Long-range Translational Order Research Articles

Lateral organization of cholesterol molecules in lipid-cholesterol assemblies.

We present results of an off-lattice simulation of a two-component planar system, as a model for lateral organization of cholesterol molecules in lipid-cholesterol assemblies. We explore the existence of "superlattice" structures even in fluid systems, in the absence of an underlying translational long-range order, and study their coupling to hexatic or bond-orientational order. We discuss our results in context of geometric superlattice theories and "condensation complexes" in understanding a variety of experiments in artificial lipid-cholesterol assemblies.

Real-space imaging of structural transitions in the vortex lattice ofV3Si

The predictions of nonlocal London theory are confirmed by real-space measurements of the hexagonal-to-square transition in the vortex lattice structure of ${\mathrm{V}}_{3}\mathrm{Si}.$ We observe that the lattice transforms from hexagonal to nearly square over the field range of 0--4 T for fields applied along the [001] direction. Above $\ensuremath{\approx}0.75\mathrm{T},$ we find that the lattice orientation is strongly linked to the symmetry of the underlying ${\mathrm{V}}_{3}\mathrm{Si}$ crystal and has a (100) symmetry plane. Near the rhombus-to-square transition at 4 T, we observe anisotropic long-range translational order, consistent with predictions of the elasticity of the lattice near this transition.

Face-Centered Cubic and Hexagonal Closed-Packed Nanocrystal Superlattices of Gold Nanoparticles Prepared by Different Methods

Dodecanethiol-stabilized gold nanoparticles with similar average size organize into different superlattice structures depending upon the method of preparation of the nanocrystals. Particles synthesized by the inverse micelle technique preferentially assemble into face-centered cubic (fcc) structures with long-range translational and orientational ordering. Gold nanoparticles obtained by the solvated metal atom dispersion (SMAD) method behave like “hard” spheres and predominantly organize into hexagonal close-packed (hcp) nanocrystal superlattices with long-range translational ordering. Different packing behavior results from differences in nanoparticle core morphologies induced by the synthetic method; fcc ordering is preferred by single crystalline nanoparticles, while hcp is preferred by polycrystalline nanoparticles. A combination of optical microscopy, transmission electron microscopy (TEM and HRTEM), selected area electron diffraction (SAED), atomic force microscopy (AFM), and X-ray diffraction (XRD) were used to characterize both the dispersed nanoparticles and the nanocrystal superlattices.

X-ray-induced disordering of the dimerization pattern and apparent low-temperature enhancement of lattice symmetry in spinelCuIr2S4

At low temperatures, spinel ${\mathrm{CuIr}}_{2}{\mathrm{S}}_{4}$ is a charge-ordered spin-dimerized insulator with triclinic lattice symmetry. We find that x rays induce a structural transition in which the local triclinic structure is preserved, but the average lattice symmetry becomes tetragonal. These structural changes are accompanied by a thousandfold reduction in the electrical resistivity. The transition is persistent, but the original state can be restored by thermal annealing. We argue that x-ray irradiation disorders the lattice dimerization pattern, producing a state in which the orientation of the dimers is preserved, but the translational long-range order is destroyed.

Density distribution in the liquid-vapor interface of a dilute alloy of Pb in Ga

This paper is concerned with the calculation of the density distribution along the normal in the liquid-vapor interface of a dilute alloy of Pb in Ga. The results of self-consistent quantum Monte Carlo simulations of that distribution are in good agreement with the experimentally inferred distribution. In particular, the simulations reproduce the finding that the excess Pb in the liquid-vapor interface forms a monolayer that is the outermost stratum of the interface. However, the 1000-atom simulation sample has a cross section of only 70 atoms, so the area of the liquid-vapor interface in these simulations is too small to permit development of long-range translational order in the Pb monolayer, and the simulations do not reproduce the experimental finding of hexagonal crystalline order in that monolayer.

