Structural and optical properties of barium titanium borate glasses doped with ytterbium

Barium titanium borate glasses doped with ytterbium ions were fabricated via standard melt quenching technique. The building structure of the glass matrices doped with ascendant ratios of ytterbium ions were studied using Raman and FTIR spectroscopies. The UV–Vis–NIR optical absorption spectra were investigated and used to calculate optical bandgaps, Urbach energies, refractive indices, metallization criterion, optical basicity, and dispersion parameters. The absorption and emission cross-sections and gain spectra for 2F5/2 → 2F7/2 transition of ytterbium ions were investigated. The high values of the emission cross-sections of the studied glasses make them strong candidates for laser and amplifier applications.


Introduction
Alkali/alkaline earth borate glasses doped with transition metal elements, rare earth elements or both attracted the interest of researchers due to the importance of these glasses in developing many technological applications such as solid-state lasers, solar energy converters, optical fibers, and electronic devices [1][2][3]. Barium borate glasses have acquired great importance due to their unique optical properties, low melting point, high thermal and mechanical stability, and good solubility of rare earth ions as well as transition metals [4][5][6]. The fundamental structural units of borate-based glasses are trigonal BO 3 and tetrahedral BO 4 which can combine to form different structural groups such as diborates, tetraborates, orthoborates, pentaborates, metaborates, and boroxol rings. The coordination number of the boron atom can be easily changed from three to four or vice versa depending on the type and the concentration of the added modifier [7][8][9][10].
The introduction of transition metals into glasses improves the structural, optical, electrical, and magnetic properties of them due to the multiplicity of valance states of these elements, which depend mainly on the glass composition and melting conditions [8,11,12]. Among transition metal oxides, TiO 2 is a useful glass constituent for preparation some special optical glasses and glass-ceramics. Titanium ions usually exist in the glassy host in trivalent and tetravalent valence states and participate in the glassy matrix with TiO 4 , TiO 6 , and sometimes TiO 5 structural groups [13].
Barium titanate-based glasses are promising materials due to their unique and distinctive structural, optical, and electrical properties which make them good candidates in many modern applications such as sensors and transducers, electronics, bioactive materials, non-linear optical devices, and reversible electrodes [14,15]. The incorporation of barium titanate with any glass former helps to form a homogeneous glass matrix and enhances the radiation shielding properties of this matrix [16]. Glasses containing rare earth elements as luminescent centers are considered as an important class of photonic materials due to their unique and distinct spectroscopic properties resulting from f-f transitions in the visible and near to mid IR spectral ranges [17,18]. The luminescent properties of these glasses are mainly dependent on the glass type, composition, and the ratio of the rare earth elements [19].
The objective of this work is to investigate the impact of Yb 3? ions on the structural and optical properties of barium titanium borate glasses as optical materials.

Experimental details 2.1 Glass fabrication
Pure chemicals of boric acid (H 3 BO 3 ), titanium dioxide (TiO 2 ), barium carbonate (BaCO 3 ), and ytterbium oxide (Yb 2 O 3 ) were used as starting materials to synthesize Yb 3? -doped barium titanium borate glasses by the standard melting-quenching method. Appropriate molar ratios of the starting materials were weighed, thoroughly mixed, and melted in a porcelain crucible using an electric furnace (VECSTAR, UK) at 1100 ± 10°C for 2 h. The molten materials were rotated and checked every half hour to obtain a high degree of homogeneity, then casted into slightly warm stainless-steel molds and rapidly moved to a muffle furnace for annealing at 330 ± 5°C for half hour. The molar composition of the synthesized glasses and their codes are presented in Table 1.

Density and molar volume measurements
Archimedes method was utilized for measuring the density (q) of the bulk glasses by weighing them in both of air and xylene (0.86 g/cm 3 ) based on the next relation: where W a is the glass weight in air, W x is the glass weight in xylene, and q x is the xylene density. The molar volume (V m ) of the glasses is estimated using the relation V m = Mwt/q, where Mwt is the glass molecular weight.

