Two-dimensional Long-range Order Research Articles

Changes in Pt(111) Two-dimensional Long-range Order Induced by Slow Mercury Adsorption and Alloying

A long-term cyclic voltammetry study of Pt(111) electrode in dilute solutions of mercury sulfate (5 × 10–8–5 × 10–7 M Hg2SO4 + 0.5 M H2SO4) has shown that a slow transformation of Pt(111) surface takes place. This transformation leads to a decrease in the bi-dimensional long-range order of the surface. The interpretation of the process involves the increase in mobility of Pt atoms and surface alloying in the presence of mercury. Similar processes of Pt(111) surface disordering take place in acid solution of copper sulfate with the addition of Hg2SO4. The penetration of Hg atoms beneath the Pt(111) topmost layer proceeds when only a fraction of the mercury monolayer is deposited on the electrode surface.

Electron diffraction study on the long-range-ordered metastable Fe-Nd-B phase

Abstract We report a new long-range ordered phase formed in the spherulites of an annealed melt-spun Fe89Nd7B4 ribbon. This ordered phase appears in the intermediate stage of the crystallization process of the amorphous alloy and is thus metastable. The unit cell is based on the D03 structure, in which 4a or 4b (multiplicity and Wyckoff letter) sites are occupied by Nd and a portion of Fe atoms. Long-range ordering occurs in the [100] and [110] directions, with respective displacement vectors of ¼[111] and ½[001] of the D03 unit cell at antiphase boundaries. The [110] diffraction pattern clearly indicated the presence of the two-dimensional long-range order with superperiods M = 5.5 and 6.0 in the [001] and [110] directions respectively. Dark-field images revealed that the spherulites initially crystallize into a disordered bcc Fe phase and that the ordering proceeds as the spherulites grow.

Detailed analysis of the voltammetry of Rh(111) in perchloric acid solution

The preparation and surface treatment of a rhodium single crystal with (111) orientation are described. Surface characterization by scanning tunnelling microscopy (STM) in air, including topography and atomic-scale pictures, is reported. Hexagonal surface domains one atomic diameter thick are observed with edges parallel to the dense rows of the basal orientation; three or four atomic levels are included in this distribution. The atomic resolution reveals a surface lattice with the 2 x 2 periodicity, probably formed by oxygen adatoms. The voltammetric electrochemical study was carried out using perchloric acid solution which is known to give a reduction of the perchlorate anion at an Rh electrode. The reduction of perchlorate is revealed at low sweep rates. The effect of the formation of chloride anions or other anionic reduction products on the voltammetric response of this electrode was investigated in detail. A dramatic effect was found regarding the unusual reversible adsorption state around 0.6 V, which is very often compared with the unusual adsorption state of Pt(111) in the same solution. A quantitative analysis of the various adsorption states is given. The unusual state is shown to be sensitive to the electrochemical oxidation of the surface above a potential threshold of 1.080 V (RHE), similar to the behaviour of Pt(111). The presence of this state is thus shown to be characteristic of two-dimensional long-range order.

A possible new FeCu alloy phase with two-dimensional long-range order

A possible new FeCu alloy phase with two-dimensional long-range order

Electrochemical study of step reconstruction on platinum surfaces belonging to the [0 [formula omitted]1] zone between Pt(311) and Pt(111)

