DIELECTRIC PROPERTIES OF STRAINED ICE. I : EFFECT OF PLASTIC STRAINING

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1 DIELECTRIC PROPERTIES OF STRAINED ICE. I : EFFECT OF PLASTIC STRAINING K. Itagaki To cite this version: K. Itagaki. DIELECTRIC PROPERTIES OF STRAINED ICE. I : EFFECT OF PLASTIC STRAIN- ING. Journal de Physique Colloques, 1987, 48 (C1), pp.c1-143-c < /jphyscol: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1987 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 JOURNAL DE PHYSIQUE Colloque C1, suppl6ment au no 3, Tome 48, mars 1987 DIELECTRIC PROPERTIES OF STRAINED ICE. I : EFFECT OF PLASTIC STRAINING K. ITAGAKI U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, NH , U.S.A. R6sumt. Des effets de relaxation ont 6t6etudi6s sur des monocristaux de glace. Lorsque la dc formation plastique augmente, la relaxation de la contrainte croit lingairement avec le temps. Abstract. The effect of plastic straining on single crystals of ice was examined. As strain increased plastically, relaxation strength increased linearly as the relaxation time increased. I. Introduction Large dielectric dispersion in ice in the audiofrequency range has drawn the attention of many researchers, and many reports have been published on the subject. Although the results generally seem to agree, small discrepancies are noted. Usually they are attributed to chemical impurities, and efforts have been made to clarify the effect of specific impurities. One point common to these studies is that they all disregard the effect of straining. In cases where electrodes have been frozen into the ice, cracking during cooling caused by the difference in the thermal expansion coefficients of ice and electrodes has been reported (1). Brill and Camp (2) reported on the effect of elastic deformation on the dielectric properties of ice, but they observed no effect due to plastic deformation. VonHippel et al. (3) reported considerabb change in both relaxation strength and relaxation time for spectra 1, 2, 3 and 4 (their designation) due to annealing. During my dielectric relaxation studies I have frequently been unable to balance the GR 1615 impedance bridge unless I switched to the negative G range for some of the freshly prepared ice samples. Plotting such negative readings on a Cole-Cole plot produced a "tail" on the negative (lower) half of the K'-K " plane. After annealing of some 10 days at -lo C, such negative "tails" gradually shortened to the classical Debye type semicircle without a tail. Upon prolonged annealing, a large, low-frequency tail similar to the ones usually observed gradually developed on the positive (upper) side of the Cole-Cole plane. Details are reported in an accompanying paper. Most previous reports have completely disregarded the effect of straining caused by sample preparation. Some give little or no description of sample preparation, so that one is unable to estimate the original strain. Further study of the effects of straining and sample preparation methods on dielectric relaxation properties are needed. The behavior observed in this study was complex, but definite effects of plastic straining were observed. Elastic strain also has some effect, but it disappears when the stress is removed. 2. Experimental Method Electrode systems With a combination of three electrodes and three blocking electrode films, a total of six types of electrode systems were used. Sone of these were conventional but others were rather novel. Two of them used mercury for the electrode material to avoid stiess due to direct contact with solid electrodes. Article published online by EDP Sciences and available at

3 JOURNAL DE PHYSIQUE Force to Bridge Fig. 1. IAercury electrode system (System B) with shear loading device. System A: This system used miniature mercury electrodes. A 2-mm-diameter active electrode was surrounded by a guard ring electrode. This particular system was used exclusively to measure the dielectric relaxation of hoarfrost crystals, since they are at most 5 mm in size. No film was used. Since this system has been described in a previous paper (41, no further description will be given. System B: This larger mercury electrode system was designed to give shear stress perpendicular to an electric field. With conventional solid electrode systems ice would deform unevenly under shear stress, generating an air gap and making lower frequency capacitance measurement unreliable. As shown in Figure 1, the bottom mercury pool serves as a high-potential electrode, while the measuring electrode and guard ring sit on top of the ice sample. Two types of flexible film, latex rubber and Saran, were used for flexibility. The shear force was generated by a 25.4-mm (I-in.) diameter pneumatic cylinder and was applied as shown in Figure I. The dielectric relaxation of the film was measured separately, and the effects were subtracted from the measurement made on the ice and film combination as series capacitors. Some of the measurements were made without film, since it was possible to separate the mercury in the measuring electrode from the guard ring by surface tension. System C. This was a conventional solid electrode system made of brass. As shown in Figure 2, the measuring electrode with guard ring was fixed, while pressure was applied through a highpotential electrode supported on steel balls to allow it to shift freely laterally. This way only compressive force could be applied to the ice samples. The same pneumatic cylinder used in System B generated the compressive force. to Air Pressure Controller Pneumatic Cylinder '-~ce Sornple Fig. 2. Electrode System C used for compressive loading.

