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Journal of Crystal Growth 286 (2006) 162–172

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On the structure of nanorods and nanowires with pentagonalcross-sections

J. Reyes-Gasgaa,b,�,1, J.L. Elechiguerraa, C. Liub, A. Camacho-Bragadob,J.M. Montejano-Carrizalesc, M. Jose Yacamana,b

aDepartment of Chemical Engineering, Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USAbTexas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA

cInstituto de Fısica, Universidad Autonoma de San Luis Potosı, 78000 San Luis Potosı, S.L.P., Mexico

Received 28 May 2005; received in revised form 27 September 2005; accepted 27 September 2005

Available online 10 November 2005

Communicated by M.S. Goorsky

Abstract

Here, we present a comprehensive study on the structure of multi-twinned decahedral-based nanorods and nanowires (Dh-NWs),

specifically for the case of silver. We have demonstrated that their high-resolution transmission electron images (HRTEM) can be

interpreted as a Moire pattern contrast based on a multi-twinned decahedron, and that their selected-area electron diffraction (SAED)

patterns can be also completely generated through the same multi-twinned decahedron basis. We propose that the structure of these

nanowires can be interpreted as a chain of decahedra joined along the vertex, which is parallel to the five-fold symmetry axis. This chain

can be generated through [1 1 1] growth for FCC structures.

r 2005 Elsevier B.V. All rights reserved.

PACS: 81.07.�b; 81.10.�h; 68.37.Lp; 61.14.Lj

Keywords: A1. Characterization; A1. Electron microscopy; B1. Metal; B1. Nanomaterials

1. Introduction

In recent years, nanostructured materials have beenwidely investigated due to their potential applications inmany different areas such as catalysis, optoelectronics,biological sensors and nanofabrication [1–3]. Among themost interesting nanomaterials are metallic nanostructuressuch as nanoparticles, nanorods and nanowires. It has beendemonstrated that, in the case of noble metal nanomater-ials, the optical and physicochemical properties are highlyinfluenced by shape and size [4–6]. This has driven researchtoward the development of synthesis routes that allow abetter control of morphology and size [7,8].

e front matter r 2005 Elsevier B.V. All rights reserved.

rysgro.2005.09.028

ing author. Department of Chemical Engineering,

of Texas at Austin, Austin, TX 78712-1063, USA.

1 6709; fax: +1 512 475 8485.

ess: jreyesgasga@mail.utexas.edu (J. Reyes-Gasga).

m Instituto de Fısica, Universidad Nacional Autonoma de

do Postal 20-364, 01000 Mexico, DF, Mexico.

In the case of face-centered cubic (FCC) materials, thesynthesis of anisotropic materials is not as simple as fornon-cubic crystal structures. However, there have beenrecent reports about the synthesis of 1-D nanostructures ofgold [9–11], silver [12–15] and copper [16,17] among others.All these materials have been synthesized using differentmethods, including hard-template [18], bio-reduction [19]and solution phase syntheses [13,14,17]. One of the mostemployed synthesis techniques for the production ofmetallic nanostructures is the polyol method. In thismethod, a metallic precursor is dissolved in a liquid polyol(typically ethylene glycol) in the presence of a cappingagent such as poly vinyl pyrrolidone (PVP). By controllingthe reaction parameters such as molar ratio betweencapping agent and metallic precursor, temperature, reac-tion time and the order of addition of reactants, areasonable control of the size and morphology can beachieved [20]. Recently, it has been demonstrated that, forthe case of silver, by adjusting some of these variables, a

ARTICLE IN PRESSJ. Reyes-Gasga et al. / Journal of Crystal Growth 286 (2006) 162–172 163

range of controlled morphologies such as nanocubes andnanowires can be produced [8].

Several of these reports indicate that some of these 1-Dnanostructures possess a remarkable five-fold multi-twinned structure, including the nanowires synthesized bythe polyol method [12,16,19,21–25]. Their cap resembles adecahedron and there is experimental evidence of apentagonal cross-section all across the long axis of thenanostructure, with a contrast quite similar to the onefound in multiple-twinned particles (MTPs) [23]. Based onthese observations, and even when the growth mechanismstill needs to be completely elucidated, it has been mainlyproposed that they evolved from a multi-twin decahedralnanoparticle growing in the [1 1 0] direction with thecapping agent assisting to direct the structure by stabilizingmore effectively the new-formed {1 0 0} facets than the{1 1 1} facets [22,24]. Thus, the final habit of the nanorodsand/or nanowires corresponds to an elongated pentagonaldipyramid [16,21,22,24,25]. This habit structure agrees withan early report of Melmed and Hayward [26]. Theyobserved whiskers of nickel, iron and platinum with astructure composed of five twins arranged about theircommon [1 1 0] axis. Therefore, we will study thesenanowires as a model to exemplify this type of structure,bearing in mind that all our findings are applicable for anyfive-fold twinned FCC metallic nanorods and/or nano-wires.

