Step by step – theories developed through the years

2.2.1. Tammann theory

Many different theories describing the structure of glasses and melts have been developed during the past 100 years. The first theory was proposed by Tammann (Tammann, 1903; Tammann, 1923; Tammann, 1933), who said that glasses have exactly the same structure as the melt. He assumed that structure of liquids is largely retained and it stays intact during the cooling.

2.2.2. Goldschmidt theory

Second hypothesis by Goldschmidt defined a glass structure from his chemical investigations (Goldschmidt, 1926). Goldschmidt assumed that to create the glass there is needed a cation/anion ratio between 0.2 and 0.4 which is exactly in such glass forming compounds as SiO2, P2O5 or B2O3 and even BeF2 solidifying to a glass.

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2.2.3. Zachariasen – Warren theory and fundamental groups of ions

In 1932 Zachariasen (Zachariasen, 1932) proposed a new theory which was confirmed by Warren (1933) with the X-ray diffraction. They discovered that in the vitreous SiO2 glass the smallest unit is a SiO4 tetrahedron. The tetrahedra create a disordered three-dimensional network. The new idea was also introducing a “coordination number”

term (an average number of nearest neighbours); for example, in the SiO4 tetrahedron in SiO₂ glass this number equals 4; and for B₂O₃ glass coordination number for planar trigonal BO₃ unit is 3 (Fig. 8).

Zachariasen – Warren theory assumes that oxides are trying to form the polyhedral groups as the smallest units building the structure and such two polyhedra may be linked just to one corner. On the other way, the polyhedron cannot have more than six corners. The anions like O^2- or S^2- create the bridges between pairs of polyhedra because they cannot be connected to more than two central atoms of polyhedra. Minimum three corners of a polyhedron need to be bonded with the neighbouring polyhedra through anion bridges (in silicate melts: bridging oxygens).

The bridges between polyhedra will be broken, if the large cation appears in the structure (e.g. Na⁺ or Mg²⁺). Then oxygen from the additional oxide will go to a free corner of the separate tetrahedra and the cation will balance the negative charge of the tetrahedra and causes the breaking of the network by reason of its size (Vogel, 1965).

Fig. 8. Coordination number of the atom, congruous with the geometric shape. The number of blue linear triangular tetrahedral square trigonal planar bipyramidal

tetragonal pentagonal octahedral cubic pyramidal bipyramidal

Zachariasen (1932) has classified the ions creating the glass structure into three groups: network formers (e.g. Si, B, P, Ge, As and Be with coordination number 3 or 4), network modifiers (like Na, K, Ca or Ba with coordination number higher than 6) and intermediate oxides (e.g. Al, Mg, Zn, Pb, Be, Nb or Ta with coordination number between 4 and 8). The intermediate oxides can be either the network formers or network modifiers.

With the present stage of knowledge about the glass structure the scientists distinguish more groups (Fig. 9):

- network formers (e.g. Si⁴⁺, Al³⁺, Fe³⁺ or Ti⁴⁺) arranged in the tetrahedra and creating the network owing to the covalent bonding forces;

- network modifiers (alkali or alkaline-earth metal cations) – make with oxygen weaker covalent and metal bonds and they have mostly octahedral coordination.

They connect with an oxygen and through that they generate non-bridging oxygens;

- charge balancers (alkali or alkaline-earth metal cations) compensating the negatively charged tetrahedrally coordinated units. There is loose exchange between network modifiers and charge balancer depending on the composition of the melt;

- bridging oxygens (BO) – oxygen atoms bonding two central atoms of the tetrahedra;

- non-bridging oxygens (NBO) – oxygen atoms bonding one central atom of tetrahedra with some other atom (e.g. network modifier).

Fig. 9. Fundamental groups of ions in the melt. Description in the text.

Si

⁴⁺

network former charge balancer

non-bridging oxygen network modifier network former

Na⁺

Si

⁴⁺

Al

³⁺

bridging oxygen

2.2.4. Dietzel theory, field strength and bonds in the structure

The next big step in the knowledge about structure of the glasses was made by Dietzel (1942). He developed the Goldschmidt’s hypothesis and took into consideration also the field strengths of the ions. During the cooling, the central atoms are trying to keep the surrounding atoms in the closest possible packing. If the central atoms have the same value of field strength, then the homogenisation of the melt can not occur and melt divides into separate phases. In the case of the cations with different field strength, the oxygens will create a closest packing near to the atom with stronger field. The cation with the lowest field strength gets a higher coordination number and is bonded to the tetrahedron with negative charge, e.g. [SiO₄]^4-.

Copolymerisation is possible when also separate structural units have similar chemical properties. The difference between donor – acceptor properties of two bonded elements determines the covalence (degree of ionicity) of the chemical bond. The strength of such bond can be described by a term

γ

_Φ:

n n orb

γ

_Φ =r ₊ , (Eq. 6)

where In is the ionisation potential of the n^th electron and rⁿ⁺orb is the orbital radius of an ion with a charge n⁺(Godovikov, 1979). In other words, it says about Coulomb forces between the n^th electron and the atomic core with charge n⁺ (see Table 1).

In vitreous silicate melt only one type of bonds occurs, namely between network forming Si and the oxygens. Because Si⁴⁺ cations have the strongest

γ

_Φ parameter with oxygen, the structure of this melt should be very strong and that would explain the slowest (the longest) relaxation time. Smaller ionicity of the bond with oxygen show successively Al³⁺ and Fe³⁺.

Al³⁺ and Fe³⁺ are network formers in peralkaline melts and build the tetrahedra with one negative charge (Mysen et al., 1985c). Hierarchy of the charge balancer is the same for both: K⁺, Na⁺, Ca²⁺, Fe²⁺, Mg²⁺ (Mysen, 1987). To create a stable Al- and Fe-tetrahedra these units need to be charge balanced by cations with smaller

γ

_Φvalue than respectively Al³⁺ and Fe³⁺. Hess and Wood (1982) also showed that compensation the Al-tetrahedra will first occur by cations with lower field strength and then together with increasing

γ

_Φ.

Tab. 1. Force characteristics

γ

_Φ of cation (Godovikov, 1979).

Cation

γ

_φ

Si⁴⁺ 225.6

Al³⁺ 128.7

Ti⁴⁺ 94.8

Fe³⁺ 86.3

K⁺ 7.3

Ba²⁺ 11.5

Sr²⁺ 16.4

Na⁺ 18.5

Ca²⁺ 22.1

Li⁺ 28.5

Fe²⁺ 44.4

Mg²⁺ 61.1

The experiments with glasses containing Fe-tetrahedra (Dingwell & Virgo, 1988 a, b) showed that the most stable cation to compensate a negative charge of Fe³⁺ unit is K, then Na, Ba, Sr, Ca and the less stable in this group is Mg.

In the fully polymerized melt (without NBO) the most important bonds are these between oxygen and network formers. The bonds between network former ions are covalent and their average bond valence is above ¾ of the valence unit, v.u.) and they are not willing to change the structure. Network modifiers create weak bonds (e.g. Na average bond valences below 0.2 v.u.) (Wispelaere et al., 2004). Na-O and Al-O bonds are longer than Si-O, but Si-O energy bond is at about 20% higher than energy of Al-O bond (Stein &

Spera, 1993).

Im Dokument Physical and thermodynamic properties of aluminosilicate melts as a function of composition (Seite 21-25)