Basic theory of sodalite framework modelling

All modelling requires an acceptable theoretical starting point. The fundamental equations which are common to all sodalite models are presented and their relationship with the zeolite framework is discussed. Natural sodalite has an ordered structure with its T atoms (T=Al,Si) distinguished and situated on specific A1 and Si sites and a Si/Al ratio of 1. The structure has the symmetry of the cubic space group P43n. To develop a model 

The primary building unit of all zeolite frameworks is the TO4 tetrahedron. A regular TO4 tetrahedra will have four equal T-0 bonds of constant length t, and six equal tetrahedron edge distances, 0...0 of length E. If the distance from the T atom to the midpoint of 0...0 is represented as d, the following equations represent the relationships between E, t and d  

In sodalite, the fractional coordinates of a select TO4 tetrahedron are as follows  

The choice of oxygen atoms satisfies the space group I43m and a is the unit cell parameter. The relationship between the distance t, ao and the oxygen coordinates is given as  

Since all tetrahedron edges are equal, the value of z can be obtained as a function of x. Applying Pythagoras s theorem to the appropriate coordinates leads to  

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