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Register a new userModeling of disordered materials: radial distribution function vs. vibrational spectra as a protocol for validation
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F. Gaspari
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As molecular dynamics is increasingly used to characterize non-crystalline materials, it is crucial to verify that the numerical model is accurate enough, consistent with experimental data and can be used to extract various characteristics of disordered systems. In most cases the only derived property used to test the realism of the models has been the radial distribution function. We report extensive ab-initio simulation of hydrogenated amorphous silicon that demonstrates that although agreement with the RDF is a necessary requirement, this protocol is insufficient for the validation of a model. We prove that the derivation of vibrational spectra is a more efficient and valid protocol to ensure the reproducibility of macroscopic experimental features.
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We study a recently introduced and exactly solvable mean-field model for the density of vibrational states $mathcal{D}(omega)$ of a structurally disordered system. The model is formulated as a collection of disordered anharmonic oscillators, with random stiffness $kappa$ drawn from a distribution $p(kappa)$, subjected to a constant field $h$ and interacting bilinearly with a coupling of strength $J$. We investigate the vibrational properties of its ground state at zero temperature. When $p(kappa)$ is gapped, the emergent $mathcal{D}(omega)$ is also gapped, for small $J$. Upon increasing $J$, the gap vanishes on a critical line in the $(h,J)$ phase diagram, whereupon replica symmetry is broken. At small $h$, the form of this pseudogap is quadratic, $mathcal{D}(omega)simomega^2$, and its modes are delocalized, as expected from previously investigated mean-field spin glass models. However, we determine that for large enough $h$, a quartic pseudogap $mathcal{D}(omega)simomega^4$, populated by localized modes, emerges, the two regimes being separated by a special point on the critical line. We thus uncover that mean-field disordered systems can generically display both a quadratic-delocalized and a quartic-localized spectrum at the glass transition.
We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an exponentially decaying density of states. The instanton solutions describe excitations, which become localized due to the disorder-induced fluctuations, which lower the sound velocity in a finite region compared to its average value. The exponentially decaying density of states (known in electronic systems as the Lifshitz tail) is governed by the statistics of a fluctuating-elasticity landscape, capable of trapping the vibrational excitations.
Landaus theory of phase transitions is adapted to treat independently relaxing regions in complex systems using nanothermodynamics. The order parameter we use governs the thermal fluctuations, not a specific static structure. We find that the entropy term dominates the thermal behavior, as is reasonable for disordered systems. Consequently, the thermal equilibrium occurs at the internal-energy maximum, so that the minima in a potential-energy landscape have negligible influence on the dynamics. Instead the dynamics involves normal thermal fluctuations about the free-energy minimum, with a time scale that is governed by the internal-energy maximum. The temperature dependence of the fluctuations yields VTF-like relaxation rates and approximate time-temperature superposition, consistent with the WLF procedure for analyzing the dynamics of complex fluids; while the size dependence of the fluctuations provides an explanation for the distribution of relaxation times and heterogeneity that are found in glass-forming liquids, thus providing a unified picture for several features in the dynamics of disordered materials.
Improving the efficiency and accuracy of energy calculations has been of significant and continued interest in the area of materials informatics, a field that applies machine learning techniques to computational materials data. Here, we present a heuristic quantum-classical algorithm to efficiently model and predict the energies of substitutionally disordered binary crystalline materials. Specifically, a quantum circuit that scales linearly in the number of lattice sites is designed and trained to predict the energies of quantum chemical simulations in an exponentially-scaling feature space. This circuit is trained by classical supervised-learning using data obtained from classically-computed quantum chemical simulations. As a part of the training process, we introduce a sub-routine that is able to detect and rectify anomalies in the input data. The algorithm is demonstrated on the complex layer-structured of Li-cobaltate system, a widely-used Li-ion battery cathode material component. Our results shows that the proposed quantum circuit model presents a suitable choice for modelling the energies obtained from such quantum mechanical systems. Furthermore, analysis of the anomalous data provides important insights into the thermodynamic properties of the systems studied.
Using molecular dynamics simulations we investigate the dependence of the structural and vibrational properties of the surfaces of sodo-silicate glasses on the sodium content as well as the nature of the surface. Two types of glass surfaces are considered: A melt-formed surface (MS) in which a liquid with a free surface has been cooled down into the glass phase and a fracture surface (FS) obtained by tensile loading of a glass sample. We find that the MS is more abundant in Na and non-bridging oxygen atoms than the FS and the bulk glass, whereas the FS has higher concentration of structural defects such as two-membered rings and under-coordinated Si than the MS. We associate these structural differences to the production histories of the glasses and the mobility of the Na ions. It is also found that for Na-poor systems the fluctuations in composition and local atomic charge density decay with a power-law as a function of distance from the surface while Na-rich systems show an exponential decay with a typical decay length of $approx2.3$~AA. The vibrational density of states shows that the presence of the surfaces leads to a decrease of the characteristic frequencies in the system. The two-membered rings give rise to a pronounce band at $approx880$~cm$^{-1}$ which is in good agreement experimental observations.
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