Dielectric properties of transition metal oxide glasses

J O f I R N A L OF

ELSEVIER

Journal of Non-CrystallineSolids 185 (1995)84-93

Dielectric properties of transition metal oxide glasses L. Murawski *, R.J. Barczyfiski Faculty of Applied Physics and Mathematics, Technical University of Gdahsk, G. Narutowicza 11 / 12, 80-952 Gdahsk, Poland

Received22 September1994

Abstract Dielectric properties of iron and vanadium phosphate glasses containing different glass modifiers have been studied in a broad range of frequency and temperature by the absorption current and with an ac transformer bridge. The dielectric spectra exhibit a peak that can be related to the electron transfer between iron atoms in different valency states. This peak and the de conductivity revealed a similar activation energy. The data obtained were interpreted in the framework of a new model of relaxation in glasses recently proposed by Hunt.

1. Introduction Many glasses containing transition-metal ions (TMI), for instance iron or vanadium, are electronic conducting semiconductors [1,2]. A general condition for semiconducting behaviour is the coexistence of transition metal ions in more than one valence state, for instance Fe 2+ and Fe 3+, so that conduction can take place by a transfer of electrons from low- to high-valence ions. Charge transport in these glasses is usually considered in terms of small-polaron hopping theory [3,4]. The dielectric properties of various TMI glasses have been investigated by many authors [1,5-8] who conclude that dielectric relaxation is consistent with the mechanism of electron hopping in pairs of transition metal ions (pair approximation model). Experimental evidence of this behaviour is a power law of ac conductivity tra¢= A to s observed over many decades of frequency. The interpretation

* Correspondingauthor. Tel: 48-58 472 563. Telefax: +48-58 472 821. E-maih [email protected].

usually involves analysis of the temperature dependence of s ( T ) which makes it possible to find the relevance of hopping mechanism in terms of pair approximation [9,10]. The dielectric loss peak is observable only if the de conductivity is separated from the total conductivity which often yields a large experimental error. At frequencies near the relaxation peak, the dielectric loss current is usually much smaller than the conduction current. Namikawa [11] for example has concluded that the dielectric loss current at the relaxation peak of a typical TMI glass is about 20% of the conduction current. This makes it difficult to observe dielectric relaxation spectra. To avoid such difficulties, we applied the absorption current method of dielectric loss measurement. The dielectric loss can be detected because it is measured as the discharging current which is inherently separate from the conduction current. So far, only Namikawa has reported dielectric relaxation spectra obtained by absorption current method in TMI glasses. An interesting property of these materials is that the dielectric and mechanical relaxation processes

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L. Murawski, R.I. Barczyhski /Journal of Non-Crystalline Solids 185 (1995) 84-93

have the same activation energy as their dc conductivity [13] which suggests that the same mechanism is responsible for all three phenomena. The correlation between the electrical conductivity, o'dc, and the frequency, fmo, of the dielectric relaxation peak can be demonstrated by the BNN (Barton [14], Nakajima [15], Namikawa [12]) relation O'dc ---- 21r f mO 80( '~s -- ,~oo) P ,

85

local (parallel) character and a pair approximation holds. In the frequency range below the peak, the series processes are non-local and can be treated as percolation of individual particles over macroscopic distance in clusters or chains. In this paper we have applied this theory to the results of dielectric measurements in several transition metal oxide glasses.

