Orientational Order-disorder Phase Transition Research Articles

Collective pattern formation in a binary mixture of self-propelled particles

We have studied the collective behaviour of a binary mixture of self-propelled particles (SPPs) with non-identical motile properties. The two types of SPPs with low and high velocity is modelled in a two-dimensional system with periodic boundary conditions (PBCs) at a fixed particle density. The two types have two widely different velocities. The alignment interaction rule and angular noise similar to Vicsek Model (VM) is implemented in this model. Both inter and intra-particle interactions are considered among the SPPs. The system exhibits various self-organised pattern formation and phase segregation which mainly depends on the angular noise present in the system. Without any restriction of interaction or repulsion among the particles, the SPPs phase-separated into dense structures. The orientational order-disorder phase transition is studied, and nontrivial results are obtained. Cluster size distribution (CSD) for the entire system is also studied at the transition region. The CSD exhibits a power-law behaviour at the transition, with an exponent that of the standard percolation.

Dramatic softening of the negative thermal expansion material HfW2O8 upon heating through its WO4 orientational order-disorder phase transition

HfW2O8 undergoes a dramatic softening where the average bulk modulus (P = 52–414 MPa) drops from 69 GPa at 298 K to 48 GPa at 430 K as the temperature of the WO4 orientation order-disorder transition is approached. This is accompanied by increasingly negative thermal expansivity (−10 ppm·K−1 to −15 ppm·K−1) and reversible WO4 orientational disordering upon compression in α-HfW2O8. Additionally, α-HfW2O8 becomes elastically softer upon compression at constant temperature. The α→β phase transition temperature decreases by ∼30 K between 52 and 414 MPa. Above this phase transition, no further temperature-dependent softening or pressure-dependent changes in the coefficient of thermal expansion occurred.

Path-integral Monte Carlo study of asymmetric quantum quadrupolar rotors with fourth-order propagators

The recently-proposed fourth-order propagator based on the multi-product expansion has been applied to path-integral Monte Carlo calculations for asymmetric quantum quadruploar rotors fixed at face-centered cubic lattice sites. The rotors are observed to undergo an orientational orderdisorder phase transition at a low temperature when the electric quadrupole-quadrupole interaction is strong enough. At intermediate interaction strength, a further decrease of temperature after the first transition to the ordered phase results in a reentrant transition back to the disordered phase. The theoretical phase diagram of these asymmetric rotors determined by using fourth-order path-integral Monte Carlo calculations is found to be in good quantitative agreement with the experimental one for solid hydrogen deuteride. This leads us to conclude that the fourth-order propagator can be effectively implemented for an accurate path-integral Monte Carlo calculation of a quantum many-body system with rotational degrees of freedom.

Friction and Adhesion between C60 Single Crystal Surfaces and AFM Tips: Effects of the Orientational Phase Transition

We have investigated the nanotribological properties of C60 single crystal (111) and (100) surfaces around its orientational order-disorder phase transition temperature, approximately 260 K, by atomic force microscopy and frictional force microscopy (AFM/FFM) in high vacuum. Results show that for both surfaces across the phase transition temperature, the friction force and the adhesive force between a C60 coated AFM tip and the C60 crystal surfaces exhibit discontinuous behavior. The friction force within the applied external load range in the low temperature phase is significantly larger than that in the high temperature phase, with no obvious change in the slope of the friction force curves (the friction coefficient) in the low and high temperature phases. The abrupt change in friction was found to be caused mainly by the abrupt change in adhesion, which, in turn, can be qualitatively understood through changes in the van der Waals interaction and the short-range Coulomb interaction associated with the structural changes across the phase transition. Compared to most other degrees of freedom, the rotation of C60 molecules was found to have little effect on friction and is an ineffective energy dissipation channel.

Neutron powder diffraction study of the orientational order–disorder phase transition in calcite, CaCO3

Neutron powder diffraction studies of calcite on heating towards the orientational order–disorder phase transition show that the phase transition is not a simple analogue of an Ising-like transition, but more similar to a rotational analogue of Lindemann melting. The transition is precipitated by the librational amplitude of the carbonate molecular ions exceeding a critical value rather than a result of a statistical entropy of ‘wrong’ orientations. Using tested interatomic potentials the single-particle orientational potential and nearest-neighbour orientational interactions have been calculated.

Effect of C60 molecular rotation on nanotribology.

The effect of C60 molecular rotation on the nanotribological properties of C60 single crystal surfaces has been studied by atomic/frictional force microscopy. The orientational order-disorder phase transition, in which the high temperature C60 free rotation is reduced to a low temperature hindered rotation, is shown to give rise to an abrupt change in friction and adhesion. This change in frictional force is quantitatively consistent with the observed change in adhesion. The similar slopes of the friction versus load curves in both phases indicate that the friction coefficient in the two phases remains about the same. Hence the C60 rotation does not provide an additional energy dissipation channel in the friction process.

