Introduction to Nanotechnology

3.2. STRUCTURE 45
various masses at the detector. The charge q of the nanosized ion is ordinarily
known, so in practice it is the mass m that is determined. Generally the material
forming the nanoparticle is known, so its density p = m/ V is also a known quantity,
and its size or linear dimension d can be estimated or evaluated as the cube root of
the volume: d = (V)1'3 = (m/p)'I3.
The mass spectrometer that has been described made use of the typical magnetic
field mass analyzer. Modern mass spectrometers generally employ other types of
mass analyzers, such as the quadrupole model, or the time-of-flight type in which
each ion acquires the same kinetic energy ;mu2 during its acceleration out of the
ionization chamber, so the lighter mass ions move faster and arrive at the detector
before the heavier ions, thereby providing a separation by mass.
Figure 3.9 gives an example of a time-of-flight mass spectrum obtained from soot
produced by laser vaporization of a lanthanum-carbon target. The upper mass
spectrum (a) of the figure, taken from the initial crude extract of the soot, shows lines
from several fidlerene molecules: c60, C,,, c76, C,,, cg2, C,,, and Lac,,. The latter
corresponds to an endohedral fidlerene, namely, C,, with a lanthanum atom inside
the hllerene cage. The second (b) and third (c) mass spectra were obtained by
successively separating Lac,, from the other fdlerenes using a technique called
high-performance liquid chromatography.
3.2.4. Surface Structure
To obtain crystallographic information about the surface layers of a material a
technique called low-energy electron diffraction (LEED) can be employed because at
low energies (10-100 eV) the electrons penetrate only very short distances into the
surface, so their diffraction pattern reflects the atomic spacings in the surface layer. If
the diffraction pattern arises from more than one surface layer, the contribution of
lower-lying crystallographic planes will be weaker in intensity. The electron beam
behaves like a wave and reflects from crystallographic planes in analogy with an
X-ray beam, and its wavelength I, called the de Broglie Wavelength, depends on the
energy E expressed in the units of electron volts through the expression
which differs from Eq. (3.1) for X rays. Thus an electron energy of 25.2 eV gives a
de Broglie wavelength I equal to the Ga-As bond distance in gallium arsenide
(3'I2a/4 = 0.2442 nm), where the lattice constant a = 0.565 nm, so we see that low
energies are adequate for crystallographic electron diffraction measurements. An-
other technique for determining surface layer lattice constants is reflection high-
energy electron diffraction (WEED) carried out at grazing incidence angles where
the surface penetration is minimal. When 8 is small in the Bragg expression (3.2),
then I must be small, so the energy E of Eq. (3.6) must be large, hence the need for
higher energies for applying MEED diffraction at grazing incidence.