(1)

where p is a constant. Namikawa has shown that this relation is fulfilled with p = 1 in several TMI glasses except for P2Os-WO3 glass, for which p = 10. The concentration of charge carriers in TMI glasses is large and the dielectric loss as well as the de conductivity is due to the same migrating carriers. However, it is difficult to explain the dielectric loss peak and the observed power-law behaviour of the frequency-dependent ac conductivity from the point of view of the pair approximation model. Hunt [16,17] recently published several papers where he presents a new proposal to explain dielectric relaxation in glasses. His basic idea is to distinguish two cartier migration processes in two frequency ranges: below and above the dielectric loss peak. Above the peak, relaxation processes have a

2. Experimental Four different sets of glass samples (in mol %) were prepared: I, 50P205 - (50 - x)FeO - xMO (where M = Mg, Ca, Ba and x = 0, 10, 20, 30, 40); II, 50P205 - (50 - x)V205 - xMO (where M = Mg, Ca, Sr, Ba and x = 10, 20, 30, 40); III, ( 1 0 0 - x ) 1)205 - x V 2 0 5 (where x = 40, 50, 60, 70); IV, (100 - x)TeO 2 - xV205 (where x = 40, 50). The melting of glass of systems I and II was conducted in air at 1573 K in an alumina crucible. Vanadium phosphate glasses were melted in the temperature range from 1173 to 1523 K depending on the V205 content. The melt was poured on a brass plate which was preheated to 500 K and formed into button-shaped

1E-05=

1MHz

"10

2.2

~

214

216

lkHz

218

3

312

3'.4

3'.6

3.8

IO00/T [l/K] Fig. 1. Temperature dependences of crt (11); orac (A); O-dc ( × ) in 50P2Os-50FeO glass. The arrows indicate the temperature of the dielectric loss peak.

L. Murawski, R.L Barczyhski/Journal of Non-CrystaUine Solids 185 0995) 84-93

86

samples. After annealing at temperature below the glass transition, the samples were ground and polished to 1 mm thick. For the electrical conductivity and dielectric measurements, gold electrodes with a guard ring were evaporated on the samples heated to 150°C in vacuum. A capacitance bridge (General Radio 1615A) was used for ac measurements in the frequency range from 20 Hz to 100 kHz. At higher frequencies, the measurements were carded out using a VHF bridge (Tesla BM431E) in two-terminal configuration. The absorption current was measured only in iron glasses with a typical apparatus with a high-speed current amplifier. The time constant of the measuring circuit was short enough to measure the charging and discharging currents in periods corresponding to a frequency of 100 Hz. The validity of Ohm's law and the superposition principle was confirmed for all iron-containing glasses but not for PzOs-V205 glasses. In vanadate glasses, it was impossible to avoid a small electrode effect caused by water, which is always incorporated in these glasses. The dielectric loss was calculated from the discharge current

using the Hamon approximation [18]. The dielectric relaxation spectra were observed in the low-frequency region down to 10 - 4 az.

3. Results Fig. 1 shows the total measured conductivity, ort = Ordc -'l- Orac , a t different frequencies as a function of reciprocal temperature for a typical iron phosphate glass. The contribution of o'= to the total conductivity is also shown. The arrows indicate the temperature of the dielectric loss peak, which was estimated from the Arrhenius plot of the dielectric loss peak frequency obtained from the absorption current measurements. It can be noticed that in the dielectric loss peak the contribution of o'= to the total conductivity does not exceed 20%. A similar result has been reported by Namikawa [11]. The frequency dependence of o'= for different temperatures is shown in Fig. 2. It is a typical dependence observed in amorphous materials that follow the relation tr= = A to', where s is a function of temperature, which de-

1 E-04 448K 1E-O5

294K

1 E-07

S=0.63

S=0.73

1 E-09 1E+03

1E+04

1E+05

1E+06

1E+07

1E+08

f [Hz]

Fig. 2. The ac conductivity,~=, as a functionof frequencyin 50P2Os-5OFeOglassfor differenttemperatures: II, 294 K; +, 323 K; *, 348 K; O, 398 K; X, 423 K; &, 448 IL

87

L. Murawski, R.I. Barczyftski/Journal of Non-Crystalline Solids 185 (1995) 84-93

41 290K , ~ " ~ 315K 335K 3.51 ,/ 300~ ~ ~ ~ 3[ ~/ . / ~ ~C~ ~

360K

._/~v'-~

385K

2.5

o~ o ol ...............o 1

~

.....

i'o

......

i oo .