Spectroscopic measurements
Raman spectra were recorded in the wavenumber range 40-3750 cm -1 using SENTERRA Raman microscope (Bruker, Germany) with a laser excitation wavelength of 785 nm and power of 50 mW. The FTIR absorption spectra were recorded using computerized FTIR spectrometer (Bruker, Vertex 70v, Germany) covers the wavenumber range 4000-400 cm -1 . The UV-vis-NIR absorption spectra were recorded using a single monochromatic spectrophotometer (JASCO, V-770, Japan) covers the wavelength range 2500-190 nm. XRD spectra were recorded using a diffractometer (Philips, PW-1390) in 2H range from 5°to 70°.
3 Results and discussion 3.1 XRD spectra Figure 1 shows the XRD spectra of the studied glasses in the range of 5°-70°. The non-presence of a sharp peak in the XRD pattern confirms the

Density and molar volume
The dependance of the density (q) and molar volume (V m ) of the studied glasses on Yb 2 O 3 content is shown in Fig. 2 [21]. The obtained values of the density and molar volume are presented in Table 2.
The obtained values of the density and molar volume are utilized to calculate some physical parameters such as Yb 3? ions concentration (N), Yb 3? ions separation (R), oxygen packing density (OPD), and mean boron-boron separation (\d B-B [) based on the next relationships [7,23,24]: where x Yb2O3 is the molar fraction of Yb 2 O 3 , N A is Avogadro's number, z is the number of oxygen atoms in the glass composition, and x B2O3 is the molar fraction of B 2 O 3 . The N values increase as the con-  Table 2.

FTIR absorption spectra
The FTIR spectra of the studied glasses are shown in Fig. 4. The spectrum of the base undoped glass (BTiBaYb0) reveals a small band in the region 458-501 cm -1 with two peaks at 469 and 483 cm -1 due to vibration of barium ions [37]. Furthermore, a broad band in the region 545-760 cm -1 with its peak at 625 cm -1 is ascribed to vibration of titaniumoxygen bond in TiO 6 groups [38]. Moreover, a broad band in the region 776-1167 cm -1 is attributed to stretching vibration of BO 4 groups [39]. In addition, a broad band in the region 1195-1569 cm -1 with its center at 1384 cm -1 is attributed to stretching vibration of boron-oxygen bond in BO 3 groups [40]. A medium band in the region 1573-1728 cm -1 with two peaks at 1618 and 1638 cm -1 is ascribed to vibration of water and OH groups [39,41]. The incorporation of Yb 2 O 3 into glass matrix with different ratios leads to the following modifications: (i) The intensity of the first band (458-501 cm -1 ) decreases with increasing the concentration of Yb 3? ions. (ii) The second band (545-760 cm -1 ) becomes more broadened and splits into two bands centred at 572 and 721 cm -1 due to the bending modes of various borate groups and the vibrations of TiO 4 groups, respectively [38,41]. (iii) The intensity of the third band (776-1167 cm -1 ) increases with increasing the concentration of Yb 3? ions. (iv) The fourth band (1195-1569 cm -1 ) becomes more broadened and splits into two bands with their peaks at 1207 and 1384 cm -1 due to the stretching vibrations of BO 4 and BO 3 groups, respectively, in the BTiBaYb1 and BTiBaYb5 glasses [39,40]. (v) The intensity of the fifth band (1573-1728 cm -1 ) decreases with increasing the concentration of Yb 3? ions. The obtained analysis from FTIR spectra are consistent and in agreement with that of Raman spectra. Table 2 Density (q), molar volume (V m ), ytterbium ions concentration (N), mean ytterbium ions separation (R), oxygen packing density (OPD), and mean boron-boron separation (\d B-B [) of Yb 2 O 3 -doped barium titanium borate glasses

Optical absorption spectra
The optical absorption spectra of the studied glasses are displayed in Fig. 5. The base undoped glass (BTiBaYb0) exhibits an absorption band in the UV region due to the existence of inevitable iron impurities within the raw materials [42]. The addition of Yb 2 O 3 with different ratios leads to the formation of distinctive broad absorption band in the NIR region at 977 nm due to the electronic transition from the 2 F 7/2 ground state to the 2 F 5/2 higher excited state [43]. The intensity of this band increases as the ratio of Yb 2 O 3 increases.

