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4 Fullerenes and the Wave-Particle Duality

4 Fullerenes and the Wave-Particle Duality

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Fig. 5.55 (a) Two-slit diffractometer setup for demonstrating the wave-particle duality. A beam

of particles passes through a double slit in the form of a wave and produces an interference pattern.

The experiments on C60 (b) demonstrate this effect. The molecule may absorb or emit radiation

when passing through the apparatus (dotted wave). Provided the wavelength of this radiation is

much larger than the distance of the slits, the interference pattern is unaffected, i.e., decoherence

is negligible [5.211]. (b) Far-field diffraction of C60 using velocity selection with a mean velocity

v¯ = 117 m/s and a width v/v ∼ 17%. The circles are the experimental data and the line represents

a Kirchhoff–Fresnel diffraction model. The van der Waals interaction between the molecule and

the grating is taken into account by a reduced slit width [5.205]. (Reprinted with permission from

[5.211] (a) and [5.205] (b). © 1999 Nature Publishing Group (a) and © 2003 American Association

of Physics Teachers (b))



5.5



Summary



261



Fig. 5.56 Upper panels: 3D structures of tetraphenylporphyrin (TPP) C44 H30 N4 (m = 614 amu;

left) and the fluorofullerene C60 F48 (m = 1,632 amu; right). Lower panels: (a) De Broglie near-field

interference fringes of TPP using a Talbot–Lau interferometer. (b) Quantum interference fringes of

C60 F48 in a Talbot–Lau interferometer. (Reprinted with permission from [5.212]. © 2003 American

Physical Society)



It was found that the decay of quantum coherence (see Sect. 7.2) and interference

happened at precisely the rate predicted by theory (see [5.203].



5.5 Summary

Three types of carbon nanostructures have been synthesized: carbon nanotubes,

monatomic layers of carbon atoms (graphene), and fullerenes. Carbon nanotubes

are because of their high mechanical strength and their high thermal and electronic conductivities of particular interest for application. In addition, they can

be used as tips for scanning probe microscopy in deep trenches or with chemical sensitivity. Starting from carbon nanotubes, more complex nanostructures (pea

pods, etc.) can be fabricated. A great many of nanotubes of other materials have

been synthesized. In graphene, the electrons exhibit the behavior of massless Dirac

fermions and quantum Hall effect. Graphene nanostripes are semiconducting with

high-quality transistor action even at room temperature. Fullerene molecules with

the most prominent C60 structure and many other cage-like carbon molecules

can be doped and form a variety of carbon compounds. Fullerene-like structures



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have also been formed from other materials. Fullerenes have been used for probing the quantum mechanical wave-particle duality up to particles masses of ca.

1,600 amu.



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Chapter 6



Nanocrystalline Materials



The design of nanocrystalline solids with novel properties different from the

chemically identical coarse-grained counterparts was an early and most fruitful contribution to nanoscience [6.1, 6.2]. Nanocrystalline materials are polycrystals with

a crystallite size usually in the 10-nm range and atomically disordered crystallite

interfaces with a substantial volume fraction. The macroscopic properties are, therefore, dominated by the small crystallite size, giving rise to confinement effects, and

the interfacial structure. Crystallites and interfaces may be of the same or of different chemical composition, composites of different materials may be fabricated,

dimensionality may play a role, and a plethora of synthesis routes is available (see

Chap. 3). The wide field is covered by early reviews [6.3–6.6], monographs [6.7,

6.8], and an encyclopedia (see [6.9]). In this chapter, recent developments in the

field of nanocrystalline solids will be reviewed, including aspects such as atomic

simulation, structure of interfaces, plasticity, strength, superplasticity, fatigue, composites, ceramics, diffusion, and surface-induced manipulation of the properties of

nanomaterials.



6.1 Molecular Dynamics Simulation of the Structure

of Grain Boundaries and of the Plastic Deformation

of Nanocrystalline Materials

Among the various atomic-level simulation approaches, molecular dynamics (MD)

has proven particularly useful for studying nanocrystalline solids [6.10–6.13]. In

deformation studies by MD, rather large plastic strains can be considered, enabling

the deformation under very high grain boundary and dislocation densities. However,

in addition to being limited to relatively small model systems consisting of typically

millions of atoms, the fundamental limitations inherent to the MD approach are well

known, pertaining mainly to the reliability of the interatomic potentials used and the

relatively short time period (of typically 10 ns) over which the dynamics of the system can be probed. This leads to extremely high strain rates exceeding 107 s−1 ,

much higher than in experiments, requiring rather high stresses. While the empirical interatomic forces used in most MD simulations are computationally highly

H.-E. Schaefer, Nanoscience, DOI 10.1007/978-3-642-10559-3_6,

C Springer-Verlag Berlin Heidelberg 2010



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efficient, they are unable to fully capture the many body nature of electronic bonding. Interestingly, however, a comparison between many body and pair potentials

used in simulations of grain boundaries (see [6.11]) revealed only few qualitative

differences, suggesting that many body effects may not dominate, e.g., the grain

boundary (GB) behavior. The dynamic properties of defects (e.g., dislocations, grain

boundaries, and precipitates) which dictate the mechanical properties of materials

should be computed directly using quantum mechanics-based total-energy methods.

However, the number of atoms necessary to do so exceeds available computational

resources and will for years to come (see [6.14]). The challenge, therefore, is to

identify the real physical processes (see [6.11]), so that the information extracted

from simulations focuses on a careful classification of the atomic processes occurring, e.g., during plastic deformation (see [6.12]), taking into account the interplay

between GB structure and deformation mechanisms, as discussed in the following

sections.



6.2 Grain Boundary Structure

Coarse-grained polycrystals contain GBs with very much differing structures and

with a wide spectrum of energies and properties (see [6.11, 6.15]). Special highangle GBs contain no dislocations and their properties are perfect-crystal like

(Fig. 6.1a) with low energies, low atomic diffusivities, and low mobilities but

with high sliding resistance and cohesion. Grain boundaries of this type, i.e., twin

boundaries, play a role in the process of deformation twinning (see [6.11]). In lowangle or dislocation boundaries the atomic structure consists of periodic arrays

of dislocations and their properties are characterized by isolated lattice dislocations and their interactions. In the general high-angle GB, dislocation cores are

completely overlapping yielding a GB structural atomic disorder similar to an amorphous material, which is characterized by the local radial distribution function, g(r)

(Fig. 6.1b).

According to MD simulations [6.11], the structure of GBs in nanocrystalline Pd

(Fig. 6.1c) is fully disordered and virtually identical to that of high-angle (110)

twist boundaries (Fig. 6.1b), i.e., to the universal structure of the high-energy GBs

in coarse-grained Pd. These simulations for nanocrystalline Si and Pd [6.11] show

that the randomly oriented grains are connected by a glassy intergranular “phase”.

These observations are consistent with simulations of the phonon density of states

and of the related free energy [6.16] which indicate that below a critical grain size

(1.5–3 nm) nanocrystalline microstructures are thermodynamically unstable with

respect to the amorphous phase.

Temperature-dependent structural and dynamical transitions in thermal equilibrium are additionally predicted by MD simulations in highly disordered high-energy

GBs in Si and Pd bicrystals (see [6.11]) at a critical temperature Tc below the

melting temperature Tm (Fig. 6.1d). At T>Tc the splitting of the second g(r) peak

observed at low temperatures (Fig. 6.1c) has disappeared. This transition has a

profound influence on the high-temperature GB properties, such as GB migration,



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