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Effect of Cu substitution on conductivity of Ni–Al ferrite
Journal of Physics and Chemistry of Solids 61 (2000) 1529–1534 www.elsevier.nl/locate/jpcs
Effect of Cu substitution on conductivity of Ni–Al ferrite S.S. Ata-Allah*, M.K. Fayek Reactor and Neutron Physics Department, Nuclear Research Center, Atomic Energy Authority, P.O. Box 13759, Cairo, Egypt Received 20 April 1999; accepted 30 November 1999
Abstract Electrical properties of Cu substituted Ni–Al ferrite Ni1⫺xCuxAlyFe2⫺yO4, with (0:0 ⬍ x ⬍ 1:0 and y 1:0) are investigated by a.c. conductivity measurements in the frequency range (10 2 –10 5 Hz) and over the temperature range (300–600 K). The obtained results of these materials reveal a semiconducting behavior at low concentration of Cu. A semiconducting-to-metallic transition has been observed with increasing Cu content in these compounds. All studied compositions exhibit a transition with change in the slope of conductivity versus temperature curve. This transition temperature is found to decrease linearly with increasing Cu concentration x. The results of conductivity measurements are explained in the light of the cation–anion–cation and cation–cation interactions at the octahedral B-sites. 䉷 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Oxides; D. Semiconductivity; D. Electrical conductivity
1. Introduction Oxide spinels have long been a topic of interest in the solid state sciences, because of their usefulness as magnetic materials, semiconductors, pigments, catalysts and refractors [1]. Among the spinel ferrites, the CuFe2O4 exhibit switching, changing semiconductive properties [2]. Conductivity and thermoelectric power in polycrystalline ferrites have been studied both theoretically and experimentally [3–9], where the conductivity studies furnish data on Ne`el temperature, cation distribution and activation energy. Particularly, in mixed ferrite containing Cu 2⫹ and other divalent cation like Ni 2⫹, these studies can be useful in elucidating the role of Cu 2⫹ ions. The study of mixed ferrites, Zn–Cu [10], Ni–Cu [11], Co–Cu [12] and Fe2O3 –(Al2O3)x –(CuO)1⫺x [13] show interesting cation distribution and magnetic properties. Substitution of some trivalent nonmagnetic ions such as Al 3⫹ for Fe 3⫹ in spinel ferrites is made for special magnetic and electrical functions. The introduction of nonmagnetic ions (e.g. Al 3⫹) on octahedral sites in the inverse spinel NiFe2O4 will reduce the saturation magnetization and alter their magnetic and electric properties [8]. Several oxides containing transitionelement cations have physical properties that suggest the existence of cation–cation interaction via direct overlap of cation d-electron wave functions. Such interactions are * Corresponding author.
distinguished from those that occur via an anion intermediary. They have been independently proposed to account on the one hand, for certain magnetic interactions, on the other, for some interesting electrical property. In this respect, nickel and copper, are interesting elements. Copper is very interesting owing to its great number of coordination, octahedral, pyramidal, tetrahedral and square planar. The present experimental study has been intended to conduct a.c. conductivity measurements for the ferrite series Ni1⫺xCuxAlyFe2⫺yO4 at different temperatures in the frequency range (10 2 –10 5 Hz) aiming to clarify the effect of replacing Cu and Al for Ni and Fe on the electric behavior of this system.
2. Experimentals Polycrystalline (Cu–Ni) aluminum ferrites having the compositional formula Ni1⫺xCuxAlyFe2⫺yO4, with (0:0 ⬍ x ⬍ 1:0 and y 1:0) were prepared using the usual ceramic method. The single-phase cubic spinel structure for these samples is confirmed by the X-ray powder diffraction measurements. The details of the method of preparation and X-ray measurements were reported earlier [9]. The electrical measurements were carried out on the polycrystalline samples in the form of a disc with diameter ⬃1 cm and thickness ⬃4 mm. Complex impedance techniques over the temperature range 300–600 K were applied using the two-probe method with lock-in amplifier in the frequency
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Fig. 1. Conductivity as ln s versus 1000=T for NiFe2O4 and Ni1⫺xCuxAl FeO4 (with x 0:0 and 0.25) at different frequencies.
range 10 2 –10 5 Hz. Samples were kept under vacuum ⬃1:3 × 10⫺4 Pa during the measurements.
