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Electrical properties of copper phosphate glasses II. Dielectric properties
Journal of Non-Crystalline Solids 79 (1986) 353-366 North-Holland, Amsterdam
353
ELECTRICAL PROPERTIES OF COPPER PHOSPHATE GLASSES II. Dielectric properties Alicia DURAN, Jos6 R. JURADO and Jos6 M. FERNANDEZ NAVARRO lnstituto de Cerhmica y Vidrio, C.S.1.C., Arganda del Rey, Madrid, Spain
The ac and dc electrical properties of the P2Os-BaO-CuO glass system have been measured. TSPC and TSDC experiments and dc conductivity as a function of time indicate the predominantly electronic character of these glasses. The conduction process can be basically explained by a polaron hopping model in an adiabatic regime. Conductivity values which depend on the glass microstructure and switching phenomena are observed. The filamentary-feature of this process suggests a Poole-Frenkel mechanism. A Debye dielectric relaxation non-simple process is deduced from the frequency and temperature dependence of loss tangent and dielectric constant. The activation energies agree with those determinated from dc measurements, suggesting a unique electronic hopping conduction mechanism in both regimes. The ac and dc electrical properties are strongly affected by the glass composition and essentially by the redox Cu÷/Cut ratio. A conduction model accounting for ac and dc behaviour is finally proposed.
1. AC electrical behaviour
Although there is abundant literature about the dielectric properties of glasses containing transition metallic ions (TMI) [4,20-23] only a few papers have been published concerning the dielectric behaviour of glasses containing copper as the only TMI, [4,12]. In this work, the dielectric properties have been studied using ac measurements, analyzing their dependence on temperature and frequency. Loss tangent, tg 3, dielectric constant, c', and total conductivity, ot, have been obtained, by varying the temperature between 20-200°C and frequency between 1 0 - 1 0 6 H z . The measurements were made with the two points method. The sample, situated inside the sample holder, is in contact with two polished and cleaned brass electrodes, the same device being used for room and high temperatures. The AC bridge system is used. A Wayne-Kerr-Un. Bridge B224 was utilized for taking data at a fixed frequency of 1 kHz, while the frequency dependent measurements were obtained by a Hewlett-Packard impedance analyzer, model 419 2A LF. The equipment allows the direct measurement of capacity, loss tangent and conductance values. Fig. 1 shows the loss tangent versus the frequency logarithm, at different temperatures, for the glass $1/2. The characteristic peaks of a dielectric 0022-3093/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
14
166 °C
.~1 °C
I
2
Fig. 1. Loss tangent versus frequency, glass S1/2.
Sa
22
30-
5 Log "v~
4
GLASS
5
S1/2
6
E-
E
rn
~b
A. Dur&n et aL / Electrical properties of copper phosphate glasses 11
355
dispersion process can be observed similar to those appearing in iron and vanadium glasses [20,23]. The wide and unsymmetrical peaks shift to higher frequencies with increasing temperatures. This behaviour indicates a Debye dielectric relaxation process, the width and shape of these peaks being very useful for a study of the dielectric properties and the kind of process taking place. The Debye equations describing this relaxation phenomenon show a singular value r 0 and a narrow and symmetrical peak with a well-defined frequency of maximum absorption. Such a model is, however, too simple. In a condensed phase the environments of different molecules will vary; the magnitude of the interacting forces, of the directing forces, or of the thermal fluctuations will all change from place to place and from time to time. Probably, every dipole or ion in its own situation has, at any moment its own intrinsic relaxation time. In measurements an average over all possible conditions will normally be obtained and a spread of relaxation times distributed around the most probable value will generally follow. For such a distribution G ( r ) of relaxation times, the complex dielectric constant results, e*=e~+(e
,~° G(T) d r _ e ~ ) j 0 1 1 +io~r
(1)
where f ~ G ( r ) d r = 1. When a distribution of relaxation times is introduced irrespective of its form, the frequency of maximum absorption is still given by Oama×= 1 / r o,
(2)
where r 0 is now the most probable relaxation time. The dielectric constant measurements show that e' changes sharply with frequency between 102 and 105 Hz, then decreases more slowly with increasing v. A shift of the inflection points to higher frequencies with increasing temperature is also observed. The bistable dipole model provides a basis for understanding the temperature dependence of the dielectric properties of glass. The probability of a transition of the oscillating charge in terms of Boltzmann statistics is expressed as
~0 = A exp( - E a / R T
).
(3)
As r = l~o, then r = ro e x p ( E a / R T
(4)
),
where E a is an activation energy for the relaxation process and r 0 is an intrinsic relaxation time. By combining eq. (4) and the Debye equations it is possible to describe the temperature variation in the location of the tg ~ loss peak, the maximum appearing at J
-1/2
Vm~× = V o ( e s / e ~ )
exp(-E,/RT).
(5)
356
A. Durhn et al. / Electrical properties of copper phosphate glasses H
GLASS S I / 2 5" o
43
o
o
d
I
t
2
2,5
105/T[°K] Fig. 2. Log /)max versus 1/T, glass S1/2.
S2/i SYSTEM o $2/1 • S2/2
I0-
,,~.,-/
. s2/,
o~-'"
/
o
.
~- ~=.____._o .......--~/=~
,~o Fig. 3. Dielectric constant ~' versus temperature, series S2/i.
~bo
~o
357
A. Dur?m et al. / Electricalproperties of copper phosphate glasses II
o
$2/1
$2/I
SYSTEM
o $2/2 •
S2/3
• $2/4
So
o--..
