SQU Journal for Science, 2015, 20(1), 70-76 © 2015 Sultan Qaboos University 70 Crystal Field Parameters and Optical Parameters of Nd 3+ in Sodium Bismuth Silicate Glass Vinoy Thomas 1 , Ramakrishna P.G.P.S. Sofin 2 *, Mathew Allen 3 and Hysen Thomas 1 1 Department of Physics, Christian College Chengannur-689122, University of Kerala, India. 2 Department of Physics, College of Science, Sultan Qaboos University, P.O. Box 36, PC 123, Al Khod, Sultanate of Oman. 3 UDSMM, Université du Littoral Côte d'Opale, 59140 Dunkerque, France. *Email: sofins@squ.edu.om. ABSTRACT: Neodymium doped sodium bismuth silicate glasses were prepared by the melt quench technique. Optical absorption spectra of the Nd 3+ ion in the present glassy systems were recorded in the UV-Vis-NIR region. Taylor series expansion method was adopted for theoretical evaluation of various crystal field parameters such as the Slater-Condon (F2,F4,F6), spin orbit  f4 and Racah parameters (E1,E2,E3). Oscillator strength and electric dipole line strength of the observed transitions were evaluated with the help of Judd-Ofelt (JO) theory. Radiative transition probability (A), total radiative transition probability (At), radiative life time (rad), branching ratios () and integrated absorption (a) cross section for stimulated emission between the meta stable state 4 F3/2 and 4 IJ ( J= 15/2,13/2,11/2 and 9/2) levels were calculated using JO parameters. Optical basicity of the glass was found to increase with the addition of bismuth. Keywords: Silicate glasses; Optical absorption spectroscopy; Racah parameters. انصوديوو انزجاجى انمشوبة بايونات اننوديوو موثعوامم مجال انبهور و انعوامم انضوئية نسيهيكات بز تومس يسنانن و ه اثيوم ،سوفيناو كاريشنا بيالي جوباال ر ،تومس ينويف Nd ذحضيز سيهكاخ صىديىو انثشيىز انشجاجيح انًشىتح تايىَاخ انُىديىو ذى :مهخص 3+ . كًا ذى قياص يطياف خًاديإلاتىاسطح ذقُيح انشوتاٌ Ndانضىئً اليىَاخ يرصاص اإل 3+ نحساب عىايم انًجال يرذاديح اإل( Taylorكًا ذى اسرخذ يد سهسهح ذيهز ) UV-Vis-NIR فً هذا انُظاو فً حيش spin orbitو Slater-Condon(F2,F4,F6)َظزيا يثم: انثهىري انًخرهفح كذنك ذى حساب شذج Racah parameters (E1,E2,E3)و حرًانيح إ وشعاعً إلاَرقال حرًانيح اإلإنحساب كم يٍ Judd-Ofelt (JO)تُظزيح سرعاَح تاإلانًالحظح َرقاالخ نإلانرذتذب وشذج خط ثُائً انقطة انكهزتً تيٍ ييرا انحانح انًسرقزج َثعاز اإلانًركايهح انًىحاج يٍ يرصاصيح اإلو انُسثح انفزعيح ويساحح انًقطع شعاعً اإلانًركايهح وعًز انحياج شعاعيح َرقانيح اإلاإل نهحانح. نىحظ سيادج انقاعذج انضىئيح نهشجاجخزي األو انًسرىياخ .انضىئً و يعايالخ راخاإليرصاص يطيافانشجاج ، سيهيكاخ : كهمات مفتاحية 1. Introduction ver since the discovery of the solid state laser in 1961, a great deal of effort has been made to study the optical properties of rare earths and rare earth doped systems due to their unique uses in optical amplifiers, fiber lasers, telecommunications and display devices [1-3]. Attractive optical absorption and emission in the UV-vis-NIR region of the rare earths make them ideal candidates for optical applications in this region. A large variety of laser glasses doped with the Nd 3+ ion have been investigated with the purpose of generating efficient emission around 1050 nm [4] . Heavy-metal silicate glasses possess lower phonon energies compared to other oxide glasses and display strong visible and near infra-red fluorescence of rare earth ions within the system [5]. Though there have been a large number of reports on various rare earth doped glassy systems, the synthesis and optical analysis of neodymium doped bismuth silicate glasses has rarely been studied. At comparatively low Bi2O3 content (≤10 mol%), Bi2O3 incorporates into the interstices of glass as a network changer which does not cause a