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

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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-C1-147. �10.1051/jphyscol:1987121�.

�jpa-00226266�

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

K. ITAGAKI

U.S. A r m y Cold Regions Research and Engineering Laboratory, Hanover, NH 03755-1290, U.S.A.

R6sumt. Des e f f e t s d e relaxation ont 6 t 6 e t u d i 6 s sur des monocristaux d e glace. Lorsque la d C formation plastique augmente, la relaxation d e l a contrainte croit lingairement a v e c l e temps.

Abstract. The e f f e c t of plastic straining on single crystals of ice was examined. As s t r a i n in- creased plastically, relaxation strength increased linearly a s t h e relaxation t i m e increased.

I. Introduction

Large dielectric dispersion in ice in t h e audiofrequency range has drawn t h e a t t e n t i o n of many researchers, and many reports have been published on t h e subject. Although t h e results general- ly seem t o agree, small discrepancies a r e noted. Usually they a r e a t t r i b u t e d t o chemical impur- ities, and e f f o r t s have been made t o clarify t h e e f f e c t of specific impurities. O n e point com- mon t o these studies is t h a t they a l l disregard t h e e f f e c t of straining. In c a s e s where electrodes have been frozen into t h e ice, cracking during cooling caused by t h e difference in t h e t h e r m a l expansion coefficients of i c e and electrodes has been reported (1). Brill and C a m p (2) reported on t h e e f f e c t of elastic deformation on t h e dielectric properties of ice, but they observed no e f f e c t due t o plastic deformation. VonHippel et al. (3) reported c o n s i d e r a b b change in both

relaxation strength and relaxation t i m e f o r s p e c t r a 1, 2, 3 and 4 (their designation) due t o anneal- ing.

During my dielectric relaxation studies I have frequently been unable t o balance t h e G R 1615 impedance bridge unless I switched t o t h e negative G range f o r s o m e of t h e freshly prepared ice samples. Plotting such negative readings on a Cole-Cole plot produced a "tail" on t h e nega- t i v e (lower) half of t h e K'-K " plane. A f t e r annealing of some 10 days a t -lO°C, such negative

"tails" gradually shortened t o t h e classical Debye type semicircle without a tail. Upon prolonged annealing, a large, low-frequency tail similar t o t h e ones usually observed gradually developed on t h e positive (upper) side of t h e Cole-Cole plane. Details a r e reported in a n accompanying paper.

Most previous reports have completely disregarded t h e e f f e c t of straining caused by sample pre- paration. Some give little or no description of sample preparation, so t h a t one is unable t o esti- m a t e t h e original strain. Further study of t h e e f f e c t s of straining and sample preparation meth- ods o n dielectric relaxation properties a r e needed. The behavior observed in this study was com- plex, but definite e f f e c t s of plastic straining w e r e observed. Elastic strain also has some ef- f e c t , but i t disappears when t h e s t r e s s is removed.

2. Experimental Method Electrode systems

With a combination of t h r e e electrodes and t h r e e blocking electrode films, a t o t a l of six types of electrode systems were used. S o n e of these were conventional but others were r a t h e r novel.

Two of them used mercury f o r t h e electrode material t o avoid s t i e s s due t o direct c o n t a c t with solid electrodes.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987121

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Force

to Bridge

Fig. 1. IAercury e l e c t r o d e system (System B) with shear load- ing device.

System A: This system used miniature mercury electrodes. A 2-mm-diameter a c t i v e e l e c t r o d e was surrounded by a guard ring electrode. This particular system was used exclusively t o meas- ure t h e dielectric relaxation of hoarfrost crystals, since they a r e a t most 5 mm in size. No film was used. Since this system has been described in a previous paper (41, no f u r t h e r description will be given.

System B: This larger mercury e l e c t r o d e system was designed t o give shear s t r e s s perpendicular t o an e l e c t r i c field. With conventional solid electrode systems ice would deform unevenly under shear stress, generating a n a i r g a p and making lower frequency capacitance measurement unre- liable.

