CHAPTER 1. FLUORESCENT SILICON CLUSTERS 21 CaF$_{2}$ substrates and transferred to ambient air (Ehbrecht et al., 1997). Owing to a continuous supersonic beam and a pulsed CO$_{2}$ laser, the part of the beam containing clusters was also pulsed. A velocity selector was employed to select velocity segments of the cluster pulse, and the cluster mass was measured by time-of-flight mass spectrometry (Ledoux et al., 2002). The average number of atoms in the clusters, N , was found to vary from N = 395, corresponding to an average diameter, D , of 2.47 nm to N = 9070, corresponding to D = 7.03 nm. The diameters were deduced using a spherical particle model, where V$_{unit}$ = 0.1601 nm 3 is the volume of the unit cell of bulk crystalline silicon. Equation 1.3 takes into account the fact that the unit cell has a diamond cubic structure and contains eight atoms. It is assumed that bulk and nanoparticle densities are the same. These samples were photoexcited at 488 nm using continuous laser radiation, and the resultant fluorescence spectrum was measured. Each sample showed an almost symmetric fluorescent band whose peak wavelength decreased with particle diameter. The size-dependent fluorescence wavelength shifts agreed with the results one might anticipate from quantum confinement. Deviations were attributed to partial oxidation of the surface layer, which could also be seen in high resolution transmission electron microscopy (HRTEM) images (Laguna et al., 1999). The oxide shell thickness could be correlated linearly to the cluster diameter. The smallest clusters of 6 nm in diameter had an oxide shell with a thickness of 0.81 nm, whilst the largest particles had a diameter of 34 nm had a 3 nm thick oxide shell (Hofmeister et al., 1999). The HRTEM images showed that the nanoparticles had a crystalline core. A number of different silicon lattice planes were identified from diffraction rings. D ( N ) = $^{(}$3 N 4 π V$_{unit}$$^{)}$$^{1}$$^{/}$$^{3}$ (1.3)