Quasicrystal structures studied by high-resolution transmission electron microscopy

Structural investigations, using a transmission electron microscope (TEM), have been highly beneficial for the analysis of icosahedral and decagonal quasicrystals. Many structural properties of quasicrystals can be recognized and quantified by electron diffraction patterns alone. Nevertheless, a much more complete understanding of the real structure of quasicrystals can be achieved by the analysis of high-resolution transmission electron microscopy (HRTEM) images. Compared to diffraction-based techniques, HRTEM offers several advantages, however, special points which must be considered in the interpretation of HRTEM images will be discussed. For the case of 2-dimensional quasicrystals, e.g. the decagonal phases, HRTEM images can directly reveal the (projected) atomic structure as well as the long-range translational order. This is possible because 2-dimensional quasicrystals are periodic along one direction and the atoms thus form periodic atom columns as in crystalline materials. Therefore, the imaging theory established for crystals can similarly be applied to electron micrographs of 2-dimensional quasicrystals taken with the electron beam parallel to the unique periodic axis. It is evident, that possible limitations due to projection effects along the electron beam direction have to be considered in the interpretation of the images. HRTEM images of decagonal quasicrystals have frequently been employed to differentiate between disorder and order, i.e., to infer the difference between a random and perfect quasiperiodic tiling, respectively.

Non-linear theory of elastic microshear in periodic structures. Instability of homogeneous deformation

A theory of a crystal lattice with substantially non-linear interaction between the atoms during arbitrary mutual displacements under conditions of elastic shear of a layer is proposed. The energy of two-dimensional deformations contains periodic and gradient terms. The equilibrium equation in the form of the sine-Helmholtz equation (with two characteristic coherence lengths) is solved accurately. It is shown that a shear virain homogeneous along the layer unstable and is stabilized by modulations. As a result, a superstructure with long periods arises, i.e. there is a change in the long-range translational order. Relations are obtained, linking the size and the amplitude of the displacement field, which provide the conditions for the superstructure to exist. A bifurcation transition from purely elastic deformation of the lattice to elastoplastic deformation is found.

Induced long-range order in crosslinked ‘one-dimensional’ stacks of fluid monolayers

Ordinary crystals are characterized by long-range translational order in all three dimensions. In lower-dimensional systems, in contrast, translational order is destroyed through the ‘Landau–Peierls instability’ — displacements from periodic ordering due to thermal fluctuations whose amplitude increases with the size of the system1,2,3,4. This effect is well known for layered systems ordered in one dimension, such as surfactant membranes5,6, smectic (layered) liquid crystals7 and liquid crystalline polymers8, which form ordered stacks of fluid monolayers. Smectic liquid-crystal polymers can be weakly crosslinked to form percolating elastomeric networks that still allow mobility on a molecular scale9,10. In these smectic elastomers, fluctuations of the fluid layers are coupled to distortions of the underlying network, and are therefore energetically penalized11, even though the network of crosslinks has a random nature and thus no three-dimensional translational order. Here we present a high-resolution X-ray diffraction study of a smectic elastomer that reveals the effects of crosslinking on long-range ordering. We find that the introduction of a random network of crosslinks enhances the stability of the layered structure against thermal fluctuations and suppresses the Landau–Peierls instability so as to induce ‘one-dimensional’ long-range ordering at length-scales up to several micrometres.

A Crystal Model for the Icosahedral Phase

A crystal model is proposed that is in good agreement with the experimental electron diffraction patterns and high-resolution electron-microscopy images of the icosahedral phase in Mn–Al and related systems. Structurally, the model has long-range periodic translational order with a large unit cell (space group Im {\bar3}) containing 10038 atoms as well as orientational order characterized by symmetry close to the m {\bar3\bar5} point group. Such a periodic structure can explain the origin of the crystallographically forbidden icosahedral symmetries. The icosahedral phase may thus be considered as a complex cubic crystal.

