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The awarded funds have supported our efforts to develop a self-consistent description of structural and electronic anomalies in several classes of amorphous materials of potential use in energy storage and conversion, including vitreous semiconductors with optical gaps in the visible range and glassy ionic melts.  The outstanding questions include the origin and transport of charge carriers in vitreous semiconductors, and the molecular mechanism of conductance in ionic melts.  Owing to the exceedingly long relaxation times in these systems and relatively large correlation lengths, there are presently no reliable ab initio methods to quantitatively assess the characteristics of the listed materials that are key for their successful application, including: accurate atomic positions and the dynamics in the activated transport regime, the electronic structure, optical transition frequencies, and charge trapping.  We have achieved significant progress in elucidating several aspects of these long-standing problems, as described below:

1) We have discovered that semiconducting quenched liquids and frozen glasses exhibit a set of peculiar electronic states of topological origin.  These states reside at transient strained regions arising during structural reconfigurations between distinct aperiodic states intrinsic to quenched melts.  The strained regions are domain walls separating the distinct aperiodic states; their number is about 10²⁰ cm^-3 in all glassformers owing to the universal dynamics of deeply supercooled melts.  Even though located near the middle of the forbidden gap, the topological states are rather extended in one direction while being centered at under- and over-coordinated atoms.  The states are predominantly filled and serve as a non-paramagnetic source of charge carriers that might alone account for the observed magnitude of DC-conductivity and a number of irradiation-induced phenomena in amorphous semiconductors, including: ESR signal, midgap absorption, distinct types of photoluminescence, and the fatigue of photoluminescence.  The proposed mechanism provides a novel method to estimate several key optical-transition frequencies.  In our subsequent work, we have established the specific atomic motifs that are responsible for the mass transport and the topological states in a very important class of amorphous semiconductors, namely is chalcogen and pnictogen containing alloys, which are the leading contender for the next generation computer memory.  Interesting connections with classic statistical models have been uncovered that provide a potential route for first-principles estimates of the structure and electronic spectrum of these compounds.  In addition, the predicted presence of an electronic, nearly T-independent contribution to the domain surface tension may account for the apparent disagreement between the kinetic and thermodynamic fragility in chalcogenides.

2) We have formulated a novel approach to liquid activated dynamics, in which the activated transitions between the numerous alternative aperiodic configurations are mapped onto the dynamics of a long range classical Heisenberg model with 6-component spins and anisotropic couplings.  The spin length is an order parameter for the glass-to-crystal transition.  The spin model exhibits a continuous range of behaviors between two limits corresponding to frozen-in shear and uniform compression/dilation.  The two regimes correspond to strong and fragile liquid behavior respectively; they are separated by a continuous transition controlled by the anisotropy in the spin-spin interaction, which is directly related to the Poisson ratio of the material.  The latter ratio and the ultra-violet cutoff of the theory determine the liquid configurational entropy.  The liquid-to-spin mapping provides a microscopic framework for computing the configurational entropy and relaxational spectrum of specific substances and provides a potential route to obtaining glass structures corresponding to realistic quenching rates.

3) We have computed, on a molecular basis, the viscosity of a deeply supercooled liquid at high shear rates.  The viscosity is shown to decrease at growing shear rates, owing to an increase in the structural relaxation rate as caused by the shear.  We have explained why the onset of this non-Newtonian behavior occur universally at a shear rate significantly lower than the typical structural relaxation rate, by about two orders of magnitude.  This results from a large size - up to several hundred atoms - of the cooperative rearrangements responsible for mass transport in supercooled liquids and the smallness of individual molecular displacements during the cooperative rearrangements.  We predict that the liquid will break down at shear rates such that the viscosity drops by about a factor of 30 below its Newtonian value.  These phenomena are predicted to be independent of the liquid's fragility.  In contrast, the degree of non-exponentiality and violation of the Stokes-Einstein law, which are more prominent in fragile substances, will be suppressed by shear.

The ACS Petroleum Research Fund G grant has been instrumental in advancing the PI's career, both as a source of support of graduate students and the first indication of national recognition of the PI's independent research.  The outcomes of the research have served, among other things, as preliminary results for a number of extensive research proposals to federal and private foundations and led to the PI's being awarded by the Beckman Young Investigator Award by Arnold and Mabel Beckman Foundation and, recently, the NSF CAREER Award.  Two graduate students were partially supported by the grant.  One of them, Mr. Dmytro Bevzenko, is expected to receive a Ph. D. in Chemical Physics based on the research support by PRF.