Parameterising complex Te-O distances 1 Te-O peak fitting

The Te-O peaks were fitted using the leading edges of both neutron and X-ray data (weighted to 50% each) as shown in Fig. 6.12. The second Te–O(II) peak was fitted from the residual of the T(r) after the Te–O(I) peak was fitted. The same process was done for the third Te–O(III) peak. The fit parameters obtained are shown in Table 6.4.

Figure 6.12: Fitted Te-O peaks for 17.5PbO-82.5TeO2 glass from NXFit

In the plateau region, (for x < 15 mol%) the average nTeO is approximately constant and has

the value of 3.69(9). The error is represented by the difference between the value obtained by peak fitting and that obtained by integration of the Te–O peak manifold, arising from the first coordination sphere from which the other contributions (O–O, Pb–O, and Te–O(IV)) are removed. The large error is associated with the limitation in Qmax of the X-ray data which

broadens the TX_{(r) and lowers the quality of the fit. It seems that the fraction of the [TeO} 3]

units present in pure TeO2 glass is retained in PbO-TeO2 glass for x < 15 mol% PbO and

suggests that Pb2+ _{changes the TeO}

110 plateau region, the NBOs (O1b) created by adding PbO, combined with the pre-existing terminal oxygens (O1a) of the [TeO3] units, are sufficient to supply the required coordination

for Pb2+ _{without the need for creating more NBOs (O1c) by the formation of the [TeO}

3]– unit.

This only breaks the TeO2 bridges and does not transform units, hence the short range Te-O

environments (distance distribution) are similar for x < 15 mol%, as shown in the comparison of T(r) of these glasses with a-TeO2.

Table 6.4: Peak parameters for Te-O and Pb-O peaks obtained from NXFit

Te environment x / mol% PbO <r> / Å nTeO

10.0 1.98 3.69(12) 12.5 1.99 3.70(6) 15.0 1.98 3.68(10) 17.5 1.97 3.64(4) 20.0 1.98 3.58(8) Average 1.98(1) – PbTe5O11 3.70

For x = 17.5 mol%, the average nTeO obtained is 3.64(4). Within error, this value is not

significantly different from those in the plateau region but this composition can be considered to fall within the post-plateau region by comparison of its TN_{(r) with that of a-}

TeO2 (Fig. 6.9) where the contribution of short Te-O distances corresponding to rTeO in the

created [TeO3]– units (O1c) is visible as indicated by the mismatch of the leading edge. This

nTeO value is similar to that of the 20 mol% Li2O glass and, as shown in Fig. 6.10, the

normalised T(r)/wTeO is identical to the T(r)/wTeO of the 20 mol% NullLi2O glass, proving the

similarity of the Te environment (distance distribution) in these compositions. In this post plateau region, the value of b = 2.1 is obtained by fitting the two data points. This value is significantly larger than the value in Li2O-TeO2 glasses (b = 0.8).

6.5.4 Extension of the TeO

model

6.5.4.1

Plateau region

Based on the similarity of the first peak in TN_{(r) of 10, 12.5, and 15 mol% PbO tellurite glasses}

to that of pure TeO2 glass, it is reasonable to infer that the proportions of [TeO4] and [TeO3]

units present in these glasses are similar, giving an average nTeO value of 3.69(9). This

assumption is consistent with the results obtained by simultaneously fitting the X-ray and neutron diffraction data. These compositions are therefore in the plateau region. In considering the TeO2 model, the value of average nTeO in the plateau region from here on will

111 be fixed at 3.70 to make the average nTeO in PbO–TeO2 similar to that in Li2O–TeO2 so that

the b value obtained is comparable to the Li2O-TeO2 system. This nTeO value corresponds to:

n

= 3.70 = (0.3)[Te3] + (0.7)[Te4]

6.1

Therefore, in RPbO–1TeO2 glass with R and 1 units of PbO and TeO2 respectively,

RPbO–1TeO

=> 0.3[Te3]+ 0.7[Te4] + 0.3[O1a] + 2R[O1b] +

(1.7-R)[O2] + R[Pb]

6.2

From this equation, the deviation composition xD can be determined based on these

assumptions:

(1) Pb2+ _{is coordinated to an average of 8 oxygen atoms as will be discussed in}

Section 6.5.5 later (Bond valence for Pb–O is therefore 0.25 v.u., average rPbO is ~2.62 Å)

(2) Te–O1a has a bond valence value of 1.5 v.u., therefore O1a could coordinate 2 Pb2+

(3) Te–O1b (determined from PbTe5O11) has a bond valence value of 1.4 v.u.,

therefore O1b could coordinate to the average number of 2.4 Pb2+ _ions

Therefore, combining (1), (2), and (3) 8(NPb) ↔ 2(NO1a) + 2.4(NO1b) 8(R) ↔ 2(0.3) + 2.4(2R)

R ↔ 0.1875

xD = R/(1+R) ≈ 15.8 mol%

This xD value agrees well with the experimental nTeO(x) plot in Fig. 6.13 where xD is a value

between 15 and 17.5 mol% of PbO. Therefore when Pb2+ _{is coordinated to 8 oxygen atoms}

and each Pb-O bond has the average bond valence value of 0.25 v.u, all O1a and O1b, are fully bonded to Pb2+ _{at 15.8 mol%, which means that x = 10, 12.5, and 15 mol% PbO tellurite}

glasses are within the plateau region of nTeO.

