Bulk Order-disorder Transition Research Articles

Surface segregation at the binary alloy CuAu (100) studied by low-energy ion scattering

We present results from an experimental study of segregation at the CuAu (100) surface. It is shown that Au enrichment in the top surface layer persists up to temperatures far beyond the bulk order–disorder transition temperature. From the gradual desegregation at higher temperatures a segregation energy of −0.30eV was determined. Our results are in quantitative agreement with calculations by Tersoff predicting oscillatory concentration depth profiles with decreasing amplitudes at higher temperatures. For the layer selective surface analysis we used low-energy He+ and Na+ scattering. Data interpretation and quantification were supported by numerical simulations with the MARLOWE code to which we had added the special features of trajectory resolved analysis and anisotropic thermal vibrations of surface atoms.

Ordering and segregation of aCu75Pt25(111)surface: A first-principles cluster expansion study

Configurational thermodynamics for ${\mathrm{Cu}}_{75}{\mathrm{Pt}}_{25}\phantom{\rule{0.3em}{0ex}}(111)$ surfaces is examined by a first-principles calculation in conjunction with the cluster-expansion technique. The calculated surface segregation profile just below the bulk order-disorder transition temperature exhibits Pt segregation to the top and the third layers and Cu segregation to the second layer. No long-range ordered structure is found at the top layer. However, the simulated short-range-order parameter shows a small negative value, indicating a weak ordering tendency at the ${\mathrm{Cu}}_{75}{\mathrm{Pt}}_{25}$ alloy surface. This fact can be interpreted by the competition between the layer-confined spontaneous $p(2\ifmmode\times\else\texttimes\fi{}2)$ ordering tendency and the Pt segregation and interlayer surface ordering, which certainly disrupts the $p(2\ifmmode\times\else\texttimes\fi{}2)$ ordering. Five possible surface ground-state structures are found for the bulk $L{1}_{2}$ structure. The surface ground-state structures exhibit strongly localized electronic states composed of Pt and Cu $d$ states at the topmost layer around $3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ below the Fermi energy, which is consistent with the previous ultraviolet photoelectron spectroscopy measurement. One of the surface ground-state structures possesses additional surface states just below and above the Fermi energy, which are composed of Pt $d$ states at the topmost layer. A significant ordering effect on the surface electronic states is confirmed for the ${\mathrm{Cu}}_{75}{\mathrm{Pt}}_{25}$ alloy.

Composition of the first atomic layers of (0 0 1)-oriented AuCu 3 crystal measured with the use of directional Auger electron spectroscopy at 400 K< T

Changes of the composition of the first, second, and third atomic layers of (0 0 1)-oriented AuCu 3 crystal having the bulk order–disorder transition at T c =663 K were determined with the use of Auger peak heights for Au and Cu M 23VV transitions recorded with the retarding field analyzer for the incidence angle of the primary electron beam equal to 8° and 60°, for the sample temperature ranging from 400 to 1000 K. The relative atomic concentration of gold in the first atomic layer (Au1) remains almost constant from 630 K (Au1≈0.47) to 900 K (Au1≈0.45). Above 900 K the decrease is much faster and Au1 approaches 0.35 at 1000 K. The relative atomic concentration of gold in the second atomic layer (Au2) remains constant and equal to about 0.17 from 630 to 900 K. Above 900 K it increases up to 0.31 at 1000 K. However, a large systematic error is possible in Au2 determination. No specific changes of Au1 and Au2 are observed in the vicinity of the bulk order–disorder transition temperature T c . The relative atomic concentration of gold in the third atomic layer Au3 starts to decrease in the vicinity of T c and this decrease lasts up to 900 K. The presented results are compared with the theoretical and experimental literature data. Apart from some common general trends, appreciable quantitative differences are indicated.

