Unit cell packing efficiency

Finally, it should be noted that the XeF molecule exhibits a definite tendency to donate a fluoride ion and form the XeFj cation, which is isoelectronic and isasmic-tural with IF] as expected from the VSEFR model. The structure of solid XeF is complex, wilh 144 molecules of XeF per unit cell however there are no discrete XeF molecules. The simplest way to view the solid is as pyramidal XeF cations extensively bridged by free fluoride ions. Obviously, these bridges must contain considerably covalent character. They cause the xenon-containing fragments to duster into tetrahedral and octahedral units (Fig. 6.ISa,b). There are 24 tetrahedra and eight octahedra per unit cell, packed very efficiently as pseudospheres into a CujAu structure (Fig, 6.ISc)."-i The structure thus provides us with no information about molecular XeF, but it does reinforce the idea that the VSEPR-correct, square pyramidal XeF] is structurally stable. 

A substitution of the methyl group in the para-position (Fig. 36) causes a larger expansion of the unit cell along c. The crystal packing of the resulting structure is still an efficient one, however the p-substituted methyl introduces already some steric hindrance into the structure the shortest distance of the methyl from its surroundings (adjacent phenyl walls ) is 3.56 A as compared to the normal van der Waals methyl — — phenyl distance of about 3.7 A49>. This steric misfit could be responsible for the preferential complexation of host 25 with m-cresol rather than with p-cresol. 

The unit cell volume of the hemibenzene complex is 1077.9 A and the calculated ceU volume for two molecules of Yb (acac) 3 (OH 2) (931.8 A ) and liquid benzene (147.6 A at 25° C) is 1079.4 A . These figures suggest no unusual disorder has taken place and the efficiency of packing of the molecules are about the same for both solvated and unsolvated structures. 

Four Sg molecules, i.e., 32 atoms occupy one unit cell the space group is P2/c, the density is 2.19 gm/cm , i.e., larger than that of either a- or /3-sulfur. Thus, y-sulfur contains more efficiently packed cyclooctasulfur than any other crystal. The crystals decompose upon standing. 

The lines in the figure divide the crystal into identical unit cells. The array of points at the corners or vertices of unit cells is called the lattice. The unit cell is the smallest and simplest volume element that is completely representative of the whole crystal. If we know the exact contents of the unit cell, we can imagine the whole crystal as an efficiently packed array of many unit cells stacked beside and on top of each other, more or less like identical boxes in a warehouse. 

The structure of C(CH20N02)4, like C(CH20H)4, the alcohol from which it is formed, has a bimolecular tetragonal unit cell, D2l/4, P42iC, a0 = 9.33, c = 6.66 A. The body-centered structure, 3 2PTOT(t), is shown in Figure 11.11. The compact molecule with high symmetry packs efficiently in the body-centered structure. 

Crystalline solids consist of periodically repeating arrays of atoms, ions or molecules. Many catalytic metals adopt cubic close-packed (also called face-centred cubic) (Co, Ni, Cu, Pd, Ag, Pt) or hexagonal close-packed (Ti, Co, Zn) structures. Others (e.g. Fe, W) adopt the slightly less efficiently packed body-centred cubic structure. The different crystal faces which are possible are conveniently described in terms of their Miller indices. It is customary to describe the geometry of a crystal in terms of its unit cell. This is a parallelepiped of characteristic shape which generates the crystal lattice when many of them are packed together. 

In the unit cell, the almost rod-like molecules are found to be arranged like match sticks in a matchbox and the packing efficiency is high resulting in no cavities in the structure, which could be occupied by solvent molecules. In addition, benzyl-substituted titanocene dichloride derivatives resemble to a certain degree fatty acid molecules due to their shape and lipophilicity, which will become important in the albumin binding part later on. 

With 68.0% of the volume of the cell being occupied by the two atoms, the fraction of free space in this structure is 32.0%. Therefore, it represents a more efficient packing model than does the simple cubic model. Also, each atom is surrounded by eight nearest neighbors in the bcc structure, and there are two atoms per unit cell, which means it is preferable to the simple cubic structure on this basis also. 

A quantitative measure of how efficiently spheres pack into unit cells is called packing efficiency, which is the percentage of the cell space occupied by the spheres. Calculate the packing efficiencies of a simple cubic cell, a body-centered cubic cell, and a face-centered cubic cell. Hint Refer to Figure 11.22 and use the relationship that the volume of a sphere is where r is the radius of the sphere.)... 

Packing efficiency. Percentage of the unit cell space occupied by the spheres. (11.4) Paramagnetic. Attracted by a magnet. A paramagnetic substance contains one or more unpaired electrons. (7.9)... 

Crystalline solids consist of particles tightly packed into a regular array called a crystal lattice. The unit cell is the simplest portion of the crystal that, when repeated, gives the crystal. Many substances crystallize in one of three types of cubic unit cells, which differ in the arrangement of the particles and, therefore, in the number of particles per unit cell and how efficiently they are packed. 

Packing Efficiency and the Creation of Unit Cells The unit cells found in nature result from the various ways atoms are packed together, which are similar to the ways macroscopic spheres—marbles, golf balls, fruit—are packed for shipping or display (Figure 12.25). 

---