Effect of Nd3 + concentration on the physical and absorption properties of sodium-lead-borate glasses

Abstract

The effect of increasing the rare earth ion concentration on the physical and spectroscopic properties of Nd3 + doped sodium-lead-borate glasses have been studied for the compositions (10-x) Na2O-30PbO-60B2O3-xNd2O3, where x = 1.00, 1.25, 1.50, 1.75 and 2.00 mol %. Optical band gaps, cut-off wavelengths and various spectroscopic parameters (E¹, E², E³, F2, F4, F6 and xi4f) have been determined from the room temperature absorption spectra. Judd-Ofelt theory has been employed to determine the intensity parameters omega2, omega4 and omega6 which in turn are used to evaluate radiative transition probability (A), branching ratio (beta) and radiative lifetime (tauR) for the fluorescent level 4F3 / 2. The omega2 parameter and hence the non-symmetric component of electric field acting on Nd3 + ion is found to be highest for glass with 1.75 mol% of Nd2O3. Because of the poor resolution of hypersensitive transition, the covalency of the Nd-O bond has been characterized by the relative intensity of 4I9 / 2 ->4F7 / 2, 4S3 / 2. The highest covalency has been predicted for glass with 2 mol% Nd2O3. The radiative properties are found to improve with an increase in concentration of Nd2O3 for the present study.

Optical materials; Glasses; Optical properties; Judd-Ofelt theory

REGULAR ARTICLES

Effect of Nd^{3 +} concentration on the physical and absorption properties of sodium-lead-borate glasses

S. Mohan^I; K. S. Thind^II; G. Sharma^II

^ILecturer in Physics, BBK DAV College for Women, Amritsar, India

^IIDepartment of Physics, Guru Nanak Dev University, Amritsar, India

ABSTRACT

The effect of increasing the rare earth ion concentration on the physical and spectroscopic properties of Nd^{3 +} doped sodium-lead-borate glasses have been studied for the compositions (10-x) Na₂O-30PbO-60B₂O₃-xNd₂O₃, where x = 1.00, 1.25, 1.50, 1.75 and 2.00 mol %. Optical band gaps, cut-off wavelengths and various spectroscopic parameters (E¹, E², E³, F₂, F₄, F₆ and x_4f) have been determined from the room temperature absorption spectra. Judd-Ofelt theory has been employed to determine the intensity parameters W₂, W₄ and W₆ which in turn are used to evaluate radiative transition probability (A), branching ratio (b) and radiative lifetime (t_R) for the fluorescent level ⁴F_{3 / 2}. The W₂ parameter and hence the non-symmetric component of electric field acting on Nd^{3 +} ion is found to be highest for glass with 1.75 mol% of Nd₂O₃. Because of the poor resolution of hypersensitive transition, the covalency of the Nd-O bond has been characterized by the relative intensity of ⁴I_{9 / 2}®⁴F_{7 / 2}, ⁴S_{3 / 2}. The highest covalency has been predicted for glass with 2 mol% Nd₂O₃. The radiative properties are found to improve with an increase in concentration of Nd₂O₃ for the present study.

Keywords: Optical materials; Glasses; Optical properties; Judd-Ofelt theory

I. INTRODUCTION

Physical and spectroscopic properties of silicate, borate and phosphate glasses doped with various rare earth (RE^{3 +} ) ions have been extensively investigated in the past, and many technological and commercial applications have been realized [1-4]. Neodymium has been most widely studied as doping agent and has come out to be most applicable for laser action, since neodymium lasers can operate with high efficiency, even at room temperature.

Since, a maximum laser output requires an optimum concentration of Nd^{3 +} it becomes important to study the spectroscopic properties as a function of concentration of rare earth ions. Both higher and lower concentrations lead to lower laser efficiencies. The lower efficiencies at higher concentrations are due to nonradiative self-quenching process.

Borate glass is a particularly suitable optical material because of its high transparency, low melting point, high thermal stability, different coordination numbers, and good solubility of rare-earth ions [5-6]. Further, heavy metal oxide glasses have reduced phonon energy. Thus, the incorporation of heavy metal oxides such as PbO or Bi₂O₃ into the borate glass matrix leads to an increase in its quantum efficiency of luminescence from the excited states of rare-earth ions. Further, RE-doped alkali borate glasses are interesting for studying effects of alkali ions on the glass forming network, particularly around the rare-earth ions. It is well established that the addition of an alkali oxide has a strong influence on the boron coordination and the structural groups, depending on the type and concentration of the alkali oxide [7].

