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1.
The electrical properties of magmatic rocks (diabase and granite porphyry) from the complex dike located in the Main Caucasian (Akhtychaisk) fault zone are examined at temperatures of 100?C1000°C. It is established that the increase in the electrical conductivity from granite porphyry to diabase is caused by the decreased quartz content, increased total content of iron oxides FeO and Fe2O3, as well as the fine-grained texture of diabases and their secondary alterations. The pattern of temperature dependence of specific electrical conductivity observed in granite porphyry and diabases reflects the polymorphic transformation of the monoclinic structure to the triclinic structure (the MT-transformation), which occurs in the feldspar component of the rock. Another factor responsible for the shape of the mentioned temperature dependence is that the formation of an extrinsic mechanism of conduction is dominated by the defects (associated into complexes) in the crystal lattices of the minerals. This allows determining the energy of formation and migration of lattice defects and the energy of association of the lattice defects into complexes, which play an important role in the natural metamorphic processes. The AC measurements for the granite porphyry revealed frequency dispersion of the electrical conductivity, which decreases with increasing temperature.  相似文献   

2.
Spectral induced polarization as well as complex electrical measurements are used to estimate, on a non-invasive basis, hydraulic permeability in aquifers. Basic laboratory measurements on a variety of shaly sands, silts and clays showed that the main feature of their conductivity spectra in the frequency range from 10-3 to 103 Hertz is a nearly constant phase angle. Thus, a constant-phase-angle model of electrical conductivity is applied to interpret quantitatively surface and borehole spectral induced polarization measurements. The model allows for the calculation of two independent electrical parameters from only one frequency scan and a simple separation of electrical volume and interface effects. The proposed interpretation algorithm yields the true formation factor, the cation exchange capacity and the surface-area-to-porosity ratio, which corresponds to the inverse hydraulic radius. Using a Kozeny–Carman-like equation, the estimation of hydraulic permeability is possible.  相似文献   

3.
There are clear differences in the electrical conductivities of the crustal granites of the Qinghai-Tibet Plateau.Because these granites are among the major rock types on the Qinghai-Tibet Plateau, it is very important to detect the electrical conductivity of granites under high temperatures and pressures to study the electrical conductivity structure of this area. Using impedance spectroscopy at a frequency range of 10.1–106 Hz, the electrical conductivity of the muscovite-granite collected from Yadong was investigated at a confining pressure of 1.0 GPa and temperatures ranging from 577 to 996 K, while the electrical conductivity of the biotite-granite collected from Lhasa was investigated at a pressure of 1.0 GPa and temperatures ranging from587 to 1382 K. The calculated activation enthalpies of the Yadong muscovite-granite sample is 0.92 eV in the low-temperature range(577–919 K) and 2.16 eV in the high-temperature range(919–996 K). The activation enthalpies of the Lhasa biotite-granite sample is 0.48 eV in the low-temperature range(587–990 K) and 2.06 eV in the high-temperature range(990–1382 K). The change in the activation enthalpies of the granites at different temperature ranges may be associated with the dehydration of the two samples. The electrical conductivities of the granite samples obtained in the laboratory using impedance spectroscopy correspond well with field observations conducted near the sampling points, both in terms of the actual conductivity values and the observed variations between the low-temperature and high-temperature regimes. This correlation of laboratory and field conductivities indicates that the conductivities of the crustal rocks in the two regions closely correspond to granite conductivities.We calculated the electrical conductivities of muscovite-granite and biotite-granite samples using the effective medium and HS boundary models. When applied to the crustal rocks of southern Tibet, the results of the geophysical conductivity profiles lie within the range of laboratory data. Thus, the electrical characteristics of the crustal rocks underlying the southern Qinghai-Tibet Plateau can largely be attributed to granites, with the large changes to high conductivities at increasing depths resulting from the dehydration of crustal rocks with granitic compositions.  相似文献   

