Fig. 3: UO₂ and CaF₂ results.

a, b Inelastic neutron scattering results in two additional fluorite structured materials, UO₂ and CaF₂. The scattering intensity as a function of [0,0,L] and energy is shown, with integration across a large range in [H,H,0]. The highest phonon energy from the second Longitudinal Optic (LO₂) mode in both materials is shown as an orange dotted line. The scattered intensity is indicated by the color scale. c, d The intensity of the Nonlinear Propagating Mode (NPM) as a function of [0,0,L] and [H,H,0] is shown across an energy range indicated in the figure. Three reciprocal zones have a visible NPM in UO₂, with the maximum energy occurring at the same location in reciprocal space as the maximum of the first Longitudinal Optic (LO₁) mode, at odd values of L (L = 5, 7, and 9 reciprocal lattice units (r.l.u.) are visible). However, in CaF₂ the maximum energy is not the same between the NPM and the LO₁ mode, with the maximum of the LO₁ mode occurring at odd values and the NPM maximum occurring at even values of L. The most visible NPM in CaF₂ occurs at L = 8 r.l.u. as shown in d, which corresponds to a minimum of the LO₁ mode. Additional maxima are visible at L = 4 and L = 6 r.l.u.