Variation of structure and optical material dispersion in lead borate glass containing multi valence chromium and germanium cations

In pursuit of manufacturing glass having a high refractive index and low dispersion, a series of lead and borate glasses containing germanium and chromium oxide by composition 25B2O3-73.8PbO-xGeO2-(1.2 − x)Cr2O3, with 0 ≤ x ≤ 1.2 mol.%, are prepared. IR measurements are carried out to explore the structure of as-prepared samples. The deconvoluted IR peaks revealed presence of bridging oxygen up to x = 0.6 mol%. At x > 0.6 mol% none bridging oxygen is the dominant. The dependence of the measured hydrostatic density and corresponding molar volume for the studied compositions are analyzed and discussed. The dispersion curves of refractive index (n) and absorption index (k) are calculated in the spectral range 300–2500 nm. The effect of increasing the ratio GeO2/[GeO2 + Cr2O3] on the calculated dispersion energy, lattice energy, oscillator energy and material dispersion are deduced. For photonic applications, the wavelength at zero material dispersion for the investigated samples is calculated and compared with other systems based on Borates, silicates and Germinate fiber. The results recommend that the present glass could be used in different modern optoelectronics devices.


Introduction
The accelerated use of infrared spectrum of light has led to the development of new optical materials for several advanced optical devices and systems. Photonics, where light can be controlled by light, is a superior example of these highly developed applications. In the core of photonic technologies lie the refractive indices of the used materials (Abdel-Baki and El-Diasty 2013). Photonic devices such as ultrafast optical switches, power limiters, real time holography, self-focusing, white-light continuum generation need exploitation 1 3 564 Page 2 of 21 of glasses with higher nonlinear index of refraction, materials which have high refractive index, high damage threshold and a large region of high transparency. Low light scattering loss is expected in oxide glasses because they have lower glass transition temperature. In addition, oxide glasses with mixed cation compositions are thermally stable and have controllable refractive index variation. In this regard, borate glass is considered as one of the most popular and excellent glass forming materials (Abdel-Baki et al. 2007). The profits of using B 2 O 3 in glass formation are reduction of melting temperature, increased thermal stability and mechanical strength, and enhanced chemical durability. Borate glasses contain π-electron on the B-O ring, thus considerable values for their optical nonlinearity are expected ). GeO 2 -based glasses are transparent in the near infrared region and have a lower glass transition temperature, T g , and lower phonon energy than SiO 2 -based glasses. Borate glasses doped by chromium ions showed large optical nonlinearity due to the large hyper-polarizability of Cr 2 O 3 (Abdel Wahab et al. 2009). Glasses containing cations such as Pb 2+ with an outer electron shell of 18 + 2 electrons should have higher polarizabilities and lower melting temperatures (El-Diasty et al. 2014a, b). Lead-germanium glasses are good transmission in the IR region up to 4.5 mm and are promising materials for applications such as lasing materials, upconverting phosphors, and optical waveguides (Balda et al. 2000).
In the present work, the structural changes due to introducing germanium oxide on the expense of chromium oxide in lead borate network are recorded using FTIR measurements in the wave number range 400-1400 cm −1 . Indeed, the measured hydrostatic density as a sensitive parameter for structural changes is measured with corresponding calculated molar volume. The dependence of linear optical parameters such as energy gap, Urbach energy and number of oscillating dipoles on the molar ratio of GeO 2 /[GeO 2 + Cr 2 O 3 ] are also evaluated. On the other hand, the calculated material dispersion together with the inter-band parameters is used to appraise wavelength at zero material dispersion which illustrate function of the studied compositions in the field data communication through optical fiber.

