Structural features of a Lennard-Jones system at melting and crystallization

The structural features of the crystallization and melting of a system of particles whose pair interaction is described by the Lennard-Jones potential have been considered. The bond order parameter method is used to quantitatively describe the orientational short-range order. The rotational invariants of the second (q _l ) and third (w _l ) orders are calculated for each particle of the system. These calculations require only information on the snapshot of atom positions, which is quite easily obtained in experiments, and provide the distribution functions of particles in q _l and w _l (where l is the rank of an invariant; the results for l = 4, 6 are presented), which are important characteristics of the phase state of the system. It has been shown that the cumulant of the distribution of particles in w ₆ is very sensitive to the destruction/formation of the short-range orientational order in the Lennard-Jones system and, correspondingly, can be used as a criterion of the melting and crystallization of this system.     

Lattice dynamics and melting features of Li and Na

The high-pressure melting of Li and Na has been studied using ab initio calculations of the lattice dynamics. It has been shown that the recently discovered anomalous melting of Na is adequately explained by the phonon spectrum behavior and, accordingly, the thermal vibration amplitudes under compression. In a simple approach using the Lindemann criterion, the nonmonotonic behavior of the melting curve T _m(p) of Na has been quantitatively described within very wide pressure and temperature ranges, and, in particular, the melting temperature drop at p ～ 1 Mbar down to values lower than those at normal pressure. This approach leads to a nonphysical discontinuity of the melting curve T _m(p) of Li near the bcc-fcc-liquid triple point. This is due to the “softness” of the phonon spectrum of the bcc phase of Li that is the necessary condition for the existence of the high-temperature bcc phase. The melting of Na and Li is used as an example to determine why the Lindemann criterion is efficient in some situations and is inapplicable in the other cases.     

On the criterion of the crystal-liquid phase transition

A localization criterion is proposed for the crystal-liquid phase transition (PT). According to this criterion, the PT begins when the E _d/k _b T ratio reaches a boundary value E _d(s)/k _b T _m such that a solid phase is present above it and a liquid phase is present below it in a phase diagram. Here, E _d is the energy of atom delocalization, k _b is the Boltzmann constant, T is the temperature, and E _d(s) is the delocalization energy for a solid phase at melting point T _m. This criterion is shown to generalize the Lindemann criterion of melting to the case of crystallization and the Löven criterion of crystallization to the case of melting. This localization criterion is found to be applicable for both normally melting substances and substances that melt with a decrease in the specific volume upon the transition into a liquid phase. The relation of the localization criterion to the vacancy and diffusional criteria of the crystal-liquid PT has been studied. The inequality T _N < T _m, where T _N is the temperature of the onset of crystallization, is explained using the localization criterion. The calculated values of the T _N /T _m ratio coincide well with the experimental estimates. The maximum value of T _N /T _m is likely to be most probable in crystals with a bcc structure and a small value of the Grüneisen parameter. The T _N /T _m ratio is analyzed at the points in the PT where no change in the specific volume occurs and an entropy jump is nonzero.     

Anisotropic defect-mediated melting of two-dimensional colloidal crystals

The melting transition of anisotropic two-dimensional (2D) crystals is studied in a model system of superparamagnetic colloids. The anisotropy of the induced dipole-dipole interaction is varied by tilting the external magnetic field off the normal to the particle plane. By analyzing the time-dependent Lindemann parameter as well as translational and orientational order we observe a 2D smecticlike phase. The Kosterlitz-Thouless-Halperin-Nelson-Young scenario of isotropic melting is modified: dislocation pairs and dislocations appear with different probabilities depending on their orientation with respect to the in-plane field.     

Ordering behaviors of the F.C.C. and B.C.C. phase alloys in the InMg,LiMg and AlZn systems

Expressions of the band-structure energy and the electrostatic energy characterized by the usual long-range and short-range order parameters are given to a binary alloy of simple metals with the f.c.c.-type or b.c.c.-type structure.The ordering energy and the local ordering energy are calculated for the InMg, LiMg and AlZn systems. The numerical results explain successfully the facts that the InMg system has the Ll₀-type and Ll₂-type ordered phases, each of which exists over a wide range of concentration and that the LiMg system has a local order with a negative short-range order parameter, while the AlZn system has that with the positive one. A lattice distortion in the Ll₀-type ordered structure of InMg is also discussed.     

Molecular dynamics study of orientational melting and thermodynamic properties of C<Subscript>60</Subscript>@C<Subscript>240</Subscript> nanoparticles

The barriers to relative shell rotation and other energy characteristics of C₆₀@C₂₄₀ two-shell carbon nanoparticles (“onions”) with outer shells of different shapes are calculated. The disturbance of the orientational order in the mutual arrangement of shells with an increase in temperature (orientational melting) is studied by the molecular dynamics method. The intershell orientational diffusion is represented by the Arrhenius relationship, and the Arrhenius parameters are calculated numerically. A definition is proposed for the temperature of short-range order disturbance in systems that undergo melting without structural change. The calculated temperature of orientational melting of the C₆₀@C₂₄₀ nanoparticle is approximately equal to 60 K.     

