Two superlattices

The treatment of such order-disorder phenomena was initiated by Gorsky (1928) and generalized by Bragg and Williams (1934) [5], For simplicity we restrict the discussion to the synnnetrical situation where there are equal amounts of each component (x = 1/2). The lattice is divided into two superlattices a and p, like those in the figure, and a degree of order s is defined such that the mole fraction of component B on superlattice p is (1 +. s)/4 while that on superlattice a is (1 -. s)/4. Conservation conditions then yield the mole fraction of A on the two superlattices... 

By convention, surface superlattices are given names like 31/2 x 1 R 30° this is Wood s 20 notation of 1964 [8], [9]. This notation describes the symmetry of the superlattice, but does not identify its origin—that is, the exact point where the superlattice is anchored (even though this is a very desirable datum for aficionados of chemisorption). The 3m x 1 R 30° superlattice means that (1) the fls and b axes of the superlattice crystal lie in the plane of the surface of index hkl (whose axes we call abM and bbki), (2) the first superlattice axis as is 31/2 times longer than the first surface axis fl(3) the second superlattice axis bs is equal in length to the second surface axis b/ h (4) these two superlattice axes fls and bs are then rotated by 30° clockwise. An alternative notation uses... 

Figure A2.5.18. Body-centred cubic arrangement of (3-brass (CiiZn) at low temperature showing two interpenetrating simple cubic superlattices, one all Cu, the other all Zn, and a single lattice of randomly distributed atoms at high temperature. Reproduced from Hildebrand J H and Scott R L 1950 The Solubility of Nonelectrolytes 3rd edn (New York Reinliold) p 342.

One fiirther method for obtaining surface sensitivity in diffraction relies on the presence of two-dimensional superlattices on the surface. As we shall see fiirtlrer below, these correspond to periodicities that are different from those present in the bulk material. As a result, additional diffracted beams occur (often called fractional-order beams), which are uniquely created by and therefore sensitive to this kind of surface structure. XRD, in particular, makes frequent use of this property [4]. Transmission electron diffraction (TED) also has used this property, in conjunction with ultrathin samples to minimize bulk contributions [9]. 

Figure Bl.21.3. Direct lattices (at left) and corresponding reciprocal lattices (at right) of a series of connnonly occurring two-dimensional superlattices. Black circles correspond to the ideal (1 x 1) surface structure, while grey circles represent adatoms in the direct lattice (arbitrarily placed in hollow positions) and open diamonds represent fractional-order beams m the reciprocal space. Unit cells in direct space and in reciprocal space are outlined.

Islands occur particularly with adsorbates that aggregate into two-dimensional assemblies on a substrate, leaving bare substrate patches exposed between these islands. Diffraction spots, especially fractional-order spots if the adsorbate fonns a superlattice within these islands, acquire a width that depends inversely on tire average island diameter. If the islands are systematically anisotropic in size, with a long dimension primarily in one surface direction, the diffraction spots are also anisotropic, with a small width in that direction. Knowing the island size and shape gives valuable infonnation regarding the mechanisms of phase transitions, which in turn pemiit one to leam about the adsorbate-adsorbate interactions. 

Andres R P ef a/1996 Self-assembly of a two-dimensional superlattice of molecularly linked metal clusters Science 273 1690... 

A new chapter in the uses of semiconductors arrived with a theoretical paper by two physicists working at IBM s research laboratory in New York State, L. Esaki (a Japanese immigrant who has since returned to Japan) and R. Tsu (Esaki and Tsu 1970). They predicted that in a fine multilayer structure of two distinct semiconductors (or of a semiconductor and an insulator) tunnelling between quantum wells becomes important and a superlattice with minibands and mini (energy) gaps is formed. Three years later, Esaki and Tsu proved their concept experimentally. Another name used for such a superlattice is confined heterostructure . This concept was to prove so fruitful in the emerging field of optoelectronics (the merging of optics with electronics) that a Nobel Prize followed in due course. The central application of these superlattices eventually turned out to be a tunable laser. 

Colloidal crystals . At the end of Section 2.1.4, there is a brief account of regular, crystal-like structures formed spontaneously by two differently sized populations of hard (polymeric) spheres, typically near 0.5 nm in diameter, depositing out of a colloidal solution. Binary superlattices of composition AB2 and ABn are found. Experiment has allowed phase diagrams to be constructed, showing the crystal structures formed for a fixed radius ratio of the two populations but for variable volume fractions in solution of the two populations, and a computer simulation (Eldridge et al. 1995) has been used to examine how nearly theory and experiment match up. The agreement is not bad, but there are some unexpected differences from which lessons were learned. 

Carlo-simulations for LI2 superlattice including saddle-point energies for atomic jumps in fact yielded two-process kinetics with the ratio of the two relaxation times being correlated with the difference between the activation barriers of the two sorts of atom. 

The core structure of the 1/2 [112] dislocation is shown in Fig. 4. This core is spread into two adjacent (111) plames amd the superlattice extrinsic stacking fault (SESF) is formed within the core. Such faults have, indeed, been observed earlier by electron microscopy (Hug, et al. 1986) and the recent HREM observation by Inkson amd Humphreys (1995) can be interpreted as the dissociation shown in Fig. 4. This fault represents a microtwin, two atomic layers wide, amd it may serve as a nucleus for twinning. Application of the corresponding external shear stress, indeed, led at high enough stresses to the growth of the twin in the [111] direction. 

That w changes with phase has been shown49 for the tetragonal CuAu superlattice and the face-centered cubic solid solution from measurements of the enthalpies of formation of these two phases. Such measurements for the f.c.c. phase lead to w = 373 cal/g atom, in good agreement with the 350 cal/g atom derived by... 

Two requirements should be satisfied in order to achieve the enhancement in strength of the superlattices modulation wavelength (X.) in the scale of nanometre and sharp interfaces between layers. There is an optimum for a superlattice film to achieve the maximum strength, as shown in Fig. 12 [100-102]. The strength of the superlattice film will de-... 

Superhard materials implies the materials with Vickers hardness larger than 40 GPa. There are two kinds of super-hard materials one is the intrinsic superhard materials, another is nanostructured superhard coatings. Diamond is considered to be the hardest intrinsic material with a hardness of 70-100 GPa. Synthetic c-BN is another intrinsic superhard material with a hardness of about 48 GPa. As introduced in Section 2, ta-C coatings with the sp fraction of larger than 90 % show a superhardness of 60-70 GPa. A typical nanostructured superhard coating is the heterostructures or superlattices as introduced in Section 4. For example, TiN/VN superlattice coating can achieve a super-hardnessof56 GPa as the lattice period is 5.2 nm[101]. 

The proposed technique seems to be rather promising for the formation of electronic devices of extremely small sizes. In fact, its resolution is about 0.5-0.8 nm, which is comparable to that of molecular beam epitaxy. However, molecular beam epitaxy is a complicated and expensive technique. All the processes are carried out at 10 vacuum and repair extrapure materials. In the proposed technique, the layers are synthesized at normal conditions and, therefore, it is much less expansive. The presented results had demonstrated the possibility of the formation of superlattices with this technique. The next step will be the fabrication of devices based on these superlattices. To begin with, two types of devices wiU be focused on. The first will be a resonant tunneling diode. In this case the quantum weU will be surrounded by two quantum barriers. In the case of symmetrical structure, the resonant... 

Two-Dimensional and Three-Dimensional Superlattices Syntheses and Collective Physical Properties... 

Chapter 8 presents evidence on how the physical properties of colloidal crystals organized by self-assembly in two-dimensional and three-dimensional superlattices differ from those of the free nanoparticles in dispersion. 

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