Disordered planes

Most fiindamental surface science investigations employ single-crystal samples cut along a low-index plane. The single-crystal surface is prepared to be nearly atomically flat. The surface may also be modified in vacuum. For example, it may be exposed to a gas that adsorbs (sticks) to the surface, or a film can be grown onto a sample by evaporation of material. In addition to single-crystal surfaces, many researchers have investigated vicinal, i.e. stepped, surfaces as well as the surfaces of polycrystalline and disordered materials. 

Unwanted stmctures in the film plane—often found within LB films fonned from simple rodlike molecules or from molecules polymerized after deposition—can be problematic, since many possible applications of such films require a unifonn stmcture within the plane. On the other hand, however, the production of a system in which the stmcture within the plane is so disordered that there exist no stmctural features large enough to cause problems would also render applications possible. In tliree-dimensional materials, for example, both inorganic glasses and many polymers are capable of transmitting light without any appreciable scattering for substantial distances. 

Hydrated bilayers containing one or more lipid components are commonly employed as models for biological membranes. These model systems exhibit a multiplicity of structural phases that are not observed in biological membranes. In the state that is analogous to fluid biological membranes, the liquid crystal or La bilayer phase present above the main bilayer phase transition temperature, Ta, the lipid hydrocarbon chains are conforma-tionally disordered and fluid ( melted ), and the lipids diffuse in the plane of the bilayer. At temperatures well below Ta, hydrated bilayers exist in the gel, or Lp, state in which the mostly all-trans chains are collectively tilted and pack in a regular two-dimensional... 

Diffraction is usefiil whenever there is a distinct phase relationship between scattering units. The greater the order, the better defined are the diffraction features. For example, the reciprocal lattice of a 3D crystal is a set of points, because three Laue conditions have to be exactly satisfied. The diffraction pattern is a set of sharp spots. If disorder is introduced into the structure, the spots broaden and weaken. Two-dimensional structures give diffraction rods, because only two Laue conditions have to be satisfied. The diffraction pattern is again a set of sharp spots, because the Ewald sphere cuts these rods at precise places. Disorder in the plane broadens the rods and, hence, the diffraction spots in x and y. The existence of streaks, broad spots, and additional diffuse intensity in the pattern is a common... 

It may occasion surprise that an amorphous material has well-defined energy bands when it has no lattice planes, but as Street s book points out, the silicon atoms have the same tetrahedral local order as crystalline silicon, with a bond angle variation of (only) about 10% and a much smaller bond length disorder . Recent research indicates that if enough hydrogen is incorporated in a-silicon, it transforms from amorphous to microcrystalline, and that the best properties are achieved just as the material teeters on the edge of this transition. It quite often happens in MSE that materials are at their best when they are close to a state of instability. 

FIG. 14 Phase diagram of the quantum APR model in the Q -T plane. The solid curve shows the line of continuous phase transitions from an ordered phase at low temperatures and small rotational constants to a disordered phase according to the mean-field approximation. The symbols show the transitions found by the finite-size scaling analysis of the path integral Monte Carlo data. The dashed line connecting these data is for visual help only. (Reprinted with permission from Ref. 328, Fig. 2. 1997, American Physical Society.)... 

To the best of our knowledge, there was only one attempt to consider inhomogeneous fluids adsorbed in disordered porous media [31] before our recent studies [32,33]. Inhomogeneous rephca Ornstein-Zernike equations, complemented by either the Born-Green-Yvon (BGY) or the Lovett-Mou-Buff-Wertheim (LMBW) equation for density profiles, have been proposed to study adsorption of a fluid near a plane boundary of a disordered matrix, which has been assumed uniform in a half-space [31]. However, the theory has not been complemented by any numerical solution. Our main goal is to consider a simple model for adsorption of a simple fluid in confined porous media and to solve it. In this section we follow our previously reported work [32,33]. 

FIG. 13 Phase diagram of a vector lattice model for a balanced ternary amphiphilic system in the temperature vs surfactant concentration plane. W -I- O denotes a region of coexistence between oil- and water-rich phases, D a disordered phase, Lj an ordered phase which consists of alternating oil, amphiphile, water, and again amphi-phile sheets, and L/r an incommensurate lamellar phase (not present in mean field calculations). The data points are based on simulations at various system sizes on an fee lattice. (From Matsen and Sullivan [182]. Copyright 1994 APS.)... 

Draw ratio Degree of crystallinity Lattice disorder coefficient (k) Average crystallite size perpendicular to the crystallographic plane (hkl) Dhki (nm) ... 

The region from the Helmholz plane into the solution, across which the potential varies exponentially attaining a value of zero at some distance in this region the ions are subjected to both ordering electrical forces and disordering thermal forces. 

Figure 4-10. Sketch of Hie operations applied ui a colacial dimer formed by two slilbene molecules separated by 4 A when investigating the role of positional disorder. The modilicalions are induced by (I) the translation of one molecule along the chain-axis direction (II) the translation of one molecule along the in-planc transverse axis (III) the rotation of one slilbene unit around its long axis and (IV) the rotation of one slilbene molecule around the slacking axis while keeping the parallelism between the molecular planes.

B) The model of De Wolff disorder gives no explanation for the line broadening of reflections which are not affected by this type of lattice disorder. Chabre and Pannetier ascribed this effect to a micro twinning of the ramsdel-lite/rutile lattice on the planes [0 2 1] and [0 6 1], These faces are believed to be growth planes of EMD [45, 46],... 

Figure 15. Arrangement of the Mn - O layers and separating sheets according to Giovanoli [3]. The layer structure can be (a) completely ordered or (d) completely disordered (turbostratic disorder). The cases (h) and (c) represent situation between the two extremes, (b) Disorder of the interlayer atoms or molecules but an ordered stacking of the Mn - O layers with constant layer distance, (c) Disorder of the interlayer atoms and an incommensurate shift of the complete Mn - O sheet within the layer plane, resulting in an incommensurate superstructure along the r -direction (perpendicular to the layer) and in a diffuse distribution of the electron density in this layer, resulting in a lower contribution of this layer to the 0 0 / reflections. (Adapted from Ref. [47]).

Pandya et al. have used extended X-ray ascription fine structure (EXAFS) to study both cathodically deposited -Ni(OH)2 and chemically prepared / -Ni(OH)2 [44], Measurements were done at both 77 and 297 K. The results for / -Ni(OH)2 are in agreement with the neutron diffraction data [22]. In the case of -Ni(OH)2 they found a contraction in the first Ni-Ni bond distance in the basal plane. The value was 3.13A for / -Ni(OH)2 and 3.08A for a-Ni(OH)2. The fact that a similar significant contraction of 0.05A was seen at both 77 and 297K when using two reference compounds (NiO and / -Ni(OH)2) led them to conclude that the contraction was a real effect and not an artifact due to structural disorder. They speculate that the contraction may be due to hydrogen bonding of OH groups in the brucite planes with intercalated water molecules. These ex-situ results on a - Ni(OH)2 were compared with in-situ results in I mol L"1 KOH. In the ex-situ experiments the a - Ni(OH)2 was prepared electrochemi-cally, washed with water and dried in vac-... 

The basic building block of carbon is a planar sheet of carbon atoms arranged in a honeycomb structure (called graphene or basal plane). These carbon sheets are stacked in an ordered or disordered manner to form crystallites. Each crystallite has two different edge sites (Fig. 2) the armchair and zig-zag sites. In graphite and other ordered carbons, these edge sites are actually the crystallite planes, while in disordered soft and hard carbons these sites, as a result of turbostratic disorder, may not... 

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