Atomic Density Function Research Articles

Atomic density function theory and modeling of microstructure evolution at the atomic scale

The atomic density function kinetic theory of a spontaneous atomic rearrangement at the atomic scale is developed. In this theory, the evolution of the system is described not by the individual movement of each atom in the same system but by the evolution of the atomic density functions, which are averages over the time-dependent ensemble. The temporal evolution of atomic densities is driven by the free energy relaxation. The thermodynamic aspects of the instability of the homogeneous liquid state and the formation of crystalline and amorphous state are discussed. Examples of self-assembling of atoms in the formation of a three-dimensional nanocrystal, and the two-dimensional diffusionless transformation in the crystalline and amorphous states are considered. The modeling reveals the special features of displacive phase transformations in the crystalline state through a transient stress-accommodating state. It also demonstrates that the thermodynamic relaxation of the liquid below its critical instability point produces a relaxed amorphous state that is practically a metastable phase.

Higher-order thermal motion tensor analysis and atom disorder in cubic melanophlogite

The structure of the high temperature form of melanophlogite (MEP) at 84 °C was refined by using a least squares refinement that was based on the Gram-Charlier expansion of the atomic probability density functions (PDF) up to the fourth-order terms. The refinements of 95 variable parameters on the space group Pm3n converged to R = 0.0275 (Rw = 0.0313) for the 607 observed reflections in single crystal X-ray diffraction. The PDFs for three types of O atom (in total, there were four types, O1 to O4) were both broad and strongly distorted from an ellipsoidal shape: unimodal for O1, bimodal for O2, and concave-spheroidal for O4. Their zero-contours covered areas with radii of 0.75-1.0 A in sections perpendicular to the shortest axes of thermal ellipsoids. The characteristic appearance of the PDF is interpreted as arising from disordered atoms in the 12 domains of low MEP. The tetragonal cell of low MEP, which is a (2 × 2 × 1)-superstructure of high MEP, is three-fold rotationally twinned around [111] (of the cubic cell) and, then antiphase translation in [100], [010] and [110] generates antiphase domains to result into a cubic average structure.

Atomic density and light intensity dependences of theRb2molecule formation rate constant in a magneto-optical trap

In this paper, we report the measurement of molecular formation rate constant of ${\mathrm{Rb}}_{2}$ directly in a magneto-optical trap (MOT). The ground state molecules are detected by two-photon ionization, resonantly enhanced through the intermediate ${a}^{3}{\ensuremath{\Sigma}}_{u}^{+}\ensuremath{\rightarrow}{2}^{3}{\ensuremath{\Pi}}_{g}$ molecular band. We have measured the rate constant as a function of atomic density to conclude that the molecules ${\mathrm{Rb}}_{2}$ are formed in the MOT by a photoassociation process caused by the trapping laser beams. We also measured the rate constant as a function of the trapping laser intensity. The results here presented are of importance to future experiments involving trapping of cold molecules.

Molecular-dynamics study of nanofragmentation during relaxation in after-loaded solids

The possibility of nanofragmentation development during the initial relaxation stage in the subsurface layer of a solid after preliminary loading is studied by computer simulation using the molecular dynamics method. It is established that disoriented nanoblocks can form in the initial stage of relaxation. This fragmentation arises in the region of strain localization in the vicinity of stress concentrators and then spreads in depth of the material. In the region of strain localization, the radial distribution function (RDF) of atomic density exhibits smeared maxima corresponding to peaks in the RDF of the ideal fcc crystal structure. In the crystal region free of strain localization, the RDF peaks exhibit splitting caused by the strain-induced symmetry breakage. The obtained results suggest that fragmentation is the possible mechanism of relaxation of internal stresses in loaded solids.

Direct determination of volume changes in ion-beam-irradiated SiC

A single crystal 6H-SiC wafer was sequentially implanted in two areas at 873 and 295 K using 2.0 MeV Au2+ ions under off-axis conditions. Identical Au depth profiles, as a function of atomic areal density, were obtained for both irradiation temperatures. X-ray photoelectron spectroscopy (XPS) and analytical electron microscopy were used to determine the one-dimensional expansion in the amorphous state produced at 295 K relative to that in the slightly damaged state produced at 873 K, based on the Au reference markers. In addition, the redshift of the plasmon-loss peak in the electron energy loss spectroscopy (EELS) was used to measure the local density changes. Comparison of the three methods indicates that the XPS and EELS methods were the most reliable, yielding a volume expansion of (11.5±2)% for the amorphous state in 6H-SiC at 295 K. The volume expansion in the slightly damaged state at 873 K was determined to be 0.9% by EELS.

