One-dimensional Linear Chain Research Articles

Oxygen adsorption on Ag(110) studied by the FI-STM

Atomic-resolution STM images of the Ag(110) clean surface were obtained successfully using a high-performance UHV-mode FI-STM. When the surface was exposed to oxygen, one-dimensional linear chains with various separation widths were observed, corresponding to the ( n × 1) LEED patterns. It was concluded that these linear chains consist of the Ag-O-Ag component, similar to the case of the Cu(110)-O system.

Scanning tunneling microscopy of oxygen adsorption on the Ag(110) surface

Our high-performance UHV-mode FI-STM/STS (field ion-scanning tunneling microscopy/spectroscopy) was used for the analysis of oxygen adsorption on the Ag(110) clean surface. When the surface was exposed to oxygen, one-dimensional linear chains with various separation widths were observed, corresponding to the ( n × 1) LEED patterns. It was concluded that these linear chains consist of AgOAg components, similar to the case of the Cu(110)O system.

Second-order spin-wave results for the quantum XXZ and XY models with anisotropy.

A second-order spin-wave analysis is given for the quantum Heisenberg antiferromagnet with anisotropy on the one-dimensional linear chain, two-dimensional honeycomb lattice, and three-dimensional simple-cubic and body-centered-cubic lattices. A similar analysis is given for the quantum XY model with anisotropy on the one-dimensional linear chain, two-dimensional triangular and honeycomb lattices, and three-dimensional simple-cubic, body-centered-cubic, and face-centered-cubic lattices. The singular behavior at the isotropic point is discussed in detail. We find that the quantum spin reduction of the isotropic Heisenberg antiferromagnet on a two-dimensional honeycomb lattice is much stronger than that on a square lattice.

Electronic structure of one-dimensional linear halogen-bridged gold chains

The band structures of linear halogen-bridged mixed-valent gold chains of the form {AuI1IX2L2-AuIL2).. (X = bridging CI, Br; L = terminal-ligand SH2, CI, and/or H) were studied by using the extended Hiickel method. The valence band was found to be a ligand lone-pair combination-a result unexpected from studies on analogous platinum chains. The variation of the band gap as a function of different geometries is in agreement with experimental results.

The crystal structure of Tl5Te3and its relationship to the Cr5B3type

Single crystals of Tl 5 Te 3 have been synthesized from stoichiometric mixtures of the elements in a two step reaction. Tl 5 Te 3 crystallizes in the tetragonal space group I 4/ mcm (No. 140) with a = 8.930(2) Å and c = 12.589(4) Å. The structure is isopointal to the Cr 5 B 3 structure type but differs in some details. The interatomic distances clearly show a separation into Tl 2 Te molecular-like fragments (Tl – Te = 3.16 Å; [unk] Tl – Te – Tl = 78.5°) and one-dimensional infinite linear TlTe chains (Tl – Te = 3.15 Å). The axial ratio c / a and the positional parameters indicate unambiguously that Tl 5 Te 3 and Cr 5 B 3 belong to definitively separated branches of the Cr 5 B 3 structure type.

Time-dependent dissociation of a geminate electron-hole pair in crystalline lattices

Abstract Using the Monte Carlo technique, the time dependence of the dissociation of a Coulombically bound electron-hole pair has been simulated for both a regular cubic lattice and a one-dimensional linear chain as a function of applied electric field. In contrast to pair recombination, the dissociation kinetics turn out to be strongly affected by the stochastic character of carrier diffusion in the vicinity of the maximum potential. The results are compared with the predictions of an analytical treatment and discussed in terms of experimental realization.

Magnetic properties of the quasi one-dimensional Heisenberg linear chain antiferromagnet: manganocene

Magnetic susceptibility measurements on the rhombic form of manganocene, Mn(C 5H 5) 2, are reported between 0.94 and 297.5 K. A pronouced minimum in the 1/x corr m versus T curve is located at T min = 141 ± 1 K. The results are well reproduced by the solution of Fisher to the quasi one-dimensional Heisenberg linear chain modified such as to include interchain interaction for J/k = −14 K, g = 2x = −5 K. A less accurate approximation to the experimental results has been achieved in terms of the pair model ( J/k = −22.5 K, g = 2.0). The results are in excellent agreement with the zigzag chain structure of C 5H 5Mn units reported for the compound.

