J. Phys. Chem. B 1997, 101, 6219-6222
6219
Dielectric Properties of Ice Containing Ionic Impurities at Microwave Frequencies Takeshi Matsuoka,*,† Shuji Fujita, and Shinji Mae Department of Applied Physics, Faculty of Engineering, Hokkaido UniVersity, N13 W8, Sapporo 060, Japan ReceiVed: October 11, 1996; In Final Form: May 1, 1997X
The relative complex dielectric permittivities of ice containing ionic impurities have been measured at 5 GHz with the cavity resonator method in the temperature range -80 to -2 °C. The contained impurities are NaCl, HNO3, and H2SO4, and the impurity concentration of the samples was between 10-5 and 10-3 M (molarity). The dielectric loss of ice increased with the increases in temperature and contained impurity concentration. The sharp increase in dielectric loss values of ice containing NaCl, HNO3, and H2SO4 was observed immediately above the eutectic points -21, -43, and -73 °C, respectively. The change shows that the liquid phase of the contained impurity is formed in ice above the eutectic point. A microscope observation showed that the liquid phase in the ice sample occurs at triple junctions as veins and at grain boundaries as lens-shaped inclusions, and 90% of the liquid existed as lens inclusions. We discuss the possible mechanisms which govern the dielectric loss of ice containing impurities by the change of the volume fraction and impurity concentration of the liquid phase inclusions with the temperature.
Introduction Knowledge of the relative complex dielectric permittivity (* ) ′ - i′′) of ice at microwave frequencies is necessary for understanding remote sensing signatures in polar regions. As investigators have reported over the course of nearly 50 years,1,2 significant discrepancies exist in the values of the imaginary part, ′′ (dielectric loss), which is difficult to measure due to the low loss factor of ice at these frequencies. The general behavior of the dielectric loss of ice is characterized by the highfrequency tail of the Debye relaxation spectrum with a relaxation frequency in the kilohertz range and by the low-frequency tail of the far-infrared absorption bands due to lattice vibrations. The superposition of these tails leads to a deep minimum of dielectric loss centered at 2-4 GHz, and the values are of order 10-4. Ma¨tzler and Wegmu¨ller3 performed the precise measurement of the dielectric losses of ice and slightly saline ice at mainly -15 and -5 °C in the frequency range 2-100 GHz. These investigators discussed that most of the old data at microwave frequencies showed higher losses, partly because of impurities present in the ice and partly because of measurement errors. Recently, Matsuoka et al.4 made a precise and complete data set of dielectric properties of pure ice in the frequency range 5-35 GHz and in the temperature range -80 to -5 °C. In the case of ice containing sea salts, some studies were performed at microwave frequencies.5-7 Vant et al.5 studied the 10 GHz dielectric properties of sea ice with the ice type having a sea salt concentration of 10-2 M (molarity). In addition, Vant et al.6 extended the study with the concentration up to 10-1 M over a wide frequency range. Fujita et al.8 and Matsuoka et al.,9 respectively, reported the dielectric properties of ice containing acids (HCl, HNO3, and H2SO4) and ice containing NaCl. Fujita et al.8 and Matsuoka et al.9 showed that the dielectric loss of ice was linearly increased with the acids or NaCl concentration. Both measurements were performed mainly in the concentration range 10-3-10-2 M and in the * Corresponding author. E-mail:
[email protected]. † Present address: Institute of Low Temperature Science, Hokkaido University, N19 W8, Sapporo 060, Japan. X Abstract published in AdVance ACS Abstracts, June 15, 1997.