Structural properties of amorphous carbon films by molecular dynamics simulation

Structure and properties of amorphous carbon film was investigated by molecular dynamics simulation using a Tersoff potential for carbon–carbon interaction. Quantitative determination of coordination numbers, atomic density, and pair correlation function was adapted to investigate the relationship between incident energies and structural properties. The structural properties of the amorphous carbon film made by the simulations were compared with those of the films deposited by filtered vacuum arc (FVA) process. As in the experimental result, the structural properties of the modeled film have their maximum values when the incident energy of deposited atoms is between 50 and 75 eV. At the optimum kinetic energy condition, we could observe in pair correlation functions that significant amount of carbon atoms were placed at a meta-stable site of atomic distance of 2.1 Å. By melting and quenching simulation of diamond lattice, it could be shown that the population of the meta-stable site is proportional to the quenching rate. These results suggest that the hard and dense diamond-like film could be obtained when the localized thermal spike due to the collision of the high-energy carbon ion can be effectively dissipated to the lattice.

Structural properties of amorphous carbon films by molecular dynamics simulation

Structure and properties of amorphous carbon film was investigated by molecular dynamics simulation using a Tersoff potential for carbon–carbon interaction. Quantitative determination of coordination numbers, atomic density, and pair correlation function was adapted to investigate the relationship between incident energies and structural properties. The structural properties of the amorphous carbon film made by the simulations were compared with those of the films deposited by filtered vacuum arc (FVA) process. As in the experimental result, the structural properties of the modeled film have their maximum values when the incident energy of deposited atoms is between 50 and 75 eV. At the optimum kinetic energy condition, we could observe in pair correlation functions that significant amount of carbon atoms were placed at a meta-stable site of atomic distance of 2.1 Å. By melting and quenching simulation of diamond lattice, it could be shown that the population of the meta-stable site is proportional to the quenching rate. These results suggest that the hard and dense diamond-like film could be obtained when the localized thermal spike due to the collision of the high-energy carbon ion can be effectively dissipated to the lattice.

Polarization resonance on S–D two-photon transition of Rb atoms

This work describes the observed effects in the polarization resonance of the 5S 1/2–5D 5/2 atomic transitions of 87Rb atoms induced by both Faraday effects and coherent light induced anisotropy of the atoms when immersed in different levels of constant magnetic field intensities. Specifically, linear collision broadening and frequency shift of the polarization resonance, as a function of Rb atomic gas density, were measured in a temperature controlled magnetically shielded cell. From the results, density-dependent line broadening and line frequency shift were observed with the coefficients of (3.53 ± 0.09) × 10 −10 and (−1.66 ± 0.09) × 10 −10 cm 3 Hz, respectively. Additionally, fluorescence and polarization signals illustrated an amplitude dependency on atomic density.

Local Atomic Structure and Conduction Mechanism of Nanocrystalline Hydrous RuO2 from X-ray Scattering

Hydrous ruthenium oxide (RuO2·xH2O or RuOxHy) is a mixed proton−electron conductor which could be used in fuel cells and ultracapacitors. Its charge-storage (pseudocapacitance) and electrocatalytic properties vary with water content and are maximized near the composition RuO2·0.5 mol % H2O. We studied the atomic structure of RuO2·xH2O as a function of water content from x = 0.84 to 0.02 using X-ray diffraction and atomic pair density function (PDF). Even though the diffraction patterns of samples containing 0.84 to 0.35 mole of water are suggestive of “amorphous” structures, the PDF analysis clearly shows that up to 0.7 nm, the short-range atomic structure of all of these RuO2·xH2O samples resembles that of the anhydrous rutile RuO2 structure. We conclude that RuO2·xH2O is a composite of anhydrous rutile-like RuO2 nanocrystals dispersed by boundaries of structural water associated with Ru−O. Metallic conduction is supported by the rutile-like nanocrystals, while proton conduction is facilitated by the structural water along the grain boundaries. This structural picture explains the charge-storage and electrocatalytic properties of RuO2·xH2O in terms of competing percolation networks of metallic and protonic conduction pathways, that vary in volume as a function of the water content of the RuO2·xH2O. The control and optimization of electron and proton conducting volumes and pathways will lead to improved performance and guide the design of new materials.

