BCC Spring Model

Concepts Shown:

Interatomic forces, equilibrium spacing in crystalline solids, and interstitial positions in BCC.

Equipment:

nine racketballs (r=1") and metal springs (l= 2" for edges and 1.25" for center atom connections) to make BCC unit cell, one oversized ball (roughly double the size of a raquetball), and one ball considerably smaller than a racquetball (e.g. ping pong ball).

Procedure:

1. Pull and twist BCC model. This shows the springs stretching and compressing which models the repulsive and attractive forces between atoms.
2. Insert the large ball into the structure. Note how it does not fit well in an interstitial position due to the large displacement of the surrounding atoms.
3. Insert the small ball into the BCC structure. Note how it fits into the interstitial site quite easily.
Science:

1. Using figure on next page, explain how the equilibrium position of an atom in the structure is a result of the system minimizing its energy. There are two forces, attractive and repulsive, which control the equilibrium distance between atoms. The attractive force is a coulombic force, [eq], and the repulsive force arises from electron shells that overlap between atoms, [eq].The equilibrium spacing is determined by the cancellation of these two forces: FA + FR = 0. This translates into a minimum energy by [eq].
2. Derive the size of the interstitial position: Note the BCC spring model is NOT a hard shell model since the atoms along the [111] direction are not touching. The derivation below is for the spring model; however, it is the same method of deriving the interstitial space for the hard shell model. This derivation is for an ideal interstitial position in the BCC structure: [eq]
3. Since the large atom does not fit in this position (r > 0.875"), it will displace a 'racketball' atom and become a substitutional atom, and this pair is known as a Frenkel defect.
4. Since the radius of the ping pong ball atom is less than the radius of the interstitial site (r < 0.875"), it will stay in these sites. An example is a solid solution of carbon atoms ( < 0.2 wt%) in iron.

Roberta Dean