Phason Relaxation Mechanisms in Al-Pd-Mn Single-Quasicrystals

Quasicrystals represent a new state of condensed matter which exhibits long-range quasiperiodic translational order and orientational order with noncrystallographic symmetry. Mechanical spectroscopy was applied for the study of defect properties in stable icosahedral single-quasicrystalline Al-Pd-Mn samples. Two mechanical loss maxima appear at 360 K and 870 K for a measuring frequency of f3 Hz. The relaxation parameters for both peaks were determined as H = 0.98 eV, T τ -1 = 4.5.10 -14 s -1 for the low temperature peak, and H = 4.0 eV, τ∞ -1 = 3.0.10 24 s -1 for the high temperature peak, respectively. Both peaks are related to phason defects which are characteristic for the quasicrystalline structure.

Existence of Critical Disorder and Vanishing of Mass by Replica-Symmetry Breaking in Random Sine-Gordon Model

A study is made of the sine-Gordon model with random amplitude bearing the lattice pinning potential and the random pinning potential, using the variational-replica method developed by M\(\acute{e}\)zard and Parisi. We find the existence of the critical strength of disorder below which the long-range translational order of the lattice is maintained and above which the replica-symmetry is broken. It is shown that the replica-symmetry breaking leads to the vanishing of the mass due to the lattice pinning potential. A phase diagram in the temperature-disorder plane is discussed.

Step-density-wave phase of crystalline interfaces.

The combined effect of striction and crystallinity can produce a state for vicinal crystalline interfaces, which we call the step-density-wave (StDW) phase due to its resemblance to the charge-density-wave phase of one-dimensional conductors. This phase arises due to a spontaneous periodic distortion of the surface commensurate with the steps, which creates a potential that localizes them. In many cases of interest the energy gain of step localization is greater than the energy cost of the elastic distortion, thus favoring the StDW phase. There is true long-range translational order of the step positions relative to the surface distortion, which makes the StDW phase similar to traditional smooth interfaces. The surface distortion and associated step waves are not fixed rigidly in space, however, but only relative to each other. Therefore, in the absence of pinning by impurities, the combined system of steps with associated surface elastic distortion can move freely in response to an external force (for example, under crystal growth conditions) so that in this respect it resembles a rough interface. In this paper we demonstrate the existence of the StDW phase and study the phase transitions between the rough phase of wandering steps and the StDW phase. \textcopyright{} 1996 The American Physical Society.

Can The Icosahedral Phase Be Modeled as a Crystal?

We propose a crystal model that is in excellent agreement with the experimental electron diffraction patterns and high-resolution electron microscopy images of the icosahedral phase in Mn-Al and related systems. Structurally, the model has long-range translational order with a large unit-cell (Im3 space group) containing 10038 atoms, as well as orientational order characterized by symmetry close to the m35 point group which is commonly assigned for quasicrystals.Fig.l(a)-(c) show, respectively, the SAD patterns of the so-called twofold, threefold, and fivefold axes observed in rapid quenched Al-14at%Mn. Simulation of the corresponding SAD patterns (Fig.l(d)-(h)) suggested that they did not result from a single zone-axis diffraction, but from several closely orientated zone axes. For example, Fig.1(f) was generated by the superposition of the [305], [508], and [8 0 13],…. axes (denoted as N-<305>); the rotation angles from the [001] axis to each axis are 30.96°, 32.01°, and 31.61 °, respectively. All are very close to 31.71 °, which is the angle between a twofold and a fivefold axis in the m35 point group. In a conventional electron diffraction experiment, if the [001] axis of the crystal is rotated 31.71° around the [010] axis, these three zone axes would simultaneously satisfy the Bragg conditions and cannot be separated. Such superposition in the projected diffraction pattern, especially when the unit-cell is large, can yield a pseudo-fivefold symmetry which is indistinguishable with a true fivefold symmetry in SAD.