I
q
I
4
5
6
Log v )
Fig. 4. Dielectricconstant c' versus frequency,series S2/i. Fig. 2 shows /"max against 1 / T for glass S1/2. E a w a s calculated according to eq. (5); the linear dependence indicates that the relaxation mechanism is a thermally activated process; the energy value, E a = 1.20 eV, coincides with the value obtained from dc measurements, suggesting that the conduction mechanism in both regimes is the same. The three series of glasses studied present an analogous temperature and frequency dependence of both tg 8 and c', and the considerations applied to glass S1/2 can be extended to every glass considered. The temperature dependence of the dielectric constant ~', measured at 1 kHz, is similar for the three series; fig. 3 represents the $ 2 / 1 system behaviour. Fig. 4 shows the frequency dependence of ~' for the same series of glasses, measured at room temperature. A strong temperature and frequency dependence of dielectric constants for glasses with high Cu + content is observed; this variation diminishes with decreasing Cu+/Cu~ ratio, ~' becoming T and 1, independent for very low cuprous contents. 1.1. A C conductivity
The total conductivity, or, of the glasses has been calculated from the tg and e' values obtained by varying the temperature and frequency; a t is given by (i t = Od c qL Oac.
(6)
A. Durhn et al. / Electrical properties of copper phosphate glasses I1
358
\ -6
S1/i
~
o $1/2
\
o $I/3 • Sl/4
\\
-7
SYSTEM
-I0.
I I
I 2
3
K)3/T [°K] Fig. 5. Log o t versus 1 / T at 1 kHz, series S 1 / i .
Fig. 5 exhibits the dependence of conductivity on 1/T for the series S1/i glasses. Every curve presents two stretches of different slopes, with a transition temperature within a narrow range for all the compositions. A similar behaviour is observed in the other two series, S R / i and S2/i. The temperature dependence of ot implies two different activation energies for the conduction process. Phonon activated transport mechanisms predict an analogous behaviour [4,24]. The temperature variation of the total conductivity, measured at different frequencies for glass $1/2, shows an anomalous feature. Normally, ot increases with increasing frequencies; in this case all the curves intersect, and a small diminution of conductivity with frequency is observed. This pattern may be understood in two ways. If the glass is phase-separated and the precipitated phase has greater conductivity than the matrix phase, and if it is surrounded by a barrier through which the carriers must tunnel, a diminution of conductivity with frequency is predicted when v >~ Vmax [26]. The TEM observation of glass $ 1 / 2 showed an important phase separation after thermal treatment, as was pointed in Part I. If the treatment is prolonged or the glass is subjected to high fields, Cu20 crystallization appear which can be perfectly detected by X-ray diffraction. Thus, although the separated phase composition has not been determined, it is likely that this phase is enriched in cuprous oxide and it has a higher conductivity than the matrix phase. On the other hand, some reaction between the sample and the electrodes
359
A. Durfm et al. / Electrical properties of copper phosphate glasses H -5
• s2/]
S2/i
SYSTEM
-6
_
• s2/4
-7
•
mo
•
-8-
-9
-I0
I
- -
4
--I
I
I
5
6
7
Log
Fig. 6. Log ot versus frequency, series S2/i.
was observed; the a p p e a r a n c e o f electrochemical i n t e r a c t i o n s can also explain this a n o m a l o u s behaviour. T h e frequency d e p e n d e n c e of the c o n d u c t i v i t y has also b e e n studied. Fig. 6 shows the S 2 / i system data, the other two series results b e i n g similar. T h e linear v a r i a t i o n of log o t against log ~ indicates that O t O~ P n .
T a b l e 1 represents n values of the S 1 / i a n d S 2 / i series glasses, c a l c u l a t e d b y the m i n i m u m square m e t h o d . A s can b e observed, n varies f r o m 0 . 8 - 0 . 9 for low Cu + c o n t e n t s to 0.6 for higher c o n t e n t s of c u p r o u s copper.
Table 1 Cu+/Cut variation of n parameter Glass
Cu +/Cut
n
$1/2 S1/3 S1/4 S1/5 $2/1 $2/2 $2/3 $2/4
0.34 0.13 0.02 0.04 0.21 0.06 0.09 0.03
0.62 0.87 0.89 0.99 0.56 0.75 0.56 0.80
A. Dur&n et al. / Electrical properties of copper phosphate glasses H
360
In the polaronic model, the conductivity fits the equation Ot (Z ~,0.8
and the mechanism can explain the behaviour of some glasses. However, the lower values of n suggest a more complex process, in which other contributions to the hopping conduction can appear.
2. Electrical behaviour and redox equilibrium The Mott expression for the conductivity predicts a dependence on the T M I concentration in its low valency state such as
oo:c(1 -c) with a m a x i m u m appearing at c = 0.5. Fig. 7 shows the dc conductivity logarithm (measured at room temperature), against the C u + / C u t ratio; ode values at 550 K follow the same form. Three aspects can be observed: an initial increase, a subsequent stabilization between 10 and 30 mol.% of Cu ÷ and a strong increase of the conductivity for higher contents of cuprous copper. This pattern does not agree with the behaviour
/
/
-8-
"7
-IC
-12
/
I
0,I
I
0,2 Cu÷ICu!
Fig. 7. Log Ode versus C u + / C u t ratio.
I
0,3
0,4
361
A. Durhn et al. / Electrical properties of copper phosphate glasses II
I00 °C- I kHz
/
-8
o
c)
-I0
• S1 li
-12
o $21 i o SP,/i
I
O, 1
0,12
(~3
I
0,4
Cu+/Cut Fig. 8. Log ot versus Cu+/Cut ratio.
predicted by Mott. To explain it, it has been necessary to use structural arguments. Tsuchiya and Moriya [12] have measured the chemical durability of phosphate glasses containing copper oxide. The copper dissolution curves in relation to the C u + / C u t ratio show a maximum near 0.27 and a minimum around C u + / C u t = 0.5. By comparing these curves to figs. 7 and 8 it can be noted that the minimum values of o appear in the maximum copper dissolution range, increasing strongly when the dissolution of copper decreases. This behaviour suggests the existence of two different sites for the Cu + ions: one, forming C u + - O - C u 2+ bonds, responsible for the hopping conduction, by electron transference between localized sites, Cu+_O_Cu
2+ ----) C u Z + _ O _ C u
+
and the other in clusters, within which Cu + ions should have a higher mobility, being able to act as charge carriers in the ionic conduction contribution detected by TSDC. On the other hand, Drake and Scanlan [3] have concluded from the apparent molar volume of oxygen (AMV) behaviour in phosphate glasses containing copper, that the Cu + and Cu 2+ ions are in different ligand field
362
A. Durhn et al. / Electrical properties of copper phosphate glasses H
14 ¸
o
0 r3
E
12
Y no
e ~
e
0
o Q
o
I 0,I
,D
o Q
I 0,2
o o----E~ o
I
0,3
~,
I 0,4
Cu+/Cut
Fig. 9. AMV of oxygen in copper phosphate glasses.
