Localization, Disorder, and Entropy in a Coarse-Grained Model of the Amorphous Solid

Abstract

We study the role of disorder in producing the metastable states in which the extent of mass localization is intermediate between that of a liquid and a crystal with long-range order. We estimate the corresponding entropy with the coarse-grained description of a many-particle system used in the classical density functional model. We demonstrate that intermediate localization of the particles results in a change of the entropy from what is obtained from a microscopic approach using for sharply localized vibrational modes following a Debye distribution. An additional contribution is included in the density of vibrational states g(ω) to account for this excess entropy. A corresponding peak in g(ω)/ω2 vs. frequency ω matches the characteristic boson peak seen in amorphous solids. In the present work, we also compare the shear modulus for the inhomogeneous solid having localized density profiles with the corresponding elastic response for the uniform liquid in the limit of high frequencies.

Replica Field Theory for a Generalized Franz–Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation

“…Static approaches, other than dynamical ones such as the MCT, are relevant to investigate the FEL or the configurational entropy [ 17 , 18 , 19 , 20 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 ]. These include replica theory [ 17 , 18 , 19 , 20 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ], density functional theory (DFT) [ 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , …”

“…The static theories commonly focus on local minima of free-energy functionals without considering fluctuations due to the mean-field approximation. On the one hand, the DFT determines the metastable state by exploring a local minimum of the free-energy density functional [ 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 ]. Given the inhomogeneous density distribution as overlapping Gaussians centered around a random lattice, previous studies have confirmed that Gaussian distribution with a large spread creates the optimum density profile.…”

“…Static approaches, other than dynamical ones such as the MCT, are relevant to investigate the FEL or the configurational entropy [17][18][19][20]. These include replica theory [17][18][19][20][29][30][31][32][33][34][35][36][37][38], density functional theory (DFT) [39][40][41][42][43][44][45][46][47][48][49][50][51][52], and a combination of the replica theory and DFT [53][54][55][56][57]. The static theories commonly focus on local minima of free-energy functionals without considering fluctuations due to the mean-field approximation.…”