Activation energies of hopping of vanadium 3<i>d</i>¹ small polaron in 0.7V₂O₅-(0.3-x)P2O₅-x(As₂O₃/Sb₂O₃)<i> </i>(x=0, 0.05) glasses by EPR spectroscopy and DC electri

Indian Journal of Chemistry

Yol. 4SA, November 2006, pp. 2400-240S

Activation energies of hopping of vanadium 3i small polaron in 0.7V20s-(0.3-x)P2 0s-x(As2 03/Sb203 ) (x=O, 0.05) glasses by EPR

spectroscopy and DC electrical conductivity measurements

B B Das* & 0 Mohanty

Department of Chemistry, Pondicherry University, Pondicherry 60S 014, India Email: das_b_b@yahoo.com

Received 1 May 2006; revised 16 Septeillber 2006

The three glasses in the 0.7Y20,-(0.3-x)P205-x(As20,/Sb20,) (x= 0, O.OS) system, G 1 (x=O), G2 (x=O.OS: As20,) and G3 (x=O.OS: _Sb20,) have been prepared by melting the appropriate amounts of the batches in silica crucibles in the temperature -1120 K and quenching in air. The glassy phase has been ascertained by powder X-ray diffraction of the samples which shows a broad peak around

2S o

^{in 20 vanishing at hi}gher diffraction angles typical of glassy phase. ErR studies of the glasses in the range 10-473 K show that the lineshapes are isotropic in nature. The observed valucs of the g- matrices are similar in all the glasses in the rnnge 10-473 K which shows that the octahedra containing thc paramagnetic sites arc similar in all the glasscs. The y4+(3d^l) small polaron activation energies of hopping are lower in the casc of G2 (1.16xl 0-1 eY) and G3 (1.27x I 0-1 eY) as compared with that of G 1 (S.27x I 0-" eY) due to the formation of As-Y or Sb-Y _d11-dll bonds, which is absent in the case of the binary glass G I. The Log (!'Iv (J-Iz)) versus I

o 'r r

(K-¹⁾ plots of the glasses in the range 10-473 K are characterized by three regimes, viz. COOTe» I , w01c=1 and co01c« 1 where COo is the resonance frequency in rnd/s and 1e is the correlation time of the polaron in the glassy matrices. The calculated values of the Y"\3d^l) small polaron hopping activation cncrgies due to viscosity effect on the tumbling of the paramagnetic sites in the I'cgime COOTe« I is found to bc - 100 times higher than the activation energy of hopping (E[PR) due to life time broadening of the EPR lineshapes in the rcgime COOTe» I , which again are significantly different from the activation energies obtained for the glasses G I-G3, as 0.3S8, 0.619 and 0.S09 eY, respectively from the DC electrical conductivity in the range -300-473 K. It shows that the mechanism DC electrical conductivity in these glasses is different from the mechanism of EPR line narrowing.

IPC Code: Int. CI.⁸ GOI R33/60

Like the crystallinel and amorphous"" vanadium pent-

'd d' h h 4 S d' 6

OXI e, vana tum p osp ate ', vana tum arsenate, vanadium phosphoarsenate⁵.7

and vanadium phospho- antimonate⁷, glasses are known to contain mixed valence y4+(3d') and y5+ ions, Due to the presence of these ions, these glasses are II-type semiconductors, and the semiconductivity arises from the thermally excited hopping of the vanadium 3dl electron which is essentially a small polaron⁸-10 from a y4+ to a yS+

, 45711-iJ I ' I d ' I I' 14 h sIte ' " -. t IS a so reporte 1Il t 1e tterature t at the thermal hopping rate of the vanadium

3i

polaron has marked effect on the electron paramagnetic resonance lineshapes. Even at a very low temperature, the thermal hopping rate of the small polaron is fast enough to smear out the electron-nuclear hyperfine interaction to give rise to the motionally narrowed lineshapes. In such a situation, it is shown that the derivative peak-to-peak linewidth is a measure of the

activation energy of hoppinglS of the small polaron, We report here the studies mainly 011 the various types of activation energies of hopping (EEPR) of the vanadium 3j small polaron of 0.7Y20S-(0.3-X)P20S- x(As₂0₃/Sb₂0₃) (x= 0, 0.05) glasses obtained from the variation of derivative EPR peak-to-peak linewidths in the range 10-473 K and compare these activation energies with those obtained from the DC electrical conductivity measurements in the glasses,