As shown in Figure 1, t h e bottom mercury pool serves a s a high-potential electrode, while t h e measuring e l e c t r o d e and guard ring s i t on t o p of t h e ice sample. Two types of flexible film, latex rubber and Saran, were used f o r flexibility.

The shear f o r c e was generated by a 25.4-mm (I-in.) diameter pneumatic cylinder a n d was ap- plied a s shown in Figure I. The dielectric relaxation of t h e film was measured separately, and t h e e f f e c t s were subtracted from t h e measurement m a d e on t h e ice and film combination a s series capacitors. Some of t h e measurements were made without film, since i t was possible t o s e p a r a t e t h e mercury in t h e measuring electrode f r o m t h e guard ring by s u r f a c e tension.

System C. This was a conventional solid electrode system made of brass. As shown in Figure 2, t h e measuring electrode with guard ring was fixed, while pressure was applied through a high- potential electrode supported on s t e e l balls t o allow i t t o shift freely laterally. This way only compressive f o r c e could be applied t o t h e ice samples. The s a m e pneumatic cylinder used in System B generated t h e compressive force.

to Air Pressure Controller

Pneumatic Cylinder

'-~ce Sornple

Fig. 2. Electrode System C used f o r compressive loading.

Ice preparation

S a m p l e s w e r e initially c u t w i t h a bandsaw a n d t h e n finished by die-drawing, using a n a l u m i n u m d i e w i t h a n e n t r a n c e opening of a b o u t 10x 50:mn t h a t t a p e r e d t o a 6x 30 m m slot. T h e d i e w a s w a r m e d by a h e a t e r wire wrapped around i t s o t h a t t h e original i c e p i e c e could be m e l t e d down t o t h e e x i t s l o t size. T h e d i e slid down a pair of guides under i t s own weight. Since a load of only a b o u t 150 g w a s applied t o t h e i c e t h r o u g h t h e l a r g e a r e a of t h e d i e s u r f a c e , m e c h a n i c a l s t r e s s w a s minimized.

Thus p r e p a r e d , t h e i c e s a m p l e s w e r e m o u n t e d b e t w e e n e l e c t r o d e s , s o m e w i t h f i l m t o provide a blocking e l e c t r o d e , a n d s o m e without. C a p a c i t a n c e a n d c o n d u c t a n c e m e a s u r e m e n t s w e r e m a d e using a GR 1615 t r a n s f o r m e r t y p e c a p a c i t a n c e bridge. This bridge c a n s w i t c h balancing capaci- t a n c e a n d c o n d u c t a n c e f r o m t h e s i d e n o r m a l l y used t o t h e sample-side a r m of t h e bridge. O n t h e G R 1615 t h i s a r r a n g e m e n t i s m a r k e d n e g a t i v e c a p a c i t a n c e a n d c o n d u c t a n c e . O c c a s i o n a l l y s o m e a n o m a l o u s behavior w a s observed in t h e d i e l e c t r i c d a t a . F o r e x a m p l e t h e bridge could, n o t b e b a l a n c e d unless e i t h e r t h e c o n d u c t a n c e o r c a p a c i t a n c e a r m w a s b r o u g h t i n t o t h e n e g a t i v e r a n g e . S i n c e f r e e z i n g of i c e o n t o t h e e l e c t r o d e o r f i l m m a y c a u s e s u c h a n o m a l o u s behavior, s o m e s a m p l e s w e r e d e l i b e r a t e l y f r o z e n o n t o t h e e l e c t r o d e s . In t h i s p a p e r only t h e e f f e c t of s t r a i n - ing will be discussed. D e t a i l e d d e s c r i p t i o n s of s a m p l e p r e p a r a t i o n by various m e t h o d s a r e given in t h e a c c o m p a n y i n g paper.

