Properties of nanostructure [79-82]

All materials are composed of proper chemical bonds with atoms, including metallic bond, ionic bond, covalent bond, Van der waal’s bond and hydrogen bond.

The bonding length is the distance between two atoms as the net interaction force is zero. And the curve integrated by the net interaction force to the atom interval can obtain the lowest potential at this length of bonding. These bonding properties not only correspond to the mechanical properties of the materials but also the thermal properties. Solid status material is not just the agglomeration of atoms; the energy levels of each electron form the bonding orbits and anti-bonding orbits, and the number of orbit increases with the number of chemical bonding. As the number of orbit increases, the difference between the energy levels decreases and results in the continuous energy states. The distribution and value of the solid state energy level are highly related to the species and number of the bonding atoms, and influence the physics or chemical properties such as electric property, optical property, magnetic property and photoelectric properties. Nanostructure is the one-dimensional material with volume lies in 1 to 100 nm, including nanoparticles and quantum dots. In these nanomaterials, the number and distribution of the atoms change rapidly with the decrease in material size. Thus the bonding properties and the energy level properties is quite different from the bluk matrials. There are four effects such as surface effect,

small size effect, quantum size effect and quantum confinement effect listed below.

1.2.4.1 Surface effect

With the scale becomes small, the number of atoms on the particle surface increases. Because of these surface atoms are not completely coordinated, it is unstable and possesses high surface potential, thus, it possesses high chemical activity and easily bonds with other atoms. The activity effect of surface atoms is the major factor to produce the activity of the inert-noble metal catalyst. The number of near atoms on the particle surface is smaller than that inside the particle. With large ratio of the surface area, it will result in the reduction of the bonding length and the variation of the lattice arrangement. Because of the reduction in bonding length, the Curie temperature（Tc）therefore decreases with the smaller particle size. Besides, in tiny metal particles, because the surface energy increases due to the particle shrinkage, the necessary heat to diffuse atoms is much smaller than the bulk materials. It is the reason why that the melting point of the metal nanoparticles decreases so fast.

1.2.4.2 Small size effect

In order to prevent the motion of dislocations, the decrease in particle size is applied. This method is applied to increase the mechanical intensity of the polycrystal.

In many materials, the σy (or hardness H) increases with the particle size decreased and can be expressed by the Hall-Pectch equation：

σy = σo + Kd^-1/2 (1-8) H = Ho + Kd^-1/2 (1-9) Where, σ0, H0 and K are the constants and d is the average particle diameter. In general, the value of K is positive, and σy or H is linearly proportional to the value of d^-1/2. In the nanocrystals, however, the scale is close to the intervals of the near dislocations, so the relation of the hardness and the particle size can not be explained by the above formula. It has the complex relations of positive K value, negative K value and mixed positive-negative K value. Due to the grain boundaries with great volume ratio in the nanocrystal, the plasticity, strike toughness and break toughness are improved. The high mechanical intensity and the super plasticity precise-ceramics could be obtained by controlling the crystal size at the critical range.

1.2.4.3 Quantum size effect

In the theorem of energy band, the energy levels of metal near the Fermi energy level is a continuous distribution. As the particle size decreases, it becomes to the discrete energy level. Furthermore, the Kubo theorem describes the relation between the interval of electron energy level δ and the diameter (d) of the metal nanoparticle:

³ Where, N is the total number of the conduction electrons, EF is the Fermi level. It could see that the decrease in the particle diameter increases the energy of band gap.

This quantum size effect results in the broadening of the energy band gap in the nanoscale semiconductors and the discontinuous energy level of the valence band and the conduction band. With a decrease in the size of the nanoscale semiconductor particle, the blue shift in the absorption spectrum is observed due to the enlargement of the energy band gap. The emission wavelength resulted from the energy band gap in the nanoscale semiconductor shifts to the short wavelength because of the broadening in the energy gap. In other word, the different emission color can be obtained by controlling size of the particles.

1.2.4.4 Quantum confinement effect

According to the Heisenberg uncertainty principle, the actual position and the momentum of an electron or a photon can not be obtained at the same time. If the electron is restricted in a small nanoscale space, the momentum range is wide. And if the momentum range is wide, average energy of the electrons is high. Thus on the boundaries of this range, there exists the phenomenon of quantization jumping, as shown in Figure 1-25. If the particle radius (r) of the nanoscale semiconductor is

smaller than the Bohr radius (aB) of the exciton, the average mean free path of electron is restricted in a small space, then the electron and hole are easy to be combined to a excition. The absorption energy band of the excition resulted from the overlapping of the electron and hole’s wave functions not only has strong excitionic energy-band-gap absorption coefficient but also has great light emission phenomenon as being excited by light.