Ordering behaviors of the F.C.C. and B.C.C. phase alloys in the InMg,LiMg and AlZn systems

Expressions of the band-structure energy and the electrostatic energy characterized by the usual long-range and short-range order parameters are given to a binary alloy of simple metals with the f.c.c.-type or b.c.c.-type structure.The ordering energy and the local ordering energy are calculated for the InMg, LiMg and AlZn systems. The numerical results explain successfully the facts that the InMg system has the Ll₀-type and Ll₂-type ordered phases, each of which exists over a wide range of concentration and that the LiMg system has a local order with a negative short-range order parameter, while the AlZn system has that with the positive one. A lattice distortion in the Ll₀-type ordered structure of InMg is also discussed.     

Monte Carlo simulation of the three-dimensional XY model with bilinear–biquadratic exchange interaction

The three-dimensional XY model with bilinear–biquadratic exchange interactions J and J′, respectively, has been studied by Monte Carlo simulations. From the detailed analysis of the thermal variation of various physical quantities, as well as the order parameter and energy histogram analysis, the phase diagram including two different ordered phases has been determined. There is a single phase boundary from a paramagnetic to a dipole–quadrupole ordered phase, which is of second order in a high J/J′ ratio region, changing to a first-order one for 0.35⩽J/J′⩽0.5. Below J/J′=0.35 there are two separate transitions: the first one to the quadrupole long-range order (QLRO) phase at higher temperatures, followed by another one to the dipole–quadrupole long-range order (DLRO) phase at lower temperatures. The finite-size scaling analysis yields values of the critical exponents for both the DLRO and QLRO transitions close to the values for the conventional XY model which includes no biquadratic exchange.     

Molecular adsorption and growth of n-butane adlayers on Pt(1 1 1)

The molecular adsorption of n-butane and the growth of n-butane adlayers on Pt(1 1 1) was investigated using molecular beam techniques, temperature-programmed desorption (TPD) and low-energy electron diffraction (LEED). It is found that as the surface coverage of n-butane increases, structural changes occur in the adlayer at surface temperatures near 98 K that are accompanied by changes in the binding energy and mobility of the adsorbed species. The film growth process can be divided into four distinct coverage regimes. At low coverages (θ<0.14 ML, where 1 ML is defined as one butane molecule per Pt atom) a disordered monolayer forms in which the butane molecules prefer to lie parallel to the surface in order to minimize their binding energy. At coverages from 0.14 to 0.20 ML, ordered regions develop within the monolayer in which the butane molecules also lie parallel to the surface. The binding energy in the ordered phase is lower than that in the disordered phase due to repulsive intermolecular interactions. A more densely-packed ordered phase begins to form at 98 K after the low-coverage ordered phase saturates at 0.20 ML. The experimental results suggest that the n-butane molecules tilt away from the surface in the high-coverage ordered phase. Finally, a disordered second layer phase forms after the high coverage ordered phase saturates at 0.35 ML. The molecules in the second layer are very mobile at 98 K and rapidly diffuse to the edges of the beam spot. Interchange of molecules between the second layer and ordered monolayer is found to govern the net rate of second layer diffusion at surface temperatures less than 133 K. The adsorption probability of n-butane on Pt(1 1 1) continuously increases with increasing coverage, with no significant dependencies on the structure of the n-butane adlayer. This finding indicates that the long-range arrangements and molecular orientations of a mobile alkane adlayer have a negligible influence on the intrinsic adsorption dynamics, suggesting that the energy transfer processes that facilitate adsorption are highly localized.     

Ordering behaviors of Cd−Mg and Cd−Zn alloys with the h.c.p.-type structure

The structure dependent energy and the ordering energy for an h.c.p.-type binary alloy composed of simple metals are derived from a basis of the method of pseudopotentials. The expressions of the energies are characterized by the long-range and short-range order parameters.The long-range ordering energy is calculated for alloys in the Cd?Mg system. The numerical results reproduce well the fact that the Cd?Mg system has the B19-type ordered phase around the stoichiometric composition of MgCd and the D0₁₉-type ones around Mg₃Cd and MgCd₃. The calculated local ordering energies explain successfully the existence of a short-range order in the Cd?Mg system and also the insolubility between Cd and Zn.     