environments. This fact can explain the high activation energies of these glasses. Austin and Mott [2] have suggested that the ~0 energy may consist of two terms: that corresponding to the excitation energy of carriers from one kind of site to the other and the polaron hopping energy between equivalent sites. Drake and Scanlan [3] have fulfilled this interpretation with the assumption that some of the Cu ÷ and Cu 2÷ ion sites occupy a spread of energy levels that just overlap, producing impurity levels available for phonon activated hopping transport. The dielectric properties and their characteristic parameters are also dependent on the redox ratio Cu +/Cut. Fig. 8 represents the total conductivity against this ratio, showing a similar qualitative behaviour to dc conduction. The dielectric constant, c', takes constant values up to 10 mol.% of Cu ÷, and then increases with increasing C u ÷ / C u t ratio. Tsuchiya and Moriya [12] have reported similar results in binary copper phosphate glasses. Analyzing as a whole the temperature and frequency dependence of the dielectric constants of glasses with different Cu ÷ contents and the redox relation dependence of ~' and ot, different local coordinations of Cu ÷ and Cu 2+ ions appear to be probable. Fig. 9 [3] shows the apparent molar volume (AMV) of oxygen in a series of copper phosphate glasses containing Cu ÷ and Cu 2÷ with the same total Cu
A. Durdm et al. / Electrical properties of copper phosphate glasses I1
363
content. From this curve, the authors deduce that the Cu + and Cu 2+ ions are in different structural environments, suggesting that the Cu + coordination is similar in crystalline Cu 2° and in the phosphate glasses. C u 2 0 has a singular crystalline structure, the cuprite, in which the metallic ion is linearly coordinated with two oxygen atoms, whilst the Cu 2+ ions are present in these glasses in a distorted octahedral oxygen environment. By comparing the dc and ac conductivity graphs against the C u + / C u ' ratio with the AMV curves, it appears reasonable to associate the redox relation dependence of the conductivity with the different structural sites of cuprous and cupric ions.
3. Conduction mechanism
From dc measurements a hopping conduction mechanism, according to the polaronic model has been proposed. The main features of the process fit this model rather well, although the activation energies which result are too high. These large energies can be explained if it is supposed that the conduction is ruled by a polaron hopping mechanism between non-identical sites. The ac measurements introduce new data for a better understanding of the conduction process. Activation energies involved in the dielectric relaxation process coincide with those calculated from dc measurements, implying a unique conduction mechanism in both regimes. More evidence supporting this is supplied by the similarity between the ac and dc conductivity curves against the Cu+/Cu~ ratio. The cuprous content dependence of the AMV of oxygen and the copper dissolution diagrams clearly indicates that the local coordinations of Cu + and Cu 2+ ions are different, also suggesting the existence of cuprous ions in different structural environments. Thermoelectric measurements have proved that the Seebeck coefficient is temperature independent [3]. A simple explanation of this feature is the assumption that some of the Cu + and Cu 2+ ion sites occupy a spread of energy levels that just overlap. The electron exchanging among some centres produces impurity levels available for phonon activated bond edge hopping. The ac conductivity tests have also showed the redox ratio dependence of n in the relation between conductivity and frequency (a t cc v ~). For low cuprous contents, n - 0.8, near the value predicted for a phonon activated mechanism and when the C u + / C u t ratio increases, n takes lower values. It is possible to explain this phenomenon taking into account the different structural sites that cuprous ion can occupy. In the low Cu + content range, these ions are likely to be dispersed and linked to the vitreous network, forming C u + - O - C u 2+ bonds. Thus, the conduction would be produced by electron transference between localized ,dtes, in agreement with the small polaron model.
364
A. Durhn et al. / Electrical properties of copper phosphate glasses H
As the Cu + ion content increases, and according to the AMV behaviour, the cuprous ions would tend to cluster in environments similar to those occupied in crystalline Cu20. In this region, the n value decreases, indicating that the conduction mechanism is not only phonon activated. The impurity levels suggested by Drake and Scanlan provoke an additional conduction by the band edge effect. However, this mechanism is also phonon activated and the frequency dependence of the conductivity thus results in n -- 0.8. The crystalline cuprous oxide is an intrinsic p semiconductor, whose gap is around 1.5 eV. The impurity levels, being acceptors, are situated at 0.3-0.6 eV from the valency band edge. At room temperature, and below 300°C, Cu20 is generally unstable, showing a great trend to gain oxygen. This feature reinforces its p-type (by holes) conduction and explains the appearance of photoconductivity effects [27]. The structural environments that the cuprous ions occupy in glasses with high Cu + contents, similar to those of Cu20, may probably show the same kind of electrical behaviour as the crystalline state. The impurity levels in the energy gap will produce an overlap in the conduction and valency bands, because it is an amorphous material. Under this condition a delocalized states band conduction contribution should be possible. This mechanism is frequency independent for ~, < 101° Hz. Thus the diminution of n in glasses with high Cu + contents, should be explained as the result of a polaron hopping process and a band conduction contribution. The cooperative rearrangement on switching involves a readjustment of the coordinating oxygen positions such that the Cu + and Cu 2+ ion environments become nearly the same. Thus, the energy levels of the two sets of impurity band described before, will tend to overlap one another, increasing the number of the carriers and the mobility as a result of the Mott semiconductor-metal transition. The shifting of the coordinating anions, without the rupture of any valency bands, leads to the conducting form in which the local environment of each centre is effectively identical. On the other hand, a local precrystalline structure should result from the rearrangement of Cu 2O by molecular clusters. The interaction among the ionic sites and the field is enhanced, under high fields, by the highly polarizable matrix. The local temperature increases in the preswitching process may produce a phase separation similar to that resulting after heat treatment. During switching, the high temperatures locally reached act on the segregated nuclei, provoking the crystallization of the conduction paths. The Cu20 phase is the only kind of crystal that appeared, this fact supporting the structural hypothesis proposed. Thus the conduction process in barium phosphate glasses containing copper as the unique TMI should be explained as a combined mechanism of polaronic hopping with a band edge effect contribution, and with extended states band conduction when the ratio Cu +/Cu, is high enough.