.

.

.

.

' ~'ooo

f[Hz] Fig. 3. Dielectric loss factor, e~, versus frequency at different temperatures for 50P205-30FeO-20CaO glass.

creases with increasing temperature. At room temperature the average value of s is 0.7 for glasses containing V205 and 0.75 for iron glasses. Glasses

containing 10-15% transition metal oxides exhibit s higher than 0.8. Fig. 3 presents a typical dielectric loss spectra

0.06359K_ 373K 395K 0.050.040,030.020,01 0 10 Fig. 4,

1O0

1000 f[Hz]

10000

100000

M" a s a function of frequency at different temperatures for 50P2Os-5OFeOglass.

L. Murawski, R.]. Barczyhski/Journal of Non-Crystalline Solids 185 (1995) 84-93

88

obtained in TMI glass. The loss factor, e~(w), was calculated from the results of absorption current measurements. It should be noticed that e~(to) is related to the total dielectric loss e" and ac conductivity by crt

O'd¢

09~ 0

O)~ 0

~" . . . .

+ ,~7(,o)

(2)

where o"t = O'de+ O'ae

(3)

and ora¢= w e 0 s ~ ( w ) .

x (mol%)

W,c (eV)

WR~ (eV)

W~ (eV)

Wx~ (eV)

10 CaO 20 CaO 30 CaO 10 BaO 20 BaO 30 BaO 0

0.64 0.72 0.76 0.58 0.71 0.70 0.63

0.68 0.69 0.70 0.62 0.68 0.74 0.63

0.64 0.72 0.65 0.66 0.61

0.67 0.70 0.74 0.48 0.52 0.68 0.59

(4)

In the electric modulus representation [19] in which the complex electrical modulus, M *, is defined as M * = l / e * , where e* is the complex permittivity, 1 M*=--=

Table 1 Activation energy of dc conductivity, Woo dielectric losses, W ~ , electric modulus, WM, and internal friction, WIF, in glasses: 50P205-(50- x)FeO- xMO, where M = Ca, Ba

e'

e"

+i

= M ' + iM".

(5)

The conductivity, o-t, is related to 8 * by e* = 8' - ie" = e ' - i ( o ' / w % )

(6)

The experimental data of M" obtained by ac bridge measurements are shown in Fig. 4. The temperature dependence of the frequency of the peaks of dielectric relaxation, e~, and electric modulus, M", is shown in Fig. 5. The plot log fm versus 1/T is linear within the observable temperature and frequency ranges, so that we assume that fm is given by a simple Arrhenius formula: fm = fm0exp( -

W/kT).

(7)

1E+04= 1 1E+0~ 2 1E+02 ,~, 1E+01

~

•

1E+0(

1E-01

1 E-02 2.2

214

216

218 3 1000/T [l/K]

312

314

3.6

Fig. 5. Temperaturedependencesof dielectricrelaxation(•), electricmodulus( [] ) and internalfriction( * ) in: (1) 50P20s--40FeO-10BaO; (2) 50PzOs-30FeO-20BaO;(3) 50P2Os-20FeO-30CaOglasses.

L. Murawski, Rd. Barczyhski /Journal of Non-Crystalline Solids 185 (1995) 84-93

As shown in Table 1, the activation energy, W, of the de conductivity, the dielectric relaxation is the same within experimental error. For comparison, we have also included in Table 1 data previously reported by Chomka and Samatowicz [13] of the activation energy for internal friction. These results confirm the correlation between the dc conductivity, dielectric relaxation and internal friction. We have found that the dielectric loss peaks obey the BNN relation (Eq. (1)). If we assume that p = 1 in our glasses then the BNN relation is fulfilled for A e = E s --6® = 11.4-13.4 in the system with CaO and for A e = 17.6-18.7 in BaO-containing glasses. The magnitude of dielectric relaxation, A e, is very close to its value obtained from the Kramers-Krrnig relation assuming that the relaxation spectra in these glasses are symmetrical.