Pentagonal arrangement in MTPs is quite known. MTPnanoparticles of transition metals with FCC lattice metals[27,28] and some other materials such as carbon [29] havebeen reported. Five-fold symmetry nanoparticles have beenthe subject of intense research during the last 50 years. Thepioneering work of Ino and Ogawa [30] and Allpress andSanders [31] described gold nanoparticles with icosahedraland decahedral structures in terms of a multi-twinnedmodel. Later, Marks described icosahedral nanoparticles interms of a multi-twinned structure composed of 20tetrahedrons joined on their {1 1 1} facets [32–34]. Basedon these studies, the basic structure of a decahedral particlecan be described as the junction of five tetrahedron singlecrystals with twin-related adjoining faces. The theoreticalangle between two (1 1 1) planes is �70.51, so by joiningfive tetrahedra, which are bounded by {1 1 1} facets, a gapof �7.51 is generated. Thus, the space cannot be filled byjust joining five tetrahedrons and some form of internalstrain is necessary giving place to dislocations and otherstructural defects [27,28]. These defects are also observed inthe transmission electron microscope (TEM) cross-sectionimages of the beforementioned nanorods and nanowires[23].

The structure of these 1-D nanomaterials, includingsilver nanowires produced by the polyol method, has beendescribed as five triangular prisms joined in such a way thatthey show the {1 0 0} planes on their sides and are cappedby {1 1 1} planes, growing along the [1 1 0] direction.However, to date, the actual physical mechanism thatallows the growth of such a structure is not clear and a

comprehensive understanding of the structure is required.Several groups have made important contributions bystudying the five-fold twinned structure of differentmetallic nanorods and nanowires [16,21,23,25] via electronmicroscopy. Nevertheless, all of them proposed a nanowirecomposed of five long triangular single-crystal prisms.In this work, we analyze the experimental features of

high-resolution transmission electron microscopy(HRTEM) images and selected-area electron diffraction(SAED) patterns of silver nanowires with pentagonalcross-sections. Our findings demonstrate that a decahe-dral-based model is necessary for a full interpretation ofthe experimental results. Therefore, we discuss the struc-ture of the FCC metallic nanostructures with pentagonalcross-sections (named here as Dh-NW) on a decahedral-based model.In particular, we discovered that both HRTEM images

and SAED patterns can be easily interpreted on the basisof a multi-twin decahedron. In addition, we found that theobserved contrast of HRTEM images can be explained interms of Moire fringes generated from the overlapping ofthe silver FCC unit cell planes arranged in the fivetetrahedra that compose the decahedron. Finally, wepropose that the structure of these five-fold multi-twinnednanowires is better interpreted as a chain of decahedrajoined along the vertex, which is parallel to the five-foldsymmetry axis. From this idea, our report differs from allprevious works and provides new insights about theremarkable structure of five-fold twinned FCC metallicnanorods and nanowires.

2. Experimental procedure

Silver nanowires were synthesized by the polyol reduc-tion of silver nitrate (AgNO3) in presence of PVP. In atypical synthesis, 5mL of pure ethylene glycol and 5mL ofa 0.36M solution of PVP in ethylene glycol were refluxed ina three-necked flask at 160 1C with vigorous stirring forabout 60min. After that, 2.5mL of a 0.12M solution ofAgNO3 in ethylene glycol was injected drop-wise into thereaction flask in no less than 6min. As the first drops ofAgNO3 were added, the mixture turned yellow. Withcontinuous injection, it became gradually turbid for a finalgray color. After 60min the reaction was stopped, allowingthe product to cool to room temperature. The silvernanowires were purified by centrifugation, the reactionproduct was diluted in deionized water (5� in volume) andthe supernatant was removed. This last process wasrepeated at least two times.Scanning electron microscopy of the nanowires was

conducted using the scanning electron microscopes (SEM)Hitachi 4500F operated at 15 kV, and a Cs-Corrected SEMJEOL-JSM7700F microscope operated at 2 and 30 kV.This last SEM allows us to observe the sample in differentmodes, i.e. SEM, TEM and scanning TEM (STEM) with aresolution of 0.6 nm. Transmission electron microscopywas conducted in a HRTEM, JEOL 2010F equipped with

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Schottky-type field emission gun, ultra-high resolution polepiece (Cs ¼ 0:5mm), and a STEM unit with high-angleannular dark-field (HAADF) detector operating at 200 kV,and a Cs-corrected FEI-TECNAI microscope operated at200 kV. For digital image processing, the Digital Micro-graph (GATAN) software was used. To simulate theelectron diffraction patterns, the SimulaTEM software [35]was employed.