Atomic mechanism of the heating-induced phase transitions of the simple monatomic glasses

Atomic mechanism of the heating-induced phase transitions of the monatomic Lennard-Jones (LJ) glass has been studied via molecular dynamics (MD) simulations. Monatomic LJ glass was heated up at two different heating rates, crystallization occurs at the lowest one and further heating leads to the melting of LJ crystal. Thermodynamics of the phase transitions and corresponding evolution of structural properties upon heating have been analyzed in details. Atomic mechanism of a crystallization of the glassy state was monitored via spatio-temporal arrangements of the atoms involved in the 1421 bond-pair of the fcc crystalline structure. The 1421 bond-pair was detected via the Honeycutt-Andersen analysis [J.D. Honeycutt, H.C. Andersen, J. Phys. Chem. 91 (1987) 4950]. We found that crystallization of the monatomic LJ glass occurs via homogeneous local rearrangements of atoms in the glassy matrix and we found an important role of the liquid-like atoms (existed in the glassy state) in crystallization of the system. In addition, spatio-temporal arrangements of the liquid-like atoms in the system upon further heating were shown in order to clarify the atomic mechanism of a melting of the obtained LJ crystal. Liquid-like atoms were defined by the Lindemann melting criterion. Our results provide previously un-reported data and give deeper understanding of the heating-induced phase transitions in the less stable metallic glasses, which have been observed in practice.     

Orientational order in CO and N2 monolayers on graphite studied by X-ray diffraction

X-ray diffraction has been used to study the structure and orientational phase transitions of CO and N₂ adsorbed on graphite (Papyex). Both form orientationally ordered 2√3 × 2√3 R30° commensurate phases on graphite at low temperatures (10 K). The in-plane herringbone structure of N₂ has been confirmed but CO has more orientational disorder than N₂, which may be associated either with tilting, random static or systematic, of the molecules away from the surface and/or with orientational order of shorter range than the centre of mass order. In the first case the average tilt would have to be about 26° and in the second case the orientational correlation length would have to be 200 Å compared with 450 Å for the translational order. The orientational phase transition is sharp for N₂, occurring over the range 27–30 K, in agreement with previous work. For CO the transition is broad and starts at lower temperatures. This and the structural data indicate that a point quadrupolar interaction is not a suitable model for comparing the properties of N₂ and CO layers. The orientational phase transition in the incommensurate phase of N₂ is found to be broad and occurs below 20 K. For CO it is sharper than for the commensurate phase and occurs at a higher temperature. The lattice parameter changes by 0.75% across the orientational phase transition. For both N₂ and CO there is evidence of translational disorder in the commensurate phases but it cannot be interpreted quantitatively.     

Relationship between crystalline order and melting mechanisms of solids

The mechanism for homogeneous nucleation of the liquid phase in Lennard-Jones solids is studied by combining the Landau free energy approach with some of the methodology developed to characterise transition path ensembles. The second-order bond orientational order parameter, Q ₆ which indexes the overall degree of crystalline order, is shown to provide a dynamically significant collective coordinate describing the melting process. Trajectories generated from configurations sampled in the vicinity of the maximum in the Landau free energy curve, F(Q ₆), are shown to have equal likelihood of teminating in either the solid or liquid-like free energy minima. It is also demonstrated that Q ₆ is necessary but not sufficient as a dynamical coordinate to describe melting and it is necessary to explore possiblities for additional coordinates which are critical for initiating melting. Our sudy suggests that the additional coordinates for describing the melting process would be some type of localised defect, much smaller in spatial extent than the size of the critical nucleus predicted by classical nucleation theory.      

Lindemann criterion and the anomalous melting curve of sodium

Recent reports of the melting curve of sodium at high pressure have shown that it has a very steep descent after a maximum of around 1000 K at 31 GPa. This maximum does not occur due to a solid-solid phase transition. According to the Lindemann criterion, this behaviour should be apparent in the evolution of the Debye temperature with pressure. In this work, we have performed an “ab initio” analysis of the behaviour of both the Debye temperature and the elastic constants up to 102 GPa, and find a clear trend at high pressure that should cause a noticeable effect on the melting curve.     

Orientational correlations and order in A3C60

A tight-binding method which has been previously applied to study the effect of uncorrelated orientational disorder on conduction-band properties is extended here to the case of systems with long-range order and/or short-range correlations. The density of states and conductivity are not highly sensitive to the specific short-range correlations, so long as the system is not too close to being fully ordered. Hence the strong effects of disorder found previously appear to be robust and should play an important role in the interpretation of normal-state properties of A₃C₆₀.     