large-scale structural rearrangement of the local glassy network. At higher concentrations of Bi2O3 (>10 mol%), Bi2O3 enters into glasses as a network former and a large-scale structural rearrangement of the local glass network takes place, which leads to significant variation of its optical properties [6-7]. In this context, an optical analysis of neodymium doped bismuth (10 mol%) sodium silicate glass is deserving of special attention and importance. The purpose of the present study is to derive various spectroscopic parameters such as Slater Condon, Racah, spin-orbit and Judd Ofelt parameters and to evaluate the   f4  E CRYSTAL FIELD PARAMETERS AND OPTICAL PARAMETERS 71 radiative parameters, such as radiative transition probability, radiative life time and absorption cross section for stimulated emission for the possible transitions. 2. Experimental A neodymium (1.5 mol %) doped sodium bismuth silicate glassy system with composition (in mol%) 15 Na2O- 10Bi2O3-75 SiO2 was prepared by the well-known melt quenching method. Appropriate amounts of Bi2O3 (99.99% purity, Sigma Aldrich), Na2CO3 and SiO2 (99.99% purity, Sigma Aldrich) were mixed and ground continuously using an agate mortar. The powder mixture was placed in a porcelain crucible and melted in a box furnace at a temperature of 1200 0 C for 3 hours. The melt mixture was poured into a stainless steel mold heated to 100 0 C. Then the sample was annealed at a temperature of 200 0 C for 1hour. The density of the sample was measured by Archimedes’ principle using xylene as the immersion liquid. The U-V Visible-NIR absorption spectrum of the sample was measured on a UV-Visible-NIR spectrophotometer Varian Cary 5000 in the wavelength span of 450 nm to 950 nm. 3. Results and discussion Figure 1 shows the optical absorption spectra of 1.5 mol % Nd2O3 doped sodium bismuth silicate glass. The transitions of the Nd 3+ ion occurs due to the transition from the ground state 4 I9/2 to various excited states [8-9]. The location intensity and breadth of the absorption bands are determined by the interaction of Nd 3+ ions with the local crystalline field. Each absorption band usually consists of a multiplicity of stark levels; unlike the regular local crystal field experienced by Nd 3+ in crystalline hosts, the crystal field’s sites in glass are randomly distributed. This distribution results in the inhomogeneous broadening of the absorption spectra of the Nd 3+ ion. Figure 1. Absorption spectra of Nd 3+ in sodium bismuth silicate glass. 3.1 Bonding properties and nephleuxetic ratio Indirect but convincing information regarding the RE-ligand bond strength can be obtained from the nephelauxatic ratio(β). The nephelauxatic ratio is given by   ⁄ (1) where νm and νa are the wavenumbers (cm -1 ) of the particular transitions in the host matrix and aqua, respectively. The larger value of the nephelauxatic ratio indicates a reduction in the strength of the covalent bond between the RE ion and ligand. The nephelauxatic parameter is directly related to the bonding parameter (δ) as ̅ ̅ ⁄ (2) and ̅ is the average value of the β for observed transitions. The positive or negative sign of δ indicates covalent or ionic bonding of the rare earth-ligand bond. The small positive value of δ (0.0166) in the sodium bismuth silicate glass indicates the decrease in strength of covalency of the RE-O bond in the prepared sodium bismuth silicate glass compared to other silicate glass systems [10]. 