Tellurite And Fluorotellurite Glasses For Active And Passive

2. Literature review; MDO 14
2.2.2.2. Goldschmidt’s radius ratio criterion
Goldschmidt’s theory as to the structure of inorganic oxide glasses in 1926 led to the
development of all other modern structural theories of glass formation [1]. Goldschmidt,
who is also considered the father of modern crystal chemistry, derived empirical rules for
glass formation [2]. His general observation was: for a simple oxide of formula MmOn (M
cation), that glass formation is only possible when the ratio of atomic radii, ra/rc
(where c denotes cation, and a anion), falls between 0.2 to 0.4 [1]. This condition is met
for oxides SiO2, B2O3 and P2O5. Later, after publication of this theory, it was also found
glass-formers GeO2 and BeF2 (if F is substituted for O) also satisfied the criterion [2].
In crystal chemistry, the cation / anion ratio determines how many anions can be
packed around a given cation, i.e. the co-ordination number of the compound. Most
crystals with a cation / anion radius ratio of 0.2 to 0.4 have a co-ordination number (CN)
of 4 with anions at the corners of a tetrahedron. Therefore Goldschmidt was led to believe
that tetrahedral arrangement of oxygen ions around a cation M was necessary for glass
formation [1]. It is important to note once again that these observations were purely
empirical, and no attempt was made to try and explain why this should be so. Also, by
considering the radius ratio of the ions and co-ordination number, it is assumed the oxide
is purely ionic. This is not strictly correct as many glass-forming oxides have covalent
character (e.g. SiO2), which must be kept in mind [1].