Electrical properties and mineralogical investigation of Egyptian iron ore deposits

Electrical properties and mineralogical investigation of Egyptian iron ore deposits

Materials Chemistry and Physics 114 (2009) 313–318 Contents lists available at ScienceDirect Materials Chemistry and Physics journal homepage: www.e...

952KB Sizes 1 Downloads 61 Views

Materials Chemistry and Physics 114 (2009) 313–318

Contents lists available at ScienceDirect

Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys

Electrical properties and mineralogical investigation of Egyptian iron ore deposits M.M. Gomaa a,∗ , A.A. Shaltout b , M. Boshta b a b

National Research Centre, Geophysical Sciences Dep., El Behooth St., 12622 Dokki, Cairo, Egypt National Research Center, Physics Division, El Behooth St., 12622 Dokki, Cairo, Egypt

a r t i c l e

i n f o

Article history: Received 23 June 2008 Received in revised form 6 August 2008 Accepted 14 September 2008 Keywords: X-ray diffraction Dielectric properties Electrical conductivity Iron ores

a b s t r a c t Electrical properties and X-ray diffraction of 20 hematite sandstone samples of the most economically interesting Egyptian iron ore deposits have been investigated. Samples were collected from two different areas in Egypt (Aswan and Bahariya). Complex impedance measurements in the frequency range from 10 Hz to 100 kHz were performed at room temperature (∼20 ◦ C). The observed dielectric behavior was characterized by Maxwell–Wagner interfacial polarization at low frequencies and bulk polarization at relatively higher frequencies. The frequency dependence on conductivity shows a classical relaxation behavior followed Jonscher’s universal law. The measured electrical properties vary strongly with the frequency and sample composition. The difference in the electrical properties may be attributed to the fluctuations in the concentration of the sample constituents and to the degree of heterogeneity of the grains. The XRD-patterns of Egyptian iron ore deposits prove that the main phases are hematite and quartz. © 2008 Elsevier B.V. All rights reserved.

1. Introduction The electrical properties of materials consisting of a mixture of metals and dielectrics are extremely sensitive function of the relative concentrations of the components. Furthermore, the electrical properties of the material depend on the components in which they are distributed throughout the volume of the material which can be explained by X-ray diffraction. In addition, the electrical response of multicomponent system depends basically upon the volume fraction and electrical properties of each individual component [1,2]. Due to the presence in a mixture, the individual components will interact, leading to the development of a region of distinct electrical and physical properties. AC measurements yield information which can be used to determine the conduction process applicable. Three main conduction models are applicable to materials, the hopping model, the variable hopping model and the band theory [3,4]. Recently, the DC electrical properties of various materials have been extensively studied, but relatively little work has been carried out on their AC electrical behavior [5,6]. The effective electrical properties of mixtures depend basically on the particle size [7], particle shape [8], the effective conductivity and dielectric constant of the interstitial constituents [9], heterogeneity and randomness of the mixture, and the frequency of the applied field [10].

∗ Corresponding author. Tel.: +20 115985275; fax: +20 233370931. E-mail address: [email protected] (M.M. Gomaa). 0254-0584/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2008.09.012

The composite properties of rocks vary appreciably with frequency [11]. At low frequency range, the effective conductivity is gradually increasing function of frequency, while the effective dielectric constant is much more strongly dependent on frequency [12,13]. Electrical characteristics have been interpreted as being caused by geometric or textural heterogeneities of the rock system [12,14], or were related to electrical and electrochemical processes developed at the interfaces between rock grains [1,15]. Interactions between charged particles give rise to double layer around these particles. Polarization of such layer by an applied electric field has been pointed out as the main mechanism for the anomalous behavior observed in rocks [16,17]. Knight and Abad [18] observed a power law dependence of the dielectric constant on the frequency and that was related to the texture of the sandstone samples. The power law response is thought to be due to the random nature of the constituents within the samples [19,20]. Dry sandstone samples without a metallic component at room temperatures are good dielectrics with conductivity value of the order of 10−10 S m−1 and a relative dielectric constant of the order of several units. For a combination of sand and hematite, the interface gives rise to large values of dielectric constant with strong frequency dependence [21,22], which can be explained by surface conductivity and polarization processes. In the absence of an applied electric field, ions are free to move. When an oscillating electric field is applied, the ions polarized around the rock grains give rise to large dipoles and to large apparent dielectric constants [21–23]. As the frequency increases, ions have