Experimental
A series of lead borate glasses of compositions 25B 2 O 3 -73.8PbO-xGeO 2 -(1.2-x) Cr 2 O 3 (x≤ 1.2 mol %) as listed in Table 1 are prepared. The used materials were of chemically pure grade, in the form of H 3 BO 3 , Pb 3 O 4 , Cr 2 O 3 and GeO 2 . The glass is prepared by melt quenching technique using platinum 2% rhodium crucibles in an electric furnace. The amount of the glass batch was 50 g/melt. The batch was pre-heated at 500-600 °C for almost an hour to evaporate the carbonates. The temperature of melting was 950-1000 °C, the duration of melting was one hour after the last traces of batches were disappeared. The glass melt was continuing stirred during the preparation to avoid the presence of air micro bubbles. Then the melt was poured onto stainless steel mould and annealed at around 350 °C to remove the thermal strains. Transparent glass slabs were prepared by grinding and polishing of the prepared samples with paraffin oil and minimum amount of water. The thickness of the glass slabs was about 3 mm. Polishing was completed with stannic oxide and paraffin to reach a surface roughness less than λ/3, where is the wavelength. The surface roughness was tested by interferometric method. Infrared absorption measurements are carried out at room temperature by drying and grounding the investigated glass. The obtained powder is mixed with potassium bromide and grounded again to obtain homogeneous mixture. The mixture is then pressed mechanically at 70 MPa pressure in the form of discs. The hydrostatic density of the investigated samples is measured by Archimedes principle at room temperature using xylene as an immersion liquid. Two beam spectrophotometer model JASCO670 UV-Vis-NIR is used to measure reflectance and transmittance coefficients of as prepared optical slabs. With sampling interval 2 nm and resolution limit of 0.2, the accuracy of measuring T(λ) and R(λ) is 0.004. All optical measurements are carried out at room temperature and in the entire spectral range 200-2500 nm.

FTIR measurements
The FTIR spectrum of the investigated compositions is shown in Fig. 1. The obtained absorption peaks of the FTIR spectrum show many features, as x increases from 0 to1.2 mol%, which are related to the structural aspects from which it can be seen as follows: The spectrum consist mainly of four main regions which are positioned in the ranges 407-554 cm −1 , 611-782 cm −1 , 786-1131 cm −1 and 1131-1500 cm −1 (Abdel-Baki et al. 2007). The peak detected in the first region and lie in the range 470-484 cm −1 may be due to the presence of metallic ions such as Pb‫‬ and Ge‫‬ , the symmetric bending vibration mode of Pb-O in PbO 4 (Moustafa et al. 1994;Culea et al. 2010;Narendrudu et al. 2016;Reddy et al. 2006;Khanna 2000), and Ge-O-Ge symmetric stretching vibrations (Gowda and Anavekar 2004;Chelcea et al. 2011). In this region a band due to CrO 2− 4 structural units is also possible (Chelcea et al. 2011). The observed peaks in the second region at 708-713 cm −1 are attributed to the combined vibrations of the BO 3 (Vijay et al. 2015) and PbO 4 groups (Varshneya1994), bending vibration of the B-O-B linkage in the borate network (ElBatal et al. 2014;Kamitsos et al. 1987Kamitsos et al. , 1981, and the stretching mode of Ge-O-Ge bonds in GeO 6 units (Narendrudu et al. 2016;Tenny and Wong 1972).
The absorption peak observed at 875-893 cm −1 , is assigned to B-O bond stretching of BO 4 (Doweidar et al. 2013;Iordanova et al. 1994) overlapped with asymmetric stretching vibration of CrO 2− 4 structural unit (Doweidar and Saddeek 2010). While the peak centered at about 1000 cm −1 , is assigned to penta-borate group (Doweidar and Saddeek 2010) and B-O-Pb vibrations. This peak shifts toward lower energy with increasing GeO 2 content.