4. Discussion The Hunt [16,17] theory describes dielectric relaxation in electronic and ionic conducting glasses. His basic concept is to differentiate two relaxation processes in two frequency ranges: below and above the dielectric loss peak. In the high-frequency range (to > tom), the relaxation processes have a local (parallel) character and can be described as hopping between the centers in pairs. In this range a distribution in relaxation time with an exponential dependence of random variables, i.e., R - the hopping distance, is known to give non-Debye behaviour with ~c cx tos, s < 1 [20]. Consequently, the pair approximation holds, which yields the conductivity expression O-t(to) = O-de[1 + A ( t o / t o m ) S ] ,

(8)

where s < 1 and A is a constant which depends on the type of pair approximation relevant in the network. The crossover frequency is the frequency of peak, tom, at which the individual parallel pair processes percolate and that cause the appearance of series processes. The series processes in the lowfrequency range are non-local and can be treated as percolation of individual particles over macroscopic distances in clusters or chains. For to < tom, a fractal

89

Table 2 Parameters of numerical fitting for 50P205 -30FeO-20CaO

t CC)

K(d)

r

A

s

17 27 42.5 62 86.5

0.001 0.0012 0.0019 0.0025

1.44 1.30 1.4 1.22

0.045 0.065 0.053 -

0.67 0.665 0.67 -

structure of dusters is responsible for relaxation currents and the conductivity has the form O't(to) = Ordc[ 1 "k"K ( d ) ( t o / t o m ) r ] ,

(9)

where r.= 1 + d - df > 1; d is the dimensionality of the space containing relevant clusters and d~ is the fractal dimensionality of such clusters. K ( d ) is a dimensionally dependent constant related to the statistics of the contributing clusters. We have applied this theory to the results of dielectric loss measurements in transition metal oxide glasses. The calculated values of K(d), r, A and s are given in Table 2. These parameters were obtained by fitting the theoretical relation of 8~(to) to the experimental curves from Fig. 3 assuming that ~'(to) is linear in a log-log scale below and above the peak. From Eqs. (7) and (8), e~(to) are seen to be

for

< Wm O)r - 1

8'~( to) = o'dcK( d ) - 80tom~

(10)

and for to > tom tos-1

= O-

oa--$

80 tom

(11)

The values of s and r are reasonable and this result may confirm the applicability of Hunt's theory to our glasses. If transport takes a place in three dimensions, it is possible to calculate d o which is the fractal dimensionality of the cluster. Knowing (from Table 2) that the average value of r = 1.4 and assuming d = 3, one can find that df = 2.6. This means that in clusters the percolation paths also have three-dimensional character. It is fairly difficult to say anything about the dependence of s and r on temperature because of the limited amount of data, so we evaluated only average values of r and s.

90

L. Murawski, RJ. Barczy~ski/Journal of Non-Crystalline Solids 185 (1995) 84-93

1 E-04}I

10MHz

1E-09

1E-1( ,, ., . . . . . . . . . . . . . . . . ,,r", .... . . . . . 1E-13 '1E'1~' 1E-11 1E-10 1E-09

'1E:08

'. . . . . . . . '1'E'.-07 ' '1'E'06

1E-05

% [~%m -1] Fig. 6. Room temperature ac conductivity, o'~, as a function of dc conductivity, o'd~,in different TMI glasses. X, TeO2-V2Os; I , p2os-v2os; +, P2Os-FeO; A, P2Os-FeO-MO; D, P2Os-V2Os-MO; M = Mg, Ca, Sr, Ba. This implies that on a l o g - l o g scale o,=--f(C&c) should be linear with a slope of (1 - s). Fig. 6 shows that dependence for all glasses investigated. It should be noted that ~ c was measured by an ac bridge. From the slope we have obtained s = 0.70 for f = 10

One can notice in Eq. (11) that ~c a trot. From the BNN relation, tom = crdc/8oA¢ and the result obtained for cra~ is S

1--s

crac=A(toeo A s ) trac

.