Geometry effect on the magnetic ordering of geometrically frustrated rectangular and triangular magnets

We investigate the effect of geometry on the ground-state ordering of artificially frustrated magnetic rectangular and triangular lattices by Monte Carlo method. By varying the vertical lattice spacing while keeping the horizontal one fixed, we show that when the ratio of vertical to horizontal lattice spacing, labeled by η, is less than 1.82, the ground state of the rectangular lattice presents long-range antiferromagnetic order and for η?1.82 the ground state changes to long-range mixed ferromagnetic and antiferromagnetic order. For the frustrated triangular lattice, the short-range ordered state as well as two long-range ordered ground states occurs transiently at η=0.87 and 2, where the energies of the two ground states with long-range order are approximately equal. In addition, the level of frustration of both frustrated lattices is found to be largely relevant to the ratio η.     

Phase transition in spin systems with various types of fluctuations

Various types ordering processes in systems with large fluctuation are overviewed. Generally, the so-called order–disorder phase transition takes place in competition between the interaction causing the system be ordered and the entropy causing a random disturbance. Nature of the phase transition strongly depends on the type of fluctuation which is determined by the structure of the order parameter of the system. As to the critical property of phase transitions, the concept “universality of the critical phenomena” is well established. However, we still find variety of features of ordering processes. In this article, we study effects of various mechanisms which bring large fluctuation in the system, e.g., continuous symmetry of the spin in low dimensions, contradictions among interactions (frustration), randomness of the lattice, quantum fluctuations, and a long range interaction in off-lattice systems.     

Premonitory effects near critical transition temperature in ordering systems – a Monte Carlo simulation

Premonitory effects manifest themselves in an ordering transition of the first kind (order) in the form of anomalously high short-range order (SRO) intensity at temperatures marginally above T _c, the critical transition temperature. This intensity located at the superlattice positions of the long-range ordered (LRO) phase is often attributed to the formation of ‘heterophase fluctuations’ resembling clusters of the LRO phase. Monte Carlo simulations in a hypothetical system showing FCC-to-L1₂ ordering transition have been carried out here to shed some light on this phenomenon and to look into the atomic configurations that make up these fluctuations.     

Linebroadening in DF-ODMR spectra of triplet excitons in the anthracene-1, 2, 4, 5-tetracyanobenzene single crystal near its structural phase transition

The temperature evolution of the DF-ODMR spectra of triplet excitons in the A-TCNB crystal has been studied in the vicinity of its order-disorder phase transition at T_c=204 K. Linewidth measurements were carried out for two selected orientations of the magnetic field in which the two crystal sites of the ordered phase appear as magnetically inequivalent and equivalent, respectively. In the former case the linebroadening observed near T_c was attributed to changes in the long-range order parameter and to the short-range clustering formation along the slacks. In the second case the sharp increase in the linewidth near T_c was interpreted and briefly discussed in terms of the critical slowing down of the fluctuations in the order parameter associated with the phase transition.     

Relaxation kinetics of the long-range order parameter in a non-uniform system studied by the phase field method using the free energy obtained by the cluster variation method

The order-order relaxation process of the long-range order parameter in the non-uniform L1 0 ordered phase is investigated by the hybridized calculation using the phase field method (PFM) and the cluster variation method (CVM). The resultant kinetics are composed of three processes sufficiently differing in the relaxation rates. The first and second processes correspond to antisite ordering-disordering relaxation within the ordered domain and relaxation due to a wetting-antiwetting of the antiphase boundary respectively. The third process is due to a coarsening of the ordered domain and its relaxation rate is fairly slow compared with the relaxation rates of the first and second processes; this is consistent with experimental observation. It is noted that the present result of relaxation kinetics involving the three processes is obtained only by the hybridized calculation using the PFM and CVM.     

Surface diffusion in an adsorbed system with competing order parameters

A spin-1 lattice gas model with stochastic dynamics is developed and applied to the surface diffusion in an adsorbed system possessing an internal degree of freedom. Both the chemical diffusion coefficient (D) and the relaxation rate (T) associated with the internal degree of freedom are examined. The coverage dependence of these quantities is studied within the conventional approximation, with the various static averages estimated by a Monte Carlo method. A mean field theory treatment is also given. Particular emphasis is given to the effects that the various phase transitions of the system have upon the behavior of D and T. The ordering of the internal degree of freedom is found to have an important influence on diffusion, leading to a highly reduced diffusion coefficient in the ordered regions. The connection to surface diffusion in adsorbed systems with solid orderings is pointed out. The importance of thermodynamic properties in determining the behavior of the diffusion coefficient in such systems is indicated.     

