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Indian Journal of Pure & Applied Physics Vol. 43, October 2005, pp. 777-782 Dielectric dispersion and microwave dielectric study of marbles in support of radar investigations R J Sengwa* & A Soni Microwave Research Laboratory, Department of Physics, J N V University, Jodhpur 342 005, Rajasthan Recevied 13 February 2004; revised 11 August 2005; accepted 16 August 2005 The dielectric permittivity ε′ and loss ε′′ of nine marble samples collected from open marble mines of Makarana, Rajsamand, Ambhaji and Kesariyaji of Rajasthan were studied in the frequency range 100 Hz-100 kHz and also at 10.1 GHz at room temperature. It is found that the ε′ values of dry marbles decrease with increase in frequency in the range 100 Hz100 kHz. All the studied marbles are governed by the Cole-Cole dielectric dispersion. The values of static dielectric constant εo, high frequency limiting dielectric constant ε∞, dielectric relaxation strength Δε, distribution parameter α, and relaxation time for dipole rotation τ were determined from the complex Cole-Cole plots. All these samples have α values greater than 0.5 and their Δε values vary significantly. Further, wide variation in ac conductivity σ is also observed for different samples. The effect of sample bulk density and variation in the chemical composition on low frequency and microwave permittivity of the studied marbles have been recognized. The measured values of dielectric permittivity of these marbles were also compared and discussed with the earlier reported ε′ values of marbles and limestones of other regions. The precise microwave dielectric measurements of marbles and recognization of their dependence on petrological and chemical composition are interesting and can be used in support of radar investigations of the Earth’s geology. Keywords: Geological materials, Marbles, Dielectric constant, Cole-Cole plots, Relaxation time IPC code: G01R27/26 1 Introduction Due to variation in bulk density, mineralogical composition and crystalline structure of rocks and minerals, their dielectric measurements over wide frequency range had been the subject of several researchers1-11. Geological materials exhibit the dielectric dispersion in low frequency region, which can be represented by Cole-Cole arcs12. After several attempts, it is established that the dielectric properties of rocks and sediments are primarily a function of mineralogy, frequency, water saturation, porosity, rock texture, component geometry and electrochemical interactions2,7,11. Dielectric dispersion studies in low frequency region are helpful to understand the behaviour of induced polarization2,7 in the materials, while high frequency dielectric measurements are useful in planning ground penetrating radar surveys13-15, in microwave remote sensing9,16 of the Earth’s geology of these materials deposited areas and calibration of time domain reflectometry measurements17,18. In the present paper, the dielectric dispersion behaviour of popular variety marbles of different areas of Rajasthan state has been studied. Marbles are ___________ *Email: [email protected] limestones, which have been crystallized by heat or pressure during metamorphic processes. Different names of marbles are derived from the locality where they are found, the formation in which they occur, from some peculiarity of structure, colour etc. 2 Experimental Details 2.1 Materials Marble samples of different varieties were obtained from the marble mines of Makarana (MK1, MK2 and MK3), Rajsamand (RS1, RS2 and RS3), Ambaji (AM) and Kesariyaji (KS1 and KS2). Selected samples alongwith their chemical compositions are presented in Table 1. 2.2 Samples preparation for dielectric measurements Marble rocks were cut by a diamond wheel cutter and polished to obtain thin plates of thickness ;1.5 mm. Surfaces of the prepared samples were polished to get very smooth in order to ensure good electric contacts. Silver plated brass plates were used for the fabrication of parallel plate capacitors with sample as dielectrics for the dielectric study in the frequency range 100 Hz–100 kHz. X–band rectangular waveguide dimension size samples were prepared INDIAN J PURE & APPL PHYS, VOL 43, OCTOBER 2005 778 Table 1—Chemical composition of marbles (percentage by weight) Specimen number Colour Makarana marbles MK1 white MK2 dirty white MK3 light pinkish Rajsamand marbles RS1 pure