Ordering phenomena and phase transitions in the physisorbed quantum systems H2, HD and D2

Abstract Recent experimental results of H2, HD and D2 films physisorbed on graphite are briefly reviewed. In particular, the monolayer phase diagrams, the order-disorder transition of the commensurate (C) phase and the commensurate-incommensurate (C-IC) transition are discussed. It will be shown that the melting transition of the C phase belongs to the three-state Potts universality class, and that the C-IC transition occurs via a series of novel intermediate phase, which could be identified as density-modulated phases characterized by striped and hexagonal patterns of domain walls. Due to this rich variety of phenomena, the hydrogen isotopes can be considered as model systems for two-dimen…

Deuterium monolayers physisorbed on krypton-plated graphite: A two-dimensional Ising system

Abstract Neutron-diffraction measurements were used for the first time to investigate the influence of the modification of the graphite substrate potential and of the susbrate symmetry caused by a preadsorbed layer of krypton (Kr). It will be shown that D2 on Kr/graphite presents a new 2D Ising system. The order-disorder transition of this system has been studied.

Dipolar and orientational glass formation in two-dimensional films of CO mixtures

Heat-capacity and dielectric measurements have been performed to study orientational and dipolar order and disorder phenomena in submonolayer films of CO and binary mixtures of CO physisorbed on graphite and boron nitride (BN). With both methods transitions to quadrupolar and dipolar ordered low-temperature phases have been found for pure CO. Calorimetric measurements revealed that the dipolar transition of CO on graphite belongs to the universality class of the two-dimensional (2D) Ising model. It will be shown that in dilute mixtures of CO with CH 4 molecules a dramatic suppression of this phase transition occurs. This effect turned out to be much stronger than that previously observed in…

Thermal Excitation of Fourth Sound in Liquid Helium II

In narrow channels filled with helium II two wave modes propagate, fourth sound1–3 and the fifth wave mode.4–6 According to new results of theoretical studies,7–8 it has been predicted that it should be possible to excite both wave modes mechanically by vibrating the diaphragm of a condenser microphone as well as thermally by periodically heating the surface of a solid body (e.g., a resistance layer). Shapiro and Rudnick3 have produced and detected fourth-sound signals mechanically. In the present contribution it will be experimentally verified that it is also possible to excite fourth sound thermally. Since the theory7,8 gives the result that fourth sound can be generated thermally only if…

The commensurate-incommensurate transition of hydrogen monolayers physisorbed on graphite

We present a neutron diffraction study of the commensurate-incommensurate (C-IC) transition of hydrogen monolayers physisorbed on the basal planes of exfoliated graphite. It is shown that the solid intermediate phase detected by specific-heat measurements can be described in terms of a striped domain-wall phase with superheavy walls. Comparison with simple models with fixed domain sizes is made. The results are in agreement with recent LEED experiments of Cui and Fain and provide an experimental realization of C-IC transition theories.

Sound conversion phenomena at the free surface of liquid helium. I. Calculation of the coefficients of reflection, transmission, and transformation of sound waves incident on the liquid-vapor interface of helium

On the basis of a set of boundary conditions describing quite generally mass and energy transport processes across the free surface of helium II, the acoustic coefficients of reflection, transmission, and transformation of first sound, second sound, and the sound wave propagating in the vapor are calculated in the case of perpendicular incidence of sound waves against the liquid-vapor phase boundary. Considering rigorously the influences of the Onsager surface coefficients, the isobaric thermal expansion coefficients, and the thermal conductivities of the liquid and the vapor, we derive sets of equations from which the acoustic coefficients are determined numerically. For estimations, simpl…