3. Results and discussion Figs. 1 and 2 show the variation of conductivity as (ln s ) with reciprocal of temperature as 1000=T at different frequencies (100, 50, 10, 1 KHz and 500 Hz) for the prepared samples NiFe2O4 and Ni1⫺xCuxAlFeO4 where x ranges from 0.0 to 1.0. It is clearly observed from these
Fig. 2. Conductivity as ln s versus 1000=T for Ni1⫺xCuxAl FeO4 (with x 0:5; 0.75 and 1.0) at different frequencies.
figures that the conductivity s increases with increasing temperature for NiFe2O4 sample, in a behavior similar to that exhibited by most semiconducting materials [5]. The frequency dependence of conductivity for this sample is clear at low temperature, but at high temperature it decreases and becomes frequency independent at a certain temperature. This temperature (850 K) is taken as the Ne`el point, which separates the ferrimagnetic region where s is frequency dependent, and the paramagnetic region where s is frequency independent.
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change at 365 and 345 K for x 0:75 and 1.0, respectively. Substitution of copper by these values in these samples reflects a very small dependence of the conductivity on temperature at low frequency. The frequency dependence of conductivity in these samples is clear at high frequency range and low temperature region. The transition-metal cation in octahedral sites is interstices of an anion sublattice. In this case, the electrostatic interactions between anion and cation electrons cause splitting of the cation 3d-level into a more stable triply degenerate t2g level (dxy, dyz, dzx atomic orbitals directed away from neighboring anions) and less stable, doubly degenerate eg level (d z 2 ; dx2 ⫺y2 atomic orbitals directed towards neighboring anions) [14]. There are two factors, which determine the sign of the spin–spin interaction between any pair of cations: 1. The relative coordination of their anion octahedral. 2. The number of cation outer electrons.
Fig. 3. Variation of conductivity as log s with the compositional parameter x for Ni1⫺xCuxAlFeO4 at room temperature.
Replacement of Fe with Al in NiFe2O4, results in increasing the conductivity with increasing temperature. However, at a certain temperature (469 K), conductivity begins to decrease with increasing temperature at low frequency range. The frequency dependence of the conductivity for this sample increases with increasing temperature in contrast to the behavior of the NiFe2O4 sample. Replacing Cu instead of Ni in the NiAlFeO4 compound affects the dependence of conductivity on both temperature and frequency as follows: At x 0:25; the conductivity increases with increasing temperature at higher frequency and begins to decrease at (451 K). For the low frequency range, the conductivity has a slight dependence on temperature. Conductivity in this sample still has frequency dependence over the whole range of temperature. At x 0:5; in the high frequency range the conductivity is increased with increasing temperature with abrupt change at 427 K. In the intermediate range of frequency (1– 10 kHz), conductivity is found to decrease with increasing temperature showing the abrupt change at the same value of temperature (427 K). In the low frequency range, conductivity is nearly temperature independent. Conductivity in this sample has frequency dependence over the whole range of temperature. As the copper concentration increases in these spinel ferrites; the conductivity is found to decrease with increasing temperature only at high frequency with remarkable
Anderson [15] pointed out that if the cation–anion–cation angle is 90⬚, the cation–anion–cation interactions are weak. Therefore, the predominant interactions are assumed to be of cation–cation interactions. On the contrary, when the cation–anion–cation angle be 180⬚ or as small as 120⬚, the cation–anion–cation interactions are optimal. It is noted that although only one mechanism contributes significantly to the spin–spin coupling of any cation pair, the two mechanisms may compete against one another. Goodenough [16] pointed out that in the rocksalt-type structure as NiO and MnO, FeO and CoO both the cation–anion–cation interactions and the cation–cation interactions can be simultaneously present in this structure