In this paper we present experimental results concerning the effect of thermal and electrochemical oxygen adsorption on the surface structure of platinum faces vicinal to Pt(111) in the [0 1 1] zone whose ordered equilibrium surface structure, when clean, is denoted by Pt(S)[ n (111)×(100)]. Two different types of electrochemical behaviour have been observed depending on terrace width. Under the effect of oxygen adsorption, surfaces with n ⩾ 4 develop a well-marked adsorption state at 0.115 V which reflects the formation of (110) sites to the detriment of the (100) step sites which would normally correspond to the orientation of the sample. This phenomenon can be avoided by cooling the sample under an H 2 + Ar atmosphere, or the step order can be almost totally restored by applying a fast cycling treatment under the same conditions as those used to restore the two-dimensional long-range order in Pt(100) samples. A hard-sphere model of the perturbed surfaces based on a (100) step reconstruction is used to analyse quantitatively the corresponding voltammograms leading to results in agreement with the geometry of the (110) kink sites formed after oxygen desorption. The electrochemical behaviour of orientations with n ⩽ 4 has also been studied. The absence of the adsorption state related to (110) sites after oxygen adsorption-desorption indicates the stabilization of (100) sites when narrow terraces are intrinsic to the orientation of the sample. For Pt(311), representing the turning point of the [0 1 1] zone, analysis of the voltammograms obtained after thermal or electrochemical oxygen adsorption reveals the existence of a microfaceting process leading to the formation of multi-atomic (100) and (111) microfacets no wider than three or four atomic rows.

The role of the crystalline surface structure of platinum electrodes in the electrooxidation of d-glucose in acid solutions : Part I. Pt(100) and vicinal faces: The effect of two-dimensional long-range order

Glucose electrooxidation on Pt(100) and on a set of stepped surfaces containing (100) terraces has been investigated in sulphuric and in perchloric acid media. A concentration of 10 −2 M has been chosen from the study of the glucose concentration effect which shows that higher concentrations favour the inhibition of the oxidation reaction on (100) sites. This voltammetric study suggests that in the various steps of the glucose oxidation process a dual path mechanism develops, one of them involving active intermediates, the other one leading to poisoning species responsible for the blocking of the surface electrode. The blocking species is formed during glucose electrooxidation. Thus, this species was formed at a controlled potential, then isolated and identified electrochemically as CO by using a modification of the dissociative adsorption technique. The role of the dimension of the (100) domains on the formation of this species has also been investigated showing that wide (100) surface domains are blocked preferentially. The oxidation rate of the active intermediates increases also when the dimensions of the (100) domains increase as follows from both the effect of cooling conditions during the thermal treatment of Pt(100) and the behaviour of stepped surfaces with increasing (100) terrace widths. In the latter case linear relations between the glucose oxidation rate and (100) terrace site density are found both in sulphuric and in perchloric acid media for surfaces containing wide (100) terraces. An oxidation step appearing at 0.31 V specific to perchloric acid medium for air cooled Pt(100) samples as well as for surfaces containing narrow (100) terraces is ascribed to glucose oxidation on (100) terrace edge sites. This kind of site would remain blocked for glucose oxidation by adsorbed bisulphate anions in sulphuric acid medium.

Electrochemical monitoring of the thermal reordering of platinum single-crystal surfaces after metallographic polishing from the early stage to the equilibrium surfaces

In this paper the voltammetry of hydrogen adsorption-desorption on platinum is presented as an alternative standard laboratory method to monitor a complex surface reorganization process such as that occurring during the thermal reordering of the thick perturbed layer resulting from the polishing of oriented platinum samples. By using an electrochemically perturbed Pt (111) surface as a test surface sensitive to atomic reorganization, a thermal decontamination procedure has been developed which allows the cleaning of a disordered platinum surface with minimum change in its initial crystalline structure. This decontamination procedure has been applied successfully to newly polished Pt (111), (100), (110) and (775) surfaces. After decontamination, no preferential site distribution relative to their crystalline direction is detected as resulting from polishing. The modification of the clean perturbed surface during annealing to its final equilibrium state is described, giving evidence for the disappearance of the surface defects. The significant diminution of the mean total electric charge during the reordering process is related to the elimination of the microroughness present on the newly polished surfaces. The effect of a cooling atmosphere, either air or a H 2-Ar stream, after the flame-cleaning procedure was also studied with the well-ordered samples. Major differences for the two types of cooling were observed for Pt (100), giving rise to two types of voltammograms, while for Pt (111) no difference was detected. The differences are interpreted in terms of surfaces with different degrees of two-dimensional long-range order. On the other hand, it is demonstrated that the rearrangement of randomly distributed (110) sites in steps with long-range order along the step rows makes the corresponding hydrogen adsorption state narrower.