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temperature range -30 to -3 °C at 9.7 GHz with the standing wave method. More detailed investigations are necessary to understand the effects of impurities on the dielectric loss of ice. For example, it is necessary to examine the dependence of the distribution of impurities in ice when the temperature is down to about -80 °C and the concentration is down to 10-6-10-5 M; this is the order of impurity concentration in natural ice in polar ice sheets. In this study, the method of measurement is the cavity resonator method, which is suitable for low loss material such as ice, and the frequency used for measurement is 5 GHz. Prepared samples are polycrystalline ice containing NaCl, HNO3, or H2SO4. We discuss the temperature and concentration dependence of dielectric loss of ice containing ionic impurities in the temperature range -80 to -2 °C and the impurity concentration range 10-5-10-3 M. Experiments Cavity Resonator Method. A cylindrical cavity was used to measure the permittivity of ice at 5 GHz. The value of the unloaded quality factor was more than 10 000, making measurement of small losses of ice possible. The cavity operating in the TE011 mode has a diameter of 95 mm and length of about 50 mm. Source signals for the cavity resonator measurements were generated using an HP 83623A synthesized sweeper. The resonant signals were detected by a crystal detector and amplified by an NF 5610B lock-in amplifier. The detailed experimental procedures are described in Matsuoka et al.4 The resonator was set in a freezer with the temperature controlled at (0.3 °C. The measurement was done by heating the sample from -80 to -2 °C with a heating rate of about 0.1 °C per minute. Preparation of Ice Samples. Ice samples were made from distilled and ion-exchanged water containing either NaCl, HNO3, or H2SO4, and the impurity concentration of the bulk solution was about 0.005 M. The solutions were set in the freezer at -20 °C and frozen in cylindrical glass containers with diameters of 100 mm. The freezing rate, controlled by a heater around the containers, was 10 mm thickness per day. The samples were cut from the bulk and shaped with a diameter of 95 mm and thickness of about 4.1-4.6 mm. The prepared samples were © 1997 American Chemical Society
6220 J. Phys. Chem. B, Vol. 101, No. 32, 1997
Matsuoka et al. (order of 10-4 M) plotted versus temperature at 5 GHz. The measured values of ′ and ′′ of pure ice agreed well with those of Matsuoka et al.,4 which is a reliable data set at microwave frequencies. The ′ values of ice containing impurities agree well with ′ values of pure ice within the estimated errors ((1%) caused by the uncertainty of sample position in the cavity and the dielectric anisotropy in ice.10,11 Although the ′ of solution is expected to be one order larger than that of ice, the increase of ′ in ice containing impurities caused by liquid inclusions was not observed because of the small volume fraction of the inclusions. As shown in Figure 1b, the ′′ of ice containing impurities is larger than that of pure ice, and the variations of ′′ with temperature were different, depending on the type of impurities. The sharp change in the ′′ values were observed at the eutectic points of NaCl, HNO3, and H2SO4 at -21, -43, and -73 °C, respectively. Although the drastic change of ′′ in NaCl ice was reported by previous studies,9,12 it has not been reported for low concentration of the impurity such as 10-4 M. The drastic changes of ′′ in HNO3 and H2SO4 ice were observed for the first time. The change at the eutectic points clearly shows that the liquid phase due to the contained impurity is formed in the polycrystalline ice above the eutectic point. Though it has been reported that chloride can be incorporated in an ice lattice with a solubility limit of 1-2 × 10-4 M,13 the growing conditions seem to have rejected most of the solute for NaCl ice used in this study. The measurement of ′′ in the samples containing acids, HNO3 and H2SO4, and salt, NaCl, showed a linear relationship between the increase of ′′ and the concentration of impurity. The impurity concentration dependence of ′′ is expressed by the following equation
′′ ) ′′pure +
Figure 1. Temperature dependence of permittivities of ice containing impurities at 5 GHz: (a) the real part, (b) the imaginary part, and (c) the temperature dependence of ′′ per unit concentration of impurities.
polycrystalline, and the average grain diameters were 5.6-6.0 mm. The samples each contained a small amount of air bubbles distributed at the center of the samples in a diameter of between 5 mm and 10 mm, because the direction of the freezing front was oriented to the center of the cylindrical glass container. After the dielectric measurements were taken, the concentrations of impurities in the samples were measured by ion chromatography with melted ice samples. Since the distribution of impurities in the samples was inhomogeneous, each sample was divided into three sections with different distances from the center of the sample in order to examine the impurity distribution. Then, we determined the effective concentration of the sample by taking account of the impurity distribution and the electric field distribution for the TE011 mode in the cavity resonator. Results Dielectric Measurement. Parts a and b of Figure 1, respectively, showed the real part, ′, and the imaginary part, ′′, of permittivity of pure ice and ice containing impurities
d′′ dC
(1)
where ′′pure is the imaginary part of permittivity of pure ice and C is the impurity concentration expressed by molarity. The increases of ′′ per unit concentration, d′′/dC, (M-1), are plotted versus temperature in Figure 1c. The concentration of H2SO4 is also expressed by molarity, because the H2SO4 has only one hydrogen ion dissociated at liquid concentrations above 1 M. The estimated errors of the d′′/dC values were about (5% for NaCl and (12% for acids. Fujita et al.8 reported that the d′′/dC values at a certain temperature were independent of the type of acid in the concentration range 10-3-10-2 M and linearly dependent on H+ concentration, while Figure 1c shows that distinguishable differences exist between the d′′/dC values of HNO3 and H2SO4 ice. The d′′/dC values of HNO3 ice are 20-30% smaller than that of H2SO4 ice. Microscope Observation. The distribution of impurities in the samples was observed through a microscope. For all samples containing impurities, the impurities were presented as liquid inclusions in veins at triple junctions and in 30-150 µm-diameter lens-shaped inclusions at grain boundaries. The numbers of inclusions increased closer to the center of the diskshaped sample. From the microscope observation of the sample containing 1.97 × 10-4 M H2SO4, the cross section of triple junctions in the sample was found to be about 1 × 10-5 mm2 at -20 °C. We use the model of ice grains as semiregular truncated octahedra.14 This model leads to a volume fraction of the veins at the triple junctions, νt, of about 6 × 10-6. The observed volume fraction of the lens inclusions at grain boundaries, νl, was about 5.8 × 10-5.