Lattice effects in solids under hydrostatic pressure by neutron pair density function analysis

Applications of the atomic pair density function, PDF, as a tool for determining short to intermediate range distortions in crystalline solids has gained momentum in recent years because of increased recognition of the significance of lattice effects to the intrinsic properties of materials. The analysis is carried out without assuming lattice periodicity as is commonly done with ordered solids since, by definition, local effects are aperiodic. Despite improvements on its accuracy by using synchrotron radiation and pulsed neutron sources that significantly reduce statistical error, its use has been limited on results from ambient conditions or as a function of temperature. This is because systematic errors are difficult to determine especially in high background environments such as with pressure measurements. Experiments of this kind can be quite useful, however, and for this reason a procedure is described in this paper for extracting local atomic information using real-space analysis under pressure. Although the corrections are first order approximations, the accuracy is comparable to other simpler experimental geometries.

Magnetometry in dense coherent media

The rotation of the polarization direction of linearly polarized light produced by the nonlinear magneto-optic effect has been proposed as a sensitive measure of small magnetic fields. In this paper, the advantages of this technique in optically thick media for precision magnetometry are discussed. Results are presented for measurements of this rotation for resonant light in optically dense Rb vapour under various conditions, with and without buffer gas. The sensitivity of the measurements of small magnetic field is investigated as a function of laser frequency, laser power, beam diameter and atomic density for D 1 line of 87Rb.

Charge localization in CMR manganites: Renormalization of polaron energy by stress field

Polaron stability and charge localization in colossal magnetoresistive manganites are known to be critically influenced by the atomic structure through the ionic size effect. We propose that this effect does not arise from changes in the electronic bandwidth, as is commonly believed, but from the renormalization of the polaron formation energy due to the long-range elastic field around a polaron, which changes the effective coupling constant by nearly a factor of 2. Results of a pulsed neutron atomic pair density function analysis, that support this proposal, are presented. We also discuss the application of this model to the question of the stability of spin-charge stripes in superconducting cuprates.

Sensitive magnetometry based on nonlinear magneto-optical rotation

Application of nonlinear magneto-optical (Faraday) rotation to magnetometry is investigated. Our experimental setup consists of a modulation polarimeter that measures rotation of the polarization plane of a laser beam resonant with transitions in Rb. Rb vapor is contained in an evacuated cell with antirelaxation coating that enables atomic ground-state polarization to survive many thousand wall collisions. This leads to ultranarrow features $(\ensuremath{\sim}{10}^{\ensuremath{-}6} \mathrm{G})$ in the magnetic-field dependence of optical rotation. The potential sensitivity of this scheme to sub-$\ensuremath{\mu}\mathrm{G}$ magnetic fields as a function of atomic density, light intensity, and light frequency is investigated near the $D1$ and $D2$ lines of ${}^{85}\mathrm{Rb}.$ It is shown that through an appropriate choice of parameters the shot-noise-limited sensitivity to small magnetic fields can reach $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{G}/\sqrt{\mathrm{Hz}}.$

Molecular surfaces from the promolecule: A comparison with Hartree–Fock ab initio electron density surfaces

A new molecular surface, the promolecule electron density isosurface arising from the superposition of spherical atomic electron density functions, is compared and contrasted with the Hartree–Fock ab initio electron density isosurface, the fused-sphere van der Waals (CPK) surface, and the smooth Connolly surface. From application to a number of small to medium-sized molecules, including several amino acids, the promolecule surface is shown to be very similar to the Hartree–Fock electron density isosurface but, in contrast, is trivial to calculate. The promolecule electron density surface constructed with a contracted hydrogen atom provides remarkably reliable, and consistent, estimates of ab initio surface areas (typically within 0.5%) and volumes (routinely overestimated by less than 4%). Differences between ab initio and promolecule surfaces are explored visually by mapping the deformation density on the promolecule surface. To highlight the usefulness of the promolecule surface, a promolecule 0.002 au isosurface of the small protein crambin is shown. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 933–942, 2000

Molecular electronic density fitting using elementary Jacobi rotations under atomic shell approximation