Different orbitals for different spins for solids: Fully variationalab initiostudies on hydrogen and carbon atomic chains, polyene, and poly(sulphur nitride)

The spin unrestricted-Hartree-Fock (UHF) method (the fully variational version of the different-orbitals-for-different-spins crystal-orbital method) is applied to four infinite one-dimensional model-system linear chains of hydrogen and carbon atoms, polyene [i.e., ${(\mathrm{CH})}_{x}$] and poly(sulphurnitride). The calculations were performed by using the linear-combination-of-atomic-orbitals (LCAO) approximation evaluating exactly all the integrals over atomic orbitals within a given interaction radius. The part of the correlation energy which is taken into account by the method as well as the width of the forbidden energy gap are studied as function of the geometry parameters of H and C chains. It is concluded that the electrons lying around the Fermi level are strongly correlated by this method, while the other electrons are practically not correlated at all. No metal-insulator transition can be described by the method for the H and C chains. The very large gap obtained with the equidistant model of polyene chains supports the assumption that the model with alternating bond lengths should be preferred. In contrast to what is a common assumption, the UHF stabilization energy per unit cell is much smaller than the forbidden bandwidth owing to self-consistent rearrangement of electrons.

Time-dependent correlations between a pair of distinguishable particles hopping on a uniform one-dimensional chain

We derive equations for the time-dependent correlation function describing the relative motion of a pair of distinguishable particles hopping on a one-dimensional linear chain with all sites equivalent. This correlation function is directly proportional to the magnetization relaxation rate (${T}_{1}^{\ensuremath{-}1}$) in NMR experiments when the relaxation is due to the dipolar interaction between hopping spins. The equations are exact in the limit where the concentration of vacancies on the chain is small and, we believe, yield qualitatively good results for other concentrations. In the limit where the frequency $\ensuremath{\omega}$ is much less than the hopping rate we predict that the correlation function and thus ${T}_{1}^{\ensuremath{-}1}$ are proportional to ${\ensuremath{\omega}}^{\ensuremath{-}\frac{3}{4}}$. For three-dimensional systems the relaxation rate is frequency independent in this limit while crude (and incorrect) one-dimensional arguments lead to a ${\ensuremath{\omega}}^{\ensuremath{-}\frac{1}{2}}$ dependence.

Two-point correlation functions for a distinguishable particle hopping on a uniform one-dimensional chain

We derive the two-point correlation function for a distinguishable-particle hopping on a one-dimensional linear chain with all sites equivalent. The solution is obtained from a multiple-scattering equation derived from first principles. The results are similar to results obtained from computer experiments and phenomenological arguments.

ChemInform Abstract: MAGNETIC SUSCEPTIBILITY OF ONE‐DIMENSIONAL LINEAR CHAINS OF FERROMAGNETICALLY COUPLED CU2X6(2‐) DIMERS

Chemischer InformationsdienstVolume 6, Issue 11 Organoelement Compounds ChemInform Abstract: MAGNETIC SUSCEPTIBILITY OF ONE-DIMENSIONAL LINEAR CHAINS OF FERROMAGNETICALLY COUPLED CU2X6(2-) DIMERS CHEE CHOW, CHEE CHOWSearch for more papers by this authorR. D. WILLETT, R. D. WILLETTSearch for more papers by this authorB. C. GERSTEIN, B. C. GERSTEINSearch for more papers by this author CHEE CHOW, CHEE CHOWSearch for more papers by this authorR. D. WILLETT, R. D. WILLETTSearch for more papers by this authorB. C. GERSTEIN, B. C. GERSTEINSearch for more papers by this author First published: March 18, 1975 https://doi.org/10.1002/chin.197511439AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume6, Issue11March 18, 1975 RelatedInformation