Dielectric Properties of Ice Containing Impurities
J. Phys. Chem. B, Vol. 101, No. 32, 1997 6221
Figure 2. Arrhenius plot of molar conductivity against reciprocal temperature for our experimental data at 5 GHz (solid symbols), previous microwave data at 9.7 GHz (open symbols), and DC models (solid lines) of triple junctions (3gb) for NaCl, HNO3, and H2SO4 and two-grain boundaries (2gb) for NaCl.
We assume that impurities cannot exist in ice grains but rather in the grain boundaries as solution. Under this assumption, the concentration of impurities in the inclusions at a certain temperature, T, is estimated from the relation between the freezing point, Tf, and the impurity concentration. Taking the sample containing overall 1.97 × 10-4 M H2SO4 as an example, since T is equal to Tf in equilibrium, the volume fraction of the solution, νsol, is 6.3 × 10-5 at -20 °C. Thus, we can estimate that in this study 90% of the solution in the sample is present as lens inclusions at grain boundaries. A similar volume ratio of veins and lenses, νt/νl, has been observed for all samples containing NaCl, HNO3, and H2SO4. Discussion Comparison with Previous Studies. The molar conductivity, dσ/dC, is expressed by
dσ d′′ ) 2πf0 dC dC
(2)
where 0 is the permittivity of free space, f is the frequency, and S m-1 M-1 is the unit of molar conductivity. The Arrhenius plot of molar conductivity against reciprocal temperature for data obtained in this study is shown in Figure 2. Wolff and Paren15 proposed the two-phase model that the DC conductivity of polar ice was due to a network of veins at triple junctions containing concentrated acid solution. The DC molar conductivity was calculated from the conductivity of the bulk solution with the geometric factor and factor representing the volume fraction of the solution. The geometric factor is 1/3 or 2/3, depending on the geometry of the veins at triple junctions or sheets at grain boundaries. Similar calculations with NaCl as the solution have been performed by Moore and Fujita.16 The DC molar conductivities calculated from the two-phase model15 and the measured microwave molar conductivities of acids8 and NaCl9 for artificially doped ice in the concentration range 10-310-2 M at 9.7 GHz are also shown in Figure 2. The Arrhenius activation energies given by the gradients of the molar conductivities for the DC models are about 0.34 eV for NaCl and 0.27 eV for acids, which are similar to or smaller than our results at microwave frequencies above -15 °C. However, between -15 °C and the eutectic points, the activation
Figure 3. Temperature dependence of ′′ of solution independent of the volume fraction at 5 GHz. The values of ′′ of solution are calculated from Figure 1c and the freezing point curves and tables in Weast.17 The dashed curve is extrapolated down to -40 °C.