Materials and Methods

The compositions of the three glasses studied are as follows: G 1 (x=O), G2 (x=O,05:As₂0₃) and G3 (x=0.05:Sb20₃₎ in the 0.7Y20S-(0.3-x)P20S-x(As20,/

Sb20₃) (x=O, 0,05) system. The glasses were prepared from reagent grade chemicals. Calculated amounts of vanadium pentoxide (Y205), diammonium hydrogen orthophosphate, H(NH4)2P04, as source of phosphorus

DAS & MOHANTY: ACTIYATION ENERGIES OF HOPPING OF THE SMALL POLARON IN GLASSES 2401

Table I - Observed density and concentrations of the y4+ and y⁵+ iOIlS, glass transition temperature (Tg), small polaron radius ( 1',,) and the averagc transition-metal (TM) and ion separation (R), in the glasses G 1-G5 of the 0.7Y"0₅-(0.3-X)P20₅-x(As₂0:'/ Sb₂0₃)

(x= 0, 0.05) system Glass Density COIlC. Y~+ Conc. y⁵+

(g/cm') (per g) (per g)

GI 2.869 9.616xl02o 6.383x1021

G2 2.886 6.142xl02o 10.866x1021

G3 2.810 5.981 x I 0²⁰ 10.833xl021

pentoxide (P₂0_S), arsenic trioxide (AS20₃₎ and antimony trioxide (Sb₂0₃) were mixed thoroughly with acetone for 2 h to prepare the batches. The glasses were prepared by melting the batches in silica crucibles at around 1120 K and then quenching in air by pressing between two dry ice cold aluminium plates. Formation of NH3 due to decomposition of H(NH4)2P04 at high temperature allowed the partial reduction of y⁵+ in Y 20₅ to y4+ ions. The glassy phases of the samples were ascertained by powder X-ray diffraction patterns (Model ISO-DEBYEFLEX 2002) of the samples, which show a broad peak at lower diffraction angles and vanishes at higher diffraction angles characteristic of glassy phase. A MOM (Hungary) derivatograph was used to record the differential thermal analysis (DT A) and the Thermogravimetric (TG) traces of the glasses in the range 295-I 273 K. The X-band EPR lineshapes of the glasses at 10 and 285 K were recorded on a Bruker spectrometer system (ER 2000) fitted with a double cavity TEllO, while the lineshapes at 77, 300, 323, 373,423 and 473 K were recorded on a Varian E-I 09 spectrometer system. Tn order to record the derivative peak-to-peak linewidths variation as function of temperature faithfully, the lineshapes were recorded at sufficiently low microwave power to avoid saturation.

In both the cases, 100 kHz magnetic field modulation was used. The measured values of the g-matrices were calibrated with respect to the resonance lines of Bruker strong pitch (g=2.0028) at 10 and 285 K, and with respect to the resonance line of DPPH (gDPPH=2.00354)16 for the lineshapes at 77 K. The DC electrical resistivity of the glasses was measured using a 'Keithly' digital electrometer (model 619) in the range 295-573 K at 10-4 torr in a quartz cell. The thermo-emf of aPt, (Pt + 10% Rh) thermocouple were measured using a Keithly Digital Multi meter (model 1954) which were then converted to the tem- peratures using the standard table. The concentrations of y4+ ions were determined by wet chemistry method and the density values of the glasses were determined by liquid displacement method.

Small polaron radius Average TM io~ Tg

r" (A) separation (R) (A) (K)

2.073 5.065 675

1.786 5.864 645

1.789 5.947 673

Results and Discussion

Table 1 shows the observed values of the density, concentrations of the y4+ and yS+ ions in the glasses G I-G3. The values of the density as well as the concentrations of the y4+ and yS+ ions are found to be plausible for such systemss. The concentrations of y-l+

ions are found to be one order of magnitude higher than those of the yS+ ions, showing thereby that the y4+ ions exist as defect centres in the glassy matrices.