Optical bandgap and Urbach energy
Moot and Davis theory is utilized to calculate the optical bandgap energy (E g ) from the optical absorption edge. The absorption coefficient (a) relevant to the absorption edge is determined using the relationship a = 2.303 A/d, where A is the optical absorption and d is the glass thickness. The relationship between a and E g is given by [44]: where hm is the incident photon energy, B is constant, and r is the electronic transition index which holds the value of 2 for indirect allowed transition. Figure 6 shows Tauc's plots, i.e., (aht) 1/2 versus ht for all glasses. The values of E g are determined by extrapolating the linear parts of the curves to intercept the ht-axis at zero absorption coefficient. The values of E g are recorded in Table 3 and found to be 3.198, 3.168, 3.140, and 3.115 eV for BTiBaYb0, BTiBaYb1, BTi-BaYb3, and BTiBaYb5 glasses, respectively. The observed decrease in the values of E g is ascribed to the excess of the non-bridging oxygens inside the glass network with increasing the ratio of Yb 2 O 3 [45,46]. Also, the absorption spectrum fitting (ASF) method is utilized to calculate the optical bandgap energy (E ASF g ). According to the ASF method, Eq. (6) can be written in terms of optical absorbance (A) and photon wavelength (k) as follow [47,48]: where D ¼ ½Bd hc ð Þ rÀ1 =2:303, d is the glass thickness, h is Planck's constant, c is the light speed, and k g is the photon wavelength corresponding to the E ASF g . Figure 7 shows the plots of (A/k) 1/2 versus k -1 for all glasses. The values of k À1 g are determined by extrapolating the linear parts of the curves to intercept the k -1 -axis at zero absorbance. The values of E ASF g are calculated from Eq. (8) and recorded in Table 3.
The values of E ASF g are found to be 3.194, 3.170, 3.137, and 3.113 eV for BTiBaYb0, BTiBaYb1, BTi-BaYb3, and BTiBaYb5 glasses, respectively. From Table 3, it can be seen the values of E g and E ASF g are matched and in agreement with each other which enhances the formation of non-bridging oxygens. The  Table 3. Urbach energy (DE) is a measure of the disorders inside the glassy matrix and related to the logarithm of the absorption coefficient through the relationship [49]:   The values of DE are calculated by obtaining the reciprocal of the slope of the linear parts of ln (a) versus hm plots and are recorded in Table 3. The plots of ln (a) vs. ht for all glasses are presented in Fig. 8. The values of DE are found to be 0.210, 0.279, 0.228, and 0.255 eV for for BTiBaYb0, BTiBaYb1, BTiBaYb3, and BTiBaYb5 glasses, respectively. The BTiBaYb1 glass has the highest value of DE, and thus the highest degree of disorders. The BTiBaYb0 glass has the lowest value of DE, and thus the lowest degree of disorders which means more homogeneity and stable structure with minimal defects [49,50].

Refractive index and dispersion parameters
The average values of the optical bandgaps ðE avg g Þ are employed to calculate the corresponding linear refractive indices (n DÀS ) at high frequencies using Dimitrov-Sakka relationship [45]: The values of n DÀS are recorded in Table 3 and observed to increase with increasing the ratio of Yb 3? ions because of the increase in polarization within the glass matrix at high frequencies as mentioned in the next section.
Wemple-DiDomenico (WDD) model is used to calculate the static refractive index (n o ) at low frequencies, i.e., the refractive index at zero frequency ðht ffi 0Þ. The mathematical equation that expresses WDD model is as follows [51]: where n is the refractive index, E o is the single oscillator energy, E d is the dispersion energy, and hm is the incident photon energy. The values of E o and E d are determined by graphing n 2 À 1 À Á À1 versus ht ð Þ 2 as shown in Fig. 9 Table 4 and found to decrease as the ratio of Yb 3? ions increases. The observed decrease in E d values indicates the increase in the degree of structural disorder of the glasses as the ratio of Yb 3? ions increase which is in line with the Urbach energy results [52]. The observed decrease in E o values is in line with the optical bandgap results. When hm tends to zero, Eq. (11) can be written in the next form:  Table 4. The values of E o and E d are employed to calculate the optical spectrum moments ðM À1 &M À3 Þ and static dielectric constant ðe 1 Þ from the next relations [51]: The values of M À1 ; M À3 ; ande 1 are recorded in Table 4. The values of M À1 ande 1 are found to decrease with increasing the concentration of Yb 3? ions while the values of M À3 increase.
The average oscillator strength (S o ) and average oscillator wavelength (k o ) are calculated using Sellmeier dispersion formula [53]:  Table 5.
The linear optical susceptibility v ð1Þ , third order non-linear optical susceptibility v ð3Þ , and non-linear refractive index n 2 are calculated from the relationships [53]: The values of v ð1Þ , v ð3Þ , and n 2 are recorded in Table 5 and found to decrease with increasing the concentration of Yb 3? ions due to the great decrease in the values of E d compared to that of E o . Figure 11 shows the variations of linear, static, and non-linear refractive indices as a function of Yb 2 O 3 content. The observed linear behavior of n DÀS in Fig. 11 is represented by an empirical equation as follows: where x Yb2O3 is the molar fraction of Yb 2 O 3 . The linear refractive index of the studied glasses strongly depends on the concentration of Yb 3? ions. Figure 12 shows the variations of third order non-linear optical susceptibility and static dielectric constant as a function of of Yb 2 O 3 content.