314

M.M. Gomaa et al. / Materials Chemistry and Physics 114 (2009) 313–318

less time to polarize and contribute more to the conductivity, since they are more in phase with the applied oscillating electric field. The addition of a small amount of conductor to the sample may increase the conductivity and decreases the dielectric constant. The air is one of the important factors in representing the dielectric properties of the mixture. These effects come from physical reactions of the grain interface and can be considered as surface contributions to the complex electrical conductivity of a porous system [21,22]. The most probable polarization mechanism is the orientation polarization of molecules or hopping of ions along the surface [21,22,24]. Chelidze et al. [22] concluded that the polarization of non-conducting particle coated with a conducting one and embedded in an AC field leads to high dielectric values at low frequencies. This explains why the addition of small quantities of conductor to a porous rock causes a strong dielectric values at low frequencies. Hematite as a rock occurs in many types of igneous, metamorphic and sedimentary rocks. The largest and most economically important hematite deposits are mainly of sedimentary origin, forming from the weathering of iron bearing minerals. In these sedimentary deposits, hematite is thought to have precipitated from lakes or seas by organic and/or chemical processes. The hematite often occurs with intermixed layers of quartz or chert. This study has thrown the light upon the nature of Egyptian iron ores, its group minerals, its crystal structure and their relation with the electrical properties. The iron ore deposits of these localities vary greatly in their mineralogical and chemical composition. In the present work, the electrical properties and the X-ray diffraction of 20 iron ore deposits from East Aswan (Eastern Desert) and Bahariya Oasis (Western Desert) were demonstrated. The electrical measurements have been measured in a dry condition in the frequency range from 10 Hz to 100 kHz at room temperature (∼20 ◦ C). Mechanisms of conduction and polarizations were presented under different constituent concentrations of the present samples. XRD patterns were also demonstrated in order to investigate the different phases of the different constituents and understand the crystal structure of the different natural pattern of these samples.

2.2. Bahariya iron ore deposits Bahariya iron ores deposits in the western desert of Egypt have been also chosen for the present study and it represents the second source of iron ore in Egypt. The Bahariya iron ore deposits are generally capped [25] by an alluvial cover and/or quartzite. The upper part of the ore body is usually composed of hard goethite with some pockets of manganiferous hematite or conglomerate. The lower part is composed of manganiferous hematite with some pockets of hard goethite, and may be changed, especially at its lower parts, into pisolitic and oolitic goethite without manganese pockets. The main minerals associated with the ore include halite, gypsum, barite, quartz and clayey material. 3. Experimental work 3.1. X-ray diffraction The X-ray diffraction measurements have been carried out by using Siemens 500 instruments. The applied current in the X-ray tube was 36 mA and the applied voltage was 45 kV. Cu target was used in Siemens 500 instruments. X-ray diffraction measurements were carried out overnight at interval of the diffraction angle ( = 0.01). The peaks of these XRD patterns correspond to those of the theoretical patterns from the ASTM data file to determine the crystal structures, lattice parameters, and crystal planes (h k l) for all phases found on Egyptian iron ore samples. 3.2. Electrical measurements Electrical and dielectric properties of 20 hematitic sandstone samples of Egyptian iron ore deposits in Aswan and Bahariya have been investigated. Complex impedance measurements were carried out at room temperature (∼20 ◦ C). Data were performed in the frequency range from 10 Hz up to 100 kHz using Hioki 3522-50 LCR Hitester Impedance Analyzer. The measurement system was discussed elsewhere [27–29]. In order to measure the electrical response of the sample under investigation, the effect of heterogeneity and randomness of the mixture was eliminated by grinding the samples. The samples were grinded for 3 min (600 rpm) by MiniMill 2, PANalytical, Netherlands (particle size ∼1 ␮m), Afterwards, the samples were pressed at 120 kN for 1 min by pressing machine (Herzog hydraulic HTP40, UK). The samples become like a homogenous pellets produced by the mentioned press tool. Samples dimensions were in the order of 3-mm thickness and 40-mm diameter. The homogenous pellet samples were measured electrically at a relative atmospheric humidity (∼50%). The samples were initially evacuated and measured in an isolated chamber. A voltage of 1 V was applied and the current density in the sample was ∼ =4 × 10−6 (␮A cm−2 ). The complex relative dielectric constant is given by, ε∗ = ε − iε ;

