Long-range Order Parameter Research Articles

Crystal structure, Raman spectroscopy, far-infrared, and microwave dielectric properties of (1−x)La(MgSn)0.5O3–xNd(MgSn)0.5O3 system

The complex perovskite system (1−x)La(MgSn)0.5O3–xNd(MgSn)0.5O3 with the composition (x=0–1) was prepared by the solid state reaction method. Structural and spectroscopic studies were carried out to understand the variation of dielectric properties with x. Rietveld refinement was carried out with the initial model obtained by using the structure prediction and diagnostic software. The symmetry of the compositions was determined to be monoclinic with space group P21/n, which corresponds to the a−a−c+ tilting system, and the long-range order parameter was found to decrease with an increase in neodymium concentration. Raman spectra were analyzed by fitting the A1g-like mode to a Lorentzian peak shape. Intrinsic dielectric parameters were estimated by fitting infrared reflectance spectra with the four-parameter semiquantum model. Transverse optic phonon mode strengths and average phonon damping were calculated. The origin of increase in the intrinsic loss with the composition variation is discussed. Microwave measurements were carried out in the frequency range of 9–11 GHz. The dielectric constant decreases and the temperature coefficient of resonant frequency becomes less negative with the increase in neodymium concentration.

Layer dependent composition of AuCu3(100) in the semi-infinite and thin film geometry

Abstract We compare the experimental data for the concentration profiles measured by the directional Auger electron spectroscopy for the binary alloys AuCu 3 fcc(1 0 0) with the conclusions obtained in the frame of theoretical model describing the surface properties in terms of the order parameters. The interpretation of the theoretical results in the context of measurements performed by means of various experimental techniques shows that the simultaneous description of the concentration profile and the long-range order parameters is rather difficult to agree the experimental behaviour. We show, however, that a very good agreement can be achieved when the interaction constants are considered to be temperature dependent.

CoPt alloy grown on the WSe 2(0 0 0 1) van der Waals surface

The structural and magnetic properties of 3-nm-thick CoPt alloys grown on WSe 2(0 0 0 1) at various temperature are investigated. Deposition at room temperature leads to the formation of a chemically disordered fcc CoPt alloy with [1 1 1] orientation. Growth at elevated temperatures induces L1 0 chemical order starting at 470 K accompanied with an increase in grain size and a change in grain morphology. As a consequence of the [1 1 1] growth direction, the CoPt grains can adopt one of the three possible variants of the L1 0 phase with tetragonal c-axis tilted from the normal to the film plane direction at 54°. The average long-range order parameter is found to be 0.35(±0.05) and does not change with the increase in the deposition temperature from 570 to 730 K. This behavior might be related to Se segregation towards the growing facets and surface disorder effects promoted by a high surface-to-volume ratio. Magnetic studies reveal a superparamagnetic behavior for the films grown at 570 and 730 K in agreement with the film morphology and degree of chemical order. The measurements at 10 K reveal the orientation of the easy axis of the magnetization lying basically in the film plane.

Statistical Thermodynamics and Ordering Kinetics of D0<sub>19</sub>-Type Phase: Application of the Models for H.C.P.-Ti–Al Alloy

Using the self-consistent field approximation, the static concentration waves approach and the Onsager-type kinetics equations, the descriptions of both the statistical thermodynamics and the kinetics of an atomic ordering of D019 phase are developed and applied for h.c.p.-Ti–Al alloy. The model of order–disorder phase transformation describes the phase transformation of h.c.p. solid solution into the D019 phase. Interatomic-interaction parameters are estimated for both approximations: one supposes temperature-independent interatomic-interaction parameters, while the other one includes the temperature dependence of interchange energies for Ti–Al alloy. The partial Ti–Al phase diagrams (equilibrium compositions of the coexistent ordered α2-phase and disordered α-phase) are evaluated for both cases. The equation for the time dependence of D019- type long-range order (LRO) parameter is analyzed. The curves (showing the LRO parameter evolution) are obtained numerically for both temperature-independent interaction energies and temperature-dependent ones. Temperature dependence of the interatomic-interaction energies accelerates the LRO relaxation and diminishes a spread of the values of instantaneous and equilibrium LRO parameters versus the temperature. Both statistical-thermodynamics and kinetics results show that equilibrium LRO parameter for a non-stoichiometry (where an atomic fraction of alloying component is more than 0.25) can be higher than for a stoichiometry at high temperatures. The experimental phase diagram confirms the predicted (ordered or disordered) states for h.c.p.-Ti– Al.

