynthesis, and real-time video recording equipped electron microscopes for characterisa-tion of MTP's, respectively. Brieu, Gillet (1983)15) studied by means TEM tilt seriesthe internal structure of rod-like decahedra grown by reduction of Ni salts in organicsolutions. Matsui communicated the observation of MTP's of cubic BN formed by e-beam irradiation of hexagonal BN. Leclercq et al. reported on decahedral particles offerric oxide (g-Fe2O3) grown from the vapour phase. Nepijko et al.16) (1984) analysedlattice defects in MTP's of Au grown on NaCl. Marks (1984a) and Howie, Marks17)discussed intensively the surface structure, the energetics, and elastic strains in MTP'sand introduced a model of faceted decahedral particles obtained by a modified Wulffconstruction (Marks 1984b18)). Renou, Rudra19) communicated HREM studies onicosahedral and decahedral particles of Pd on MgO. The series of thin film studies isopened by Matsumoto, Matsui who obtained fivefold twinned structure in CVD dia-mond grown on Si and proposed hydrocarbon cage molecule models as precursors. Sunet al. found fivefold twinned structures in deposits of TiCN with h110i texture. Hall,Fawzi studied fivefold twinned structures in electrocrystallised Ni deposits with h110itexture and proposed a successive twinning mechanism. Fivefold twinned rod-like parti-cles of CVD grown TiN were reported by Millers, Kuzjuk�evics who also observed re-
8 Hofmeister: Fivefold Twinned Structure
11) see also Yacaman et al. 1979; Yang; Yang et al.12) see also Smith, Marks 198113) see also Hofmeister 198414) see also Schabes-Retchkiman et al. 198415) see also Brieu, Gillet 1988; Gillet, Brieu 198916) see also Nepijko et al. 198617) see also Marks 1985a18) see also Marks 1985b19) see also Renou, Penisson; Penisson, Renou
entrant faces at the planes of the rods. Narayan et al. (1988)20); van Landuyt et al.;Williams et al. (1990a)21); Wild et al.; and DeNatale et al. studied by HREM therole of fivefold twinned structures for microstructure, orientation and h110i texture for-mation of CVD diamond thin films. Hiraga et al. observed fivefold twinned structuresin BN thin films grown by CVD. Fivefold twinned structures formed in the solid phasecrystallisation of amorphous thin films of Ge were investigated by Okabe et al. andHofmeister et al. (1991)22). The first observation of fivefold twinned structure in com-posite materials was reported by Dahmen, Westmacott23) who found pentagonalneedle-shaped precipitates of Ge in Al. Real-time video recording of contrast fluctuationsand corresponding structural rearrangements of small metal particles including multiplytwinned configurations were carried out by IIJIMA, Ishihashi; Smith et al.; and Wallen-berg et al.24). Iijima (1987) observed pairs of stacking faults and small angle grainboundaries in one of the twinned units of decahedral particles of Si formed by inert gasaggregation. Giorgio, Urban25) studied by HREM, image processing and contrast cal-culation the structure of MTP's of Ag prepared by an inert gas cluster source within amolecular beam apparatus. Herrera et al. reported on Pd decahedra with incoherenttwin boundaries. A HREM study on lattice defects in decahedral particles of Pd grownby vapour deposition on KI was published by Hofmeister (1991). Hall et al. em-ployed electron diffraction on a molecular beam of free Ag particles from inert gas aggre-gation to determine the fraction of MTP's depending on the source conditions. Buffatet al. considered complicated cases of contrast appearance of MTP's of Au in a HREMand image calculation study. MTP's of Sm observed in cluster beam deposition by Melli-non et al. showed a transition from rhombohedral to fcc structure.