white RS2 pinkish gray RS3 brownish Ambaji marble AM pure white Kesariyaji marbles KS1 greenish KS2 greenish CaO SiO2+MgO Fe2O3+Al2O3 AI LOI 44.80 44.24 52.08 1.34+6.85 4.54+3.22 0.60+1.61 0.27+0.63 0.15+0.77 0.13+1.07 1.22 6.52 1.82 43.61 39.23 42.87 30.80 47.88 38.92 1.42+19.74 4.90+0.20 11.38+3.82 0.47+0.55 0.53+0.77 1.58+0.62 2.06 5.82 6.82 44.74 38.88 36.21 54.32 0.32+0.40 0.06+0.26 1.06 42.08 24.08 18.20 18.88+5.23 22.16+5.03 2.51+1.79 1.66+1.02 22.70 31.02 24.70 21.38 from the same marble rock for the measurements of dielectric constant at 10.1 GHz. 2.3 Dielectric measurements The values of ε′ and ε′′ of marble specimens in the frequency range 100 Hz–100 kHz were determined by measuring the capacitance and dissipation factor of the parallel plates capacitors with sample as dielectric. A standard three-terminal dielectric cell is used for this purpose. These measurements were made with automatic Keithley LCZ meter model 3330. The values of ε′ and ε′′ at 10.1 GHz were determined employing the short-circuited waveguide method19,20 for rectangular waveguide operating in TE10 mode at room temperature. 3 Results and Discussion 3.1 Low frequency dielectric dispersion The evaluated permittivity (ε′) values of dry marble specimens were presented against frequency in Fig. 1. These plots show dispersion, which is pronounced at lower frequencies and in some specimen is comparatively very large. Table 1 shows that marbles are considered to behave as very heterogeneous dielectrics with components having differing ε′. In geologic materials, low frequency dispersion is believed to be due to polarization associated with charge build-up at grain boundaries or at grain imperfections of the sample particles of various dielectric properties2,7,21. Further, the contribution of grain sizes is also an important factor in controlling the low frequency values of ε′. Figure 1 shows that the low frequency values of Kesariyaji samples (KS1 Fig. 1—ε′ versus log f plots of marbles and KS2) are comparatively very high. Further Rajsamand (RS3) and Makarana (MK3) also show significantly high ε′ values in comparison to the other studied specimen i.e. MK1, MK2, RS1, RS2 and AM. Table 1 shows that the specimens KS1 and KS2 have significantly higher percentage of Fe2O3+Al2O3 in SENGWA & SONI: MICROWAVE DIELECTRIC STUDY OF MARBLES 779 their heterogeneous composition. Similarly, in case of Rajsamand Marbles and Makarana marbles, specimens RS3 and MK3 have higher percentage of Fe2O3+Al2O3. From the comparative ε′ values (Fig. 1) with percentage of Fe2O3+Al2O3 in the specimen composition (Table 1), it can be concluded that the higher percentage of Fe2O3+Al2O3 increases the ε′ values of these marble specimen of same locality. Earlier, Emerson and Welsh22 also studied dielectric dispersion of one specimen of marble and two different specimen, of limestone of Mt. Moss mine, Australia. The mineralogical composition of marble sample and one limestone sample is identical to the Ambaji (AM) specimen used in the present study. They observed very low dielectric dispersion. Further, Emerson and Welsh22 reported ε′ values of the marble and limestone specimen in the frequency range 1 Hz–160 kHz which are in good agreement with the ε′ values of AM sample in the same frequency range. But in case of another limestone specimen, which is admixture of a variety of ultrafine submicron grains of silicate and oxide mineral, they observed higher permittivity. In case of KS1 and KS2, the contribution in observed high ε′ values may be due to the variation in their chemical composition. Loss tangent (tanδ = ε′′/ε′) values of these samples are plotted against logf in Fig. 2. In case of RS3 only, loss tan δ peak frequency is found. The observations of these plots might lead us to speculate that loss tan δ peak frequency would be lower than 100 Hz in MK1, MK2, MK3, S1, RS2 and AM while it may be above 100 kHz in case of KS1 and KS2. Figure 3 shows the variation of ac conductivity of these samples. For all these samples almost a linear behaviour is observed between log σ and log f. In geological materials conduction is expected to be by motion of weakly bound ions in the lattice or defects in the ionic bonded structure. Comparatively high value of conductivity is observed in case of KS1 and KS2, which is due to the presence of higher percentage of Fe2O3+Al2O3 in their chemical composition. Further, significant variation in ac