Appendix C
Plasmon Energies and Inelastic Mean Free Paths
The following table lists the atomic number Z, atomic weight A, and density ρ
of some common elements and compounds, together with their chemical symbol
and crystal structure, using the notation: a = amorphous, b = body-centered cubic,
c = cubic, f = face-centered cubic, h = hexagonal, l = liquid, o = orthorhombic,
r = rhombohedral, t = tetragonal.
The measured “plasmon” energy E
p
(generally the maximum of the main energy-
loss peak below 40 eV) and its full width at half-maximum E
p
are mostly taken
from Daniels et al. (1970), Colliex et al. (1976a), Raether (1980), Colliex (1984),
and Ahn (2004). The quantity λ
fe
is a plasmon mean free path calculated from the
free electron formula, Eq. (3.58), assuming E
p
= 0 but based on the tabulated
value of E
p
, with m = m
0
and β = β
∗
as specified below.
The last two columns give inelastic mean free paths measured by Iakoubovskii
et al. (2008b) for energy losses up to 150 eV, using 200-keV incident electrons, a
probe convergence semiangle of α = 20 mrad, and collection semiangle β = 20
mrad, giving an effective collection angle β
∗
of typically 12 mrad, according to
Eq. (4.73). The plasmon mean free path λ
p
represents just the collective valence-
electron component of inelastic scattering. Differences between λ
p
and λ
i
reflect
single-electron excitation, for example, an inner-shell ionization edge occurring
below 150 eV.
The total inelastic mean free path λ
i
is the appropriate quantity to use in Eq. (5.1)
for thickness measurement. At E
0
= 100 keV, values of λ
i
are about a factor of 1.45
lower than at 200 keV; see Section 5.1, Table 5.2.
419
R.F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope,
DOI 10.1007/978-1-4419-9583-4_8,
C
Springer Science+Business Media, LLC 2011