Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEnergy Gap and the Ideal Glass as a Defective Crystal: A Lattice Model of Monatomic Systems
93
0
0.0
(
0
)
Authors
P. D. Gujrati
Ask ChatGPT about the research
No Arabic abstract
We use the cell model to justify the use of a lattice model to study the ideal glass transition. Based on empirical evidence and several previous exact calculations, we hypothesize that there exists an energy gap between the lowest possible energy of a glass (the ideal glass IG) and the crystal (CR). The gap is due to the presence of strongly correlated excitations with respect to the ideal CR; thus, one can treat IG as a highly defective crystal. We argue that an excitation in IG requires energy that increases logarithmically with the size of the system; as a consequence, we prove that IG must emerge at a positive temperature T_{K}. We propose an antiferromagnetic Ising model on a lattice to model liquid-crystal transition in a simple fluid or a binary mixture, which is then solved exactly on a recursive (Husimi) lattice to investigate the ideal glass transition, the nature of defects in the supercooled liquid and CR analytically, and the effects of competing interactions on the glass transition. The calculation establishes the gap. The lattice entropy of the supercooled liquid vanishes at a positive temperature T_{K}>0, where IG emerges but where CR has a positive entropy. The macrostate IG is in a particular and unique disordered microstate at T_{K}, just as the ideal CR is in a perfectly ordered microstate at absolute zero. This explains why it is possible for CR to have a higher entropy at T_{K} than IG. The demonstration here of an entropy crisis in monatomic systems along with previously known results strongly suggests that the entropy crisis first noted by Kauzmann and demonstrated by Gibbs and DiMarzio in long polymers appears to be ubiquitous in all supercooled liquids.
rate research
Read More
A range of ferroic glasses, magnetic, polar, relaxor and strain glasses, are considered together from the perspective of spin glasses. Simple mathematical modelling is shown to provide a possible conceptual unification to back similarities of experimental observations, without considering all possible complexities and alternatives.
The local coordination numbers of As$_2$Se$_3$ glass were determined by a combination of anomalous x-ray scattering experiments, reverse Monte Carlo calculations, and {it ab initio} molecular dynamics simulations. The well-known `8-$N$ bonding rule proposed by Mott breaks down around the As atoms, exceeding the rule by 7--26%. An experimental prediction based on mean-field theory agrees with the present experimental and theoretical results. The fourfold coordinated As atoms likely form As-As wrong bond chains rather than ethan-like configurations, which is identified as the origin for the breakdown of the `8-$N$ bonding rule.
A comparative study between PbTiO$_3$, PbZrO$_3$, and the solid solution PbZr$_{0.5}$Ti$_{0.5}$O$_3$ is performed on the soft mode lattice dynamics within the first Brillouin Zone. We consider the six unique B-site orderings for PbZr$_{0.5}$Ti$_{0.5}$O$_3$ representable within the 2$times$2$times$2 primitive perovskite supercell as well as the virtual crystal approximation (VCA) to extract the phonon dispersion relations of a high-symmetry cubic-constrained form using density functional perturbation theory. We find that the most unstable modes in the rock-salt ordered structure and the VCA, like pure PbZrO$_3$, are antiferrodistortive (AFD) whilst lower symmetry arrangements are dominated by $Gamma$-point ferroelectric (FE) instabilities like pure PbTiO$_3$. Despite similarities in the phonon dispersion relations between the rock-salt ordered supercell and the VCA, the character of modes at high symmetry points are found to be different. In particular, the a$^{0}$a$^{0}$c$^{-}$ & a$^{0}$a$^{0}$c$^{+}$ AFD instabilities of the rock-salt ordering are replaced with a$^{-}$b$^{-}$c$^{-}$ & a$^{+}$b$^{+}$c$^{+}$ instabilities within the VCA. Such a rotation pattern is not seen in any of the supercell-based calculations thus serving as a quantitative example of the inability of the method to represent accurately local structural distortions. Single modes are found exhibiting dual order parameters. At the zone centre, some arrangements show mixed FE & antipolar soft modes (due to Pb motion tansverse to the polar axis) and at long wavelengths all arrangements have soft modes of a mixed antipolar & AFD character. These are described with direct analysis of the eigendisplacements.
An argument that relaxor ferroelectricity in the isovalent alloy $mathrm {Ba(Zr}_{1-x}mathrm{Ti}_{x})mathrm{O}_3$ can be understood as an induced moment soft pseudo-spin glass on the B-ions of the $mathrm{ABO}_{3}$ matrix is extended to the experimentally paradigmic but theoretically more complex heterovalent relaxor $mathrm {Pb(Mg}_{1/3}mathrm{Nb}_{2/3}mathrm{)O}_3$ (PMN). It is argued that interesting behaviour of the onset of non-ergodicity, frequency-dependent susceptibility peaks and precursor nanodomains can be understood from analagous considerations of the B-ions, with the displacements of the Pb ions a largely independent, but distracting, side-feature. This contrasts with conventional conceptualizations.
The high frequency dynamics of glassy Selenium has been studied by Inelastic X-ray Scattering at beamline BL35XU (SPring-8). The high quality of the data allows one to pinpoint the existence of a dispersing acoustic mode for wavevectors ($Q$) of $1.5<Q<12.5$ nm$^{-1}$, helping to clarify a previous contradiction between experimental and numerical results. The sound velocity shows a positive dispersion, exceeding the hydrodynamic value by $approx$ 10% at $Q<3.5$ nm$^{-1}$. The $Q^2$ dependence of the sound attenuation $Gamma(Q)$, reported for other glasses, is found to be the low-$Q$ limit of a more general $Gamma(Q) propto Omega(Q)^2$ law which applies also to the higher $Q$ region, where $Omega(Q)propto Q$ no longer holds.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
