Bet structure

In the tetragonal transformation, the bcc structure is not the local maximum of the D parameter. Although the bcc stracture has a higher density if it is compressed along the tetragonal axis, many elements take this structure. On the other hand, the bet structure is the local maximum of the D parameter in the tetragonal distortion but no metal takes this structure. These results indicate that density is not an important factor for the choice of crystal stracture. 

It should be noted that it is also impossible to explain the insulating nature of A4C60 even if one takes into account the bet structure of the material. See, for example, S. C. Erwin, in Buckminsterfullerenes (eds W. E. Billups and M. A. Ciufolini), VCH Publishers, New York, 1992. 

Figure 3.14. Crystallographic representation of tlie phase transformation from austenite to martensite. Two neighboring fee unit cells of austenite associate, resulting in a body-centered tetragonal (bet) unit cell. A postanneal known as tempering converts the bet structure to a-Fe. Also shown is the placement of an interstitial carbon atom, remaining in an octahedral site among lattice iron atoms.

K+, Rb+ and Cs+ form salts with Cgg which contain monomeric fulleride ions at all temperatures. The structure of these salts is I4/mmm body centered tetragonal (bet) structure at all temperatures [4,59,60], except CS4C60 at room temperature and below, which is Immm orthorhombic (bco) [61]. According to our present knowledge, the fulleride ions in these phases are not rotating [4,60]. Thus the effect of the crystal field must be taken into account. 

Body-centered tetragonal (bet) structure cerium, 278—280, 279/ europium, 431... 

However, other theoretical works showed that the yield stress or viscosity goes tlirough a maximum as the particle volume fraction increases, and the maximum appears at a very high particle volume fraction [105-107]. Under the reaction of an electric field, the spherical particle was assumed to form tlie body-centered tetragonal (bet) structure, and the yield stress could be estimated using the many-body electrostatic interaction method proposed... 

Figure 42. The static yield stress Ts of the bet structure, normalized by 2 ( PiF), plotted as a function of particle volume fraction ( ) for several values of a. Sm is the dielectric constant of dispersing medium, — a- )l a + 2), and a is the dielectric constant ratio of the particle to the dispersing medium, a SpI, and E is the electric field strength.

The electric-tield-induced phase transition in an ER suspension was found to be different from that in general colloidal suspensions. Tao and Martin [55, 56] predicted theoretically tliat the bet structure has an energy lower than that of the fee (face-centered cubic) and other structures, based on dipolar interaction energy calculations. The dipolar interaction energy per particle for various crystal structures is shown in I able 3. The bet crystal structure is shown in Figure 6. 

Figure 6 Three dimensional body-centered tetragonal (bet) structure. The particles have radius r and are not shown to scale.

The laser diffraction method [57] was employed to experimentally determine the crystal structure within the flbrillated columns by using a uniform glass microsphere/silicone oil system, and a bet structure was observed as predicted. The diffraction pattern is shown in Figure 7 for monodispersed glass beads of various sizes. The structure constants determined from the laser diffraction experiment were found to agree very well with the theoretical calculation based on dipolar interaction energy. Table 4 lists the experimentally determined and theoretically calculated structure constants for the bet structure formed by the silica spheres. The experimental data are consistent witli the proposed bet structure. 

The bet structure was also observed by using confocal scanning laser microscopy (581. The bet crystal structure of the monodispersed silica sphere of radius 0.525 pm dispersed into an index matched mixture of 16 wt.% water and 84 wt.% glycerol under an electric field 1 kV/mm is shown in Figure 8 for the suspension of the particle volume fraction about 10 vol%. When the particle volume fraction reaches 45 vol%, without an applied electric field the particles are arranged in fee structure as shown in Figure 9a. Under the reaction of the an electric field of 1 kV/mm and 500 kHz, the fee structure is transformed into the bet structure as shown in Figure 9b. These... 

Figure 9. Bleclric field induced solid-solid transition from fee structure under zero electric field to the bet structure under an electric field. The image shows raw con focal microscope data of a sample of volume fraction 45 vol%. a) A plane parallel to the electrodes before the A -field was turned on. b) The same area about 6 h after an -field (about 1 kV/mm and 500 kHz) is applied perpendicularly to the image plane. Large areas of the eryslal have transformed into bet order, identified by the square configurations. Reproduced with permission from Dassanayakc, S. Fradcn, A. van Blaaderen, J. Chem. Phys. 112(2000)3851...

A yield stress equation was also derived on the basis of the dielectric loss mechanism, as described in the preceding chapter. Under the assumption that only interfacial polarization would contribute to the ER effect and the ER particle would form the bet structure under an electric field, a yield stress equation could be expressed in Eq. (69) or Eq. (70) in Chapter 8, which obviously indicates that the yield stress of an ER fluid would increase with the square of the applied electric field, the particle volume fraction and the dielectric constant of the liquid medium. Those predictions agree very well with previous experimental results [75-77]. 

Fig. 11 SEM images of magnetite (Fe304) colloidal crystals in the Tagish Lake meteorite. The morphology is inset at the upper right in each image, (a) Colloidal crystal with the bet structure composed of octahedral, crystalline nanoparticles of Fc304 bounded by 111 faces, (b) Colloidal crystal with the fee structure. The morphology of theconstituent particles is rhombic-dodecahedral, bounded only by 110 faces, (c) Colloidal crystal with the fee structure composed of particles bounded by 100, 110, and 311 faces. Reprinted with permission from the American Chemical Society. ...

A second precipitating phase, known as 7", can be formed by substituting V or Nb (sometimes called Columbium [Cb]) for the A1 to form NisV or NisNb. These form a bet structure with the V or Nb on the comer lattice sites. Although the coherency is lost in one dimension (1-D), this phase is useful for strengthening alloys such as Inconel 718 where the operating temperatures are not as extreme. 

Fig. 10. The body-centered tetragonal AU4V structure, with the Au atoms placed in ideal positions of 0.2,0.4,0- —0.2, —0.4,0 —0.4, 0.2,0 and 0.4, -0.2, 0 around each V atom the exact values have not been determined. The (disordered) fee unit cell is shown by the dashed lines. In the fee structure a = 4.04 A with an average volume/atom ratio of 16.5 A. When transformed to the idealized bet structure, one of the a axes shrinks to 3.98 A (the c axis) and the other two a axes shrinks to 4.03 A, resulting in a drop of the average volume per atom to 16.2 A (after Chin et...

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