Precision estimates of interatomic distances using site occupancies, ionization potentials and polarizability in Pbnm silicate olivines

All interatomic distances [D(calc.)j] in Pbnm silicate olivines are linearly related with M1 and M2 site occupancy through a relationship of the type: O(calc.)j = Y.sYatoij Xis + ~j, where toij,, ~j are adjustable coefficients, and Xi, are the fractions of ith ion in site s. The precision attained by this relation, based on seven divalent ions (Mg, Fe, Ca, Mn, Co, Ni, Zn), is satisfactory, the mean difference ID(calc.) -D(obs.)l always being less than 0-005 A for each distance. Moreover, all to;j, coefficients are related to properties of ions through a relation of the type: w;j __ Z - I/2 fl/4 Z ~ - Klj.(Y.,,= llm)i + K2jag + K3j; where Y-m: lira is the sum of the ionization potentials for the ith ion up to its valency state (Z), a { is its polarizability, and Klj,, K2js and K3j, are numerical constants. The existence of this strict dependency is predictable, based on the concept of effective nuclear charge and its relationship with polarizability and ionic potentials. As a consequence, all interatomic distances may be simulated through an equation of the type: D(calc.)j = Y-s{ Wlj:~[X~:( Yz= llm)i - l/2]} + ~s[W2js~'.i(Xi otfl/4)] + W3j, where Wlj.., W2j and W3j are adjustable parameters which directly involve the ionization potentials and polarizabilities of the ions.