Nearest-neighbor Approximation Research Articles

Measurements and calculation of magnetic susceptibility of low-concentrated semimagnetic semiconductor GdxY2-O3

The low-concentrated gadolinium-yttrium mixed oxides GdxY2-xO3 (x = 0.02, 0.06, 0.10) were synthesized. Magnetic susceptibility was measured by the Faraday method in a temperature range 4 <T < 270 K and behaviour in accordance with the Curie-Weiss law was obtained. Starting from the exclusive 24d-site occupancy of Gd3+ ions for concentrations x ≤ 0.41 and from the short range of superexchange Gd(24d)-O-Gd(24d) interaction, the temperature dependence of the magnetic susceptiblity was calculated using the isolated cluster model in the nearest-neighbour approximation. If random distribution of magnetic ions is assumed, good agreement between calculated and experiments χ-1(T) data can be found only for the lowest concentration x = 0.02. Making use of both geometric and modified distributions, the enhancement of the clusterisation of the magnetic cations for increased concentrations x = 0.06 and 0.10 was found

Random-field Ising model with second-neighbour interaction

A random-field Ising model with second-neighbour interaction has been investigated using the new effective-field theory. The phase diagrams are examined in detail for the square lattice in a random field obeying the bimodal symmetric distribution. A tricritical point is found in the system, in contrast to the corresponding nearest-neighbour interaction Ising model. In particular, the tricritical phase diagram for a body-centered cubic lattice in nearest-neighbour approximation is also determined.

Intermolecular potential energy of water clathrates: the inadequacy of the nearest-neighbor approximation

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTIntermolecular potential energy of water clathrates: the inadequacy of the nearest-neighbor approximationKevin A. Sparks and Jefferson W. TesterCite this: J. Phys. Chem. 1992, 96, 26, 11022–11029Publication Date (Print):December 1, 1992Publication History Published online1 May 2002Published inissue 1 December 1992https://doi.org/10.1021/j100205a075RIGHTS & PERMISSIONSArticle Views179Altmetric-Citations48LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (2 MB) Get e-Alerts

Thermodynamics of alternating (s,s') chains in the nearest-neighbor Ising-model approximation.

The exact solutions of the so-called (1/2,s'${)}_{\mathit{N}}$ ferrimagnetic z-z chain made up of two sublattices have been previously derived by using the transfer-matrix method. In this paper, we generalize this method to (s,s'${)}_{\mathit{N}}$ chains, with arbitrary s and s'. We give a general expression for the correlation length \ensuremath{\xi} and the product ${\mathrm{\ensuremath{\chi}}}_{\mathrm{\ensuremath{\parallel}}}$T in the low-temperature range. We specifically discuss the case of the moment-compensated chain in the low-temperature limit and generalize the results previously obtained. We show that, in this limit, the chain behaves as an assembly of quasi-independent, quasirigid blocks, each with length \ensuremath{\xi}, and that, in the low-temperature range, the product ${\mathrm{\ensuremath{\chi}}}_{\mathrm{\ensuremath{\parallel}}}$T behaves as \ensuremath{\xi}${\mathit{M}}^{2}$, with M the thermal-average magnitude of the magnetic moment attributed to the unit cell.

Monte Carlo analysis of order-disorder reactions in binary alloys with hexagonal structure

The phase diagrams of binary alloys with hexagonal crystal structure have been calculated by means of Monte Carlo simulations taking into account anisotropic nearest neighbour interactions. The anisotropy is assumed between interactions within a basal plane (0 0 1) and those between such planes. This is an attempt to account for the experimentally observed deviation from the ideal hexagonal close packed c/a ratio. Various values of the anisotropy ratio have been assumed in order to produce a series of prototype diagrams. In the isotropic case, the structure difference between the hexagonal close packed and the face centered cubic structures disappears in a nearest neighbour approximation and the phase diagram is topologically the same for both structures. The ordered structures B19 and DO 19 are the hexagonal variants of the ordered FCC structures L1 0 and L1 2, respectively. When the interactions within the (0 0 1) planes are stronger than those between such planes, an A 2B phase appears at compositions between the ordered B19 and DO 19 phases. When they are weaker, two kinds of new phases (R n and T n with the limiting variants R 1 ≡ B19 and T 1 ≡ DO 19) appear between them. These new phases have not been observed so far in real systems. It is found that the phases R 2 and T 2 are stable at high temperatures and there should be a chance to observe at least these phases in real alloys. The corresponding phase diagrams are presented.

Equilibrium correlation function in post-Galilean approximation of a scalar field

The exact formula for the equilibrium one-dimensional binary distribution function for scalar particles, interacting by the potential 1/r, is obtained in the post-Galilean approximation. To take into account the post-Galilean corrections (i.e. the values of the order of O(c−2), where c is the velocity of light), the temperature shift is suggested. It means that in this relativistic approximation we can use the classical coordinate distribution function with the shifted temperature parameter.We also calculate the configuration integral of this system in the thermodynamic limit in the nearest neighbour approximation.