The last five years of the period to be reviewed are rich in variety of new materials atwhich fivefold twinned structures were found. Haluska et al. achieved to grow extre-mely large (2mm) decahedra of fullerite (C60). Arita et al. found Yb fivefold twinnedpentagonal rods from inert gas aggregation synthesis. Fivefold twinned structures ofCVD diamond thin films with superposition of twin units were studied by Shechtmanet al. (1993a)26). Hofmeister et al. (1993a, b)27) investigated the amorphous to crystal-line transition and the evolution of a multiply twinned nanocrystalline fabric in Ge thinfilms. Romanov et al. communicated the observation of CdTe pentagonal whiskers withfacetted hollow channels inside. Fivefold twinned structures in TiN and SiC thin filmswith h110i texture grown by CVD were reported by Cheng, Hon28). Hofmeister(1994b)29) studied interlinked networks of fivefold twins in electrocrystallised thin filmsof Ni. Fivefold twinned crystallites of CuInSe2 grown by vapour deposition from a three-source molecular beam epitaxy system were introduced by Wada et al.. Rupprechter
Cryst. Res. Technol. 33 (1998) 1 9
20) see also Narayan et al. 1989; Narayan; Narayan, Nandedkar21) see also Williams et al. 1990b22) see also Hofmeister et al. 199223) see also Douin et al.24) see also Malm et al.25) see also Altenhein et al.26) see also Shechtman et al. 1993b27) see also Hofmeister 1994a; Hofmeister, Junghanns 1994; Hofmeister, Junghanns 199528) see also Cheng et al.29) see also Hofmeister, Atanassov 1996
et al. (1994)30) informed on MTP's in Rh epitaxially grown particles. Lu et al. disclosedthat formation and growth of MTP's in electrocrystallised layers of Au depend on theelectric potential during deposition. Wang et al. communicated an optimised techniquefor CVD synthesis of fivefold twinned diamond thin films. Fivefold twinned structures inBaTiO3 were observed by Recnik, Kolar. Volkov et al. utilised ligand stabilisation toform 561 atoms Pd clusters of icosahedral structure. Cluster induced formation and solidphase crystallisation of amorphous Si particles proceeding mainly by multiple twinningwas studied by Hofmeister et al. (1996)31). Jarsetz et al. presented a low temperaturemetalorganic route of synthesis of Ni particles including also MTP's. The formation ofMTP's due to transformation to a higher symmetrical arrangement was discussed byKrafczyk et al. according to experimental findings from the literature.
3. Materials and processes
As described above (see ch. 1.1) fivefold twinned structures in principle may be found inany crystalline material which allows twinning on alternate coplanar twin planes enclosingan angle of about 2/5. At first instance, these are fcc and dc crystals which in additionexhibit a low twin boundary energy and a surface anisotropy so as to favour growth shapesdeviating from the single crystalline Wulff construction. Experimental proof of this hasbeen obtained up to now for Fe, Co and most of the fcc transition metals, i.e. Ni, Cu, Rh,Pd, Ag, Pt and Au, and for the group IV dc crystals of C, Si and Ge, respectively. Asrecorded in the historical review (see ch. 2.) structures like those of Rh multiply twinnedparticles shown in Fig. 2 (Rupprechter et al 1994, 1995) have been found very frequentlyfor the above materials. Additionally, one observation of MTP's was reported for the hexa-gonal close packed Mg (Ohno, Yamauchi). The number of multiply twinning in elementalmaterials is completed by the lanthanides Sm (Mellinon et al.) and Yb (Arita et al.).
From the characteristics of fivefold twinned structures it is quite natural that theynot only occur in elemental crystals, but also in compounds with appropriate crystalstructure. As early as 1964 multiple twinning was observed in AgBr (Skillman, Ber-ry). Since then 9 more binary and ternary compounds with fivefold twinned structureshave been found. These are the nitrides and carbides: BN (Matsui; Hiraga et al.), TiN(Millers, Kuzjuk�Evics; Cheng, Hon), TiCN (Sun et al.), SiC (Cheng, Hon), thesemiconductors GaP (Ernst, Pirouz), CuInSe2 (Wada et al.) CdTe (Romanov et al.),and the oxides Fe2O3 (Leclercq et al.) and BaTiO3 (Recnik, Kolar). The summaryof materials must be completed by the molecular crystal fullerite (C60), the materialfrom which the up to now largest MTP's are known (Haluska et al.), and by compositematerials like Ge precipitates in Al alloys (Dahmen, Westmacott) or Ag precipitatesin glasses modified by ion exchange (Dubiel et al. 1991), respectively.
