Indian Jurnal f Engineering & Materials Sciences Vl. 4, Fehruary 1997, pp. 28-32 Transprt prperties f zinc-bismuth xide glasses OS Dhte", S V Pakade" & S P Yawale" a Department f Physics, Vidya Bharati Cllege, Karanja (Lad) 444 los, India b Department f Physics, Gvernment Vidarbha Mahavidyalaya, Amravati 444 604, India Received II April 1996; accepted 11 September 1997 Zinc-bismuth xide glasses f 10-25 ml% f zinc xide are prepared having thickness between 0.35-0.42 cm and diameter 0.60-0.95 cm. Physical prperties such as density (d), mlar vlume (V), hpping distance (R), numbe~ f ins per cc (N) and plarn radius (rp) are als reprted. plarn radius is fund arund 1.85 A which shws frmatin f small plarns. Measurements f de electrical cnductivity are reprted in the temperature range 443-573K. - Lg 0 versus lit and -lg 1.1. versus 11T plts exhibited linearity. Hpping cnditin given by Hlstein was applied. Plarn band-width (J) satisfy the inequality which shws adiabatic hpping cnductin. The density f Fermi level and the density f lcalised states are fund t be clse t each ther. The physical and transprt prperties f glasses are f great interest because f their applicatins in industry and many allied areas 1-). Transprt prperties f semicnducting glasses are als interesting because they prvide useful infrmatin regarding hpping mechanism. The de cnductivity and hpping mechanism in Bi z O)-B 2 0 J glasses, cntaining 20-80 ml% f Bi 2 0 3 have been discussed by Yawale and Pakade 4. Temperature dependent activatin energy is bserved. Tw types f hpping cnductins are nrmally bserved in xide glasses, i.e., (i) adiabatic and (ii) nn-adiabatic. Hlstein' suggested mdel fr the bservatin f hpping cnductin in glasses. The mixed inic-electrnic cnductin is bserved in PbO-Bi 2 0 3 -Ga20 3 glasses", Electrical cnductin in sme sl-gel silicate glasses is studied by Ghsh and Chakravrty". In this study, analysis f the results f cnductivity data is interpreted with the light f the phnnassisted nearest-neighbur hpping and variable range hpping mdels. V20S-P20S-ZnO glasses shw adiabatic hpping cnductin I. This hpping cnductin is mainly cntrlled by the activatin energy. The detailed study f many xide glasses regarding cnductivity and ther parameters was dne by Sayer and Mansingh". The glass systems studied with Biz0 3 (such as B203-Bi 2 03. V20~-Bi203 etc.) shws adiabatic hpping cnductirr':", In the present wrk, the variatin f dc electrical cnductivity with temperature in the range 443-573K, with an intentin t bserve the behaviur f the cnductin mechanism in ZnO- Bi z 0 3 glasses have been reprted. The physical prperties have als been reprted. The treatment given by Friedman and Hlstein? is applied t bserve the adiabatic r nn-adiabatic hpping cnductin. Experimental Prcedure ZnO - Bi z 03 glasses were prepared frm AR grade chemicals. Apprpriate amunt f the different chemicals in pwder frm was weighed n K-Ry mnpan balance having an accuracy f ± 10 ug. Hmgenizatin f the apprpriate mixture f the cmpnents f chemicals was achieved by repeated grinding. The hmgeneus mixture was then placed in a fireclay crucible in a furnace. Melting was carried ut in cntrlled cnditins at temperature ranging frm 1000 t 1500 ± 10 C fr 2 h. All glasses were quenched at 200 C in a steel disc and annealed at 350 C fr 2h. The details f glass preparatin are reprted elsewhere", The amrphus nature f the glass samples was checked by taking X-ray diffractin patterns. All the samples were fund t be amrphus in nature. Using Archimedes principle the densities f glass samples were measured, using benzene as a buyant liquid. The accuracy in the measurement f density was ± 0.001 g/cm '. The de electrical cnductivity (0) was measured by determining the resistance f glass sample. The cnductivity f the glass samples was measured by a bridge-type circuit reprted earlier". The vl-