Specific heat of the diluted magnetic semiconductor Zn 1− xCo xSe

We report on the low-temperature specific heat of Zn 1− x Co x Se. Above 10 K a contribution from nearest-neighbor coupled Co ions is visible, whereas at lower temperatures more distant magnetic ions contribute to the specific heat. The data can be described in the extended nearest-neighbor pair approximation.

Specific heat of Cd1-xCoxS and Cd1-xCoxSe at low temperatures.

The specific heat of two diluted magnetic semiconductors, ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$S and ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$Se, both having the wurtzite structure, has been measured in the temperature range 0.4--4.0 K, and in various magnetic fields up to 2.8 T. In the dilute limit (x\ensuremath{\simeq}0.001), both materials exhibit broad maxima in the specific heat resulting from the zero-field splitting, 2D, of the ground orbital state of the ${\mathrm{Co}}^{2+}$ ion. From quantitative analysis we have obtained D/${\mathit{k}}_{\mathit{B}}$=0.97\ifmmode\pm\else\textpm\fi{}0.03 K for ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$S, and D/${\mathit{k}}_{\mathit{B}}$=0.72\ifmmode\pm\else\textpm\fi{}0.03 K for ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$Se. For larger concentrations x of ${\mathrm{Co}}^{2+}$ ions (x=0.0077), exchange interactions have to be included in the theoretical model. We have used the nearest-neighbor pair-correlation approximation (NNPA), with the distance dependence of the exchange integral given by ${\mathit{J}}_{\mathit{i}}$(${\mathit{R}}_{\mathit{i}}$)\ensuremath{\sim}(${\mathit{R}}_{\mathit{i}}$${)}^{\mathrm{\ensuremath{-}}\mathit{n}}$. This approximation describes the specific-heat data quite well in the present case. The best fit of the NNPA curve has been achieved for n=6.0\ifmmode\pm\else\textpm\fi{}1.0, which is very close to that for Mn-based diluted magnetic semiconductors.

H�ckel framework study on the superconducting vibronic interaction in (AB) N chains

Superconducting vibronic interaction in the vibronic superconductivity motif has been studied in the Huckel framework for (AB) N chain systems. Within the on-site and nearest-neighbor approximation a new vibronic constant, ∂α/∂L, has been introduced, of which the importance has been discussed. The effect of the vibronic operator, Δ, has also been studied. It is also concluded that the size-dependence of the superconducting vibronic interaction also exists in the (AB) N chain systems.

Validity of the nearest-neighbor approximation in the evaluation of the electrophoretic manifestations of DNA curvature

The validity of a theoretical nearest-neighbor model based on conformational energy calculations, for translating the deterministic fluctuations of DNA base sequences in superstructural elements, is tested on the electrophoretic data of 450 multimeric, duplex oligonucleotides with different sequence, periodicity, and complexity, corresponding to all the experimental data so far published. An accurate semiempirical linear relation between the gel electrophoretic retardation and the dispersion of the theoretical curvature was found which allows a prediction of electrophoretic anomalies of DNA tracts, e.g., the cyclic permutation gel assays, with great confidence. Such a pattern of agreement allows the interpretation of the gel electrophoresis retardation as due to an increase of activation energy required in straightening the DNA axis.

Dirac-like behaviour of a non-relativistic tight binding Hamiltonian in one dimension

We study a linear periodic chain using opposite-parity wave-functions, localized in alternative sites, as a tight-binding LCAO basis. In the first nearest-neighbour approximation and in the continuum limit, we show that the 1-dimensional equation for the quantum amplitudes becomes Dirac-like. We study the electron-hole dynamics in this “relativistic” framework. We discuss in particular the “zitterbewegung” and the limit of vanishing “rest mass”.

Raman spectra of tetramethylammonium–trimethylammonium mixed ion vermiculite clay intercalation compounds

AbstractThe composition dependence of the Raman spectra of the mixed ion vermiculites [(CH3)4N+]1‐x [(CH3)3NH+]x‐V (V = vermiculite) have been studied in the range 0 ⩽ x ⩽ 1. The torsional mode frequencies exhibit a small shift (ca. 2 cm−1) to lower energy with increasing x and their composition dependence is distinct from that shown by the corresponding modes of Cs1‐xRbx‐V. These differences are attributed to a variation of the guest‐host force constants and in particular to the interactions between the guest ions and the basal oxygens, which depend strongly on the size difference,ΔD, between the guest ion pairs. Using a van der Waals‐type force model and the nearest neighbor approximation, the torsional mode frequencies of the pure end‐member compounds of the two mixed ion systems discussed above have been successfully accounted for.

Thermodynamic and spectroscopic study of bulge loops in oligoribonucleotides

Thermodynamic parameters for bulge loops of one to three nucleotides in oligoribonucleotide duplexes have been measured by optical melting. The results indicate bulges Bn of An and Un have similar stabilities in the duplexes, GCGBmGCG + CGCCGC. The stability increment for a bulge depends on more than its adjacent base pairs. For example, the stability increment for a bulge is affected more than 1 kcal/mol by changing two nonadjacent base pairs or by adding terminal unpaired nucleotides (dangling ends) three base pairs away. Thus a nearest-neighbor approximation for helixes with bulges is oversimplified. Many of the non-self-complementary strands used in this study were observed to form homoduplexes. Such duplexes with GA mismatches were particularly stable.