Data analysis

C a p a c i t a n c e a n d c o n d u c t a n c e o r D f a c t o r w e r e g e n e r a l l y m e a s u r e d at f r e q u e n c i e s f r o m 20 hz t o 1 0 0 k H z in m u l t i p l e s of 2 a n d 5 (20,50,100,200,500 e t c . ) . T h e d a t a w e r e r e c o r d e d in f i x e d f o r m a t o n d a t a s h e e t s . S i n c e v a r i o u s f i l m s w e r e i n s e r t e d b e t w e e n t h e i c e a n d t h e e l e c t r o d e s , t h e c o n t r i b u t i o n of t h e f i l m w a s s u b t r a c t e d a n d t h e n c o n v e r t e d i n t o t h e r e a l a n d i m a g i n a r y p a r t s of t h e d i e l e c t r i c c o n s t a n t . T h e s e a n d o t h e r c o m p u t a t i o n s a n d d a t a p l o t t i n g w e r e d o n e w i t h a n HP9020 c o m p u t e r . E a c h set of original d a t a , t o g e t h e r w i t h c o n v e r t e d d a t a a t e a c h f r e q u e n c y m e a s u r e d , a n d plots, w e r e p r i n t e d on o n e s h e e t . T h e f i r s t t h r e e l i n e s g a v e t h e b a s i c v a r i a b l e s , s u c h a s t h e version of t h e p r o g r a m used, t h e f i l e n a m e , t h e run n u m b e r , d/A ( t h i c k n e s s / a r e a ) , f i l m i n f o r m a t i o n , t e n i p e r a t u r e , a n d e l a p s e d t i m e f r o m s a m p l e p r e p a r a t i o n . T h e n e x t g r o u p of 1 2 l i n e s c o n t a i n e d o r i g i n a l d a r a f o r f r e q u e n c y , c a p a c i t a n c e , a n d c o n d u c t a n c e , a n d c a l c u l a t e d d a t a f o r t h e r e a l a n d i m a g i n a r y p a r t s of t h e d i e l e c t r i c c o n s t a n t s ( K ' a n d K "), K " x u , K "jw a n d t a n 6 .

This w a s f o l l o w e d by t a b u l a t e d r e s u l t s in 1 1 c o l u m n s , o n e f o r e a c h p a i r of f r e q u e n c i e s (20-50 Hz, 50-100 Hz, etc.):

Line 1. T h e r e l a x a t i o n t i m e c a l c u l a t e d f r o m K ' v s K "/w.

Line 2. T h e r a t i o of Rt ( r e l a x a t i o n t i m e by K " ~ w ) / R ~ ( r e l a x a t i o n t i m e by K"/W). T h e r e l a x a - t i o n t i m e s c a n b e c a l c u l a t e d f r o m t h e s l o p e of e i t h e r t h e K ' v s ~ " x w o r K ' v s K"/W plot f o r e a c h set of t w o c o n s e c u t i v e f r e q u e n c i e s (20 a n d 50, f o r example). If t h e relaxation was t h e Debye t y p e both r e l a x a t i o n t i m e s would a g r e e , m a k i n g t h i s r a t i o u n i t y , a n d would r e m a i n c o n s t a n t o v e r t h e c o n s i d e r a b l e f r e q u e n c y r a n g e of t h e m e a s u r e m e n t s . In r e a l i t y t h e y s e l d o m a g r e e d b e c a u s e t h e r e l a x a t i o n p r o c e s s i s g e n e r a l l y of a non-Debye t y p e having wide distribution. T h e r a t i o shown o n l i n e 2 is a n index of deviation f r o m Debye t y p e relaxation, which we c a l l t h e "Debye index."

Line 3. R e l a x a t i o n s t r e n g t h .

