Structures of Clusters

Cryst. Res. Technol. 35 2000 6–7 731–743

With regard to different preparation techniques of inert gas aggregation for Cu and of aqueous chemicalmethods for ligand stabilised particles of CdS and Cu the structure of nanoparticles is discussed. In thelatter case, long needles of micrometer lengths and nanometer diameters are prepared which have thestructure of multiply twinned particles like truncated decahedra. For interpretation purposes highresolution electron microscopy was performed together simultaneously with computer simulations byphase grating approximation or multi-slice technique in combination with image processing.

Keywords: structure, cluster

(Received May 4, 2000; Accepted July 1, 2000)

1. Introduction

In order to obtain information on the structure and morphology of small clusters innanometer dimensions by means of high resolution electron microscopy (HRTEM) it hasbecome useful to perform computer simulations of cluster models. Very often the computersimulations were done by phase grating approximation, c.f., ALPRESS et al. (1973), COWLEYet al. (1976) and HUTCHISON (1976) or by the more advanced multi-slice technique, c.f.COWLEY et al. (1957) and GOODMAN et al. (1974). Very helpful for the symmetryinterpretation and the measuring of structural data like lattice parameters and thecorresponding lattice angles is the calculation of the power spectra (PS) of the images, i.e.,square of the Fourier transform of the images. In the following, some results of differentnanoparticle preparations will be presented. The authors will mainly concentrate on coppernanoparticles although an example of hexagonal and cubic CdS clusters will also be given(VOGEL et al., 1997). The results of the preparation techniques described here will be theinert gas aggregation technique (GRANQVIST et al., 1976) and a chemical reaction techniqueresulting in ligand stabilised clusters, c.f. VOGEL et al. (1997) and LISIECKI et al. (2000).

2. Inert gas aggregation

Cu clusters have been prepared in the size range between 1 and 10 nm diameter. It could beshown that large clusters, i.e., larger than 5 nm, showed either the fcc structure of the bulkwith cuboctahedral shapes or, more often, like Wulff polyhedra. The smaller clusters mainlyshowed the structure of multiply twinned particles (MTP) like icosahedra or decahedra(URBAN et al., 1996). Examples of cuboctahedra are shown in Figs. 1 and 2. Models,computer simulations together with PS and HRTEM images are shown in the [110], and[001] orientations, respectively. The particle diameters in the experimental images are 5.9

J. URBAN, H. SACK-KONGEHL, K. WEISS, I. LISIECKI*, M.-P. PILENI*

Fritz-Haber-Institut der Max-Planck-Gesellschaft, Abt. Anorganische Chemie,14195 Berlin*Université Paris VI, U.P.M.C. Laboratoire SRSI, 75005 Paris

Structures of Clusters

Dedicated to Prof. Dr. J. Heydenreich on the occasion of his 70th birthday

732 J. URBAN et al.: Structures of Clusters

nm. Figs. 3, 4 and 5 show icosahedra in the three main orientations also together with theexperimental images, i.e., 5-, 3- and 2-fold orientations. The diameters of the experimentalimages are 3.5, 4.7 and 4.4 nm, respectively.

Fig.6 shows a decahedral nanoparticle in the 5-fold orientation. The particle diameter is 4nm. Often, truncated decahedral or icosahedral structures are discussed, which were notobserved for particles prepared with the inert gas aggregation technique. Such structures willbe discussed below.

The existence of MTPs for small particles may be explained as follows: The surface ofMTPs consist of 20 (111) planes and 10 (111) for icosahedra and decahedra, respectively.Seeing that the surface energy of the (111) plane is smaller than the (100) plane it is obviousthat the total surface energy of MTPs is smaller than that of cuboctahedra consisting of 6(100) planes and 8 (111) planes. However, in the case of MTPs, internal strain has to beintroduced in order to fill necessary gaps between the tetrahedral subunits. MTPs, therefore,consist of deformed tetrahedral subunits. The internal strain increases with increasingparticle size. Therefore, with an increase in the particle size beyond a critical size, theunstrained fcc structure is energetically more favourable even if the number of (111) planesdecreases at the cost of (100) planes.