From the values of the concentrations of the y4+ and

yS+ ions, we calculate the values of the small polaron radius (rp) and the average transition-metal (TM) ion separation (R) using reported relationsl7

.l8

and the values are given in Table 1. The fairly low values of rp suggest that vanadium 3d^l sIllall polaron is strongly localized on a y4+ site. As expected, the values of I'p

are found to be less than those of R in all the glasses.

Figure 1 shows the DT A and TG traces of gl asses G 1- G3 in the temperature range 300-1273 K. The glass transi tion temperature (Tg) in the glasses is found to be 675, 645 and 673, respectively (Table 1). The presence of the glass transition temperature also confirms the formation of glasses in the above compositions.

In Figs 2A-2C, we present the EPR lineshapes of the glasses G I -G3 recorded at 10, 77, 285, 300, 323, 373, 423 and 473 K, respectively. The figures show that all the lineshapes are isotropic without any hyperfine structures even at 10 K excepting in the case of the glass Gl which indicates 5IY(I=7/2) 8-line hyperfine lines. The above observation of the unresolved EPR lineshapes is ascribed to the Illotional narrowingl4 of the lineshapes due to the thermal hopping of vanadium

3i

small polaron from a y-l+

site to a y5+ site. Furthermore, it is interesting to mention here that the EPR lineshape of glass G I recorded at 4.2 K showed axially symmetric 16-line feature, typical of a y4+ (3d^l) small polaron localized on a single sIY(l=7/2) site^S.14. These studies further indicated that in the case of motionally narrowed EPR lineshapes, the temperature variation has marked effect on the EPR peak-to-peak linewidths.

2402 INDIAN 1 CHEM, SEC A, NOVEMBER 2006

745 EXO

I

.6.T Gl

1

G2 G3

ENOO

0, 0

5_

50

VI )g 100

- I

- - - - - _ __ _ _ _ _ Gl - - -- - - G 2

:E ¹⁵⁰ _ ____ _ ____ _ _ _ _ ____ _ G3

~ Ol ²⁰⁰

273 473 673 873 1073 1273 .

TEMPERATURE ,T(K)

Fig. I -OT A and TG traces of glasses G I (x=O), G2 (x=0.05:As₂0,) and G3 (x=0.05:Sb₂0,) of the 0.7V₂0S- (O.3-X)P20S-x(As20,/Sb20,) (x=O, 0.05) system (temperature=

300-1273 K).

From the observed isotropic lineshapes, we calculate the values of the g-matrices as listed in Table 2. The table shows negative g-shift in all the glasses, which shows the positive sign of the spin- orbit coupling constant of the paramagnetic site in all the glasses. It is important to mention here that from our earlier studies on the glass G I, we concluded that the paramagnetic site formed in the glass is vanadyl (Y02+) ions.14 where the vanadium is in a distorted octahedral environment of six oxygens with the vanadyl oxygen forming the apex Y=O bond. The unit is visualized as [O=Y04/2··OII2]. Furthermore, the values of the g-matrices do not show any significant variation in the temperature range 10-473 K for a glass, and also with respect to the variation in composition from G I to G3 at any of the above temperatures. It shows that the octahedra containing the paramagnetic site are not significantly different from one another in terms of bonding around the paramagnetic site within the composition range as well as studied temperature range 10-473 K. It is important to mention here that our IR spectral resultss discussed elsewhere showed the formation of tetrahedral [OPOld , [OAS03/2] and [OSb0₃₁₂] units

111 the glasses G l(x=O), G2(x=O.OS:As20₃) and G3(x=0.OS :Sb₂0₃).

In Fig. 3, we show the plots of Log (flv(Hz» versus 10³fT (KI) of the glasses G I-G3 in the temperature range 10-473 10³fT (K·^I), where !1v is the derivative peak-to-peak linewidth in hertz. In the inset of the figure we show the expanded plot of the 10³fT (K·^I)