A. DurUm et al. / Electrical properties of copper phosphate glasses I1
365
4. Conclusions The electrical and dielectric properties of the P2Os-BaO-CuO glass system allow a better understanding of the behaviour of these materials clarifying the character of the conduction and the mechanism ruling this process. - T h e time dependence of dc conductivity indicates that conduction is mainly electronic for temperatures higher than that corresponding to the maximum of the TSPC curve. The initial polarization is interpreted as a dielectric relaxation process. Electrode polarization has not been observed. The polarization peak in the TSPC curve suggests a relaxation process which is probably produced by a trapped level density. The TSDC peak hints at a small dipolar contribution to the conduction. - The temperature dependence of the dc conductivity shows that the electronic conduction process is ruled by the activation energy W. The data fit the small polaron model in adiabatic regime. The high energy values are explained by supposing different coordination sites for Cu + and Cu 2+ ions, a term of carriers excitation between different sites appearing, which is added to the polaron hopping energy. - T h e linear behaviour of log I against V 1/2 during the preswitching process implies a thermal ionic (Shottky) or electronic (Poole Frenkel) mechanism. For fields of about 5 x 103 V, negative resistance and switching phenomena appear. The filamentary crystallization produced in this process points to a Poole-Frenkel preswitching process. - T h e temperature and frequency variation of the loss tangent and dielectric constant is explained as a Debye dielectric relaxation process with a relaxation times distribution G(-r). The activation energies of this process coincide with those obtained in a dc regime, suggesting that the conduction mechanism is the same in both regimes. - T h e frequency dependence of total conductivity fits the equation o t cc u", n being a function of the ratio C u + / C u t . For low Cu + contents n agrees with the theoretical predictions for phonon activated conduction mechanisms. The values obtained for higher cuprous copper concentrations may be explained by the appearance of delocalized states originating a band conduction contribution. - B y comparing the patterns of dc and ac conductivity curves against the redox relation, to the AMV curve, it may be concluded that the Cu + and Cu 2 ~ ions are in different coordination environments. - F r o m all the data a structural pattern of these glasses and a conduction mechanism model can be advanced. Some cuprous ions, dispersed and linked to the vitreous network, and forming C u + - O - C u 2+ bands, would be responsible for the polaronic and band edge conduction, both of them phonon activated. Cu + ions situated in the other environment, similar to that occurring in crystalline Cu20, could originate a delocalized states band conduction.
366
A. Dur&n et al. / Electrical properties of copper phosphate glasses H
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
C.F. Drake, I.F. Scanlan and A. Engel, Phys. Status Solidi 32 (1969) 193. I.G. Austin and N.F. Mott, Adv. Phys. 18 (1969) 41. C.F. Drake and I.F. Scanlan, J. Non-Crystalline Solids 4 (1970) 234. A.K, Bandyopadhyay, PhD Thesis, University of Sheffield (1976). M. Sayer and A. Mansingh, Phys. Rev. B6 (1972) 4629. I.G. Austin and M. Sayer, J. Phys. C7 (1972) 905. H. Hirashima and T. Yoshida, XI Int. Congress on Glass. Vol. II, Prague (1977) p. 365. O.S. Ershov, 1.V. Dimakov, T.P. Markova and M.M. Shultz, Inorg. Mater. Consult. Bur. Transl. 8 (1982) 1606. M. Regan and C.I. Drake, Mat. Res. Bull. 6 (1971) 487. M. Sayer and G.F. Lynch, J. Phys. C6 (1973) 3674. G.R. Moridi and C.A. Hogarth, 7th Int. Conf. on Amorphous and Liquid Semiconductors. Edinburgh University (1977) 688. T. Tsuchiya and T. Moriya, Cent. Glass Ceram. Res. Inst. Bull. 22 (1975) 2; 55. G.J. Simmons and G.W. Taylor, Phys. Rev. B6 (1972) 4793. B. Dutta and D.E. Day, J. Non-Crystalline Solids 48 (1982) 345. H.M. Gupta and R.J. Overstraeten, J. Phys. C7 (1974) 3560. F. Cusso P6rez, Ph D Thesis. Universit~t Aut6noma, Madrid (1980). C.M. Hong and D.E. Day, J. Am. Ceram. Soc. 64 (1981) 2; 61. M. Sayer et al., J. Appl. Phys. 42 (1971) 2857. C.K. Shih and G.J. Su, VII Int. Congress on Glass, Sect. 1-33. Paper 48, Brussels (1965). A. Mansingh, J.M. Reyes and M. Sayer, J. Non-Crystalline Solids 7 (1972) 12. G.S. Linsley et al., J. Non-Crystalline Solids 4 (1970) 208. K.W. Hansen, J. Electrochem. Soc. 112 (1965) 994. K.W. Hansen and M.T. Splann, J. Electrochem. Soc. 113 (1965) 895. D. Adler, Amorphous Semiconductors (CRC Press, Chemical Rubber Co., Cleveland, 1971). L.L. Hench and H.F. Schaake, Electrical properties of glass, in: Introduction to Glass Science, eds., L.D. Pye, H.J. Stevens and W.C. La Course (Plenum, New York, 1972) p. 583. G.R. Moridi and C.A. Hogarth, 2nd European Conference on Condensed Matter, Budapest (1974). A.V. Ioffe and A.F. Ioffe, Zh. Eksp. Teor. Fiz. 6 (1936) 737.
