We prove that solutions to the quintic semilinear wave equation with variable coefficients in ${{\mathbb {R}}}^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to \infty$, but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the $L^{6}$ norm of the solution as $t\to \infty$.

Secondary fluorescence (SF), typically a minor error in routine electron probe microanalysis (EPMA), may not be negligible when performing high precision trace element analyses in multiphase samples. Other factors, notably wavelength dispersive spectrometer defocusing, may introduce analytical artifacts. To explore these issues, we measured EPMA transects across two material couples chosen for their high fluorescence yield. We measured transects away from the fluorescent phase, and at various orientations with respect to the spectrometer focal line. Compared to calculations using both the Monte Carlo simulation code PENEPMA and the semi-analytical model FANAL, both codes estimate the magnitude of SF, but accurate correction requires knowledge of the position of the spectrometer with respect to the couple interface. Positioned over the fluorescent phase or otherwise results in a factor of 1.2–1.8 of apparent change in SF yield. SF and spectrometer defocusing may introduce systematic errors into trace element analyses, both may be adequately accounted for by modeling. Of the two, however, SF is the dominant error, resulting in 0.1 wt% Zn apparently present in Al at 100 μm away from the Zn boundary in an Al/Zn couple. Of this, around 200 ppm Zn can be attributed to spectrometer defocusing.