EVALUATION OF BULK MODULUS AND RING DIAMETER OF SOME TELLURITE GLASS SYSTEMS

Transcription

1 Chalcogende Letters Vol. 12, No. 2, February 2015, p EVALUATION OF BULK MODULUS AND RING DIAMETER OF SOME TELLURITE GLASS SYSTEMS R. EL-MALLAWANY a*, M.S. GAAFAR b, N. VEERAIAH c a Physcs Dept., Faculty of Scence, Menofa Unv., EGYPT. b Physcs Dept., College of Scence, Al-Majmaah Unv., Al-Zulf, Saud Araba. b Permanent address: Ultrasonc Department, Natonal Insttute for Standards, Gza, Egypt c Department of Physcs, Acharya Nagarjuna Unversty, Nagarjuna Nagar , A.P. Inda. Bulk modulus (K bc ) and Posson s rato (Ϭ cal ) for 25 glass compostons of the followng fve tellurte glass seres TeO 2 WO 3 PbO, TeO 2 V 2 O 5 B 2 O 3, TeO 2 WO 3 K 2 O, TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 have been evaluated usng bond compresson model. Structural parameters lke: number of bonds per unt volume, average stretchng force constant, rato of calculated bulk modulus to expermental bulk modulus (K bc /K e ), atomc rng sze of the glass network rng dameter and average crosslnk densty have been evaluated. (Receved December 16, 2014; Accepted February 10, 2015) Keywords: Tellurte glasses; acoustc propertes; bulk modulus and Posson s rato; Atomc rng sze. 1. Introducton In materals engneerng desgn predcton and understandng over the physcal propertes are essental to develop new class of functonalzed materals. The modfcaton of propertes nduced by the addton of transton metal oxdes (TMO) or rare earth oxdes (REO) nto host glass matrx lke tellurte glasses have attracted a lot of attenton due to ther physcal propertes and applcatons [1-14]. In the present work, theoretcal bulk modul K bc wll be calculated and the rato of the calculated bulk modulus K bc to the collected expermental bulk modulus K e wll be evaluated. Also, rng dameter l, average stretchng force constant F, number of bonds per unt volume, average crosslnk densty nc and Posson s rato ϭ cal for every glass composton were evaluated and dscussed. Such studes are helpful for understandng the medum range structure of tellurte glasses. 2. Theoretcal Background The structure of oxde glasses can be descrbed n terms of bond compresson model [15,16]. The model was based on two assumptons: () The elastc modul depends only on the connectvty of the network (number of bonds per caton) and on the average force constant. Accordng to ths model calculated bulk modulus K bc and the frst-order stretchng-force constant f, can be estmated usng the relatons; 2 K n r f /9 (GPa) (1) bc * Correspondng author: raoufelmallawany@yahoo.com b

2 68 In Eq. (1), the number of bonds per unt volume n b of glass s gven as, n b n f N n N f f A / M )2( where N f s the number of formula unts per unt volume, x s the mole fracton of the th oxde, n f s the number of network bonds per glass formula unt, r s the bond length, ρ s the densty of the glass, N A s the Avogadro s number and M s average glass molecular weght. The stretchng force constant f of every bond present n the glass network s calculated [16] usng f (3) r Accordngly, the average bond stretchng-force constant F for a three-dmensonal polycomponent oxde glasses can be estmated [16] usng F x n f / x n (4) () The rato between the calculated bulk modul and the expermental one (K bc /K exp ) s assumed to be drectly proportonal to the atomc rng sze l. The atomc rng sze s defned as the rng permeter (number of bonds tmes bond length dvded by ) and s gven by the relaton [15]; 0.26 ( ) F nm (5) Kexp where K e s the expermental bulk modulus and F b s the bond bendng force constant of the glass, to the frst approxmaton, may be taken as proportonal to the average bond stretchng force constant F. The average crosslnk densty per unt formula of glass s gven as, 1 n c x ( nc ) ( Nc) (6) Where n c s the number of crosslnk densty per caton whch equals the number of brdgng bonds per caton mnus 2 [8], N c s the number of catons per glass formula unt and s the total number of catons per glass formula unt. The calculated Posson s rato wll be calculated accordng to the next equaton [16] th 0.28 n c (7) 3. Dscussons Values of number of bonds per unt volume of glass n b, average bond stretchng-force constant F, calculated bulk modulus Kbc and rato (K bc /K e ) for each glass composton are also presented n Table 1 for 25 glass compostons of the followng fve tellurte glass seres TeO 2 WO 3 PbO, TeO 2 V 2 O 5 B 2 O 3, TeO 2 WO 3 K 2 O, TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 by usng Equ.1 to Equ. 5. The dscussons wll as follows