Metallization criterion and optical basicity
Lorentz-Lorentz equation correlates the molar refraction (R m ) of the studied glasses with the linear refractive index (n DÀS ) and molar volume (V m ) as follows [54]: The molar electronic polarizability (a m ) is proportional to the molar refraction (R m ) and given by: The values of R m and a m are calculated and listed in Table 6. As seen from Table 6, the R m and a m tend to increase with increasing the ratio of Yb 3? ions. The metallization criterion (M C ) is utilized to obtain information about the non-metallic behavior of solids based on the relation [45]: when the value of M C approaches one, the material is classified as an insulator while when the value of M C approaches zero, the material classified as a metal. The values of M C of the studied glasses are calculated and found to decrease from 0.400 to 0.394 with increasing the concentration of Yb 3? ions. The values of M C (0.394-0.400) lie in between insulators and metals, i.e., the studied glasses behave as semiconductors. The dependance of the molar electronic polarizability and metallization criterion on the Yb 2 O 3 content is presented in Fig. 13. The oxide ion polarizability a O 2À n DÀS ð Þ and optical basicity Kðn DÀS Þ of the studied glasses can be calculated based on the linear refractive index using the next relations [55]: K n DÀS ð Þ¼1:   Table 6.

Absorption-emission cross sections and gain spectra
The absorption r abs (k) and emission r emis (k) crosssections for 2 F 5/2 ? 2 F 7/2 transition of Yb 3? ions are calculated based on the the optical absorbance (A), Yb 3? ions concentration (N), and glass thickness (L) by the next relationships [56]: where Z l and Z u are the partitioning functions of the lower and upper states, respectively, E Zl is the energy difference between the ground state and upper state manifold, and T is the room temperature. The obtained values of the absorption and emission crosssections for 2 F 5/2 ? 2 F 7/2 transition are displayed in Fig. 15. The peaks of the emission cross-section (r emis ) have the values of 16.284 9 10 -21 , 20.062 9 10 -21 , and 16.315 9 10 -21 cm -2 for BTi-BaYb1, BTiBaYb3, and BTiBaYb5 glasses, respectively. The high values of r emis make the present glasses strong candidate for laser and amplifier applications. Moreover, the wide emission is helpful for the creation of tunable and ultra-short pulse lasers [57]. The optical gain coefficient G(k) can be calculated based on the values of the absorption and emission cross-sections using the next relation [56]: where P is the rate of population inversion of 2 F 5/ 2 ? 2 F 7/2 transition and taken as: 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0. The obtained values of G(k) are displayed in Fig. 16, and it is noted that the gain coefficient and gain band increase as the value of P increases, and the gain will be completely flat when the value of P is greater than 0.6. Furthermore, the gain spectra exhibit positive values in the wavelength range 971-1010 nm when the values of P are greater than 0.3.

Data availability
The datasets generated during the current study are available from the corresponding author on reasonable request.

Research data policy
The datasets are presented in the main manuscript.

Declarations
Conflict of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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