Cu clusters were also oxidised and characterised according to their structure. Theoxidation was performed either before the cluster aggregation by adding oxygen to theaggregation gas, i.e., Argon, or after cluster nucleation by exposing the clusters to oxygen fordifferent lengths of times, c.f. URBAN et al. (1997). Following several intermediate states notunder discussion here, see URBAN et al. (1996), the final state of oxidation leads to the bulkcuprite structure Cu2O. Several examples of models, computer simulations, PS andexperimental HRTEM images are shown in various orientations: [001], [110], [112] and[111] in Figs. 7-10.

3. Ligand stabilised particles.

a) CdS:

CdS ligand stabilised clusters were prepared by aqueous chemical methods describedelsewhere, c.f. KHOSRAVE et al. (1995) and NOSAKA et al. (1988). The structures are that ofSphalerite (cubic) and Wurtzite (hexagonal). The results of hexagonal clusters are shown inFigs. 11-14 in the [001], [011], [100] and [211] orientations.

Often, a combination of cubic (in the [111] orientation) and hexagonal structures (in the[001] orientation) are unavoidable. For both structures this can be nicely demonstrated byincluding stacking faults. Fig. 15 shows computer simulations and PS for different CdSmodels, i.e., cubic with stacking faults and hexagonal structures. The stapeling in the modelsfrom top to bottom is abcabcabc, abcabcab, abcabab and ababab for the cubic structure in the[111] orientation and ababab for the hexagonal structure in the [001] orientation.

b) Cu:

The preparation of ligand stabilised pure Cu clusters is described elswhere, c.f., Lisiecki etal. (2000). It is to be underlined that together with sphere-like clusters, long needles andcylinders could be synthesised. Fig. 16 shows one example of a long needle of 21 nmdiameter and 900 nm length. Fig. 17 displays part of the needle by larger magnification. Atfirst glance, a cubic structure with stacking faults was suggested. Therefore, tilt series aroundthe long axis of the needles were performed. An example of only two tilts is shown in Fig.18,i.e., 00 and 180. It turned out, however, that from the PS two typical patterns which wereperiodically repeated were obtained. The typical pattern 00 was repeated for tilts of ±360and

Cryst. Res. Technol. 35 (2000) 6-7 733

were shown to be alike. For the tilt at +180 the pattern in the PS was repeated at –180.However, for the 00 and ±360 tilts lattice planes are visible from the middle part of the rodsonwards to both sides, whereas for the ±180 main lattice planes were only visible on the left-or right-hand side, respectively. This finding, together with the observed reflections in the PScould not be explained by stacking faults in the cubic structures. We therefore tried differentstructures remembering that small spheric Cu clusters showed MTP structures.

Fig. 19 shows a model, top row, computer simulation, middle row, and corresponding PS,bottom row, of a truncated decahedral particle, or, in other words, with additional inserted(110) planes, in three different orientations. The orientations in the models from left to rightare: 5-fold axis, [001] direction and [1-10] direction, i.e., parallel to the (001) for the latterorientation. The latter two orientations are defined with respect to the first irradiateddeformed tetrahedral subunit of the decahedron. If the orientation in the [001] direction isdefined as 00 tilt then the [1-10] orientation is obtained by the 180 tilt around the 5-fold axiswhich is common for all five subunits. It is obvious from Fig.19 that tilts by 360 alwaysproduces the same images. Same applies to 180 tilts. However, for the latter tilts, negative orpositive tilts result in imaging of lattice planes on opposite sites. By comparing the PS of theexperimental images of Fig.18 with that of the model in Fig.19 it can be seen that all existingreflections are also present in the model. The reflections are created from different subunits.However, some reflections are due to multiple scattering events. A complete discussionthereof is given elsewhere, c.f. LISIECKI et al. (2000). It is concluded that the model oftruncated decahedra is in very good agreement with the experiments.

Model calculations of icosahedral structures with additional intermediate planes trying toform needles were also performed but did not bring up acceptable agreement withexperimental results. That is why such structures had to be excluded and will not bediscussed here.

4. Conclusion

Structural characterisation of differently prepared nanoparticles can be performed byHRTEM in combination with computer simulations and the evaluation of the PS. It could bedemonstrated that Cu clusters prepared by inert gas aggregation show structures deviatingfrom the bulk for small particle diameters below 5 nm resulting in multiple twinned particles.

