Mohammed Lach-hab

Electronic structure calculations of lead chalcogenides PbS, PbSe, PbTe

In this work, we have extended our study of the mechanical properties and the electronic structure of PbTe to include other Pb chalcogenide compounds (PbSe, PbS). The calculations were performed self-consistently using the scalar-relativistic full-potential linearized augmented plane wave method. Both the local density approximation (LDA) and the generalized gradient approximation (GGA) to density-functional theory were applied. The equilibrium lattice constants and the bulk modulus of a number of structures (NaCl, CsCl, ZnS) were calculated as well as the elastic constants for the structures (NaCl, CsCl). The NaCl structure is found to be the most stable one among all the three phases considered. We have found that the GGA predicts the elastic constants in good agreement with experimental data. Both the LDA and GGA were successful in predicting the location of the band gap at the L point of the Brillouin zone but they are inconclusive regarding the value of the band-gap width. To resolve the issue of the gap, we performed Slater–Koster (SK) tight-binding calculations, including the spin–orbit coupling in the SK Hamiltonian. The SK results that are based on our GGA calculations give the best agreement with experiment. Results are reported for the pressure dependence of the energy gap of these compounds in the NaCl structure. The pressure variation of the energy gap indicates a transition to a metallic phase at high pressure. Band structure calculations in the CsCl structure show a metallic state for all compounds. The electronic band structure in the ZnS phase shows an indirect band gap at the W and X point of the Brillouin zone.

Electronic structure calculations of PbTe

Abstract The full potential linearized augmented plane wave (LAPW) method was applied to study the electronic structure of the PbTe compound. Calculations of the band structure, density of states, strain energy and total energy as a function of lattice constant have been performed in the B1(NaCl) and B2(CsCl) structures. The equilibrium lattice constant, the band gap, the pressure variation of the energy gap, the bulk moduli and the elastic constants are compared with experiment and other calculations. We found that the local density approximation results in an energy gap that overestimates the experimental value, in contrast to most materials where the energy gap is underestimated. We propose a simple way to adjust the gap to the experimental value by performing a Slater–Koster fit and then varying the p on-site parameter of Pb. The inclusion of the spin–orbit coupling term in the tight-binding Hamiltonian fit is shown to produce significant changes in the band structure. With these two steps, the calculated band gap is found to be in good agreement with experiment. In the case of PbTe (CsCl) structure, our calculation finds no gap in the bands, contradicting recent experimental data.

Framework-Type Determination for Zeolite Structures in the Inorganic Crystal Structure Database

In this work a structural characterization of zeolite crystals is performed by identifying the framework type to which each zeolite belongs. The framework type is assigned for 1433 zeolitedatabase entries in the FIZ/NIST Inorganic CrystalStructureDatabase (ICSD) populating 95 framework types. These entries correspond to both natural and synthetic zeolites. Each ICSD entry is based on published work containing crystallographic information of the zeolite crystalline structure and some physical and chemical data. Today, the Structure Commission of the International Zeolite Association recognizes crystalline materials as belonging to the “zeolite” family only if they possess one of the approved framework types by the organization. Such information is of fundamental importance for identifying zeolites, for reference, for zeolite standards, for supporting the discovery of new zeolites, and for crystalline substance selection based on application. Unfortunately, framework-type information is not contained in the ICSD records. The long term goal of this work is filling such gap. Although the ICSD contains an extensive collection of zeolites, inclusion of zeolites belonging to the 191 accepted framework types could substantially expand such collection. The structural determination was achieved via several structuralanalysis methods based on numerical-computer implementations.

On the Concentration Dependence of the Cluster Fractal Dimension in Colloidal Aggregation

We have undertaken the task to calculate, by means of extensive numerical simulations and by different procedures, the cluster fractal dimension (d) of colloidal aggregates at different initial colloid concentrations. Our first approach consists in obtaining d from the slope of the log-log plots of the radius of gyration versus size of all the clusters formed during the aggregation time. In this way, for diffusion-limited colloidal aggregation, we have found a square root type of increase of the fractal dimension with concentration, from its zero-concentration value: d = d0f + a φβ, with d0f = 1.80 ± 0.01, a = 0.91 ± 0.03 and β = 0.51 ± 0.02, and where φ is the volume fraction of the colloidal particles. In our second procedure, we get the d via the particle-particle correlation function gcluster(r) and the structure function Scluster(q) of individual clusters. We first show that the stretched exponential law gcluster(r) = Ard −3e−(r/ξ) gives an excellent fit to the cutoff of the g(r). Here, A, a and ξ are parameters characteristic of each of the clusters. From the corresponding fits we then obtain the cluster fractal dimension. In the case of the structure function Scluster (q), using its Fourier transform relation with gcluster(r) and introducing the stretched exponential law, it is exhibited that at high q values it presents a length scale for which it is linear in a log-log plot versus q, and the value of the d extracted from this plot coincides with the d of the stretched exponential law. The concentration dependence of this new estimate of d, using the correlation functions for individual clusters, agrees perfectly well with that from the radius of gyration versus size. It is however shown that the structure factor S(q) of the whole system (related to the normalized scattering intensity) is not the correct function to use when trying to obtain a cluster fractal dimension in concentrated suspensions. The log-log plot of S(q) vs. q proportions a value higher than the true value. Nevertheless, it is also shown that the true value can be obtained from the initial slope of the particle-particle correlation function g(r), of the whole system. A recipe is given on how to obtain approximately this g(r) from a knowledge of the S(q), up to a certain maximum q value.

