Orientational Order-disorder Transition Research Articles

Monte Carlo calculations for solid CO and N2overlayers physisorbed on graphite

Monte Carlo calculations are reported for solid overlayers of CO and N2 physisorbed on the graphite basal plane. The effect of compression on the ground state structure and the orientational order-disorder transitions is examined. For N2 there is good agreement with experiment but this is not the case for CO where it appears that our intermolecular potential corresponds to a molecule which is too small.

Phase transitions in diatomic molecular monolayers

Orientational order-disorder transitions in simple diatomic molecular monolayers (such as N2 and O2 on different substrates) have been studied using various theoretical techniques. The nature of such a phase transition and physical mechanisms driving it are discussed for two types of systems; one with fixed centers of mass (CM) and the other where the CM-lattice structure is allowed to change at the phase transition. The latter provides a simple example of a ferroelastic phase transitions in 2 dimensions.

Raman studies of lattice vibrations in weak charge-transfer complexes: Naphthalene-tetrachlorophthalic anhydride

Low-frequency (15–150 cm −1) Raman spectra of naphthalene (N) : tetrachlorophthalic anhydride (TCPA) complex and its individual parent molecules were recorded at room temperature and at 77 K. The results suggest that the crystal structures for the complexes and for TCPA are in good agreement with those determined by X-ray studies. Within the temperature range studied, no orientational order-disorder phase transitions were observed for all the crystals investigated. The observed 26.7 cm −1 lattice mode in N : TCPA might be assigned as the interaction coordinate for complex formation.

A correlated variational wave function for the orientational ground state of solid methane

We introduce a correlated variational wave function of the Jastrow type that is able to represent the ground state of solid CH4 through the orientational order–disorder transition. To describe the local orientation in a weakly ordered phase a new kind of pocket state is introduced, that is derived from the imaginary time propagator of a free top. The effect of short range correlations between the orientational zero point fluctuations is evaluated for pure meta (total spin=2) methane in the disordered and the ordered phases of the James and Keenan (JK) model. The T-A tunnel energy in fully converted methane is calculated in the same approximation and corrections to the mean field values are found to be large. While the difference in energy between the partially ordered phase II and the fully ordered JK phase III is found to be small, the latter remains marginally the more stable, in contrast to experiment.

Neutron diffraction study of the commensurate-incommensurate phase transition in a methane submonolayer adsorbed on graphite

Neutron diffraction experiments have been performed on a 0.7 layer of methane adsorbed on the basal plane of graphite, in the temperature range [44–54 K], with a careful study of the commensurate-incommensurate phase transition (CIT) previously observed. The coherence length and mean methane-methane distance vary continuously at the transition. The critical temperature is found to be 49±0.5 K. No orientationally ordered structure is found below this transition. Moreover, the diffraction intensities are best fitted taking into account a molecular isotropic rotational motion for all temperatures within the range studied, suggesting that the CIT is not correlated with an orientational order-disorder transition.

Neutron diffraction study of the commensurate-incommensurate phase transition in a methane submonolayer adsorbed on graphite

Neutron diffraction experiments have been performed on a 0.7 layer of methane adsorbed on the basal plane of graphite, in the temperature range [44–54 K], with a careful study of the commensurate-incommensurate phase transition (CIT) previously observed. The coherence length and mean methane-methane distance vary continuously at the transition. The critical temperature is found to be 49 ± 0.5 K. No orientationally ordered structure is found below this transition. Moreover, the diffraction intensities are best fitted taking into account a molecular isotropic rotational motion for all temperatures within the range studied, suggesting that the CIT is not correlated with an orientational order-disorder transition.

Generalized mean-field theory: Formulation, thermodynamic consistency, and application to the isotropic-nematic-smectic transitions in liquid crystals

A generalized mean-field theory, incorporating the "classical" mean-field theories but having a richer structure, is formulated. Thermodynamic consistency is established for this generalized theory. As an application of the formalism, a treatment of coupled orientational and translational order-disorder transitions is presented, resulting in self-consistency equations requiring no numerical integration but exhibiting the essential features of the isotropic-nematic-smectic transitions in liquid crystals.

X-ray evidence for a structural phase transition in the organic two-dimensional conductor (BEDT-TTF) 2Cl0 4(C 2H 3Cl 3) 0.5

By x-ray diffuse scattering experiments, the formation of the superstructure with the periodicity 2a × b × 2c was found below about 200K in the organic two-dimensional conductor (BEDT-TTF) 2Cl0 4(C 2H 3Cl 3) 0. The origin of the superstructure is considered to be an orientational order-disorder transition of the molecule C 2H 3Cl 3.

