Crystal Structure of Phases

Due to aperture restrictions, selected area methods are only applicable for examining areas of perhaps 0.5 Xm or more in diameter. It is also possible to obtain spot patterns from much smaller areas—down to as little as a nanometer or so in diameter—by using a focused incident electron beam, rather than an aperture, to limit the sample area under examination. Such microdiffraction patterns are somewhat more complex due to the nonparallel illumination, but they may also contain more information. For example, so-called convergent-beam electron diffraction (CBED) patterns provide three-dimensional information about the compounds crystal chemistry and can be used as a sensitive fingerprint for a given atomic structure.  

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In this paper we examine electron diffraction fiber patterns of the homopolymer polytetrafluoroethylene (-CF2 CF2-)n PTFE, in which the resolution is sufficient to yield much more accurate values of layer line heights than were available from the previous x-ray diffraction experiments (1) on the crystal structure of Phase II, the phase below the 19°C transition (2). On the basis of x-ray data, the molecule was assigned the conformation 13/6 or thirteen CF2 motifs regularly spaced along six turns of the helix. This is equivalent to a 132 screw axis. The relationship between the molecular conformation and the helical symmetry has been studied by Clark and Muus (3) and is illustrated in Figure 1. The electron diffraction data of high resolution enabled us to determine if this unusual 13-fold symmetry was exact or an approximation of the true symmetry. We have also... 

Determination of the crystal structure of phase II by Lonsdale in 1929 unequivocally settled over 70 years of debate concerning the geometry and bonding of aromatic molecular systems. The measured bond lengths and crystal structure of hexamethylbenzene are shown in Fig. 9.6.1. The hexamethylbenzene molecules lie within planes approximately perpendicular to (111). Phase III is structurally very similar to phase II, but differs from it mainly by a shearing process between molecular layers that results in a pseudo-rhombohedral, more densely packed arrangement. 

Phase X has been observed in a number of studies on hydrous potassium-bearing systems (Trpnnes, 1990, 2002 Inoue et al., 1998a Luth, 1997). Its stability relations have been studied by Konzett and Fei (2000), who found that it breaks down between 20 GPa and 23 GPa at 1,500-1,700 °C. Its breakdown products were reported by Konzett and Fei (2000) to be K-hollandite, y-Mg2Si04, majorite, Ca-perovskite, and fluid. Hence, phase X is not succeeded by another hydrous potassic solid phase, and is therefore the hydrous potassic (solid) phase with the highest-pressure stability. The crystal structures of phase X and some related phases were determined by Yang et al. (2001). 

Yang H., Konzett J., and Prewitt C. T. (2001) Crystal structure of phase X, a high pressure alkali-rich hydrous silicate and its anhydrous equivalent. Am. Mineral 86, 1483-1488. 

Determining the crystal structure of phase V has been challenging for several reasons, including (i) its coexistence with other phases due to an incomplete transformation of phase III and/or the metastability of other high temperature phase IV and II, (ii) the presence of large lattice distortion and (iii) highly preferred orientation. Nevertheless, the x-ray data... 

Nimmo. J.K. Lucas, B.W. Solid-state phase transition in triethylenediamine. N(CH2CH2)3N. I. The crystal structure of phase II at 298 K. Acta Crystallogr.. B 1976. 32. 348-353. 

The constitution of the C-Fe-Mo system is of great interest not only because molybdenum is one of the main alloying elements in tool and heat-resisting steels, but also because the complete C-Fe-Mo phase diagram is required in many other applications. Most of the available literature on the C-Fe-Mo system is devoted to investigation of the structure and properties of molybdenum steels. The data on phase relations and crystal structure of phases are presented mainly in the works listed in Table 1. 

Ahrens, T.J., Anderson, D.L., and Ringwood, A.E. (1969), Equation of State and Crystal Structures of High-Pressure Phases of Shocked Silicates and Oxides, Rev. Geophys. 7, 667-707. 

Figure 6.4 Crystal structure of ar-tetragonal boron. This was originally thought to be B50 (4Bi2 + 2B) but is now known to be either B50C2 or B50N2 in which the 2C (or 2N) occupy the 2(b) positions the remaining 2B are distributed statistically at other vacant sites in the lattice. Note that this reformulation solves three problems which attended the description of the or-tetragonal phase as a crystalline modification of pure B ...

Whether the adsorbed hydrogen is produced from the gas phase or from aqueous solution, it appears that the presence of hydrogen atoms distorts the crystal structure of the metal surface, and this results in a surface solubility which is higher than that of the bulk. The depth of this distortion is not clear, but it seems possible that the distorted zone may play an important part in initiating brittle-fracture processes. 

The second way in which an electroactive species such as lithium can be incorporated into the structure of an electrode is by a topotactic insertion reaction. In this case the guest species is relatively mobile and enters the crystal structure of the host phase so that no significant change in the structural configuration of the host lattice occurs. 

Although the phase which appears to be very stable for plutonium has not been observed in other An02 S03 H20 systems, phases of identical composition have been observed for Zr, Hf and Ce. The crystal structure of the zirconium compound Zr2(0H)2-(SOO 3 (H20) i,, is well known 05). One very interesting feature of the M02 S03 H20 systems for Zr, Hf and Co is that there are a large number of phases which have been observed. Some of these correspond to phases which are known for Th, U and Np. For zirconium, a series of basic sulfates is known to include Zr2(0H)2-(SOi,) 3 (H20)i, and two modifications of Zr(0H)2S0i, as the major constituents (5). Other basic sulfates such as Zr(OH)2S0if,H20,... 

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