Incommensurate Model Research Articles

Chemisorbed halogen adlayers on Fe(110): Electronic band structure and surface geometry

A series of overlayer structures, starting with a c(3 × 1) geometry are formed during the dissociative chemisorption of chlorine, bromine, and iodine on Fe(110). These adlayers provide an opportunity to systematically examine the corresponding changes in electronic band structure as a function of coverage and adsorbate. At coverage levels greater than θ = 1 3 low-energy electron diffraction patterns obtained from the halogen-covered Fe(110) surface evolve continuously with coverage. The electronic band structure was examined as a function of coverage and adsorbate species via angle-resolved ultraviolet photoelectron spectroscopy. It is concluded that the electronic band structure measurements support an incommensurate structural model for halogen overlayer geometry on Fe(110) in which an overlayer lattice, that is in general incommensurate with the substrate, rotates and compresses with increases in coverage. An alternative interpretation of the diffraction results based on antiphase domain boundaries within the overlayer is not consistent with the photoemission data. The incommensurate model emphasizes adatom-adatom interactions over adatom-substrate interactions while the reverse is true for the antiphase boundary model.

Relativity within Moose (“Mossi”) Culture: Four Incommensurable Models for Social Relationships

Relativity within Moose (“Mossi”) Culture: Four Incommensurable Models for Social Relationships

Molecular-dynamics study of phase transitions between incommensurate and commensurate phases.

Two models, one with an incommensurate phase, another with only commensurate phases have been simulated with the molecular-dynamics method, in order to study the mechanisms of the phase transitions in these systems. In the incommensurate model the mechanism relies on nucleation and growth of stripples. The commensurate-commensurate phase transition occurs in a system with a weak coupling along the modulation direction and is driven by the planar-nuclei mechanism. A planar nucleus nucleates and grows within a layer of a crystal. To transform one phase into another a large number of planar nuclei is needed. A kinetic run from one commensurate phase to another produces a spectrum of the diffuse scattering function which fills the gap between the characteristic wave vectors of the two commensurate phases.

Analysis of special states at the postulated mobility edge in the incommensurate models in 1.d

Scale dependent numerical analysis of the transmission is presented for the novel “packeted states” and the critical states in two different incommensurate models. Previous work suggests [6] this could be a numerically easy example of studying the mobility edge problematic.

Electronic spectra and mobility edges in a one-dimensional incommensurate model

Numerical studies on the one-dimensional lattice with incommensurate potentials En=1.9(cos(0.7n)+1/3cos(1.4n)) are performed. Fine structures of electronic density of states are shown. Mobility edges with precise positions are found and the nature of the eigenstates is discussed. From the eigenfunctions calculation, the authors also reveal that the 'resonant states' evolve to extended states gradually as the energy increases from the bottom of the spectrum.

Localization properties of incommensurate disordered one-dimensional systems.

We investigate the localization properties of incommensurate disordered one-dimensional models already introduced in a previous work [Phys. Rev. B 27, 7379 (1983)]. We show that these properties depend more on the type of disorder introduced than on the incommensurate model or wave vector used.

Neutron diffraction study of magnetically ordered Tm2Fe3Si5.