Saisudha et al. [8] have investigated the effect of the lead borate matrix on the optical properties of the Nd^{3 +} ions. Large stimulated emission cross sections have been reported [9] stressing the suitability of different Nd^{3 +} doped lead borate and bismuth borate glasses for laser action. Studies of NMR and fluorescence of Nd^{3 +} doped binary alkali borate glasses have also been published [10, 11]. However, to the best of our knowledge, rare earth doped alkali lead borate glasses have not been studied in any great detail. Motivated by these considerations we have prepared sodium-lead borate glasses doped with Nd^{3 +} , and studied the effects of the Nd^{3 +} concentration on physical and spectroscopic properties.

II. EXPERIMENTAL

A series of Nd^{3 +} doped sodium-lead-borate glasses of the type (10-x) Na₂O-30PbO-60B₂O₃-xNd₂O₃, where x = 0.5, 1.0, 1.5 and 2 mol % were prepared by the melt quenching technique. Appropriate amounts of the raw materials, Na₂CO₃, PbO, B₂O₃ and Nd₂O₃ of 99.9 % purity, were thoroughly mixed and ground in an agate mortar in 20 g batches. The prepared batches were heated in a silica crucible at 450-500 ºC for 2 hours to ensure decarbonisation of the sodium carbonate. The temperature was then raised and maintained at 1000 ºC for about one hour. The mixture was occasionally stirred to ensure homogeneous mixing of all constituents and to obtain bubble-free samples. Finally, the mixture was poured into a preheated brass mould and annealed near the glass transition temperature in order to eliminate internal mechanical stress. Samples of good optical quality were selected and sliced, grinded and polished in order to study their spectroscopic properties. The chemical compositions of the samples are summarized in Table 1.

By applying Archimedes principle, the densities of the prepared samples were measured with benzene as the immersion liquid. The density was calculated using the formula:

where W_a is the weight in air, W_b is the weight in benzene, and r_b is the density of benzene. All weight measurements were made using a Dhona single pan balance.

The refractive index was measured at a temperature of 30 ºC, with an Abbe refractometer using mono-bromonaphthalene as adhesive coating. Optical absorption spectra were recorded at room temperature using a spectrophotometer (Shimadzu), working in the UV-visible range.

III. RESULTS AND DISCUSSION

A. Physical properties

The physical properties provide an insight into the atomic arrangements in a glass network. The concentration of the rare-earth ions is an important parameter, which affects the laser gain of the host material. The number density N of the laser-active ions i.e. the number of ions per cubic centimeter can be evaluated using the relation [12]

where r is the density of the glass, N_A is the Avagadro's number, x is the mole fraction of rare earth oxide and is the average molecular weight of the glass.

Some other physical properties which include molar volume (V_M), polaron radius (r_p), internuclear distance (r_i), field Strength (F), dielectric constant (e) and molar refraction (R_M) were determined from the density, average molecular weight, refractive index and concentration of the rare-earth ions, using standard formulae [12]. All the above mentioned physical properties are listed in Table 2.

The density is found to increase with the increase in concentration of Nd^{3 +} ions upto 1.5 mol% of Nd₂O₃. It then decreases for 1.75 mol% and then again shows an increase for higher concentration of Nd₂O₃. A possible reason of decrease in density could be the formation of non-bridging oxygen (NBO's) atoms around 1.75 mol% concentration of neodymium oxide. The clustering of rare earth ions can be one of the factors which contribute to the variation in density at higher concentrations. The behavior of molar volume mainly depends upon the density of glasses and as expected in the present case, it follows a trend opposite to density. The variation of density and molar volume with concentration of Nd₂O₃ is presented in Fig. 1.

The polaron radius is found to decrease with the increase in neodymium oxide content. This result agrees with the literature [13]. The internuclear distance for rare earth ions shows an expected decrease on increasing Nd₂O₃ content. The molar refraction, which depends on the refractive index, density and average molecular weight of glass, shows a minimum around 1.5 mol% of Nd₂O₃.

B. Energy band gap and cut-off wavelength

Optical absorption spectrum of Nd^{3 +} doped sodium-lead-borate glass in the wavelength range 400-950 nm is shown in Fig. 2. This sample contains 1 mol% Nd₂O₃. Spectra of other samples are similar in shape with small differences in absorbance.

Optical band gaps for direct and indirect transitions have been obtained following Mott and Davis [14], using the equation

where B is a constant, a is the absorption coefficient, wis the angular frequency and values of n are 1/ 2 and 2 for direct and indirect transitions respectively.

To calculate the width of the energy tail, DE, of the density of states, the model proposed by Urbach [15] and Tauc [16] is followed. The following relation has been used to determine the width of the energy tail:

where C is a constant.

Values of direct and indirect mobility gap, width of mobility tail and the cut-off wavelength for the present glass system are presented in Table 3. The indirect and direct mobility gap both show a maximum for 2 mol% and a minimum for 1mol% concentration of Nd₂O₃. The direct mobility gap shows an increase upto 1.5 mol%, decreases for 1.75 mol% and then again shows an increase. The indirect mobility gap does not follow a uniform variation. The variations of cut-off wavelength agree with the trend followed by direct mobility gap. The cut-off wavelength for various concentrations of Nd^{3 +} in sodium-lead-borate glasses is presented in Fig. 3.