conductivity is observed for entire marble specimen. The complex plane plots (ε′′ versus ε′) of these marble samples are plotted in Fig. 4. It is found that the dielectric dispersion of all these samples is governed by Cole-Cole relaxation behaviour to a dipole reorientation process. Earlier, several researchers2,3,8,14,23-25 also reported the Cole-Cole Fig. 2—Tan δ versus log f plots of marbles (○ – MK1, Δ – MK2, □ – MK3, ∇ – AM, ● – RS1, ▲ – RS2, ■ – RS3, – KS1 and ▼ – KS2) dielectric dispersion in different geologic materials. The Cole-Cole equation12 for dielectric dispersion is ε∗ ( ω) = ε′ − j ε′′ = ε ∞ + εo − ε∞ 1 + ( j ωτ ) 1− α where εo is the low frequency limiting value of permittivity or static dielectric constant, ε∞ the high frequency limiting value of permittivity, ω the angular frequency, τ the characteristic relaxation time of the dipole rotation in the system and the α parameter controls the broadness of the distribution (0 < α < 1). The values of εo and ε∞ were obtained by extrapolation of the Cole-Cole plots corresponding to low frequency region and high frequency region on the real axis respectively. The values of τ and α were evaluated26 from the relation v/u = (ωτ)1−α. Where u and v are the distances from the experimental points 780 INDIAN J PURE & APPL PHYS, VOL 43, OCTOBER 2005 Fig. 3—Log σ versus log f plots of marbles (○ – MK1, Δ – MK2, □ – MK3, ∇ – AM, ● – RS1, ▲ – RS2, ■ – RS3, – KS1 and ▼ – KS2) of Cole-Cole diagram to ε∞ and εo respectively on the permittivity axis. The evaluated values of εo, ε∞, dielectric strength Δε = εo – ε∞, α and τ are recorded in Table 2. Table 2 shows that the εo values of these marbles of different regions vary in the range 13.5 – 101. The significant variation is also observed in the εo values of same locality marbles. The determined ε∞ values of these samples were found in the range 8.5 – 11.5. The dielectric strength Δε values of MK1, AM and RS2 are very small while in case of MK3, RS3, KS1 and KS2, high values of Δε were observed. Table 2 shows that the observed α values of all these marble samples are higher than 0.5. This indicates a distribution of relaxations, which is consistent with the inhomogeneous structure of these samples23. The significant variation in the τ values suggests that different radius particles contributed in the dipole rotation, which is also influenced by the diffusion coefficient of counter ions in the vacancies or defects in the samples2. 3.2 Microwave dielectric behaviour The ε′ values of dry geologic materials in microwave region6,9,27 are almost independent of the Fig. 4—Cole-Cole plots of marbles frequency. Further, it is also confirmed9 that the bulk density of rock accounts for 50% of the observed variance in the ε′ values, whereas the loss factor ε′′ is very poorly correlated with the bulk density. Similar to bulk density, constituents of chemical composition of the rock equally affected the values of microwave dielectric permittivity. Sharif11 measured the values of ε′ and ε′′ of various oxides at 10 GHz (Table 3). Due to different values of ε′ and ε′′ of these oxides at microwave frequency, the variation in dielectric constants of these oxide bearing geologic materials is expected with the percentage change in their chemical SENGWA & SONI: MICROWAVE DIELECTRIC STUDY OF MARBLES 781 Table 2—Values of εo, ε∞, Δε, α, τ, density (d) and microwave dielectric constants (ε′ and ε′′) of marble specimens Specimen number Makarana marbles MK1 MK2 MK3 Rajsamand marbles RS1 RS2 RS3 Ambaji marble AM Kesariyaji marbles KS1 KS2 εo ε∞ Δε α τ (ms) d (g/cc) 13.45 23.55 52.50 10.10 9.90 11.50 3.35 13.65 41.00 0.52 0.69 0.52 2.630 4.960 5.100 2.70 2.75 2.72 8.06 7.22 7.39 0.57 0.35 0.33 20.15 14.80 68.00 9.60 9.80 9.00 10.55 5.00 59.00 0.68 0.69 0.62 4.720 3.740 0.590 2.82 2.64 2.70 6.86 7.10 7.21 0.41 0.28 0.40 15.70 10.60 5.10 0.68 0.540 2.69 8.03 0.27 101.00 89.00 8.50 10.50 92.50 78.50 0.65 0.65 0.042 0.015 2.72 2.65 6.40 5.80 1.02 0.45 10.1 GHz ε′ ε′′ Table 3—Values of ε′ and ε′′ of different oxides at 10 GHz (ref. 11) Oxides CaO SiO2 MgO Al2O3 Fe2O3 ε′-jε′′ 8.22-j0.12 4.43-j0.04 5.03-j0.17 12.66-j1.31 16.58-j0.93 composition constituents. Table 1 shows that the percentage chemical compositions of these marble specimens are different, while the bulk density is nearly the same (Table 2). In case of Rajsamand marbles, the bulk density varies by approximately + 4% of their average value of