From the historical review (see ch. 2.) it comes clear that there is a large number ofvarious processes and specific techniques by which multiply twinned structures in smallparticles and thin films may be generated. Generally, these differ by the state of thematerial applied in the synthesis. We distinguish synthesis i. from the vapour phase, ii.from the liquid phase, and iii. from the solid phase, respectively. The first point (i.)includes (a) heterogeneous nucleation and growth of particles and thin films by various
10 Hofmeister: Fivefold Twinned Structure
30) see also Rupprechter et al. 1995; Rupprechter et al. 199731) see also Hofmeister 1997; Hofmeister et al. 1997a; Dutta et al.
methods of physical and chemical vapour deposition on substrates, and (b) homogeneousnucleation and growth of particles by inert gas aggregation which may be collected atappropriate sampling probes for ex-situ investigation. Most of the work on metalMTP's, as those `classic' studies of Ino; Allpress, Sanders; and Gillet, Gillet; aswell as their successors, have been done according to the process scheme given in (a) bythermal evaporation of the metal within an evacuated chamber and condensation of themetal vapour on substrates like mica, MgO or alkali halides. Chemical vapour depositionmostly has been applied for thin film formation, e.g. of diamond (see e.g. Shechtmanet al.) from precursor molecules the decomposition or reaction of which provided thespecies to be deposited. The process scheme given in (b) mainly is used for mass pro-duction of particulates of the corresponding material (Hayashi et al.) and for in-situinvestigations of the particles (Solliard et al.).
The second point (ii.) includes (a) growth from the melt, (b) precipitation by reduc-tion of salts in solutions, and (c) electrodeposition from salts in solutions, respectively.Melt grown fivefold twinned grains of Si and Ge have been reported as early as 1964(Faust, John). The first reference to solution grown MTP's of AgBr also dates back to1964 (Skillman, Berry). Later on, metal colloid precipitation by reduction of metalsalts from solutions frequently has been used for wet chemical routes of transition metalparticle synthesis (see e.g. Uyeda et al.), and still is important in metal-in-insulatorcomposite formation by the sol-gel-process (Dubiel et al., 1997). The process scheme (c)mainly has been applied in the thin film deposition of protective metal coatings, mostlyof Ni (see e.g. Hall, Fawzi). Fivefold twinned grains as the one shown in Fig. 3 (Hof-
Cryst. Res. Technol. 33 (1998) 1 11
Fig. 2. Decahedral particle of Rh in edge orientation (rhombic profile) with crossed f200g latticeplane fringes of the (001) oriented base unit and f111g lattice plane fringes of both the (112)oriented top units.
meister, Atanassov) are the main constituents in films with h110i texture formed byappropriately choosing the coating conditions.
The third point (iii.) includes (a) precipitation from solid solutions in crystalline andglassy hosts and (b) solid phase crystallisation from the amorphous phase. Fivefoldtwinned rods of Ge precipitated upon thermal treatment from Al/Ge alloys (Dahmen,
12 Hofmeister: Fivefold Twinned Structure
Fig. 3. Fivefold twinned grain in an electrodeposited thin film of Ni with (110) texture. The fiveboundaries of the primary twins meeting at the encircled fivefold axis are marked by arrowheads.Arrows point to secondary twin boundaries. The circular inset shows the SAED pattern of this grain.
Fig. 4. Multiply twinned particle of Ag in glass the prolate shape of which is due to deformationby stretching the glass at elevated temperature. Dotted lines mark the twin boundaries of thepreviously spherical particle. The circular inset represents the diffractogram (Fourier transform)of this particle slightly tilted away from the fivefold orientation.
Westmacott) are the most striking example of the process scheme (a). Multiplytwinned metal particles precipitated from glasses modified by ion exchange or ion iom-plantation frequently occur upon appropriate treatment (Dubiel et al. 199132)). As de-monstrated by Fig. 4 MTP's of Ag in a glass matrix keep their structural peculiaritiesalso upon stretching the glass at elevated temperatures which by creep processes de-forms the nearly spherical particles to prolate shape (Hofmeister et al. 1997b). Theamorphous-to crystalline phase transition according to process scheme (b) has been stu-died intensively for thin films of Ge (Okabe et al.; Hofmeister et al. 199133)) andsmall particles of Si (Hofmeister et al. 199634)) which exhibit a distinct tendency tofivefold twinned structure formation.
4. Formation mechanisms
The formation of fivefold twinned structures has been a matter of debate from the begin-ning. In view of the great variety of materials and processes involved it is quite obviousthat they cannot be attributed to a uniform mechanism of formation. In general, onecan distinguish three of such formation mechanisms: i. by nucleation and layer-by-layergrowth, ii. by successive growth twinning, and iii. by deformation twinning.