and he stated that for 5 ⱕ m ⱕ 8 (where, m is the number of electrons in d-levels) as in NiO the cation–anion–cation interaction must be stronger. In the case of strong cation– anion–cation interactions and weak cation–cation interactions, the materials have semiconductor (or insulator) behavior. But, if cations of the same element but different valence, are simultaneously present, the materials may have metallic type s–T character below a ferromagnetic Curie temperature [16]. In case of strong cation–cation interactions between octahedral B-site cations, these materials have a metallic behavior, and may become semiconductor at low temperature. The compositions under investigation are transitionmetal-oxide semiconductors with the spinel structure, which are known to be low-mobility materials. Their transport properties are often considered to arise from charge transfer between octahedral cations by hopping of localized d-electrons. This hopping mechanism is confined to the valence distribution of cations that occupy the oxygen octahedral site. In the present system Ni1⫺xCuxAlFeO4 where 0:0 ⱕ x ⱕ 1:0; the Mo¨ssbauer effect results [9] showed that Ni 2⫹, Cu 2⫹, Al 3⫹ ions are occupying the octahedral sites as:
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Table 1 The activation energy (eV) below transition temperature (TN) for NiFe2O4 and the ferrite system Ni1⫺xCuxAlFeO4 Frequency (kHz)
NiFe2O4
x 0:0
x 0:25
x 0:5
x 0:75
x 1:0
100 50 10 5 1 500 Hz
0.2545 (6) 0.2364 (0) 0.2380 (5) 0.2078 (2) 0.0567 (4) 0.0449 (5)
0.0641 (8) 0.1460 (9) 0.1388 (8) 0.1330 (0) 0.1429 (8) 0.1606 (2)
0.1667 (1) 0.1518 (2) 0.1011 (1) 0.0772 (4) 0.0343 (8) 0.0283 (2)
0.1691 (0) 0.1633 (7) ⫺0.0073 (7) ⫺0.1065 (4) ⫺0.0345 (8) ⫺0.0117 (8)
⫺0.1988 (7) ⫺0.2727 (4) ⫺0.1740 (8) ⫺0.0866 (5) ⫺0.0194 (4) ⫺0.0163 (4)
⫺0.3372 (2) ⫺0.3156 (0) ⫺0.1237 (1) ⫺0.1241 (3) ⫺0.1956 (6) ⫺0.0802 (0)
2⫹ 3⫹ 2⫺ Fe 3⫹ Ni2⫹ 1⫺x Cux Al O4 ; where the parentheses refer to the tetrahedral A-site and the square brackets refer to the octahedral B-site. For the NiFe2O4 sample with cation distribution Fe3⫹ Ni2⫹ Fe3⫹ O2⫺ 4 the cation–cation interaction is less predominant, but the cation–anion–cation interaction is stronger between [Fe 3⫹ –O 2⫺ –Fe 3⫹] and [Ni 2⫹ –O 2⫺ – Ni 2⫹]. As pointed out from the crystal field theory and ligand field theory, and the splitting of d-level of the transition metal ions in octahedral coordination, it was found that the splitting of 3d of Ni 2⫹ is 10 Dq, where for Fe 3⫹ is zero [14]. This means that, the Ni 2⫹ –O 2⫺ –Ni 2⫹ interaction is the most predominant in this sample. By substitution of Al 3⫹ with electronic configuration (2,8,3) in the NiFe2O4 sample with y 1:0 in place of Fe at the octahedral site, the [Fe 3⫹ –O 2 –Fe 3⫹] interaction is no longer predominant. In addition, the presence of Al 3⫹ in the octahedral site screens [Ni 2⫹ –O 2 –Ni 2⫹] interaction, which is only predominant in this sample. This results in a decrease of the conductivity and increase of the activation energy especially for low frequency range as shown in Fig. 3 and Table 1, respectively. The substitution of copper in place of Ni in octahedral site leads to the presence of a cation–cation interaction between Cu–Cu. This results in an increase of conductivity by increasing Cu content in this spinel system as shown in Fig. 3. As the substitution of Cu is progressed in the unit cell, the cation–cation interaction becomes the predominant one, leading to a transition from semiconducting-to-metallic behavior in this system as illustrated in Fig. 2 (for x 0:75 and 1.0). At high frequency, the conductivity decreases with increasing temperature and at low frequency, there is nearly frequency and temperature independence of conductivity. The relation between ln s and 1000=T (Figs. 1 and 2) show very interesting remarks.
• The NiFe2O4 sample has a semiconductor behavior with positive temperature coefficient of conductivity (TCC) ds=dt in the whole range of temperature and frequency. • Samples with copper content x 0:0 and x 0:25 are showing a semiconducting behavior with positive (TCC) till the transition temperature TN; where a negative (TCC) is observed and a transition from semiconductor-tometallic behavior occurred at higher temperature and low frequency.