3. Results

3.1. Electron microscopy

Fig. 1 shows SEM images of the obtained Dh-NW. Inthe inset the pentagonal morphology of a single nanowire isclearly observed. Fig. 2 shows both scanning (Fig. 2(a))and transmission (Fig. 2(b)) electron images of the Dh-NW

Fig. 1. SEM image of the synthesized silver nanowires. Inset shows an

SEM image of the pentagonal cross-section of these nanowires.

Fig. 2. Cs-corrected scanning (a) and transmission electron images of the synth

field (c) modes. Note the lines presented in the bright- and dark-field images

internal structure of the nanorod.

when they are observed in the STEM unit. Note here theinternal lines presented by the nanowires, which are betterobserved when the image is recorded in the dark-field (DF)image mode (Fig. 2c). In SEM images, the number of linesproduced only from the edges of the pentagonal nanowirecan vary from two to one, depending on the angle betweenthe nanowire and the electron beam. For the case of TEMimages, the maximum number of lines corresponding to theedges of the nanowire will be always three. Thus, any otherline will have another structural source.HAADF image contrast is mainly related to differences

in atomic number [36] and intensity varying as �Z2. Evenwhen the nanowires are only composed of silver, asindicated by EDS X-ray analysis, HAADF STEM imagesalso provide structural information. In the presence ofcrystal defects, contrast will also result from inelasticdispersion [37,38]. Fig. 3 shows two HAADF images of theDh-NW. The line observed in the center of the nanowireshown in Fig. 3(a) corresponds to one of its edges. In Fig.3(b) a bright region is observed. The brighter contrast ofthis region should be produced by the internal strainnecessary to close the gap in the decahedral structure, and

esized silver nanorods and nanowires in the bright-field (b) and in the dark-

, mainly from the nanorod, labeled ‘‘1’’. These lines are produced by the

Fig. 3. HAADF images of two different Dh-NWs. Note the bright region

observed in (b).

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Fig. 5. Characteristic SAED patterns of the Dh-NW. Their indexation

indicates that they correspond to the overlapping of the (a) [1 0 0] and

[1 1 2] zone axes, and the overlapping of the (b) [1 1 1] and [1 1 0] zone axes,

respectively. Note the existence of an aperiodic sequence of diffraction

spots in (a).

J. Reyes-Gasga et al. / Journal of Crystal Growth 286 (2006) 162–172 165

correspond to the structural feature that produces thebright lines presented in Figs. 4(a) and (b).

It is well known that in TEM images, the contraststrongly depends on the diffraction conditions under whichthe images are taken, and interpretation is not straightfor-ward. The bright line observed in Figs. 4(a) and (b) is in astrong diffraction condition, and in cases such as Fig. 4(a),a slight twist along the length of the nanowire is observed.Meanwhile, Fig. 4(c) shows a dark-field image in weakbeam condition (WBDF), which indicates the existence of ahigh density of linear defects along the longer axis of thenanowire. It is also important to note the crack at the tip ofthe nanowire (indicated by an arrow in Fig. 4(c)) that arisesfrom the multi-twinned structure.

The main SAED patterns from individual nanowirestaken by directing the electron beam perpendicular to theirlong axis are presented in Fig. 5. The orientation of thenanowire with respect to the electron beam is shown in thecorresponding insets. It is important to note that rotationalong the long axis of the nanowires revealed a rotationalperiodicity of 361, which is expected from the five-foldsymmetry of the structure. Both SAED patterns are easilyinterpreted as the overlapping of the [1 0 0] and [1 1 2] zoneaxes (Fig. 5(a)) and the overlapping [1 1 1] and [1 1 0] zoneaxes (Fig. 5(b)) of the silver FCC unit cell, respectively. Thepresence of an aperiodic sequence of diffraction spots inFig. 5(a) is relevant. This aperiodic sequence cannot beinterpreted on the basis of the indexation of mentionedplanes (see Refs. [22,23,25]).