Structural freedom, topological disorder, and the irradiation-induced amorphization of ceramic structures

The susceptibility to irradiation-induced loss of long-range translational and orientational order during amorphization of crystalline solids, a process which usually amounts to topological disordering, can be understood on the basis of available structural freedom which depends on the redundancies present in structural connectivity. A surprisingly good correlation has been established between the critical accumulated energy deposited per atom — or displacements per atom (dpa) — required for amorphization during ion irradiation and the calculated structural freedom for the structure type irradiated over a wide range of non-metal structural types. These include AO, AO 2, A 2O 3, ABO 3, ABO 4, A 2B 2O 7 and A 2BO 4 compact structure types, in which weakest links can often be identified, as well as less-compact network structures. The present contribution specifically compares the order of susceptibility to amorphization — in these more complex oxide structures and in the simpler network structures Si 3N 4, SiC, Be 2SiO 4, AlPO 4, Si, SiO 2, P 2O 5 and graphite — on the basis of structural connectivity and discusses the anomalous susceptibility of SiC.

Network topology in aperiodic networks

Topological descriptions are an attractive alternative to conventional crystallographic formalism for describing crystals and are essential for describing aperiodic states lacking long-range translational and orientational order. In networks, topological connectivity approaches are usefully applied in making assessments of glass-forming ability and in providing a local description of network structure which can assess extendability. The structural freedom required to form aperiodic networks is directly related to connectivity, and the range of allowable structural possibilities can be enumerated using combinatorial geometry. Detailed applications to periodic and aperiodic network silicas are reviewed.

Backbone ordering in amphiphile monolayers

In this paper we describe a lattice density functional theory for the rotator-herringbone phase transition in a liquid supported monolayer system of long chain acids or alcohols. It is assumed that both phases have long-range translational order and that the rotator phase is characterized by a uniform distribution of backbone orientation. We find that orientational interactions among the backbone planes are sufficient to drive a second order transition, and we characterize the phase of the system by a parameter associated with the width of the peaks in a distribution which describes the orientations of the backbones. We also briefly discuss generalizations of the theory to include lattice vibrations and distortions.

Structural-diffraction analysis of nanocrystalline materials

We have studied the structure and phases of boron nitride and zirconium dioxide (both have a wide spectrum of crystalline sizes) using x-ray analysis and electron diffraction microscopy. We show that, even when the crystallites are of order 100 nm, their diffraction pattern is similar to that of other nanocrystalline materials. This pattern is dictated by the high degree of dispersion and the lattice distortions of the crystallites' periphery. The distortions in these materials are caused by internal stresses. In boron nitride the stress relaxes by polygonization of the peripheral regions. This destroys the long-range translational order and leads to the formation of intercrystallite regions due to incoherent binding between crystals. In zirconium oxide short-range order is destroyed by variations in the lattice constants in the regions near the crystal faces.

Magnetic structures of high Tc superconductors: technique for decoration and data analysis

A description of the experimental set up for the decoration of vortex lattices is presented together with an analysis of the decoration parameters. A particular characteristic of our experimental set up is that the production and transfer of ferromagnetic particles towards the superconductor surface can be controlled. Examples of vortex lattice decorations, related to different types of studies, are reported with different analyses of the structure, and the long-range translational and bond-orientational microscopic order of decorated patterns.

Medium-range structural order in covalent amorphous solids

Despite their lack of long-range translational and orientational order, covalent amorphous solids can exhibit structural order over both short and medium length scales, the latter reaching to 20 A or so. Medium-range order is difficult to measure experimentally and to interpret unambiguously, but a variety of techniques have allowed several types of characteristic structural ordering to be identified and their origin elucidated.

Quasicrystal Structure and Properties

Quasicrystals possess long-range positional order, but noncrystallographic orientational order. Since 1 984, when Shechtman and coworkers ( 1 , 2) discovered icosahedral order in rapidly quenched AI6Mn, the field has blossomed into an active subject of research in metallurgy, crystallography, and condensed matter physics. Much of the work done to date, and the main focus of this review concerns the problem of quasicrystal structure. Although important open questions in this area remain, we now under­ stand many fundamental structural principles. For example, it is now well established that equilibrium quasicrystal phases exist, and that they possess long-range quasiperiodic translational order. One cannot yet specify the location of each atom; however, much is known about the description of the structures. First, the recognition that related crystalline compounds consist of interpenetrating atomic clusters