Figure 3.

Schematics of the relationship between I_incoh(Q, t) and S_incoh(Q, $\omega$). In (a), curve a-I shows the expected behavior of I_incoh(Q, t) for a static particle where no exchange of energy occurs between the incoming neutrons and the sample. As shown in a-II, after a time-Fourier transformation of I_incoh(Q, t), one obtains a δ-function-shaped S_incoh(Q, $\omega$), which broadens when convoluted with the experimental resolution (see a-III). In (b), the particles under analysis perform motions upon, for example, heating and I_incoh(Q, t) gradually decays (b-II) and S_incoh(Q, $\omega$) becomes broader (b-II). In (c), an unconstrained diffusive motion is depicted, which leads to a gradual decay of I_incoh(Q,t) over Q (c-I) reaching the limit of I_incoh(Q, $\infty$) = 0, and S_incoh(Q, ω) broadens as a function of Q (c-II). In (d), the motions of particles within a constrained geometry are depicted and I_incoh(Q, t) plateaus at a finite value at $t\to \infty$.