Heat transport of helium II in restricted geometries

The linear heat transport of helium II contained in porous powder samples with mean pore diameters of 1.25µm, 0.17µm and 0.02µm was systematically studied in the temperature range between 0.8 K and 2 K. The effective thermal conductivity was determined by steady-state heat flow measurements and the effective thermal diffusivity by transitory temperature measurements. The experimental results are interpreted by a simple theoretical model. In the framework of this model the linear heat transport consists of two contributions: the laminar flow of the normal fluid (T≳1.4 K) and a diffusion mechanism (T≲1.4 K). At low temperatures (T≲1.2 K) the mean free paths of the elementary excitations of he…

Thermodynamic and neutron diffraction studies of the nucleation of solid4He on graphite

The nucleation of solid layers of4He on the surface of exfoliated graphite (Grafoil) was investigated by thermodynamic and neutron diffraction measurements. The thermodynamic measurements consisted of recording isopycnals in the vicinity of the melting curve. The isopycnals show a rounding in comparison to the bulk ones, which can be explained by a continuous solidification of4He on the surface of graphite in a layer-by-layer mode in the van der Waals field of the substrate. Moreover, we found a hysteresis behavior of the isopycnals, probably due to defect states in the solidified film. The thickness of the solid film is estimated by means of a simple solidification model. The neutron diffr…

Ellipsometric study of the physisorption of benzene on graphite

The optical thickness of benzene on the (001) surface of a graphite single crystal has been studied by ellipsometry. Ellipsometric adsorption isotherms have been measured in the temperature range from 180 to 290 K. The maximum thickness of the adsorbed benzene film is constant in this temperature range and compares favourably with the value expected for one monolayer of molecules lying flat on the surface.

Real-space observation of xenon adsorption and desorption kinetics on graphite (0001) by photoemission electron microscopy

Abstract The growth and desorption of Xe monolayers on the basal plane of graphite has been investigated by real-space imaging using photoemission electron microscopy. Adsorption kinetics was studied at different substrate temperatures (39–65 K), corresponding to different growth modes. Coexisting phases showed up as different grey values in the image. Typical domain sizes of the 2D solid phases around 60 K are of the order of one to several μm. The domains exhibit an elongated shape with their long axis oriented preferentially parallel to step edges of the substrate. With increasing coverage the brightness of the domains increases, the 2D gas-phase regions shrink and finally disappear at h…

Neutron scattering study of melting ofHe3surface layers

The melting of the incommensurate phase of $^{3}\mathrm{He}$ submonolayers adsorbed on Grafoil was investigated by elastic neutron scattering. The temperature dependence of the nearest-neighbor distance, the coherence length, and the peak intensity of the structure factor can be explained by a simple model assuming a melting transition which is driven by thermally created lattice defects.

MEASUREMENTS OF THE ATTENUATION OF FOURTH SOUND IN HELIUM II

Measurement of the velocity and attenuation of fourth sound in helium II

The velocity and the attenuation of fourth sound have been measured in liquid helium at temperatures between 0.8 K and the λ point, along the vapor pressure curve. The measurements were made using the resonance technique and the helium was contained between small pores in packed powder specimens. From the velocity, it could be determined that the sound propagates under “adiabatic” conditions. According to theory, the attenuation of fourth sound consists of two contributions: surface losses due to heat exchange with the resonator body and volume losses due to dissipative processes associated with the viscosity coefficients η and ζ3. The results of our attenuation measurements are in agreemen…

Diffusive motions in HD films physisorbed on graphite

Abstract High-resolution quasielastic neutron scattering was used to study diffusive motions in two-dimensional liquid and solid phases of deuterium hydride submonolayers adsorbed on graphite (Papyex). For the first time it could be unambiguously clarified that the novel reentrant fluid phase at the commensurate–incommensurate transition has the character of a viscous fluid.

Theoretical Studies of the Propagation of Sound in Channels Filled with Helium II

The two-fluid nature of liquid helium II leads to the possibility of several types of wave motion, e.g., first sound, second sound, fourth sound, and the fifth wave mode. First and second sound appear in the bulk liquid. The characters of these wave modes alter materially if helium is bounded by solid walls, e.g., between two plane-parallel plates forming a channel. This paper reports upon the calculation of the properties of wave modes which can exist in such channels.