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The band centered at about 1208-1240 cm −1 , is assigned to asymmetric stretching vibrations of B-O bond of triangular BO 3 present in ortho-borate group (Iordanova et al. 1994) and shifts toward lower wave number with the increase in GeO 2 content. The band centered at about 1310 cm −1 is attributed to the presence of pyro-borate, ortho-borate groups contain BO 3 (Doweidar and Oraby 1997;Kimand and Bray 1976;Bray and O'Keefe 1963) and disappeared at x > 0.8 mol%. The absorption peak appeared in the wave number range  Kamitsos et al. 1987Kamitsos et al. , 1981Doweidar and Oraby 1997) stretching vibrations of the borate triangles with non-bridging oxygen (NBO) in various borate groups (Chelcea et al. 2011), and the asymmetric stretching vibration modes of Ge-O-Ge bonds (Narendrudu et al. 2016).Moreover, in Fig. 1 the intensity of the third region decreases as x increase from x = 0.0 mol% (GeO 2 = 0, Cr 2 O 3 = 1.2) to x = 0.2 mol% (GeO 2 = 0.2, Cr 2 O 3 = 1.0) and increases in intensity for x > 0.2. On the other hand, the broadness of band at 1200-1500 cm −1 decrease as x varies from 0.0 to 1.2 mol%.
Quantitative analysis of the spectrum shown in Fig. 1 is attained by calculating N4 which represents the ratio of BO 4 tetrahedral units to the total concentration of boron atoms in the studied glass i.e., N4 = concentration of BO 4 /total concentration of (BO 3 + BO 4 ) units (Kim and Bray 1976). This was done by deconvoluting IR absorbance peaks shown in Fig. 1. It should be noted that the deconvolution process is used to separate broad bands of the IR spectrum into its several symmetrical Gaussian bands by considering the position and area of each band related to the vibrations of a particular structural unit. The deconvolution process was applied on the investigated samples by sub-dividing the spectrum of each composition into different spectral regions and then fitting each band with Gaussian function. The area and the position of each Gaussian peak are recorded for quantitative analysis of the measured spectrum (Bray and O'Keefe 1963). The area under absorption peak is considered to be proportional to the concentration of structural units emerging it. Figure 2 illustrates the deconvoluted IR peaks for the studied compositions 25B 2 O 3 -73.8PbO-xGeO 2 -(1.2-x)Cr 2 O 3 with x = 0.0, 0.6 and 1.2 (as an example). The dependence of the calculated N4 on the molar ratio of GeO 2 /[GeO 2 + Cr 2 O 3 ] is illustrated in Fig. 3. This figure demonstrates that increasing the molar ratio of GeO 2 from zero (sample 1) up to 0.2(sample 2) and at x = 1.0 (sample 6) and x = 1.2 mol% (sample 7) N4 does not change against composition. For GeO 2 > 0.2 mol%, N4 increases to maximum at x = 0.6 mol% of GeO 2 followed by a decrease as the ratio increase up to 0.8 mol%. This means that increasing GeO 2 content in lead borate host network in the range of GeO 2 = 0.2-0.6 mol% increases the number of bridging oxygen (BO). Above x = 0.6 mol%, N4 decreases as GeO 2 increase to 0.8 mol%.This means increasing of non-bridging oxygen (NBO) in the lead-borate network over the ratio of bridging oxygen. Similar behavior of N4 is observed in lead borate network using NMR measurements (Doweidar et al. 2013;Iordanova et al. 1994;Doweidar and Saddeek 2010;Doweidar and Oraby 1997;Kimand Bray 1976;Bray and O'Keefe 1963). These measurements clarified that introduction of PbO from 10 up 50%, the fraction of four coordinated boron atoms BO 4 increase over three coordinated boron atoms BO 3 . Further increase of PbO over 50% decreases the number of BO 4 with anomalous point at 50% of PbO (Leventhal and Bray 1965). Furthermore, the same trend of Fig. 3 is also observed in the literature for many B 2 O 3 oxide glasses (Priven 2000).