Kinetics of ordering in Ni1.50Sn (‘Ni3Sn2’) as revealed by the variation of the lattice parameters upon annealing

X-ray powder diffraction was employed to reveal the structural changes occurring upon annealing of quenched, hexagonal Ni_1.50Sn below its equilibrium ordering temperature, leading finally to long-range ordered, orthorhombic Ni_1.50Sn. The changes in the diffraction patterns indicate that the features of the low-temperature phase develop gradually in two main stages. Ex situ and in situ time-resolved X-ray powder diffraction analysis of the first stage was employed to monitor at various temperatures the time dependence of the lattice axial ratio c/a associated with the formation of long-range order in small domains. Data evaluation using an ‘equivalence-time’ method gave a value of 165–170?kJ/mol for the activation energy of the ordering, indicative of lattice-site changes of Ni atoms.     

Second-order phase transition with coexistence of short-range and long-range ferromagnetic interactions in Ba1.7La0.3FeMoO6 compound

In this work, the magnetic properties and critical behavior around ferromagnetic–paramagnetic (FM–PM) phase transition in Ba_1.7La_0.3FeMoO₆ compound have been investigated in detail. This compound exhibits a second-order magnetic phase transition with Curie temperature T_C = 345 K. The critical exponents β, γ, and δ that are determined by using the modified Arrott plots (MAP), the Kouvel–Fisher (KF) and the critical isotherm analysis agree very well. Our results indicate a coexistence of short-range and long-range ferromagnetic (FM) interactions in Ba_1.7La_0.3FeMoO₆ compound. The existence of long-range FM interactions in this compound can be associated with the crystal structure of materials with long-range Fe/Mo ordering parameter and strength of double-exchange interaction, whereas the existence of the short-range FM interactions can be explained by magnetic inhomogeneity and FM clusters.     

Low energy electron diffraction and auger electron spectroscopy studies of the structure of adsorbed gases on solid surfaces

Low energy electron diffraction (LEED) studies of the structure of adsorbed molecules on crystal surfaces revealed that ordered surface structures predominate under most conditions of the experiments. In the absence of chemical reactions with the substrate, the degree of ordering depends on the heats of adsorption, ΔH_ads, and the activation energies for surface diffusion, ΔE_D1. Since ΔH_ads is usually markedly larger than ΔE_D1, small changes of substrate temperature facilitate ordering without appreciable increase in desorption rates. The surface structures of adsorbed gases that have been reported so far have been tabulated. For molecules whose size is compatible with the interatomic distance of the substrate, rules of ordering can be proposed that permit prediction of the structure of the adsorbed layer that is likely to form. These rules indicate close packing due to attractive interactions in the adsorbed layer, and that the rotational multiplicity of the substrate is likely to be maintained by the adsorbate structure. When molecules whose dimensions are larger than the substrate interatomic distance are adsorbed, the conditions that control ordering are more complex and simple rules may not be readily applicable.The surface structures of adsorbed gases have also been studied on high Miller Index substrate surfaces. These surfaces are characterized by ordered steps separated by terraces of low index surface orientation. Many gases have different ordering characteristics on stepped surfaces than on low index crystal faces due to the stronger substrate-adsorbate interactions in these surfaces. The dissociation of diatomic molecules at steps induces the formation of new types of surface structures (frequently one-dimensional) and the dehydrogenation of hydrocarbons at steps induces the formation of ordered carbonaceous surface structures that would not nucleate on low index substrate planes.So far, mostly work function changes upon adsorption gave indication of the magnitude of charge transfer upon adsorption and on forming of new surface chemical bonds. Most recently, chemical shifts of the Auger transitions of the substrate atoms and of the adsorbed molecules upon chemisorption, have been found to provide additional information on charge redistribution during adsorption.     