ε =

2. Samples 2.1. Aswan iron ore deposits Aswan iron ore deposits in the eastern desert of Egypt have been chosen for the present study in order to understand the composition and texture of this sediment. The heavy minerals in the Nubian sandstone in Aswan have been found to be mainly iron ores, zircon, tourmaline and futile [10]. Attia [25] considered that the Nubian sandstone is of marine origin. Lithologically, Aswan sandstone is essentially composed of conglomerates, sandstones, sandy shales, clays and quartzitic bands [10,25]. The iron ore bands are often associated with ferruginous sandstones and clays. Nakhla and Shehata [26] supposed that the iron ores of east Aswan are composed of cryptocrystalline hydrated hematite (Fe2 O3 –nH2 O), microcrystalline hematite, clay minerals, cryptocrystalline and amorphous silica, quartz possesses a sub angular to sub-rounded form and some other ingredients. X-ray diffraction proved the presence of hematite and quartz with the occasional presence of chamosite in some ore specimens. According to pervious semi-quantitative spectrographic analysis [26] of iron ore samples there is a wide range of variation in chemical composition. A brief outline on the geochemical nature of the most important elements present in Aswan iron ore deposits are Fe, Si, Ca, Mg, Mn, P, S, Cu, Ti, Ni, Cr and Zr.

Cp C0

&

ε =

Gp  · C0

 

&

C0 = ε0 ×

A d

(1)

where A, d, Cp , Gp , , ε , and ε0 are the cross sectional area of the sample, sample thickness, the parallel capacitance, the parallel conductance, the angular frequency, relative dielectric constant and the permittivity of free space (8.85 × 10−12 F m−1 ), respectively. The measured parameters are both series and parallel capacitance and resistance at different frequencies. In the series mode, the complex impedance Z is given by, Z = Rs − iXs ;

Xs =

1 Cs

(2)

where Rs is the series resistance (real impedance), Xs is the reactance and Cs is the series capacitance. The complex resistivity * is given by, ∗ = Z ×

  A d

;

=

1 ∗

(3)

For the parallel model,

 

 = Rp ×

A d

;

=

1 

(4)

where Rp ,  are the parallel resistance and conductivity.

4. Results and discussions 4.1. Results of electrical properties Generally, the increasing of conductor constituents increases the conductivity and decreases the dielectric constant. The conductivity increases due to the increase of conduction paths between the

M.M. Gomaa et al. / Materials Chemistry and Physics 114 (2009) 313–318

315

There is no change in the conductivity at low frequencies for samples BA1 and BA2. It is observed that the conductivity shows a frequency dependent behavior for all the samples under study. At relatively high frequencies, curves tend to merge with each other with a constant slope (Fig. 1). Generally the conductivity increases with increasing frequency with a characteristic wn dependence, with n ∼ 0.75, n is the power law exponent which generally varies between 0 and 1 depending on many parameters (grain size, grain shape, texture, etc.). The value of n decreases with increase of interaction between the grains and the surrounding surfaces. Samples BA1 and BA2 show a flat response with wn dependence. The phenomenon of the conductivity dispersion in solids is generally analyzed using Jonscher’s law [19]. The exponent n represents the degree of interaction between mobile ions with the grains around them. According to Jonscher models [19], the interaction between all dipoles participating in the polarization process is characterized by the parameter n. A unit value of n implies a pure Debye case, where the interaction between the neighboring dipoles is almost negligible and the only conductive element is the DC resistance. 4.1.2. Relation between dielectric constant and frequency Fig. 2a and b shows the variation of the dielectric constant against frequency for Aswan and Bahariya iron ores deposits. With the increase of the conductor concentration the air gaps in the sample decrease and thus generally increase the dielectric constant to a certain limit before the grains just begin to touch each other, this is why the sample (AS4) has the highest dielectric constant. When the grains touches each others there is no air gap between them and the dielectric constant comes to its lowest value, this is why the sample (AS10, and BA7) has the lowest dielectric constant

Fig. 1. Variation of the conductivity with frequency for Aswan (a) and Bahariya (b) iron ore deposits.