Hydrostatic density and molar volume
Measurement of hydrostatic density is considered as an important tool to investigate the structural compactness and the variation of dimensions of interstitial holes. Figure 4a shows the dependence of the measured hydrostatic density as function of GeO 2 / [GeO 2 + Cr 2 O 3 ] molar ratio in lead-borate network for the studied samples. This figure demonstrates that the density shows an oscillatory behavior against the increase of GeO 2 . Furthermore, this figure shows that increasing GeO 2 with ratio 0.2 mol% (sample 2) increased the density followed by a decrease to minimum density when GeO 2 content ratio is increased to 0.4 mol% (sample 3). In addition, for sample (4) (x = 0.6 mol%) the density increases by ratio 20%. Increasing GeO 2 beyond 0.6% has a little effect on the density.
The molar volume of glass composition could be calculated using the following equa-   (1) in the studied composition range (x = 0-1.2 mol%) produces a reverse trend to that obtained in Fig. 4a. The anomalous behavior observed in Fig. 4 which is due to replacement of Cr 2 O 3 with GeO 2 in the investigated PbO-B 2 O 3 glass could be explained as follows: It is known that the structure of lead borate network which is rich in lead (as the investigated case) consists mainly of two sub-networks realized by Bray et al. ( , 1992 and Takaishi et al. (2000). The first sub-group is for Borate oxide network and composed of two building blocks normal triangle coordination BO 0 3 and fourfold tetrahedral coordination BO − 4 which are connected together through oxygen atom to form B-O-B (borate bridging oxygen). Indeed, the second sub-network contains triangle coordination pyramids PbO 3 which are linked to each other by oxygen atoms to form Borate bridging oxygen Pb-O-Pb. The building block PbO 3 is also observed in PbO-SiO 2 composition (Takaishi et al. 2000;Imaoka et al. 1986). These two sub-networks are linked together via fourfold tetrahedral coordination tetrahedral of borate network to develop Pb-O-B covalent bonds (El-Diasty et al. 2014a, b).
The transition metal such as Chromium can exit in host network by two oxidation states where, Cr 3+ which act as a modifier while Cr 6+ plays the role of former with CrO 2− 4 building unit (Abdel-Baki et al. 2007). Chromium as a former converts not only BO 3 building units to BO 4 but also PbO 3 into PbO 4 (Warren 1941;Wang et al. 1991;Rada et al. 2013). This conversion process increases the number of bridging oxygen (BO) and consequently increases the compactness of the studied PbO-B 2 O 3 network accompanied by a decrease in its molar volume (Fig. 4). On the other hand, GeO 2 enters the host network with GeO 4 unit which has a role of former (Vijay et al. 2015). Introducing GeO 2 by 0.2 mol% (sample 2) increases the density due to creation of bridging oxygen which causes a decrease of the molar volume. Definitely it is also argued to presence of two formers Cr 6+ and GeO 4 at the same time in the structural network of lead-borate. Reducing molar fraction of Cr 2 O 3 to 0.8 mol% (sample 3) causes the valence of Cr 6+ to decrease to lower valence, which means appearance of its role as a modifier (Cr 3+ ) which indicates a creation of non-bridging oxygen (NBO) and partial transformation of BO 4 into BO 3 and PbO 4 into PbO 3 structural units. Part of this transformation is compensated due to presence of GeO 2 in the host network. This partial compensation takes place as a result of its role as a former (Vijay et al. 2015). After that increasing ratio of GeO 2 content not only eliminate the former role of Chromium but also transforms GeO 4 into GeO 6 and also transformation of BO 3 and PbO 3 into BO 4 and PbO 4 in sequence. Figure 5 shows the dependence of the measured transmittance, T(λ), on the applied wavelength for the studied samples. In this figure transmittance exhibit one deep depression in the UV and visible regions of spectrum. Furthermore, an increase in the magnitude of T is seen as GeO 2 content increases up to sample (2) followed by a decrease for samples (3). As x > 0.6 mol % causes an increase in the magnitude of T. Indeed, the cut off wavelength, λ cutoff , shows a red shift against the increase in the GeO 2 content from 0.0 mol % (sample 1) up to 0.6 mol% (sample 4) and a decrease of Cr 2 O 3 with the same ratio.