4.
Measurement of complex electrical conductivity as a function of frequency is an extremely sensitive probe for changes in pore and crack volume, crack connectivity, and crack surface topography. Such measurements have been made as a function of pore fluid chemistry, hydrostatic confining pressure, as well as uniaxial and triaxial deformation. This paper will; (1) describe the effects of triaxial deformation on the complex electrical conductivity of saturated porous rocks, (2) use the electrical data to model the mechanical stress-strain behaviour, and (3) compare the modelled behaviour with the stress-strain behaviour measured during the deformation. Experimental conductivity data tracks how the rock undergoes compaction with progressive loss of crack volume, followed by dilatation due to new crack formation, growth of existing cracks, crack interlinkage, and finally failure, as axial strain is increased. We have used the complex electrical data to produce a direction-sensitive (anisotropic) crack damage parameter, and used it to calculate the effective Young's modulus by employing the models of Walsh and Bruner. Comparison of the synthetic stress-strain curves so produced, with the experimentally derived stress-strain curves shows good agreement, particularly for undrained tests. This modelling is an improvement on similar curves produced using isotropic crack damage parameters derived from acoustic emission data. The improvement is likely to be due to the directional sensitivity of the electrical conductivity measurement, and its ability to discriminate between the formation of isolated cracks, and those cracks that contribute to the inter-connected crack space i.e. those cracks upon which transport properties of the rock such as electrical conductivity, and mechanical properties depend most critically during triaxial deformation.  相似文献   

5.
Frequency dependent electrical properties of minerals and partial-melts   总被引：4，自引：0，他引：4  
The resistance to current flow of minerals and partial-melts is a frequency dependent electrical property. Measurements of the frequency dependent electrical impedance of single crystal olivine, polycrystalline olivine, dunites, metapelites, and partial-melts, between 10–4 and 105 Hz, when plotted in the complex impedance plane, reveal arcs that correspond to different conduction mechanisms in the material being studied. In polycrystalline materials, two impedance arcs related to material properties (as opposed to electrode properties or electrode-sample interactions) are observed. Each impedance arc is activated over a distinct range of frequency, that is, the mechanisms occur in series. Based on experiments comparing single and polycrystalline impedance spectra, experiments on samples with different electrode configurations, and on samples of varying dimension, the mechanisms responsible for these impedance arcs are interpreted as grain interior conduction ( gi ), grain boundary conduction (in polycrystalline materials; gb ), and sample-electrode interface effects, from highest to lowest frequency, respectively. Impedance spectra of natural dunitic rocks reveal analogous behavior, that is, gb and gi add in series. The grain boundaries do not enhance the conductivity of any of the materials studied (a direct result of the observed series electrical behavior) and, under certain conditions, limit the total conductivity of the grain interior-grain boundary system. By examining the frequency dependence of the electrical properties of partial-melts, it is possible to gain information about microstructure and the distribution of the melt phase and to determine the conditions under which the presence of melt enhances the total conductivity. Impedance spectra of olivine-basalt partial-melts indicate that at least two conduction mechanisms occur in series over the frequency range 10–4-105 Hz, similar to the observed electrical response of melt-absent polycrystalline materials. In a sample containing isolated melt pockets the intermediate frequency grain boundary impedance arc is modified by the presence of melt indicating series conduction behavior. In a sample with an interconnected melt phase the high frequency grain interior impedance arc is modified by the melt phase, indicating the initiation of parallel conduction behavior. Because field EM response versus frequency curves are used to derive conductivity versus depth profiles, it is important to perform laboratory experiments to understand the frequency-dependent electrical behavior of Earth materials. Activation energies determined from studies that measure conductivity at a single frequency may be erroneous because of the shift of the dominant conduction mechanism with frequency as temperature is varied.  相似文献   