two electrodes, while the dielectric constant decreases due to the decrease of air gap between the grains. Also, frequency, pressure and chemical reaction may lead to the same results as the conductor concentration [4,5]. The samples are mainly hematite as a conductor and sand as insulator and the measured conductivity of the samples ranges from insulator to semiconductor. Lima and Sharma [7] have shown that the effective electrical conductivity and dielectric permittivity of shaly sands depend basically on the conductor volume content in the sand and the frequency of the applied electrical field. 4.1.1. Relation between conductivity and frequency Fig. 1a and b depicts the variation of the conductivity versus frequency for the twenty samples of Aswan and Bahariya iron ore deposits. As concentration increases, more continuous paths are formed between electrodes and more conductor paths (conductivity) from the conductor grains are added to the current and consequently increase the conductivity. There is supposed to find a critical concentration and a critical frequency. Critical concentration is found when the conductor grains (hematite) begin to contact with each other, forming the first continuous path of conductor between the two electrodes. This critical concentration is not clear at the Aswan area samples whereas nearly all the samples did not reach that concentration, but it can be seen clearly in, Fig. 1b, for samples BA1 and BA2. Also, other samples show the beginning of this behavior (samples BA6 and BA10). The same is done for the critical frequency. Critical frequency is found when the curve changes its slope with the increase of frequency due to the change in the mechanisms of conduction in the sample.

Fig. 2. Variation of the dielectric constant with frequency for Aswan (a) and Bahariya (b) iron ore deposits.

316

M.M. Gomaa et al. / Materials Chemistry and Physics 114 (2009) 313–318

conducting particles in the material is increasing. Only the samples with no dispersion (BA3 and BA10 as an example) with frequency obey Jonscher’s universal law [30]. 4.1.4. Relation between real and imaginary parts of complex impedance (Z) Fig. 4a–c shows the variation of the imaginary part versus the real part of complex impedance for Aswan and Bahariya iron ore deposits. It is clear from the figure that conduction paths show an arc in the impedance plane. With the increase of concentration the angel between that arc and the Im Z (imaginary impedance) increases. For higher concentrations this arc is expanded to be a part of semicircle or depressed semicircle. In Fig. 4a the samples shows

Fig. 3. Variation of the loss tangents with frequency for Aswan (a) and Bahariya (b) iron ore deposits.

(Fig. 2a and b). Increasing the frequency decreases the dielectric constant until the sample reaches the value of the insulator component (quartz) [6]. The samples BA1 and BA2 (Fig. 2b) have high dielectric values, especially at high frequencies. The dielectric constant (ε ) is frequency dependent (ε ∝ wn−1 ; n ∼ −0.25) nearly for all the samples under study. The dispersive nature of the relaxation may be attributed to the broad distribution of relaxation times of the dipoles. The low-frequency dielectric dispersion is widely found in many systems in which less mobile charge carriers dominate the behavior [19]. Generally, the dielectric constant has two regions with different slopes with the variation of frequency. The low frequency slope is steep (≈−0.25) and it decreases until it reaches a slope of ≈−0.1 (sample BA7). The anomalous dielectric properties of the present samples can also be interpreted using percolation theory. This theory predicts that, when the conductive fraction (hematite) increases, clustering of conductive inclusions develops and the thickness of insulating gaps between conductive clusters decreases, causing a large increment in the capacitance of the sample. Further increases in the conductive component cause the shunting of insulating capacitive gaps. 4.1.3. Relation between loss tangents with frequency Fig. 3a and b shows the loss tangent (tan ı = ε /ε ) versus frequency. Samples AS1 and AS4 give their maximum at 200 Hz. The diagram of the loss tangent versus frequency (Fig. 3a) is naturally subdivided into two segments, while it can be subdivided into three segments for Fig. 3b (sample BA2). The decreasing tan ı at low frequencies (Fig. 3b, below 20 Hz) indicates that the fraction of

Fig. 4. Variation of the real with imaginary parts of the complex impedance (Z) for Aswan (a) and Bahariya (b and c) iron ore deposits.

M.M. Gomaa et al. / Materials Chemistry and Physics 114 (2009) 313–318

Fig. 5. XRD-patterns of Aswan (AS) iron ore deposits. 1 represent the peaks of Fe2 (SiO4 ), 2 to SiO2 , 3 to Fe2 O3 , 4 to Fe3 O4 and 5 to Mn3 O4 .