• The compound with x 0:5 is very interesting one where, at high frequency a metallic behavior with positive (TCC) is observed and by lowering the frequency it becomes flat with ds=dt 0 where a transition from semiconductor-to-metallic behavior occurs at lower frequency. At higher concentration of copper x 0:75 and 1.0 a metallic behavior becomes predominant over the whole temperature range especially at higher frequency. In Ni1⫺xCuxAlFeO4 compounds the total conductivity at a given frequency v is considered as two components:
s total v s 0 ⫹ s v
1
Where, s 0 is the d.c. conductivity due to excitation of electrons from the localized states to the conduction bands, and s v is the a.c. conductivity due to the hopping conduction. The conductivity s v obeys the empirical formula of frequency dependence given by the power law [17]
s v Bv s
2
Where, B is a constant and 0:0 ⬍ s ⬍ 1:0: Figs. 4 and 5 show the relation between ln s and ln(v ) for the present spinel system. It is clear that the power law of Eq. (2) is generally obeyed with the exponent s falling in the range 0:0 ⬍ s ⬍ 1:0: It is noticed that at the higher end of the frequency range, the NiFe2O4 sample shows a flattening of the characteristic towards what might be for the d.c. conductivity [18]. Also at high temperature (⬃660 K) the relation is flat. Another feature of this relation is the temperature dependence of the lower frequency response, which is much stronger than that of the high frequency. For NiFe2O4 and NiAlFeO4 samples, this response is only at a high temperature. Replacing Ni by Cu with x 0:5–1:0 in this system, the flattening of the characteristic is observed at the lower end of the frequency and increased with increasing temperature as shown in Fig. 3. In the CuAlFeO4 sample, at higher temperature and frequency the exponent s is exceeding unity. The implication of this is that the dielectric loss is rising with increasing frequency, while for s ⬍ 1; it is falling [18]. Fig. 6 shows the variation of the exponent s of the power law Eq. (2) for s falling in the range 0:0 ⬍ s ⬍ 1:0: It is clearly observed from this figure that the frequency dependence of conductivity increases in NiFe2O4 with
S.S. Ata-Allah, M.K. Fayek / Journal of Physics and Chemistry of Solids 61 (2000) 1529–1534
Fig. 4. Conductivity as ln s versus ln v for NiFe2O4 and Ni1⫺xCuxAlFeO4 (with x 0:0 and 0.25) at different temperatures.
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Fig. 5. Conductivity as ln s versus ln v for Ni1⫺xCuxAlFeO4 (with x 0:5; 0.75 and 1.0) at different temperatures.
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Fig. 7. A plot of the transition temperature TN with the compositional parameter x for Ni1⫺xCuxAlFeO4 spinel ferrites. Fig. 6. Variation of the exponent s of the power law with temperature for NiFe2O4 and Ni1⫺xCuxAlFeO4 (with 0:0 ⱕ x ⱕ 1:0).
References
increasing temperature then decreases and finally becomes constant. Substitution of Al increases the frequency dependence of conductivity with temperature, also the replacement of Ni by Cu with (x 0:25 and 0.5) has the same effect. However, at higher copper concentrations (x 0:75 and 1.0), this dependence decreases with increasing temperature. The transition temperature TN is determined from the variation of the conductivity as a logarithmic scale (ln s ) with reciprocal of temperature as 1000=T at different frequency (Figs. 1 and 2). For NiFe2O4, it is the point where the conductivity becomes frequency independent. For compounds with x 0:0 and 0.25 the transition is at the point where the conductivity starts to decrease with increasing temperature. At x 0:5 until x 1:0 it is at the abrupt changes in the conductivity with temperature at high frequency. This relation between TN and the compositional parameter x is shown in Fig. 7, where the substitution of Fe with Al in NiFe2O4 decreases TN from 850–469 K and the substitution of Ni with Cu results in a linear decrease of TN with copper content x. This is in agreement with Gilleo studies for superexchange interaction for various oxides [19], which indicated that the Ne`el temperature depends primarily upon the number of Fe 3⫹ –O 2 –Fe 3⫹ linkages. In our ferrites spinels NiFe2O4 and Ni1⫺xCuxAlFeO4, TN depends not only on the number of Fe 3⫹ –O 2 –Ni 2⫹ linkages but also, upon the number of Ni 2⫹ –O 2 –Ni 2⫹ linkages. Replacement of Ni with Cu in these samples decreases the number of Ni 2⫹ –O 2 –Ni 2⫹ linkages and therefore the Ne`el temperature is decreased.
[1] J.C. Waerenborgh, M.O. Figueiredo, J.M.P. Cabrol, L.C.J. Pereiro, J. Solid State Chem. 111 (1994) 300. [2] S.R. Sawant, R.N. Patil, Indian, J. Appl. Phys. 20 (1982) 353. [3] S.H. Kang, S.H. Chang, H.I. Yoo, ICF7, 3-3pl, Bordeaux, France 1996. [4] T.Gron, K. Barner, Ch. Kleeberg, I. Okonska-Kozlowska, ICF7, 4-3p7, Bordeaux, France, 1996. [5] M.K. Fayek, F.M. Sayed Ahmed, S.S. Ata-Allah, M.K. Elnimer, M.F. Mostafa, J. Mater. Sci. 27 (1992) 4813. [6] M.K. Fayek, M. Elnimer, S. Ata-Allah, F.M. Sayedahmed, Phys. Status Solidi A 143 (1994) 379. [7] B.K. Kuamer, P.K. Singh, P. Kishan, J. Appl. Phys. 61 (1987) 4379. [8] P.V. Reddy, J. Appl. Phys. 63 (1988) 3783. [9] M.K. Fayek, S.S. Ata-Allah, H.S. Refai, J. Appl. Phys. 85 (1999) 325. [10] R.G. Kulkarni, V.U. Patil, J. Mater. Sci. 17 (1982) 843. [11] A.A. Chani, A.I. Etyhh, A.A. Mohamed, Ferrite, Proc. Int. Conf., Sept. 1980, Japan, pp. 216. [12] Ph. Tailhades, C. Villette, A. Rousset, G.C. Kulkarni, K.R. Kannan, C.N.R. Rao, M. Lenglet, J. Solid State Chem. 141 (1998) 56. [13] S.H. Lee, K.P. Chee, Y.B. Lee, K.S. Oh, Solid State Commun. 74 (1990) 1. [14] I. Bunget, M. Popescu, Physics of Solid Dielectrics, Editura Stiinsificaˆ Si Enciclopedica˜, Bucharest, 1978. [15] P.W. Anderson, Phys. Rev. 79 (1950) 350. [16] J.B. Goodenough, Phys. Rev. 6 (1960) 1442. [17] M. Pollak, T.H. Geball, Phys. Rev. 122 (1961) 1745. [18] A.K.J. Jonscher, Dielectric Relaxation in Solids, Chelsca, London, 1986. [19] M.A. Gilleo, Phys. Chem. Solids 13 (1960) 33.
