It is shown that the normalized rms fluctuation of the shear modulus on the medium-range order scale in glasses correlates with fragility: the higher fragility, the smaller the fluctuation amplitude. The latter is calculated within the heterogeneous elasticity theory using the data on the boson peak in glasses. On a smaller scale corresponding to cooperative structural relaxation, the normalized rms fluctuation of the infinite-frequency shear modulus was estimated using the data on the decoupling of viscosity and diffusion in supercooled liquids. These fluctuations are much smaller in amplitude, and, in contrast, they increase with increasing fragility. Extrapolation predicts intersection of both rms fluctuations and disappearing of the boson peak at the upper limit to fragility ≈180.
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