Tetragonal lattice face-centered

A supersonic free jet mixture of metal particles in argon has been studied by electron diffraction. Particles of Bi, Pb, and In of 40-95 A were measured. Changes in crystal structure from that of bulk metal were observed for clusters in the 50-60 A diameter range (2000-4000 atoms/particle). Indium growing particles changed from tetragonal to face-centered cubic as size increased. Lattice parameters of the microcrystals were found to decrease as the cluster size increased. Apparently a high proportion of surface atoms in small clusters favors crystal defects... 

Fig. 2. Structures for the solid (a) fee Cco, (b) fee MCco, (c) fee M2C60 (d) fee MsCeo, (e) hypothetical bee Ceo, (0 bet M4C60, and two structures for MeCeo (g) bee MeCeo for (M= K, Rb, Cs), and (h) fee MeCeo which is appropriate for M = Na, using the notation of Ref [42]. The notation fee, bee, and bet refer, respectively, to face centered cubic, body centered cubic, and body centered tetragonal structures. The large spheres denote Ceo molecules and the small spheres denote alkali metal ions. For fee M3C60, which has four Ceo molecules per cubic unit cell, the M atoms can either be on octahedral or tetrahedral symmetry sites. Undoped solid Ceo also exhibits the fee crystal structure, but in this case all tetrahedral and octahedral sites are unoccupied. For (g) bcc MeCeo all the M atoms are on distorted tetrahedral sites. For (f) bet M4Ceo, the dopant is also found on distorted tetrahedral sites. For (c) pertaining to small alkali metal ions such as Na, only the tetrahedral sites are occupied. For (h) we see that four Na ions can occupy an octahedral site of this fee lattice.

Orthorhombic crystals are similar to both tetragonal and cubic crystals because their coordinate axes are still orthogonal, but now all the lattice parameters are unequal. There are four types of orthorhombic space lattices simple orthorhombic, face-centered orthorhombic, body-centered orthorhombic, and a type we have not yet encountered, base-centered orthorhombic. The first three types are similar to those we have seen for the cubic and tetragonal systems. The base-centered orthorhombic space lattice has a lattice point (atom) at each comer, as well as a lattice point only on the top and bottom faces (called basal faces). All four orthorhombic space lattices are shown in Figure 1.20. 

Zirconium Hydride. ZrH2 ( ) mw 93.24 ( ) grey-blk pdr, does not form a well defined -compd it exists in five cryst phases, the e phase is a face-centered tetragonal cryst lattice that approximates the formula closely mp, air auto-ign temp of 270° d 5.6g/cc. V si sol in HF or coned acids. Prepn is either by heating Zr with H2, forming the metal in the presence of H2, reduction of zirconia with Ca hydride in the presence of H2 at 600—1000°, or by the com-bstn of Zr in H2... 

Worked Example Why is a C-centered tetragonal lattice not possible Because the C faces are square, C centering would be equivalent to redefining the a and b vectors (as a and b ) to produce a primitive tetragonal lattice with a unit cell of one half of the volume, as shown below. 

Worked Example Why is an A-centered tetragonal lattice not possible Because centering only on the A faces (or only on the B faces) would destroy the fourfold symmetry and hence the lattice would not be tetragonal. The question of why centering on both the A and B faces is also disallowed is left as an exercise for the reader. 

Why is there no face-centered tetragonal space lattice Why is there no base-centered tetragonal ... 

Unit cells are further subclassified as simple cubic/ face-centered cubic, body-centered cubic, base-centered rhombic, etc. but in order to avoid duplication in classification (Exercise 3), certain of the possibilities are left out (for example, face-centered tetragonal, side-centered rhombic), Actually 14 distinct types of space lattice are recognized. A number of cubic unit ceils and one body-centered tetragonal cell... 

The face-centered tetragonal unit cell can be transformed to body-centered tetragonal in which the lattice sites occupied are ... 

P0O2 at low temperature, possesses a face-centered cubic symmetry similar to fluorite, but converts into a high-temperature tetragonal form at 80 °C. The two allofropic forms coexist, even at room temperature. This is due to the heat evolved by a particle collisions with the crystal lattice. 

In the tetragonal crystal system the base-centered lattice (C) is reduced to a primitive (P) one, whereas the face-centered lattice (F) is reduced to a body-centered (I) cell both reductions result in half the volume of the corresponding unit cell (rule number three). 

The latter example is illustrated in Figure 1.27, where a tetragonal face-centered lattice is reduced to a tetragonal body-centered lattice, which has the same symmetry but half the volume of the unit cell. The reduction is carried out using the transformations of basis vectors as shown in Eqs. 1.6 through 1.8. 

At first glance, the list of Bravais lattices in Table 2-1 appears incomplete. Why not, for example, a base-centered tetragonal lattice The full lines in Fig. 2-4 delineate such a cell, centered on the C face, but we see that the same array of lattice points can be referred to the simple tetragonal cell shown by dashed lines, so that the base-centered arrangement of points is not a new lattice. However, the base-centered cell is a perfectly good unit cell and, if we wish, we may choose to use it rather than the simple cell. Choice of one or the other has certain consequences, which are described later (Problem 4-3). 

Uranium and thorium nitride halides are related to the above. The series A/N.Y (M = U. Th A = Cl. Br, I) have the PbFCI structure (see Fig. 23) [246, 247. 248]. The corresponding fluorides have the LaOF structure [249, 250] which is an ordered superstructure of fluorite with a rhombohedral or tetragonal distortion [251, 252]. UNF and I hNF. therefore, crystallize with MN4F4 cubes while the anions center the tetrahedral sites (see Fig. 24). Yellow ThNH crystallizes on a face-centered cubic lattice [253]. 

The thermochromism of Ag2[HgI4] is due to an order-disorder transition which involves no less than three phases. According to Ketalaar (33), both the yellow low-temperature 0 modification and the red high-temperature oc form contain iodide ions which are cubic close-packed, while the silver and mercury ions occupy some of the tetrahedral holes. The 0 form has tetragonal symmetry, with the mercury ion situated at the corners of a cubic unit cell and the silver ions at the midpoints of the vertical faces. As the temperature is increased it becomes possible for the silver and mercury ions to occupy each others lattice sites and also the two extra lattices sites Hop and bottom face centers of the unit cubel which were unoccupied at lower temperatures. Above 52°C. the mercury and silver ions are completely disordered. The a modification has. therefore, averaged face-centered cubic symmetry. More recently, magnetic (39) and dielectric polarization (37, 39) measurements confirm the presence of a third phase, the 0 modification. With an increase... 

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