Two-dimensional layers

The pursuit of further miniaturization of electronic circuits has made submicrometer resolution Hthography a cmcial element in future computer engineering. LB films have long been considered potential candidates for resist appHcations, because conventional spin-coated photoresist materials have large pinhole densities and variations of thickness. In contrast, LB films are two-dimensional, layered, crystalline soHds that provide high control of film thickness and are impermeable to plasma down to a thickness of 40 nm (46). The electron beam polymerization of CO-tricosenoic acid monolayers has been mentioned. Another monomeric amphiphile used in an attempt to develop electron-beam-resist materials is a-octadecylacryUc acid (8). 

Phase transitions in two-dimensional layers often have very interesting and surprising features. The phase diagram of the multicomponent Widom-Rowhnson model with purely repulsive interactions contains a nontrivial phase where only one of the sublattices is preferentially occupied. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are molecular layers of H2, D2, N2 and CO molecules on graphite substrates. We review the path integral Monte Carlo (PIMC) approach to such phenomena, clarify certain experimentally observed anomalies in H2 and D2 layers, and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are analyzed via PIMC as well. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions where quantum effects play a role. 

The structure of graphite. Graphite has a two-dimensional layer structure with weak dispersion forces between the layers. 

Graphite forms extended two-dimensional layers (see Fig. 5.22). (a) Draw the smallest possible rectangular unit cell for a layer of graphite, (b) How many carbon atoms are in your unit cell (c) What is the coordination number of carbon in a single layer of graphite ... 

Fig. 14.3 Polyhedral packing plots for the two-dimensional layers of [RE(P2S6),/2(PS4)P in the series of solids A2RE(P2S6)i/2(PS4), where A=K, Cs RE = Y, La. Rare-earth polyhedra are striped PS4 polyhedra are black phosphorous atoms in P2S6 are shown as black circles. Alkali atoms are not shown for clarity. Although these phases have distinctly different structures based on space group symmetry and atomic positions, the compounds are clearly related upon close inspection of the building blocks.

Fig. 4.5. (a) Field due to two-dimensional body, (b) field caused by two elementary masses, (c) the field due to thin two-dimensional layer. 

Pillared clays (MELS) are aLso covered in this review. MELS have three-dimensional network structure like zeolites, and, unlike clays, which have two-dimensional layered structures, pillared cationic and anionic clays have been studied. Phthalocyanins intercalated in anionic clays have given interesting results for wastewater purification (Vaccari, 1998). 

The presence of triethylenetetramine in the hydrothermal synthesis of open-framework zinc phosphates results in a number of frameworks with one- to three-dimensional structures. The structures include one-dimensional ladders, two-dimensional layer structures, and one structure where the tetramine is bound to the zinc center. The structural type was highly sensitive to the relative concentration of the amine and phosphoric acid.411 Piperazine and 2-methylpiperazine can be used as templating molecules in solvothermal syntheses of zinc phosphates. The crystallization processes of the zinc compounds were investigated by real time in situ measurements of synchrotron X-ray powder diffraction patterns.412... 

The phenomenon of nucleation considered is not limited to metal deposition. The same principles apply to the formation of layers of certain organic adsorbates, and the formation of oxide and similar films. We consider the kinetics of the growth of two-dimensional layers in greater detail. While the three-dimensional case is just as important, the mathematical treatment is more complicated, and the analytical results that have been obtained are based on fairly rough approximations details can be found in Ref. 3. 

In order to derive approximate laws for the growth of a two-dimensional layer, we consider a simplified model in which all isolated clusters, i.e. clusters that do not touch another cluster, axe circular. For the moment, consider a single such cluster of radius r(t). New particles can only be incorporated at its boundary. Assuming that this incorporation is the rate-determining step, the number N(t) of particles belonging to the cluster obeys the equation ... 

Another demonstration of the impact of upd on bulk deposition is provided by Pb and T1 deposition on Ag(lll) and Ag(lOO), where the orientation of the three-dimensional crystallites reflects the epitaxially relationship established by the upd layer [341]. For example, in the case of Pb deposition on Ag(lll) [395], a two-dimensional layer, Ag(lll)[110] compressed 2D hep Pb [110] R 4.5°, is initially formed followed by nucleation of a three-dimensional cluster having the same orientational relationship, Ag(lll)[110] 3DPb(lll)[110] R4.5°. 

Smectic mesophase with in-plane short-range positional molecular order, weakly coupled two-dimensional layers and long-range bond orientational molecular order. 

Most silicate-like polymers can be divided into three major classes the network structures based on a three-dimensional tetrahedral geometry (such as quartz), layered geometries with stronger bonding occurring within the two-dimensional layer (such as talc), and linear structures. 

Densities of molecules adsorbed on surfaces are in moles per unit area, which we win give the symbol rij for species j. Typical units of nj are moles per cm. There is a maximum density rijo of molecules packed in a two-dimensional layer on a flat surface when all molecules touch or reach Hquidlike or soHdlike densities. We call this density a monolayer, whose density is approximately the inverse of the square of the molecular diameter, which is less than 1 x lO molecules/cm2 for all molecules (Figure 7-21). We wiU find it convenient also to define a coverage of adsorbed molecules as the fraction of the monolayer density dj,... 

A large fraction of the material science research, and an important chapter of solid state physics are concerned with interfaces between solids, or between a solid and a two dimensional layer. Solid state electronics is based on metal-semiconductor and insulator-semiconductor junctions, but the recent developments bring the interface problem to an even bigger importance since band gap engineering is based on the stacking of quasi two dimensional semiconductor layers (quantum wells, one dimensional channels for charge transport). 

If we define a non-dimensional temperature 0 = 2kT/crystal face (an F face) on which two-dimensional layer growth takes... 

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