Another important observation arises from the tip of thenanowires. The measured angle between the sides of the tipand the sides of the main body is approximately 301, as can

Fig. 4. (a) and (b) Dark-field TEM images of the Dh-NW. In this case, the str

because the defect is in the Bragg diffraction condition. (c) Weak-beam dark-fi

stress that exists along the length of the nanowire is clearly observed.

be seen in Fig. 6. Therefore, from electron microscopyanalysis, it can be seen that the habit for the Dh-NWscorresponds to the Johnson solid number J16, i.e. anelongated pentagonal dipyramid [39], which is schemati-cally shown in Fig. 7. For an FCC unit cell and supposing abody grown in the [1 0 0] direction, the angle between the{1 1 1} edges of the pentagonal pyramid with the body is451 (Fig. 7(b)), while for a body grown parallel to the [1 1 0]axis is 351 (Fig. 7(c)). On the other hand, for a decahedroncomposed of five tetrahedrons projected perpendicularly tothe five-fold symmetry axis, as shown in Fig. 7(d), theprojected half angle between the exposed {1 1 1} facets is301. From this analysis, it is clear that the observed anglebetween the edges of the tip and the body of the Dh-NWs isbetter reproduced by a decahedral tip.

ong contrast observed along the length of the nanostructures is produced

eld image of the tip of a single nanowire. In this case, the high density of

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Fig. 6. Images of the tip of the Dh-NWs: (a) SEM and (b) Cs-corrected

TEM images. The angle formed between the edges of the cap and the sides

of the main body is approximately 301.

Fig. 8. HRTEM images of the (a) edge and (b) central part of a Dh-NW.

The corresponding FFT of the enclosed regions are shown in the insets. In

(a), the FFT is along [1 1 0] while in (b), it corresponds to the overlapping

of [1 1 0] and [1 0 0].

Fig. 7. (a) Schematic representation of the habit of the Dh-NWs, which

corresponds to an elongated pentagonal dipyramid (Johnson solid J16). In

the case of an FCC unit cell, for a body grown parallel to the [1 0 0], the

angle between the edge of the pentagonal pyramid and the main axis of the

body is 451 (b), while for a body parallel to the [1 1 0] axis is 351 (c). (d) In a

decahedron composed of five tetrahedrons, the half angle between exposed

{1 1 1} facets perpendicular to the five-fold symmetry axis is 301.

J. Reyes-Gasga et al. / Journal of Crystal Growth 286 (2006) 162–172166

3.2. Image processing

Figs. 8(a) and (b) correspond to HRTEM images of theDh-NW in the edge and in the center, respectively. Thecorresponding fast Fourier transforms (FFT) of the areasenclosed by a square are shown in the insets. Theindexation of the FFT in Fig. 8(a) indicate that theobserved spots correspond to the [0 1 1] zone axis, whiletheir additional splitting is due to the edge of the nanowire.The FFT in Fig. 8(b) is more complicated. The arrange-ment of the spots indicates that they correspond to theoverlapping of two zone axes: [0 1 1] and [1 0 0]. Fig. 9(f)shows that by digitally processing the previous two zone

axes together, the image of the enclosed area in Fig. 8 iscompletely regenerated.The observation that different zone axes are overlapped

in many of the FFTs of the Dh-NWs is important, andindicates that the observed contrast in their HRTEMimages is mainly produced by Moire contrast. Therefore,we will analyze the contrast presented in the HRTEMimages of these nanowires on the basis of a Moire opticaleffect.Fig. 10 shows a Cs-corrected HRTEM image from an

area close to the tip of one nanowire (a lower amplificationof the same nanowire is shown in Fig. 6(b)). It is clear thatthe image is composed by two types of atomic arrange-ments: a square arrangement in the upper right part of theimage and a more complicated arrangement enclosed in theimage by a square. In addition, observing the image at agrazing angle along the direction indicated by the arrowlabeled ‘‘m’’, a modulation is presented. The FFT from thesquare arrangement of atoms corresponds to the [1 0 0]zone axis, while that from the complex arrangement isproduced, in principle, by the overlapping of the [1 0 0] and[1 1 2] zone axes. In fact, this last FFT corresponds to theSAED pattern shown in Fig. 5(a), including also theaperiodic sequence of spots. Therefore, the contrastproduced by the enclosed region in Fig. 10 corresponds,in principle, to a Moire contrast created by the [1 0 0] and[1 1 2] zone axes. So let us to study this last contrast in moredetail.The images presented in Fig. 11 were obtained by

digitally processing different spots in the FFT of theenclosed complex region of Fig. 10. Fig. 11(d) was obtainedusing only the spots from the [1 0 0] zone axis, while Fig.11(e) was obtained with the spots from the [1 1 2] zone axis.Finally, Fig. 11(f) results by processing together both axes,i.e. [1 0 0] and [1 1 2]. In Fig. 12, the processed imagepresented in Fig. 11(f) can be observed in better detail, andcompared with the enclosed region in the experimentalimage shown in Fig. 10. At first glance they seem quitesimilar. However, by observing Fig. 12 at a grazing anglealong the directions indicated by the arrows, it is noted that

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Fig. 9. Digitally processed images from the enclosed region in Fig. 8(b) using (a) only the [0 1 1] spots, (b) only the [1 0 0] spots and (c) both the [0 1 1] and

[1 0 0] spots.