Orientationally disordered solid monolayers of tetramethylsilane on graphite and a bilayer nature of the 2-D fluid

A calorimetric investigation of the monolayers (MLs) of tetramethylsilane (TMS) adsorbed on graphite demonstrates two remarkable features: (i) occurrence of an orientational order–disorder phase transition in the 2-D solid (at 107 K at the coverage θ<1 and at 138 K at 1< θ<2) accompanied by a large entropy change (ranging from Rln8 to Rln3) depending on the coverage, and (ii) possible formation of a fluid bilayer around 220 K, above the 2-D critical temperature. A high-resolution incoherent neutron scattering experiment reveals a considerable motional disorder in the disordered 2-D solid.

Ground state of the quantum anisotropic planar rotor model: A finite size scaling study of the orientational order–disorder phase transition

The ground state properties of the quantum anisotropic planar rotor (QAPR) model, which was constructed to describe the orientational ordering of homonuclear diatomic molecules on inert surfaces, are investigated theoretically using diffusion Monte Carlo. The implementation of the descendant weighing (DW) technique due to Casulleras and Boronat [Phys. Rev. B 52, 3654 (1995)] is used, for which an alternate derivation is presented, based on the path-integral representation of the imaginary time propagator. We calculate the order parameter and then perform finite size scaling in order to search for a critical reduced rotational constant Bc* at zero temperature. Our simulation results indicate that a critical rotational constant is at Bc*≈0.25. The behavior of the kinetic and potential energies show strong evidence for local, single-rotor tunneling as the driving mechanism for the phase transition. A Gaussian mean-field treatment is also presented, in which the most important mechanism is local, single-rotor tunneling. While quantitatively the mean-field phase transition is not in agreement with the simulation results, the energy curves show qualitative similarities. In both cases, the phase transition occurs at the point where the kinetic energy reaches a maximum as a function of the reduced rotational constant B*.

Characteristic of interface effect in Cu–C60 granular films

In this letter, Cu–C60 granular film is prepared with coevaporation method at room temperature. The conductance of the film is measured by in situ method, and its microstructure is characterized by transmission electron microscopy. The charge transfer from Cu to C60 is investigated with Raman spectroscopy. The results indicate that the sample has the uniformly granular microstructure. The interaction between C60 and Cu at the Cu–C60 interfaces, which significantly affects the orientational order–disorder phase transition of C60 and induces the phase transition of C60 in the temperature range from 219 to 248 K. The mechanism of the characteristic of such phase transition is discussed.

Orientational order of ultrathin C60 films on graphite

Low-energy electron diffraction and electron energy-loss spectroscopy have been applied to study C60 thin films on a graphite substrate. Well-ordered C60 overlayers with close-packed face-centred cubic (fcc) (111) lattice structure have been prepared on graphite at 380K. Cooling of the C60 multilayers to 100K resulted in a (2×2) superlattice. This structure transformation has been identified as the surface orientational order–disorder phase transition, in analogy to the bulk orientational fcc–simple cubic (sc) transition. We found that this transition was either completely absent or severely frustrated in a (sub)monolayer region. By comparison with data available from other substrates, we propose that the strong C60–graphite interaction, revealed by our annealing measurements, together with the lack of appropriate corrugation on the graphite surface, may be responsible for suppression of the surface orientational ordering of the first monolayer of C60 on graphite.

The structure, slip systems, and microhardness of C60 crystals

The structure and microplasticity of high-purity fullerite C60 have been investigated comprehensively. The crystalline structure, lattice parameters, and phase transitions have been studied by x-ray diffractometry in the temperature range 30–293 K. It is found that the temperature corresponding to the orientational order–disorder phase transition is Tc=260 K. A considerable number of regions with stacking faults discovered in the samples leads to blurring of the fcc→sc phase transition in the temperature interval Tc±3 K. The a(T) dependences of the lattice parameter display peculiarities at the following characteristic temperatures: Tc at which the lattice parameter jump Δa/a=3.3×10−3 is observed, and the temperatures T0≃155 K, and Tg≃95 K which are associated with the beginning and end of molecular orientation freezing. It is shown that the formation of orientational glass is accompanied by a considerable increase in the width of x-ray reflections. The slip geometry and the temperature dependence of microhardness HV are studied in the temperature interval 81–293 K. It is shown that a system of the {111}〈110〉 type is the only slip system in the fcc and sc phases. The value of HV depends on the indentation plane: HV111&amp;gt;HV100. Below Tc, the microhardness increases abruptly (by approximately 30%). The temperature interval of this anomaly decreases after annealing of the crystal in vacuum. At T&amp;lt;T0, the HV(T) dependence becomes much stronger. It is shown that the hardness of C60 normalized to the elastic shear modulus is higher than the hardness of typical molecular crystals at comparable homologic temperatures.