axis in the range 2.0-3.6 10³fT (KI) which contains the bottleneck region. In this temperature range, the variation of Log (flv (Hz» with inverse temperature exhibits interesting behaviour. From 10 K, the derivative peak-to-peak linewidth, flv (Hz), decreases up to 373 Kin Gl, 323 Kin G2 and 300 Kin G3 and then increases in all the glasses up to 473 K. We explain this behaviour by invoking the correlation time^l9, Tc of the vanadium 3d^l small polaron in the glassy matrices. In the temperature range from 10 K to the minimum of each of the three plots where the derivative peak-to-peak linewidth, flv (Hz), decreases linearly is characterized by the situation^{l9 O}nTc» 1,} where o}o is the resonance frequency in radfs. In this regime the spin-lattice relaxation time, TI, is not equal to the spin-spin relaxation time (T₂) and the overall derivative peak-to-peak linewidth is the motionally narrowed 14 situation in the viscous system which is governed by the lifetime broadening of the excited states, i.e. by TI • flv, the derivative EPR peak-to-peak linewidth in Hz is calculated by using the relation 15:

flv::.::: flvo exp (EEPRfkT), ... (1) where flvo is the pre-exponential factor and ^EEPR is the activation energy of hopping of the small polaron, k is the Boltzmann constant and T is the absolute tempera- ture. ^EEPR values of the glasses in the range which is characterized by WoTt

»

1 are calculated from the slopes of the plots (Fig. 3) obtained by linear fit and are shown in Table 2. The ^EEPR values show stiff decrease from S.27xlO-4 in Gl to 1.16x10·⁴in G2 and 1.27xlO-4 in G3. In order to rationalize this, we first consider the electronic structures of the glass formers such as P20S in G 1, and of the additional glass formers AS203 in G2 and Sb203 in G3. In P205, P has oxidation state +S (2l') and the bonding in thc network with Y atom is through the oxygens of the phosphate groups. Thus, any exchange of y4+ (3i) small polaron to the neighbouring y⁵+(3cP) site occurs through the Y-O-Y bridge only rather than a very long bridge such as V-O-P-O-Y. Moreover, p5+ has closed shell configuration and the energy difference with the 3s and 3p are fairly high. So, p5+ is less likely to take part in the polaron exchange process.

DAS & MOHANTY: ACTIVATION ENERGIES OF HOPPING OF THE SMALL POLARON IN GLASSES 2403

(A) _~ ^(a) (8)

==Y=lal

_(b) ^(C)

_~

^{( a) ( b)}

( c)

~

^(b)

*ICI ~

^{( d)}

~

^{( c)} _(e) ^(d)

~

^(d)

~

^{( e)}

(q)

(I) (1)

(I)

(g) ( g)

(g)

( h) (h)

(h)

1360 ₅₄₄₀ 1360 2400 54401360 2400 5440

MAGNETIC FIELD (GJ

Fig. 2-(A) EPR lincshapes of thc glass G 1 (x=O) of thc 0.7V20,-(0.3-x)P20s-(As203/Sb203) (x=O, 0.05) system at (a) 473 K, (b) 423 K, (c) 373 K, (d) 323 K, (e) 300 K, (f) 285 K, (g) 77 K, and (h) 10 K; (I3) EPR lineshapes of the glass G2 (x=0.05) of the 0.7V20s-(0.3-x)P:,Os-x(As20iSb203) (x=O, 0.05) system at (a) 473 K, (b) 423 K, (c) 373 K, (d) 323 K, (e) 300 K, (f) 285 K, (g) 77 K, and (h) 10 K; and (C) EPR lincshapes of the glass G3 (x=0.05) of the 0.7V 20s-(0.3-x)P20s-x(As203/Sb203) (x=O, 0.05) system at (a) 473 K, (b) 423 K, (c) 373 K, (d) 323 K, (e) 300 K, (f) 285 K, (g) 77 K, and (h) 10 K.

Tablc 2 - Obscrvcd g-matriccs andthc activation cncrgics of hopping of the small polaron (EEPR) and the DC activation energy at 300-573 K of thc glasscs G I-G3 [O.7V 20s-(0.3-x)P20,-x(As203/ Sb₂0 3) (x= 0, 0.(5)]

Glass No. g-matrix

10K 77K 285K 300K 323K 373K 423K

Gl 1.964 1.965 1.960 1.963 1.965 1.964 1.964 G2 1.963 1.965 1.963 1.960 1.966 1.963 1.965 G3 1.965 1.966 1.964 1.964 1.963 1.965 1.965