Effect of Cu substitution on conductivity of Ni–Al ferrite S.S. Ata-Allah*, M.K. Fayek Reactor and Neutron Physics Department, Nuclear Research Center, Atomic Energy Authority, P.O. Box 13759, Cairo, Egypt Received 20 April 1999; accepted 30 November 1999
Abstract Electrical properties of Cu substituted Ni–Al ferrite Ni1⫺xCuxAlyFe2⫺yO4, with (0:0 ⬍ x ⬍ 1:0 and y 1:0) are investigated by a.c. conductivity measurements in the frequency range (10 2 –10 5 Hz) and over the temperature range (300–600 K). The obtained results of these materials reveal a semiconducting behavior at low concentration of Cu. A semiconducting-to-metallic transition has been observed with increasing Cu content in these compounds. All studied compositions exhibit a transition with change in the slope of conductivity versus temperature curve. This transition temperature is found to decrease linearly with increasing Cu concentration x. The results of conductivity measurements are explained in the light of the cation–anion–cation and cation–cation interactions at the octahedral B-sites. 䉷 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Oxides; D. Semiconductivity; D. Electrical conductivity
1. Introduction Oxide spinels have long been a topic of interest in the solid state sciences, because of their usefulness as magnetic materials, semiconductors, pigments, catalysts and refractors [1]. Among the spinel ferrites, the CuFe2O4 exhibit switching, changing semiconductive properties [2]. Conductivity and thermoelectric power in polycrystalline ferrites have been studied both theoretically and experimentally [3–9], where the conductivity studies furnish data on Ne`el temperature, cation distribution and activation energy. Particularly, in mixed ferrite containing Cu 2⫹ and other divalent cation like Ni 2⫹, these studies can be useful in elucidating the role of Cu 2⫹ ions. The study of mixed ferrites, Zn–Cu [10], Ni–Cu [11], Co–Cu [12] and Fe2O3 –(Al2O3)x –(CuO)1⫺x [13] show interesting cation distribution and magnetic properties. Substitution of some trivalent nonmagnetic ions such as Al 3⫹ for Fe 3⫹ in spinel ferrites is made for special magnetic and electrical functions. The introduction of nonmagnetic ions (e.g. Al 3⫹) on octahedral sites in the inverse spinel NiFe2O4 will reduce the saturation magnetization and alter their magnetic and electric properties [8]. Several oxides containing transitionelement cations have physical properties that suggest the existence of cation–cation interaction via direct overlap of cation d-electron wave functions. Such interactions are * Corresponding author.
distinguished from those that occur via an anion intermediary. They have been independently proposed to account on the one hand, for certain magnetic interactions, on the other, for some interesting electrical property. In this respect, nickel and copper, are interesting elements. Copper is very interesting owing to its great number of coordination, octahedral, pyramidal, tetrahedral and square planar. The present experimental study has been intended to conduct a.c. conductivity measurements for the ferrite series Ni1⫺xCuxAlyFe2⫺yO4 at different temperatures in the frequency range (10 2 –10 5 Hz) aiming to clarify the effect of replacing Cu and Al for Ni and Fe on the electric behavior of this system.
