High-order Commensurate Phases Research Articles

A one-dimensional high-order commensurate phase of tilted molecules.

We report on the formation of a high-order commensurate (HOC) structure of 5,14-dihydro-5,7,12,14-tetraazapentacene (DHTAP) molecules on the highly corrugated Cu(110)–(2 × 1)O surface. Scanning tunnelling microscopy shows that the DHTAP molecules form a periodic uniaxial arrangement in which groups of seven molecules are distributed over exactly nine substrate lattice spacings along the [1̄10] direction. DFT-calculations reveal that this peculiar arrangement is associated with different tilting of the seven DHTAP molecules within the quasi one-dimensional HOC unit cell. The orientational degree of freedom thus adds a new parameter, which can efficiently stabilize complex molecular structures on corrugated surfaces.

Commensurate-incommensurate transition and strain relief patterns in monolayer C60 on Cd(0001)

We have studied the commensurate-incommensurate phase transition, rotation epitaxy, and strain relief patterns in ${\mathrm{C}}_{60}$ overlayers grown on Cd(0001) with a low-temperature scanning tunneling microscopy. When deposited at low temperature (\ensuremath{\sim}200 K), ${\mathrm{C}}_{60}$ molecules form the 10\ifmmode\times\else\texttimes\fi{}10 high-order commensurate (HOC) phase with two different half-unit cells, resembling the $\mathrm{Si}(111)\text{\ensuremath{-}}7\ifmmode\times\else\texttimes\fi{}7$ surface. Postannealing at room temperature (RT) results in the transition from HOC phase to incommensurate phase, in which strain relaxation takes place in the form of periodic vacancies and ${\mathrm{C}}_{60}$ heptamer arrays. In the case of RT deposition, parallel stripe domain walls appeared in the commensurate $2\sqrt{3}\ifmmode\times\else\texttimes\fi{}2\sqrt{3}$ R30\ifmmode^\circ\else\textdegree\fi{} phase. These results provide essential information for understanding the strain relaxation mechanism, and the role of substrate temperatures in the process of ${\mathrm{C}}_{60}$ thin films growth.

Dielectric susceptibility of quantum Ising model: Simulated monoclinic A2BX4-type ferroelectrics

To explain the anomalous increase in the permittivity of monoclinic Rb2ZnI4 at low temperatures, the dielectric susceptibilities of modulated structures are calculated. A quantum Ising model is reduced from a lattice Hamiltonian by the mean field approximation and two-quantum-level approximation. The susceptibilities of modulated phases remain to be finite values at zero temperature as in the uniform ferroelectric phase, if the quantum effect works. Furthermore, the susceptibilities of the incommensurate and high-order commensurate phases increase at low temperatures. Since the ferroelectric phase can be realized with accompanying strong discontinuity, such an increase is different from the phenomenon during the lock-in transition. The phase diagram and the temperature dependence of susceptibility are calculated. With the selection of a proper set of parameters, the theoretical results agree qualitatively with experimental reports of (Rb1−xKx)2ZnI4.

"Devil's staircase"-type phase transition in NaV2O5 under high pressure.

The "devil's staircase"-type phase transition in the quarter-filled spin-ladder compound NaV2O5 has been discovered at low temperature and high pressure by synchrotron radiation x-ray diffraction. A large number of transitions are found to successively take place among higher-order commensurate phases with 2a x 2b x zc type superstructures. The observed temperature and pressure dependence of modulation wave number q(c), defined by 1/z, is well reproduced by the axial next nearest neighbor Ising model. The q(c) is suggested to reflect atomic displacements presumably coupled with charge ordering in this system.

Adsorption and structure of N2 on Pt(111)