In the case of CdS spherical particles prepared by chemical means as ligand stabilisedclusters, the structure was determined as hexagonal and cubic (Wurtzite and Sphalerite).

Recently discovered needle-like Cu clusters performed also by chemical means weresurprisingly characterised as truncated decahedra.

Acknowledgment

We thank Professor S.K. Kulkarni, University of Pune, India for the preparation of CdS clusters.

References

Alpress, J.G., Sanders, J.V.: J. Appl. Cryst. 6 (1973) 165Cowley, J.M., Moodie, A.F.: Acta Cryst. 10 (1957) 609Cowley, J.M., Iijima, S.: The direct imaging of Crystal Structures, Ed. H.R. Wenk (Springer, Berlin,

Heidelberg, New York 1976) p.123Goodman, P., Moodie, A.F.: Acta Cryst A30 (1979) 280Granqvist, C.G., Buhrman, J.: J.appl. Phys. 47 (1976) 2206Hutchison, J.L.: Lattice images, Ed. J.A. Venables (Academic, London 1976) p. 241Khosravi, A.A., Kundu, M., Kuruvilla, B.A., Shekhavat, G.S., Gupta, R.P., Sharma, A.K., Vyas, P.D.,

Kulkarni, K.S.: Appl. Phys. Lett. 67 (1995) 2506


Lisiecki, I., Filankembo, A., Sack-Kongehl, H. Weiss, K., Pileni, M.-P., Urban, J.: Phys. Rev. B 61(2000) 4968-74

Nosaka, Y., Yamagushi, Miyama, H., Hayashi, H.: Chem. Lett. (1988) 605Urban, J., Sack-Kongehl, H., Weiss, K.: Z. Phys. D 36 (1996) 73-83Urban, J., Sack-Kongehl, H., Weiss, K.: High Temparature and Materials Science 36 (1997) 155-72Vogel, W., Urban, J., Kundu, M., Kulkarni, S.K.: Langmuir 13 (1997) 827-32

Fig. 1: Cu cuboctahedron in the [110]orientation together with the PS.Top row: computer simulation,bottom row: experimantal image.

Fig. 2: Cu cuboctahedron in the [001]orientation.Top: computer simulation,bottom: experimental image.


Fig. 3: Cu icosahedron orientedalong the 5-fold axis.Top: computer simulation,bottom: experimental image.

Fig. 4: Cu icosahedron orientedalong the 3-fold axis.Top: computersimilation,bottom: experimental image.


Fig. 5: Cu icosahedron orientedalong the 2-fold axis.Top: computer simulation,bottom: experimental image.

Fig. 6: Cu decahedron orientedalong the 5-fold axis.Top: computersimulatio,bottom: experimental image.


Fig. 7: Cu2O cuprite oriented

along [001].Top: computer simulation,bottom: experimental image.









Fig. 11: CdS hexagonalWurtzite along [001].Top: computer simulation,bottom: experimental image.

Fig. 12: CdS hexagonalWurtzite along [011].Top:computer simulation.Bottom: experimental image.





Fig. 15: Computer simulations and PS of CdS,partly with stacking faults. From top to bottom:cubic, stapeling: abcabcabc, [111] orientation,stapeling: abcabcab, [111] orientation,stapeling: abcabab, [111] orientation stapelingababab, [111] orientaion, hexagonal, stapelingababab, [001] orientation.


Fig. 16: Ligand stabilised Cu needle. Fig. 17: Needle of Fig.16 in larger magnification.

Fig. 18: Two tilts of needle in Fig.16. Left: 00 tilt, right: +180 tilt.


Fig. 19: Truncated decahedron. Top row: model, middle row: computer simulation, bottom row: PS in differentorientations. From left to right: 5-fold axis, 00 tilt [001], +180 tilt [1-10].

Contact information:

Prof. Dr. J. URBAN

Fritz-Haber-Institut der Max-Planck-GesellschaftAbt. Anorganische ChemieFaradayweg 4-614195 Berlin

e-mail: [email protected]

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Structures of Clusters