Other Crystal Structures

Corundum (0A/2O3) structure displays trigonal (or rhombohedral) symmetry. When considering an ionic configuration (A/3+)2 (02 )3, the point group 

Ashcroft, N.D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976) 

Dresselhaus, G. Dresselhaus, A. Jorio, Group Theory Application to the Physics of Condensed Matter (Springer, New York, 2008) 

Group Theory in Quantum Mechanics (Pergamon Press, Oxford, 1964) 

Kittel, Introduction to Solid State Physics, 7th edn. (Wiley, New York, (1996) 

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First, the stability of the fitted Llo structure relative to other crystal structure with the same composition can be studied. In the present case we calculated the cohesive energies of fully relaxed B2 and structure 40 compounds and found 4.41eV and 4.50 eV, respectively. These are both lower than the cohesive energy of the Llo structure. Structure B19 was also investigated but relaxation always transformed this structure into Llo. 

Now the gradual decline in intensity for h — 4, 8,12 (Table I) requires that uy = -J-, and hence % = -J-. This puts the two sets of metal atoms in the same place, and is hence ruled out. It may also be mentioned that structure 1 would place eight metal atoms on a cube diagonal, giving a maximum metal-metal distance of 2.03 A, which is considerably smaller than metal-metal distances observed in other crystals. Structure 2, dependent on one parameter u, has structure factors... 

Any two samples of a particular mineral, whatever their source or place of origin, have the same basic composition and characteristic crystal structure moreover, no two different minerals have identical chemical composition and crystal structure (see Textboxes 8 and 21). Quartz, for example, is a common and abundant mineral composed of silicon dioxide, a compound that occurs naturally not only as quartz but also in other crystal structures, known as polymorphs (polymorphs are minerals that have the same chemical composition but different crystal structure), some of which, listed in Table 23, have been used for a variety of purposes. The crystal structure, which is essential for the characterization of solid materials, is just one of a wide range of physical properties, that is, properties not involving chemical differences, which provide convenient criteria for characterizing and identifying solids. 

Figure 4.7 shows top-down views of the fee (001), (111), and (110) surfaces. These views highlight the different symmetry of each surface. The (001) surface has fourfold symmetry, the (111) surface has threefold symmetry, and the (110) has twofold symmetry. These three fee surfaces are all atomically flat in the sense that on each surface every atom on the surface has the same coordination and the same coordinate relative to the surface normal. Collectively, they are referred to as the low-index surfaces of fee materials. Other crystal structures also have low-index surfaces, but they can have different Miller indices than for the fee structure. For bcc materials, for example, the surface with the highest density of surface atoms is the (110) surface. 

Earlier, we mentioned that other crystal structures can have different Miller indices than the fee structure. In the hexagonal close-packed (hep)... 

Here again certain trends were observed, and the most influential factor was the crystal structure which the superconducting material adopted. The most fruitful system was the NaCl-type structure (also referred to as the B1 structure by metallurgists). Many of the important superconductors in this ceramic class are based on this common structure, or one derived from it. Other crystal structures of importance for these ceramic materials include the Pu2C3 and MoB2 (or ThSi2) prototypes. A plot of transition temperature versus the number of valence electrons for binary and ternary carbides shows a broad maximum at 5 electrons per atom, with a Tc maximum at 13 K. 

Platinum crystal surfaces that were prepared in the zones indicated by the arrows at the sides of the triangle are thermally unstable. These surfaces, on heating, will rearrange to yield the two surfaces that appear at the end of the arrows. There is reason to believe that the thermal stability exhibited by various low and high Miller index platinum surfaces is the same for other fee metals. There are, of course, differences expected for surfaces of bcc solids or for surfaces of solids with other crystal structures. 

R. C. Haddon (AT T Bell Laboratories, U.SA.). I was wondering, are there any other crystal structures, besides the one you showed, of the long polyacetylene molecules for structures known ... 

Computational results were obtained using Spartan 08 (Wavefunction Inc., Irvine, CA) and software programs from Accelrys Software Inc. with graphical displays generated by the Discovery Studio Visualizer. Where protein structures have been downloaded from the RCSB Protein Data Bank the full references and PDB IDs have been given. I wish to acknowledge the use of the Chemical Database Service at Daresbury for access to other crystal structures. Again, full primary sources can be found in the references. 

Henceforth, crystal structure analyses of carbohydrates (class 45), amino acids (class 48), purines and pyrimidines (class 44) and nucleosides and nucleotides (class 47) are referenced by means of their Cambridge Crystallographic Data Base REFCODES. All other crystal structure analyses are referenced in the General Index. 

Ice at 0°C has a hexagonal structure. At temperatures below about --80 C a cubic, diamond-type structure can be obtained. Shallcross and Carp>enter found that H2O vapor condensed at very low temperatures sometimes forms amorphous solid and sometimes a mixture of the cubic and hexagonal forms (1835). Ice prepared or annealed above — 80°C takes the hexagonal form and remains in this crystal form even though the solid is recooled to — 196°C. There are other crystal structures which become stable at high pressures. 

In the high-temperature form of this mineral, the A1 and Si atoms are distributed at random (in 1 3 proportion) over the tetrahedral sites available to them. At lower temperatures, other crystal structures become thermodynamically stable, with partial ordering of the A1 and Si sites. 

Few other crystal structures of metal dithiophosphonates have been reported. These include the trans isomers of the O-ethylphenyldithiophosphonates of palladium(II) and platinum(II), M[S2P(OEt)Ph]2 (M = Pd, Pt), along with a report of cis-trans isomerization of the planar palladium(II) complex.114 The crystal structures of palladium and platinum /nmv-bis[(7-methyl (4-methoxyphenyl)phosphonodithioato] complexes, M[S2P(OMe)C6H4OMe-p]2, (M = Pd and Pt) have also been reported.107,108... 

In 1984 the crystal structures of (Ti(OPr )2(OC(ONHCH2Ph))2)2 (52) and (Ti(OEt)(OC-(OEt))2)(ON(Ph)CPh))2 (53) were determined 576 Since then the propensity of the tartrate ligand to adopt multiple binding modes was confirmed by a number of other crystal structures 577... 

In addition to these deviations from the ideal structure, other crystal structure defects e.g., stacking faults) are the subject of line profile analyses. Correction by taking into account instrumental contributions is of even greater importance in the study of defects and microstructure (LPA), as discussed in Chapter 13. 

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