Line 4. T h e low f r e q u e n c y e n d of t h e dispersion s p e c t r a c a l c u l a t e d f r o m d a r a b e t w e e n t h e f r e q u e n c i e s i n d i c a t e d in e a c h of t h e 1 1 c o l u m n headings. T h e i n t e r s e c t i o n of t h e K ' vs K "xw l i n e w i t h t h e a b s c i s s a i s t h e high f r e q u e n c y e n d a n d t h e i n t e r s e c t i o n of t h e K ' vs K "/w i i n e with t h e a b s c i s s a i s t h e low e n d of t h e r e l a x a t i o n s p e c t r a . T h e d i f f e r e n c e i n K ' b e i x e e n t h e low a n d high e n d s i s t h e r e l a x a t i o n s t r e n g t h (Rs(Trx)) o f t h e s p e c t r a , shown in l i n e 3.

Line 5. Relaxation s t r e n g t h per unit relaxation t i m e . In o r d e r t o find t h e peak in t h e relax- a t i o n s p e c t r u m , t h e following a n a l y s i s w a s made. F i r s t , r e l a x a t i o n t i m e s c a l c u l a t e d f r o m con- s e c u t i v e sets of d a t a w e r e r e - o r d e r e d in d e s c e n d i n g o r d e r of r e l a x a t i o n t i m e , T I , T 2

...

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The results of t h e analysis were plotted below t h e tabulated data. The usual Cole-Cole plot

( K ' vs K " ) shared a common abscissa with t h e plots of ( K ' vs K " x u ) and ( K ' vs ~ " / u x but had a different ordinate, depending on t h e values of K " x w

.

Both relaxation t i m e Ti vs. relaxation strength Rs(Ti) (data points identified by run number) and relaxation t i m e vs. relaxation peak Y(Ti) were plotted a t log-log s c a l e with t h e s a m e abscissa of -6 t o 0 (logarithm of t h e relaxation t i m e t o 1 s). The ordinate for relaxation strength Rs is 1 t o 10,000 (logarithm is 0 t o 4). The scale of t h e relaxation peak is fixed t o 3 t o 9 (log 103 t o log 109).

The peak relaxation amplitude generally coincided with t h e s t e e p e s t slope of t h e relaxation t i m e vs relaxation strength curve. When t h e ice was well annealed and t h e Cole-Cole plot was close t o a semi-circle, t h e relaxation amplitude plot showed a very sharp peak. In order t o check t h e validity of this analysis a model d a t a s e t combining t w o Debye t y p e relaxations having t h e usu- ally observed values of relaxation t i m e and strength was generated by computer and analyzed t h e s a m e way a s t h e real data. This analysis indicated a very sharp relaxation amplitude peak, sharper than t h e peak occasionally observed in t h e measurements of well-annealed samples.

3. Results and Discussion

More than 600 s e t s of measurements were made in t h e course of this study on about 50 variously prepared samples; 200 measurements made on 10 samples were devoted t o observation of t h e e f f e c t s of straining. Some samples w e r e allowed t o anneal f o r up t o t w o months, during which time frequent measurements were made t o observe t h e e f f e c t s of annealing. On some of t h e samples, negative conductance o r negative c a p a c i t a n c e was observed. Since such anomalies were persistent and systematically changed with stress, t e m p e r a t u r e or time, we concluded t h a t they could not have been caused by t h e measuring system but only by t h e ice samples themselves.

Detailed discussion of this may be found in a n accompanying paper. Further anomalous behav- ior, e x t r e m e l y low dielectric relaxation strength, was found in dislocation-free hoarfrost crys- tals. This has already been discussed in detail and therefore no f u r t h e r discussion will be given here. Since t h e whole d a t a s e t is extensive, only general f e a t u r e s will be discussed here; a com- plete discussion will be published elsewhere.

The samples were strained in t h r e e configurations: in shear in t h e basal plane and in compres- sion both parallel t o and a t 45 degrees t o t h e C-axis. For simple shear loading, System B was used; because t h e electrodes used were mercury covered with a dielectric film, no a i r g a p ef- f e c t problems could arise. The die-drawing produced a very f l a t sample surface, s o t h a t t h e flexible film could follow i t s gentle undulations. L a t e r we found t h a t t h e mercury could b e re- tained by surface tension s o some t e s t s were made without film. However, no difference was observed a f t e r t h e e f f e c t of t h e film was subtracted. Straining of t h e order of a f e w percent could cause t h e surface tension barrier t o break down due t o deformation of t h e i c e surface.

