Face-centred cubic crystal

EXAFS spectra of platinum metal, having a face-centred cubic crystal stmcture, have been obtained at 300 K and 673 K. Explain what qualitative differences you might expect. How many nearest-neighbour atoms are there in this stmcture Illustrate your answer with a diagram. 

We begin by looking at the smallest scale of controllable structural feature - the way in which the atoms in the metals are packed together to give either a crystalline or a glassy (amorphous) structure. Table 2.2 lists the crystal structures of the pure metals at room temperature. In nearly every case the metal atoms pack into the simple crystal structures of face-centred cubic (f.c.c.), body-centred cubic (b.c.c.) or close-packed hexagonal (c.p.h.). 

Except for Ceo, lack of sufficient quantities of pure material has prevented more detailed structural characterization of the fullerenes by X-ray diffraction analysis, and even for Ceo problems of orientational disorder of the quasi-spherical molecules in the lattice have exacerbated the situation. At room temperature Cgo crystallizes in a face-centred cubic lattice (Fm3) but below 249 K the molecules become orientationally ordered and a simple cubic lattice (Po3) results. A neutron diffraction analysis of the ordered phase at 5K led to the structure shown in Fig. 8.7a this reveals that the ordering results from the fact that... 

Crystal structure Martensite (body centred cubic) austenite (face centred cubic)... 

Their normal crystal structure, at ambient conditions, corresponds to the body-centred cubic cI2-W-type structure. At very low temperatures, the close-packed hexagonal hP2-Mg-type structure has been observed for Li and Na, while for Rb and Cs the face-centred cubic close-packed cF4-Cu-type structure is known at high pressure. No polymorphic transformation has been reported for potassium. 

With the exception of He, solid noble gases crystallize in the face-centred-cubic Bravais lattice and their cohesive energies (eV atom ) are 0.02 for Ne, 0.08 for Ar, 0.11 for Kr and 0.17 for Xe (Ashcroft Mermin, 1976 p. 401). VanderWaals-Londonforces areexpressedby theLennard-Jonespotential f/u a — CaZ> ,... 

AFMs have also been used to eshmate the cohesive energy of ionic materials with face-centred-cubic structure (Fraxedas et al., 2002a). In these experiments an ultrasharp AFM hp (hp radius / < 10 nm) indents a hat surface of a single crystal and the dynamical mechanical response of the surface during indentahon is transformed into a force plot (applied force vs. penetrahon). It turns out that the... 

In a face centred cubic crystal of atomic volume F the packing density is as follows (Langmuir, J.A.G.S. xxxvill. 2748, 1916). 

A powder diffraction pattern establishes that silver crystallizes in a face-centred cubic unit cell. The 111 reflection is observed at 0=19.1°, using Cu-Ka radiation. Determine the unit cell length, a. If the density of silver is 10.5x10 kg m and Z=4, calculate the value of the Avogadro constant. (The atomic mass of silver is 107.9.)... 

Calcium oxide crystallizes with a face-centred cubic lattice, a=481 pm and a density /)=3.35x10 kg m calculate a value for Z (Atomic masses of Ca and 0 are 40.08 and 15.999, respectively.)... 

Photonic crystals have only been studied in the laboratory for two decades, but naturally occurring examples exist, with the best known being the gemstone opal. Opals consist of tiny spheres of silica arranged in a face centred cubic structure. These are thought to have formed from colloidal silica solutions, and the colour depends on the size of the spheres. 

If the 100 mA 770 reflections are absent then the crystal Is likely to be face-centred cubic. 

Figure 7.1 Three common crystal lattices adopted by elements (a) body-centred cubic packing, (b) cubic closest packed (or face-centred cubic) and (c) hexagonal closest packed...

The first attempt to calculate realistic wave functions for electrons in metals is that of Wigner and Seitz (1933). These authors pointed out that space in a body-or face-centred cubic crystal could be divided into polyhedra surrounding each atom, that these polyhedra could be replaced without large error by spheres of radius r0, so that for the lowest state one has to find spherically symmetrical solutions of the Schrodinger equation (6) subject to the boundary condition that... 

We shall now discuss the method of crystal growth and the electronic properties of GaAs, a typical example of a III-V compound which is expected to become more useful than Si and Ge in the near future, concentrating on the relation between non-stoichiometry and physical properties. GaAs has a zinc blende type structure, which can be regarded as an interpenetration of two structures with face centred cubic lattices, as shown in Fig. 3.29. Disregarding the atomic species, the structure is the same as a diamond-type... 

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