Cubic structures

In this illustration, a Kohonen network has a cubic structure where the neurons are columns arranged in a two-dimensional system, e.g., in a square of nx I neurons. The number of weights of each neuron corresponds to the dimension of the input data. If the input for the network is a set of m-dimensional vectors, the architecture of the network is x 1 x m-dimensional. Figure 9-18 plots the architecture of a Kohonen network. 

Krypton is present in the air to the extent of about 1 ppm. The atmosphere of Mars has been found to contain 0.3 ppm of krypton. Solid krypton is a white crystalline substance with a face-centered cubic structure which is common to all the "rare gases."... 

At 31OC, lanthanum changes from a hexagonal to a face-centered cubic structure, and at 865C it again transforms into a body-centered cubic structure. 

The metal has a bright silvery metallic luster. Neodymium is one of the more reactive rare-earth metals and quickly tarnishes in air, forming an oxide that spalls off and exposes metal to oxidation. The metal, therefore, should be kept under light mineral oil or sealed in a plastic material. Neodymium exists in two allotropic forms, with a transformation from a double hexagonal to a body-centered cubic structure taking place at 863oC. 

As with other related rare-earth metals, gadolinium is silvery white, has a metallic luster, and is malleable and ductile. At room temperature, gadolinium crystallizes in the hexagonal, close-packed alpha form. Upon heating to 1235oG, alpha gadolinium transforms into the beta form, which has a body-centered cubic structure. 

Figure 1.4 (a) Close packing of atoms in a cubic structure, showing six... 

In the face-centred cubic structure tirere are four atoms per unit cell, 8x1/8 cube corners and 6x1/2 face centres. There are also four octahedral holes, one body centre and 12 x 1 /4 on each cube edge. When all of the holes are filled the overall composition is thus 1 1, metal to interstitial. In the same metal structure there are eight cube corners where tetrahedral sites occur at the 1/4, 1/4, 1/4 positions. When these are all filled there is a 1 2 metal to interstititial ratio. The transition metals can therefore form monocarbides, niU ides and oxides with the octahedrally coordinated interstitial atoms, and dihydrides with the tetrahedral coordination of the hydrogen atoms. 

In compound materials - in the ceramic sodium chloride, for instance - there are two (sometimes more) species of atoms, packed together. The crystal structures of such compounds can still be simple. Figure 5.8(a) shows that the ceramics NaCl, KCl and MgO, for example, also form a cubic structure. Naturally, when two species of atoms are not in the ratio 1 1, as in compounds like the nuclear fuel UO2 (a ceramic too) the structure is more complicated (it is shown in Fig. 5.8(b)), although this, too, has a cubic unit cell. 

Fig. 16.3. Covalent ceramics, (a) The diamond-cubic structure each atom bonds to four neighbours.

Silicon atoms bond strongly with four oxygen atoms to give a tetrahedral unit (Fig. 16.4a). This stable tetrahedron is the basic unit in all silicates, including that of pure silica (Fig. 16.3c) note that it is just the diamond cubic structure with every C atom replaced by an Si04 unit. But there are a number of other, quite different, ways in which the tetrahedra can be linked together. 

Pure silica contains no metal ions and every oxygen becomes a bridge between two silicon atoms giving a three-dimensional network. The high-temperature form, shown in Fig. 16.3(c), is cubic the tetrahedra are stacked in the same way as the carbon atoms in the diamond-cubic structure. At room temperature the stable crystalline form of silica is more complicated but, as before, it is a three-dimensional network in which all the oxygens bridge silicons. 

When the wind encounters objects in its path such as an isolated structure, the flow usually is strongly perturbed and a turbulent wake is formed in the vicinity of the structure, especially downwind of it. If the structure is semistreamlined in shape, the flow may move around it with little disturbance. Since most structures have edges and corners, generation of a turbulent wake is quite common. Figure 17-23 shows schematically the flow in the vicinity of a cubic structure. The disturbed flow consists of a cavity... 

In the solid state, the Ceo molecules crystallize into a cubic structure with a lattice constant of 14.17A, a nearest neighbor Ceo-Ceo distance of 10.02A [41], and a mass density of 1.72 g/cm (corresponding to 1.44 Ceo... 

Figure 3.27. The first Brillouin zone of the facc-ccntrcd cubic structure, after Pippard.

Tetrameric structures based on distorted cubic structures are also found for (CH3Li)4 and (C2H5Li)4. These tetrameric structures can also be represented as being based on a... 

Figure 13.2 The cubic structure of skutterudite (C0AS3). (a) Relation to the ReOs structure (b) unit cell (only sufficient Co-As bonds are drawn to show that there is a square group of As atoms in only 6 of the 8 octants of the cubic unit cell, the complete 6-coordination group of Co is shown only for the atom at the body-centre of the cell) and (c) section of the unit cell showing CoAsg octahedra comer-linked to form AS4 squares.

Figure 21.3 Two representations of the structure of perovskite, CaTi03, showing (a) the octahedral coordination of Ti, and (b) the twelve-fold coordination of Ca by oxygen. Note the relation of (b) to the cubic structure of Re03 (p. 1047).

The thermal strain measurements described above have the common feature of anisotropic behaviour in a supposed isotropic state (cubic structure). These observations go well beyond the short-range, static strain fields associated with the lattice impurities responsible for Huang scattering. This then raises the question of the temperature at which the lattice symmetry changes and the implications of this for the central mode scattering. 

From Fig. 3.11, it can be seen that by increasing the chromium content while maintaining a limited amount of nickel-equivalent elements, first mixed martensite-ferrite structures are produced and then fully ferritic. This is 6-ferrite, that is a body-centred cubic structure stable at all temperatures. Relative to martensite it is soft, but it is also usually brittle. For this latter reason, usage has in the main been in small section form. This and some other disadvantages are offset for some purposes by attractive corrosion resistance or physical properties. 

Structure Although massive chromium has a body-centred cubic structure, electrodeposited chromium can exist as two primary modifications, i.e. a-(b.c.c.) and (c.p.h.). The precise conditions under which these forms of chromium can be deposited are not known with certainty. Muro" showed that at 40°C and 2-0-22 A/dm the deposit was essentially a-chromium but small amounts of 0- and 7- were present, while Koch and Hein observed... 

Allotropy in the solid state can also arise because of differences in crystal structure. For example, solid iron has a body-centered cubic structure (recall Figure 9.16, page 246) at room temperature. This changes to a face-centered structure upon heating to 910°C. 

According to these authors all gas hydrates crystallize in either of two cubic structures (I and II) in which the hydrated molecules are situated in cavities formed by a framework of water molecules linked together by hydrogen bonds. The numbers and sizes of the cavities differ for the two structures, but in both the water molecules are tetrahedrally coordinated as in ordinary ice. Apparently gas hydrates are clathrate compounds. 

The solid is polymorphic, with a cubic structure above 1.4°C. A bond length of 1.816 A has been obtained from EXAFS measurements at 10K, while vapour phase measurements give Os-F of 1.831 A [22],... 

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