DHOTE et al: ZINC-BISMUTH OXIDE GlASSES 29 tage drp methd was adpted. The vltage drp acrss a standard resistance (1 MQ) was measured by digital multimeter DT-850 (Japan) having input impedance 10 9 The errr in the resistance measurement was less than 2%. Results and Discussin Physical prperties f all the glass samples such as density (d), mlar vlume (V), hpping distance (R), number f Zn ins per cc (N), and plarn radius (rp) are reprted in Table 1. The number f Zn ins per cc (N) are estimated frm density f the glass. The density is increased frm 6.282 t 7.223 g ern"? with the increase f Bi 2 0 3 cntent and is fund t be f the rder as brate glasses in general10. Nature f ins entering the netwrk decides the structure f the glass and hence the density f the glass. The plt f d exptl versus ml % f ZnO and mlar vlume (V) versus ml % f ZnO is shwn in Fig. 1. It is bserved that vlume increases with increase in ZnO cntents up t 20 ml% f ZnO and then decreases. Additin f ZnO in Bi 2 0 3 increases the number f nn-briding xgyen atms and hence the increase in density with Bi 2 0 3 ml%. The value f the plarn radius is fund t be arund 1.85A which suggests the frmatin f small plarns. The number f Zn ins per cc are fund t be f the rder f 10 22 The de electrical cnductivity f semicnducting xide glasses fr the hpping f plarns in a nn-adiabatic apprximatin is given by Ne 2 Kv a= ((1- C) exp (- 2aR) exp (- W/kT) kt... (1) Where N is the number f metal in sites per unit vlume and (l represents the electrn wave functin decay cnstant. R is the hpping distance, W is the activatin energy and C is fractin f sites ccupied by plarns. The plarn hpping energy'l-", W H is given by W H = w.,!2 i =- (lir -1/ R) 4 p p... (2) Where 1/ Ep = 1/ GO - 1/ Es is the effective dielectric cnstant, E GO and Es are the infinite frequency and static dielectric cnstants. The plarn radius'? (rp) is given by rp=(1i2~3t/6)1/3.r... (3) In generalised, plarn mdel", the plarn bandwidth (J) is given by W= WH-J... (4) where J is related t the electrn wave functin verlap n adjacent sites. The de cnductivity (a) measured in the temperature range 443-573K is shwn in Fig. 2. It is bserved that the plt f - lg a versus 11T shws a linear nature (Fig. 2). In this regime cnductivity f glass increases with rise in temperature. Frm the slpe f curve, fr every glass, activatin energy (W) is estimated and reprted in Table 2. It is bserved that the activatin energy (W)varies frm 0.2444 t 0.3942 ev. Fr the examinatin f the nature f hpping cnductin (adiabatic r nn-adiabatic) the cnditin given by Hlstein! is applied, suggesting that Table I-Physical parameters f ZnO-Biz03 glasses Glass cmpsitin ml % Density (d) Mlar vlume Hpping N.fins Plarn radius g cm? (V) distance (R) percc(n) (:k) ZnO Bi 2 03 cm 3 ml- 1 A 10 22 cm- 3 25 75 6.282 58.86 4.606 1.023 1.855 20 80 6.366 61.10 4.664 0.985 1.879 15 85 6.813 59.93 4.634 1.004 1.867 t 90 7.223 59.18 4.614 1.017 1.859 Table 2- Transprt prperties f ZnD-Bi 2 0 3 glasses Glass cmpsitin ml % Activatin Plarn binding Plarn hpping Activatin Plarn bandwidth (ev) energy ( W) energy (w.,) energy ( W H )Eq. (2) energy(w) ZnO Bi 2 03 frm Fig. 2 ev ev ev ev J r 25 75 0.2444 0.6618 0.3309 0.2445 0.0865 0.0056 20 80 0.3942 0.6536 0.3268 0.3943 0.0674 0.0055 15 85 0.3163 0.6607 0.3304 0.3162 0.0141 0.0055 t 90 0.3450 0.6605 0.3303 0.3450 0.0147 0.0055
30 INDIAN J. ENG. MATER. set, FEBRUARY 1997 8r-----------------------~60 'i' eu.~ 7 ~ u - - 55~ e3it w n3.!. 6~--~--~--~~--~---L~50 10 15 20 25 ZnO, ml.,. Fig. I-Density (D) and mlar vlume (V) against cmpsitin f ZnO (ml %) the plarn bandwidth, J shuld satisfy the inequality, r» (2 ktw H ht )114.(11(.1)0/ Jt )112 fr adiabatic hpping... (5) J <J *fr Nn-adiabatic hpping where,f*=(2ktwh/jt)1/4.