Fig. 10. Cs-corrected HRTEM image from an area close to the tip of a

single nanowire. Observing this image in a grazing angle, a modulation

along the direction indicated by the arrow can be seen. The upper right

inset shows the FFT from the square arrangement of atoms indicated by

the arrow, and corresponds to the [1 0 0] zone axis. The lower right inset

shows the FFT from the region enclosed by a square. This FFT

corresponds to the overlapping of the [1 0 0] and [1 1 2] zone axes and it

is consistent with the diffraction pattern shown in Fig. 5(a). The aperiodic

sequence is indicated by arrows.

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the modulated contrast presented in Fig. 10 is notobtained. In fact, Fig. 12 is completely periodic in alldirections, while Fig. 10 is not.

To understand the origin of the modulation in Fig. 10, itis necessary to take into account the aperiodic sequencementioned in Fig. 5 and also observed in the FFT of theenclosed region in Fig. 10. Fig. 13(a) shows the processedimage using a filter that includes the aperiodic sequence ofspots indicated in Fig. 10. In this case, when the processed

image is observed along the direction indicated by thearrow denoted by ‘‘m’’, the modulation does not appearyet. In Fig. 13(b), the image was obtained by including thereflection spot (2 2 0). Once again, by observing at a grazingangle along the direction indicated by the arrow ‘‘m’’, themodulation is present. Therefore, the structure presents amodulation along the [1 1 0] direction. By observing at agrazing angle along the directions indicated by the arrowslabeled as ‘‘p’’, both images also show an aperiodicarrangement of lines.From this analysis, we can conclude that the origin of the

contrast shown in Fig. 10 is related with a Moire effectbetween the [1 0 0] and [1 1 2] zone axes with the convolu-tion of both the aperiodic sequences along the [1 0 0] or[1 1 1] direction (depending on the overlapped zone axistaken as reference), and the modulation along the [1 1 0]direction.

4. Discussion

4.1. On a model for the Dh-NWs

4.1.1. The decahedron

Five-fold MTP nanoparticles can be described as thejunction of five tetrahedron single crystals to form adecahedron with twin-related adjoining faces [23,27,28].We will analyze first the multi-twinned decahedron modelto find the type of FCC atomic arrangement that canproduce the observed contrast in the Dh-NWs.It is well known that the edges of the tetrahedron are

oriented along the /1 1 0S directions, that their faces arethose of the family {1 1 1}, as shown in Fig. 14, and thatthe normal vectors to all of the /1 1 0S directions areparallel to /1 0 0S. The stereographic projection of the

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Fig. 11. Digitally processed images using different spots from the FFT of the enclosed region indicated in Fig. 10: (a) spots only from the [1 0 0] zone axis,

(b) spots only from the [1 1 2] zone axis, (c) spots from both [1 0 0] and [1 1 2] zone axes. Note that the contrast of interest (f) is produced by the convolution

of these spots.

Fig. 12. Magnification of the processed image shown in Fig. 11(f). This

image is completely periodic in all directions and the modulation observed

in Fig. 10 is not present.

Fig. 13. Digitally processed images including the aperiodic sequence

indicated in Fig. 10: (a) without including the (2 2 0) reflection spot and (b)

including the reflection spot (2 2 0). Observing these images along the

direction indicated by the arrow ‘‘m’’ we see that (a) does not present any

modulation while (b) does. Along arrow ‘‘p’’, both images show an

aperiodic arrangement of lines.

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tetrahedron, shown in Fig. 14(b), can help us describe the‘‘two types’’ of two-fold symmetries produced by theirrelative position of the edges. Those two types have beenindicated in Figs. 14(a) and (c) as ‘‘1’’ and ‘‘2’’,respectively.