Structure and orientational ordering of nitrogen molecules physisorbed on graphite

The structure and orientational ordering of nitrogen molecules physisorbed on graphite have been studied by low-energy diffraction (LEED). A two-sublattice in-plane herringbone structure with glide lines along two perpendicular directions is inferred from LEED patterns at T < 30 K from the monolayer where the molecular centers have the commensurate ( 3 × 3 ) 30° structure. The orientational order-disorder transition of this commensurate phase was examined by superlattice spot intensity and angular profile measurements for 20 < T < 38 K. A rapid drop in superlattice intensity is observed near 27 K. The persistence of some intensity to 38 K. is suggestive of residual short-range orientational ordering and perhaps finite size or heterogeneity effects. For increasing coverage at T = 15 K, there is first a transition to a previously unobserved uniaxial incommensurate phase and then a transition to an apparently triangular incommensurate phase. The orientational superlattice spots are clearly present in the uniaxial phase, but are much weaker in the triangular incommensurate phase. At 31 < T < 35 K, an apparently triangular incommensurate phase with no detectable orientational superlattice spots is observed. The lattice constant versus equilibrium vapor pressure curve has been determined in the latter case assuming a continuous transition. The lattice constants of the incommensurate phases are used to place limits on the extent of possible phase-coexistence regions between the commensurate, uniaxial incommensurate, and triangular incommensurate phases. The LEED patterns from the bilayer at T = 15 K indicate a double-period superlattice structure of the triangular incommensurate phase which does not have the glide line symmetries of the commensurate monolayer. Some effects of heterogeneity on these phase transitions are discussed. A phase diagram for 10 < T < 40 K is proposed.

Two-DimensionalO2Adsorbed on Graphite

Properties of two-dimensional O 2 adsorbed on graphite are calculated in the extremely low-coverage δ region and for monolayers, with use of pattern-recognition optimization and Monte Carlo techniques. Equilibrium configurations and orientations, orientational order-disorder, melting, and dissociation transitions are predicted at various O 2 densities. Phase characteristics, including a plastic crystallite phase, are compared with experiment.

Physical mechanisms in the phase transitions of sodium superoxide

We consider the various physical mechanisms that contribute to the ground-state energy (${E}_{g}$) of the ordered pyrite (OP) and the marcasit\'e ($M$) phases of Na${\mathrm{O}}_{2}$. We find that the ionic and molecular-crystal contributions to ${E}_{g}$ (Madelung potential, ${\mathrm{O}}_{2}^{\ensuremath{-}}$-${\mathrm{Na}}^{+}$ and ${\mathrm{O}}_{2}^{\ensuremath{-}}$-${\mathrm{O}}_{2}^{\ensuremath{-}}$ repulsion, Van der Waals and quadrupole-quadrupole interaction between ${\mathrm{O}}_{2}^{\ensuremath{-}}$ molecules) favor the OP structure by an energy of 2204 K per ${\mathrm{O}}_{2}^{\ensuremath{-}}$ molecule. Contributions to ${E}_{g}$ arising from splitting of the orbital degeneracy of the ${\mathrm{O}}_{2}^{\ensuremath{-}}$ ion, quadrupole---electric-field gradient interaction, and antiferromagnetic exchange coupling between ${\mathrm{O}}_{2}^{\ensuremath{-}}$ spins favor the $M$ structure by 2468 K per ${\mathrm{O}}_{2}^{\ensuremath{-}}$ molecule. An estimate of the librational zero-point energies in both phases suggests that the energies of the two phases are very close to each other. Within the present accuracies of our calculation we cannot definitely conclude that $M$ structure has lower energy at $T=0$ as seen experimentally. However the molecular orientations obtained in each phase from energy minimization agree well with the experiment. The first-order phase transition from OP to disordered pyrite (DOP) has been studied in a molecular-field approximation. The results are in reasonable agreement with experiment. We find that ${\mathrm{O}}_{2}^{\ensuremath{-}}$-${\mathrm{Na}}^{+}$ repulsion plays an important role in the observed orientational order-disorder transition. The theoretical value of the order-disorder transition temperature is calculated to be 300 K compared to 223 K obtained experimentally. The discontinuity in the entropy at the transition is calculated to be $k\mathrm{ln}1.62$ whereas the experimental value is $k\mathrm{ln}2.35$. The possible sources of discrepancy between theory and experiment are discussed.

Nuclear magnetic resonance in solid ethylene at high pressure: I. The phase diagram of solid ethylene at high pressure

This article is the first in a series of four papers dealing with an NMR investigation into the effects of hydrostatic pressure on the phase transitions and the molecular motions in solid and liquid C 2H 4 at pressures ranging from 0 to 2500 bar and at temperatures from 77 to 140 K. The most interesting result of this study is the detection of a so far unknown orientational order-disorder transition in solid ethylene at pressures above 468 bar. The parameters of the new solid I-solid II-liquid triple point are 110.36 ± 0.1 K, 468 ± 6 bar. The present paper is predominantly concerned with the accurate determination of the new transition lines of solid ethylene. In addition the charge in volume along one of the melting lines has been measured by NMR. From the slopes of the transition lines and the volume changes at one of the melting lines the entropy and volume changes at all three transitions lines at the triple point have been determined.