Ordering and Phase Transitions in Adsorbed Monolayers of Diatomic Molecules

X-ray diffraction study of CF3Cl monolayers adsorbed on graphite (001)

X-ray diffraction experiments have been performed on mono- and submonolayers of CF3Cl physisorbed on the (001) surfaces of exfoliated graphite. Five quasi-twodimensional solid phases including the commensurate 2×2 phase, an electrically ordered phase and a disordered incommensurate phase have been observed. A phase diagram is proposed and the various phase transitions are discussed.

Realization of a two-dimensional Ising system: Deuterium physisorbed on krypton-preplated graphite

Volumetric adsorption isotherm, calorimetric, and neutron diffraction measurements were used to characterize the quantum system ${\mathrm{D}}_{2}$ coadsorbed on graphite preplated by a monolayer of Kr. From the results obtained by these methods a detailed phase diagram of the complete submonolayer coverage range up to the initial stages of bilayer formation could be constructed. The dominant feature of the phase diagram is a commensurate $(1\ifmmode\times\else\texttimes\fi{}1)[\frac{1}{2}]$ structure, which was determined by neutron diffraction. Three phase transitions of this phase were studied: The order-disorder transition at the critical point which, according to the influence of the co…

Thermodynamic and Neutron-Diffraction Studies of H2 and D2 Multilayers Physisorbed on Graphite

The evolution of physisorbed films from two-dimensional (2D) to bulk behavior is a topic of high current interest.1 In this context the behavior of the quantum systems H2, HD and D2 is of particular relevance because of the following reasons: 1. Due to the strong influence of the quantum zero-point energy the hydrogen isotopes are highly compressible. This leads to strongly compressed monolayers2,3 before further layer condensation occurs. This property makes these systems significant for the exploration of conditions of multilayer growth. It is generally believed,1,4–6 that the incompatibility between the adsorbate and bulk lattice structures gives rise to lateral strains between the overl…

Orientational Ordering ofN2OMolecules Adsorbed on Graphite (0001): A Novel Commensurate Pinwheel Structure

The structure and orientational ordering of N2O molecules physisorbed on graphite (0001) is investigated applying x-ray, neutron, and low-energy electron diffraction techniques. Combining the results of the three techniques, we find that N2O forms a highly ordered, hexagonal, commensurate (sqrt[21]xsqrt[21])R10.89 degrees phase. The unit cell contains seven molecules which are arranged in a seven-sublattice pinwheel structure, unexpected for linear molecules on a hexagonal lattice. Potential energy calculations corroborate these results.

Heat-capacity and neutron-diffraction studies of HD monolayers physisorbed on graphite

Abstract The phase diagram of HD monolayers physisorbed on graphite is studied in detail by using heat-capacity and neutron-diffraction measurements. The following features are observed: At low coverages the system forms a commensurate (C) (√3 × √3)R30° phase and at coverages near monolayer completion an incommensurate (IC) two-dimensional solid phase. The order-disorder transition of the C phase belongs to the three-state Potts universality class. The C-IC transition occurs via two intermediate phases, i.e., the α phase and a novel phase, which is interpreted as an α-IC coexistence region. Though the molecule HD is a strongly incoherent neutron scatterer, for the first time elastic neutron…

Specific heat studies of ortho-deuterium monolayers physisorbed on graphite

The specific heat of ortho-deuterium monolayers physisorbed on graphite (Grafoil) has been studied in detail at about 100 coverages in the total density range below monolayer completion and at temperatures between 2 and 40 K. Several interesting new features were observed: At the completion of the commensurate 3 × 33 R30° phase the system undergoes an order-disorder transition at T = 18.1 K. This temperature turns out to be 2.34 K lower than that of para-hydrogen on graphite, which elucidates the significant influence of the quantum zero-point energy on these systems. From the heat-capacity data a value of 0.31 ± 0.02 is deduced for the critical exponent a which is in good agreement with th…