2. Experimentals Polycrystalline (Cu–Ni) aluminum ferrites having the compositional formula Ni1⫺xCuxAlyFe2⫺yO4, with (0:0 ⬍ x ⬍ 1:0 and y 1:0) were prepared using the usual ceramic method. The single-phase cubic spinel structure for these samples is confirmed by the X-ray powder diffraction measurements. The details of the method of preparation and X-ray measurements were reported earlier [9]. The electrical measurements were carried out on the polycrystalline samples in the form of a disc with diameter ⬃1 cm and thickness ⬃4 mm. Complex impedance techniques over the temperature range 300–600 K were applied using the two-probe method with lock-in amplifier in the frequency
0022-3697/00/$ - see front matter 䉷 2000 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(00)00010-X
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Fig. 1. Conductivity as ln s versus 1000=T for NiFe2O4 and Ni1⫺xCuxAl FeO4 (with x 0:0 and 0.25) at different frequencies.
range 10 2 –10 5 Hz. Samples were kept under vacuum ⬃1:3 × 10⫺4 Pa during the measurements.
3. Results and discussion Figs. 1 and 2 show the variation of conductivity as (ln s ) with reciprocal of temperature as 1000=T at different frequencies (100, 50, 10, 1 KHz and 500 Hz) for the prepared samples NiFe2O4 and Ni1⫺xCuxAlFeO4 where x ranges from 0.0 to 1.0. It is clearly observed from these
Fig. 2. Conductivity as ln s versus 1000=T for Ni1⫺xCuxAl FeO4 (with x 0:5; 0.75 and 1.0) at different frequencies.
figures that the conductivity s increases with increasing temperature for NiFe2O4 sample, in a behavior similar to that exhibited by most semiconducting materials [5]. The frequency dependence of conductivity for this sample is clear at low temperature, but at high temperature it decreases and becomes frequency independent at a certain temperature. This temperature (850 K) is taken as the Ne`el point, which separates the ferrimagnetic region where s is frequency dependent, and the paramagnetic region where s is frequency independent.
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change at 365 and 345 K for x 0:75 and 1.0, respectively. Substitution of copper by these values in these samples reflects a very small dependence of the conductivity on temperature at low frequency. The frequency dependence of conductivity in these samples is clear at high frequency range and low temperature region. The transition-metal cation in octahedral sites is interstices of an anion sublattice. In this case, the electrostatic interactions between anion and cation electrons cause splitting of the cation 3d-level into a more stable triply degenerate t2g level (dxy, dyz, dzx atomic orbitals directed away from neighboring anions) and less stable, doubly degenerate eg level (d z 2 ; dx2 ⫺y2 atomic orbitals directed towards neighboring anions) [14]. There are two factors, which determine the sign of the spin–spin interaction between any pair of cations: 1. The relative coordination of their anion octahedral. 2. The number of cation outer electrons.
Fig. 3. Variation of conductivity as log s with the compositional parameter x for Ni1⫺xCuxAlFeO4 at room temperature.
Replacement of Fe with Al in NiFe2O4, results in increasing the conductivity with increasing temperature. However, at a certain temperature (469 K), conductivity begins to decrease with increasing temperature at low frequency range. The frequency dependence of the conductivity for this sample increases with increasing temperature in contrast to the behavior of the NiFe2O4 sample. Replacing Cu instead of Ni in the NiAlFeO4 compound affects the dependence of conductivity on both temperature and frequency as follows: At x 0:25; the conductivity increases with increasing temperature at higher frequency and begins to decrease at (451 K). For the low frequency range, the conductivity has a slight dependence on temperature. Conductivity in this sample still has frequency dependence over the whole range of temperature. At x 0:5; in the high frequency range the conductivity is increased with increasing temperature with abrupt change at 427 K. In the intermediate range of frequency (1– 10 kHz), conductivity is found to decrease with increasing temperature showing the abrupt change at the same value of temperature (427 K). In the low frequency range, conductivity is nearly temperature independent. Conductivity in this sample has frequency dependence over the whole range of temperature. As the copper concentration increases in these spinel ferrites; the conductivity is found to decrease with increasing temperature only at high frequency with remarkable