Reconstruction on rows and steps of Si(112) and Si(223)

We have investigated Si(112) and Si(223) by using scanning tunneling microscopy and low-energy electron diffraction. A well-developed two-dimensional long-range order of atomic structures in the corresponding macroscopic orientations could not be observed in the present experiment. Instead, the surfaces exhibited large facets of 7×7 reconstructed Si(111) and various modes of local reconstructions, which predominantly occurred on rows and steps in the [1̄10] direction. A frequently observed doubling of periodicity could in either case be explained by dimerization of atoms or by the presence of adatoms. On Si(223) a fivefold periodicity of the ideal atomic distance along [1̄10] was found in addition.

Ordered interface phases and segregation equilibria

AbstractAny interaction between segregating atoms and/or between segregating and matrix atoms can lead to two-dimensional long-range order (LRO) within the segregated layer if the temperature is low enough. Long-range order has a strong influence on the segregation isosteres; it can eventually introduce completely new phenomena such as phase separation. It is studied within the framework of the Ising model using exact series expansions. Segregation isosteres are given for various bulk concentrations, values of segregation, and interaction enthalpies both for ‘ferromagnetic’ LRO (attractive interaction between like atoms) and ‘antiferromagnetic’ LRO (attraction between unlike atoms). Asymptotic formulae for some limiting cases and a simple procedure to extract the values of the parameters from certain experiments are described, and a comparison with experimental results is shown to yield consistent thermodynamic data.

Spin fluctuations in random magnetic-nonmagnetic two-dimensional antiferromagnets. II. Heisenberg percolation

In this paper we report an extensive study using neutron scattering techniques of the spin fluctuations in the two-dimensional diluted near-Heisenberg antiferromagnet ${\mathrm{Rb}}_{2}{\mathrm{Mn}}_{c}{\mathrm{Mg}}_{1\ensuremath{-}c}{\mathrm{F}}_{4}$. The concentrations studied are $c=0.54$, $c=0.57$, and $c=0.60$; the site-percolation concentration for the nearest-neighbor square lattice is ${c}_{p}=0.593$ so that these experiments span the percolation threshold. The point $c={c}_{p}$, $T=0$ represents the percolation multicritical point which terminates the line of second-order transition of the infinite network. We give a detailed description of the theory of the magnetic behavior around the percolation point; as the temperaturelike scaling field we suggest $\ensuremath{\mu}(T)={\ensuremath{\kappa}}_{1}(T)$ where ${\ensuremath{\kappa}}_{1}(T)$ is the inverse correlation length for the associated one-dimensional chain; for the static structure factor we propose the formula $\mathcal{S}(|{c}_{p}\ensuremath{-}c|,\ensuremath{\mu},\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}})\ensuremath{\propto}{\ensuremath{\kappa}}^{\ensuremath{\eta}}{({\ensuremath{\kappa}}^{2}+{Q}^{2})}^{\ensuremath{-}1}$, where $\ensuremath{\kappa}=\ensuremath{\kappa}(|{c}_{p}\ensuremath{-}c|,0)+\ensuremath{\kappa}(0,\ensuremath{\mu})$; that is, we assume that the geometrical and thermal inverse correlation lengths are simply additive. The $c=0.60$ sample is found to have a smeared second-order phase transition at about 8 K to a state with two-dimensional long-range order but only weak correlations in the third direction. The spin fluctuations in the precritical region are essentially identical to those in the concentrated systems, thus demonstrating that the phase transition in the $c=0.60$ infinite network is little affected by the proximity to the percolation threshold. For the $c=0.54$ and $c=0.57$ samples the correlation lengths and susceptibility increase with decreasing temperature down to about 3 K, below which temperature they saturate; for both samples the inverse correlation length is well described by the simple formula $\ensuremath{\kappa}=\ensuremath{\kappa}(\ensuremath{\Delta}C,0)+{[{\ensuremath{\kappa}}_{1}(T)]}^{0.9\ifmmode\pm\else\textpm\fi{}0.05}$; the susceptibility follows the law $\mathcal{S}(0)\ensuremath{\sim}{\ensuremath{\kappa}}^{1.5\ifmmode\pm\else\textpm\fi{}0.15}$; both results are consistent with our scaling crossover formula and the assumption of the importance of the underlying one-dimensional links in the percolation clusters. The corresponding thermal critical exponents are ${\ensuremath{\nu}}_{T}=0.9\ifmmode\pm\else\textpm\fi{}0.1$ and ${\ensuremath{\gamma}}_{T}=1.5\ifmmode\pm\else\textpm\fi{}0.15$ compared with the percolation exponents ${\ensuremath{\nu}}_{p}=1.36$ and ${\ensuremath{\gamma}}_{p}=2.43$, so that the experimental crossover exponent is $\ensuremath{\varphi}=1.56\ifmmode\pm\else\textpm\fi{}0.15$. There is currently no first-principle theory which properly accounts for this value of the crossover exponent, although the experiment includes within the errors the value $\ensuremath{\varphi}=1.7$, appropriate to a self-avoiding walk ansatz for the principal paths along which the correlations spread.