Therefore, to build the decahedron presented in Fig.15(a), it is necessary to join five tetrahedra along a common[1 1 0] edge, say the edge numbered as ‘‘2’’. As mentionedbefore, there is a twin relationship between the adjoiningfaces, and the joined five tetrahedrons can not completelyfill the space. However, for clarity, our model does notpresent the gap of 7.51. It is also important to mention that

our idealized decahedron allows to consider that the [1 1 0]direction parallel to the five-fold axis is perpendicular tothe /1 1 0S of its edges, and that the normal vectors to allof them are parallel to /1 0 0S.For simplicity of the following analysis, we designated

all the tetrahedra that compose the decahedron asindependent ‘‘crystals’’. By analyzing the decahedron inprojection along the five-fold symmetry axis, some possiblepaths followed by the electrons in the TEM are schema-tized in Fig. 15(b). Each line represents an individual beamthat travels exactly through the center of each crystal, andis represented by en, with n ¼ 1, .., 5. Because of thesymmetry of the decahedron, beams e1 and e5 (travelingthrough crystals 2 and 3), and beams e2 and e4 (travelingthrough crystals 4 and 5) will encounter the same structural

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Fig. 15. (a) Decahedron formed with five tetrahedra. (b) Schematic

representation of the interaction of the electron beam with the decahedron

in a TEM. Each line represents an individual electron beam traveling

along the structure of the decahedron through different paths.

Fig. 14. (a) The tetrahedron in relation to the cube and its (b)

crystallographic relationships. A stereographic projection (c) is shown

along the [1 1 1] zone axis. Note that all the tetrahedron facets are {1 1 1},

while all the edges are /1 1 0S. Also note that the edge labeled ‘‘1’’ is

perpendicular to the edge labeled ‘‘2’’.

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arrangement inside the decahedron, while beam e3 willcome across crystal 1 and the twin boundary formed bycrystals 3 and 4.

Now, using a (1 1 0) cubic lattice diagram in real space(Fig. 16), the zone axis for any traveling en beam can befound. To accomplish this, it is necessary to measure thedistance at which each en reach the edge of thecorresponding crystal. These distances are indicated inFig. 15(b) as h1, h2 and h3. Then, a tetrahedron is drawn atthe origin of the (1 1 0) lattice and each hi distance ismarked along its edges. By joining the origin of the latticewith the points generated by these distances, the Miller

index of a particular beam can be immediately determined.Following these indications, the zone axes for the abovebeams are [1 0 0], [1 1 2] and [2 2 1]. So, crystals 3 and 4 arein the zone axis [1 1 2], crystals 2 and 5 are in [1 2 2], andcrystal 1 is in [1 0 0]. Because of symmetry considerations,(1 1 2) and (1 2 2) are similar planes.The path of beam e3 is very special. As mentioned above,

it goes first through crystal 1 and just after that, encountersthe boundary between crystals 3 and 4. Because thisboundary is the edge where two tetrahedrons are joined, itrests along the [1 1 0] direction. In fact, this boundary is theorigin of the bright line observed in Figs. 4(a) and (b). Inthe vicinity of the vertex, say for example the region closeto beams e1 and e5, the zone axis is also close to [1 1 0].When the decahedron is tilted by 181 around the [1 1 0]

direction, the electron beam travels along the pathindicated by e6 in Fig. 15. Here, crystals 4 and 5 areobserved along the [1 1 1] zone axis. In this case, the pathindicated by e7 is close to the vertex. Similar to the case ofe5, the path of e7 is also close to the [1 1 0] zone axis. Crystal2 is also observed along the [1 1 0] zone axis because theelectron beam will be traveling parallel to its edge.Therefore, the main possible Moire images that can be

observed in the HRTEM images of the Dh-NWs areformed by the planes {1 0 0} and {1 1 2}, {1 1 1} and {0 1 1},and {1 1 0} and {1 0 0}, exactly as those observed experi-mentally.

4.1.2. Basis for a 3-D model of the Dh-NW

As commented previously, the Dh-NW habit has beendescribed as an elongated pentagonal dipyramid. However,there are different ways to build this Johnson Solid. Onethat is currently reported as the structure of the Dh-NWsconsists of five triangular prisms in such a way that theypresent {1 0 0} planes on their sides and are capped by{1 1 1} planes growing along the [1 1 0] direction[16,22,23,25]. This model is completely in agreement withthe description in the previous section, because thedecahedron was projected along the five-fold symmetryaxis.We generated this model and obtained its corresponding

electron diffraction pattern using the SimulaTEM software[35]. Our results are presented in Fig. 17. The model is apolyhedron of 12 vertices (two poles and 10 vertices at theequator), 25 edges, 10 equilateral triangular faces and fivesquared lateral faces. It was grown from a decahedron bythe addition of atomic layers. Each layer was composed bytwo sub-layers: one is the equator of the decahedra and theother is the immediate layer over the equator. The finalmodel is composed of 24,739 atoms with 20 intermediate(1 1 0) planes. Fig. 17(a) shows our model and its simulatedelectron diffraction pattern along the [1 0 0] direction(corresponding to e3 in Fig. 15(b)). On the other hand,Fig. 17(b) shows both the model and simulated diffractionpattern but rotated 181 with respect to Fig. 17(a)(corresponding to e6 in Fig. 15(b)).