Magnetic susceptibility of one-dimensional linear chains of ferromagnetically coupled hexahalodicuprate(2-) dimers

Magnetic susceptibility of one-dimensional linear chains of ferromagnetically coupled hexahalodicuprate(2-) dimers

Specific heat of TMMC in the region of low temperature magnetic phase transition

Specific heat measurements on the one-dimensional linear chain antiferromagnet TMMC in the temperature range 0.4–4.0 K show an anomaly at 0.83 K indicative of a three-dimensional magnetic phase transition. Above 0.83 K, that part of the specific heat not related to the phase transition, shows a linear and quadratic dependence on temperature in agreement with measurements at higher ( T > 1.5 K) temperatures. The interchain coupling does not appear to be responsible for the observed low value of the linear term. Application of a 15 kG magnetic field along the c-axis broadens the specific heat anomaly and shifts the maximum value from 0.83 K to about 1.0 K.

The characterization of calcium iridium oxides

Several calcium iridium oxides were prepared by solid state reactions and by a hydroxide precipitation technique. These phases were characterized by X-ray powder diffraction data, electrical and magnetic properties. The calcium-rich phase, Ca 4IrO 6, was an insulator exhibiting Curie-Weiss behavior above 77°K with a Weiss constant of −47°K and a magnetic moment of 1.76 μ B. Ca 2IrO 4 is a semiconductor and the temperature-dependent susceptibility above 77°K was analyzed in terms of one-dimensional linear chains of octahedrally coordinated Ir 4+ ions. Two CaIrO 3 phases were isolated, but only the orthorhombic perovskite modification was sufficiently pure for magnetic studies. It was Pauli paramagnetic with metallic conductivity.

Partial Test of the Universality Hypothesis: The Case of Different Coupling Strengths in Different Lattice Directions

High-temperature series expansions are used to examine the dependence of critical-point exponents upon lattice anisotropy (different interaction strengths in different directions in the lattice). The two-spin correlation function ${C}_{2}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ is calculated to tenth order in ($\frac{1}{{k}_{B}T}$) for the Ising Hamiltonian ${\mathcal{H}}_{l \mathrm{anis}}=\ensuremath{-}{J}_{\mathrm{xy}}\ensuremath{\Sigma}\stackrel{\mathrm{xy}}{〈\mathrm{ij}〉}{S}_{i}^{z}{S}_{j}^{z}\ensuremath{-}{J}_{z}\ensuremath{\Sigma}\stackrel{z}{〈\mathrm{ij}〉}{S}_{i}^{z}{S}_{j}^{z}$ for a wide range of anisotropy parameters $R\ensuremath{\equiv}\frac{{J}_{z}}{{J}_{\mathrm{xy}}}$ and for both the sc and fcc lattices; here the first summation is over all pairs of nearest-neighbor sites whose relative displacement vector ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}_{\mathrm{ij}}$ has no $z$ component, while the second summation is over all other pairs of nearest-neighbor sites. Hence for $R=0$, both the sc and fcc lattices reduce to the two-dimensional square lattice, while in the limit $R\ensuremath{\rightarrow}\ensuremath{\infty}$, the sc becomes a one-dimensional linear chain and the fcc becomes two noninteracting three-dimensional bcc lattices. The series for ${C}_{2}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ are then used to obtain series of corresponding lengths for the specific heat, susceptibility, and second moment. Analysis of these series yields results consistent with the universality hypothesis of critical-point exponents. Specifically, it is found that when lattice anisotrophy is introduced, the critical-point exponents studied (the susceptibility exponent $\ensuremath{\gamma}$ and the correlation length exponent $\ensuremath{\nu}$) do not appear to change from their values for an isotropic lattice. The problem of next-nearest-neighbor interactions is treated using similar methods in Paper II of this series (and briefly discussed in this paper).

On a unique continuum representation for the linear chain problem

An exact unique continuum representation for the one-dimensional linear chain problem has been constructed. Some aspects of intermediate approximations are discussed.