He + ion irradiation-induced disordering in L1 0-FePd thin films: Ion fluence dependence

Highly ordered, epitaxial, isotope-periodic [ nat FePd/ 57 FePd] multilayers were prepared by molecular beam epitaxy and irradiated with 130 keV He + ions to fluences of up to 1.49 × 10 16 atoms cm −2 . Electron microscopy showed a gradual accumulation of defects and disordering in irradiated samples. A significant decrease in the long-range order parameter was observed by X-ray diffraction analysis. However, the structural changes remained local, as nuclear resonant X-ray reflectometry confirmed that the isotope multilayer maintained good periodicity.

The effective interdiffusivity, structure, and magnetic properties of [Fe∕Pt]n multilayer films

This paper reports the influence of the deposition temperature and the wavelength of the periodicity on the effective interdiffusivity, microstructure, and magnetic properties of annealed [Fe∕Pt]n multilayer films (MLs). It was found that both the deposition temperature and periodicity of [Fe∕Pt]n MLs have a significant influence on the effective Fe–Pt interdiffusivity, microstructure, and magnetic properties of the annealed films. It was also observed that the magnitude of the effective interdiffusion coefficient, the L10 grain size, and the long-range order parameter were positively correlated. This result suggests that nonequilibrium reaction kinetics are desirable for the reduced temperature formation of the L10 FePt phase.

最近の研究から Ｌ１０型ＦｅＰｄ規則合金ナノ粒子の長範囲規則度

Hard magnetic properties of FePd nanoparticles originate from their L10-type tetragonal ordered structure with high magnetocrystalline anisotropy energy. In order to know correlations among the long-range order (LRO) parameter (S), the particle size and the anisotropy energy, we employed a new technique to determine LRO parameter of single L10-FePd nanoparticle using nanobeam electron diffraction (NBD) . The LRO parameter was determined by quantitative analysis of NBD intensities recorded on imaging plates together with intensity calculations considering the multiple scattering of electrons. In taking NBD patterns, hh0 systematic reflections were excited using a transmission electron microscope with a field emission gun operated at 300 kV. Specimen thickness was evaluated by electron holography. The obtained order parameters of individual nanoparticles larger than 8 nm are almost around the mean LRO parameter (S=0.79) determined by selected area electron diffraction. In contrast, the parameters gradually decrease as the particle size decreases below 8 nm (S=0.60-0.73) . The low degree of order in very small particles is responsible for the coercivity (anisotropy energy) decrease of the L10 nanoparticles in smaller sized region. Experimental conditions required for NBD analysis are presented in detail and the possible experimental errors of the determined LRO parameters are discussed.

Electron holography study of the temperature variation of the magnetic order parameter within circularly chained nickel nanoparticle rings

The magnetic structure within circular chains composed of 30-nm-diameter, polymer-coated nickel particles was studied by electron holography. The magnetic flux closure due to dipolar coupling was confirmed at zero external magnetic field. Its long-range order parameter was determined from the magnitude of the electron phase shift, and it was found to decrease more rapidly than that of bulk nickel as a function of temperature. The results of Monte Carlo simulations indicated that the temperature variation of the order-parameter was explained in terms of weakened dipolar coupling field ascribed to the decay of the bulk magnetization and enhanced thermal fluctuations.