4 The pneumatic cylinder allowed us to control the force from outside the cold box without opening the lid, thus avoiding any disturbance. A polyethylene bag used as a barrier film allowed little sublimation to occur. Ice preparation Samples were initially cut with a bandsaw and then finished by die-drawing, using an aluminum die with an entrance opening of about 10x 50:mn that tapered to a 6x 30 mm slot. The die was warmed by a heater wire wrapped around it so that the original ice piece could be melted down to the exit slot size. The die slid down a pair of guides under its own weight. Since a load of only about 150 g was applied to the ice through the large area of the die surface, mechanical stress was minimized. Thus prepared, the ice samples were mounted between electrodes, some with film to provide a blocking electrode, and some without. Capacitance and conductance measurements were made using a GR 1615 transformer type capacitance bridge. This bridge can switch balancing capacitance and conductance from the side normally used to the sample-side arm of the bridge. On the GR 1615 this arrangement is marked negative capacitance and conductance. Occasionally some anomalous behavior was observed in the dielectric data. For example the bridge could, not be balanced unless either the conductance or capacitance arm was brought into the negative range. Since freezing of ice onto the electrode or film may cause such anomalous behavior, some samples were deliberately frozen onto the electrodes. In this paper only the effect of straining will be discussed. Detailed descriptions of sample preparation by various methods are given in the accompanying paper. Data analysis Capacitance and conductance or D factor were generally measured at frequencies from 20 hz to 100 khz in multiples of 2 and 5 (20,50,100,200,500 etc.). The data were recorded in fixed format on data sheets. Since various films were inserted between the ice and the electrodes, the contribution of the film was subtracted and then converted into the real and imaginary parts of the dielectric constant. These and other computations and data plotting were done with an HP9020 computer. Each set of original data, together with converted data at each frequency measured, and plots, were printed on one sheet. The first three lines gave the basic variables, such as the version of the program used, the file name, the run number, d/a (thickness/area), film information, teniperature, and elapsed time from sample preparation. The next group of 12 lines contained original dara for frequency, capacitance, and conductance, and calculated data for the real and imaginary parts of the dielectric constants (K' and K "), K "xu, K "jw and tan6. This was followed by tabulated results in 11 columns, one for each pair of frequencies (20-50 Hz, Hz, etc.): Line 1. The relaxation time calculated from K' vs K "/w. Line 2. The ratio of Rt (relaxation time by K"~w)/R~(relaxation time by K"/W). The relaxation times can be calculated from the slope of either the K' vs ~"xw or K' vs K"/W plot for each set of two consecutive frequencies (20 and 50, for example). If the relaxation was the Debye type both relaxation times would agree, making this ratio unity, and would remain constant over the considerable frequency range of the measurements. In reality they seldom agreed because the relaxation process is generally of a non-debye type having wide distribution. The ratio shown on line 2 is an index of deviation from Debye type relaxation, which we call the "Debye index." Line 3. Relaxation strength. Line 4. The low frequency end of the dispersion spectra calculated from dara between the frequencies indicated in each of the 11 column headings. The intersection of the K' vs K "xw line with the abscissa is the high frequency end and the intersection of the K' vs K "/w iine with the abscissa is the low end of the relaxation spectra. The difference in K' beixeen the low and high ends is the relaxation strength (Rs(Trx)) of the spectra, shown in line 3. Line 5. Relaxation strength per unit relaxation time. In order to find the peak in the relaxation spectrum, the following analysis was made. First, relaxation times calculated from consecutive sets of data were re-ordered in descending order of relaxation time, TI, T2... Tn. The amplitude of relaxation strength Y(Ti) at a certain relaxation time Ti can be defined as the relaxation strength at Ti plus the contribution of the neighboring relaxation times Ti-1 and Ti+l per unit relaxation time as:

