Abstract:
With computer simulations of the hard sphere model, we examine in detail the microscopic pathway connecting the metastable melt to the emergence of crystalline clusters. In particular we will show that the nucleation of the solid phase does not follow a two-step mechanism, where crystals form inside dense precursor regions. On the contrary, we will show that nucleation is driven by fluctuations of orientational order, and not by the density fluctuations. By considering the development of the pair-excess entropy inside crystalline nuclei, we confirm that orientational order precedes positional order. These results are at odd with the idea of a two-step nucleation mechanism for fluids without a metastable liquid-liquid phase separation. Our study suggests the pivotal role of bond orientational ordering in triggering crystal nucleation.

Abstract:
Using Brownian dynamics simulation, we study the orientational order in melting transition of colloidal systems with $'$soft$'$ Yukawa potential. The bond-orientational order parameter $\Phi_{6}$ and the bond-orientational order function $g_B(r)$ are calculated in two-dimensional systems. It is found that a two-stage transition and the hexatic phase are indeed existent in two-dimensional melitng, which is consistent with the prediction of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. For comparing with the melting process in three-dimensional systems, the probability distribution of single-particle local order parameter is introduced. Based on the extensive simulations, it is qualitatively suggested that the breakdown of local order only occurs on the fractional part of the colloidal systems for the two-dimensional melting, but in three-dimensional melting, this breakdown takes place on the whole systems at the same time.

Abstract:
We investigate the orientational order of transverse polarization vectors of long, stiff polymer molecules and their coupling to bond orientational and positional order in high density mesophases. Homogeneous ordering of transverse polarization vector promotes distortions in the hexatic phase, whereas inhomogeneous ordering precipitates crystalization of the 2D sections with different orientations of the transverse polarization vector on each molecule in the unit cell. We propose possible scenarios for going from the hexatic phase, through the distorted hexatic phase to the crystalline phase with an orthorhombic unit cell observed experimentally for the case of DNA.

Abstract:
We study the formulation of bond-orientational order in an arbitrary two dimensional geometry. We find that bond-orientational order is properly formulated within the framework of differential geometry with torsion. The torsion reflects the intrinsic frustration for two-dimensional crystals with arbitrary geometry. Within a Debye-Huckel approximation, torsion may be identified as the density of dislocations. Changes in the geometry of the system cause a reorganization of the torsion density that preserves bond-orientational order. As a byproduct, we are able to derive several identities involving the topology, defect density and geometric invariants such as Gaussian curvature. The formalism is used to derive the general free energy for a 2D sample of arbitrary geometry, both in the crystalline and hexatic phases. Applications to conical and spherical geometries are briefly addressed.

Abstract:
From Landau-Alexander-McTague theory and Monte-Carlo simulation results we show that the modulated liquid obtained by subjecting a colloidal system to a periodic laser modulation has long range bond-orientational order and non-zero shear rigidity. From infinite field simulation results we show that in the modulated liquid phase, the translational order parameter correlation function decays to zero exponentially while the correlation function for the bond-orientational order saturates to a finite value at large distances.

Abstract:
Local structure characterization with the bond-orientational order parameters q4, q6, ... introduced by Steinhardt et al. has become a standard tool in condensed matter physics, with applications including glass, jamming, melting or crystallization transitions and cluster formation. Here we discuss two fundamental flaws in the definition of these parameters that significantly affect their interpretation for studies of disordered systems, and offer a remedy. First, the definition of the bond-orientational order parameters considers the geometrical arrangement of a set of neighboring spheres NN(p) around a given central particle p; we show that procedure to select the spheres constituting the neighborhood NN(p) can have greater influence on both the numerical values and qualitative trend of ql than a change of the physical parameters, such as packing fraction. Second, the discrete nature of neighborhood implies that NN(p) is not a continuous function of the particle coordinates; this discontinuity, inherited by ql, leads to a lack of robustness of the ql as structure metrics. Both issues can be avoided by a morphometric approach leading to the robust Minkowski structure metrics ql'. These ql' are of a similar mathematical form as the conventional bond-orientational order parameters and are mathematically equivalent to the recently introduced Minkowski tensors [Europhys. Lett. 90, 34001 (2010); Phys. Rev. E. 85, 030301 (2012)].

Abstract:
A number of computational studies have reported evidence of a metastable liquid-liquid phase transition (LLPT) in models of tetrahedral liquids under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artifacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artifacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid region relax orders of magnitude faster than those associated with bond-orientational order. Here, we unambiguously demonstrate that this hypothetical behavior is irrelevant to the LLPT in the ST2 model of water. We show that density is the slowly relaxing variable in the vicinity of the high density liquid at all conditions where LLPT behavior has been reported. These results complement our previous calculations showing that density and bond-orientational relaxation are highly coupled at lower densities. Consequently, at no conditions relevant to the LLPT in ST2 do we find that density relaxes significantly faster than bond-orientational order, as incorrectly predicted by this competing hypothesis.

Abstract:
We present an Atom-Pair Bond (APB) theory for the energy of a metallic bond based on the ideas of covalent bonding proposed by Pauling. An expression is derived which accurately predicts the signs of the heats of formation of binary alloys. It also explains the characteristics of the Rajasekharan-Girgis lines and their ability to predict accurately concomitant and mutually exclusive structure types in phase diagrams. Evidence is provided to show that the charge transfer on the atom-pair bond which is central to the present theory decides the experimentally observed volume changes on alloying.

Abstract:
Rajasekharan and Girgis reported that binary systems with intermetallic compounds of a particular crystal structure form a straight line on a map using Miedema parameters. In this paper, the universality of that observation is examined. Observations from a study of 143 binary systems that crystallize in six different crystal structures at AB3 composition are discussed. Prediction of concomitant and mutually exclusive structure types in binary metallic phase diagrams, and of phase transitions among different structure types, has been demonstrated. This behavior is unexpected because Miedema parameters are isotropic in nature and structural energies are generally assumed to be small. We argue in this paper that each point on the map stands for the energy of an unlike atom-pair (A-B) bond, with the bond energy remaining nearly the same at all compositions in the phase diagram. This argument is confirmed by comparing the nearest-neighbour (A-B) bond lengths for the compounds of the structure types CaCu5 and CsCl, when concomitant with MgCu2 structure type. This fact leads to an important conclusion that one can define a bond energy for the metallic unlike-atom-pair bond as is usually done for a conventional chemical bond.

Abstract:
We present a study of the structural properties of the crystalline phases for a planar bilayer of particles interacting via repulsive Yukawa potentials in the weak screening region. The study is done with Monte Carlo computations and the long ranged contributions to energy are taken into account with the Ewald method for quasi-two dimensional systems. Two first order phase transitions (fluid-solid and solid-solid) and one second order transition (solid-solid) are found when the surface density is varied at constant temperature. A particular attention is pay to the characteristics of the crystalline phases by the analysis of bond orientational order parameters and center-to-center correlations functions.