Model of structural phase transitions in(CH3NH3)2CdCl4-type compounds

A model has been proposed describing the structural phase transitions in ${(\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3})}_{2}$Cd${\mathrm{Cl}}_{4}$ perovskite layer-type compounds as orientational order-disorder transitions of the C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$ groups. Each C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$ group has four possible equilibrium orientations in the cavities between the corner-sharing Cd${\mathrm{Cl}}_{6}$ octahedra and interacts with its nearest neighbors via two- and four-particle interactions. The four-particle interactions describe the fact that the energy of a given configuration of four C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$ groups surrounding a Cd${\mathrm{Cl}}_{6}$ octahedron depends on the number of N-H\dots{}Cl bonds leading to the axial Cl sites of this octahedron, whereas the two-particle interactions describe the direct coupling between the C${\mathrm{H}}_{3}$ ends of the methylammonium groups as well as the indirect coupling via the N-H\dots{}Cl bonds leading to the equatorial Cl sites. In the absence of lattice distortions, the sequence of phase changes is: $\frac{I4}{\mathrm{mmm}}\ensuremath{\rightarrow}\mathrm{Cmca}\ensuremath{\rightarrow}\frac{P{4}_{2}}{\mathrm{ncm}}\ensuremath{\rightarrow}\mathrm{Cmca}$. Due to nonlinear coupling between the motion of the C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$ groups and the rotation of the Cd${\mathrm{Cl}}_{6}$ octahedra, a monoclinic distortion of the lattice sets in as soon as the orthorhombic order parameter exceeds a critical value. For certain reasonable values of the coupling parameters one can thus reproduce the experimentally observed sequence of phase changes: $\frac{I4}{\mathrm{mmm}}\ensuremath{\rightarrow}\mathrm{Cmca}\ensuremath{\rightarrow}\frac{P{4}_{2}}{\mathrm{ncm}}\ensuremath{\rightarrow}\frac{P{2}_{1}}{b}$.

Theory of phase transitions in solid methanes. X. Centering around Phase II in solid CH4

Thermal, spectroscopic, and other properties of methane solids, especially those concerning Phase II of solid CH4 in nuclear spin species equilibration, are theoretically studied from a unified point of view, i.e., the extended James–Keenan model. It assumes a rigid lattice and treats the molecular motions with respect to the rotational degress of freedom in the crystal potential given by Yasuda [Prog. Theor. Phys. 45, 1361 (1971)]. Two adjustable parameters are introduced in order to adapt the assumed crystal potential to the actual situation in the solid state of CH4. Most of the calculations are carried out in the framework of the molecular field method in quantum statistical mechanics. The eight-sublattice antiferrorotational structure is assigned to Phase II. Thus we have two kinds of site Hamiltonians in this phase, the symmetry groups of which are the direct product groups ?hOh and ?dD2d. Basis functions are doubly symmetry adapted under each of these symmetry groups. Rotational functions are included up to J=8 (sometimes up to J=10). The accuracy of the calculations is tested and the errors in level spacings are estimated at a few percent. The level scheme obtained for Oh-site features hindered rotations, is independent of temperature, and applies also to all molecules in Phase I. The level scheme of D2d site bears the librational character in its lower energy part and has the lowest levels split through quantum tunneling (the tunneling levels). These level schemes are compared with the results of neutron inelastic scattering experiments and satisfactory agreements are obtained. The two-term crystalline field employed is justified through comparison with the result of the neutron diffraction experiment on Phase I of CD4. The transition between Phases I and II turns out to be of first order, and the reason for this is given. The nature of the transition is new, being neither the rotational melting proposed by Pauling nor the orientational order–disorder transition by Frenkel. Thermodynamic quantities are worked out, including the free energy, entropy, internal energy, specific heat, and the mean square of the proton spin angular momentum. Anomalous behaviors of the specific heat at low temperatures are studied in detail and compared with observation. The predicted structure of the tunneling levels is again and conclusively confirmed by experiment. The negative thermal expansion observed below about 10 K is nicely reproduced with an additional assumption on the response of the crystal potential upon varying the lattice spacing. The transition between Phases II and III observed at elevated pressure is qualitatively discussed with special reference to the role played by Oh molecules in Phase II, and a quantum nature of the transition below about 10 K is pointed out. The main predictions made in this report are as follows: (1) The tunneling levels have such temperature dependences below about 4 K that their level spacings at 0 K are about 10% larger than those at 4 K. Their effects on the Schottky anomaly in the specific heat and on the nuclear susceptibility at around 1 K are described in detail. (2) Apparently unusual quantum effects are predicted on the transition temperatures between Phases I and II. That of CD4 is the highest and those of CH4 and CT4 appear at about the same temperature. (3) Solid solutions of CH4 and Kr or Xe have double phase transitions in a certain CH4-rich region, the lowest temperature phase having no orientational order. If the conversion is not allowed, the lower transition does not occur. (4) Solid solutions of CH4 and CD4 have triple transitions in a certain CH4-rich region, the lowest temperature phase having the same structure as Phase II. (5) The tunneling levels of T species split into two levels, the upper one has the degeneracy six and the lower one the degeneracy three, and the separation is 0.01 K.