3 69 Table 1: Number of bonds per unt volume (n b ), calculated bulk modulus K bc, expermental bulk modulus Ke, rato (K bc /K e ), Average atomc rng dameter (l), Average stretchng force constant (F) TeO 2 WO 3 PbO, TeO 2 V 2 O 5 B 2 O 3, TeO 2 WO 3 K 2 O, TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 glasses. No Glass compostons TeO 2 WO 3 V 2 O Nb 2 O ZnO PbO K 2 O B 2 O Er 2 O n b x10 28 (m -3 ) K bc GPa K e GPa Ref Ref Ref Ref Ref Ref (K bc / K e ) l (nm) F (N/m) n c Ϭ cal

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5 71 a- Values of the number of bonds per unt volume n b (calculated by equaton 2) ncreased from to 9.133, from to m -3 from to m -3, from to m -3 and from to m -3 for TeO 2 WO 3 PbO, TeO 2 V 2 O 5 B 2 O 3, TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 glasses as the content of the last component ncreases respectvely. Whle t decreases from to m -3 for TeO 2 WO 3 K 2 O glasses. Recently, t has been found that n b = 8.680, 9.550, 9.499, and for 80(TeO 2 )-5(TO 2 )- (15 - x)(wo 3 )-(x)a n O m, (x)a n O m = 0.01Nb 2 O 5, 5Nb 2 O 5, 3Nd 2 O 3, 5Nd 2 O 3 and 5Er 2 O 3 mol%[11], b- The stretchng force constant F (calculated by equaton 4) has been decreased from 205 to 194, from 218 to 202 and from to 189 N/m, from 207 to N/m and from to 205 N/m for TeO 2 WO 3 PbO, TeO 2 V 2 O 5 B 2 O 3, TeO 2 WO 3 K 2 O, TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 glasses respectvely, c- The calculated bulk modulus K bc (calculated by equaton 1) ncreased from to GPa, from to GPa, from to GPa and from to GPa for TeO 2 WO 3 PbO, TeO 2 V 2 O 5 B 2 O 3, TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 glasses respectvely and decreased from to GPa for TeO 2 WO 3 K 2 O glasses. Values of K bc for TeO 2 glass was GPa [20] and the behavor of the calculated bulk modulus has the same trend as that of the expermental bulk modulus for each tellurte glass seres, d- The atomc rng sze l (calculated by equaton 5) has been decreased from to nm, from to nm and from to nm for TeO 2 WO 3 PbO, TeO 2 V 2 O 5 B 2 O 3 and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 glasses respectvely. But t ncreased from to and from to nm for TeO 2 WO 3 K 2 O and TeO 2 Nb 2 O 5 ZnO glasses, e- Varaton of rato of (K bc /K e ) wth the calculated rng dameter l has been shown n Fg.1 shows that the rato (K bc /K e ) range 2.0 (PbO tellurte glass seres), 2.5 (K 2 O tellurte glass seres), 2.0 (B 2 O 3 tellurte glass seres), 2.0 (ZnO tellurte glass seres), 2.3 (Er 2 O 3 tellurte glass seres) and calculated rng dameter l 5.0 nm ndcatng that elastc constants of tellurte glasses calculated usng equatons 1 to 5 are nearly n agreement wth those measured by ultrasonc method and consstent wth the rato of pure TeO 2 glass [20]. The fgure shows that hgh values of both (K bc /K e ) and atomc rng sze l for TeO 2 WO 3 K 2 O glasses are responsble for very open three dmensonal structure wth respect to pure TeO 2 glass. Due to lower values of the calculated atomc rng sze l and rato of (K bc /K e ) for TeO 2 V 2 O 5 B 2 O 3, TeO 2 WO 3 PbO, TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 glasses have closer three dmensonal structure than pure TeO 2 glass. The TeO 2 WO 3 PbO glasses show the low values of the rato (K bc /K e ) whle TeO 2 WO 3 K 2 O glasses have the hgh values of (K bc /K e ) aganst rng dameter. The atomc rng sze l of TeO 2 glass was 5.0 nm [20]. Recently, t has been found that (K bc /K e ) =2.46, 2.69, 2.44, 2.22 and 2.09 whle the atomc rng sze l = 0.491, 0, 0.486, and nm [8] for TeO 2 PbO WO 3 glasses. Prevously, the rato (K bc /K e ) = 2.3 has been calculated for pure TeO 2 glass [20, 9]. Ths result also ndcates that tellurte glasses can be consdered as dense packng structure,