Magic numbers in the mass spectra of transition metal cluster beams indicate thecause of the first mechanism, i.e. preferred formation of closed shell structures with ico-sahedral shape (Martin et al. 1990; 1991). These clusters obey the building plan ofMackay icosahedra as it has been shown recently for five-shell Pd clusters of 561 atomsby direct imaging (Volkov et al.). Such clusters may evolve from a 13 atoms icosahe-dral nucleus and maintain there shape by layer-by-layer growth so to arrive at particleswith sizes of several nanometers. Accordingly, pentagonal decahedra may evolve from a7 atoms nucleus of decahedral shape. During growth the non-crystallographic packing ofatoms of the nucleus readily is transformed to a fivefold twinned arrangement of transla-tionally ordered units the small size of which easily enables compensation of angularmisfits.
Slightly different from this scenario for fcc materials is the case of dc materials whichaccording to their bonding characteristics exhibit a 20 atoms dodecahedron and a 15atoms truncated pentagonal bipyramid as analogues to icosahedral and decahedral nu-clei, respectively. Hydrogenated carbon clusters of 15 and 20 atoms, the carbon cage ofwhich corresponds to that of the hydrocarbon molecules hexacyclopentadecane and do-decahedrane, respectively, are believed to be effective in the nucleation of diamond bymethane decomposition (Matsumoto, Matsui). Similarly, a 15 atoms Ge cluster isproposed to form the nuclus of fivefold twinned structures in Ge tin films (Okabeet al.). Attachment in crystallographically favorable position of atoms on the 15 atomstruncated pentagonal bipyramid will lead to a fivefold twinned crystallite. A more ex-tended cluster of 100 atoms is proposed as prototype of clusters formed in the plasmaenhanced CVD of amorphous Si particles which may serve as nuclei of fivefold twinnedstructures occuring during crystallisation of the particles (Hofmeister 1997). The mod-el is based on a 20 atoms core of dodecahedral shape the 12 pentagonal faces of which
Cryst. Res. Technol. 33 (1998) 1 13
32) see also Dubiel et al. 199733) see also Hofmeister, Junghanns 1994; Hofmeister, Junghanns 199534) see also Dutta et al., Hofmeister et al. 1997a
are decorated by truncated pentagonal bipyramids. The 100 atoms cluster shown inFig. 5 has six fivefold axes from which fivefold twinning may originate in 12 directions.The tetrahedral bond is preserved with bond angles and bond lengths only slightly dif-ferent from that of dc Si. Each of the 60 outer atoms have one unsaturated (dangling)bond. Always three neighbouring truncated pentagonal bipyramids surround a point atwhich a tetrahedron with dc lattice readily may nucleate. This cluster model first hasbeen proposed by Gerstengarbe as the building block of a possible quasicrystallinephase of Si.
The second mechanism, successive growth twinning, already discussed by Allpress,Sanders, first has been observed during in-situ investigation of the epitaxial growth ofAu on MgO (Yagi et al.). In an ex-situ study on the growth of Au on AgBr (Hofmei-ster 1984) the formation of primary, secondary and ternary twins at preexisting tetra-hedral particles as well as the completion of icosahedral particles by continuation oftwin formation at decahedral particles was shown in detail. The formation of fivefoldtwinned structures by successive growth twinning on alternate cozonal twin planes alsohas been observed in the solid phase crystallisation of Ge thin films (Hofmeister, Jun-ghanns 1993a, b). Fig. 6 shows the HREM image and an atomic model of a threefoldtwin junction with (110) zone axis formed by successive twinning. This characteristicconfiguration occurs by twinning on f111g planes of the parent unit (I) and the twinunit (II) opposite to those forming the re-entrant edge (A). If the newly formed twinunits (III) and (IV) meet at the threefold twin junction (B) a second order twin boundaryof higher energy (conincidence site lattice of type S � 9, see Neumann et al.) may result.Alternatively, by introducing two more first order twin boundaries, indicated by the shortpieces of dashed lines originating at (B), the threefold twin junction may transform to afiveld twin junction as evidenced by the image. In aggreement with experimental findingsthe latter route of twin growth is favoured because of energetic reasons.