Evaluation of optical constants and data reduction
A method of data reduction based on an iteration technique (Khashan and El-Naggar 2000) is used to calculate precisely the attenuation factor η which represents the modifications caused to the electromagnetic wave, during its propagation in the material of refractive index n and absorption index k. The attenuation factor is given by = exp(− d) where d is the sample thickness and α is the absorption coefficient of the sample, = 4 k . The real part, n, of the complex dielectric constant n−ik is given by (Khashan and El-Naggar 2000), where R s is the interface reflection coefficient. As a first iteration η is taken as a unity. A rough value of R s and T s are obtained using the following relations (Khashan and El-Nag-  Furthermore, the achieved final value of η jointly the corresponding values of R s and k Eq. (2) are substituted in Eq. (1) to yield the refractive index n at a given wavelength.
The calculated refractive index (n) through studied spectral range for each of the investigated compositions is shown in Fig. 6. In the whole spectrum a remarkable increase of the refractive index takes place from sample (1) up to sample (4) followed by a decrease in magnitude for samples (5) and (6). This trend may be due to the variation in the measured hydrostatic density (Fig. 4) of the samples besides the high bond polarizability of Cr 3+ which shows a direct proportionality with refractive index (El-Diasty et al. 2006). The observed increase of N4 between samples (1) and (4) as shown in Fig. 3 is an evidence to the decrease of Cr 3+ and its high bond polarizability which plays a role of modifier and also presence of GeO 4+ as a former which led to the increase of refractive index. On the other hand, the decrease of N4 between samples (4) and (7) means a more transformation of Cr 6+ into decrease of Cr 3+ and transformation of GeO 4 into GeO 6 . The conversion of GeO 4 into GeO 6 increases its role as a former which in turn modify the refractive index as observed in Fig. 6.

Optical band gap parameters measurements
Concerning to Tauc's theory (Tauc 1974), the optical band gap energy for direct and indirect transitions determined, Fig. 7, with an error in the order of 0.02 eV, using the formula: where α o isa temperature independent constant related to the extent of the band tailing, ν is the light frequency, h is Planck's constant. In Eq. (3) the exponent r = 0.5 for allowed direct  Table 1.

Width of localized band tail states
The width of the band tail localized states could be evaluated using Urbach energy, E U which could be calculated from the slope of the linear part of lnα against photon energy as: where α is the optical absorption coefficient and hν is the photon energy. The calculated values of E U are shown in Fig. 8b and inserted in Table 1. In this figure, the width of the localized states band tail illustrates a decrease of E U as a general trend against the increase of GeO 2 on the expense of Cr 2 O 3 . This behavior could be explained as follows: the oxygen dangling bond or non-bridging oxygen [NBO] is a localized structural defect and compose of one half of the permanent broken oxygen bond (Skuja 1998;Vaccaro 2009). These defects are formed in the host network by introduction of a modifier cation such as Cr 3+ (as present study). The modifier ions break the connected building blocks through oxygen bond to create Non-bridging oxygen defect. The negative oxygen bonds create a state in the pseudo energy gap. The energy position and density of these states depends on density of NBO defects (Abdel- Wahab et al. 2018). Therefore, the decrease of the width of localized states shown in Fig. 8b against composition means a decrease of number of non-bridging oxygen and an increase of bridging oxygen which is due to the conversion of BO 3+ into BO 4+ in the host structural network. Furthermore, the decrease of the density of states in energy gap explains the increase of the optical energy gaps illustrated in Fig. 8a.

Position of the fermi level
The dispersion of the extinction coefficient k(λ) could be used to evaluate the energy position of the Fermi level by applying Fermi-Dirac distribution function (Khashan and El-Naggar 2000) of the form: where k(E) is the maximum value of absorption index, E F is the energy position of Fermi level, E is the photon energy, K B the Boltzmann constant and T is the absolute temperature. Equation (5) could be rearranged to yield: Plotting the left-hand side of Eq. 6 as function of E yields a curve. Extrapolating the straight part of the curve to x-axis at y = 0 will give value of E F . The calculated values of E F as function of composition are added to Table 1. The relative high value of E F indicates that the studied glass compositions behave like an insulator.