317

Fig. 6. XRD-patterns of Bahariya (BA) iron ore deposits. 1 represents the peaks of Fe2 (SiO4 ), 2 to SiO2 , 3 to Fe2 O3 , 4 to Fe3 O4 and 5 to Mn3 O4 .

only the arc with different angels (different concentrations). That means that there is not any conduction paths between the electrodes and/or the concentration of the samples is below the critical concentration. Fig. 4b shows the arc with different angels from the Im Z (samples BA3 to BA10). That means that all these samples have no conduction paths between the electrodes or have concentrations below the critical concentration. Samples BA1 and BA2 (Fig. 4b) shows a semicircle. The increase of the slope of the arc and its movement towards a semicircle is an indicator of the increase of the continuous paths of the conducting medium. Fig. 4c illustrates the behavior of sample BA1 indicating a highest conduction paths with highest concentration. 4.2. X-ray diffraction results The X-ray diffraction measurements have been carried out by using Siemens 500 instruments. The X-ray powder diffraction patterns of a representative Aswan iron ore deposits (AS) are shown in Fig. 5. As can be seen in the pattern, reflections representative of Fe2 O3 , Fe3 O4 , Fe2 (SiO4 ), Mn3 O4 and SiO2 . The reflection peaks of Fe2 O3 (hematite) at 2 = 24.2, 33.2, 35.65, 40.88, 54.2 are the main peaks which corresponding to the plans (0 1 2), (1 0 4), (1 1 0), (1 1 3), and (1 1 6), respectively. These reflection peaks are slightly changed its intensity with position changing. Also, the XRD patterns of Aswan (AS) iron ore deposits show a few reflection peaks of Fe3 O4 at 2 and (h k l) are 34.1 (0 2 3), 34.66 (1 1 1), 47.5 (1 3 2), 58.87 (1 3 4). Furthermore, Fe2 (SiO4 ) peaks at 2 and (h k l) are 57.35 (1 5 2), 69.1 (3 4 0) and 82.68 (3 5 2) which are relatively low intensity comparing with that of Fe2 O3 peaks. While it shows a three very low intensity reflection peaks for Mn3 O4 at 2 (h k l) 36.45 (2 0 2), 77.5 (4 0 4), 80.6 (3 1 6) and only one reflection peak for SiO2 at 2 = 21.1 (1 1 1). The diffraction patterns of Aswan samples have approximately the same phases with slightly change in the peak intensity. Therefore, the electrical properties of these samples show the same behavior as mentioned above (Figs. 1a, 2a and 3a). X-ray powder diffraction patterns of Bahariya (BA) iron ore deposits are shown in Fig. 6. As can be seen in the pattern, reflections representative of Fe2 O3 , Fe3 O4 , Fe2 (SiO4 ), Mn3 O4 and SiO2 . The reflection peaks of Fe2 O3 (hematite) at 2 = 24.2, 33.2, 35.65, 40.88, 54.2 are the main peaks which corresponding to the plans (0 1 2), (1 0 4), (1 1 0), (1 1 3), and (1 1 6), respectively. These reflection peaks are slightly changed its intensity with position changing. Also, the XRD-pattern of Bahariya (BA) iron ore deposits show a few reflection peaks of Fe3 O4 at 2 and (h k l) are 34.1 (0 2 3), 34.66 (1 1 1), 47.5 (1 3 2) and 58.87 (1 3 4). In the case of Fe2 (SiO4 ), the

Fig. 7. XRD-patterns of Bahariya (BA) iron ore deposits where the peaks 2 for SiO2 and 3 for Fe2 O3 .