353
ELECTRICAL PROPERTIES OF COPPER PHOSPHATE GLASSES II. Dielectric properties Alicia DURAN, Jos6 R. JURADO and Jos6 M. FERNANDEZ NAVARRO lnstituto de Cerhmica y Vidrio, C.S.1.C., Arganda del Rey, Madrid, Spain
The ac and dc electrical properties of the P2Os-BaO-CuO glass system have been measured. TSPC and TSDC experiments and dc conductivity as a function of time indicate the predominantly electronic character of these glasses. The conduction process can be basically explained by a polaron hopping model in an adiabatic regime. Conductivity values which depend on the glass microstructure and switching phenomena are observed. The filamentary-feature of this process suggests a Poole-Frenkel mechanism. A Debye dielectric relaxation non-simple process is deduced from the frequency and temperature dependence of loss tangent and dielectric constant. The activation energies agree with those determinated from dc measurements, suggesting a unique electronic hopping conduction mechanism in both regimes. The ac and dc electrical properties are strongly affected by the glass composition and essentially by the redox Cu÷/Cut ratio. A conduction model accounting for ac and dc behaviour is finally proposed.
1. AC electrical behaviour
Although there is abundant literature about the dielectric properties of glasses containing transition metallic ions (TMI) [4,20-23] only a few papers have been published concerning the dielectric behaviour of glasses containing copper as the only TMI, [4,12]. In this work, the dielectric properties have been studied using ac measurements, analyzing their dependence on temperature and frequency. Loss tangent, tg 3, dielectric constant, c', and total conductivity, ot, have been obtained, by varying the temperature between 20-200°C and frequency between 1 0 - 1 0 6 H z . The measurements were made with the two points method. The sample, situated inside the sample holder, is in contact with two polished and cleaned brass electrodes, the same device being used for room and high temperatures. The AC bridge system is used. A Wayne-Kerr-Un. Bridge B224 was utilized for taking data at a fixed frequency of 1 kHz, while the frequency dependent measurements were obtained by a Hewlett-Packard impedance analyzer, model 419 2A LF. The equipment allows the direct measurement of capacity, loss tangent and conductance values. Fig. 1 shows the loss tangent versus the frequency logarithm, at different temperatures, for the glass $1/2. The characteristic peaks of a dielectric 0022-3093/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
14
166 °C
.~1 °C
I
2
Fig. 1. Loss tangent versus frequency, glass S1/2.
Sa
22
30-
5 Log "v~
4
GLASS
5
S1/2
6
E-
E
rn
~b
A. Dur&n et aL / Electrical properties of copper phosphate glasses 11
355
dispersion process can be observed similar to those appearing in iron and vanadium glasses [20,23]. The wide and unsymmetrical peaks shift to higher frequencies with increasing temperatures. This behaviour indicates a Debye dielectric relaxation process, the width and shape of these peaks being very useful for a study of the dielectric properties and the kind of process taking place. The Debye equations describing this relaxation phenomenon show a singular value r 0 and a narrow and symmetrical peak with a well-defined frequency of maximum absorption. Such a model is, however, too simple. In a condensed phase the environments of different molecules will vary; the magnitude of the interacting forces, of the directing forces, or of the thermal fluctuations will all change from place to place and from time to time. Probably, every dipole or ion in its own situation has, at any moment its own intrinsic relaxation time. In measurements an average over all possible conditions will normally be obtained and a spread of relaxation times distributed around the most probable value will generally follow. For such a distribution G ( r ) of relaxation times, the complex dielectric constant results, e*=e~+(e
,~° G(T) d r _ e ~ ) j 0 1 1 +io~r
(1)
where f ~ G ( r ) d r = 1. When a distribution of relaxation times is introduced irrespective of its form, the frequency of maximum absorption is still given by Oama×= 1 / r o,
(2)
where r 0 is now the most probable relaxation time. The dielectric constant measurements show that e' changes sharply with frequency between 102 and 105 Hz, then decreases more slowly with increasing v. A shift of the inflection points to higher frequencies with increasing temperature is also observed. The bistable dipole model provides a basis for understanding the temperature dependence of the dielectric properties of glass. The probability of a transition of the oscillating charge in terms of Boltzmann statistics is expressed as
~0 = A exp( - E a / R T
).
(3)
As r = l~o, then r = ro e x p ( E a / R T
(4)
),
where E a is an activation energy for the relaxation process and r 0 is an intrinsic relaxation time. By combining eq. (4) and the Debye equations it is possible to describe the temperature variation in the location of the tg ~ loss peak, the maximum appearing at J
-1/2
Vm~× = V o ( e s / e ~ )
exp(-E,/RT).
(5)
356
A. Durhn et al. / Electrical properties of copper phosphate glasses H
GLASS S I / 2 5" o
43
o
o
d
I
t
2
2,5
105/T[°K] Fig. 2. Log /)max versus 1/T, glass S1/2.
S2/i SYSTEM o $2/1 • S2/2
I0-
,,~.,-/
. s2/,
o~-'"
/
o
.
~- ~=.____._o .......--~/=~
,~o Fig. 3. Dielectric constant ~' versus temperature, series S2/i.
~bo
~o
357
A. Dur?m et al. / Electricalproperties of copper phosphate glasses II
o
$2/1
$2/I
SYSTEM
o $2/2 •
S2/3
• $2/4
So
o--..