In the case of As₂0](G2) and Sb₂0](G3), As or Sb atoms form covalent bonds with three oxygens atoms and has a lone pair of eleclron in it.~ non-handing orbital. Tllis lone pair or electrons llll(ki' Sllit:lblc condition of symmetry and cncrgi' is ciun:IlcLi to Illl' empty ri-orbitals of tile tr:ln~ition-lllel:I! (V in tllis case) thereby I'onning addition:I! 'dircct honds' wilh the transition-met:ti. Furthcrmore, since /\s or Sb atoms havc I'airly low cnel'gy 4ri- 01' 5d-mbit:Iis, rcspectively back-bonding occurs thl'Ough the

Activation cncrgt (eV)

473K EITR (cV) E[PR(CV) E_DC (eV) _Tc

(WOTe» I) (woTe« I) (s)

1.964 5.27x I 0.⁴ 0.021 0.358 1.64x I 0.¹¹ 1.964 1.16x 10.⁴ 0.010 0.619 1.70xI0·¹¹ 1.965 1.27 x 10.⁴ 0.010 0.509 1.7 Ox 1 0.¹¹

donation of electrons from the 4d-orbitals of V to the corresponding d-orbitals of the As or Sb atoms. As a result, Illultiple bond formation occurs between As or .'-;b with y-I+ sitc in thcse gl:lSSCS. Thi~ type of bonding does not occur in the easc or glass G I containing P :ltOlllS. As :1 result, clectl'on exchange becomes more rC:lsible in the cases or As₂0₃-containing glass G2 and Sb₂01-contai:ling glass G3 through the As-Vol' Sb-V, ri_l I-ill I bonding, as compared with that of the glass G I in which slich bonciing docs not occur. This

2404 ^{INDIAN J CHEM}, SEC A, NOVEM13ER 2006

N J:

;;-

<l

1:

8.9

8.8

..J 8.7

8.6

r~ ^{: o}

^{. 8.9}

~e ^~

^{0- G1}

^~:

/

^{"N I > ~ Ol 8.8 8.7}

rg

^{-' 0 8.6}

[J I

0 ^8.5

o

20

.c. ^ffi 1: «1

- O- --- 'O __ .~_£J. 6)ntr?~

(0 1: «1 ---o:~H

...

oe m t =1 (u t »1

-~O- G1 ^{0 C} wo\:::::1 ^{0 C}

...-0- ^G2

0... - 8- G3 u- o

o __ 0----

«~o--- ^{(I) 'l} »1

(1)0\ ooo't

e=1 oC

2.4 3.0

10³fT (K')

40 60

10³JT(K')

80

3.6

100

Fig. 3-Log (L'w (I-Iz)) vcrsus I O'IT (K·¹) plots of the glasses G I (x=O), G2 (x=O.05:As20,) and G3 (x=0.05:Sb20J) of the 0.7VP,,-(0.3-x)P20,-x(As20.iSb20,) (x=O, 0.05) system in the tcmperature rangc 10-473 K. f1v is thc derivativc EPR peak-to- peak lincwidth.

situation results in significant lowering of the thermally excited activation energy of hopping of the small polaron in glasses G2 and G3 as compared with the glass G I.

However, in the case of the glasses G2 and G3, the Table 2 shows that the glass G3 has slightly higher activation energy of hoppi ng (l.27x I O-~ G Hz) as com- pared to that in the glass G2(1.16xI0-4 GHz). This interesting result is rationalized as follows: the ionic radii²⁰ of As³+ and As⁵+ ions are 0.58

A

and 0.34

A,

respectively, whereas the ionic radii of Sb³+ and Sb⁵+ are 0.76

A

and 0.60

A,

respectively. The charge/ionic radius ratio is higher in the cases of the As³+ and As⁵+ ions as compared with the corresponding Sb³+ and Sb⁵+ ions in the glasses G2 and G3, respectively. Thus, the more polarizing As]+ and Ass+ ions in G2 facilitate polaron hopping from V~\3dl) as compared with the Sb³+ and Sb⁵+ ions in G3 thereby decreasing the activation energy in G2 as compared with G3.