The magnetic ordering of ${\mathrm{Er}}_{2}$${\mathrm{Fe}}_{3}$${\mathrm{Si}}_{5}$ has been studied by neutron-diffraction techniques at low temperatures. At 4.3 K, the crystal structure is tetragonal (space group $\frac{P4}{\mathrm{mnc}}$, $a=10.393$ \AA{}, $c=5.428$ \AA{}). The atomic positional parameters were determined by Rietveld refinement of the data. Magnetic scattering peaks at positions incommensurate with the chemical cell are observed below 2.85 K. Below about 2.55 K, a second set of magnetic peaks appears, at positions commensurate with the chemical cell, but with the tetragonal $a$ axis doubled. Between 2.55 and 2.45 K, the two sets of magnetic peaks coexist, and hysteresis of about 0.01 K is observed. In this temperature region, peaks from the incommensurate phase steadily decrease in intensity as temperature is reduced until, below 2.45 K, only commensurate peaks are present. The commensurate peaks increase in intensity as the temperature is reduced down to the lowest temperatures studied. Rietveld refinement of data taken at 1.83 K shows the magnetic intensities to be well accounted for by a noncollinear magnetic structure whose principal features are the following: (1) ordering occurs only at Er-atom sites, the moment being $8.2{\ensuremath{\mu}}_{B}$ at 1.83 K, and (2) the moments are ordered in the (001) planes with a noncollinear arrangement along the $〈110〉$ set of directions, the $c$ glide planes of the chemical structure being retained in the magnetic cell (space group ${C}_{p}\mathrm{cc}{m}^{\ensuremath{'}}$)). For the incommensurate model, all elements of the commensurate arrangement are retained, but a sinusoidal modulation along [001] with a wavelength of about $5.7c$ is introduced. This wavelength is independent of temperature to within \ifmmode\pm\else\textpm\fi{}3%. Specific-heat measurements were also performed on the sample. These measurements show three peaks, one at 2.75 K corresponding to the onset of magnetic order and two others at 2.45 and 2.43 K in the coexistence region of the incommensurate and commensurate phases.

Density of states near the fluctuation boundary of the spectrum of one-dimensional incommensurable structures

This paper shows that in one-dimensional incommensurable models, the singularity of the density of states at the fluctuation boundary of the spectrum is, as a rule, a power singularity, in contrast to the exponential singularity characteristic of the disordered analogs of these models.

Neutron-diffraction study of magnetically orderedEr2Fe3Si5

The magnetic ordering of ${\mathrm{Er}}_{2}$${\mathrm{Fe}}_{3}$${\mathrm{Si}}_{5}$ has been studied by neutron-diffraction techniques at low temperatures. At 4.3 K, the crystal structure is tetragonal (space group $\frac{P4}{\mathrm{mnc}}$, $a=10.393$ \AA{}, $c=5.428$ \AA{}). The atomic positional parameters were determined by Rietveld refinement of the data. Magnetic scattering peaks at positions incommensurate with the chemical cell are observed below 2.85 K. Below about 2.55 K, a second set of magnetic peaks appears, at positions commensurate with the chemical cell, but with the tetragonal $a$ axis doubled. Between 2.55 and 2.45 K, the two sets of magnetic peaks coexist, and hysteresis of about 0.01 K is observed. In this temperature region, peaks from the incommensurate phase steadily decrease in intensity as temperature is reduced until, below 2.45 K, only commensurate peaks are present. The commensurate peaks increase in intensity as the temperature is reduced down to the lowest temperatures studied. Rietveld refinement of data taken at 1.83 K shows the magnetic intensities to be well accounted for by a noncollinear magnetic structure whose principal features are the following: (1) ordering occurs only at Er-atom sites, the moment being $8.2{\ensuremath{\mu}}_{B}$ at 1.83 K, and (2) the moments are ordered in the (001) planes with a noncollinear arrangement along the $〈110〉$ set of directions, the $c$ glide planes of the chemical structure being retained in the magnetic cell (space group ${C}_{p}\mathrm{cc}{m}^{\ensuremath{'}}$)). For the incommensurate model, all elements of the commensurate arrangement are retained, but a sinusoidal modulation along [001] with a wavelength of about $5.7c$ is introduced. This wavelength is independent of temperature to within \ifmmode\pm\else\textpm\fi{}3%. Specific-heat measurements were also performed on the sample. These measurements show three peaks, one at 2.75 K corresponding to the onset of magnetic order and two others at 2.45 and 2.43 K in the coexistence region of the incommensurate and commensurate phases.

Wave functions at a mobility edge: An example of a singular continuous spectrum

An incommensurate model is solved for Liouville-number commensuration, intermediate between the rational and the usual irrational case. The spectrum is singular continuous. The states are sparse at infinity with a hierarchic structure. The spread of a wave packet is oscillatory on any given time scale, the amplitude of oscillation increasing with the time scale.