The adsorption and structure of monolayer N2 films on Pt(111) have been investigated in a combined experimental and theoretical study. Using specular helium scattering, the heat of adsorption for the unconstrained N2 monolayer was found to be q1=158±5meV per molecule, and the 2D heat of condensation was found to be q2D=21±3meV. At low temperature (20K), the nitrogen molecules arrange in a (3×3) high-order commensurate phase. This structure irreversibly transforms into a (4×4) structure after annealing at 40K or if N2 is directly adsorbed at this higher temperature. Increasing the coverage beyond completion of the unconstrained monolayer, the (3×3) phase experiences a Novaco–McTague rotation of±4.2° out of the [11̄0] high-symmetry direction and, in some cases, a secondary rotation by ∼19.8°. Based on realistic interaction potentials, the structure of the N2 monolayer is investigated by molecular dynamics simulations. The (3×3) and (4×4) structures are obtained as respective equilibrium structures for slightly different coverages with the same total binding energy per molecule in both cases. With increasing temperature, the (4×4) structure becomes the most stable phase. In the (3×3) phase, each unit cell contains four molecules, and the adlayer is aligned with the close packed direction of the Pt(111) substrate. The unit cell of the (4×4) phase contains seven molecules, and the close packed direction of the adlayer is rotated by 19.1° with respect to the substrate [11̄0] direction. Within the two structures, the molecules exhibit a different in-plane herringbone orientational order. Furthermore, the molecular dynamics simulations provide evidence for an orientational transition within the (4×4) phase at about 30K.

Adsorption and structure of N 2 on copper(110)

The adsorption and structure of ultrathin physisorbed N 2 films on Cu(110) has been investigated in a combined experimental and theoretical study. Using specular helium scattering the heat of adsorption for the unconstrained N 2 monolayer was determined to q st = 88 meV per molecule and the 2D heat of condensation to q 2D = 5.5 meV. In the coverage range up to one monolayer the nitrogen molecules form a complex ( 4 1 1 3 ) high-order commensurate phase with an oblique, quasi-hexagonal unit cell. Increasing the coverage beyond completion of the unconstrained monolayer, the adlayer first undergoes a phase transition into a weakly compressed phase before the condensation of the bilayer sets in. In the bilayer the N 2 molecules are arranged in a slightly distorted hexagonal structure. Using realistic interaction potentials, the structure of the N 2 monolayer is investigated by detailed total energy calculations. As a result, the most stable structure is found to be the ( 4 1 1 3 ) phase in agreement with experiment. In addition, the arrangement of the nitrogen molecules has been determined: the unit cell contains seven N 2 molecules arranged in a novel type of 7-sublattice pinwheel structure. Molecular dynamics simulations corroborate this structure and further demonstrate its remarkable thermal stability.

Influence of mode polarizations on the inelastic He-scattering spectrum: High-order commensurate Xe monolayer adsorbed on Cu(110)

The phonon dispersion curves for monolayer Xe adsorbed on Cu(110) were measured along the {ovr {Gamma}}{ovr X} and {ovr {Gamma}}{ovr Y} directions using inelastic He scattering. The dispersion along these two orthogonal high-symmetry directions is fundamentally different as a consequence of the substrate anisotropy. Coupled dynamics calculations using a slab model are performed on the square low-order commensurate c(2{times}2) structure and on the (26{times}2) high-order commensurate phase of the Xe monolayer, the latter being stable at low temperature. The calculations allow a quantitative interpretation of the hybridization and avoided crossings between the longitudinal and perpendicular monolayer branches and the Rayleigh mode along {ovr {Gamma}}{ovr X}. They can also account for the unexpected behavior of the monolayer longitudinal mode along {ovr {Gamma}}{ovr Y}, revealing a different type of dynamical coupling between this monolayer branch and the longitudinally polarized Rayleigh mode of the substrate. This coupling is responsible for a polarization exchange by which both modes become susceptible to He scattering detection. {copyright} {ital 1997} {ital The American Physical Society}

Orientational Ordering on a Corrugated Substrate: Novel Pinwheel Structure forN2Adsorbed on Cu(110)

The structure and orientational ordering of ${\mathrm{N}}_{2}$ molecules adsorbed on the Cu(110) surface is investigated in a combined experimental and theoretical study. Using He atom diffraction we find that monolayer ${\mathrm{N}}_{2}$ forms a high-order commensurate phase with an oblique unit cell. Minimum energy calculations based on realistic potentials show that the unit cell contains seven ${\mathrm{N}}_{2}$ molecules arranged in a novel type of pinwheel structure unexpected for linear molecules adsorbed on a smooth surface. Molecular dynamics simulations corroborate this structure and its remarkable thermal stability.