Static and dynamic critical behavior at orientational phase transitions in molecular crystals

Critical behavior at orientational order-disorder transitions in plastic molecular crystals is discussed. Primary emphasis is placed on an analysis of the coherent elastic and inelastic neutron cross sections. It is shown that in molecular crystals, where the multipolar operators describing the orientational interaction between pairs of molecules have several components, it is necessary to take into account the full vector character of the order parameter when calculating static and dynamic scattering laws. In the case of the I-II transition in C${\mathrm{D}}_{4}$, the recent experimental neutron-scattering results of Press et al. are well understood on the basis of a molecular-field-type analysis of the James and Keenan Hamiltonian.

Studies of the dielectric constant in solid H2,4He, and Ne

Measurements of the static dielectric constant e and of the resulting polarizability αCM defined by the Clausius-Mosotti relation are reported for several molecular solids under conditions of quasiconstant density. The range of measurements was between 0.4 and about 15 K, and pressures up to about 1 kbar were used. In solid H2, the changes of α as a function of ortho concentration are reported at 4.2 and 12 K, from which it is concluded that [α(ortho)−α(para)]/α≃0.005, which is approximately 2 1/2 times larger than in the liquid phase. Furthermore the temperature change of αCM is studied for various densities at comparable ortho concentrationsX. Particular attention is paid to the orientational order-disorder transition in solid H2 withX≃0.65, where αCM shows an abrupt change that appears to be a function ofX, density, and thermal history. In general αCM is lower in the ordered (cubic) phase than in the disordered (hexagonal) phase. The temperature change of αCM in almost pure para-H2, measured between 4 and 0.4 K, is presented and is compared with other recently reported experiments. It is concluded that the mechanism that produces the change of αCM withT and at the order-disorder phase transition is not understood. In solid Ne, measurements of αCM are reported for one sample assumed to be at zero pressure and one where the density is quasiconstant. There is a strong temperature dependence in αCM for the former above 5 K (in agreement with previous findings), while for the latter αCM appears to be constant within the uncertainties introduced by strain-induced hysteresis effects. The sample of solid4He, investigated between its melting point at 4.3 and 0.8 K at constant density, shows a very weak temperature dependence of αCM, which is also consistent with previously reported measurements.

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.

Der Einflu� des elastischen Gitters auf den Orientierungs�bergang von festem Ortho-Wasserstoff in Molekularfeldn�herung

We calculate the influence of the elastic lattice on the orientational order-disorder transition in fcc solid ortho-hydrogen. The angular momentaJ = 1 of the molecules are coupled by quadrupole-quadrupole interaction which we reduce within the space group Pa 3 to the Ising model approximation. Local mechanical equilibrium requires the lattice to adjust itself to the forces caused by the inhomogeneous fluctuations in the angular momentum configuration. Following Wagner [6] this results in a 4-angular-momentum interaction with long range and short range contributions depending on the one-phonon Green function of the lattice. We use a Debye phonon spectrum and the molecular field approximation in order to obtain numerical results. According to the first order nature of the phase transition we get a pressure drop at the critical pointTc of 9.7 bar. The experimental value is estimated to be 8 bar. Compared to the rigid lattice the phase transition on the elastic lattice is smoothed out by the short range contribution. This corresponds to a reduction of the discontinuity of the order parameter at the critical pointTc by about 13%. The phase transition will vanish completely if we increase the magnitude of the short range terms by a factor of three.

Proton spin relaxation in ethylene. “A new high pressure phase”

Proton magnetic resonance measurements reveal on orientational order-disorder transition in solid ethylene at pressures above 468 bar near the melting line. There are strong indications that the rate of self-diffusion in the disordered solid is constant along the melting line.

Soft Modes in Molecular Crystals

The self-consistent phonon approximation is applied to study the temperature dependence of the libron and phonon modes for simple molecular crystals. Several linear chain models are studied to illustrate the soft mode behavior of these excitations near the orientational order—disorder transitions that occur in many molecular crystals. It is shown that both libron and phonon frequencies are strongly temperature dependent in the neighborhood of the transition in qualitative agreement with experimental observations. Both the cases of strong and weak orientational coupling are considered. The effects of the cubic anharmonic terms are also discussed.