An account is given of recent neutron diffraction studies of a number of different network glass forming systems using the ISIS pulsed neutron source. The glasses investigated comprise phosphates and silicates and the interrelationship between their various network structures is discussed. The samples studied include a single component glass and binary systems, involving either a network modifier or a conditional glass former, and the data have been extended to high values of the scattering vector magnitude, Q, to achieve high real space resolution. Peak fitting techniques are employed to extract the detailed geometry of the basic structural units and to investigate the distortions caused by the introduction of network modifiers. The data obtained are compared to various structural models and computer simulations to study the intermediate range order and to test current theories concerning the role of network modifiers in binary systems. These comparisons correctly include the necessary peak functions which define the experimental resolution in real space and are made on a quantitative basis by the use of an appropriate reliability factor.

A neutron diffraction investigation of the structure is reported for four glasses in the Na O-2-B2O3 -SiO2 system and one in the Na2O-B2O3 system. Measurements have been made to high values of the scattering vector magnitude, Q, in order to obtain high real space resolution. Of primary interest is the fraction, x(4) , of four -fold coordinated boron atoms present at each composition and the bond lengths within the borate and silicate structural units. These have been extracted using peak fitting techniques and compared both with NMR results and with the predictions of a model based on earlier NMR data. It is concluded that, within the experimental uncertainty, the values of x(4) are in agreement with the NMR results but at variance with those predicted by the model.

A summary is presented of structural data for the crystalline polymorphs existing in a wide range of binary borate glass-forming systems and is used as a basis to propose a set of topological criteria for the formation of vitreous borate networks. It is shown that this yields considerable insight concerning the structural criteria for the formation of such networks, but that the information which can be obtained is limited by the fact that many of the relevant crystalline structures have not been determined.

The presence of structural nanoheterogeneity means that sharp structural transitions at a well defined temperature or composition are an anathema to the vitreous state. Hence they should not be expected, but rather an extended transition, whose width is defined by the form and length scale of the relevant nanoheterogeneity. It should also be noted that all of the vitreous state transitions considered here, together with crystallisation at the melting point, are spatially non-uniform. This behaviour should be compared to sharp transitions that occur within the crystalline state, for example the displacive transition between α- and β-quartz, and those from a paramagnetic to a magnetically-ordered state. Such sharp transitions involve simultaneous co-operative movements across a large number identical unit cells, and hence cannot occur in the absence of a periodic structure. As a result, they are sensitive to disorder within individual unit cells, as may be seen from the case of cristobalite, where the presence of disorder reduces the αβ transition temperature, and in extremis inhibits the transition from β- to α-cristobalite.

Whereas the cybotactic theory and thermodynamic modelling have proved invaluable tools in understanding the structures and properties of alkali silicate glasses, questions have been raised as to their validity for alkaline earth and related glasses such as PbO–SiO2. The present paper discusses the specific cases of the CaO–SiO2 and PbO–SiO2 systems, and it is shown that the presence of Si[3] units (silicate tetrahedra with three bridging and one nonbridging oxygen atoms) can easily be explained in terms of the thermodynamic equilibria that underlie the model of associated solutions and the cybotactic theory. Similarly, the much more random distribution of silicate tetrahedral species in PbO–SiO2 glasses derives from the amphoteric nature of PbO. A related question concerns the relevance of atomistic structural modelling/simulation to the evaluation of structural theories of glasses, but to date all of the models of binary silicate glasses have been generated using periodic boundary conditions, which means that they are incapable of reproducing the long range disorder that characterises the vitreous state. Furthermore, it is demonstrated that, in their present form, the RMC and related computer codes, such as EPSR, are fundamentally flawed, in that they merely involve the fitting of an early crystallite model to experimental diffraction data, albeit one where the average internal structure of the crystallites is based on a large highly disordered unit cell, but the crystallites themselves have an entirely unphysical shape. It is also concluded that, to fully interpret the structure of binary and multicomponent glasses, it is essential to study the relevant phase diagram, together with the structures of the thermodynamically-stable and metastable crystalline phases that occur in that particular glass-forming system, and to understand that, since the supercooled liquid is only transiently metastable, the cybotactic/chemical grouping species present in the final glass may not necessarily be determined by equilibrium thermodynamics, but may be greatly influenced by the quench rate. The temperature range over which these crystalline phases/polymorphs are stable is also important, as is the temperature dependence of the glass transition temperature, Tg, and its relationship to the solidus temperature, Ts, at the same composition. Only in this way is it possible to derive the maximum information concerning the structure of a given glass and, much more importantly, to explain why this glass has its particular structure. It is therefore concluded that the key to developing a comprehensive theory of the formation and structure of the vitreous state lies not with ever more precise determinations of the short range order (i.e. diffraction studies), but rather in understanding the role of the thermodynamic equilibria that drive the characteristic long wavelength fluctuations in both number density and composition that distinguish the vitreous from the crystalline state.

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It has been demonstrated that both the detailed electron distributions of the constituent atoms/ions and non-Gaussian Gaussian peaks in T(r) can seriously limit the accuracy of co-ordination numbers extracted from x-ray diffraction data, whether the fit is performed in real or reciprocal space. In general, however, it is preferable to perform the fit in real space, where differences in shape between the experimental and fitted peaks are much more obvious, together with the effect of any experimental uncertainties, as represented by the noise in the resulting correlation function in the region below the first true peak. Note, also, that in reciprocal space the effects of a non-Gaussian peak shape on the extrapolation of the sinusoidal envelope to zero Q, from a high-Q fit to the interference function, Qi(Q), apply equally to neutron diffraction data, similarly limiting the accuracy of the resulting co-ordination numbers.