First-order orientational-disordering transition on the (111) surface of C60.

The temperature dependences of the triplet exciton, of the vibrational modes, and of the low-energy diffraction pattern of the (111) surface of well-ordered ${\mathrm{C}}_{60}$ films indicate that this surface undergoes a first-order orientational order-disorder phase transition at 225\ifmmode\pm\else\textpm\fi{}3 K, well below the temperature of the corresponding phase transition in the bulk of the same samples, which we find to be 260 K. The bulk phase transition is therefore initiated by the surface. To our knowledge, this is the first example of a surface orientational phase transition, a phenomenon that should occur on several other molecular crystal surfaces. \textcopyright{} 1996 The American Physical Society.

Adsorption kinetics and growth of potassium on Cu(100)

Measurements of the helium atom scattering reflectivity during growth, adsorption-desorption equilibrium and isothermal desorption of K on Cu(100) are reported. An orientational order-disorder phase transition is observed between 123 and 223 K in the submonolayer condensed phase. Adsorption-desorption isotherms have been obtained for a range of temperatures between 263 and 448 K. The data indicate a Stranski-Krastanov growth mode for this system, with the formation of 3D clusters after one monolayer, and give a heat of adsorption of about 1± 0.1 eV per atom near the completed first monolayer. The form of the isotherms suggests repulsive adsorbatc interactions in this coverage and temperature regime.

Simulation Study of Off-Center Shifts in Perovskite Systems

An orientational order-disorder phase transition in perovskites has been studied by simulation using the FEFF-5 ab initio program. Off-center shifts of the central atoms toward the <100> directions in perovskite systems have been modeled for three different phases: (i) totally disordered, (ii) partially ordered, and (iii) totally ordered structures. XAFS spectra have been simulated as a function of temperature from these modeled structures. The relative Debye-Waller factors extracted from the simulated XAFS spectra have been quantitatively analyzed using the Einstein model and a single-shell approximation.

Orientational order-disorder phase transition in calcite

We have performed inelastic neutron scattering experiments on calcite in the ordered phase, focusing on a zone boundary F-point that shows X-ray diffuse scattering. At this position we have observed an incipient soft mode along with a column of inelastic scattering ranging in energy between the soft mode energy and zero energy. The intensity of this scattering varies dramatically with temperature, and is described by an Arrhenius relation with an activation energy of 1035 K.

A magnetic model for the demonstration of phase transitions and excitations in molecular crystals

A magnetic model for the demonstration of structural properties and the lattice dynamics of molecular crystals is presented. It is used to visualize an orientational order–disorder phase transition. The orientational order of the low-temperature phase observed on the model is also obtained from a mean field calculation. A simple theory for harmonic excitations of the model is presented, which gives the dispersion relation for an infinite crystal. The frequencies of the observed resonances of the finite model are compared with the results of a numerical eigensystem analysis and with the dispersion relation. Within the limitations given by the construction of the model the results are in rather good agreement.

A mean field calculation of the librational properties of δ phase O2 monolayers on graphite

A mean field approximation is used to calculate the librational properties of δ-phase molecular oxygen monolayers on graphite at temperatures 0≤T≤20 K. The frequencies of the two libron modes are found to occur at 35.07 and 60.28 cm−1. The libron specific heat and the rms orientational fluctuations of the O2 molecules about equilibrium are also determined. It is found that the contribution of zero-point orientational fluctuations to librational behavior is large. The molecules exhibit well defined small angle librational motion at low temperatures and there is no evidence of an orientational order–disorder phase transition prior to melting at 25.6 K.

Ising theories of the plastic phase-transition in adamantane [tricyclo[3.3.1.13,7] decane

We have calculated some of the properties of adamantane crystals using three approximations to the solution of the compressible Ising model. We used an ‘atom-atom’ intermolecular potential and a single variable parameter, the low-temperature thermal expansion, which was taken from experiment. The mean-field Ising approximation gave good agreement with a wide range of crystal properties; but it failed to describe the detailed behaviour near the molecular orientational order-disorder phase transition. A series expansion solution to the Ising model, allowing clustering in both orientation and centres-of-mass, gave excellent agreement with specific heat data, even near T c. Retention of a uniform lattice, allowing only clustering in orientation, and not in centres-of-mass, was only a slight improvement on the mean-field solution. This contrasts with magnetic and alloy order-disorder systems.