6.5.4.2

Post plateau region

Since xD for PbO-TeO2 is similar to Li2O-TeO2, from Eqn 5.10, nTeO for post plateau is

nTeO = 3.70 – Qb 6.3

Where Q is the further unit added, [(0.1875 + Q)PbO–1TeO2] (Similar as M in Eqn, 5.7 and

5.8, Q is chosen to represent PbO-TeO2 glasses). As seen in Fig. 6.13, the value of b = 2.1 fits

the experimental data well, but this is obtained by using only two points, giving rise to a large error value, where the b value could be between 0.8 to 4. Fig. 6.14 compares the

112 nTeO(x) for Li, K, and Pb and their b values. In this case, a fixed value of xD is chosen to

represent Li, K, and Pb, to highlight the difference in the b values.

Figure 6.13: The determination of b value for PbO-TeO2 glasses

In the plateau region, the condition: 8(NPb) ↔ 2(NO1a) + 2.4(NO1b) is based on the assumption that rPbO values in the [PbO8] unit are similar. Adding up the contribution of

bonds from O1c;

8(NPb) ↔ 2(NO1a) + 2.4(NO1b) + 2.8(NO1c) 6.4

and substituting the fraction of each unit, we have,

8(R) ↔ 2(0.3) + 2.4(2R) + 2.8(Rb-0.1875b) where b = 2.1 6.5 This condition however creates an excess number of bonds in the plateau region: available bonds > required bonds. If the system energy is minimised when the number of available bonds matches the number of required bonds, Eqn. 6.5 can to be further broken down into various equalities. In this case, only 3; (a), (b), or (c) are considered, as follows;

(a) 8(R) ↔ 2(0.3) + 2.4(2R) + 2.8(Rb-0.1875b) where b = 1.15 6.5.a (b) 8(R) ↔ 2(0.3) + 2.4(2R) + 1.3(Rb-0.1875b) where b = 2.1 6.5.b (c) 8(R) ↔ 2(0.3) + 2.4(2R) + 2.8(Rb-0.1875b) where b = 2.1 6.5.c

113

Figure 6.14: The average nTeO for PbO-TeO2 glasses, compared with Li2O-TeO2 and K2O-TeO2 glasses.

In the case of (a), this would mean that the number of Te–O bonds broken in the transformation process of [TeO4]– to [TeO3]– unit is less that the value obtained from fitting

the nTeO (post plateau region). This b value of 1.15 is however within the error of b as

discussed. A smaller b value would mean that the the number of Pb–O1c bonds is less than the number of Pb–O1a, or Pb–O1b bonds, to be exact; for the [PbO8] unit, there are 2.8 Pb–

O1a + 4.8 Pb–O1b + 0.4 Pb–O1c bonds where the distance of Pb–O1a = Pb–O1b = Pb–O1c = ~2.6 Å. In the case of (b), this would, however, mean that rO1c–Pb is 2.31 Å (0.58 v.u.) which is

not a typical rPbO within this range of PbO composition (x < 20 mol%). Therefore, this would

indicate that, in the post-plateau region, Pb2+ _{changes its environment as a preparation to}

entering the glass former state (to start forming shorter Pb-O bond). Pb2+ _{environments in}

lead tellurite crystals vary depending on the PbO content. As discussed in Section 4.4.4, in PbTe5O11 (16.7 mol% PbO), there is 1 [PbO4+4] unit (subscript 4 + 4 means there are 4 short

and 4 longer PbO distances), this PbO distance distribution, however, can be approximated by a single Gaussian. In the much higher PbO content Pb2Te3O8 crystal (40 mol% PbO), there

are two Pb sites: [Pb4+4], and [Pb3+5]. In the 50 mol% PbO content crystal (PbTeO3), there are

2 [PbO2+6] and a [PbO8-long] units present. Based on this trend, it is apparent that, as the PbO

content increases, shorter PbO distances are formed such that, at 50 mol% PbO, the distance resembles a typical Pb-O distance for Pb2+ _{behaving as a glass former, which is the}

case in (c). This simply means O1a, O1b, and O1c are connected to Pb2+ _{at different r} PbO,

however, rPb–O1a, rPbO–O1b, and rPbO–O1c cannot be separately determined from the diffraction

114

Figure 6.15: The number of bonds in the plateau and post-plateau regions for b = 2.1, and b = 1.15.