bulk density. Therefore, the ε′ values of these marbles can be considered independent of their bulk density except in case of Rajsamand marbles. Table 2 shows that the significant variation in ε′ values of different marbles at 10.1 GHz is mostly either due to the percentage variation in their chemical composition or structure variation of component geometries. Marbles are CaCO3 (ε′;8) rich, crystalline rocks. Table 3 shows that the increase in quantity of SiO2+MgO (ε′ < 5) in the chemical composition will decrease the ε′ values of marbles. On the other hand, if there is increase in the percentage of Fe2O3+Al2O3, (ε′ > 12) in their chemical composition, the value of microwave permittivity should enhance. The higher observed ε′ value of KS1 in comparison to KS2 is due to higher percentage of Fe2O3+Al2O3 in the composition of KS1. Further, the lower ε′ values of KS1 and KS2 in comparison to other marble samples (Table 2) may be due to increase in quantity of SiO2+MgO in their composition. The observed ε′ values of MK1 and AM were found nearly equal to the ε′ value of pure CaO (Table 3). It is expected because of their chemical composition close to pure CaO. Further, MK3 also has very low percentage of other oxides in its composition in comparison to the percentage of CaO. But, low ε′ value of MK3 in comparison to ε′ value of MK1 may be due to either its high hardness or variation in components geometry. The low ε′ value of MK2 in comparison to ε′ value of MK1 is expected because of the percentage of increase of SiO2 in its composition. In case of Rajsamand marbles, the observed ε′ value of RS1 is low which is due to higher percentage of SiO2+MgO in its composition in comparison to the percentage of SiO2+MgO in the composition of RS2 and RS3, although RS1 bulk density is high. Further, it seems that the higher ε′ value of RS3 in comparison to the ε′ value of RS2 may be because of the slight increase in bulk density of RS3 and also the increase in the percentage of Fe2O3+Al2O3 in its chemical composition. The observed values of ε′ of Makarana, Rajsamand and Ambaji marbles are also in good agreement with the microwave permittivity values of dry limestone samples16,27-29. Cervelle and Jin–Kai16 reported the microwave dielectric constants of dry marbles in the range 5.22-8.15. The observed ε′ values of the studied Rajasthan marbles of various localities at 10.1 GHz were also found in the same range16. For these marble specimens, the value of microwave permittivity ε′ is 782 INDIAN J PURE & APPL PHYS, VOL 43, OCTOBER 2005 found lower than the ε∞ values obtained from ColeCole plots. The difference in ε′ and ε∞ value ranges from 1.8 to 4.7. This significant difference suggests that there may be another dispersion above 100 kHz frequencies in the studied marble samples. The microwave dielectric loss ε′′ values of these marble samples have anomalous behaviour, which confirms that iron cations introduced during marble formation play a dominant role in the dielectric loss properties22. In case of KS1, the high value of ε′′ may be due to high percentage of Fe2O3+Al2O3 in its composition. 4 Conclusions The results of the present study suggest that the heterogeneity influences significantly the low frequency permittivities. The increase in percentage of Fe2O3 and Al2O3 in the chemical composition of marbles also enhances permittivity values in low frequency region. Similar to other geologic rocks and minerals, these marbles obey the Cole-Cole dielectric dispersion behaviour. Microwave dielectric permittivity of these marble specimens of nearly equal bulk density is governed by the variance in percentage of chemical composition of different oxides in the sample. The detailed study of different marbles will contribute significantly in high frequency electromagnetic waves dielectric sensing technique because the radar investigation of the Earth’s geology depends on the average dielectric constant of the area under investigation. Further, the dielectric constant of marble samples along with their chemical composition can be used to estimate the individual contribution and interaction contribution of the sample constituents to the dielectric constant using the volumetric dielectric mixing equations. Acknowledgement The authors are grateful to the Department of Science and Technology, Government of Rajasthan, for financial assistance. 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