Diffusive and ballistic current spin polarization in magnetron-sputteredL10-ordered epitaxial FePt

We report on the structural, magnetic, and electron transport properties of an $L{1}_{0}$-ordered epitaxial iron-platinum alloy layer fabricated by magnetron sputtering on a MgO (001) substrate. The film studied displayed a long-range chemical order parameter of $S\ensuremath{\sim}0.90$, and hence has a very strong perpendicular magnetic anisotropy. In the diffusive electron transport regime, for temperatures ranging from $2\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}258\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, we found hysteresis in the magnetoresistance mainly due to electron scattering from magnetic domain walls. At $2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, we observed an overall domain wall magnetoresistance of about 0.5%. By evaluating the spin current asymmetry $\ensuremath{\alpha}={\ensuremath{\sigma}}_{\ensuremath{\uparrow}}∕{\ensuremath{\sigma}}_{\ensuremath{\downarrow}}$, we were able to estimate the diffusive spin current polarization. At all temperatures ranging from $2\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}258\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, we found a diffusive spin current polarization of greater than 80%. To study the ballistic transport regime, we have performed point-contact Andreev-reflection measurements at $4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. We obtained a value for the ballistic current spin polarization of $\ensuremath{\sim}42%$ (which compares very well with that of a polycrystalline thin film of elemental Fe). We attribute the discrepancy to a difference in the characteristic scattering times for oppositely spin-polarized electrons, such scattering times influencing the diffusive but not the ballistic current spin polarization.

Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas

We discuss the relationship between the cycle probabilities in the path-integral representation of the ideal Bose gas, off-diagonal long-range order, and Bose-Einstein condensation. Starting from the Landsberg recursion relation for the canonic partition function, we use elementary considerations to show that in a box of size L3 the sum of the cycle probabilities of length k>>L2 equals the off-diagonal long-range order parameter in the thermodynamic limit. For arbitrary systems of ideal bosons, the integer derivative of the cycle probabilities is related to the probability of condensing k bosons. We use this relation to derive the precise form of the pik in the thermodynamic limit. We also determine the function pik for arbitrary systems. Furthermore, we use the cycle probabilities to compute the probability distribution of the maximum-length cycles both at T=0, where the ideal Bose gas reduces to the study of random permutations, and at finite temperature. We close with comments on the cycle probabilities in interacting Bose gases.

Atomic-vacancy ordering in the lowest tungsten carbide W2C

Atomic-vacancy ordering in the lowest tungsten carbide W2C with an L′3-type basic hexagonal structure has been studied by neutron diffraction and X-ray diffraction. In the temperature range 2700–1370 K, the only ordered phase of the lowest tungsten carbide is shown to be the trigonal ɛ-W2C phase (space group P $$\overline 3 $$ 1m). This trigonal ɛ-W2C phase is found to form via a disorder-order phase transition channel, which includes three superstructure vectors (k 15 (1) , k 15 (2) , k 17 (1) ) of two Lifshitz stars ({k 15}, {k 17}, and to be described by two long-range order parameters (η15, η17). The distribution function of carbon atoms in the trigonal ɛ-W2C superstructure is calculated, and the corresponding region of the allowable values of the long-range order parameters η15 and η17 is found. Symmetry analysis of other possible superstructures of the lowest tungsten carbide W2C is performed, and the physically acceptable sequence of phase transformations in W2C is determined.

Atomic and vacancy ordering in carbide ζ-Ta 4C 3−x (0.28⩽ x⩽0.40) and phase equilibria in the Ta–C system