6.
The thermal effects of magmatic intrusion on the conductivity and dielectric constant of magnetic rocks from Hammamat sediments, NE desert, Cairo, Egypt (latitude ∼27° and longitude ∼33°) were investigated experimentally in the laboratory using nonpolarizing electrodes. Granitic magma was intruded into the Hammamat sediments, which are a mixture of mainly magnetite with sandstone and due to the thermal effect the area around was extensively heated and altered to different degrees. Due to this magma intrusion, magnetite was transformed (by heating) to hematite to different degrees according to its location from the intrusion. Complex impedance measurements were performed in the frequency range of 10 Hz to 100 KHz at normal temperature (∼20°C) and at a relative humidity of ∼50% RH. Samples were collected at different locations perpendicular to the core of the magma intrusion. Experimental data indicate that the electrical properties vary strongly as we move away (with distance) from the magma intrusion. The conductivity of hematite is ∼10−2 S/m and that of magnetite is ∼104 S/m. As we move from magnetite to hematite (to the core of the magma intrusion) it is supposed that the conductivity will decrease but it was found that the conductivity increases (which is supposed to be abnormal). The conductivity increases with increasing frequency from ∼10−8 S/m to ∼10−5 S/m with almost power‐law dependence on frequency. The conductivity increases in the order of one decade due to the variation from magnetite to hematite. The increase of conductivity, as we move from magnetite to hematite, was argued to be due to the heating that partially or completely melts the samples, thus the porosity of the samples was decreased and accordingly the conductivity and dielectric constant increased. It was also supposed that the grains of the conductor in the samples are coated or isolated with insulator material. A percolation behaviour for the conductivity and dielectric constant, characteristic of random conductor‐insulator mixtures, was found with distance, where continuous paths of the conductive material occur accompanied by peaking of the dielectric constant. Complex impedance plots show that as we move in the direction of altered samples (towards hematite) the relation between real and imaginary impedance changes from a linear form to an arc of a depressed semicircle and increases in depression as we move in the direction of the altered samples, which is consistent with the above interpretation.  相似文献   

7.
Transport properties (permeability and electrical conductivity) have been measured at different hydrostatic pressure runs on 7 crystalline rocks (gneisses and amphibolites) sampled from the KTB drilling project. The decrease of permeability by pressure are compared with the pressure-dependent data of the electrical conductivity (formation factor) resulting from complex impedance measurements. According to the equivalent-channel model (ECM), there exists a linear relationship between these parameters by representing both properties on logarithmic scales. The results show that it is possible to extrapolate high-pressure permeability from low-pressure (< 60 MPa) permeability data by using the pressure-dependent electrical conductivity (up to 300 MPa).  相似文献   

8.
Electrical, seismic, and electromagnetic methods can be used for noninvasive determination of subsurface physical and chemical properties. In particular, we consider the evaluation of water salinity and the detection of surface contaminants. Most of the relevant properties are represented by electric conductivity, P-wave velocity, and dielectric permittivity. Hence, it is important to obtain relationships between these measurable physical quantities and soil composition, saturation, and frequency. Conductivity in the geoelectric frequency range is obtained with Pride's model for a porous rock. (The model considers salinity and permeability.) White's model of patchy saturation is used to calculate the P-wave velocity and attenuation. Four cases are considered: light nonaqueous phase liquid (LNAPL) pockets in water, dense nonaqueous phase liquid (DNAPL) pockets in water, LNAPL pockets in air, and DNAPL pockets in air. The size of the pockets (or pools), with respect to the signal wavelength, is modeled by the theory. The electromagnetic properties in the GPR frequency range are obtained by using the Hanai–Bruggeman equation for two solids (sand and clay grains) and two fluids (LNAPL or DNAPL in water or air). The Hanai–Bruggeman exponent (1/3 for spherical particles) is used as a fitting parameter and evaluated for a sand/clay mixture saturated with water.Pride's model predicts increasing conductivity for increasing salinity and decreasing permeability. The best-fit exponent of the Hanai–Bruggeman equation for a sand/clay mixture saturated with water is 0.61, indicating that the shape of the grains has a significant influence on the electromagnetic properties. At radar frequencies, it is possible to distinguish between a water-saturated medium and a NAPL-saturated medium, but LNAPL- and DNAPL-saturated media have very similar electromagnetic properties. The type of contaminant can be better distinguished from the acoustic properties. P-wave velocity increases with frequency, and has dissimilar behaviour for wet and dry soils.  相似文献   

9.
We used regression analyses of water samples from 18 lakes, nine rivers, and one spring in Ethiopia to (a) test the hypothesis that water bodies of relatively higher salinity (K25>1000 μS cm−1) have a different conductivity to salinity relationship than waters of lower salinity (K25 < 1000 μS cm−1), and (b) develop models to predict total cations and salinity from conductivity that can be used for Ethiopian waters and other African aquatic systems of similar chemical composition. We found no statistical difference in the bilogarithmic relationships (total cations vs. conductivity; salinity vs. conductivity) for waters of higher salinity (K25 > 1000 μS cm−1) and waters of lower salinity (K25 < 1000 μS cm−1). However, comparison among our models and models from the literature suggests that developing separate equations for low and high salinity water bodies has some merit. We believe that the equations developed in this study can be used for Ethiopian waters and other African waters within the range of conductivity in this study.  相似文献   

