Closest Packing of Ions

Because it is generally favorable to keep the distance between the cation and anion as small as possible, ions frequently pack together as closely as possible. These closest-packed arrangements are very important in understanding the stmcture of solids. 

We will first consider the most efficient way to pack spherical objects, such as ping-pong balls. 

Which of the arrangements of spheres shown below is the most efficient use of space (and therefore makes the objects as close as possible)  

The arrangements (a) and (b) represent just one layer of spheres. We must now add another layer on top of (b). 

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In sodium nitrite the ferroelectric polarization only occurs in one direction. In BaTiOs it is not restricted to one direction. BaTiOs has the structure of a distorted perovskite between 5 and 120 °C. Due to the size of the Ba2+ ions, which form a closest packing of spheres together with the oxygen atoms, the octahedral interstices are rather too large for... 

THE CLOSEST PACKING OF LARGE IONS IN IONIC CRYSTALS... 

The sphalerite, wurtzite, antifluorite (Li2S), cadmium iodide, cadmium chloride, and many other arrangements also involve closest packing of the large ions. 

The edge of the LiCl unit cell is 514 pm in length. Assuming that the Li+ ions just fit in the octahedral holes of the closest packed Cl- ions, calculate the ionic radii for the Li+ and Cl- ions. Compare them with the radii given in Fig. 13.7, and discuss the significance of any discrepancies. 

The simple octahedral lOg ion presumably occurs in anhydrous salts MsIOg. Like TeO this ion has the property of stabilizing high oxidation states of metals (for example, Ni, Cu ), as in KNilOg, in which K, Ni, and I all occupy octahedral positions in an approximately hexagonal closest packing of 0 atoms. (I-O, approx. 1-85 A.)... 

Diffraction of light in two-dimensional lattices and their calculations were known in Laue s time an additional information. They have been the basis for Laue s calculation of three-dimensional diffraction lattices from X-ray experiments as a result he formulated a model of a spatial symmetrical structure of ions in a salt crystal abstract mental model. Laue proposed the use of realistic models in order to better visualize the concepts - but needed irrelevant items like balls, sticks and glue, in order to construct closest packings of spheres or spatial lattice models concrete models. 

In order to arrive at the important sodium chloride structure, one could look at and discuss the interstices in the cubic closest sphere packing model [2] interstices that are octahedral and tetrahedral can be found (see E5.8). If one fills the octahedral interstices with smaller spheres, one ends up with the sodium chloride structure (see Fig. 5.13). The larger spheres symbolize the chloride ions, the smaller spheres the sodium ions. The structure can be described as the cubic closest packing of chloride ions, whose octahedral interstices are completely filled by sodium ions. For other salt structures, only part of the octahedral sites are filled, as in aluminum oxide where the ratio of ions 2 3 applies [2],... 

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