C. Absorption spectroscopic parameters

A comparison of the optical absorption spectra of the present glass series with the standard wavelength chart of Nd^{3 +} [17], result in the identification of following spectroscopic transitions:

Using the observed band energies as E_J and the zero point energies (E_0J) and partial derivates [18], the correction factors DE^k and Dx_4f have been evaluated by the least -squares fit method. The calculated correction factors are then added to the zero-order parameters [18] to obtain the Racah parameters (E^k) and the spin-orbit interaction parameter (x_4f). The Slater integrals (F^k) have been evaluated from Racah parameters using relevant expressions [12]. The rms deviations between the energies (E_th) calculated using these parameters and the experimental energies (E_exp) are within experimental limits. These energy values are presented in Table 4. The spectroscopic parameters along with hydrogenic ratios E¹/E³ and E²/E³ determined for different concentrations of Nd^{3 +} are presented in Table 5. The, hydrogenic ratios which indicate the radial properties of Nd^{3 +} , are approximately the same for all compositions, indicating that the radial properties of Nd^{3 +} remain unperturbed with the change in rare earth ion concentration.

D. Spectral intensities and Judd-Ofelt parameters

The intensity of an absorption band can be expressed in terms of the 'oscillator strength'. The experimental oscillator strength (f_meas) of the absorption transitions has been determined using [19]

where e(n) = OD / ct is the molar extinction coefficient at mean energy n (cm ^{- 1}), with OD being the optical density, c being the molar concentration of the rare-earth ions, and t is the optical length of the glass. The intensities for all absorption bands observed in the present case have been evaluated using the area method.

According to Judd-Ofelt theory [20, 21] the oscillator strength of a transition between the initial ground state J manifold | (S;L)J ñ and a final J' manifold | (S';L')J' ñ can be calculated by the relation:

where (2J+1) is the degeneracy of the ground state of the Nd^{3 +} ions, n is the refractive index of the medium, m is the mass of the electron, and n is the mean energy of the transition, S_ed is the electric dipole line strength and S_md is the magnetic dipole line strength. The latter can be neglected in comparison to S_ed, since in the present case for Nd^{3 +} ion, the bands produced by the magnetic dipole mechanism have very low spectral intensity compared to that of the electric dipole bands. S_ed is given by

where

represents the reduced matrix elements of a unit tensor operator evaluated in the intermediate coupling approximation. Since these reduced matrix elements are host invariant, we have used the values reported by Carnall et al. [22]. The values of experimental and theoretical oscillator strengths along with their rms deviations are presented in Table 6. The smaller rms deviations indicate good agreement between the experimental and calculated oscillator strengths which shows the validity of Judd-Ofelt theory.

Substituting the oscillator strengths calculated from the absorption spectra for f_cal, and using the values of reduced matrix elements and other parameters, the Judd-Ofelt intensity parameters W_l(l=2,4,6) have been determined by least squares method. These parameters along with the intensity parameters of some related borate glasses [29, 8] are presented in Table 7. The table also includes the spectroscopic quality factor (W₄/W₆), which determines the lasing efficiency of the host.

The position, intensity and shape of certain electric dipole transitions of rare earth ions are found to be very sensitive to the environment of the rare earth ion. Such transitions are termed as hypersensitive transitions by Jorgensen and Judd [23]. These transitions are found to obey the selection rule DJ < 2, DL < 2 and DS=0 [23]. These transitions are associated with a very large value of the reduced matrix element|| U² ||²; hence hypersensitivity is much related with the W₂ parameter.

For Nd^{3 +} ion, ⁴I_{9 / 2}® ⁴G_{5 / 2}+²G_{7 / 2} is the hypersensitive transition since it obeys the required selection rule. As observed from Table, the intensity of hypersensitive transition shows a maximum for 1.75 mol% and a minimum for glass containing 1 mol % of Nd₂O₃. This indicates that the non-symmetric component of electric field acting on Nd^{3 +} ion is low for glass containing 1 mol% and high for 1.75 mol% of Nd₂O₃. The possible reason could be the formation of NBO's around 1.75 mol% concentration of Nd₂O₃ as discussed in explaining the density of the present glass system. The creation of non-bridging oxygen from bridging oxygen increases the asymmetry of the bond to the neighboring network cation. A decrease in intensity of hypersensitive transition for 2 mol% Nd₂O₃ glass can be because of clustering of rare earth ions for higher concentrations. The values of W₂ are found to be proportional to the intensities of the hypersensitive transition, in accordance with the theory [24].