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Fig. 16. Projection of the (1 1 0) cubic lattice in real space where one tetrahedron is set at the origin. The zone axes for each electron beam (en) are

indicated.

Fig. 17. Model of a Dh-NW according to Refs. [22,23] and their

corresponding simulated SAED patterns. This structure consists of five

triangular prisms based on the Ag FCC unit cell joined along the common

[1 1 0] edge. (a) Structure along the [1 0 0] direction (corresponding to e3 in

Fig. 15(b)). (b) Rotating (a) by 181 around the five-fold pentagonal axis

(corresponding to e6 in Fig. 15(b)).

Fig. 18. Simulated silver decahedron. This structure consists of five

tetrahedra based on the Ag FCC unit cell joined along the common [1 1 0]

edge. (b) Simulated diffraction pattern along the [1 1 0] direction

(corresponding to e6 in Fig. 15(b)). (d) Simulated diffraction pattern

along the [1 0 0] by rotating (a) by 181 around the five-fold pentagonal axis

(corresponding to e3 in Fig. 15(b)).

J. Reyes-Gasga et al. / Journal of Crystal Growth 286 (2006) 162–172170

In principle, the simulated diffraction patterns of thismodel and the experimental patterns shown in Fig. 5 seemto be similar. However, they are not exactly equal. Byfixing the ratios between the distances ar/ap and Hr/Hp

equal to one (Figs. 19(a), (b), (e) and (f)), the measuredratios between the distances Ar/Ap, Br/Bp, hr1/hp1 and hr2/hp2 are 0.96 (i.e. 2% of difference), 1.02 (2%), 1.04 (4%)and 0.92 (8%), respectively. We also noted that theaperiodic sequence of diffracted spots is not preciselyreproduced. Independent of these differences, we canconclude that the aperiodic sequence of diffracted spots isproduced by the twinning relationship of the five crystalsthat compose the pentagonal cross-section of the nanos-tructure.

On the other hand, the previous model does not addresssome fundamental points, such as, e.g., how a structurethat is growing along the [1 1 0] direction as five triangularprisms together suddenly stops its growth and leave a tipformed by five {1 1 1} planes. Therefore, an alternativemodel is necessary.Let us get back to the decahedron formulation. As for

the case of the previous model, we generated a model for amulti-twinned silver decahedron and simulate the corre-sponding electron diffraction pattern along the samedirections as for the previous simulated structure. Theseresults are shown in Fig. 18. For this model, we startedfrom a decahedron without a central site that has onlyseven vertices in two layers. The first layer (order 1) is

ARTICLE IN PRESSJ. Reyes-Gasga et al. / Journal of Crystal Growth 286 (2006) 162–172 171

covered by a second layer (order 2), with a shell of 47 sitesdistributed as follows: seven vertex sites of two types, 30edge sites in three layers (10 sites of one type and theequator), and 10 at the triangular faces, for a total of 54sites in the cluster. Decahedra of superior order wereformed by covering this cluster with successive shellsto obtain a final decahedron composed of 6670 atoms.Fig. 18(b) shows the corresponding simulated diffractionpattern to the direction indicated by e6 in Fig. 15(b) (181from Fig. 18(c)), while Fig. 18(d) shows the simulateddiffraction pattern along the [1 0 0] direction (correspond-ing to e3 in Fig. 15(b)). The comparison between thesimulated diffraction patterns of the five-twinned silverdecahedron and the experimental patterns from the Dh-NW presented in Fig. 5 demonstrates that there is a bettermatch among them. By fixing the ratios between thedistances ar/ad and Hr/Hp equal to one, the measureddistances (Figs. 19(c)–(f)) indicate that the ratios Ar/Ad, Br/

Fig. 19. Comparison among the simulated SAED patterns (a) and (b) of

the elongated decahedron shown in Fig. 17, (c) and (d) are the

decahedrons shown in Fig. 18, and (e) and (f) are the experimental

patterns shown in Fig. 5. The aperiodic sequence observed in the

experimental patterns is fully reproduced in the case of the decahedron,

while the elongated model generates a different aperiodic sequence.