I
q
I
4
5
6
Log v )
Fig. 4. Dielectricconstant c' versus frequency,series S2/i. Fig. 2 shows /"max against 1 / T for glass S1/2. E a w a s calculated according to eq. (5); the linear dependence indicates that the relaxation mechanism is a thermally activated process; the energy value, E a = 1.20 eV, coincides with the value obtained from dc measurements, suggesting that the conduction mechanism in both regimes is the same. The three series of glasses studied present an analogous temperature and frequency dependence of both tg 8 and c', and the considerations applied to glass S1/2 can be extended to every glass considered. The temperature dependence of the dielectric constant ~', measured at 1 kHz, is similar for the three series; fig. 3 represents the $ 2 / 1 system behaviour. Fig. 4 shows the frequency dependence of ~' for the same series of glasses, measured at room temperature. A strong temperature and frequency dependence of dielectric constants for glasses with high Cu + content is observed; this variation diminishes with decreasing Cu+/Cu~ ratio, ~' becoming T and 1, independent for very low cuprous contents. 1.1. A C conductivity
The total conductivity, or, of the glasses has been calculated from the tg and e' values obtained by varying the temperature and frequency; a t is given by (i t = Od c qL Oac.
(6)
A. Durhn et al. / Electrical properties of copper phosphate glasses I1
358
\ -6
S1/i
~
o $1/2
\
o $I/3 • Sl/4
\\
-7
SYSTEM
-I0.
I I
I 2
3
K)3/T [°K] Fig. 5. Log o t versus 1 / T at 1 kHz, series S 1 / i .
Fig. 5 exhibits the dependence of conductivity on 1/T for the series S1/i glasses. Every curve presents two stretches of different slopes, with a transition temperature within a narrow range for all the compositions. A similar behaviour is observed in the other two series, S R / i and S2/i. The temperature dependence of ot implies two different activation energies for the conduction process. Phonon activated transport mechanisms predict an analogous behaviour [4,24]. The temperature variation of the total conductivity, measured at different frequencies for glass $1/2, shows an anomalous feature. Normally, ot increases with increasing frequencies; in this case all the curves intersect, and a small diminution of conductivity with frequency is observed. This pattern may be understood in two ways. If the glass is phase-separated and the precipitated phase has greater conductivity than the matrix phase, and if it is surrounded by a barrier through which the carriers must tunnel, a diminution of conductivity with frequency is predicted when v >~ Vmax [26]. The TEM observation of glass $ 1 / 2 showed an important phase separation after thermal treatment, as was pointed in Part I. If the treatment is prolonged or the glass is subjected to high fields, Cu20 crystallization appear which can be perfectly detected by X-ray diffraction. Thus, although the separated phase composition has not been determined, it is likely that this phase is enriched in cuprous oxide and it has a higher conductivity than the matrix phase. On the other hand, some reaction between the sample and the electrodes
359
A. Durfm et al. / Electrical properties of copper phosphate glasses H -5
• s2/]
S2/i
SYSTEM
-6
_
• s2/4
-7
•
mo
•
-8-
-9
-I0
I
- -
4
--I
I
I
5
6
7
Log
Fig. 6. Log ot versus frequency, series S2/i.
was observed; the a p p e a r a n c e o f electrochemical i n t e r a c t i o n s can also explain this a n o m a l o u s behaviour. T h e frequency d e p e n d e n c e of the c o n d u c t i v i t y has also b e e n studied. Fig. 6 shows the S 2 / i system data, the other two series results b e i n g similar. T h e linear v a r i a t i o n of log o t against log ~ indicates that O t O~ P n .
T a b l e 1 represents n values of the S 1 / i a n d S 2 / i series glasses, c a l c u l a t e d b y the m i n i m u m square m e t h o d . A s can b e observed, n varies f r o m 0 . 8 - 0 . 9 for low Cu + c o n t e n t s to 0.6 for higher c o n t e n t s of c u p r o u s copper.
Table 1 Cu+/Cut variation of n parameter Glass
Cu +/Cut
n
$1/2 S1/3 S1/4 S1/5 $2/1 $2/2 $2/3 $2/4
0.34 0.13 0.02 0.04 0.21 0.06 0.09 0.03
0.62 0.87 0.89 0.99 0.56 0.75 0.56 0.80
A. Dur&n et al. / Electrical properties of copper phosphate glasses H
360
In the polaronic model, the conductivity fits the equation Ot (Z ~,0.8
and the mechanism can explain the behaviour of some glasses. However, the lower values of n suggest a more complex process, in which other contributions to the hopping conduction can appear.
2. Electrical behaviour and redox equilibrium The Mott expression for the conductivity predicts a dependence on the T M I concentration in its low valency state such as
oo:c(1 -c) with a m a x i m u m appearing at c = 0.5. Fig. 7 shows the dc conductivity logarithm (measured at room temperature), against the C u + / C u t ratio; ode values at 550 K follow the same form. Three aspects can be observed: an initial increase, a subsequent stabilization between 10 and 30 mol.% of Cu ÷ and a strong increase of the conductivity for higher contents of cuprous copper. This pattern does not agree with the behaviour
/
/
-8-
"7
-IC
-12
/
I
0,I
I
0,2 Cu÷ICu!
Fig. 7. Log Ode versus C u + / C u t ratio.
I
0,3
0,4
361
A. Durhn et al. / Electrical properties of copper phosphate glasses II
I00 °C- I kHz
/
-8
o
c)
-I0
• S1 li
-12
o $21 i o SP,/i
I
O, 1
0,12
(~3
I
0,4
Cu+/Cut Fig. 8. Log ot versus Cu+/Cut ratio.
predicted by Mott. To explain it, it has been necessary to use structural arguments. Tsuchiya and Moriya [12] have measured the chemical durability of phosphate glasses containing copper oxide. The copper dissolution curves in relation to the C u + / C u t ratio show a maximum near 0.27 and a minimum around C u + / C u t = 0.5. By comparing these curves to figs. 7 and 8 it can be noted that the minimum values of o appear in the maximum copper dissolution range, increasing strongly when the dissolution of copper decreases. This behaviour suggests the existence of two different sites for the Cu + ions: one, forming C u + - O - C u 2+ bonds, responsible for the hopping conduction, by electron transference between localized sites, Cu+_O_Cu
2+ ----) C u Z + _ O _ C u
+
and the other in clusters, within which Cu + ions should have a higher mobility, being able to act as charge carriers in the ionic conduction contribution detected by TSDC. On the other hand, Drake and Scanlan [3] have concluded from the apparent molar volume of oxygen (AMV) behaviour in phosphate glasses containing copper, that the Cu + and Cu 2+ ions are in different ligand field
362
A. Durhn et al. / Electrical properties of copper phosphate glasses H
14 ¸
o
0 r3
E
12
Y no
e ~
e
0
o Q
o
I 0,I
,D
o Q
I 0,2
o o----E~ o
I
0,3
~,
I 0,4
Cu+/Cut
Fig. 9. AMV of oxygen in copper phosphate glasses.