5 JOURNAL DE PHYSIQUE The results of the analysis were plotted below the tabulated data. The usual Cole-Cole plot (K' vs K") shared a common abscissa with the plots of (K' vs K" xu) and (K' vs ~ "/u x but had a different ordinate, depending on the values of K " x w. Both relaxation time Ti vs. relaxation strength Rs(Ti) (data points identified by run number) and relaxation time vs. relaxation peak Y(Ti) were plotted at log-log scale with the same abscissa of -6 to 0 (logarithm of the relaxation time to 1 s). The ordinate for relaxation strength Rs is 1 to 10,000 (logarithm is 0 to 4). The scale of the relaxation peak is fixed to 3 to 9 (log 103 to log 109). The peak relaxation amplitude generally coincided with the steepest slope of the relaxation time vs relaxation strength curve. When the ice was well annealed and the Cole-Cole plot was close to a semi-circle, the relaxation amplitude plot showed a very sharp peak. In order to check the validity of this analysis a model data set combining two Debye type relaxations having the usually observed values of relaxation time and strength was generated by computer and analyzed the same way as the real data. This analysis indicated a very sharp relaxation amplitude peak, sharper than the peak occasionally observed in the measurements of well-annealed samples. 3. Results and Discussion More than 600 sets of measurements were made in the course of this study on about 50 variously prepared samples; 200 measurements made on 10 samples were devoted to observation of the effects of straining. Some samples were allowed to anneal for up to two months, during which time frequent measurements were made to observe the effects of annealing. On some of the samples, negative conductance or negative capacitance was observed. Since such anomalies were persistent and systematically changed with stress, temperature or time, we concluded that they could not have been caused by the measuring system but only by the ice samples themselves. Detailed discussion of this may be found in an accompanying paper. Further anomalous behavior, extremely low dielectric relaxation strength, was found in dislocation-free hoarfrost crystals. This has already been discussed in detail and therefore no further discussion will be given here. Since the whole data set is extensive, only general features will be discussed here; a complete discussion will be published elsewhere. The samples were strained in three configurations: in shear in the basal plane and in compression both parallel to and at 45 degrees to the C-axis. For simple shear loading, System B was used; because the electrodes used were mercury covered with a dielectric film, no air gap effect problems could arise. The die-drawing produced a very flat sample surface, so that the flexible film could follow its gentle undulations. Later we found that the mercury could be retained by surface tension so some tests were made without film. However, no difference was observed after the effect of the film was subtracted. Straining of the order of a few percent could cause the surface tension barrier to break down due to deformation of the ice surface. Compression experiments were performed using System C both parallel to and at 45 degrees to the C-axis cut crystals. In order to reduce air gap effects, polyethylene film was used for most of the measurements. Later the effect of the film was subtracted from the measured data through a computer program. Also, the effects of the air gap were studied on a computer-generated model having dielectric relaxation time and strengths close to observed values. Such studies were useful for distinguishing the effect of air gaps and interpreting the meaning of the observed data. Loading time varied from about 1 hour, enough to complete one set of measurements, to 10 days. Several measurements were made during the loading. As shown in Figure 3, a linear relationship between relaxation time and relaxation strength was found in all three configurations. Numbers attached to some of the data points indicate pressure in pounds per square inch; they can be converted into pascals by multiplying by a constant of the order of 3000, depending on the size of the ice sample. Data points without numbers represent no-load conditions. Prolonged loading tended to increase the relaxation time and strength. Generally, shear straining (Runs 1-4) showed smaller relaxation strength for comparable relaxation time, and the slopes were lower. Runs 1 and 3 were short loading time experiments, and little definite trend could be found, indicating that elastic strain affects the dielectric relaxation time and strength little, while plastic straining can greatly modify them. For prolonged shear loading both relaxation time and strength tended to increase after the loading ended.

6 0 I x10-~ Relaxation Time (s) Fig. 3. Relaxation time vs relaxation strength. Compressive loading parallel to the C-axis was expected to strain the crystal only a little since no basal glide system is activated. A transducer provided to measure the strain recorded little straining. Still, considerable effects were detected (both dielectric relaxation time and strength increased up to 100 /o). Part of the increase can be attributed to the effect of the air gap. Computer model studies indicated that by adjusting the width of the air gap and the percentage of air gap covering the electrode area we could reproduce a linear relationship similar to that observed. But the air gap seems too wide and coverage varies in extent. Moreover, samples with their C-axes at 45 degrees to the compressive force, which deformed up to 42%, behaved similarly, as shown in Figure 3 (+ and x). In this case deformation of a few percent should have eliminated the air gap completely. Dielectric relaxation strength increased linearly with increase in relaxation time as the straining proceeded. If we assume segments of electrically charged strings (charged dislocations) stretched between pinning points and immersed in a viscous medium as a source of dielectric polarization, such a relationship can be predicted 15). Also, charged dislocation theory can explain the deviation from the Debye relaxetion usually observed in the course of many previous and current studies by assuming various segment length distributions. It is also possible that certain anomalous features such as negative capacitance and negative conductance can be explained by charged dislocation theory. References (1) Auty, R.P. and R.H. Cole, J. Chem. Phys. 20 (1952) (2) Brill, R. and P.R. Camp, CRREL Research Report 68 (1961). (3) vonhippel, A., D.B. Knoll and W.B. Westphal, J. Chem. Phys. 54 (1971) (4) Itagaki, K., J. Glaciol. 21 (1978) (5) Itagaki, K., CRREL Report 82-7 (1982).