The third mechanism, deformation twinning, solely has been observed in thin films upto now, but not in small particles. Thin films deposited on a substrate frequently sufferplane strain deformations arising during crystallisation (Koleshko et al.; Miura et al.).If the deposit has a distinct tendency to promote fivefold twinned structures strain re-laxation by the introduction of microtwins (Wagner, Paufler; Wegscheider et al.
14 Hofmeister: Fivefold Twinned Structure
Fig. 5. 100 atoms cluster model consisting of a dodeca-hedron (core) the faces of which are decorated by trun-cated pentagonal bipyramids (shell).
1990) may result in the formation of additional fivefold twin junctions. This processstarts with the introduction of 90� Shockley partial dislocations passing through thestrained lattice (Hwang et al.; Wegscheider et al. 1991). Continuation of this processon alternate twin planes consequently will lead to the crossing of twins. A simple case oftwin intersection, i.e. the penetration of a twin by an intrinsic stacking fault with (110)zone axis is represented by the HREM image and an atomic model in Fig. 7 observed in
Cryst. Res. Technol. 33 (1998) 1 15
Fig. 6. Multiply twinned crystallite of Ge formed by nucleation and growth twinning in amorphous Ge (right).Thin lines mark the twin boundaries formed; arrows point to second order twin configurations. The atomic model(left) of the central fivefold axis region represents the state before by further growth of subunits (III) and (IV)the threefold twin junction at (B) transforms to a fivefold twin junction.
Fig. 7. Region of a heavily twinned crystallite of Ge (right) where an intrinsic stacking fault (SF) passing throughthe matrix (M) penetrates a twin band (T), and atomic model (left) of the intersection. The stacking fault istransformed to an extrinsic one inside (T) so to form the nucleus of a secondary twin.
2 Cryst. Res. Technol., Vol. 33, No. 1
the solid phase crystallisation of Ge thin films (Hofmeister, Junghanns 1993a, b). Bypassing the first boundary (1) of the twin (T) the leading 90� partial dislocation of thestacking fault (SF) changes to a 30� partial dislocation (Wegscheider et al. 1991).Thus, within the twin band, the arriving intrinsic stacking fault is transformed to anextrinsic stacking fault. By the reverse dislocation reaction at the opposite twin bound-ary (2) continuation of an intrinsic stacking fault through the matrix M is achieved. Theextrinsic stacking fault within the twin (T) may be understood in terms of the nucleusof a secondary twin. Further extension of the secondary twin will take place by propaga-tion on adjacent planes of additional 90� partials. At the intersection of the stackingfault with the twin boundaries five- and seven-menbered rings are formed. The shearingoperation of the stacking fault passing through is accompanied by a thickening of thetwin (T) by one layer. At the end of the above dislocation reactions the newly formedsecondary twin contains some lattice distortions (Wegscheider et al. 1991) mainly lo-calized at the odd-membered rings. They may give rise to the formation of fivefold twinjunctions if, instead of a stacking fault, another twin is penetrating. The ability of five-fold twinned structures to accomodate large interfacial strains due to lattice misfit andexpansivity differences in the hetero-epitaxial CVD growth of semiconductors is reportedfor Si on sapphire, Si on spinel, and GaP on Si, respectively (Abrahams et al.; Ger-stengarbe, Neumann35); Paus et al.; Ernst, Pirouz).
Frequently, the origin of particular fivefold twinned structures cannot be attributed toonly one of the above discussed formation mechanisms. At various stages of thin filmgrowth extended structures containing several individuals of multiple twinning occur. Thishas been observed at the coalescence stage of decahedral and icosahedral MTP's of Au andAg which lead to the formation of polyparticles preserving almost completely the structureof the MTP's involved (Smith, Marks; Marks 1986). Networks of interlinked fivefoldand threefold twin junctions have been found in elctrocrystallised Ni deposits with h110itexture (Hall, Fawzi; Hofmeister, Atanassov). Comparable networks occur at ad-vanced stages of the solid phase crystallistion of amorphous thin films of Ge an example ofwhich is shown in Fig. 8 (Hofmeister, Junghanns 1994; 1995). The diffractogram(Fourier transform) of the image of this heavily twinned nanocrystalline fabric reflectsthe five azimuthal orientations achieved by twinning on cozonal twin planes. The distinctsplitting of spots, mainly to be recognized for the ring of strong (111) spots, points to thepresence of always two closely neighbouring azimuthal orientations. Since five times re-peated twinning on alternate twin planes does not meet the starting point, the resultingangular deficit will lead to a lattice misalignment. This misalignment is mainly adapted byshort segments of grown-in higher order twin boundaries that accompany the first ordertwin boundaries of the network in a considerable number. Additionally, non-coherent twinboundaries are observed where, because of non-correlated twinning events, twin bandsshow slight translational displacements with respect to each other and a rearrangement ofthe atoms in the boundary region, to meet the correct low-energy configuration, is pre-vented by energetic reasons. Relaxation of elastic strains by dislocation processes results instacking faults (SF). The occasionally observed intergrowth by twinning on planes inclinedto the film surface gives rise to linear and circular superstructures (marked by arrowheadsand circles) in the region of overlapping (Neumann et al.).