Anderson [15] pointed out that if the cation–anion–cation angle is 90⬚, the cation–anion–cation interactions are weak. Therefore, the predominant interactions are assumed to be of cation–cation interactions. On the contrary, when the cation–anion–cation angle be 180⬚ or as small as 120⬚, the cation–anion–cation interactions are optimal. It is noted that although only one mechanism contributes significantly to the spin–spin coupling of any cation pair, the two mechanisms may compete against one another. Goodenough [16] pointed out that in the rocksalt-type structure as NiO and MnO, FeO and CoO both the cation–anion–cation interactions and the cation–cation interactions can be simultaneously present in this structure and he stated that for 5 ⱕ m ⱕ 8 (where, m is the number of electrons in d-levels) as in NiO the cation–anion–cation interaction must be stronger. In the case of strong cation– anion–cation interactions and weak cation–cation interactions, the materials have semiconductor (or insulator) behavior. But, if cations of the same element but different valence, are simultaneously present, the materials may have metallic type s–T character below a ferromagnetic Curie temperature [16]. In case of strong cation–cation interactions between octahedral B-site cations, these materials have a metallic behavior, and may become semiconductor at low temperature. The compositions under investigation are transitionmetal-oxide semiconductors with the spinel structure, which are known to be low-mobility materials. Their transport properties are often considered to arise from charge transfer between octahedral cations by hopping of localized d-electrons. This hopping mechanism is confined to the valence distribution of cations that occupy the oxygen octahedral site. In the present system Ni1⫺xCuxAlFeO4 where 0:0 ⱕ x ⱕ 1:0; the Mo¨ssbauer effect results [9] showed that Ni 2⫹, Cu 2⫹, Al 3⫹ ions are occupying the octahedral sites as:
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Table 1 The activation energy (eV) below transition temperature (TN) for NiFe2O4 and the ferrite system Ni1⫺xCuxAlFeO4 Frequency (kHz)
NiFe2O4
x 0:0
x 0:25
x 0:5
x 0:75
x 1:0
100 50 10 5 1 500 Hz
0.2545 (6) 0.2364 (0) 0.2380 (5) 0.2078 (2) 0.0567 (4) 0.0449 (5)
0.0641 (8) 0.1460 (9) 0.1388 (8) 0.1330 (0) 0.1429 (8) 0.1606 (2)
0.1667 (1) 0.1518 (2) 0.1011 (1) 0.0772 (4) 0.0343 (8) 0.0283 (2)
0.1691 (0) 0.1633 (7) ⫺0.0073 (7) ⫺0.1065 (4) ⫺0.0345 (8) ⫺0.0117 (8)
⫺0.1988 (7) ⫺0.2727 (4) ⫺0.1740 (8) ⫺0.0866 (5) ⫺0.0194 (4) ⫺0.0163 (4)
⫺0.3372 (2) ⫺0.3156 (0) ⫺0.1237 (1) ⫺0.1241 (3) ⫺0.1956 (6) ⫺0.0802 (0)
2⫹ 3⫹ 2⫺ Fe 3⫹ Ni2⫹ 1⫺x Cux Al O4 ; where the parentheses refer to the tetrahedral A-site and the square brackets refer to the octahedral B-site. For the NiFe2O4 sample with cation distribution Fe3⫹ Ni2⫹ Fe3⫹ O2⫺ 4 the cation–cation interaction is less predominant, but the cation–anion–cation interaction is stronger between [Fe 3⫹ –O 2⫺ –Fe 3⫹] and [Ni 2⫹ –O 2⫺ – Ni 2⫹]. As pointed out from the crystal field theory and ligand field theory, and the splitting of d-level of the transition metal ions in octahedral coordination, it was found that the splitting of 3d of Ni 2⫹ is 10 Dq, where for Fe 3⫹ is zero [14]. This means that, the Ni 2⫹ –O 2⫺ –Ni 2⫹ interaction is the most predominant in this sample. By substitution of Al 3⫹ with electronic configuration (2,8,3) in the NiFe2O4 sample with y 1:0 in place of Fe at the octahedral site, the [Fe 3⫹ –O 2 –Fe 3⫹] interaction is no longer predominant. In addition, the presence of Al 3⫹ in the octahedral site screens [Ni 2⫹ –O 2 –Ni 2⫹] interaction, which is only predominant in this sample. This results in a decrease of the conductivity and increase of the activation energy especially for low frequency range as shown in Fig. 3 and Table 1, respectively. The substitution of copper in place of Ni in octahedral site leads to the presence of a cation–cation interaction between Cu–Cu. This results in an increase of conductivity by increasing Cu content in this spinel system as shown in Fig. 3. As the substitution of Cu is progressed in the unit cell, the cation–cation interaction becomes the predominant one, leading to a transition from semiconducting-to-metallic behavior in this system as illustrated in Fig. 2 (for x 0:75 and 1.0). At high frequency, the conductivity decreases with increasing temperature and at low frequency, there is nearly frequency and temperature independence of conductivity. The relation between ln s and 1000=T (Figs. 1 and 2) show very interesting remarks.
• The NiFe2O4 sample has a semiconductor behavior with positive temperature coefficient of conductivity (TCC) ds=dt in the whole range of temperature and frequency. • Samples with copper content x 0:0 and x 0:25 are showing a semiconducting behavior with positive (TCC) till the transition temperature TN; where a negative (TCC) is observed and a transition from semiconductor-tometallic behavior occurred at higher temperature and low frequency.
