Amorphous and crystalline phases of silica

The picture that emerges for amorphous silica is of a local structure that is very similar to that found in crystalline silicates. This similarity can be explored further by comparing the RDF for amorphous silica with the RDFs obtained experimentally from powdered samples of other crystalline silica phases. To link with experiment, we will work with the overall PDF formed by combining the separate PDFs, weighted according to the scattering power of each atom in neutron diffraction experiments (Chapter 6, Appendix J), which is called G(r):

G(r)=

k,l

c_kc_lb_kb_l(g_kl(r)− 1) (2.10)

where the sum is over pairs of atom types k and l, ck is the proportion of atom type k, and bkis the scattering power of the same atom type (this will be discussed in detail in Chapter 6). To aid clarity, we will actually plot the function D(r) = rG(r), which emphasizes the structure in the PDFs at higher values of r (as will be seen in Chapter 6 and Appendix J, this is the actual quantity that is measured in a diffraction experiment). The D(r) function for silica glass is compared with the D(r) functions for the high-temperature phases of the crystalline polymorphs of silica, cristobalite, tridymite and quartz in Fig. 2.45.

As we noted above, this analysis ignores the full three-dimensional relationship between the positions of atoms, and treats the crystal as an isotropic material.

Over the range of r to 10 Å, the closest similarity is with tridymite, with quartz having the least similarity. However, in all cases the peaks in the functions are in the same places. The main difference between the D(r) functions is that the peaks in D(r) for amorphous silica decay on increasing r as compared to the crystalline phases, which reflects the fact that the structures cease to be similar

Fig. 2.45 The functions r(g(r) − 1) for amorphous silica and three high-temperature polymorphs, obtained directly from experi-mental data. (Data for figure taken from Keen and Dove, J. Phys.: Cond. Matter 11, 9263, 1999.)

0 5 10

r (Å)

r (g(r)−1)

−5 15 0 5 10 15 20

once the periodicity of the crystal lattices has an influence on the PDFs. The important point of the comparison is that the structures of the amorphous and crystalline phases of silica have similar groups of linked SiO4tetrahdra. Both cristobalite and tridymite contain six-membered rings of tetrahedra, as shown in Fig. 2.38, with slightly different stacking of layers. Quartz has a spiral structure not found in the other polymorphs. It should also be noted that the densities of cristobalite and tridymite are very close to the usual density of silica glass, which supports the idea from the PDF analysis that the structure of silica glass uses building blocks that are very similar to these crystalline phases.

We are forced to conclude that the main difference between the structures of the amorphous and crystalline phases of silica only arise on length scales that are sensitive to the periodicity of the lattice. For phenomena that only depend on the short-range structure, glasses may be remarkably similar to related crystals.

We will discuss a comparison of the dynamic properties of the amorphous and crystalline phases of silica in Chapter 10.

Silicate glasses, like crystalline silicates, can also contain Al incorporated into the basic network of AlO4 tetrahedra. Other metal cations (such as the alkali metals, Mg and Ca) will act as charge balancing cations. These cations may occupy cavities between the tetrahedra, or else can modify the network to give octahedral coordination with oxygen atoms as in crystalline phases.

2.8 Conclusions

This chapter has been mostly concerned with examples of the range of crystal structures. We started from the simplest close-packed structures of the elements, and then developed the discussion to include more and more complex structures.

We then looked at crystal structures of compounds, again starting from the

simplest close-packed structures and extending the discussion to include more complex structures.

The structures we discussed brought out a number of important principles.

Some of these concerned the formal description of crystal structures, anticipat-ing the more detailed treatment of the next chapter. The points highlighted in this chapter have included the definition of thelattice, the idea of lattice vectors and theunit cell, and the role of symmetry. The structures also highlighted a number of factors that are important in determining crystal structures, factors such asclose-packing, ionic radii, and structural polyhedra. These factors will be properly quantified in Chapter 5.

Two other important features have been highlighted by the examples discussed in this chapter. The first is the link between structure at an atomic level and macroscopic physical properties. The second is the existence of polymorphism and phase transitions. One link between these two features is that different polymorphs may have such different structures that they have different physical properties. Moreover, the existence of a phase transition between two phases with similar structures, perhaps occuring as a result of small symmetry-breaking displacements of some of the atoms, often leads to an enhancement of the physical properties. A detailed discussion of physical properties will be given in Chapter 7, and phase transitions will be discussed in Chapter 12.

Summary of chapter

• The simplest two structures of the elements are the cubic and hexagonal close packed structures, in which close-packed planes of atoms are stacked above each other with repeats every three and two layers respectively.

• Two other important simple structures for elements are the body-centred cubic structure and the diamond structure. The simple cubic structure is of little practical relevance.

• The packing fraction for single-element structures gives the fraction of space within the crystal that is encompassed within the atoms. The close-packed, body-centred cubic and diamond structures have packing fractions 0.75, 0.68 and 0.34 respectively.

• There is, in fact, a wide range of structures available to the pure elements.

Carbon and selenium are two examples of structures that form networks of covalent bonds, and carbon, nitrogen, halogens and sulphur form molecules.

• Simple crystal structures of diatomic crystals are arranged with unlike ions forming nearest-neighbour pairs, with a range of coordination numbers.

• Some aspects of the crystal structures of compounds can be rationalized in terms of the effective radii of the constituent ions.

• Structures of more complex materials can be described in terms of networks ofcoordination polyhedra. One example is the family of silica structures, which are all formed as networks of corner-sharing SiO4

tetrahedra. A second example is the family ofperovskite structures, which are formed as networks of corner-sharing octahedra with a simple-cubic parent structure.

• Crystals of the perovskite family of structures undergo a variety of phase transitions, which give rise to changes in physical properties that can be exploited for technological applications.

• Some crystals can accommodate a certain degree of disorder. Examples include crystals with molecules that have disordered orientations, fast-ion conductors in which mobile atoms can hop between vacant interstitial sites, and liquid crystals in which molecules have ordered orientations but only partial crystalline order.

• Glasses do not have the long-range periodicity of crystals, but can have features of the short-range structure that are also found in corresponding crystal structures. A prime example is silica, whose glass phase has a network of corner-sharing SiO4 tetrahedra as in the crystalline phases.

The short-range structural order can be characterized using the pair distribution function (PDF), and there can be close similarities between the PDFs of corresponding glass and crystal phases.