16 Hofmeister: Fivefold Twinned Structure
35) see also Neumann, Gerstengarbe
5. Stability and lattice defects
The stability of fivefold twinned structures has attracted continuous interest during thefour decades under consideration, mainly because of the discrepancy between non-crys-tallopraphic packing of atoms and its extension in three-dimensional space. As pointedout above (see ch. 1.1) MTP's formed from regular fcc or dc crystal units contain spatialdiscontinuities, thereby introducing inhomogeneous strains. The additional strain andtwin energy associated with the formation of MTP's may be balanced by a reduction ofsurface energy up to a certain size above which transformation to single crystalline par-ticles of cuboctahedral shape should occur. Strain relief by structural modifications(homogeneous lattice distortions) or the introduction of lattice defects (inhomogeneouslattice distortions) may help to extend the range of stability. In the following we will gointo detail with i. stability considerations based on structural characteristics of MTP's,ii. structural modifications and lattice defects in fivefold twinned structures, and iii. sizeextrema and kinetic transformation barriers.
Fukano, Wayman calculated relative stability criteria by a simple hard sphere mod-el analysis based on the volume energy and the surface energy of fcc transition metalMTP's having icosahedral, decahedral, tetrahedral, octahedral, and pyramidal shape,respectively. Allpress, Sanders compared the relative stabilities of various particleshape models (tetrahedron, octahedron, sphere, decahedron, icosahedron) as a functionof particle size by calculating the energy per atom. Ino (1969) was the first to evaluate
Cryst. Res. Technol. 33 (1998) 1 17
Fig. 8. Heavily twinned nanocrystallinethin film of Ge with a network of inter-linked threefold and fivefold twin junc-tions. Stacking faults are marked byrectangular boxes; regions of linear andcircular superstructures due to twin-ning on planes inclined to the film sur-face are marked by arrowheads andcircles.
2*
the energy balance of transition metal MTP's by including the cohesive energy, surfaceenergy and adhesive energy (resulting from the particle-substrate interaction) as well aselastic strain energy and twin boundary energy (resulting from multiple twinning). Heobtained e.g. size limits of 27.35 nm and 273.3 nm for icosahedral and decahedral parti-cles of Ag, respectively, with the decahedra, however, being only quasi-stable. In a moredetailed semi-quantitative approach Marks (1984a)36) and Howie, Marks consideredelastic strains and surface structure of MTP's to evaluate an energy balance based on astrong faceting model and inhomogeneous two-dimensional eleasticity. They obtainedstable size regions of both, decahedral and icosahedral particles and attempted a phasediagram for small particles stability (multiply twinned and single crystalline) in depend-ence on size and temperature (Ayajan, Marks).
From real-time video recording of structural transformations in small particles duringelectron microscopy observation (Iijima, Ishihashi 1986; Smith et al.; Wallenberget al.; Malm et al.; Mitome et al.; Iijima, Ishihashi 1991) it was concluded (Ayajan,Marks; Doraiswamy, Marks) that small particles not neccessarily have a singlestable structure, but can exhibit a multitude of configurations according to local minimain potential energy. These observations are analoguous to the configurational instabil-ities on a much smaller scale predicted by computer simulations of clusters bound by theLennard-Jones potential (Hoare, Pal; Berry) which have shown that the energydifference between icosahedral, decahedral and cuboctahedral structures are very small(Gordon et al.). Because of the configurational instability inherent to small particles ofsizes smaller than about 8 nm the structural transformations may be understood interms of statistical fluctuations with the probability of a particular configuration de-pending on size and temperature (Ayajan, Marks; Doraiswamy, Marks).