Effects of a magnetic field on a modulated phase

The effects of a magnetic field on a modulated phase are studied. A modulated phase is found to have two critical fields H 1 and H 2. For a large enough magnetic field, H 1 and H 2 can be approximated by a linear law. As a result, the minimum magnetic field needed to destroy a modulated phase is a constant. The minimum magnetic field also greatly depends on the order of a commensurate phase. A very high order commensurate phase and an incommensurate phase cannot survive a magnetic field. The behaviour of a magnetoelastic chain in a magnetic field can be described by a harmless devil's staircase. The inverse temperature is found to play a role similar to that of a special magnetic field. The deeper physics underlying these new phenomena is the breaking of the left-right symmetry of a phase diagram. As a result a controllable path to a modulated phase is found.

Structure and phase transitions of xenon monolayers on Cu(110)

The structure of xenon adsorbed on the Cu(110) surface was determined in a combined experimental and theoretical study. The experimental results were obtained using helium-atom diffraction. In the entire temperature and coverage regime studied (20 K ≤ T s ≤ 70 K and Θ < 1 monolayer) the xenon adlayer can be described in terms of ( n × 2) high-order commensurate (HOC) structures, with n ≥ 7. As a result of the weak commensurability along the [11̄0] direction, a series of uniaxial first-order phase transitions between ( n × 2) structures with different n is observed as a function of coverage and annealing temperature. In most cases these transitions are not completely reversible, indicating that the apparent stability of some of the HOC phases might be due to kinetic limitations, i.e. an effective “pinning” of the adlayer by the substrate. Along the highly corrugated [001] direction, the adlayer is in perfect registry with the substrate lattice. Inside the ( n × 2) unit cell, the xenon atoms form a quasi-hexagonal array. The experimental data were compared to the minimum free-energy configurations of the xenon adlayer calculated for surface temperatures between 0 and 75 K. These calculations are based on parameterized interaction potentials fitted to the measured thermodynamic properties of xenon on Cu(110). The experimental results, in particular the stability of the various HOC phases and their sequence with temperature, is well reproduced by the calculations assuming a corrugation of the holding potential along the [11̄0] direction of about 4 meV. The energy difference between the most stable HOC structures is found to be quite small, in agreement with the observed “metastability” of the structures. The calculations further reveal that the details of the sequence and the temperature range of stability of the HOC phases strongly depends on the corrugation and the exact lattice misfit.

Domain walls and adsorbate-step interactions: an STM study of sulphur layers on Ru(0001)

The local configurations of chemisorbed sulphur on Ru(0001) were studied by STM at various coverages above Θ = 0.33 in phases with and without long range order. Sulphur was found to adsorb only in (or close to) threefold sites (fcc and hcp sites) at all coverages. Only four structural elements (p(2 × 2), (√3 × √3)R30°, c(2 × 4) and (√7 × √7)R19.1°) seem to exist in this system over the full coverage range. They form all long range ordered and one glass-like phase. These structural elements, only two of which coexist at a given coverage, are also combined to form domain wall phases and a high-order commensurate phase. The insertion of additional atoms into a pure phase of one structural element always results in domain wall formation. These walls repel each other in the domain wall phase at coverages 0.33 < θ < 0.5 and form a long range ordered phase of striped superheavy domain walls. The walls in the c(2 × 4) phase for θ < 0.5, however, are attractive, but instead of simple phase separation a short range ordered glass phase with units of c(2 × 4) and (√7 × √7)R19.1° as structural elements results. Step morphologies as well as the local structure of the adsorbate were found to depend on average sulfur concentration. For the glass phase a coupling mechanism between different terraces could be identified.

Commensurate and modulated magnetic phases in orthorhombic AC60 (A=K,Rb).

Competing magnetically ordered structures in polymerized orthorhombic A1C60 are studied. A mean-field theory for the equilibrium phases is developed using an Ising model and a classical Heisenberg model to describe the competition between inter- and intra-chain magnetic order in the solid. In the Ising model, the limiting commensurate one-dimensional and three-dimensional phases are separated by a commensurate three-sublattice state and by two sectors containing higher-order commensurate phases. For the Heisenberg model the quasi-1D phase is never the equilibrium state; instead the 3D commensurate phases exhibits a transition to a continuum of coplanar spiral magnetic phases.

Interpretation of high-order commensurate phases for an argon monolayer adsorbed on Pt(111).

Interpretation of high-order commensurate phases for an argon monolayer adsorbed on Pt(111).

Scaling of island growth in Pb overlayers on Cu(001).

