  The magnetic, electronic, and optical properties of rare earth-oxides are
directly influenced by the valency of the metallic cation. With the development
of next generation electron energy-loss spectrometers, high-energy lanthanide
fine structure can be studied with improved signal-to-noise for quantitative
analysis. Unfortunately, the behavior of rare-earth $4f$ orbital electrons is
not well understood. To establish best practices for analysis of energy-loss
spectra from lanthanide oxides, we have performed a comparative study of the
four traditional white line analysis methods extended to lanthanide $M_{4,5}$
edges resulting from $3d \rightarrow 4f$ orbital transitions using data from
Gatan's EELS Atlas. The ${M_4}/{M_5}$ spectral feature ratios were examined as
a function of $4f$ occupancy. The ${M_4}/{M_5}$ spectral feature ratio
decreases exponentially as $4f$ occupancy increases, except for a plateau
between S$\text{m}^{3+}$ and D$\text{y}^{3+}$. The full-width at half the
maximum intensity of the $M_4$ edges shows increased broadening for
S$\text{m}^{3+}$ through D$\text{y}^{3+}$. We suggest that the plateau results
from $4f$ orbital half-filling and is explained through the relationship
between electron transition probability and transition lifetime as expressed
through Fermi's Golden Rule. Of the four spectral analysis methods described,
only the integrated area method can be ascribed a quantitative physical
interpretation.