1E+03=

'..... 4-

1E+0"2

411K '~

+ +

A

+

379K "~

X

1E+01

348K

•

X X

D

331 #

+ A

r"'l (CI

1

X E3

•

,4A

O

296K •

4,,A

X

~

t.O 1E+00

+

X

I

X rm

1

I

tm

.4.,,L

X

4A

X E3 ~

~

1

•

4-

• X

i

X

X

1

1

1 E-01

1E-O 1E+01

,

,

i

' ' 1"'' E +. 0.2 . . . .

"{E+03

"'"' ' " ' '"~'"'"1E+04

f [Hz]

Fig. 7. 8" as a function of frequency in 50P2Os-20FeO-30CaO glass.

t

i J =ill

1E+05

L. Murawski, R.L Barczyhski/Journal of Non-Crystalline Solids 185 (1995) 84-93

1E+05-

1E-08

1E+OL

1E-09

~2 1E+03

1E-10

91

# d.

I E+02:

1E-11

1E+011 2.2

2.4

2.6

2.8 IO00/T [l/K]

3

1E-12 3.4

3.2

Fig. 8. The dc conductivity, O'dc, and frequency,/~"-const, as a function of reciprocal temperaturein 50P2Os-20FeO-30Ca O glass.

kHz, s = 0.74 to 0.76 for f = 1 M H z and 10 MHz. These values correspond to the average s obtained from the frequency-dependent ~¢ = A tos measured

at the same temperature. It should be mentioned that Ngai's theory also predicts the same relation between ~ c and O'dc [21].

100: 200K x

222K X

182K

X 0

167K ~

10

X

123

X

E3

154K

• X

[] r~

"4-

Y'~

4-

[]

-4-

+

Y<

•

•

•

143K

1E+01

i

i

i

i

i i i 1 ~

1E+02

i

X

•

[]

4-

0.1

• X

i

i

i

X IS]

[]

"P

-.F

+

•

•

~

X

4-

i l l l l

1E+03 f [Hz]

04

Fig. 9. e" as a function of frequency in 40P205-60V205 glass.

1E+05

L. Murawski, R.L Barczyhski/Journal of Non-Crystalline Solids 185 (1995) 84-93

92

Another result of Hunt's theory is prediction of the behaviour of the frequency dependence which can be scaled so that curves for different temperatures can be made to coincide. It easy to find out that an Arrhenius dependence should be observed not only for the peak frequency, fro, but also for any other frequency below or above the peak. Fig. 7 shows a typical dependence of ~" as a function of frequency for 50P205-30FeO-20CaO glass. For any ¢ " = constant the frequency fe,,=constant obeyed the Arrhenius relation with the same activation energy as the dc conductivity. This is presented in Fig. 8 where the frequency is plotted as a function of reciprocal temperature for e" = 10, 1 and 0.4. The de conductivity plot is also shown for comparison. Apparently all exhibit identical activation energy: 0.63 eV. The same procedure was applied to P2Os-V205 glasses where it was impossible to measure the dielectric loss by the absorption current method. Fig. 9 presents e"(to) for 60V2Os-40P205 glass measured by an ac bridge at different temperatures between 143 and 250 K. For e " = 5 we found that Wp,o = 0.34 eV. The activation energy of dc conductivity in the same range of temperatures was WDC = 0.31 eV. In Table 3 we compare the activation energies, WDC, WRD, and also internal friction, WIF [22], for all V2Os-P205 glasses. The activation energy for internal friction is slightly lower than Woc and WRO because the internal friction was measured at lower temperatures than 8" and the dc conductivity. The Hunt theory is consistent with our experimental data on mechanical and dielectric relaxation and dc conductivity in TMI glasses. The mechanical stress and also the electric field may change the probability of hopping in a certain direction. In the low-frequency range it leads to diffusion within clus-