Experimental observations of fivefold twinned structures give evidence of their exten-sion to sizes far above the size limits calculated by stability considerations. Actually,they are highly distorted and defective in most cases. To account for the absence ofobservable discontinuities in small sized (d � 12 nm) transition metal MTP's, accordingto the model of Bagley decahedra may be treated as made up of units with bodycentred orthorhombic point group symmetry and, analogously, according to the modelof Mackay icosahedra may be treated as made up of units with rhombohedral pointgroup symmetry (Heinemann et al.; Yacaman et al. Yang, Yang et al.). Both areonly slightly deviating from the fcc structure. An orthorhombic distortion of the tetrahe-dral twin units is obtained by stretching the common edge (i.e. the fivefold axis) and atthe same time compressing the direction perpendicular to this edge. A rhombohedraldistortion of the tetrahedral twin units is obtained by compressing the central distanceof the triangular bounding faces to the opposite corner (i.e. the intersection of the sixfivefold axes) and at the same time stretching the outer edges of the tetrahedra. There-by, always an angle of 72� enclosed by the twin planes is achieved. Such homogeneousdistortions frequently have been applied to match by image contrast simulations experi-mentally obtained HREM images of transition metal MTP's (Barry et al.; Gai et al;Buffat et al.).
At particle sizes distinctly above 10 nm inhomogeneous elastic strains allow ratherlarge reductions of the stored strain energy from which the possibility arises that stressrelief processes may occur which involve the formation of lattice defects (Howie,
18 Hofmeister: Fivefold Twinned Structure
36) see also Marks 1985a
Marks). Since the experimental observation and analysis of lattice defects in MTP's byelectron microscopy methods is complicated because of weak defect contrasts in astrained lattice (Marks, Smith 1983, Marks 1985c) only HREM can provide structur-al information on defect configurations and associated formation mechanisms. Typically,planar defects such as stacking faults and secondary twin boundaries associated withstrain field induced dislocation processes are observed (Marks, Smith 198137); Marks,Smith 1983; Marks 1985c; Hofmeister 1991; Hofmeister, Atanassov). Stackingfault tetrahedra generated by stress-relieving formation of vacancies (Howie, Marks)and subsequent precipitation in disc-shaped aggregates on close-packed planes have beenfound in the volume of about 60 nm sized decahedral particles of Pd (Hofmeister1991) which is the up to now only experimental indication to the role of point defects inMTP's.
A particular stress-relieving defect configuration consisting of regular arrays of stack-ing faults has been observed in fivefold twinned structures of Si and Ge (Iijima; Hof-meister, Junghanns 1991; Hofmeister, Junghanns 1993). Fig. 9 shows as an ex-ample observed in the solid phase crystallisation of amorphous Ge thin films a fivefoldtwinned particle where in one of the twin units two couples of tetrahedrally arrangedstacking faults (marked by arrowheads) meeting at stair-rod dislocations are present.The HREM image is accompanied by the atomic model of the defective twin unit drawnalong a (110) zone axis with one pair of the stacking faults (arrows). The angular latticedilatation achieved by introducing these defects leads to an angle of about 76� betweenthe boundaries of the distorted twin unit while the neighbouring twin units obviouslyremaining undistorted have an angle of about 71�. Whereas two such pairs of stackingfaults are sufficient to accomodate the angular gap on the length scale of the twinboundary extension in the present case, two to four pairs of stacking faults continued by
Cryst. Res. Technol. 33 (1998) 1 19
37) see also Smith, Marks
Fig. 9. Stress relief by angular lattice dilatation due to pairs of stacking faults (arrowheads) in one subunit of afivefold twinned crystallite of Ge in amorphous matrix (right), and atomic model (left) of one pair of stackingfaults (marked by arrows) in a twin unit.
a periodic arrangement of edge dislocations (i.e. a small angle boundary) were observedin about five times larger decahedral particles of Si (Iijima).