10.
Freshly cored samples from a microprofile (7011–7013m in depth) of the German Continental Deep Drilling Project (KTB) were taken to measure the complex electrical conductivity (1 kHz up to 1 MHz), porosity, BET-surface, permeability and density. The porosity ranged about 1 vol%, while the permeability k varied from 16.05 µD to > 0.01 µD for in-situ pressure conditions. The permeability decreased about 2 orders in magnitude up to pressures of 200 MPa. Conductivity was measured in the same pressure range on 1 M NaCl saturated samples. Thin sections and SEM analysis revealed an enrichment of carbon and ilmenite (about 1 vol%) on inner cleavage cracks of mica, thus causing an unusual high (ranging from 4.2 × 10-3 S/m to 67 × 10-3 S/m) being orders of magnitude higher than normally measured on such types of rocks (about 300 × 10-6 S/m). An inverse pressure dependence of was detected on some of the samples. Electronic conduction was confirmed by least-squares-fits of model data to the frequency dispersion of the conductivity and by measuring the time dependence of the volume conductivity and its frequency dispersion. Thus the dominating role of the reconnected network of carbon and ilmenite on the enhanced volume conductivity was proved. An increase of the conductivity due to hydrofracturing by high pore fluid pressures plays a less important role.  相似文献   

11.
《水文科学杂志》2013,58(1):253-265
Abstract

Measurements of dielectric permittivity and electrical conductivity were taken in a saline gypsiferous soil collected from southern Tunisia. Both time domain reflectometry (TDR) and the new WET sensor based on frequency domain reflectometry (FDR) were used. Seven different moistening solutions were used with electrical conductivities of 0.0053–14 dS m?1. Different models for describing the observed relationships between dielectric permittivity (K a ) and water content (θ), and bulk electrical conductivity (EC a ) and pore water electrical conductivity (EC p ) were tested and evaluated. The commonly used K a –θ models by Topp et al. (1980) and Ledieu et al. (1986) cannot be recommended for the WET sensor. With these models, the RMSE and the mean relative error of the predicted θ were about 0.04 m3 m?3 and 19% for TDR and 0.08 m3 m?3 and 54% for WET sensor measurements, respectively. Using the Hilhorst (2000) model for EC p predictions, the RMSE was 1.16 dS m?1 and 4.15 dS m?1 using TDR and the WET sensor, respectively. The WET sensor could give similar accuracy to TDR if calibrated values of the soil parameter were used instead of standard values.  相似文献   

12.
The presence of water is one of the main concerns of nuclear waste disposal in rock-salt. It can be investigated using electrical properties of the rock. Laboratory measurements of frequency-dependent resistivity and other petrophysical parameters, such as porosity, water content, and specific internal surface area, have been carried out on rock-salt from the Asse mine in Germany, in order to obtain characteristic resistivity responses for the evaluation of geoelectric field methods and to develop new methods for the estimation of the water content and saturation. The laboratory method, on a.c. half-bridge for very high impedances, allows measurements of the resistivity spectrum of rock-salt in the frequency range from 15 Hz to 10 kHz. The saturation of the samples was varied artificially and was approximately 5%, 10%, 20% and 100%. The porosity varies between 0.1% and 0.5%, the water content is approximately 0.05% or less, and the initial saturation is less than 50%. The resistivity ranges from 10 MΩm at the initial saturation down to 1 kΩm for fully saturated samples. In the low-frequency range up to 100 Hz, an Archie-type relationship may be used to estimate the water content of the rock-salt from resistivity measurements. The Archie exponent m is found to be approximately 2. The resistivity is observed to be strongly dependent on frequency. The resistivity decreases with increasing frequency, with a greater decrease for small saturations and vanishing frequency dependence at complete saturation. The relative dielectric constant was found to be 6 ± 1. Saturation dependence was not observed within this error range. The measurements imply that, by measuring resistivity in rock-salt, estimations of water content and saturation, and thus the porosity, can be made in situ. This is particularly important for the safety of nuclear waste disposal in rock-salt.  相似文献   