The structure of nonstoichiometric carbide phase ζ-Ta 4C 3− x formed in the tantalum–carbon (Ta–C) system is studied by X-ray and neutron powder diffraction and metallography. Investigated carbide ζ-TaC 0.67 crystallizes in a trigonal (rhombohedral) space group R 3 ¯ m with cell parameters a tr=1.0180(1) nm, α tr=17.64° (or a h=0.31216(2) nm, c h=3.0058(1) nm in hexagonal axes). The closely packed metal sublattice in carbide ζ-Ta 4C 3− x consists of alternating blocks where metal atoms are located in the same manner as on the FCC sublattice of the cubic carbide TaC y and the HCP sublattice of the hexagonal carbide Ta 2C y . This metal sublattice represents a transition sublattice between these FCC and HCP sublattices. An ordered distribution of atoms C and structural vacancies in carbide ζ-Ta 4C 3− x is revealed and the distribution function of atoms C is calculated for nonmetal sublattice sites, on which ordering takes place. It is shown that one long-range order parameter η describes the ordering of ζ-carbide and the η value in the investigated ζ-Ta 4C 3− x phase does not exceed 0.7. Carbide ζ-Ta 4C 3− x is stable in bulk and powdered states over a wide temperature interval of 300 to ∼2400 K and has a narrow homogeneity interval from TaC 0.65 to TaC 0.68. Microhardness of disordered and ordered tantalum carbide TaC y with the basic B1 structure and trigonal carbide ζ-Ta 4C 3− x is measured. The phase diagram of the Ta–C system is refined considering data obtained for the ζ-Ta 4C 3− x phase.

A d-wave pairing state in terms of the Zhang–Rice singlets

In cuprate superconductors doping is believed to create holes on the O-sites, which couple antiferromagnetically with holes on the Cu-sites to form the so-called Zhang–Rice singlets. Here we study a d-wave pairing state based on the Zhang–Rice singlet states. Upper and lower bounds of an off-diagonal long-range order parameter with d-wave symmetry for this state are estimated. We also introduce a concrete model with on-site Coulomb repulsion and kinds of antiferromagnetic interactions whose ground state is this d-wave pairing state.

Direct synthesis of L10-(Fe, Co)Pt nanocrystallites from (Fe, Co)–Pt–Zr–B liquid phase by melt-spinning

The ordered L10-FePt phase with a size of 20–200nm was directly formed by rapidly quenching the melt in the compositional range of 2–5at.% Zr and 17–20at.% B, and the alloys exhibit coercivity (Hc) higher than 200kA/m in an as-quenched state. In particular, the melt-spun (Fe0.50Pt0.50)78Zr4B18 alloy exhibits high Hc of 684kA/m. The melting temperature (Tm) remarkably decreases by the addition of Zr and B, e.g., from 1837K for FePt to 1345K for (Fe0.55Pt0.45)78Zr4B18. The L10 phase with Zr and B directly formed by the rapidly quenching shows high thermal stability and maintains up to Tm. The simultaneous addition of Zr and B facilitates the direct formation of the ordered L10 phase with a grain size of 20–200nm by rapidly quenching the melt through the effect of the decreasing Tm and the increasing the stability of the L10 phase by the solution of Zr and B into the phase. The substitution of Fe by Co monotonously decreases Tm from 1345K of (Fe0.50Pt0.50)78Zr4B18 to 1083K of (Co0.50Pt0.50)78Zr4B18. However, Hc drastically decreases from 684kA/m of (Fe0.50Pt0.50)78Zr4B18 to 12kA/m of (Co0.50Pt0.50)78Zr4B18, which has a single fcc structure in an as-quenched state. The decrease in Hc with increasing Co content up to Fe:Co=1:3 is caused by the decreasing of the magnetocrystalline anisotropy, which originates from the decreasing the long-range order parameter of the L10 phase.

Temperature effect on microstructure and mechanical properties of the nano-structured Ni 3Al coating

Phase composition, thin structure and morphology of the surface of the intermetallic coating are investigated by transmission electron microscopy, X-ray analysis and atomic force microscopy. It is shown that Ni 3Al is the main phase of the intermetallic coating for all investigated samples. There is a small amount of the NiAl and AlFe 3C phases. The application of temperature and ion beam treatment changes the atomic long-range order parameter and the elastic microstresses of the crystalline lattice.