6 (K bc /K e ) 72 TeO 2 [20] 3.0 (0.8-x)TeO 2 -(0.2)WO 3 -(x)pbo (0.5)TeO 2 -(0.5-x)V 2 O 5 -(x)b 2 O 3 (0.8)TeO 2 -(0.2-x)WO 3 -(x)k 2 O (0.9-x)TeO 2 -(0.1)Nb 2 O 5 -(x)zno ()TeO 2 -(0.1-x)Nb 2 O 5 -()ZnO-(x)Er 2 O I (nm) Fg.1 : Varaton of rato of (K bc /K e ) wth the calculated rng dameter l forteo 2 WO 3 PbO, TeO 2 V 2 O 5 B 2 O 3, TeO 2 WO 3 K 2 O, TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3. f- The average crosslnk densty n and Posson s rato ( c cal ) for the 25 tellurte glass compostons have been calculated by usng Equ.6 and 7. The average crosslnk densty n c ncreased from to 3.00 from to 2.636, from to and calculated Posson s rato decreased from to 0.213, from to 0.220, to for TeO 2 WO 3 PbO, TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 glasses and t has a fxed value at and calculated Posson s rato at for TeO 2 V 2 O 5 B 2 O 3 glass. Whle t decreased from to and calculated Posson s rato ncreased from to for TeO 2 WO 3 K 2 O glass. The average crosslnk densty of TeO 2 glass 2.00 and calculated Posson s rato Based on the above arguments, t s possble to presented the probable llustratons of three dmensonal structural fragmentatons as llustrated n Fg.2-a for pure TeO 2 glass networks wth TeO 4 (tbp) structural unts, Fg.2-b for glass network wth tetrahedral tungsten ons, Fg.2-c for TeO 2 glass network wth octahedral tungsten ons. Fg.2-d for TeO 2 glass network wth tetrahedral nobum ons, Fg.2-e for TeO 2 glass network wth octahedral nobum ons, Fg.2- f forteo 2 glass network wth BO 3 structural unts and Fg.2-g for TeO 2 glass network wth octahedral bsmuth ons. Regardng Er 2 O 3, the coordnaton number Er 3+ n general vares from 8-12 and hence t s dffcult to show n the form of structures. Smlarly n the case of vanadum ons these ons partcpate n the glass wth (VO 2+ ), called as vanadyl complexes and hence t s also dffcult to show n the dagram. However, n case of lead ons they partcpate both n tetrahedral and n octahedral postons lke tungsten ons n the glass network.

