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The localization length r_{loc} associated with a fast secondary relaxation in glassy Laponite is determined by X-ray photon correlation spectroscopy (XPCS) through a Debye-Waller fit of the non-ergodicity parameter. Quantitative differences are observed between the time dependence (aging) of r_{loc} in spontaneously aged and rejuvenated samples. This behavior is also reflected in the calculated shear modulus which matches well with data obtained by rheological measurements.

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