Internal Friction of Polycrystalline and Single-Crystal Ice

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Internal Friction of Polycrystalline and Single-Crystal Ice

Kuroiwa, D.; Yamaji, K.

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Preface

The i n t e r n a l s t r u c t u r e of a s o l i d has an important

i n f l u e n c e on how t h e s o l i d

w i l l

deform under an a p p l i e d

load.

A

very u s e f u l technique f o r o b t a i n i n g information

on i n t e r n a l s t r u c t u r e s

i s t o determine, a s a f u n c t i o n of

temperature and frequency of s t r e s s i n g , t h e r a t e a t which

i n t e r n a l s t r a i n energy

i s d i s s i p a t e d w i t h i n t h e s o l i d .

S c i e n t i s t s a t t h e I n s t i t u t e of Low Temperature Science

at

Holrkaido U n i v e r s i t y , Sapparo,Japan, have used t h i s tech-

nique with g r e a t success i n t h e i r i n v e s t l g a t i o n s on I c e

and snow.

The r e s u l t s of t h e i r observations should be

given s e r i o u s a t t e n t i o n i n any study on the deformation

behaviour of t h e s e m a t e r i a l s .

The present paper, t r a n s l a t e d from t h e Japanese a t

t h e r e q u e s t of t h e Snow and I c e Section of t h e D i v i s i o n

of Building Research, National Research Council, p r e s e n t s

some of t h e r e c e n t observations made a t t h e I n s t i t u t e of

Low Temperature Science on t h e i n t e r n a l f r i c t i o n of poly-

c r y s t a l l i n e and s i n g l e - c r y s t a l i c e .

It

i s the second

paper on

t h i s

s u b j e c t by t h i s group t h a t h a s been t r a n s -

l a t e d , the f i r s t b e i n g a v a i l a b l e i n t h e t r a n s l a t i o n s e r i e s

of t h e Defence Research Board (Visco E l a s t i c i t y of I c e I n

t h e Ternperzture Range

O0

-

100°C, by

K.

Yamaji and

D.

Kuroiwa, Defence Research Board T63J, August 1958).

The Division of Building Research wishes t o express

i t s a p p r e c i a t i o n t o

M r .

E.R.

Hope of t h e Defence Research

Board f o r t h e e x c e l l e n t t r a n s l a t i o n of t h i s paper.

Ottawa,

R . F .

Legget,

NATIONAL

RESEARCH

C O U N C I L

OF

CANADA

T e c h n i c a l T r a n s l a t i o n 978

T i t l e

:

I n t e r n a l f r i c t i o n of p o l y c r y s t a l l i n e and s i n g l e - c r y s t a l

ice

Authors:

Daisuke Kuroiwa and Kenju

Y a m a j i

Reference:

L o w

Temperature S c i e n c e [ ~ e i o n

~ a ~ a k u ]

,

S e r i e s

A ,

( 1 8 ) :

97-114, 1959

T r a n s l a t o r

:

E

.R.

Hope

T r a n s l a t e d from Teion Kugaku [Low Tenlpertlture S c i e n c e ] , S e r i e s A ( p h y s i c a l S c i e n c e s ) ,

-

1 8 (1959), 97-114.

INTERNAL

FRICTION OF FOLYCRYSTALZINE AND SINGLE-CRYSTAL ICE Daisuke KURODlA and ICenji Y W J I

EIokkaid6 U n i v e r s i t y , I n s t i t u t e of L o w Temperature Science,

Pure Physics S e c t i o n .

Received J u l y , 19 59. Author ' s R 6 s u d

The i n t e r n a l f r i c t i o n of p o l y c r y s t a l l i n e 3nd s i n g l e - c r y s t a l i c e was measured by a f l e x u r e v i b r a t i o n method Fn t h e temperature r m g e ODC t o -1'30'~. Fcr c o o l i n g t h e specimen, use was m d e of a c o l d box which could be r e f r i c e r a t e d by means of l i q u i d n i t r o g e n o r oxygen. The e x p e r i - mental apparatus i s shown in Figure 1.

In t h e case of p o l y c r y s t a l l i n e i c e t h e i n t e r n a l f r i c t i o n , h e r e d e s i e a t e d by t a n 6, revealed t h r e e c h a r a c t e r i s t i c v a r i a t i o n s w i t l l i n t h e nbove-mentioned temperature r a n s ( s e e Fig. 4 ) . 'dithin t h e range of O D t o -30°C t a n 6 was found t o decrease e x p o n e n t i a l l y , and, a s t h e temperature was f u r t h e r lowered, t h e r e appeared tiro peaks of t a n 6. The p o s i t i o n of t h e mwimuro of t a n 6 vinich appeared in t h e i n t e r m e d i a t e temperature ranee pro-red t o depend on t h e v i b r a t i o n frequency i n such a way t h a t it s h i f t e d towards t h e hit:ller temperature s i d e a s t h e frequency was increzsed, while t h e p o s i t i o n of t h e o t h e r peak l o c a t e d i n t h e v i c i n i t y of - 1 4 5 ' ~ was LndepenZent of t h e frequency. I n c o n t r a s t t o p o l y c r y s t a l l i n e i c e , s i n g l e - c r y s t a l i c e d i d not show ~ y t h i n g l i k e an exponential decrease i n t a n 6 i n t h e range 0' t o -30°C;

it e x h i b i t e d a t a n 6 peak which s h i f t e d with i n c r e a s i n g frequency towards t h e higher-temperature s i d e ( s e e Figs. 5, 6 ) .

