Binary Chain Research Articles

Renormalization group decimation technique for disordered binary harmonic chains

The density of states of disordered binary harmonic chains is calculated using the Renormalization Group Decimation Technique on the displacements of the masses from their equilibrium positions. The results are compared with numerical simulation data and with those obtained with the current method of Gonçalves da Silva and Koiller. The advantage of our procedure over the other methods is discussed.

A computerized methodology for structural synthesis of kinematic chains: Part 1— Formulation

In an effort to develop a fully computerized approach for structural synthesis of kinematic chains the steps involved in the method of structural synthesis based on transformation of binary chains [38] have been recast in a format suitable for implementation on a digital computer. The methodology thus evolved has been combined with the algebraic procedures for structural analysis [44] to develop a unified computer program for structural synthesis and analysis of simple jointed kinematic chains with a degree of freedom ⪖0. Applications of this program are presented in the succeeding parts of the paper.

A computerized methodology for structural synthesis of kinematic chains: Part 2— Application to several fully or partially known cases

The reliability of the computer program for structural synthesis and analysis of simple-jointed kinematic chains developed in Part 1 has been established by applying it to several cases for whuch solutions are either fully or partially available in the literature, such as 7-link, zero-freedom chains; 8- and 10-link, single-freedom chains; 12-link, single-freedom binary chains; and 9-link, two-freedom chains. In the process some discrepancies in the results reported in previous literature have been brought to light.

Renormalization group treatment for spin waves in the randomly disordered Heisenberg chain

We calculate local densities of states in the randomly disordered binary quantum Heisenberg chain using a generalization of a recently developed approach based on renormalization group ideas. It involves decimating alternate spins along the chain in such a way as to obtain recursion relations to describe the renormalized set of Green's function equations of motion. The densities of states are richly structured, indicating that the method takes into account compositional fluctuations of arbitrary range.

Chaotic scaling trajectories and hierarchical lattice models of disordered binary harmonic chains

Chaotic scaling trajectories and hierarchical lattice models of disordered binary harmonic chains

Disordered binary harmonic chains with site-dependent force constants

A hierarchical lattice model for a disordered two-component one-dimensional harmonic chain with three force constants, corresponding to the three possible pairs of nearest neighbors, is studied. Differences of as little as 20% between the various force constants can appreciably modify the density of states. These changes in the spectrum allow one to roughly characterize which type of interaction and which atoms are involved in the eigenmodes contained in certain frequency ranges.

Comment on the paper 'The effect of short-range order on the vibrational entropy of one-dimensional chains'

For original paper see J.A.D. Matthew et.al., ibid., vol.13, p.581 (1983). Matthew et. al. derived an expression for the entropy change due to disordering of an ordered one-dimensional equiatomic binary alloy at high temperatures, using the harmonic approximation and assuming a fixed-end boundary. As a first step towards the calculation of entropy changes due to disordering of ordered two- and three- dimensional binary alloys (Bakker 1982, Waegemaekers and Bakker 1983) the present author had already studied the linear chain and was able to derive in a very simple and straightforward way the exact expression for the entropy change of a binary linear chain which changes its state I of order to a state II of order.

Renormalization group treatment for the electronic spectrum of partially ordered one-dimensional alloys

A new approach is presented for the calculation of the local density of electronic states in partially ordered binary chains. The method is based on recursion relations for renormalized tight-binding Hamiltonian parameters. Diagonal, off-diagonal and environmental disorder are easily incorporated for all degrees of short-range order. The method takes into account compositional fluctuations of arbitrary range; the states are found to be localized and the calculated densities of states are richly structured. The only approximation is in the configurational averaging over species at decimated sites. The method is computationally very simple, and gives an interpolation scheme for all concentrations and degrees of short-range order, becoming exact in the ordered and dilute limits. Our results are compared with published numerical data, and schemes for improvement are discussed.

Density of states of vibrations in a disordered chain

We study the local density of vibrational states of a disordered binary chain using a renormalization approach suitable for the alloy problem. We include isotopic and spring constant disorder. Short range order effects in the alloy are taken into account in the pair approximation. We present some numerical results for the case of spring constant disorder and discuss their relevance for the interpretation of neutron scattering experiments in some metallic amorphous systems.

Electronic structure in large finite aperiodic polypeptide chains

The Fock and overlap matrices from SCF LCAO calculations for periodic polymer chains are used to estimate the interaction in a substitutionally disordered random binary polymer chain. In particular the density of electronic states for a random sequence to the peptide units glycine and serine is studied. The technique of building an aperiodic Fock matrix from periodic Fock matrices interpolates between various periodic limits and yields an estimate of the density of states for aperiodic polymer chains where direct calculations are unfeasible. This method yields a density of states for the aperiodic polypeptide chain which is generally estimated to be accurate to 0.05 eV.

Amplitude analysis of localization in one-dimensional disordered systems. Vibrational states of an isotopically disordered binary chain

The localization in one-dimensional disordered systems was studied by a direct calculation of the eigenvector of the system. The behavior of a quantity $L$ which measures the extension of the eigenvector from its amplitude maximum was determined by examining the dependence of an exponent $\ensuremath{\alpha}$ as a function of the parameters describing the disorder. It was found that, for the vibrational states of an isotopically disordered binary chain, (i) the eigenmode $\ensuremath{\omega}=0$ is still an extended but highly degenerated state, (ii) no Anderson transition was observed for the vibrational states regardless of the degree of disorder, and (iii) the degree of localization depends sensitively on the disorder parameters ${C}_{L}$ and $\ensuremath{\delta}$.