Krupke [25] pointed out that the transition intensities of ⁴I_{9 / 2}® ⁴G_{5 / 2}+²G_{7 / 2} and ⁴I_{9 / 2} ®⁴F_{7 / 2}, ⁴S_{3 / 2} are determined mainly by W₂ and W₆ respectively. The Stark splitting due to the crystal field splits these transitions in the absorption spectra into two peaks. The peak intensity ratio of the longer (I_L) and shorter (I_S) wavelength components are designated as I_L/I_S.

In the present case the Stark splitting of the hypersensitive transition ⁴I_{9 / 2}® ⁴G_{5 / 2}+²G_{7 / 2} is poorly resolved. Thus, the W₂ parameter is dominated by the crystal-field parameters rather than the covalency parameters. Consequently, no conclusion can be drawn for the covalency of the Nd-O bond using this parameter.

Hence a variation of the spectral profile of the transition ⁴I_{9 / 2}®⁴F_{7 / 2}, ⁴S_{3 / 2} is investigated. This variation is presented in Fig. 4. A higher value of intensity ratio I_L/I_S and intensity parameter W₆ indicates a higher covalency of the Nd-O bond for glass containing 2 mol% of Nd₂O₃. A lowest covalency is observed in glass with 1 mol% Nd₂O₃.

E. Radiative properties

The W_l values obtained from the absorption measurements have been used to calculate the radiative transition probability, branching ratios and radiative lifetime of the excited state ⁴F_{3 / 2}.

The radiative transition probability A(aJ,bJ') for the emission from initial state aJto a final state bJ' for an electric dipole emission has been determined using the relation [26]

where l_o is the peak wavelength of the emission bands.

The total radiative emission probability A_T (aJ)of an excited state is given by the sum of the A(aJ,bJ¢) terms calculated over all the terminal states b.

The fluorescence branching ratio b_R has been determined using:

The radiative lifetime t_R of the emission state is given as

Radiative transition probability (A), total transition probability (A_T), radiative lifetime (t_R) and branching ratio (b_R) for the excited ⁴F_{3 / 2} are summarized in Table 8. A comparison of (b_R) with vitreous borate [30] and lead borate [8] glasses has been made in the same table. The W₂ parameter becomes independent in characterizing the fluorescence properties of ⁴F_{3 / 2}® ⁴I_J transitions because the values of tensor operator || U² ||² are zero for all these transitions. Hence, the radiative properties depend on W₄ and W₆ parameters because of the triangle rule | J - J' | < l < | J + J' | [27]. The ⁴F_{3 / 2}® ⁴I_{11 / 2} transition is the potential lasing transition (l=1.06µm) for Nd^{3 +} ion. The radiative transition probability is found to increase with increase in content of Nd₂O₃. It shows a maximum for NPBN5 i.e. the glass containing 2 mol% concentration of Nd₂O₃. The radiative lifetime is inversely proportional to the linear combination of W₄ and W₆ [28]. Thus, the lowering trend noticed in t_R on increasing rare earth concentration has been attributed to the increasing values of W ₄ and W₆ parameters.

IV. CONCLUSIONS

We have determined physical and spectroscopic properties for sodium-lead-borate glasses doped with varying amounts of Nd^{3 +} . Density measurements predict the formation of non-bridging oxygen atoms around 1.75 mol% concentration of Nd₂O₃. The indirect and direct mobility gap both show a maximum for 2 mol% and a minimum for 1mol% concentration of Nd₂O₃. Absorption spectra have been analyzed using the Judd-Ofelt theory. The W₂ parameter and hence the non-symmetric component of electric field acting on Nd^{3 +} ion is found to be highest for 1.75 mol% of Nd₂O₃. The position and shape of the hypersensitive transition does not change appreciably. Therefore, the covalency of the Nd-O bond has been determined from the spectral profile of the ⁴I_{9 / 2}®⁴F_{7 / 2}, ⁴S_{3 / 2} transition. A higher value of intensity ratio I_L/I_S and intensity parameter W₆ indicates highest covalency of the Nd-O bond for glass containing 2 mol% of Nd₂O₃. The spectroscopic quality factor X = W₄/ W₆ is found to be 2-3 times larger than that of the standard laser host for Nd^{3 +} , namely YAG with X=0.3. A maximum of radiative transition probability and a minimum of radiative lifetime are observed for glass containing 2 mol% of Nd₂O₃. The variation of the spectroscopic properties suggests that it is possible to enhance the lasing properties of Nd^{3 +} in sodium-lead-borate glasses by varying the concentration of the rare-earth ions.

Received on 20 October, 2007

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Publication Dates

• Publication in this collection
  28 Jan 2008
• Date of issue
  Dec 2007

History

• Received
  20 Oct 2007