13.
The influence of environmental conditions and the thermodynamic parameters which may determine the bulk electrical conductivity of, for instance, basaltic rocks are briefly discussed. At present it is not known to what extent these numerous variables determine the electrical conductivity of rocks quantitatively, since all too many laboratory measurements did not account for the required number of variables to define the system. Thus it is difficult to decide whether or not laboratory measurements on rocks have duplicated their in-situ electrical conductivity.One approach is to calculate the bulk conductivity of rocks from conductivities of constituent minerals, since it is much easier to define the thermodynamic equilibrium conditions for a single phase system. Therefore, laboratory data of the electrical conductivity of minerals, i.e. olivines and pyroxenes, are discussed to some extent particularly in the context of point-defect concentrations as a function of pO2 and the chemical activitiesa of the binary components of the minerals.The evaluation of a quantitative relationship requires a careful sample characterization. To find a basis for a reasonable interpretation of in-situ resistivity data, the test samples should be selected in regard to those conditions which are believed to exist in the appropriate layer of the earth.  相似文献   

14.
Based on experiments on rock electrical parameter dispersion properties in both water displacing oil and oil displacing water processes, it is found that the frequency dispersion properties of electrical parameters in water-bearing rocks are quite different from those in oil-bearing rocks. Oil saturation can severely impact the rock electrical parameter dispersion properties and as the oil saturation increases, the properties are more distinguishing. The variation of formation water salinity has a significant effect on the rock resistivity, hence the modulus of the rock complex resistivity varies with water saturation and a U-shaped curve occurs over a single frequency, just like the normal resistivity. However, the effect of formation water salinity on the rock frequency dispersion is less than that of oil saturation. As a result, the rock electrical parameter dispersion properties will have a significant potential of application in the evaluation of watered-out zones as well as identification of oil-bearing zones and water-bearing zones.  相似文献   

15.
The effects of temperature, fO2 and composition on the electrical conductivity of silicate liquids have been experimentally determined from 1200 to 1550°C under a range of fO2 conditions sufficient to change the oxidation state of Fe from predominantly Fe2+ to Fe3+. Oxidation of ferrous to ferric iron in the melt has no measurable effect on the conductivity of melts with relatively low ratios of divalent to univalent cations. Under strongly oxidizing conditions a minor decrease of conductivity is detected inth highΣM2/ΣM+ ratios. It is concluded that for purposes of estimating the conductivity of magmatic liquids, fO2 may be ignored to a first approximation. Both univalent and divalent cation transport is involved in electrical conduction. Melts relying heavily on divalent cations for conduction, i.e. melts with relatively large ΣM2+/ΣM+ ratios, show strong departures from Arrheenius temperature dependence with the apparent activation energies decreasing steadily as the temperature increases. Conductivities dominated by the univalent cations, in melts with relatively small ΣM2+/ΣM+ ratios, show classical Arrhenius temperature dependence. These observations are discussed in terms of the general characteristics of the melt structure.Compositional variations within the magmatic range account for much less than an order of magnitude variation in electrical conductivity at a fixed temperature. This observation, combined with previous measurements of the conductivity of olivine (A. Duba, H.C. Heard and R. Schock, 1974) make it possible to state with reasonable confidence that melts occurring within the mantle will be more conductive by 3–4 orders of magnitude than their refractory residues. Potential applications to geothermometry are discussed.  相似文献   

16.
We report here the electrical resistivity measurements on two natural zeolites–natrolite and scolecite (from the Killari borehole, Maharashtra, India) as a function of pressure up to 8 GPa at room temperature. High-pressure electrical resistivity studies on hydrous alumino-silicate minerals are very helpful in understanding the role of water in deep crustal conductivities obtained from geophysical models. The results obtained by magneto-telluric (MT) soundings and direct current resistivity surveys, along with the laboratory data on the electrical resistivity of minerals and rocks at high-pressure–temperature are used to determine the electrical conductivity distribution in continental lithosphere. The electrical resistivity of natural natrolite decreases continuously from 2.9 × 109 Ω cm at ambient condition to 7.64 × 102 Ω cm at 8 GPa, at room temperature. There is no pressure-induced first order structural phase transitions in natrolite, when it is compressed in non-penetrating pressure transmitting medium up to 8 GPa. On the other hand scolecite exhibits a pressure-induced transition, with a discontinuous decrease of the electrical resistivity from 2.6 × 106 to 4.79 × 105 Ω cm at 4.2 to 4.3 GPa. The observed phase transition in scolecite is found to be irreversible. Vibrational spectroscopic and X-ray diffraction studies confirm the amorphous nature of the high-pressure phase. The results of the present high-pressure studies on scolecite are in good agreement with the high-pressure Raman spectroscopic data on scolecite. The thermo gravimetric studies on the pressure-quenched samples show that the samples underwent a pressure-induced partial dehydration. Such a pressure-induced partial dehydration, which has been observed in natural scolecite could explain the presence of high conductive layers in the earth's deep-crust.  相似文献   