Compression experiments w e r e performed using System C both parallel t o and a t 45 degrees t o t h e C-axis c u t crystals. In order t o reduce a i r g a p effects, polyethylene film was used for most of t h e measurements. L a t e r t h e e f f e c t of t h e film was subtracted from t h e measured d a t a through a computer program. Also, t h e e f f e c t s of t h e a i r gap were studied on a computer-gener- a t e d model having dielectric relaxation t i m e and strengths close t o observed values. Such stud- ies were useful for distinguishing t h e e f f e c t of a i r gaps and interpreting t h e meaning of t h e ob- served data. Loading t i m e varied from about 1 hour, enough t o complete one s e t of measure- ments, t o 10 days. Several measurements were made during t h e loading.

As shown in Figure 3, a linear relationship between relaxation t i m e and relaxation strength was found in all t h r e e configurations. Numbers a t t a c h e d t o some of t h e d a t a points indicate pres- sure in pounds per square inch; they can be converted into pascals by multiplying by a constant of t h e order of 3000, depending on t h e s i z e of t h e ice sample. D a t a points without numbers rep- resent no-load conditions. Prolonged loading tended t o increase t h e relaxation t i m e and strength.

Generally, s h e a r straining (Runs 1-4) showed smaller relaxation strength f o r comparable relaxa- tion t i m e , and t h e slopes w e r e lower. Runs 1 and 3 were short loading t i m e experiments, and l i t t l e definite trend could b e found, indicating t h a t e l a s t i c s t r a i n a f f e c t s t h e dielectric relaxa- tion t i m e and strength little, while plastic straining c a n greatly modify them. For prolonged shear loading both relaxation t i m e and strength tended t o increase a f t e r t h e loading ended.

Compressive loading parallel t o t h e C-axis was expected t o s t r a i n t h e c r y s t a l only a l i t t l e since no basal glide system is activated. A transducer provided t o measure t h e s t r a i n recorded l i t t l e straining. Still, considerable e f f e c t s w e r e d e t e c t e d (both dielectric relaxation t i m e and strength increased up t o 100°/o). P a r t of t h e increase c a n be a t t r i b u t e d t o t h e e f f e c t of t h e a i r gap. Com- puter model studies indicated t h a t by adjusting t h e width of t h e air gap and t h e percentage of a i r g a p covering t h e e l e c t r o d e a r e a we could reproduce a linear relationship similar t o t h a t ob- served. But t h e a i r g a p seems t o o wide and coverage varies in extent. Moreover, samples with their C-axes a t 45 degrees t o t h e compressive force, which deformed up t o 42%, behaved simi- larly, a s shown in Figure 3 (+ and x). In this c a s e deformation of a f e w percent should have elimi- n a t e d t h e a i r g a p completely.

Dielectric relaxation strength increased linearly with increase in relaxation t i m e a s t h e strain- ing proceeded. If we assume segments of electrically charged strings (charged dislocations) s t r e t c h e d between pinning points and immersed in a viscous medium a s a source of dielectric polarization, such a relationship c a n b e predicted 15). Also, charged dislocation theory c a n ex- plain t h e deviation from t h e Debye relaxetion usually observed in t h e course of many previous and current studies by assuming various segment length distributions. I t is also possible t h a t c e r t a i n anomalous f e a t u r e s such a s negative capacitance and negative conductance c a n be ex- plained by charged dislocation theory.

References

(1) Auty, R.P. and R.H. Cole, J. Chem. Phys. 20 (1952) 1309-1314.

(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) 134-144.

(4) Itagaki, K., J. Glaciol. 21 (1978) 207-217.

(5) Itagaki, K., CRREL Report 82-7 (1982).