energies for our results are about 0.18 eV for NaCl, 0.15 eV for HNO3, and 0.16 eV for H2SO4. The absolute values of molar conductivity are consistent for acids above -15 °C, especially for H2SO4, between DC models and our results of microwave frequencies. These values suggest that the contribution of the mobility of the ionic charge carrier, primarily H+, in the liquid inclusions is about 1/3 that of the bulk solution and not influenced by frequency change or by difference in geometry of liquid inclusions above -15 °C. For NaCl, the molar conductivity values at microwave frequencies are greater than the molar conductivity values of the two grain boundaries model and triple junctions model of DC. The molar conductivities of sea salt impurity, as reported by Ma¨tzler and Wegmu¨ller,3 also greatly increase with increasing frequency in the range 2-100 GHz. Dielectric Loss of Solution at Grain Boundaries. When all ionic impurities are in grain boundaries as solution, we can calculate the dielectric loss of solution, ′′sol, that includes geometric factors. The value is independent of the volume fraction in ice
′′sol )
d′′ C d′′ s ) dC νsol dC
(3)
where s is the impurity concentration of the solution at a certain temperature. In Figure 3, the temperature dependence of ′′ sol independent of the volume fraction at 5 GHz is shown. To estimate s, we use the freezing point curve in Weast17 and extrapolate the fitted curve for HNO3 down to -40 °C. Qualitatively, the temperature variation of ′′ of solution is complicated because the impurity concentration increases as temperature decreases, while the mobility of ions decreases as temperature decreases and impurity concentration increases. From our experiments, the conductivities of solution, 2πf0′′sol, are smaller than the DC conductivities of bulk solution.15 Therefore the geometric factors in ′′sol were calculated and found to be about 2/3 at -40 °C and about 1/3 at -10 °C for H2SO4. Further investigation is needed to clarify whether geometric factors change with temperature and whether other factors that change with temperature exist at microwave frequencies for artificially doped ices. Figure 3 shows that the temperature dependence and the absolute values of ′′sol of HNO3 solutions agree well with that of H2SO4 solution. Thus, it is possible that the difference
6222 J. Phys. Chem. B, Vol. 101, No. 32, 1997 between d′′/dC values of HNO3 ice and H2SO4 ice shown in Figure 1c are caused mainly by the difference of the volume fractions of the solutions determined by the freezing point curves. The reason Fujita et al.8 did not observe the difference between d′′/dC values of HNO3 ice and H2SO4 ice could be explained as follows. Fujita et al.8 used samples of two orders larger volume fraction of liquid inclusions than our study did, so it is possible that the dielectric dispersion caused by interfacial polarization, known as the Maxwell-Wagner effect, at the liquid/ice boundaries significantly affected the d′′/dC values at 9.7 GHz. Further studies will be needed to clarify the effect of the dielectric properties of the interfacial polarization and bulk solution at microwave frequencies. Acknowledgment. This work has been supported by a Grant-in-Aid for Scientific Research and Grant-in-Aid for JSPS (Japan Society for the Promotion of Science) fellows. References and Notes (1) Evans, S. J. Glaciol. 1965, 5, 773. (2) Warren, S. G. Appl. Opt. 1984, 23, 1206.
Matsuoka et al. (3) Ma¨tzler, C.; Wegmu¨ller, U. J. Phys. D: Appl. Phys. 1987, 20, 1623 (Erratum in 1988, 21, 1660.) (4) Matsuoka, T.; Fujita, S.; Mae, S. J. Appl. Phys. 1996, 80, 5884. (5) Vant, M. R.; Gray, R. B.; Ramseier, R. O.; Mikios, V. J. Appl. Phys. 1974, 45, 4712. (6) Vant, M. R.; Ramseier, R. O.; Mikios, V. J. Appl. Phys. 1978, 49, 1264. (7) Arcone, S. A.; Gow, A. J.; McGrew, S. IEEE Trans. Geosci. Remote Sensing 1986, 24, 832. (8) Fujita, S.; Shiraishi, M.; Mae, S. IEEE Trans. Geosci. Remote Sensing, 1992 30, 799. (9) Matsuoka, T.; Fujita, S.; Mae, S. Proc. NIPR Symp. Polar Meteorol. Glaciol. 1993, 7, 33. (10) Fujita, S.; Mae, S.; Matsuoka, T. Ann. Glaciol. 1993, 17, 276. (11) Matsuoka, T.; Fujita, S.; Morishima, S.; Mae, S. J. Appl. Phys. 1997, 81, 2344. (12) Hoekstra, P.; Cappillino, P. J. Geophys. Res. 1971, 70, 4922. (13) Gross, G. W.; Wong, P. M.; Humes, K. J. Chem. Phys. 1977, 67, 5264. (14) Nye, J. F.; Frank, F. C. IASH Publ. 1973, 95, 157. (15) Wolff, E. W.; Paren, J. G. J. Geophys. Res. 1984, 89, 9433. (16) Moore, J. C.; Fujita, S. J. Geophys. Res. 1993, 98, 9769. (17) Weast, R. C., Ed. Handbook of Chemistry and Physics, 70th ed.; CRC Press: Boca Raton, FL, 1989; pp D-241, D-255, D-265.