In the temperature range from the minimum of each plot for the glasses G I-G3 up to 473 K where the viscosity of the glasses decrease and tends towards frozen liquid structures, both the relaxation times are equal, i.e. TI=T21~. This regime is characterized by the situation, WIITe«1. In this regime, we calculate EEPI~

of the small polaron form the slope obtained by linear fit of the Log (Lw(Hz)) versus I 03/T (K-¹⁾ plots of the Arrehenius relation as:

6 ^-_{- 0 -}^{0 -}_G2 ^G1

- 6.-G3

2

2 3

Inverse Temperature,10001T(K)

Fig. 4-Plots of Log (piT) versus IO'IT (K-¹) where p is the DC elcctrical resistivity of the glasses G I (x=O), G2 (x=O.05:As20,) and G3 (x=O.05:Sb20,) of the 0.7V20,,-(0.3-x) p}O,-x(As20)Sb20,) (x=O, 0.(5) system in the range 295- 573 K.

... (2)

where the connotations are as In Eq. (I). It is important to mention here that because of the negative slope of the plots, the Arrehenius relation is considered to evaluate the activation energies of the glasses in this regime. The values of the activation energy are shown in Table 2 which are found to be -100 times higher than those obtained in the regime WOTe»1. These values we ascribe to the activation energy of tumbling of the paramagnetic sites due to decreasing viscosities, which affects the correlation time of the excited states.

The minimum of each plot is characterized by woTe=l. These are observed at 373,323 and 300 K, ror G I-G3, respectively which are well below the Tg values of the glasses (Table I). It shows that the point characterized by WoTc= I is dependent on the viscosity of the glasses. Using the value of temperature at the minimum of each of the plot and the resonance frequency (wo) for each glass at that temperature, we calculate the correlation time (TJ of the glasses and the values are shown in Table 2. These values are found to be -1.7xlO-¹¹ s for all the glasses.

The experimental DC electrical resistivity data of the glasses in the range -300-473 K which is

DAS & MOHANTY: ACTIVATION ENERGIES OF HOPPING OF THE SMALL POLARON IN GLASSES 2405

rearranged for linearity from the modified Arrhenius type rclation (piT = Po exp (E)kT, where p is the resistivity of the glasses) in the Log (pin versus inverse temperature, 10³1T (K') plots are shown in Fig. 4. The activation energies calculated from the slopes of the plots obtained by linear fit are found to be 0.358 eY, 0.619 eY and 0.509 eY, respectively for the glassess. These activation energies show rather increasing trend in contrast to those obtained from the Log Clw(Hz)) versus I 031T (K') plots. Furthermore, the values of the activation energies are significantly higher than those determined from the derivative EPR peak-to-peak linewidths in the regimes cooTe«1 and COOTC» 1. This result shows that the mechanism of DC electrical conductivity in the glasses is different from that of small polaron hopping in the glassy matrices which brings about temperature dependent EPR line narrowing due to lifetime broadening in the case of COOTe» 1 or affecting the small polaron hopping due to tumbling of the paramagnetic sites due to decreasing viscosities in the regime cooTe«l in the glassy phases.

It has been found that in all the glasses, the EPR lineshapes are isotropic in the temperature range 10- 473 K. The values of the g-matrices do not vary significantly for a glass in the range 10-473 K, and also with the composition from G I to G3 at a particular temperature as studied. The y4+(3d') small polaron EEPR values are lower in the case of G2 (As₂0r containing glass) and G3 (Sb₂0r containing glass) as compared with that of G 1 (Y 20 S-P20S-

containing glass) due to the formation of As- Y or Sb- Y dwdl! bonds, which is absent in the case of G l.

The Log (tw(Hz)) versus 10³1T (K-') plots of the glasses in the range 10-473 K are characterized by three regimes viz. COOTe» I, coo"[e=1 and COOTe« 1. The calculated values of the y4+ (3d') small polaron EEPR due to viscosity effect on the tumbling of the paramagnetic sites in the regime cooT,,«1 is round to be ~100 times higher than the Er.PR c1uc to life time

broadening of the lineshapes in the regime COOTe» I.

However, the small polaron EEPR values in both the regimes as above are significantly different from the activation energies (EDe) obtained form the DC electrical conductivity in the range 300-473 K.

Acknowledgement

Sincere thanks are due to Prof. C Michel for helping to record the EPR lineshapes at 10K and at 285 K.

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