7 73 Entry of K + (a) (b) (c) (d) (e) (f) (g) Fg.2: Illustratons of structural fragments of varous TeO 2 glass networks. Pure TeO 2 glass network wth TeO 4 structural unts (b) TeO 2 glass network wth tetrahedral tungsten ons (c) TeO 2 glass network wth tetrahedral tungsten ons. (d) TeO 2 glass network wth tetrahedral nobum ons (e) TeO 2 glass network wth octahedral nobum ons (f) TeO 2 glass network wth BO 3 structural unts (g) TeO 2 glass network wth octahedral bsmuth ons.

8 74 4.Concluson Medum range structure parameters of the fve famles of tellurte glasses (of 25 compostons) of TeO 2, TeO 2 WO 3 PbO, TeO 2 V 2 O 5 B 2 O 3, TeO 2 WO 3 K 2 O TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 have been deduced. From the calculated atomc rng sze l and rato of (K bc /K e ) s has been found that: TeO 2 WO 3 PbO, TeO 2 V 2 O 5 B 2 O 3, TeO 2 Nb 2 O 5 ZnO and TeO 2 Nb 2 O 5 ZnO Er 2 O 3 glasses have closer three dmensonal structure than pure TeO 2 glass, TeO 2 -WO 3 -K 2 O glass has more open three dmensonal structure than pure TeO 2 glass. Acknowledgment The authors extend ther apprecaton to the Deanshp of Scentfc Research at Majmaah Unversty for fundng ths work under project No References [1] A.A. Assad, K. Damak, R. Lachheb, A. Herrmann, E. Yousef, C. Russel, R. Maalej, Journal of Alloys and Compounds, 620, 129 (2015). [2] R. El-Mallawany, R.El-Mallawany, M.Sdkey, A.Khafagy, H.Aff, Materals Chemstry and Physcs, 37, 197 (1994). [3] Y. Gandh, N. Krshna Mohan, N. Veeraah, J. Non. Cryst. Solds, 357, 1193 (2011). [4] R. El-Mallawany, Journal Mater. Res. 7, 224 (1992). [5] A. Abdel-Kader, R. El-Mallawany, M.M. Elkholy, Journal of appled physcs, 73, 71 (1993). [6] A.El-Adawy, R.El-Mallawany, Journal of Materals Scence Letters, 15, 5 (1996). [7] M.A.Sdkey, R.A.El-Mallawany, A.A.Abousehly, Y.B.Saddeek,Materals chemstry and physcs, 74, 222 (2002). [8] S. Azanty, A.K. Yahya, J. of Non-Cryst. Solds, 378, 234 (2013). [9] R. El-Mallawany, J. Mater. Res., 5, 2218 (1990). [10] M.M. Umar, A.K. Yahya, Mater. Chem. and Phys., 142, 549 (2013). [11] R.El-Mallawany, I.Z.Hagar, M.Poulan, Journal of Materals Scence, 37, 3291 (2002). [12] M.Sdky, R.A.El-Mallawany, A.Aboushely, E.Yousef, Glass scence and technology, 75, 87 (2002). [13] R.El-Mallawany, A.Abd El-Monem, Physca Status Sold (a), 166, 829 (1998). [14] R.El-Mallawany, Materals Chemstry and Physcs, 39, 161 (1994). [15] B.Brdge, N.Patel, D.Waters, Phys. Stat. Sol.(a), 77, 655 (1983). [16] B.Brdge, A.Hgazy, Phys. Chem. Glasses, 27, 1 (1986). [17] H. Afff and S. Marzuk, Mat. Chem. & Phys., 80, 517 (2003). [18] V. Rajendran, N. Palanvelu, B. Chaudhur, K. Goswam, J. of Non. Cryst. Solds, 320, 195 (2003). [19] M.A. Sdkey, M.S.Gaafar, Phys. B: Cond. Matter., 348, 46 (2004). [20] E.F. Lambson, G. Saunders, B. Brdge, R.El-Mallawany, J. Non. Cryst. Solds, 69, 117 (1984).