As already discussed above, experimentally observed fivefold twinned structures notonly exceed the size limits based on thermodynamic considerations frequently, but alsotheir number density does not distinctly decrease below that of single crystalline parti-cles with increasing particle size (Hofmeister et al. 1982, Hofmeister 1984, Hofmeis-ter 1991). These findings rule out that MTP's as whole are frozen in a kinetically meta-stable state. In the literature reviewed above (see ch. 2) there are many impressiveexamples (a few of them are given in chronological order in Table 1) of extremly large
20 Hofmeister: Fivefold Twinned Structure
Table 1
Large sized fivefold twinned structures in various materials
Material approx. Size Type Reference
Cu 100 mm Dh Segalldc C 100 mm Dh WentorfNi 0.5ÿ3 mm Dh Schl�ottererSi 500 mm Dh Faust, JohnCo 40 mm Dh Gedwill et al.Au 200 nm Dh SchwoebelNi 8 mm Dh Downs, BrownAg 100 mm Dh Smit et al.Au 100 nm Dh, Ic Ino et al. 1972Ni 50 mm Dh Digard et al.Pd 100 nm Dh, Ic Fukaya et al.Ag 200 nm Dh, Ic KrohnGe 400 nm Dh Saito et al.dc C 600 mm Dh Pipkin, Daviesdc C 500 nm Dh Matsumoto, MatsuiBN 250 nm Dh Hiraga et al.Pd 100 nm Dh, Ic Hofmeister 1991C(60) 2 mm Dh Haluska et alYb 0.8ÿ1.5 mm Dh Arita et al.SiC 50 mm Dh Cheng et al.
Fig. 10. Platinum-carbon shadow cast-ing of a large icosahedral particle of Agthe edges of which and some surfacesteps on triangular bounding faces aredecorated by preferrential accomoda-tion of Pt clusters.
sized fivefold twinned structures of various materials which, however, mainly concerndecahedral configurations. There are only a few observation of very large icosahedralparticles and non of them exceeds the micrometer scale. Fig. 10 shows as an example thePt-C replica of an icosahedral Ag particle of nearly 200 nm in size where the metal hasbeen dissolved during preparation for TEM inspection (Krohn). The Pt-C shadow cast-ing technique clearly allows to recognize the icosahedral shape of the particle the edgesof which and additionally some steps at the triangular bounding faces are decorated byclusters of Pt. Obviously, MTP's stabilised by appropriate defect configurations can at-tain sizes like this and larger unless the equilateral growth is disturbed by coalescenceand/or transformation phenomena. Despite finally being unfavourably because of en-ergetic reasons, a kinetic barrier prevents the transformation to less defective and non-twinned structures which require more energy than available during the low temperaturegrowth processes concerned.
6. Summary
As already expressed in the introduction the main objective of this review is to traceback as complete as possible forty years of work on fivefold twinned structures. Oneimportant motivation for doing this is to give the honour of the first steps to those whoare frequently forgotten, and to enable accurate citation for future work in the field. Thework of Segall, e.g., has been cited only once in 27 years namely 1967 by Allpress,Sanders, who are Australian too, until 1984 the author of the present work started togive reference of it several times, but without successors. Another aim of this survey isto shed light on the multitude of facets of the widespread phenomenon of fivefold twin-ning. Since also an extended review like the present one cannot treat all of them indetail with equal accuracy here is the place to give reference to review articles on thesubject published previously. Although there has been done a lot of work on fivefoldtwinned structures in thin films and composites, there are available only review paperson MTP's. These are ``Structure of Small Metallic Particles'' by Gillet (1977), ``NobleMetal Clusters'' by Monot (1984), ``Phase Instabilities in Small Particles'' by Ajayan,Marks (1990), and ``Preferred Structures in Small Particles'' by Doraiswamy, Marks(1995). In 1986 van den Broek et al. gave a review on ``Early Proof of Fivefold Sym-metry'', but missed citation of Segall's work. Despite the tremendous amount of workalready spent in this field there remains enough space to be filled by future studies infavour of a thorough understanding of the phenomenon reviewed. Perspective directionsfor doing this could be atomistic modelling of formation mechanisms by moleculardynamics as well as more extensive computer simulation of HREM imaging of latticedistortions and defects.
Acknowledgements
This contribution is dedicated to Hans-Ude Nissen on the occasion of his 65th birthday. The authorwould like to thank W. Neumann for useful suggestions and critical discussions.
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