17.
Summary The electrical AC (103 Hz) resistivity of some rocks was measured in a dry regime in air and in an argon atmosphere under various heating regimes. It is shown that long-term measurements provide us additional information about factors influencing resistivity and activation energy which cannot be obtained by means of standard measurements.  相似文献   

18.
New methods for obtaining and quantifying spatially distributed subsurface moisture are a high research priority in process hydrology. We use simple linear regression analyses to compare terrain electrical conductivity measurements (EC) derived from multiple electromagnetic induction (EMI) frequencies to a distributed grid of water‐table depth and soil‐moisture measurements in a highly instrumented 50 by 50 m hillslope in Putnam County, New York. Two null hypotheses were tested: H0(1), there is no relationship between water table depth and EC; H0(2), there is no relationship between soil moisture levels and EC. We reject both these hypotheses. Regression analysis indicates that EC measurements from the low frequency EM31 meter with a vertical dipole orientation could explain over 80% of the variation in water‐table depth across the test hillslope. Despite zeroing and sensitivity problems encountered with the high frequency EM38, EC measurements could explain over 70% of the gravimetrically determined soil‐moisture variance. The use of simple moisture retrieval algorithms, which combined EC measurements from the EM31 and EM38 meters in both their vertical and horizontal orientations, helped increase the r2 coefficients slightly. This first hillslope hydrological analysis of EMI technology in this way suggests that it may be a promising method for the collection of a large number of distributed soilwater and groundwater depth measurements with a reasonable degree of accuracy. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

19.
The combination of magnetotelluric survey and laboratory measurements of electrical conductivity is a powerful approach for exploring the conditions of Earth’s deep interior. Electrical conductivity of hydrous silicate melts and aqueous fluids is sensitive to composition, temperature, and pressure, making it useful for understanding partial melting and fluid activity at great depths. This study presents a review on the experimental studies of electrical conductivity of silicate melts and aqueous fluids, and introduces some important applications of experimental results. For silicate melts, electrical conductivity increases with increasing temperature but decreases with pressure. With a similar Na+ concentration, along the calc-alkaline series electrical conductivity generally increases from basaltic to rhyolitic melt, accompanied by a decreasing activation enthalpy. Electrical conductivity of silicate melts is strongly enhanced with the incorporation of water due to promoted cation mobility. For aqueous fluids, research is focused on dilute electrolyte solutions. Electrical conductivity typically first increases and then decreases with increasing temperature, and increases with pressure before approaching a plateau value. The dissociation constant of electrolyte can be derived from conductivity data. To develop generally applicable quantitative models of electrical conductivity of melt/fluid addressing the dependences on temperature, pressure, and composition, it requires more electrical conductivity measurements of representative systems to be implemented in an extensive P-T range using up-to-date methods.  相似文献   

20.
Understanding petrographical, geochemical and electrical properties of rocks is essential for investigating minerals. This paper presents a study of the petrographical, geochemical and A.C. electrical properties of carbonate rock samples. The samples collected show six lithostratigraphic rock units. Electrical properties were measured using a non‐polarizing electrode at room temperature (～20°C) and a relative atmospheric humidity of ～50% by weight in the frequency range from 42 Hz to 5 MHz. The difference in electrical properties between the samples was attributed to the change in composition and texture between the samples. Electrical properties generally change with many factors (grain size, chemical composition, grain shape and facies). The dielectric constant decreases with frequency and increases with conductor composition. The conductivity increases with the increase of conductor paths between electrodes. Many parameters can contribute to the same result of the electrical properties. The main objective of the present study is to shed more light on the relation between the texture and geochemical composition of measured samples (carbonates that contain clays and quartz grains) through electrical laboratory measurements (conductivity and dielectric constant as a function of frequency).  相似文献   

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