Paulings rules Paulings Rules Paulings first rule states

Pauling’s rules

Pauling’s Rules Pauling’s first rule states that coordination polyhedra are formed. Coordination polyhedra are three-dimensional geometric constructions such as tetrahedra and octahedra. Which polyhedron will form is related to the radii of the anions and cations in the compound Pauling’s second rule on the packing of ions states that local electrical neutrality is maintained Pauling’s third rule tells us how to link these polyhedra together. Pauling’s fourth rule is similar to the third, stating that polyhedra formed about cations of low coordination number and high charge tend to be linked by corners. The fifth and final rule states that the number of different constituents in a structure tends to be small; that is, it is difficult to efficiently pack differentsized polyhedra into a single structure.

Atomic and ionic radii

Trends in atomic and ionic radii

1 st rule : interatomic distances & coordination

Stable and unstable coordination configuration

Cuboctahedron 12배

2 nd rule : the electrostatic valency rule

3 rd rule : Sharing polyhedra (1) ØAnion polyhedra that share edges or faces reduce the stability of a crystal because they bring cations closer together. The closer cations experience more electrostatic repulsion.

4 th rule : Sharing polyhedra (2) ØPauling’s fourth rule says that highly charged cations will tend to be as far apart as possible to minimize electrostatic repulsion.

5 th rule : The rule of Parsimony Ø The same cations in a crystal structure have the same coordination number for the same anions.

Zincblende (Sphalerite, Zn. S) structure M: fcc 격자 + X : 000 단위격자내 원자위치 M: X: 배위수 M : 4배위 X : 4배위