Valuation the inter band optical absorption type
Elliott (Elliott 1957) proposed a model to decide the main type of the fundamental absorption edge. In this model the absorption coefficient α(E) is examined using a semi-empirical relation after convoluting the total absorption coefficient with a Lorenzian function in the form (Manoogian and Woolly 1984): where α o is the absorption peak at ground state energy, Γ 1 and Γ c are the full-width at half maximum of Lorenzian and full-width of the continuum excitons, and R z is the free exciton binding energy and α 1 is the absorption at band gap. The recorded absorption spectrum at room temperature for each studied sample is fitted locally point by point to Eq. (7) taking α o , α 1 , Γ 1 , Γ c , R z and E g as adjustable fitting parameters. Figure 9 illustrates the measured absorption coefficient fitted using Eq. (7). As shown in Fig. 9 absorption coefficient increase in magnitude as GeO 2 increases on the expense of Cr 2 O 3 in lead borate network. Furthermore, the optical absorption shifts towards higher energy indicating an increase in the estimated values of the optical gap which confirms the trend in Fig. 8a. The parameters Fig. 9 Fitting of linear absorption coefficient, α, using Elliot model (Eq. 7) for all investigated samples. Open circles and solid line refer to the calculated and fitted α in sequence attained from fitting process are listed in Table 2. In this table, comparing the values of the optical energy gaps obtained from Eq. (3) ( Table 1) and Eq. (7) it could be concluded that direct is the most probable transition for the investigated sample.

Lorentz dispersion model
The interaction of propagated light waves of frequency ω and the oscillating dipoles with resonance frequency ω o in an optical medium causes a displacement of dipoles as damped oscillators. The damping is a sequence of the fact that oscillating dipoles lose its energy by collision and the damping ability of the optical medium. Furthermore, the damping term together with number of oscillators can alter not only position of the absorption peak but also the broadening of the absorption line. According to the oscillating dipole theory by Lorentz (Roa et al. 1990;Marin et al.1997;Fox 2003), the dispersion of the absorption index, k is given by: where N is the number of dipoles per unit volume, m and e are the rest mass and charge of electron in sequence, o the permittivity of vacuum = 8.854 × 10 -14 F/cm, the damping factor of the medium and f is the oscillators strength. The calculated absorption indices, of the present samples are fitted to Lorentz model (Eq. 8) with N, f, ω o and as fitting parameters as shown in Fig. 10 for sample (4) as an example. Indeed, Fig. 10 illustrates the coincidence between calculated k and that calculated using Lorentz model (Eq. 8). The composition dependence of calculated values of Lorentz fitting parameters of the presented samples are listed in Table 2. In this table the increase of GeO 2 in the structural network of Pb-B 2 O 3 decreased number of oscillating dipoles from 0.76 × 10 24 to 0.63 × 10 24 cm −3 kg −1 . Furthermore, a decrease of the damping factor from 1.3 × 10 15 (sample 1) to 0.5 × 10 15 (sample 6) accompanied by a shift towards higher frequency are argued to the high applying ordering role of Cr 2 O 3 as a transition metal and are also due to the decrease of the compactness of the material which is argued to the increase of the number of non-bridging oxygen as a structural defect in the studied samples (Fig. 11).