Surface ordering in thin films of liquid‐crystalline polymers containing fluorinated and protonated segments: Neutron‐reflectometry study

AbstractSurface‐induced layering of fluorinated and protonated segments in thin films of a main‐chain liquid‐crystalline polymer, consisting of α‐methylstilbene, bridged by a fluorinated group was revealed by neutron reflectometry. The layering was driven by the difference in surface energy of the fluorinated and protonated segments and by the inherent ordering of the polymer. The lower‐surface‐energy fluorinated segments segregated to the air surface, and the protonated segments segregated to the SiOx layer at the Si substrate. The ordering induced by the interface decayed into the film with a characteristic decay length of about 100 Å. The surface‐induced periodicity ranged from 15 to 20 Å, which is approximately equal to the molecular dimension of the repeating unit on the polymer backbone. The magnitude of segregation increased upon annealing in the liquid‐crystalline temperature range. The segregation was retained upon annealing above the bulk order–disorder transition temperature. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2817–2824, 2002

Late-stage coarsening of an unstable structured liquid film.

Thin films of poly(styrene-b-methyl methacrylate) diblock copolymers above the bulk order-disorder transition temperature, within a certain thickness range, are structurally unstable on SiO(x)/Si substrates. They dewet autophobically, forming droplets on a self-assembled brush. We investigated the late-stage evolution, coarsening, of the droplets on the brush. The average droplet cross-sectional area <S> increased with time, <S> proportional, variant t(gamma). This was accompanied by a decrease in the number of droplets per unit area with time, N(t) proportional, variant t(-gamma). We analyzed the droplet size distribution, F(S/<S>) vs S/<S>, and found that the shape of the curve was virtually identical at different stages throughout the process. This suggests that a structural self-similarity is associated with the process. A comparison of F(S/<S>) vs S/<S> data with distributions based on Ostwald ripening and coalescence cluster coarsening (dynamic and static) mechanisms strongly indicates that the dominant coarsening mechanism involved motion of droplets across the brush and subsequent coalescence, i.e., dynamic coalescence coarsening, not Ostwald ripening.

Influence of surface ordering on the wetting of structured liquids.

The substrate is shown to induce substantial ordering in diblock copolymer thin films above the bulk order-disorder transition (ODT) where, thermodynamically, a phase mixed state is favored. Initially, uniform films reorganize to form a hierarchy of transient surface patterns and stable film thicknesses that depend on the initial film thickness and on the substrate. Self-consistent field calculations of the free energy of the system for different situations, depending on the relative tendency for the different block components to be attracted to the substrate and/or free surface, provide an explanation of the formation of the stable film thicknesses. A continuum picture proposed earlier by Brochard et al. provides an explanation of the wetting characteristics of this system. In some cases the ordering destabilizes the film so that dewetting occurs (wetting autophobicity), whereas in other cases the surface ordering results in a kinetic stabilization of a film that would otherwise dewet.

Investigation of the dynamics of changes of the Cu 3 Au [formula omitted] surface in the course of ordering by low energy ion scattering

In the present work Cu 3 Au(1 0 0) alloy surface has been investigated with low energy ion scattering at temperatures below and above the bulk order–disorder transition temperature. The trajectories of Ar + low energy ions scattered from atomic chains on the surface of Cu 3 Au(1 0 0) along 〈1 0 0〉 and 〈1 1 0〉 directions were computer simulated. The dependencies of the energy of scattered ions E on the scattering angle θ and corresponding angular distributions were calculated. It has been shown that a comparison of the angular and energy distributions of ions scattered from the surface of an alloy in the process of ordering with similar distributions for pure targets made up of the alloy components permits a conclusion that two or more neighboring atoms in an alternating sequence are of the same species. The results obtained can be used to study short-range order in alloys undergoing ordering.

