Tracking microscopic irreversibility during yielding of a colloidal fractal gel with Rheo-Echo-XPCS

Understanding how microscopic structural dynamics relate to macroscopic mechanical response during yielding remains a central challenge in soft matter physics. Here, we introduce rheo-echo X-ray photon correlation spectroscopy (rheo-echo-XPCS) with nonlinear acquisition synchronized to oscillatory shear, enabling direct measurement of irreversible nanoscale dynamics under strain amplitude control. Applying this to a carbon black colloidal fractal gel, we resolve time-periodic echoes in the vorticity-direction intensity autocorrelation function whose decay encodes non-affine structural rearrangements. We find: (i)~ballistic-like decorrelation with $\tau \propto q^{-1}$ at all strains, where the decorrelation velocity $v_\tau = 1/\langle q\tau \rangle$ scales linearly with the loss tangent $\tan\delta = G''/G'$, establishing $\tan\delta$ as a direct macroscopic signature of the rate of irreversible structural decorrelation; (ii)~functional form continuous evolution from compressed exponential ($\alpha \simeq 1.5$) at low strain, consistent with three-dimensional dipolar strain fields in the intact network-to stretched exponential ($\alpha \simeq 0.5$) at high strain, reflecting a dimensional reduction from $d_f = 3$ to $d_f = 1$ as stress transmission shifts from bulk to quasi-one-dimensional filamentary backbones during network fragmentation.