Table 3 Activation energy of dc conductivity Woc, dielectric losses, WRo, and internal friction, Wit, in (100- x)P2Os-xV205 glasses

x

Woc

w~D

WIF

(mol %)

(eV)

(eV)

(eV)

40 50 60 70

0.35 0.37 0.31 0.30

0.39 0,38 0.34 0.32

0.35 0.27 0.23 0.20

ters; at higher frequencies, polaron motion takes place between paired sites with a distribution in hopping distance. According to the Hunt theory, the activation energy of dielectric relaxation in the domain of clusters and in pairs of centers is the same. This may also be true for mechanical loss. Our experimental results have confirmed that all three processes exhibit the same activation energy.

5. Conclusion

Dielectric properties of iron and vanadium phosphate glasses containing different glass modifiers over a broad range of frequency and temperature can be described in the framework of the Hunt theory. It has been shown that, in the low-frequency range, hopping in clusters has a percolative nature and takes place in three dimensions. In the high-frequency range, the pair approximation hold, and the relation between ac and dc conductivity is ~c at tr~1-s (for to = constant) in all TMI glasses investigated. Another important result that confirms the Hunt theory is that frequency scaling for e"(to) is obeyed over a wide range of frequencies. The authors would like to thank Dr A. Hunt for helpful comments.

References [1] M. Sayer and A. Mansingh, Phys. Rev. B6 (1972)4629. [2] L. Murawski, C.H. Chung and J.D. Mackenzie, J. Non-Cryst. Solids 32 (1979) 91. [3] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1. [4] I.G. Austin and N.F. Mott, Adv. Phys. 18 (1969) 41. [5] M. Sayer, A. Mansingh, J.M. Reyes and G. Rosenblatt, J. Appl. Phys. 42 (1971) 2857. [6] A. Mansingh and J.M. Reyes, J. Non-Cryst. Solids 7 (1972) 12. [7] M. Sayer and A. Mansingh, in: Non-Crystalline Semiconductors, Vol. 3, ed. M. Pollak (CRC, Boca Raton, FL, 1987) p. 1. [8] A. Mansingh, in: Non-Debye Relaxation in Condensed Matter, ed. T.V. Ramakrishnan and M. Raj Laksmi (World Scientific, Singapore, 1987) p. 249. [9] A.R. Long, Adv. Phys. 31 (1982) 553.

L. Murawsld, RJ. Barczyhski /Journal of Non-Crystalline Solids 185 (1995) 84-93 [10] [11] [12] [13]

S.R. Elliott, Adv. Phys. 36 (1987) 135. H. Namikawa, Res. Electrotech. Lab. (Tokyo) 757 (1975). H. Namikawa, J. Non-Cryst Solids 18 (1975) 173. W. Chomka and D. Samatowicz, J. Non-Cryst. Solids 57 (1983) 327. [14] J.L Barton, Verres R6fract. 20 (1966) 328. [15] T. Nakajima, Annual Report, Conf. on Electric Insulation and Dielectric Phenomena (National Academy of Sciences, Washington, DC, 1972) p. 168. [16] A. Hunt, J. Phys.: Condens. Matter 2 (1990) 9055; 3 (1991) 7831; 4 (1992) 6957.

93

[17] A. Hunt, J. Non-Cryst. Solids 134 (1991) 267; 144 (1992) 21; 160 (1993) 183. [18] B.V. Hamon, Prec. IEE (London) 99 (1952) 115. [19] P.B. Macedo, C.T. Moynihan and R. Bose, Phys. Chem. Glasses 13 (1972) 171. [20] M. Pollak and G.E. Pike, Phys. Rev. Lett. 28 (1972) 1449. [21] K. Ngai, in: Non-Debye Relaxation in Condensed Matter, ed. T.V. Ramakrishnan and M. Raj Laksmi (World Scientific, Singapore, 1987)p. 23. [22] D. Bednarczyk, thesis, Technical University of Gdafisk (1988).