0.6 Solid state and superconductors  (Page 3/9)

It is very important to understand that the stoichiometry of the atoms within the unit cell must reflect the composition of the bulk material.

Binding forces in a crystal

The forces which stabilize the crystal may be ionic (electrostatic) forces, covalent bonds, metallic bonds, van der Waals forces, hydrogen bonds, or combination of these. The properties of the crystal will change depending upon what types of bonding is involved in holding the atoms, molecules, or ions in the lattice. The fundamental types of crystals based upon the types of forces that hold them together are: metallic in which metal cations held together by a sea of electrons, ionic in which cations and anions held together by predominantly electrostatic attractions, and network in which atoms bonded together covalently throughout the solid (also known as covalent crystal or covalent network).

Close-packing

Close-packing of spheres is one example of an arrangement of objects that forms an extended structure. Extended close-packing of spheres results in 74% of the available space being occupied by spheres (or atoms), with the remainder attributed to the empty space between the spheres. This is the highest space-filling efficiency of any sphere-packing arrangement. The nature of extended structures as well as close-packing, which occurs in two forms called hexagonal close packing (hcp) and cubic close packing (ccp), will be explored in this lab activity. Sixty-eight of the ninety naturally occurring elements are metallic elements. Forty of these metals have three-dimensional submicroscopic structures that can be described in terms of close-packing of spheres. Another sixteen of the sixty-eight naturally occurring metallic elements can be described in terms of a different type of extended structure that is not as efficient at space-filling. This structure occupies only 68% of the available space in the unit cell. This second largest subgroup exhibits a sphere packing arrangement called body-centered cubic (bcc).

You should be able to calculate the % of void space using simple geometry.

Packing of more than one type of ion (binary compounds) in a crystal lattice

A very useful way to describe the extended structure of many substances, particularly ionic compounds, is to assume that ions, which may be of different sizes, are spherical. The structure then is based on some type of sphere packing scheme exhibited by the larger ion, with the smaller ion occupying the unused space (interstitial sites). In structures of this type, coordination number refers to the number of nearest neighbors of opposite charge. Salts exhibiting these packing arrangements will be explored in this lab activity.

Coordination number and interstitial sites

When spherical objects of equal size are packed in some type of arrangement, the number of nearest neighbors to any given sphere is dependent upon the efficiency of space filling. The number of nearest neighbors is called the coordination number and abbreviated as CN. The sphere packing schemes with the highest space-filling efficiency will have the highest CN. Coordination number will be explored in this lab activity. A useful way to describe extended structures, is by using the unit cell which as discussed above is the repeating three-dimensional pattern for extended structures. A unit cell has a pattern for the objects as well as for the void spaces. The remaining unoccupied space in any sphere packing scheme is found as void space. This void space occurs between the spheres and gives rise to so-called interstitial sites.