Optical dispersion of dielectric constants
The real component ɛ 1 of the complex dielectric constant could be written as (Moss et al. 1973): where ε ∞ the high frequency dielectric constant, C is the speed of light and N c m * is the ratio of free carriers concentration to the free carrier effective mass. Indeed  Table 3. Values of N c m * in Table 3 express the same trend of the refractive index shown in Fig. 6 (assuming a constant effective mass m * ).  The refractive index of the material below the inter-band absorption edge could be calculated using empirical dispersion relation of Wemple-DiDominico (1971) which has the following form:  Table 3 as function of composition. The dispersion energy parameter, E d , could be considered as a measure to the nearest neighbor cation coordination, iconicity, anion valence and effective number of dispersion electrons of the material and is given as: where β is a constant and has a values of 0.26 for halides and most oxides (Wemple and DiDominico1971), N CN is the coordination number of cation's nearest neighbor to the anion, Z a chemical valence of the anion (Z a = 2 for oxides) and N e is the effective number of valence electrons per anion (usually N e = 8) ( Wemple 1979).The calculated values of the coordination number, N CN , for the studied glass using Eq. (11) are listed in Table 3. Although the obtained values E d is affected by many parameters such as β, Z a and N e but coordination number still the most leading effect as shown in Table 3 where the highest coordination number corresponds to the highest value of E d . When wavelength is shorter than resonance frequency the role of the lattice is given by (Nassau and Wemple 1982): where E l is the lattice oscillator strength. Plotting a graphical relation for (n 2 -1) as a function of E 2 using Eq. (12) approaches a straight line with slope -E 2 and intercept E d /E o . The obtained values of E l are inserted in Table 3 as function of composition.

Wavelength at zero material dispersion
The dispersion parameters E o , E d and E l could be used to calculate material dispersion which is an important parameter for the investigated glass. The material dispersion M(λ) verify suitability of the investigated compositions to be used in fiber telecommunication. M(λ) could be expressed in terms of refractive index, n as follows: Differentiating Eq. (12) with respect to λ gives the material dispersion in terms of E o , E d and E l and n as follows (Nassau and Wemple 1982): Figure 12 shows the dependence of the material dispersion, calculated using Eq. (14), on applied wavelength in μm for investigated samples. The method of determining wavelength λ c at zero material dispersion, M = 0, is shown in Fig. 12. The obtained values of the wavelength at zero material dispersion are listed in Table 3. Calculation of λ c is necessary to balance the material dispersion against waveguide dispersion in optical fibers (Nassau and Wemple 1982). For the sake of comparison values of λ c for previously reported values of Borates (λ c = 1.27 μm), Silicates (λ c = 1.56 μm) and Germinates (λ c = 1.87 μm) (Fujino and Morinaga 1997) are added to Fig. 12. Therefore, the studied samples could be considered as appropriate glass to use in transferring data through optical fiber as illustrated in Fig. 12.

Conclusion
In the present research the dependence of the structural parameters due to replacement of Cr 2 O 3 by GeO 2 for the compositions 25B 2 O 3 -73.8PbO-xGeO 2 -(1.2-x) Cr 2 O 3 (0 ≤ x ≤ 1.2 mol%) is presented. The measured hydrostatic density and calculated molar volume for as prepared bulk samples showed an anomalous behavior which is argued to the presence of Cr 2 O 3 with its dual role as former and modifier beside the role of GeO 2 as former. The same behavior is obtained for the calculated dispersion of refractive index (n). Also, the deconvolution of the peaks of the measured IR spectrum revealed presence of bridging oxygen up to x = 0.6 mol%. Furthermore, at higher x in mole % none bridging oxygen is the dominant. Indeed, the observed increase of the calculated values of the optical gap E g are due to the decrease of the calculated localized states in the pseudo gap which means a tendency of the studied network to be more ordered due to the increase role of GeO 2 as a former. Fitting of the measured absorption coefficient using Elliott model enabled to distinguish a direct as the most probable transition in the studied samples. On the other hand, coincidence between calculated extinction coefficient k and that calculated using oscillator model of Lorentz model is observed. The density of oscillating dipoles showed a maximum at x = 0.2 mol% followed by a decrease against the increase of GeO 2 . The calculated single oscillator energy E o and dispersion energy parameter E d are used to calculate the wavelength at zero material dispersion λ c for photonic applications. The dependence of λ c on the structure showed that the present samples can be used to transmit data through optical fiber in the wavelength range 0.8687-2.1768 μm.