2 and (h k l) are 57.35 (1 5 2), 69.1 (3 4 0) and 82.68 (3 5 2) which are relatively low intensity comparing with Fe2 O3 peaks. While it shows five very low intensity reflection peaks for Mn3 O4 of 2 and (h k l) at 36.45 (2 0 2), 65.4 (3 2 3), 71.7 (1 0 7), 77.5 (4 0 4) and 80.6 (3 1 6). For some samples, one reflection peak of SiO2 has appeared at 2 = 21.1 corresponding to (h k l) = (1 1 1). The diffraction patterns of Bahariya (BA) samples have approximately the same phases with slightly change in the peak intensity for BA3, BA4, BA5, BA7, BA8 and BA9. Therefore, the electrical properties of these samples show the same behavior as mentioned above (Figs. 1b, 2b and 3b). As shown in Fig. 7, the XRD patterns of SiO2 at 2 = 21.1 disappear for samples BA1, BA2, BA6 and BA10 due to the slightly content of SiO2 in these samples comparing with other samples (sample BA7). The enhancement of the electrical properties of these samples may be due to the absence of SiO2 (quartz) phase which illustrated in Fig. (1b, 2b, 3b and 4c). 5. Conclusion The electrical properties and X-ray diffraction of 20 Egyptian iron ores samples from two different areas in Egypt (Aswan and Bahariya) have been investigated. XRD measurements prove that, the samples are mainly hematite (Fe2 O3 ) as a conductor and quartz (SiO2 ) as insulator. At frequency range from 10 Hz to 100 kHz, Complex impedance measurements were performed at

318

M.M. Gomaa et al. / Materials Chemistry and Physics 114 (2009) 313–318

room temperature (∼20 ◦ C). The frequency dependence on conductivity shows a classical relaxation behavior followed Jonscher’s universal law. The measured electrical properties vary strongly with the frequency and sample composition. The difference in the electrical properties may be attributed to the fluctuations in the concentration of the sample constituents and to the degree of heterogeneity of the grains. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

R. Knight, A. Nur, Geophysics 52 (1987) 644–654. R. Knight, J. Geomag. Geoelectr. 137 (1983) 767–776. C.A. Dias, J. Geophys. Res. 77 (25) (1972) 4956–9445. M.M. Gomaa, R.M. Elsayed, Geophys. Prosp., in press. M.M. Gomaa, M.Sc., Thesis, Cairo University, Egypt, 1996. M.M. Gomaa, Ph.D. Thesis, Cairo University, Egypt, 2004. O.A.L. De Lima, M.M. Sharma, Geophysics 57 (1992) 789–799. P.N. Sen, Geophysics 49 (1984) 586–587. P.N. Sen, Phys. Rev. B., 137, 9508–9517, 1089. N.M. Shukri, A. Ayouty, Bull. Instit. Desert, Egypt 3 (2) (1959) 65–88.

[11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]

G.R. Olhoeft, Geophysics 137 (1985) 2492–2503. P.N. Sen, Appl. Phys. Lett. 39 (8) (1981) 667–668. H.J. Vinegar, M.H. Waxman, Geophysics 49 (1984) 1267–1287. R.J. Knight, A.L. Endres, Geophysics 55 (1990) 586–594. D.J. Marshall, T.R. Madden, Geophysics XXIV (4) (1959) 790–816. S.S. Dukhin, V.N. Shilov, Dielectric Phenomena and the Double Layer in Disperse Systems and Polyelectrolytes, John Wiley and Sons, New York, 1974. W.C. Chew, P.N. Sen, J. Chem. Phys. 77 (9) (1982) 4683–4693. R. Knight, A. Abad, Geophysics 60 (2) (1995) 431–436. A.K. Jonscher, J. Phys. D: Appl. Phys. 32 (1999) R57–R70. M.M. Gomaa, Ann. Geophys., in press. T. Chelidze, Y. Gueguen, Geophys. J. Int. 137 (1999) 1–15. T. Chelidze, Y. Gueguen, C. Ruffet, Geophys. J. Int. 137 (1999) 16–34. A.A. Garrouch, M.M. Sharma, Geophysics 137 (1994) 909–917. P.W.J. Glover, P.G. Meredith, P.R. Sammonds, J. Geophys. Res. 99 (B11) (1994) 21 635–21 650. M.I. Attia, Geol. Surv., Egypt 262 (1955). F.M. Nakhla, M.R.N. Shehata, Miner. Depos. 2 (1967) 357–371. H.M. Gobara, M.M. Gomaa, Petrol. Sci. Tech., in press. M.M. Gomaa, H. Darwish, S.M. Salman, J. Mater. Sci.: Mater. Electr. 19 (2008) 5–15. H. Darwish, M.M. Gomaa, J. Mater. Sci.: Mater. Electr. 17 (2006) 35–42. S. Jankowski, J. Am. Ceram. Soc. 71 (4) (1988) C-176–C-180.