3.2 Crystal field parameters (Slater-Condon, Racah and spin-orbit parameters) The Slater-Condon parameters (F) generally represent the radial integral part of the electrostatic interaction matrix elements of a trivalent rare earth ion and can be represented as [11] RAMAKRISHNA PILLAI GOPALA PILLAI SUMESH SOFIN ET AL 72 jijik k k k drdrrRrR r r D e F )()( 22 1 2      (3) where k = 2, 4, and 6: r< and r> represent the distances from the nucleus to the nearer and farther electrons respectively. R(ri) and R(rj) represent the normalized wave functions of the i th and j th electron, Dk are constants. Similarly the spin orbit interaction parameter 4f represents the radial integral part of the spin orbit interaction matrix element and is given by    0 4 222 4 )()( drrrRr ff   (4) where r rV rcm f    )( 2 224   and V(r) is a potential function for the interaction. For a free ion these interaction parameters are constants. But, when the ion is under the influence of another interacting field (ligand field or crystal field), these parameters change due to the overlapping of the 4f wave functions of the rare earth ion with that of the surrounding ligand ion. As a result of this overlapping effect, the distance between the nucleus and the electron of the rare earth ion changes slightly, which in turn affects the energy levels and spectroscopic parameters. The observed energy levels of the neodymium ion can be calculated using the Taylor series method. In this method the energy of any level in the rare earth spectra is taken as a function of various types of interactions, such as electrostatic interaction spin-orbit interaction etc. [12]. According to this method, the energy of a rare earth ion can be represented as   f4,ki FfE  (5) where Fk is the Slater radial integral and  f4 the spin-orbit interaction parameter. Relation (5) can be expanded in a Taylor series as [13] ... E F F E EE f4 f4 j 6,4,2i i i j ojj          (6) The values of the partial derivatives were taken from the literature [8]. Knowing the values of the partial derivatives and zero order energy values, 642 ,, FFF  and   f4  can be determined. Once these  values are determined the Slater Condon parameters can be determined as 0 2 2 2 F F ΔF  0 4 4 F F F  4 6 0 66 FFF  fff 4 0 44   (7) where 0 0 0 2 4 6 4 , , and o f F F F  represent the zero order parameters. The Racah parameters ( E i ) are related to Slater-Condon parameters as 1 2 4 6 1 9 70 231 2002E F F F        2 2 4 6 1 9 3 7E F F F     3 2 4 6 1 3 5 6 91E F F F   (8) The calculated values of all the spectroscopic parameters are given in Table 1. All the spectroscopic parameters, viz. the Slater-Condon (F2,F4,F6), spin-orbit (4f) and Racah parameters (E 1 ,E 2 ,E 3 ), and the hydrogenic ratios (E 1 /E 3 , E 2 /E 3 , F 4 /F 2 , F 6 /F 2 ) are found to be constants irrespective of the matrix composition. Therefore these parameters can be considered to be fundamental constants for trivalent neodymium in a given matrix. CRYSTAL FIELD PARAMETERS AND OPTICAL PARAMETERS 73 Table 1. Calculated values of Slater-Condon( F), Racah (E  ) and spin-orbit (4f) parameters in sodium bismuth silicate glass and similar glasses. Energy parameters Sodium Bismuth Silicate [present glass] Sodium Borate [9] Sodium Phosphate [8] F2( cm -1 ) 284.36 330.05 314 F4( cm -1 ) 46.54 50.8 47 F6( cm -1 ) 2.642 5.14 4.8 4f( cm -1 ) 865.61 870.47 926 E 1 ( cm -1 ) 3993.3 5001.5 4792 E 2 ( cm -1 ) 18.13 23.89 22.6 E 3 ( cm -1 ) 486.87 494.81 471 3.3 Judd Ofelt parameters The electronic transitions of the trivalent lanthanides can be regarded as a sum of the electric dipole (fed) and magnetic dipole (fmd) contributions, i.e. F = fed+fmd (9) For rare earth ions, line strengths of magnetic dipole (md) transitions are much less than the line strengths of electric dipole (ed) transitions (S md JJ’<