Bd, hr1/hd1 and hr2/hd2 are 0.97 (i.e. 3% of difference), 0.98(2%), 0.98 (2%) and 0.99 (1%), respectively.In addition, it is clear that all the features, including the

aperiodic sequence, are observed in the decahedron model.In fact, the diffracted spots in the simulated patterns areequal in position and intensity to the experimentalpatterns. Therefore, we conclude that the observedaperiodic sequence is produced by the twinning relation-ship of the five crystals that compose the decahedralnanostructure, and that all the images described so farcorrespond to a structure based on a five-twinneddecahedron.

4.1.3. Modulation and a new model for the Dh-NW

With the previous analysis, we have demonstrated thatthe contrast observed in HRTEM images of the Dh-NWs isproduced by the Moire generated from the arrangement oftetrahedra used to built a decahedron, and that theobserved aperiodic sequence is also produced by theinteraction of the electron beam with this structure.However, in the analysis presented in the previous sections,we have not explained the modulation observed along the[1 1 0] direction.Fig. 20 shows the FFT from Fig. 10, which corresponds

to the electron diffraction pattern shown in Fig. 5(a). Inthis figure, we have indicated the wavelength, l, of themodulation and its elongation, D/2. The modulation isparallel to the [1 1 0] direction and, from direct measure-ments, its wavelength is two times d220, i.e. 0.289 nm, whileits amplitude is D/2, i.e. 1.42 nm. This modulation is aMoire pattern produced by the overlap of the fivetetrahedra that compose the decahedron, but the maincontributors are those in the [1 0 0] and [1 1 2] zone axes.The fact that the same SAED patterns are observed in

every point along the length of the Dh-NWs induces topropose that a decahedral arrangement is present all alongthe body of the nanowires, where the nanowires are formedby a chain of decahedra joined along the vertex.

Fig. 20. (a) FFT from the enclosed region shown in Fig. 10. Here, the

wavelength of the modulation observed in Fig. 13(b) is indicated. Note

that this modulation is parallel to the [1 1 0] direction, and that the

wavelength l is 2 times d220 (i.e. 0.289 nm), while the amplitude is D/2 (i.e.

0.37 nm). (b) Processed image from the FFT in (a) using the filter shown in

the inset. The wavelength l and the elongation D/2 are shown.

ARTICLE IN PRESS

Fig. 21. Schematic representation of the polyhedra formed by our model

of the Dh-NW based on a chain of decahedra. The decahedra are brought

together to form a chain along the vertex, or the tetrahedra common edge

[1 1 0]. The ‘‘spaces’’ between decahedra are filled with atoms arranged

along the [1 1 1] direction in such a way that a rectangular pyramid is

formed, resulting in the habit observed for the Dh-NWs.

J. Reyes-Gasga et al. / Journal of Crystal Growth 286 (2006) 162–172172

Therefore, we propose that the structure of the Dh-NWscan be interpreted as a chain of decahedra joined along thevertex (which is parallel to the five-fold symmetry). Fig. 21shows a schematic representation of this structural model.The ‘‘free’’ spaces between decahedra have the shape of arectangular pyramid, with a ratio between edges of 1.14,and are filled with atoms that also grow along the [1 1 1]direction of the FCC unit cell. They are, in fact, part of adecahedron branch that was growing until it was stoppedby the action of the capping agent that surrounds thenanowire, which works as a ‘‘container’’. Thus, we get theelongated pentagonal dipyramid experimentally reportedas the habit of the Dh-NW. Note that in our model, theDh-NWs are always growing along the [1 1 1] direction,although the polyhedra formed are those shown in Fig. 21.Based on this model, the observation that the tips of thenanowire expose always {1 1 1} facets is a naturalconsequence of the growth in the [1 1 1] direction.

5. Conclusion

We developed a new model for the structure of the Dh-NW based on chains of multi-twinned decahedra growingalways along the [1 1 1] direction in which the final habit ofan elongated pentagonal dipyramid is obtained, asobserved experimentally. This structure explains theobserved Moire contrast and the SAED patterns, andcan be generalized to other five-fold twinned FCC metallicnanorods and nanowires.

Acknowledgements

The authors gratefully thank Domingo I. Garcia andSamuel Tehuacanero for the technical assistance duringthis work, and R. Caudillo and J.L. Burt for their useful

comments. J.L.E. and A.C.B. acknowledge the supportreceived from CONACyT-Mexico.

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