Neutron scattering from Rb2CocMg1-cF4: observation of two-dimensional magnetic long-range order

The elastic magnetic scattering from a series of compounds exhibiting two-dimensional Ising-like antiferromagnetic behaviour, Rb2CocMg1-cF4 (c=1.00, 0.89, 0.85 and 0.70), has been examined below their Neel temperatures. The magnetic scattering from Rb2Co0.7Mg0.3F4 takes the form of almost smooth elastic Bragg rods along the c direction rather than points in reciprocal lattice space, and provides the best approximation yet found to an ideal two-dimensional long-range order. This two-dimensional magnetic long-range order is found to depend strongly on the heat treatment of the crystals and on the concentration of Mg ions, becoming less pronounced as the concentration decreases.

The structure of amorphous solids

INTRODUCTION Before the discovery of x-ray diffraction it was relatively easy to make definite statements about 'crystalline' and 'amorphous': if the outer contours of a material showed crystal faces it was considered to be crystalline, a material showing irregular contours without faces was considered amorphous. In fact, such a definition makes proper use of the word 'amorphous', the etymological meaning of which is 'without form' and not 'disordered structure'. After the discovery of x-ray diffraction many of the substances considered as amorphous turned out to be micro-crystalline and, since the internal structure is by far more essential for the understanding of the solid state than the outer contours, the word 'amorphous' was more and more used in the sense 'disordered structure' or 'frozen-in liquid structure' which means that an amorphous structure is considered essentially 'non-crystalline' and with some resemblance to the structure of liquids. It was especially the latter aspect which was pursued in the earlier studies of the glass structure1' 2 and in the interpretation of rubber elasticity3—6. The most general statement one can make about the difference between 'crystalline' and 'amorphous' is that the former implies a three-dimensional long-range order whereas the latter does not. Since intermediate structures with one-dimensional or two-dimensional long-range order exist (e.g. in liquid crystals) and the term 'amorphous' is in general not used for such structures, it is more appropriate to use the term 'non-crystalline' for all structures which do not possess a three-dimensional long-range order and reserve the term 'amorphous' for those structures which do not have a long-range order in any direction. General agreement exists as far as the absence of long-range order is concerned; however, there is a definite disagreement about the basic feature of the short-range order in liquid and liquid-like structures. One school, of which the main protagonist is Bernal7, postulates that this shortrange order bears no resemblance whatsoever to the crystalline order whereas the other, of which the principal advocate is Hosemann8, considers a 'paracrystalline' structure as representative for all types of short-range order. The attraction of the 'paracrystalline' concept is its relatively concise theory which greatly facilitates the interpretation of scattering diagrams, whereas the Bernal model does not lend itself easily to a straightforward mathematical treatment so that a quantitative check of its validity by scattering experiments is extremely difficult. It is not the aim of this paper to review the earlier work done in this field, for which one finds an excellent bibliography by Kruh9, but to discuss some