This paper, which continues a series of works on the thermodynamic modelling of properties of glasses and melts, considers in more detail the formalism of the model of associated solutions and its most recent applications to the description of chemical properties of glasses and melts, which include redox equilibria and the solubility of gases in them.

During the 20th century, three major theories were advanced concerning the structure of oxide glasses, viz. the early crystallite (discrete crystallites separated by some form of 'grain boundary'), random network (continuous statistically-disordered network) and cybotactic (continuous network with spatial fluctuations in the degree of order) theories. The problem was that, by the end of the 20th century, not one of these theories had been satisfactorily eliminated, neither as a result of x-ray or neutron diffraction studies, nor on the basis of small-angle scattering (SAXS or SANS) data, mainly due to a failure to take account of the three 'golden rules' of glass structure analysis, i.e. that it is essential to: (1) Consider the whole structure, and not just one particular aspect, (2) compare with all of the relevant experimental data, and, (3) demonstrate that it is possible to generate a consistent set of atomic co-ordinates. Once this is done, it is shown that neither the early crystallite, nor the (original or modified) random network theory, provides an adequate foundation upon which to base 21st century glass science.

The early crystallite, random network and cybotactic theories of the structure of single component glasses, such as SiO2, differ in respect of their predictions concerning the frequency of occurrence and size of crystalline-like groupings within the vitreous network, and hence in the expected form of the spatial fluctuations in their average number density, rho degrees. The RMS fluctuations in average number density, (1/2), for vitreous SiO2 and GeO2 are calculated from the zero-Q limit of the static structure factor, S(Q), and it is shown that neither the early crystallite nor the cybotactic theory can be eliminated on the basis of small-Q scattering data. On the other hand, the devitrification behaviour for both glasses indicates the presence of potential crystallisation nuclei (cybotactic groupings) corresponding to the cristobalite polymorph, and hence clusters of 6-membered shortest path rings. An stimate is made as to the frequency of occurrence of crystalline-like clusters of 6-membered rings within a Zachariasen-Warren 'random' network, assuming that the density fluctuations for such a network follow a Gaussian distribution, and that the spatial distribution of the various sized rings is statistically random. Based on the shortest path ring statistics for the Evans & King random network model of vitreous silica, it is concluded that the frequency of occurrence of cybotactic groupings in vitreous SiO2 and GeO(2 )is higher than would be expected for a purely 'random' network.

The neutron diffraction isotopic substitution technique is employed to investigate the environment of Fe3+/Fe2+ cations in a sodium borosilicate glass matrix of composition 0.210Na(2)O.0.185(11)B(2)O(3).0.605SiO(2). The neutron diffraction data were obtained using the D4c diffractometer at the Institut Laue-Langevin (ILL; Grenoble, France), and were recorded for three samples; the base glass, the base glass incorporating natural Fe2O3 (12 mol%) and a similar glass containing Fe2O3 enriched in Fe-57. The data are Fourier transformed to yield the real space total correlation function, T(r), and the first co-ordination shells of the Fe3+/Fe2+ cations are investigated via a peak fit to the isotopic difference correlation function Delta T-Fe(r). It is concluded that the iron is mainly present as Fe3+ cations, both tetrahedrally and octahedrally co-ordinated by oxygen atoms, plus a small fraction (0.07 +/- 0.01) of Fe2+ cations in octahedral co-ordination. The Fe3+ tetrahedral fraction is 0.45 +/- 0.10, and appears to exist as Fe empty set (-)(4) structural units incorporated into the network of silicate chemical groupings, with their negative charge being balanced by Na+ network modifying cations. The remaining Fe3+ cations (fraction 0.48 +/- 0.10) are thought to be predominantly octahedrally co-ordinated and associated with BO33- orthoborate anions in FeBO3 chemical groupings, which become non-stoichiometric due to the reduction of some of the Fe3+ cations to Fe2+.

Whereas the conventional definition of the static structure factor, S(Q), means that, for any sample or structural model, its value at zero Q, S(0), is identically equal to zero, the structures of ideally-disordered materials, such as single-phase liquids and amorphous solids, incorporate long-range density fluctuations that are characterised by a non-zero limiting value (S0) of S(Q≠0) as Q→0. An analysis of these density fluctuations in terms of their Fourier components leads to the definition of an ideally-disordered material as one that exhibits a continuous, isotropic distribution of Fourier wavelengths, A(Λ), that decays asymptotically to zero at Λ=∞. On the other hand, a similar analysis for a periodic boundary model reveals that the form of the intermediate-range order at higher inter-atomic distances, r, and that of the long-range density fluctuations are fundamentally different from those of a real amorphous material. The severely limited number of (especially the longer) allowed Fourier wavelengths, Λ, coupled with their strictly defined orientations within the unit cell of a periodic boundary model, means that such a model is inherently crystalline, and that no amount of orientational (polycrystalline) averaging can overcome this problem. The various methods of deriving S(Q) for both periodic-boundary and cluster models are discussed, and it is shown that, since a periodic boundary model is not ideally-disordered, a polycrystalline average does not yield a consistent value for S0, but one that is dependent on its exact method of calculation. It is therefore concluded that, to investigate the longer-range density fluctuations in amorphous materials, it is essential to employ a cluster model, rather than one generated with a periodic boundary.