Fitted electron density functions constitute an important step in quantum similarity studies. This fact not only is presented in the published papers concerning quantum similarity measures (QSM), but also can be associated with the success of the developed fitting algorithms. As has been demonstrated in previous work, electronic density can be accurately fitted using the atomic shell approximation (ASA). This methodology expresses electron density functions as a linear combination of spherical functions, with the constraint that expansion coefficients must be positive definite, to preserve the statistical meaning of the density function as a probability distribution. Recently, an algorithm based on the elementary Jacobi rotations (EJR) technique was proven as an efficient electron density fitting procedure. In the preceding studies, the EJR algorithm was employed to fit atomic density functions, and subsequently molecular electron density was built in a promolecular way as a simple sum of atomic densities. Following previously established computational developments, in this paper the fitting methodology is applied to molecular systems. Although the promolecular approach is sufficiently accurate for quantum QSPR studies, some molecular properties, such as electrostatic potentials, cannot be described using such a level of approximation. The purpose of the present contribution is to demonstrate that using the promolecular ASA density function as the starting point, it is possible to fit ASA-type functions easily to the ab initio molecular electron density. A comparative study of promolecular and molecular ASA density functions for a large set of molecules using a fitted 6-311G atomic basis set is presented, and some application examples are also discussed.

Atomic transferability within the exchange-correlation density

Starting from either the exchange or the exchange-correlation density together with Bader's definition of an atom in a molecule, an atomic hole density function can be defined. Contour maps of atomic hole density functions are able to show how the electron density of each atom in a molecule is partially delocalized into the rest of atoms in the molecule. The degree of delocalization of the atomic density ultimately depends on the nature of the atom studied and its environment. Atomic hole density functions are also used to define an atomic similarity measure, which allows for the quantitative assessment of the degree of atomic transferability in different molecular environments. In this article, contour maps for the N atom in the (N2 ,C N ,N O C ) series and the O atom in the (CO, H2CO, and HCOOH) series are presented at the Hartree-Fock and CISD levels of theory. Moreover, the transferability of N and O within the two series is studied by means of atomic similarity measures. c 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1361-1374, 2000

Molecular surfaces from the promolecule: A comparison with Hartree-Fockab initio electron density surfaces

A new molecular surface, the promolecule electron density isosurface arising from the superposition of spherical atomic electron density functions, is compared and contrasted with the Hartree–Fock ab initio electron density isosurface, the fused-sphere van der Waals (CPK) surface, and the smooth Connolly surface. From application to a number of small to medium-sized molecules, including several amino acids, the promolecule surface is shown to be very similar to the Hartree–Fock electron density isosurface but, in contrast, is trivial to calculate. The promolecule electron density surface constructed with a contracted hydrogen atom provides remarkably reliable, and consistent, estimates of ab initio surface areas (typically within 0.5%) and volumes (routinely overestimated by less than 4%). Differences between ab initio and promolecule surfaces are explored visually by mapping the deformation density on the promolecule surface. To highlight the usefulness of the promolecule surface, a promolecule 0.002 au isosurface of the small protein crambin is shown. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 933–942, 2000

Surface-Morphological Information in RHEED

Surface-morphological information obtainable from RHEED intensity and its oscillation is studied based on multiple scattering calculations. The surface atomic density and the surface step density are used as the measure of surface morphology. RHEED intensity variations from growing surfaces produced by a Monte Carlo simulation are calculated by using large unit mesh surfaces. The homoepitaxial growth on Si(100) is taken as an example. The results show that RHEED intensity varies primarily as a function of surface atomic density at a low glancing angle as long as the surface island is not so large (less than 20 atomic units). RHEED intensity variations as a function of the surface step density are calculated from surfaces with different surface step density but the same atomic density. It turns out that the dominance of the information between the surface atomic density and the surface step density can be changed by choosing the diffraction condition of the incident beam.

The use of solid physical models for the study of macromolecular assembly

The use of modern technology in the construction of accurate solid macromolecular models based on atomic coordinates and electron density functions has led us to re-examine the usefulness of physical models as tools for understanding molecular assembly and for designing detailed experimental and computational studies of the assembly process. Recent developments include the construction of new models, which have provided insights into the assembly of viruses and light harvesting complexes.

Atomic cooperation and nonlinear dynamics in a mesoscopic maser

We consider a mesoscopic maser, in which a beam of excited two-level Rydberg atoms interacts with a single radiation mode during propagation through a resonant cavity. The number of atoms in the cavity ranges from a few tens to a few hundreds. Steady-state and nonlinear dynamics are investigated both with and without a coherent driving field. At steady state, atomic cooperation can induce multistability and temporal instabilities. A novel type of bistability is predicted for the amplitude of the coherently driven cavity field as a function of atomic density. The system dynamics exhibits a variety of regimes, including chaos. We have explored them by varying the experimentally accessible parameters: atomic density, cavity linewidth and driving field amplitude.