Investigation of changes in the order parameters near antiphase boundaries in the Cu3Au alloy

Investigation of the specific features of order-disorder structural phase transitions in ordering alloys in the presence of antiphase boundaries of conservative and nonconservative types has been performed in a computer experiment by the example of the model Cu3Au alloy. The distributions of the long-range and short-range order parameters in the planes parallel to antiphase boundaries have been obtained by the Monte Carlo method for different temperatures. The mechanisms of disordering near conservative and nonconservative boundaries in ordering alloys are revealed. It is shown that the effect of diffusion of superstructural parameters is significant near nonconservative antiphase boundaries in comparison with conservative boundaries. Obviously, nonconservative boundaries can make a relatively large contribution to the effect of positive temperature dependence of the yield strength of ordering alloys with the L12 superstructure.

Order and miscibility in the otavite-magnesite solid solution

The effects of cation substitution and ordering in the otavite (CdCO3)–magnesite (MgCO 3 ) solid solution have been investigated on samples synthesized at 1 GPa in the temperature range 500–800 °C for run durations up to 120 h. A complete, disordered solid solution, with R 3 c symmetry, was obtained at 800 °C, whereas Mg and Cd show partial ordering within the cadmium dolomite stability field, with R 3 symmetry, at intermediate compositions in the temperature range 500–650 °C. Rietveld refinements for X-ray diffraction data show that variation of the a -axis is linear as a function of composition, independent of the degree of order, whereas the c -axis shows a positive deviation from linearity as a function of composition, decreasing with increasing degree of order. Octahedral bond distances of the 800 °C series vary linearly with composition. Site occupancies were used to determine the long-range order parameter, Q , for samples with R 3 symmetry. Q 4 varies linearly as a function of temperature, suggesting a tricritical phase transition with a critical transition temperature T c of 702(10) °C. EDX-TEM compositional microanalyses of samples within two-phase regions are in good agreement with Rietveld refinements, and allow better constraint of phase boundaries.

Annealing effects on the reordering of severe plastic deformed boron doped Ni3Al

X-ray diffraction (XRD) and differential scanning calorimetry (DSC) were used to investigate the reordering process of a partially disordered Ni76Al24 (0.2 wt.%B) powder with annealing times and temperature. The long-range order parameter varied linearly with temperature and a significant ordered state was observed at 773 K. The DSC measurements showed one main exothermal peak in the temperature range of 493–913 K. The maximum rate of energy release occurred at 763 ± 2 K with a total thermal effect of ΔH = 52 ± 9 j/g. The DSC peak showed a shoulder around its maximum temperature of 763 ± 2 K which was attributed to order stabilization. The presence of boron in the alloy enhanced the transformation temperature by increasing the enthalpy of vacancies migration without affecting the reaction enthalpy.

Ordering phenomena and modelling of pair interactions in Ni 3Ga compound

In the last years, intermetallics with L1 2-structure were of particular interest, both from the point of view of their fundamental properties and their practical application as materials with excellent chemical, mechanical and physical properties. In the present investigation, we have chosen Ni 3Ga as a model L1 2 compound to study (1) the equilibrium degree of order at various temperatures and (2) the kinetics of ordering and disordering. In this paper we report the method of estimating the long-range order parameter from the resistivity data and how to derive the effective pair interaction (EPI) energy. It is then compared with those evaluated from thermodynamic activity measurements and also with those converted from Compound Energy Formalism (CEF) and CALPHAD modelling. Such adequately evaluated EPI energy values can be conveniently employed for calculating point defect concentrations at various temperatures and compositions using common statistical-thermodynamic methods, as a Bragg–Williams model.

Nucleation of ordered particles at dislocations and formation of split patterns

We investigated the effect of nucleation of ordered precipitates at dislocations and the subsequent growth of particle morphology through computer simulations using a phase-field model. The model treats simultaneously precipitates, dislocations and precipitate–dislocation interactions within a single algorithm. In particular, the model takes into account the structural discontinuity associated with a dislocation that leads to the formation of antiphase domains if the dislocation is within an ordered particle. Three long-range order parameters are used to describe the antiphase domains associated with L1 2 ordering and an additional set of non-conserved order parameters is introduced to characterize dislocations. We show that heterogeneous nucleation and subsequent growth of ordered precipitates at dislocations yield various “split” patterns, whose formation has been attributed to different mechanisms in literature.