Sound conversion phenomena at the free surface of liquid helium. II. Experimental determination of acoustic coefficients and surface absorption coefficients

The acoustic coefficients of reflection, transmission, and transformation of first-, second-, and gas sound waves incident normally on the free surface of liquid helium have been determined. The experimental results are compared with the theory developed in Part I of this paper. It is shown that equilibrium theories of boundary conditions disagree with the experiments. Nonequilibrium theories, however, which take into account that mass and energy transport processes occur at the liquid-vapor interface of helium II, lead to a very good description of the experimental data below 2 K. Within experimental accuracy the measurements fully confirm several kinetic models of evaporation and energy t…

Neutron-diffraction study of end-for-end ordering in commensurate submonolayers of carbon monoxide physisorbed on the graphite basal plane

The head-tail (dipolar) ordering in commensurate submonolayer films of carbon monoxide adsorbed on graphite recently observed in heat-capacity measurements for T < 5.18 K has been investigated by neutron diffraction. It will be shown that the experimental results are consistent with an end-for-end ordered commensurate herringbone structure.

Dipolar order and disorder phenomena in pure CO and dilute (CO)1−x(Ar)x mixtures physisorbed on graphite

Abstract A detailed heat capacity study has been performed to characterize the properties of pure CO and (CO) 1− x (Ar) x mixture films physisorbed on the basal planes of graphite. The phase diagram of CO monolayers will be presented. At T c =5.18 K a phase transition to a novel low temperature phase is found with head-tail (dipolar) order of the molecules in an orientationally ordered herringbone structure. The phase transition is shown to belong to the 2D Ising universality class with anisotropic interactions between the molecules. Diluting CO weakly with Ar impurities leads to a dramatic destruction of the phase transition. This effect can be quantitatively described by the 2D random fie…

Two-dimensional electrical ordering in physisorbed monolayers

Abstract Monolayers of polar molecules CF3H, CF3Cl and CF2Cl2 have been physisorbed on the graphite (001) surface and studied by X-ray diffraction and dielectric measurements. The temperature-coverage phase diagrams of the quasitwodimensional crystalline phases are presented. The structures of the paraelectric and the electrically ordered phases have been determined. The phase transitions are discussed.

THE THERMAL EXPANSION OF HELIUM II IN RESTRICTED GEOMETRIES

Theoretical studies of the propagation of sound in narrow channels filled with helium II. I. The dispersion relations of fourth sound and of the fifth wave mode

The wave propagation in helium II bounded by two plane-parallel plates forming a narrow channel is considered. The theory is based on the complete linearized set of the Khalatnikov equations. These equations are exactly averaged over the width of the channel taking into account the boundary conditions and symmetry relations. It is shown that in narrow channels three solutions of these equations exist; (a) fourth sound, (b) the so-called fifth-wave mode, and (c) another wave mode, which is very strongly damped. The dispersion relations of these wave modes are calculated with regard to all kinetic coefficients and to the coefficient of thermal expansion. The phase velocities and absorption co…

Observation of random-field behavior in (CO)1−x(N2)xmixtures physisorbed on graphite

Heat-capacity studies have been carried out on submonolayers of (CO${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{N}}_{2}$${)}_{\mathit{x}}$ mixtures physisorbed on graphite. We find that pure CO undergoes an end-to-end ordering transition at ${\mathit{T}}_{\mathit{c}}$=5.18 K, which is shown to belong to the two-dimensional Ising universality class. In diluting CO with ${\mathrm{N}}_{2}$ the heat-capacity peaks become progressively rounded until the phase transition is completely suppressed at a ${\mathrm{N}}_{2}$ concentration of only x=0.07. The analysis of the data shows that this behavior is in quantitative agreement with predictions of the random-field theory applied to adsorbed…