Proceso de calificación de factores internos y externos ( EFE, EFI)

Using neutron diffraction data fromv-B₂O₃[18] andv-Sb₂O₃(q.v.§4.4.1), it is possible to draw a comparison between the measured total correlation function of an antimony borate glass and the simulated T(r) for a stoichiometrically-equivalent mixture of the two end-members (Fig.5-15) using the equation

T(r)= N1 N1+N2 T1(r)+ N2 N1+N2 T2(r) (5-1)

where Ni andTi(r) are the number of atoms in phase i and the total correlation func- tion for a pure sample of phase i, respectively. This approach has previously been used by Hannon et al. [29] to simulate a lead aluminate crystal that contained some impurities. There are some flaws to this method, such as the absence of correlations between the atoms in the two phases, but the model should be reasonably accurate in terms of short-range order and thus highlight any changes due to formation of the bi- nary glass. As might be expected, the B−O correlation is slightly narrower and sharper in the simulatedT(r), sincev-B₂O₃ does not contain any [BO₄] tetrahedra [9, 25]; the subsequent O_B···O_B peak is similarly narrow due to the absence of the longer oxygen- oxygen distance of the [BO₄] units. The first Sb−O correlation of the simulation also

Chapter 5. Antimony Borate Glasses

Figure 5-15 TheT(r) of the (nominal)x=0.5 sample compared with one simulated by summing weightedv-B₂O₃ [18] andv-Sb₂O₃ (q.v.§4.4.1) to- tal correlation functions. All datasets were Fourier transformed at Q_max =

30 Å−1. Labels are the primary correlations giving rise to the peaks, sec- ondary contributions are described in the main text.

differs from the measured function, with the actual sample exhibiting a less intense main peak together with more intensity at greaterr: this indicates that the proportion of more highly-coordinated antimony oxide units (probably [Sb3+O₄] pseudo-trigonal bipyramids) is greater in the binary borate glass than in thev-Sb₂O₃sample.

Most notably, the model considerably underestimates the intensity observed in the region beyond the O_Sb···O_Sb peak (approximately 2.8 Å to 3.4 Å). In the system end- members, this region is dominated by correlations in the B₂O₃ network (q.v.Fig.5-5), specifically the B···O distances that lie across and between boroxol rings (r4 andr5 in

Figure5-7, respectively). However, as can be seen from the reduced intensity of the peak at 3.6 Å, there are far fewer boroxol rings remaining in the glass system than the model predicts (consistent with the sharp reduction in the breathing mode peak in the Raman data,q.v.§5.2)—therefore, the intensity in the underestimated region must arise from another source. The quantities of [BO₄] and [SbO₄] units in the glass are too low to account for such a strong correlation. The most obvious explanation would seem to be an interaction between the B₂O₃and Sb₂O₃in the glass, for which the simulatedT(r) does not account.

Chapter 5. Antimony Borate Glasses

Figure 5-16 The interatomic distances within a [B₃O₆] boroxol ring; also shown is an attached [SbO₃] trigonal pyramid at an angleφ. Blue atoms are boron, red are oxygen, green are antimony. Note that the [SbO₃] unit is not planar.

Figure5-16 is a modification of the earlier diagram of a boroxol ring (Fig.5-7) with an attached [SbO₃] trigonal pyramid instead of a [BO₃] triangle. In addition to the B···Sb correlation (r0₇), the presence of the larger antimony oxide unit gives rise to two new X···O distances: from the boron atom to the next-nearest oxygen (NNO) on the attached [SbO₃] unit (r₅0) and similarly from the antimony atom to the NNO on the [BO₃] triangle (r9), as well as the OB···OSb distance between these two oxygen atoms

themselves (r₆0). The B−O−Sb angle φ and the non-planar character of the [SbO₃] unit permit these three new correlations to occupy a considerable range of distances. Therefore, the additional intensity observed after the O_Sb···O_Sb peak in the measured correlation functions may arise from any or all of the above.

The differences between the experimental and simulated total correlation functions in the ‘O_Sb···O_Sb to B···O (ring)’ region are prevalent throughout the compositional range studied (Fig.5-17). This indicates that the [SbO₃] units are introduced in a reasonably homogeneous distribution throughout the borate network, displacing the smaller [BO₃] triangles and cleaving boroxol rings. However, as noted earlier in§5.4.1, the persistence of the boroxol ring peak at 3.6 Å does indicate that [B₃O₆] structures continue to be present up to x=0.7, beyond the point where totally homogeneous mix-

Chapter 5. Antimony Borate Glasses

Figure 5-17 The difference between the experimental and simulated total correlation functions for the antimony borate glasses. Positive values indi- cate more intensity present in the actual experimental data than in the simu- lation, and conversely for negative values.

ing of the [BO₃] and [SbO₃] units becomes possible (x= 0.5). Therefore it appears that

some Sb−O−Sb linkages are retained at high x, but this effect does not seem to induce a heterogeneous distribution of structural units in the glass at low x.

Further evidence to support this theory is offered by the boroxol ring peak, where the experimentalT(r) consistently exhibits lower intensity than the simulation. Whilst this is consistent with a model that does not consider interactions between the antimony oxide and borate units, a steady negative trend in∆T(r) would be expected, whilst in fact ∆T(r) for x = 0.7 is less negative than the value at x = 0.6. This indicates that a large

proportion of the antimony oxide units introduced between these two compositions have formed Sb−O−Sb links, rather than disrupt the remaining [B₃O₆] rings.