environments. This fact can explain the high activation energies of these glasses. Austin and Mott [2] have suggested that the ~0 energy may consist of two terms: that corresponding to the excitation energy of carriers from one kind of site to the other and the polaron hopping energy between equivalent sites. Drake and Scanlan [3] have fulfilled this interpretation with the assumption that some of the Cu ÷ and Cu 2÷ ion sites occupy a spread of energy levels that just overlap, producing impurity levels available for phonon activated hopping transport. The dielectric properties and their characteristic parameters are also dependent on the redox ratio Cu +/Cut. Fig. 8 represents the total conductivity against this ratio, showing a similar qualitative behaviour to dc conduction. The dielectric constant, c', takes constant values up to 10 mol.% of Cu ÷, and then increases with increasing C u ÷ / C u t ratio. Tsuchiya and Moriya [12] have reported similar results in binary copper phosphate glasses. Analyzing as a whole the temperature and frequency dependence of the dielectric constants of glasses with different Cu ÷ contents and the redox relation dependence of ~' and ot, different local coordinations of Cu ÷ and Cu 2+ ions appear to be probable. Fig. 9 [3] shows the apparent molar volume (AMV) of oxygen in a series of copper phosphate glasses containing Cu ÷ and Cu 2÷ with the same total Cu
A. Durdm et al. / Electrical properties of copper phosphate glasses I1
363
content. From this curve, the authors deduce that the Cu + and Cu 2+ ions are in different structural environments, suggesting that the Cu + coordination is similar in crystalline Cu 2° and in the phosphate glasses. C u 2 0 has a singular crystalline structure, the cuprite, in which the metallic ion is linearly coordinated with two oxygen atoms, whilst the Cu 2+ ions are present in these glasses in a distorted octahedral oxygen environment. By comparing the dc and ac conductivity graphs against the C u + / C u ' ratio with the AMV curves, it appears reasonable to associate the redox relation dependence of the conductivity with the different structural sites of cuprous and cupric ions.
3. Conduction mechanism
From dc measurements a hopping conduction mechanism, according to the polaronic model has been proposed. The main features of the process fit this model rather well, although the activation energies which result are too high. These large energies can be explained if it is supposed that the conduction is ruled by a polaron hopping mechanism between non-identical sites. The ac measurements introduce new data for a better understanding of the conduction process. Activation energies involved in the dielectric relaxation process coincide with those calculated from dc measurements, implying a unique conduction mechanism in both regimes. More evidence supporting this is supplied by the similarity between the ac and dc conductivity curves against the Cu+/Cu~ ratio. The cuprous content dependence of the AMV of oxygen and the copper dissolution diagrams clearly indicates that the local coordinations of Cu + and Cu 2+ ions are different, also suggesting the existence of cuprous ions in different structural environments. Thermoelectric measurements have proved that the Seebeck coefficient is temperature independent [3]. A simple explanation of this feature is the assumption that some of the Cu + and Cu 2+ ion sites occupy a spread of energy levels that just overlap. The electron exchanging among some centres produces impurity levels available for phonon activated bond edge hopping. The ac conductivity tests have also showed the redox ratio dependence of n in the relation between conductivity and frequency (a t cc v ~). For low cuprous contents, n - 0.8, near the value predicted for a phonon activated mechanism and when the C u + / C u t ratio increases, n takes lower values. It is possible to explain this phenomenon taking into account the different structural sites that cuprous ion can occupy. In the low Cu + content range, these ions are likely to be dispersed and linked to the vitreous network, forming C u + - O - C u 2+ bonds. Thus, the conduction would be produced by electron transference between localized ,dtes, in agreement with the small polaron model.
364
A. Durhn et al. / Electrical properties of copper phosphate glasses H
As the Cu + ion content increases, and according to the AMV behaviour, the cuprous ions would tend to cluster in environments similar to those occupied in crystalline Cu20. In this region, the n value decreases, indicating that the conduction mechanism is not only phonon activated. The impurity levels suggested by Drake and Scanlan provoke an additional conduction by the band edge effect. However, this mechanism is also phonon activated and the frequency dependence of the conductivity thus results in n -- 0.8. The crystalline cuprous oxide is an intrinsic p semiconductor, whose gap is around 1.5 eV. The impurity levels, being acceptors, are situated at 0.3-0.6 eV from the valency band edge. At room temperature, and below 300°C, Cu20 is generally unstable, showing a great trend to gain oxygen. This feature reinforces its p-type (by holes) conduction and explains the appearance of photoconductivity effects [27]. The structural environments that the cuprous ions occupy in glasses with high Cu + contents, similar to those of Cu20, may probably show the same kind of electrical behaviour as the crystalline state. The impurity levels in the energy gap will produce an overlap in the conduction and valency bands, because it is an amorphous material. Under this condition a delocalized states band conduction contribution should be possible. This mechanism is frequency independent for ~, < 101° Hz. Thus the diminution of n in glasses with high Cu + contents, should be explained as the result of a polaron hopping process and a band conduction contribution. The cooperative rearrangement on switching involves a readjustment of the coordinating oxygen positions such that the Cu + and Cu 2+ ion environments become nearly the same. Thus, the energy levels of the two sets of impurity band described before, will tend to overlap one another, increasing the number of the carriers and the mobility as a result of the Mott semiconductor-metal transition. The shifting of the coordinating anions, without the rupture of any valency bands, leads to the conducting form in which the local environment of each centre is effectively identical. On the other hand, a local precrystalline structure should result from the rearrangement of Cu 2O by molecular clusters. The interaction among the ionic sites and the field is enhanced, under high fields, by the highly polarizable matrix. The local temperature increases in the preswitching process may produce a phase separation similar to that resulting after heat treatment. During switching, the high temperatures locally reached act on the segregated nuclei, provoking the crystallization of the conduction paths. The Cu20 phase is the only kind of crystal that appeared, this fact supporting the structural hypothesis proposed. Thus the conduction process in barium phosphate glasses containing copper as the unique TMI should be explained as a combined mechanism of polaronic hopping with a band edge effect contribution, and with extended states band conduction when the ratio Cu +/Cu, is high enough.