Sulfur-induced mobilization of Au surface atoms on Au(1 1 1) studied by real-time STM

The interaction of sulfur with gold surfaces has attracted considerable interest due to numerous technological applications such as the formation of self-assembled monolayers and as a chemical sensor. Here, we report on the interaction of sulfur with Au(1 1 1) at two different temperatures (300 K and 420 K) studied by real-time scanning tunnelling microscopy, low energy electron diffraction and Auger electron spectroscopy. In the low coverage regime (<0.1 ML), S adsorption lifts the herringbone reconstruction of the clean Au(1 1 1) surface indicating a lateral expansion of the surface layer. An ordered (√3 × √3)R30° sulfur adlayer develops as the coverage reaches ∼0.3 ML. At higher S coverages (>0.3 ML) gold surface atoms are removed from regular terrace sites and incorporated into a growing gold sulfide phase. At 300 K this process leads to the formation of a rough pit and mound surface morphology. This gold sulfide exhibits short-range order and an incommensurate, long-range ordered AuS phase develops upon annealing at 450-525 K. In contrast, formation of an ordered AuS phase via rapid step-retraction rather than etch pit formation is observed during S-interaction with Au(1 1 1) surfaces at 420 K. Our results shed new light on the S-Au(1 1 1) interaction.     

Calculation of the ordering of the atoms in alloys with lattices of the Cu3Au type by the Monte Carlo method

The Monte Carlo method is used to calculate the temperature dependences of the short- and long-range ordering parameters in alloys with lattices of the Cu₃Au type. A new local ordering parameter is introduced and calculated. The equilibrium structure of the ordered alloy has a clearly-expressed domain character at high temperature. Above a certain temperature T_c the alloy contains small ordered complexes with lattices of the Cu₃Au and CuAu types. The relative temperatures kT_c/w₁ derived from various theories are compared. The quantity kT_c/w₁ obtained on the basis of the best analytical approximations agrees closely with that calculated by the Monte Carlo method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 76–85, February, 1973.In conclusion, the authors wish to thank L. E. Popov for constant interest in the work and O. K. Gordeev for Idndly placing the program for computing and plotting the isolines at their disposal.     

Surface Transitions of the Semi-Infinite Potts Model II: The Low Bulk Temperature Regime

We consider the semi-infinite q–state Potts model. We prove, for large q, the existence of a first order surface phase transition between the ordered phase and the the so-called “new low temperature phase” predicted in,Li in which the bulk is ordered whereas the surface is disordered.     

Correlations of particle orientation in monolayer films

Two-dimensional and three-dimensional models of an extended layer that consists of orientation-ally ordered particles are used to describe the ordering in monolayer films. In both models, when the distance between particles of the layer increases, the correlation function decreases to zero (for the parameter of adhesion to the substrate a = 0) or remains constant (for a ≠ 0, i.e., when the energy of interaction between the particles and the substrate is taken into account). In the latter case, this means that the layers have a long-range orientation order. The proposed models of an extended monolayer can be used to interpret data obtained by the light scattering and molecular dynamics methods for Langmuir-Blodgett films with the adhesion parameter a = 0.05 and the particle-particle interaction parameter b = 0.6 in the three-dimensional model or b = 1 in the two-dimensional model. The smaller value of b in the three-dimensional layer model can be explained by a stronger effect of cooperation of particle-particle interactions as compared to the two-dimensional layer model.     

Kinetics of Polydomain Ordering at Second-Order Phase Transitions (by the Example of the AuCu<Subscript>3</Subscript> Alloy)

Kinetics of polydomain spinodal ordering is studied in alloys of AuCu₃ type. We introduce four non-conserved long-range order parameters whose sum, however, is conserved and, using the statistical approach, follow the temporal evolution of their random spatial distribution after a rapid temperature quench. A system of nonlinear differential equations for correlators of second and third order is derived. Asymptotical analysis of this system allows to investigate the scaling regime, which develops on the late stages of evolution and to extract additional information concerning the rate of decrease of the specific volume of disordered regions and the rate of decrease of the average thickness of antiphase boundaries. Comparison of these results to experimental data is given. The quench below the spinodal and the onset of long-range order may be separated by the incubation time, whose origin is different from that in first-order phase transitions. Numerical integration of equations for correlators shows also, that it is possible to prepare a sample in such a way that its further evolution will go with formation of transient kinetically slowed polydomain structures different from the final L1₂ structure.     

Specific features of the strain-induced order-disorder phase transition and its mechanisms

In the present paper, the methods of x-ray diffractometry are used to investigate the influence of plastic deformation on the long-range atomic order in alloys with L1₂, L1₂(M), and L1₂(MM) superlattices. The influence of ordering energy, initial values of the long-range order parameter, and average sizes of antiphase domains on the specific features of the dependence of long-range order parameter on the strain degree is considered. It is demonstrated that the wetted strain-induced order-disorder phase transition occurs with rapid accumulation of antiphase boundaries that play an important role in the destruction of long-range atomic order.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 21–32, September, 2004.