The growth mechanism and kinetics on stacking fault reconsidered

Making use of the first nearest neighbour approximation it is shown that the sub-step created on a (111) face of an fcc crystal by stacking fault makes the barrier for the two-dimensional (2D) heterogeneous nucleation on the surface about twice as low as that predicted by Ming et al. [J. Crystal Growth 91 (1988) 11]. Thus, the stacking fault growth mechanism is much more effective for the step generation on the growing surface as it was considered earlier.

Nonstoichiometry in steps on AB crystals (I). General aspects, including bulk imperfections

AbstractStarting with a quasichemical treatment, simple model calculations are given for the equilibrium composition in surface steps containing A and B kinks, the amount and ratio of which is varied by changing the adjacent gas composition. In connection with deviations from step stoichiometry, the total amount of kinks increases strongly.A nearest neighbour approximation has been applied to the attachment of A or B atoms at kinks from the gas phase, and also from the bulk by formation of vacancies VA or VB. These processes can be formulated separately for the two elements, taking into account the effective formation of bulk atoms of the other kind (BB or BA).

Statistical thermodynamics of monolayers of flexible-chain amphiphiles: Adding nearest-neighbor correlations to a Scheutjens–Fleer approach

In recent work, Wang and Rice have developed a lattice statistical thermodynamic model for amphiphile monolayers, based in part on the work of Scheutjens and Fleer. As in Flory–Huggins theory, their approach relies on a Bragg–Williams approximation to the probability of successful placement of a chain segment into a lattice site. This may be a poor approximation for typical monolayers, which contain relatively short hydrocarbon chains and are characterized by orientational anisotropy, particularly at high surface densities. A model is developed that incorporates intramolecular correlations in nearest-neighbor (bond) approximation and used to predict osmotic pressure and segment and bond distributions as a function of surface density. These results are compared with surface equations of state and segment distributions obtained in Scheutjens–Fleer approximation, i.e., in the absence of bond correlations. The two levels of approximation yield considerably different isotherms, although only minor differences in the segment distributions are predicted. In particular, inclusion of nearest-neighbor correlations is found to reduce greatly the magnitude of both entropic and energetic contributions to the lateral pressure.

Magnetic properties of the diluted magnetic semiconductor Zn1-xFexSe.

The magnetic specific heat and low-field ac susceptibility of the iron-based diluted magnetic semiconductor (DMS) ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Fe}}_{\mathrm{x}}$Se in the temperature range 0.4--20 K are reported. Antiferromagnetic d-d interactions and indications of spin-glass freezing are observed. These data, together with high-temperature susceptibility and high-field magnetization, are interpreted in the extended nearest-neighbor pair approximation, with an antiferromagnetic exchange between the ${\mathrm{Fe}}^{2+}$ ions. Fair agreement between theory and experiment is obtained for all the thermodynamic quantities with one set of parameters provided by independent experiments. The strength and range of the interactions, as well as the freezing mechanisms, are compared with DMS's containing ${\mathrm{Mn}}^{2+}$, and the results are discussed in relation with the existing models.

Neighborhood notion in the magnetic-properties study of magnetic materials with a dominant superexchange interaction

The steplike magnetization observed in a semimagnetic semiconductor in a high magnetic field allows an accurate determination of the exchange interaction of these compounds. Nevertheless, the results obtained from a generalized cluster model or extended nearest-neighbor pair approximation for an interaction longer than nearest neighbor do not agree well with experimental measurements (specific heat, spin-glass study, etc.). From the assumption of a preponderant superexchange, reconsidering the hypothesis of an exchange-constant decrease with the direct distance, we analyze the ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te magnetization for different Mn compositions, and we obtain good agreement with experimental results. We emphasize that to study the magnetic properties of materials in which this interaction mechanism is preponderant, the neighborhood notion should be reconsidered, taking into consideration the cation-anion-cation distances and angles.

Spatiotemporal complexity in traveling patterns.

This is a study of the nonlinear interactions of solitary waves or impulses in homogeneous, extended media. We obtain the set of ordinary differential equations for the positions of the impulses in the nearest-neighbor approximation. Solutions with constant velocity lead to pattern maps that give the successive spacings of the impulses. From among the infinitely many metastable patterns given by the maps, the system chooses one asymptotically through a hierarchical evolution.

Local-environment effects on the density of states and substitutional impurities in random alloys.

We study the electronic structure of a binary alloy using the effective-medium approximation (EMA) and we include the local environment by treating the system as a multicomponent alloy with different neighbor compositions. We use a tight-binding model in the nearest-neighbor approximation. On introducing an impurity a spectrum of levels is found. A simplified EMA which includes the local environment is developed which is as easy to evaluate as the coherent-potential approximation. By making a perturbation about the virtual-crystal approximation a simple scheme which models the splitting of impurity levels is found. We extend the EMA to consider the effects of short-range order with nonrandom correlations and find that our approximations reduce to the exact results in the appropriate limits.