Transferable tight-binding parameters for ferromagnetic and paramagnetic iron

We construct transferable tight-binding (TB) parameters for ferromagnetic and paramagnetic iron by fitting the total energy and the electronic band structure to three prototype crystal structures of Fe (BCC, both ferromagnetic and paramagnetic; and FCC, paramagnetic only) calculated by the general-potential linearized augmented plane wave (LAPW) method. We use these TB parameters to calculate the total energy and other properties of Fe in various other crystal structures, which we compare with independent LAPW results. The agreement between LAPW and TB results is very good, suggesting a realistic parametric physical description in the tight-binding approximation for any structure of Fe.

Tight-binding Hamiltonians for realistic electronic structure calculations

Abstract This article, written in honor of Eleftherios N. Economou, contains a short summary of work one of us carried out some 20 years ago in collaboration with Lefteris and reports on recent developments on the use of tight-binding Hamiltonians to perform accurate and efficient electronic structure calculations. More specifically, in this work we use the newly developed NRL tight-binding method to explore the existence of metastable phases in transition metals, present new Slater–Koster parametrizations of cubic perovskite materials and provide an extension of the Slater–Koster approach that includes the spin–orbit interaction.

Novel Approach for Clustering Zeolite Crystal Structures

Informatics approaches play an increasingly important role in the design of new materials. In this work we apply unsupervised statistical learning for identifying four framework‐type attractors of zeolite crystals in which several of the zeolite framework types are grouped together. Zeolites belonging to these super‐classes manifest important topological, chemical and physical similarities. The zeolites form clusters located around four core framework types: LTA, FAU, MFI and the combination of EDI, HEU, LTL and LAU. Clustering is performed in a 9‐dimensional space of attributes that reflect topological, chemical and physical properties for each individual zeolite crystalline structure. The implemented machine learning approach relies on hierarchical top‐down clustering approach and the expectation maximization method. The model is trained and tested on ten partially independent data sets from the FIZ/NIST Inorganic Crystal Structure Database

The effect of spin-orbit coupling on the band structure of 5d metals

We present a study of the effect of the spin-orbit interaction on the equilibrium volume, band structure, and density of states in the 5d series of the transition metals. We performed this work by creating an extension to the NRL TB method that introduces a doubling of the non-relativistic 9 × 9 spd matrix and an additional parameter originating from the atom. Our results show negligible differences in the values of the equilibrium lattice parameters, more significant changes in the states away from the Fermi level but negligible effects on the density of states at E f.

Irregular Scattering of Particles Confined to Ring-Bounded Cavities

The classical motion of a free particle that scatters elastically from ring-bounded cavities is analyzed numerically. When the ring is a smooth circle the scattering follows a regular and periodic pattern. However, for rings composed ofN scatterers the flow is irregular, of Lyapunov type. The Lyapunov exponent is found to depend logarithmically withN, which is consistent with the theoretical derivation of Chernov for polygon-shaped billiard systems. The escape time from cavities bounded by a ring ofN separated scatterers is demonstrated to follow a geometric distribution as a function of the aperture size. An empirical scaling is proposed between the Lyapunov exponent, the escape time, andN.

A Cheminformatics Approach for Zeolite Framework Determination

Knowledge of the framework topology of zeolites is essential for multiple applications. Framework type determination relying on the combined information of coordination sequences and vertex symbols is appropriate for crystals with no defects. In this work we present an alternative machine learning model to classify zeolite crystals according to their framework types. The model is based on an eighteen-dimensional feature vector generated from the crystallographic data of zeolite crystals that contains topological, physical-chemical and statistical descriptors. Trained with sufficient known data, this model predicts the framework types of unknown zeolite crystals within 1-2 % error and shows to be better suited when dealing with real zeolite crystals, all of which always have geometrical defects even when the structure is resolved by crystallography.