Monte Carlo study of the [001] surface ofCu3AuforT≠0K

Using an N-body potential with parameters determined from the $T=0$ K bulk properties (lattice constant, cohesive energy, and the elastic properties) of Cu, Au, and ${\mathrm{Cu}}_{3}\mathrm{Au},$ we investigate the effect of the [001] surface of ${\mathrm{Cu}}_{3}\mathrm{Au}$ on the ordering for temperatures below and above the bulk order-disorder transition temperature, utilizing the constant pressure, temperature and chemical potential difference Monte Carlo method. The properties studied include the stoichiometry profile, the structure factor, the average position of the atoms along the [001] direction, short-range order, wetting phenomena, and mean-square displacements. Also, various instantaneous atomic configurations are plotted. Our interest is focused on the study of the segregation of Au to the surface, while the atoms are free to relax. We find that the surface affects the ordering of the layers close to it. Segregation is found to occur in agreement with experimental results. Oscillatory segregation appeared in our results only for the case where the atoms were not allowed to relax, and in a lower intensity in some off-stoichiometry cases, i.e., ${\mathrm{Cu}}_{0.7}{\mathrm{Au}}_{0.3}$ and ${\mathrm{Cu}}_{0.8}{\mathrm{Au}}_{0.2}.$

Grain-boundary diffusion in B2 intermetallic compounds: effect of ordering on diffusion in the Fe 3Al and FeCo compounds

Grain-boundary (GB) self-diffusion in the Fe 3Al and FeCo compounds was investigated in the B-kinetic regime by the radiotracer method over temperature ranges including the bulk order-disorder transition temperatures. For iron diffusion in Fe 3Al the A2–B2 transition did not lead to any modification of the Arrhenius behavior, while a slight decrease of the triple product values below the B2-DO 3 transition is observed. In FeCo both for iron and cobalt the A2–B2 transition evokes a decrease in the pre-exponential factor of the triple product, while the diffusion activation energy is not altered. These results are tentatively interpreted in view of recent segregation experiments carried out on the free surfaces of the compounds and it is proposed that owing to segregation the order–disorder transition temperature can be considerably different in GBs from that in the bulk.

Monte Carlo simulation of Cu segregation and ordering at the (110) surface of Cu 75Pd 25

The segregation to the (110) surface of a Cu 75Pd 25 single crystal is modelled as a function of temperature by Monte Carlo simulations combined with the embedded atom method (EAM). Using EAM parameters from literature, optimised for the six transition metals of the Cu and Ni groups, does not yield satisfactory results: too low a bulk order–disorder transition temperature T c and, contrary to experimental evidence, Pd surface segregation and a disordered surface layer are obtained. These observations are contradicted by the LEIS results of Bergmans et al. [Surf. Sci. 345 (1996) 303] that revealed an ordered bulk with an oscillating concentration profile at least up to 600 K and a Cu-enriched surface. They also observed a (2×1) LEED pattern caused by ordering in the second layer. In this work the EAM parameters are recalculated and optimised precisely for the Cu–Pd alloy system under study. The results of the simulations are now in perfect agreement with the experimental findings: a bulk critical order–disorder temperature in agreement with the bulk Cu–Pd phase diagram, an oscillating concentration profile, Cu segregation to the surface and a second atomic layer exhibiting a substantial degree of ordering that accounts for the observed (2×1) LEED pattern.

Effect of Atomic Order on Iron and Cobalt Grain Boundary Diffusion in the FeCo Equiatomic Compound

ABSTRACTSimultaneous grain boundary self-diffusion of iron and cobalt in FeCo was investigated in the B-kinetic regime by the radiotracer method combined with a serial sectioning technique over the temperature range 873-1133 K, which includes the A2-B2 bulk order-disorder transition temperature. This transition leads to a decrease in both iron and cobalt mass transport mainly owing to a change in the pre-exponential factor, but not in the diffusion activation energy. Moreover, the breaking point in the Arrhenius plots is observed below the bulk order-disorder transition temperature. In view of recent surface segregation studies on Fe-Co, and according to the Fe-Co phase diagram, the results are discussed assuming an iron segregation, which decreases the A2-B2 transition temperature in grain boundaries.