• The compound with x 0:5 is very interesting one where, at high frequency a metallic behavior with positive (TCC) is observed and by lowering the frequency it becomes flat with ds=dt 0 where a transition from semiconductor-to-metallic behavior occurs at lower frequency. At higher concentration of copper x 0:75 and 1.0 a metallic behavior becomes predominant over the whole temperature range especially at higher frequency. In Ni1⫺xCuxAlFeO4 compounds the total conductivity at a given frequency v is considered as two components:
s total v s 0 ⫹ s v
1
Where, s 0 is the d.c. conductivity due to excitation of electrons from the localized states to the conduction bands, and s v is the a.c. conductivity due to the hopping conduction. The conductivity s v obeys the empirical formula of frequency dependence given by the power law [17]
s v Bv s
2
Where, B is a constant and 0:0 ⬍ s ⬍ 1:0: Figs. 4 and 5 show the relation between ln s and ln(v ) for the present spinel system. It is clear that the power law of Eq. (2) is generally obeyed with the exponent s falling in the range 0:0 ⬍ s ⬍ 1:0: It is noticed that at the higher end of the frequency range, the NiFe2O4 sample shows a flattening of the characteristic towards what might be for the d.c. conductivity [18]. Also at high temperature (⬃660 K) the relation is flat. Another feature of this relation is the temperature dependence of the lower frequency response, which is much stronger than that of the high frequency. For NiFe2O4 and NiAlFeO4 samples, this response is only at a high temperature. Replacing Ni by Cu with x 0:5–1:0 in this system, the flattening of the characteristic is observed at the lower end of the frequency and increased with increasing temperature as shown in Fig. 3. In the CuAlFeO4 sample, at higher temperature and frequency the exponent s is exceeding unity. The implication of this is that the dielectric loss is rising with increasing frequency, while for s ⬍ 1; it is falling [18]. Fig. 6 shows the variation of the exponent s of the power law Eq. (2) for s falling in the range 0:0 ⬍ s ⬍ 1:0: It is clearly observed from this figure that the frequency dependence of conductivity increases in NiFe2O4 with
S.S. Ata-Allah, M.K. Fayek / Journal of Physics and Chemistry of Solids 61 (2000) 1529–1534
Fig. 4. Conductivity as ln s versus ln v for NiFe2O4 and Ni1⫺xCuxAlFeO4 (with x 0:0 and 0.25) at different temperatures.
1533
Fig. 5. Conductivity as ln s versus ln v for Ni1⫺xCuxAlFeO4 (with x 0:5; 0.75 and 1.0) at different temperatures.
1534
S.S. Ata-Allah, M.K. Fayek / Journal of Physics and Chemistry of Solids 61 (2000) 1529–1534
Fig. 7. A plot of the transition temperature TN with the compositional parameter x for Ni1⫺xCuxAlFeO4 spinel ferrites. Fig. 6. Variation of the exponent s of the power law with temperature for NiFe2O4 and Ni1⫺xCuxAlFeO4 (with 0:0 ⱕ x ⱕ 1:0).
References
increasing temperature then decreases and finally becomes constant. Substitution of Al increases the frequency dependence of conductivity with temperature, also the replacement of Ni by Cu with (x 0:25 and 0.5) has the same effect. However, at higher copper concentrations (x 0:75 and 1.0), this dependence decreases with increasing temperature. The transition temperature TN is determined from the variation of the conductivity as a logarithmic scale (ln s ) with reciprocal of temperature as 1000=T at different frequency (Figs. 1 and 2). For NiFe2O4, it is the point where the conductivity becomes frequency independent. For compounds with x 0:0 and 0.25 the transition is at the point where the conductivity starts to decrease with increasing temperature. At x 0:5 until x 1:0 it is at the abrupt changes in the conductivity with temperature at high frequency. This relation between TN and the compositional parameter x is shown in Fig. 7, where the substitution of Fe with Al in NiFe2O4 decreases TN from 850–469 K and the substitution of Ni with Cu results in a linear decrease of TN with copper content x. This is in agreement with Gilleo studies for superexchange interaction for various oxides [19], which indicated that the Ne`el temperature depends primarily upon the number of Fe 3⫹ –O 2 –Fe 3⫹ linkages. In our ferrites spinels NiFe2O4 and Ni1⫺xCuxAlFeO4, TN depends not only on the number of Fe 3⫹ –O 2 –Ni 2⫹ linkages but also, upon the number of Ni 2⫹ –O 2 –Ni 2⫹ linkages. Replacement of Ni with Cu in these samples decreases the number of Ni 2⫹ –O 2 –Ni 2⫹ linkages and therefore the Ne`el temperature is decreased.
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