Recursion method for binary intermetallic compounds

The asymptotic behaviour of the recursion coefficients is studied. It is shown that the inclusion of tight-binding interactions between second nearest neighbours in ordered binary systems produced undamped asymptotic oscillations of the recursion coefficients. A method for testing continued fractions with this sort of behaviour of the coefficients is presented and tested for the case of the binary chain of the s orbitals. The resulting local densities of states consist of two bands with different widths. The formalism is applied to intermetallic compounds with B2 (CsCl) structure. Local partial densities of states are given for bulk TiFe and CuZn. The local partial densities of states are good approximations for X-ray L spectra, although only d orbitals have been included.

On nearest neighbor degeneracies of indistinguishable particles

Arrangement degeneracies suggested by sufficient statistics associated with binary stationary mth order Markov chains are discussed, and are shown to correspond and generalize some degeneracies arising when indistinguishable particles are placed on a one-dimensional lattice with n compartments. From these statistics it is possible to define an mth order unit. The arrangement degeneracy obtained from s 1’s and n−s 0’s so that lower order units are placed in higher order is difficult. For this case only the third order arrangement degeneracy is obtained, the first and second orders being relatively simple. These results are applied in determining the asymptotic distributions of rare events.

Short-range order effects on the electronic properties of a binary linear chain

A new technique to treat one-dimensional binary alloys, described in tight-binding approximation, capable of incorporating short-range correlations in a simple way is presented. The method is an extension of work by Faulkner and Korringa and handles spatial correlations by restricting the number of allowed configurations in the ensemble over which averages are taken. The density of electron states thus calculated exhibits rich structure, which is known to exist but is lost in treatments which neglect local correlation effects. A detailed study of the stoichiometric case with an equal number of atoms of both chemical species is presented, including up to next-nearest-neighbor correlations.

Structural synthesis by transformation of binary chains

The paper presents a general method of structural synthesis which can be used to derive all possible simple- and multiple-jointed chains of positive, zero or negative degree-of-freedom. In this method all possible chains with N links and F degrees-of-freedom are derived by the transformation of the corresponding “binary chains” with N binary links and F degrees-of-freedom. The method is illustrated by applying to the case of chains with degrees-of-freedom 1,2,0 and −1.

Frequency spectra of disordered chains with short‐range order

AbstractThe frequency spectra of five binary chains with equal atomic concentrations but various strengths of short range order are computed using Wu's approximate method. The configurations associated with the pseudolocalized resonance and localized modes are identified and the probabilities of their appearance are correlated to the short range order parameter Pij.

The dynamics of and the effect of a short range order on a segregated binary chain

physica status solidi (b)Volume 77, Issue 1 p. K5-K9 Short Note The dynamics of and the effect of a short range order on a segregated binary chain J. A. Cocks, J. A. Cocks Computing Center, University of Louisville Search for more papers by this authorShi-Yu Wu, Shi-Yu Wu Department of Physics, University of Louisville Search for more papers by this author J. A. Cocks, J. A. Cocks Computing Center, University of Louisville Search for more papers by this authorShi-Yu Wu, Shi-Yu Wu Department of Physics, University of Louisville Search for more papers by this author First published: 1 September 1976 https://doi.org/10.1002/pssb.2220770142Citations: 6 Louisville, Kentucky 40208, USA. AboutPDF 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 Citing Literature Volume77, Issue11 September 1976Pages K5-K9 RelatedInformation

UV Absorption of Styrene Statistical Copolymers in Solution

Differences have been observed between the ultraviolet absorption of certain styrene statistical copolymers and that of the corresponding mixtures of homopolymers. These effects are a function of the chemical nature and position of the substituent on the benzene ring.Analysis of the result obtained shows that the ultraviolet abscrption of styrene statistical copolymers depends on the tendency of the two monomeric units to be linked alternately along the binary copolymer chain and on the chain conformation, which in turn may favor or hinder, to a greater or lesser extent, electronic interactions between neighboring chromophore groups.

An analysis of the fine structure in the main band of a disordered chain with dilute light impurity concentrations

AbstractThe main band of a disordered binary chain is studied, using Dean's method of negative mode counting, Schmidt's method of functional equation and an approximate theory of Wu. It is found that even for dilute light impurity concentrations, the main band is not smooth as previously believed, but has fine structure. By comparing the results of these calculations, the nature of the construction of the frequency spectrum in the form of a histogram is discussed. The truncation scheme in the approximate theory of Wu is also examined.

Kinetics of clusters in a binary linear system

We consider the stochastically time-dependent behaviour of a binary linear chain of N units at temperature T and in an external field H. The kinetics is described in terms of clusters (sequences) of specified numbers of units in the same state. A coarse-grained master equation for the cluster densities on the chain is derived by an approximation due to Felderhof. We calculate the relaxation time of fluctuations, and the zero-field frequency-dependent susceptibility, of the fraction of units in a given state. Our results are compared to the phenomenological theory of irreversible thermodynamics.