Rough interfaces in fcc and bcc alloys: Influence of the order of the bulk phase transition

Using Monte Carlo simulations, we investigate the thermodynamical behavior of two different interfaces: the first one corresponds to an antiphase boundary in the ordered L12 phase on a fcc lattice and the second one corresponds to an antiphase boundary in the ordered DO 3 phase on a bcc lattice. We show that in both cases the interface undergoes a roughening transition at a temperature T R below the bulk order-disorder transition. The temperature dependence of the interface profile near T R is in good agreement with the Kosterlitz-Thouless theory. However, the two interfaces behave differently in the neighborhood of the bulk transitions. When the bulk transition is of the first order, the rough antiphase is wetted by the disordered phase and splits into two rough order-disorder interfaces. When the bulk transition is of the second order, the bulk correlation length becomes the only relevant length scale: the antiphase thickness diverges as ξ b .

X-Ray Observation of a Chemical Order Driven Morphological Transition on the Surface of anA3BType Alloy

Surface induced chemical disorder and step unpairing transition are investigated by grazing x-ray diffraction on a vicinal surface of an ${A}_{3}B$ type alloy $({\mathrm{Cu}}_{83}{\mathrm{Pd}}_{17})$. Both transformations occur below and close to the bulk order-disorder transition. The asymmetry of terraces and the order parameter reflecting chemical order in the surface layer are determined by measuring the shape of crystal truncation rods. Step unpairing and surface disordering are found to be continuous transitions.

Surface density oscillations in disordered binary alloys: X-ray reflectivity study of Cu 3 Au(001)

Au(001) surface using Synchrotron radiation and show that the intensity distribution along the specular rod exhibits the same features as in the case of liquid metals which has been discussed in recent literature. The results are discussed within the framework of the distorted wave Born approximation which allows a straightforward easy-to-apply scheme to analyze such reflectivity data in the entire -range including the total external reflection regime. The data analysis gives a direct evidence for an oscillating average density profile which is analoguous to the socalled surface layering at liquid surfaces. The experimental values for the thermal roughness indicate that surface roughness is suppressed in the ordered phase and allowed to softly grow with temperature above the bulk order-disorder phase transition. The presented experimental and theoretical study of X-ray reflectivity from binary alloys demonstrates the potential of this technique for the study of surface roughening, surface layering and surface segregation phenomena at solid and liquid surfaces.

Order-disorder phase transition of the Cu 3Au(100) surface studied by ToF-ion scattering

Cu 3Au(100) surface has been investigated with ToF-ISS at different temperatures below and above the bulk order-disorder transition temperature ( T c = 663 K). Grazing angle azimuthal scans on the surface reveal the crystallinity of the first monolayer. The polar scans measured by 2 keV Ne ion scattering aligned along the major orientations, i.e. 〈100〉 and 〈110〉, show that the surface is terminated at room temperature by an ordered and rippled CuAu layer. The 〈100〉 rows are alternatively pure Cu rows and pure Au rows while the 〈110〉 rows are made by an alternated sequence of Cu and Au atoms. When increasing the temperature close to T c, the Au focusing peak at low incidence, along the 〈110〉 rows, broadens in a first time owing to thermal vibrations, then shifts rapidly to higher incident angles when we approach the transition. This effect is interpreted as the result of the order-disorder transition at the surface, which modifies the ordered atomic sequence constituting the rows. By plotting the Au scattering yield vs. temperature at fixed azimuthal and incident angles, a strong decrease of the signal near the transition is observed. However, the transition is not abrupt, indicating possibly a second-order phase transition at the first monolayer, in opposition to the first-order'bulk transition.

Surface segregation in Cu 3Au(001)

In this work we report X-ray scattering studies of the Cu 3Au(001) surface for temperatures above the bulk order-disorder transition temperature T 0=390°C. The temperature dependence of the asymptotic Bragg tails normal to the surface gives direct evidence for an oscillatory, exponentially damped Au segregation profile. It turns out that the depth range (λ) of this surface segregation phenomenon is governed by the bulk correlation length ξ b and, thus, depends sensitively upon the temperature, in particular, we find that λ∝( T— T sp) − v upon approaching the ordering spinodal temperature T sp with v=0.49. The inplan of the asymptotic Bragg tails exhibits a broadening which changes characteristically with the normal momentum transfer L An intimate coupling between the terrace structure and the lateral coherence of the surface segregation profiles is found. First experimental results from experiments performed at the ESRF are presented which disclose surface segregation-related diffraction features in higher Brillouin zones normal to the surface. The sensitivity of this X-ray probe to details of the surface segregation profile is discussed and the experimental limits are indicated.