(hwljt)i12... (5a) The plarn bandwidth J can be estimated frm f=:e3[nef)]l12e~12... (6) Where ~EF) is the density f states at Fermi level. The values f f * and f are calculated frm abve equatins and reprted in Table 2. The effective dielectric cnstant (Ep) was evaluated by measuring the high frequency dielectric cnstant, Ep =: E"" (High frequency dielectric cnstant at 25 MHz). The lcalizatin length (a) is calculated frm the fllwing relatin 14 3 a 4 2:rR.N(EF).kT 30... (7) The frmula given by Mtt and Davis!" in variable range hpping is used t calculate the values f density f states at Fermi level M..E F ). ME)- 3 IT\ F - 4.7rWK... (8) It is bserved that the values f I are greater than the values f J" (Table 2) which suggests that, the nature f hpping cnductin is adiabatic. Similarly fr cnfirmatin f adiabatic cnductins anther methd suggested by Emin and Hlstein" is applied. Friedman and Hlstein? derived an expressin b JI 2 2-25 2 5 lit XIO- 3,IC I Fig. 2-Variatin f lg f cnductivity (0) with lit fr ~) 25% ZnO, (.) 20% ze, (6) 15% ZnO and (T) 10% ZnO glasses fr the mbility in the case f nn-adiabatic hpping, (J 3 (ej 2 K) ( 1C ) 112 ( WH) p= Ne =2 kt. kt~.exp - kt... (9) In case f adiabatic hpping cnductin Emin and Hlstein IS have derived an expressin fr the mbility, _.s.- ~(ewck ) [( WH- 1)] p - Ne - 3 kt. exp kt... (10) The plt f - lg 11 versus 1/ T (Fig. 3) gives the value f activatin energy (W= W H - f). Frm the Table 2, it is bserved that the values f activatin energy (W) calculated frm the slpe f the plts (Figs 2 and 3) are equal, but they differ with plarn hpping energy (W H ) which suggests adiabatic hpping cnductin. The cnductivity" fr the variable range hpping is predicted t be. =exp[ -(TIT)1/4]... (11) Where 0 and 0 0 are cnstant and 10 is given by... (12) Where M..E F ) is the density f states at Fermi level. Recently Triberies and Friedman 17,18 have applied perclatin thery t the small plarn hpp-
DH'OTE et al: ZINC-BISMUTH OXIDE GLASSES 31 9r-------------------------------~ 6~------------------------------~ T > T N 's u 01-11 I i ẹ.. es: b~ 01 I 2 l/tx 10 3.1(-4 2-25 Fig. 3- Variatin f lg f electrn drift mbility ( 11) with 1/ T fr (0) 25% ZnO, (e) 20% ZnO, (6.) 15% ZnO and (T) 10% ZnO glasses 2S 9L- ~ ~~----~~. 0 204 0 210 0 215 0'220-114 -1 T,K Fig. 4-Mtt T-1/4 analysis: variatin f lg 0 with T-' 114 fr (0) 25% ZnO, (e) 20% ZnO, (6.) 15% ZnO and (T) 10% ZnO glasses Table 3-Parameters btained frm Mrt's" and the perclatin mdels'"-" Glass cmpsitin ml % Effective dielectric Lcalizatin length Density f states at cnstant Ep (a) Fermi level N(E r ) ZnO Bi z 0 3 A-I loz2 ev-1cm-3 25 75 3.5 2.71 1.00 20 80 3.4 0.54 2.95 15 85 3.5 2.18 0.75 10 90 3.6 2.39 0.76 * Ep '" Ea, weie high (infinite) frequency dielectric cnstant (here at 25 MHz frequency). Lcalized states N 1022 ev-1cm --3 1.01 3.60 0.26 0.95 ing regime and evaluated the cnductivity in the disrdered systems. Cnsidering c-relatin due t energy f cmmn sites in the perclatin cluster, the fllwing expressin fr the cnductivity has been btained. 0= 0 0 exp[ -(T! T)1I4]... (13) where a 0 and T are cnstants and T is given by... (14) It is clear that the plt (Fig. 4) is linear ver the cnsidered temperature regin. The values f a, N and N(E F ) are reprted in Table 3 and fund reasnable fr lcalized states. It is bserved that the values f N are clse t the values f N(E F ) btained frm Mtt's mdel (Eq. (12)). This suggests that the parameters such as lcalizatin length and density f states btained frm bth the mdels+" are fund t be reasnable fr lcalized states and cnsistent with the glass cmpsitins. The variatin f cnductivity at fixed temperature and activatin energy with cmpsitin (ZnO ml%) is nt systematic (Plt nt shwn) because f the cntaminatin f bismuth glasses. After preparatin f the glasses the cmpsitin f chemical cnstituents taken initially changes and therefre the change in the cnductivity hence the activatin energy. Cnclusin The adiabatic hpping cnductin is bserved in ZnO-Bi203glasses. The small plarn hpping mdel is applicable. The perclatin mdel suggested by Triberies and Friedman 17.18 and Mtt's T- 114 mdel interprets the results well. The density f states at Fermi level and the density f lcalized states are fund t be clse t each ther.
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