The growth and ordering of a Pb layer deposited on Cu(001) at 150 K has been studied using atom beam scattering. At low coverage, ordered Pb islands with a large square unit cell and nearly hexagonal internal structure are formed. This is a high order commensurate phase with 30 atoms in the unit cell. From the measurement of the island diffraction peak profiles we find a power law for the mean island - size versus coverage with an exponent $n=0.54 \pm 0.03$. A scaling behavior of growth is confirmed and a simple model describing island growth is presented. Due to the high degeneracy of the monolayer phase, different islands do not diffract coherently. Therefore, when islands merge they still diffract as separate islands and coalescence effects are thus negligible. From the result for $n$ we conclude that the island density is approximately a constant in the coverage range $0.1 < \Theta < 0.5$ where the ordered islands are observed. We thus conclude that most islands nucleate at $\Theta < 0.1$ and then grow in an approximately self similar fashion as $\Theta$ increases.

Effect of hydrostatic pressure on the modulated structure of deuterated betaine calcium chloride dihydrate.

In this work we present a study of elastic neutron scattering in deuterated betaine calcium chloride dihydrate under hydrostatic pressure. This study provides clear evidence for the existence of a large number of high-order commensurate phases induced by pressure. Structural branching processes as predicted by the analysis of axial next-nearest-neighbor Ising models have been observed.

Effect of hysteresis on the phase transition between high-order commensurate phases

We argue that the phase transition between two high-order commensurate phases and the transition between two modulation wave vectors in the incommensurate phase, can be of the first order. The transition starts from the nucleation of stripple, critical energy of which increases with increasing modulation amplitude. High nucleation energy involves a considerable hysteresis, width of which might even exceed the stability intervals of the high-order commensurate phases. Hence, diffraction measurements made on such states do not allow to detect all high-order commensurate phases.

Dielectric constant in electric field biased deuterated betaine calcium chloride dihydrate

The effect of bias fields on the temperature dependence of the dielectric constant along [010] in incommensurate deuterated betaine calcium chloride dihydrate (D-BCCD) is reported. The results show that the main dielectric anomalies along this direction are very sensitive to d.c. fields favouring the homogeneous nucleation of different polar high order commensurate phases.

Triple chain model of the reconstructed Mo(001) surface.

We have studied the high-order commensurate phase of the clean Mo(001) surface at about 100 K with surface x-ray diffraction. Our quantitative structure analysis demonstrates the relevance of the periodic lattice distortion model, but the detailed displacement pattern is closer to a square wave than a sine wave. This probably arises from specific bonding, similar to that seen in W(001).

Structure of monolayer Ar on Pt(111): Possible realization of a devil's staircase in two dimensions.

The structure of Ar physisorbed on Pt(111) in the submonolayer-coverage regime has been explored by thermal He-atom scattering. On the clean Pt(111) surface Ar condenses in a hexagonal close-packed phase aligned with the substrate. At coverages \ensuremath{\Theta}\ensuremath{\lesssim}0.7 ML the Ar adlayer lattice parameter is about 3.81 \AA{}. When the Ar coverage increases above 0.75 ML a first-order phase transition into a compressed hexagonal Ar phase with a lattice constant of 3.70 \AA{} is observed. From thermal-expansion measurements and the appearance of superlattice diffraction peaks, the compressed phase is demonstrated to be a high-order commensurate phase, characterized by a (4\ifmmode\times\else\texttimes\fi{}4)R0\ifmmode^\circ\else\textdegree\fi{} commensurate unit cell containing nine argon atoms. We have found experimental evidence for further high-order commensurate phases also in the low-Ar-coverage regime. Therefore the phase diagram of the Ar/Pt(111) physisorption system is likely to be a realization of a devil's staircase in two dimensions.

Three-dimensional structure of the ordered phases of Hg on Cu(001).

The structures of ordered phases following adsorption of mercury on Cu(001) have been identified using helium-beam scattering and low-energy electron diffraction. We found that three of the four observed ordered submonolayer phases are high-order commensurate phases. The three-dimensional structure of these phases brought about by a periodic variation of the height of the Hg atoms above the Cu(001) plane has been measured. Furthermore, from a combined analysis of helium-beam scattering and angle-resolved photoemission data for a low-density Hg ordered overlayer, we deduce and quantify the departure from the atomic electron distribution of Hg due to adsorption. A model to analyze diffraction data from all these phases is also presented. We show that second-layer structural and electronic properties are influenced by those of the first layer. Adsorption at the lowest substrate temperature obtainable proceeds in a layer-by-layer mode up to three layers.