Direct Force and Friction Measurements Reflecting Structural Changes in Confined Diblock Copolymer Liquids

We have measured the normal and shear forces for a symmetric polystyrene-polyisoprene (PS-PI) diblock copolymer liquid in toluene, a good solvent for both blocks, between two mica surfaces. The aim was to investigate the structure of the macromolecular liquid when confined between surfaces separated by molecular-sized distances. The surface forces apparatus was used for these studies, and the microstructure was manipulated by varying the fraction of diblock in solution. Measurements of the equilibrium normal force profiles (intermolecular force versus separation distance between the confining surfaces) were made. All of these normal force profiles exhibited monotonic repulsive behavior. We found that in the disordered regime, as the fraction of diblock was increased, the intermolecular forces became much longer-ranged. As the fraction of diblock was further increased to concentrations near the bulk order-disorder transition (ODT), the ranges of the force profiles unexpectedly collapsed to shorter distances. In a series of dynamic surface forces experiments, the frictional force required to slide steadily one surface past the other with the macromolecular liquid intervening was measured as a function of shear rate. The shearing results reflected the same pattern of behavior exhibited in the normal force experiments. We determined that the frictional force of the most concentrated liquid was distinctly lower than that of the disordered samples at all shear rates and attribute both the equilibrium and dynamic results to be reflective to the inherent structure of the liquid. We believe that the reduction in the range of the normal force profiles and the reduction in frictional forces at the highest concentrations reflect pretransitional ordering in the confined sample. Our results are discussed in terms of surface-induced ordering and composition fluctuations, which are not accounted for in the mean-field description of polymer phase behavior.

Studies of Ordering in Small Particles

ABSTRACTDisordered clusters of the intermetallic compounds Ni3Al and Cu3Au have been produced using a high pressure sputtering technique. The clusters are either embedded in a film or studied, in-situ in an UHV electron microscope. The evolution of the ordered structure upon annealing is studied. Using a scanning transmission electron microscope, electron diffraction is obtained from individual clusters. Partial ordering is observed in Cu3Au clusters which have been annealed below the bulk order-disorder transition temperature. Under the experimental conditions, only clusters with sizes of 10–15 nm or larger show ordering.

Surface morphology change induced by bulk order-disorder transition in Cu3Au alloy

In recent years the surfaces of Cu3Au, a typical ordering alloy, have attracted interest from many aulhors[l-6], because the surface is a good example for testing general theories of the 2-D order-disorder phase transition, and also because it is a good material for studying the behavior of bimetallic alloy surfaces and their reactions with surface impurities. Previous work on Cu3Au surface mostly used macroscopic techniques and provided only information averaged over a largearea. In this work the microscopic imaging and diffraction methods are used to study the (111) surface on a more localized scale. Reflection Electron Microscopy (REM) was used to directly image the surface, and the selected-area RHEED was used to determine the local surface crystal structure and orientation.The samples used for observation are single crystal spheres prepared by melting a small piece of Cu3Au suspended on a thin Mo wire. The actual compositions of the samples are about Cu0.7Au0.3. The (111) facets on these spheres were then cleaned by the conventional ion-milling-heating method in a UHV environment.

001] Twist boundaries in Cu3Au for T ? 0 K

Four different [001] twist boundaries in Cu3Au spanning a wide range of the rotation angle are investigated for temperatures below the bulk order-disorder transition temperature. All the boundaries show almost identical behavior for the plane averaged stoichiometry and the order parameter at a given temperature. Within the accuracy of the calculations no segregation of either Cu or Au is observed to the boundary. At the boundary and below the transition temperature there is a layer which is more disordered than the rest of the crystal, and its width increases as the bulk order-disorder transition temperature is approached. This indicates wetting phenomena, which are in agreement with the experimental and theoretical results on other boundaries.