A. DurUm et al. / Electrical properties of copper phosphate glasses I1
365
4. Conclusions The electrical and dielectric properties of the P2Os-BaO-CuO glass system allow a better understanding of the behaviour of these materials clarifying the character of the conduction and the mechanism ruling this process. - T h e time dependence of dc conductivity indicates that conduction is mainly electronic for temperatures higher than that corresponding to the maximum of the TSPC curve. The initial polarization is interpreted as a dielectric relaxation process. Electrode polarization has not been observed. The polarization peak in the TSPC curve suggests a relaxation process which is probably produced by a trapped level density. The TSDC peak hints at a small dipolar contribution to the conduction. - The temperature dependence of the dc conductivity shows that the electronic conduction process is ruled by the activation energy W. The data fit the small polaron model in adiabatic regime. The high energy values are explained by supposing different coordination sites for Cu + and Cu 2+ ions, a term of carriers excitation between different sites appearing, which is added to the polaron hopping energy. - T h e linear behaviour of log I against V 1/2 during the preswitching process implies a thermal ionic (Shottky) or electronic (Poole Frenkel) mechanism. For fields of about 5 x 103 V, negative resistance and switching phenomena appear. The filamentary crystallization produced in this process points to a Poole-Frenkel preswitching process. - T h e temperature and frequency variation of the loss tangent and dielectric constant is explained as a Debye dielectric relaxation process with a relaxation times distribution G(-r). The activation energies of this process coincide with those obtained in a dc regime, suggesting that the conduction mechanism is the same in both regimes. - T h e frequency dependence of total conductivity fits the equation o t cc u", n being a function of the ratio C u + / C u t . For low Cu + contents n agrees with the theoretical predictions for phonon activated conduction mechanisms. The values obtained for higher cuprous copper concentrations may be explained by the appearance of delocalized states originating a band conduction contribution. - B y comparing the patterns of dc and ac conductivity curves against the redox relation, to the AMV curve, it may be concluded that the Cu + and Cu 2 ~ ions are in different coordination environments. - F r o m all the data a structural pattern of these glasses and a conduction mechanism model can be advanced. Some cuprous ions, dispersed and linked to the vitreous network, and forming C u + - O - C u 2+ bands, would be responsible for the polaronic and band edge conduction, both of them phonon activated. Cu + ions situated in the other environment, similar to that occurring in crystalline Cu20, could originate a delocalized states band conduction.
366
A. Dur&n et al. / Electrical properties of copper phosphate glasses H
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
C.F. Drake, I.F. Scanlan and A. Engel, Phys. Status Solidi 32 (1969) 193. I.G. Austin and N.F. Mott, Adv. Phys. 18 (1969) 41. C.F. Drake and I.F. Scanlan, J. Non-Crystalline Solids 4 (1970) 234. A.K, Bandyopadhyay, PhD Thesis, University of Sheffield (1976). M. Sayer and A. Mansingh, Phys. Rev. B6 (1972) 4629. I.G. Austin and M. Sayer, J. Phys. C7 (1972) 905. H. Hirashima and T. Yoshida, XI Int. Congress on Glass. Vol. II, Prague (1977) p. 365. O.S. Ershov, 1.V. Dimakov, T.P. Markova and M.M. Shultz, Inorg. Mater. Consult. Bur. Transl. 8 (1982) 1606. M. Regan and C.I. Drake, Mat. Res. Bull. 6 (1971) 487. M. Sayer and G.F. Lynch, J. Phys. C6 (1973) 3674. G.R. Moridi and C.A. Hogarth, 7th Int. Conf. on Amorphous and Liquid Semiconductors. Edinburgh University (1977) 688. T. Tsuchiya and T. Moriya, Cent. Glass Ceram. Res. Inst. Bull. 22 (1975) 2; 55. G.J. Simmons and G.W. Taylor, Phys. Rev. B6 (1972) 4793. B. Dutta and D.E. Day, J. Non-Crystalline Solids 48 (1982) 345. H.M. Gupta and R.J. Overstraeten, J. Phys. C7 (1974) 3560. F. Cusso P6rez, Ph D Thesis. Universit~t Aut6noma, Madrid (1980). C.M. Hong and D.E. Day, J. Am. Ceram. Soc. 64 (1981) 2; 61. M. Sayer et al., J. Appl. Phys. 42 (1971) 2857. C.K. Shih and G.J. Su, VII Int. Congress on Glass, Sect. 1-33. Paper 48, Brussels (1965). A. Mansingh, J.M. Reyes and M. Sayer, J. Non-Crystalline Solids 7 (1972) 12. G.S. Linsley et al., J. Non-Crystalline Solids 4 (1970) 208. K.W. Hansen, J. Electrochem. Soc. 112 (1965) 994. K.W. Hansen and M.T. Splann, J. Electrochem. Soc. 113 (1965) 895. D. Adler, Amorphous Semiconductors (CRC Press, Chemical Rubber Co., Cleveland, 1971). L.L. Hench and H.F. Schaake, Electrical properties of glass, in: Introduction to Glass Science, eds., L.D. Pye, H.J. Stevens and W.C. La Course (Plenum, New York, 1972) p. 583. G.R. Moridi and C.A. Hogarth, 2nd European Conference on Condensed Matter, Budapest (1974). A.V. Ioffe and A.F. Ioffe, Zh. Eksp. Teor. Fiz. 6 (1936) 737.