Influence of nematic and smectic orders on polarizability of molecules of ethyl-p-(4-ethoxybenzylideneamino-)α-methyl cinnamate liquid crystals

Experimental values of the polarizability tensor γ components of molecules of ethyl-p-(4-ethoxybenzylideneamino-)α-methyl cinnamate liquid crystals in the nematic and smectic A phases have been obtained. Quadratic dependences of the longitudinal, γ _l , and transverse, γ _t , components, the mean value $\bar \gamma $ , and anisotropy Δγ in both phases have been established as functions of the orientational order parameter S of molecules in a maximally wide range of S. The nematic-smectic A phase transition with a continuous variation of S manifests itself as kinks in the linear dependences of $\bar \gamma $ , Δγ, and γ _l on S ² and does not influence the dependence γ _t (S ²). The observed dependences have been derived in the framework of the theory of the nematic-smectic A phase transition. The factors responsible for different influences of the orientational and positional orderings of molecules on the polarizability parameters have been determined.     

Defect melting as an SO(3) lattice gauge theory

We show that defect melting is closely related to SO(3) lattice gauge theory. The phase transition of this system corresponds to a Lindemann melting parameter L≈50γ where γ≈2 is a parameter characterizing the unharmonic content in the elastic forces. This is in rough agreement with experiment. The equivalence may help in visualizing the crucial rule of defects in quark confinement.     

On graphene melting

Dynamics of disordering of graphene upon heating has been studied by computer simulation. The mechanism governing the formation of seeds for a three-dimensional grid of entangled carbon chains into which graphene is transformed upon melting has been analyzed in detail. It has been shown that the emergence of these seeds is preceded by the disruption of several interatomic bonds, accompanied with the formation of large rings or groups of adjacent rings and the formation of penta- and heptagons of their C–C bonds. The results of this work on the whole agree with the Lindemann–Lozovik criterion. The melting temperature is estimated as T_m ~ 5100 K.     

Linebroadening in DF-ODMR spectra of triplet excitons in the anthracene-1, 2, 4, 5-tetracyanobenzene single crystal near its structural phase transition

The temperature evolution of the DF-ODMR spectra of triplet excitons in the A-TCNB crystal has been studied in the vicinity of its order-disorder phase transition at T_c=204 K. Linewidth measurements were carried out for two selected orientations of the magnetic field in which the two crystal sites of the ordered phase appear as magnetically inequivalent and equivalent, respectively. In the former case the linebroadening observed near T_c was attributed to changes in the long-range order parameter and to the short-range clustering formation along the slacks. In the second case the sharp increase in the linewidth near T_c was interpreted and briefly discussed in terms of the critical slowing down of the fluctuations in the order parameter associated with the phase transition.     

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 $\text{(}\text{3}\text{×}\text{3}\text{)}$ 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.     

Analytic approach to the orientational ordering in the high pressure phase II of o-D2 and p-H2

Possible kinds of orientational order in the high pressure phase II of o-D₂ and p-H₂ are considered as bifurcations of solutions of some nonlinear equations. Before, we found this approach to be fruitful in the case of orientational ordering in o-H₂ and p-D₂. A solution with four sublattices in the hcp structure is obtained. The order parameter of this solution abruptly decreases with temperature and becomes zero in phase I. The curve of the phase boundary T_c(P) is calculated.     

Nonequilibrium states and anomalies of Young’s modulus in rare-earth cobaltites RBaCo4O7 (R = Dy-Er,Y, Lu) caused by short-range magnetic order

The elastic properties of rare-earth cobaltites RBaCo₄O₇ (R = Dy, Ho, Er, Y, Lu) have been investigated experimentally. It has been found that the temperature dependences of the Young’s modulus exhibit significant hysteresis and irreversible effects over a wide range (80–280 K) between the structural and magnetic phase transition temperatures. These effects indicate that the short-range magnetic order in the Co sub-system of the studied rare-earth cobaltites gradually develops below the structural phase transition, when the distortion of the structure relieves the frustration of exchange interactions both in the Kagome lattice and in the triangular lattice of the cobalt subsystem. At the magnetic phase transition temperature, there are weak and smoothed anomalies of the Young’s modulus, which correlate with the low dimensionality and frustration of the exchange interactions in the Co subsystem of the studied rare-earth cobaltites.     

Strong short-range magnetic order in a frustrated FCC lattice and its possible role in the iron structural transformation

The magnetic properties of a frustrated Heisenberg antiferromagnet with the fcc lattice and exchange interaction between the nearest (J ₁) and next-to-nearest (J ₂) neighbors are studied in this work. For the collinear phase with the wave vector Q= (π,π,π), the equations of the self-consistent spin-wave theory are obtained and solved numerically for the sublattice magnetization and the averaged short-range order parameter. The dependence of the Néel temperatureT _N on the ratio J ₂/J ₁ is found. It is shown that, in the case of a sufficiently strong frustration, strong short-range magnetic order persists over a wide temperature range above T _N. The possible application of this result to the mechanism of structural phase transition from α-Fe to γ-Fe is considered.