Decahedral particle

Figures 2 (b) and (c) show a diffraction pattern obtained from a particle of diameter 1.5 nm and a diffraction pattern calculated for a multiply twinned, decahedral particle. The conclusion drawn from the study of many such observed and calculated patterns obtained from gold particles in the size range of 1.5 to 2 nm contained in a plastic film is that very few particles are multiply twinned, many have one or two twin planes but more than half are untwinned (16). This suggests that, at least for this type of specimen, there is no confirmation of the theoretical prediction that the multiply twinned form is the equilibrium state for very small particles.

The other type of decahedral particle, which is often observed, corresponds to the round pentagonal particle. An example of these... 

Figu re 3.9 (a) Typical TEM image of a multiple twinned decahedral particle (b) Preferential binding of the CTAT to the lateral 100 plane of the nanorod. Adapted with permission from Ref [79] 2005 The American Chemical... 

A special group of particles that are often produced are the icosahedral (I5) and decahedral (D5) structures shown in Fig. 9. These particles have a fivefold symetry axis which is forbidden for infinite crystals. Yang (1 0) has described these particles using a non-Fcc model. The particles are composed by five (D5) and twenty (I5) tetrahedral units in twin relationship. However the units have a non-Fcc structure. The decahedral is composed by body-centered orthorhombic units and the icosahedral by rhombohedral... 

Particles of face-centered cubic metals of diameter 5 nm of more have been studied extensively by high resolution electron microscopy, diffraction and other methods. It has been shown that such particles are usually multiply twinned, often conforming approximately the idealized models of decahedral and icosahedral particles consisting of clusters of five or twenty tetrahedrally... 

Figure 5.12. Multiply twinned particles (MTPs) (a) decahedral MTP (top) and icosahedral MTP (b) an HRTEM image of Au MTP. The decahedral MTP is at the top.

For carbon, it is of course also tempting to study clusters of clusters, namely aggregation of C60 fullerenes [67-69]. This is not really a molecular cluster application since the inner structure of the fullerene, leading to dependence of the particle interaction on relative particle orientation, is largely or completely ignored. The Pacheco-Ramalho empirical potential is used frequently, and fairly large clusters up to n=80 are studied. There appears to be agreement that small fullerene clusters are icosahedral in this model. In contrast to LJ clusters, however, the transition to decahedral clusters appears to occur as early as at n=17 the three-body term of the potential is found to be responsible for this [67]. 

Fig. 13. A representative SEM image of decahedral anatase titania particles prepared by controlled gas-phase reaction of titanium(IV) chloride and oxygen at 1473 K. Most particles expose two square (001) facets and eight trapezoidal (101) facets.

As recalled in the Introduction, clusters with anomalous external shajjes, icosahedral or decahedral, have been found frequently in deposits from fee metals. Therefore, the stability and the structure have been the main questions asked about these metallic particles. Several ideas develojjed in the preceding sections may help clarify both points. 

Figure 20. Calculated X-ray scattering patterns for various types and sizes of Pt nanocrystallites. Top left 3.5 nm (a) sphalerite (b) wurtzite (c) wurtzite with one stacking fault (d) experimental powder spectmm with ca. 3.5.nm avg. crystallites. Top right Experimental powder diffraction pattern of ca. 8.0 nm crystallites (dotted line) compared to (a) spherical and (b) prolate particles (solid line) Center (a) progression of habits of cuboctahedral shapes of nanocrystals, (b) change in shape as 111 faces increase and 100 decrease, (c) decahedron and icosahedron multiply twiimed forms. Bottom left to right three successive sizes of cuboctahedral nanociystallites three successive sizes of decahedral nanociystallites three successive sizes of icosahedral nanocrystallites. From Zanchet et al. (2000), used with permission of Wiley-VCH.

Figure 6-18. Transmission electron micrographs of decahedral silver colloid crystallites. The smaller particle a) is a perfect decahedron, the larger b) retains a residual fivefold axis but is a sevenfold twin with clear discontinuities (Reproduced by permission from ref. [71].)...

The equilibrium shape of an fee particle is the truncated octahedron with magic numbers of N = 38, 201, 585,- . In Fig. 2.20 these sizes are recognizable as the points on a drawn line. Over a wide range of sizes the decahedral clusters with varying ratios of their surface edges are found to be most stable. 

Powder X-ray di action of the gold partides dispersed on alumina support produced a very broad peak at 20 = 40.0° after subtradion of the background pattern from the alumina (see Fig. 3). Recent Debye Function Analysis (DFA) shows this pattern to be consistent with decahedra (decahedral multiply twinned particles, MTPs) of about 2.2 nm mass-mean diameter [7]. X-ray diffraction from a... 

In a similar synthesis, cetyltrimethylammonium tosylate (CTAT) has been used to produce pentagonal silver nanorods [79]. It is worthy of mention here that only those seed particles with a multiple twinned decahedral structure could grow to... 

An additional reason for the 1-D growth of the decahedral seed particles is that they are strained. The twin boundaries represent areas of high energy because the preferred angle between them is 70.5°, yet 72° is available [83]. This means that there is 7.5 ° that needs to be filled, and this may promote growth at the unpassivated ends in order to reduce the overall surface energy of the crystal. 

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