We a l s o m d e some experiments t o i n v e s t i c a t e whether t a n b of i c e i s a f f e c t e d o r n o t by i n t e r n a l s t r a i n s produced a f t e r i r r a d l a t i o n with h e a t rays. It was found t h a t t h e peak of t a n 6 which appeared in t h e i n t e r m e d i a t e temperature range, i n e i t h e r p o l y c r f s t a l l i n e o r s i n g l e - c r y s t a l

i c e , .)as not influenced by t h e i n t e r n a l s t r a i n s due t o T y n d a l l ' s f i p r e s , minute c r a c k s o r t h e l i k e , r e s u l t i n g f r o n i r r a d i a t i o n ( s e e Figs. 7 , 8 ) . 'Pan b of p o l y c r y s t a l l i n e i c e in t h e range O'C t o -30°c, on t h e c o n t r a r y , was c c n s i d e r a b l y a f f e c t e d by t h e m a 1 r a d i a t i o n ( s e e Fig. 9 ) . Tdo d i f f e r e n t a c t i v a t i o n e n e r g i e s were calculated, one from t h e curve of lo^ t a n 6 versus r e c i p r o c a l a b s o l u t e tetxperature and t h e o t h e r fram t h e a l i l f t of t a n 5 observed i n t h e i n t e r - mediate tempersture r m g e ( s e e F i g s . 10-13). 'l'he f o r a e r value c a w o u t t o about 16-20 ~ c a l / m o l , and t h e i a t t e r t o 6 Kcal/mol.

I. I n t r o d u c t i o n

When a s o l i d r o d i s s e t f r e e l y v i b r a t i n g , t h e amplitude o f t h e o s c i l - l a t i o n s w i l l decay w i t h t h e pcssage o f t i m e . The r a t e o f decrement i s more r a p i d , t h e g r e a t e r t h e i n t e r n a l f r i c t i o n of t h e s o l i d . The i n t e r n a l f r i c t i o n of s o l i d s , a v e r y sensli.tive index of s t r u c t u r e , h a s l o n g been used as a

powerful method f o r a n s l y s i n g t h e i n t e r n a l struc.Lure o f m e t a l s , i n c o n n e c t i o n with t h e inlperfections o f c r y s t a l s , such as l a t t i c e d e f e c t s , d i s l o c a t i o n s , atomic i m p u r i t i e s and s o f o r t h .

I c e i s a s u b s t z n c e t h a t ~an.rl,:edly d i f f e r s i n i t s p h y s i c a l p r o p e r t i e s from m e t a l s and o t h e r soli.ds, ,md concernin:: i t s i n t e r n a l s t r u c t u r e t h e r e a r e many t h i n g s vie do no-L lnllow. T-Tc.~.s~xrements or" tlzc- i n - b e ~ n a l f r i c t i o n of i c e o v e r v ~ i r l e r c n g e s o f tc~:l.perc.tures vrould seela - t o 'ue one e f f e c t i v e means of i n v e s t i - g a t i n g i t s i n t e r n a l s t r u c - t u r e . A s our c2:tpel'irr~ntal 1r~zi;erial f o r -the i n t e r n a l f r i c t i o n m:easurexcn.ts li{e used ord:i.nary c o ~ u ? e r c i : ~ l . i c e , s i n g l e - c r y s t a l i c e prcpsrecl i n 'cize I.abor:~:i;oly, end ;:;:;:l.ncier i c e ?roc1 Greenland, brouglzt 'back t o Jap:zn by P r o f e s s o r l::?,!.:-;::ys. Thc g l a c i e r i c e i s q t l i t c difi'ferent g e n e t i c a l l y from t h e o t h c r 'iv~o t j ~ e s , bein:: for:nsd by recry:;tallizc..-Lion m d s i n t e r i n g of

p a r t i c l e s under enormous p r e s s u r e s a c t i n g over a long period of time. How t h e s e d i f f e r e n c e s of s t r u c t u r e and o r i g i n manifest theninelves i n t h e i n t e r n a l f r i c t i o n i s a question of g r e a t i n t e r e s t .

The i n t e r n a l f r i c t i o n of i c e was measured by a f l e x u r e v i b r a t i o n method. ++ The s a i d f r i c t i o n i s i n general a f u n c t i o n of t h e v i b r a t o r y f r e - quency and of temperature. In o r d e r t o extend t h e t e m p e r a t w e range of t h e measurements a s much as p o s s i b l e , t h e experimental apparatus was placed i n a cold-box which could be r e f r i g e r a t e d with l i q u i d oxygen o r l i q u i d n i t r o g e n .

Figure 1 shorio t h e general layout of t h e apparatus. PI and

P2

are t h i n b a r s of i c e , of r e c t a n g u l a r cross-section, c u t o u t of t h e same ice-block and trimmed t o e x a c t l y t h e same dimensions. P1 was used f o r temperature d e t e r - minations, and P2 f o r t h e i n t e r n a l f r i c t i o n measurenients. To each end of Pg t h i n i r o n p l a t e s a r e a f f i x e d . ( A l t e r n a t i v c l y , these p l a t e s m y be frozen on.

It i s , however, p r e f e r a b l e t o avoid doing t h i s , because krhen t h e temperature

i s lowered t o t h a t of l i q u i d oxygen, c r a c k s due t o t h e d i f f e r e n t c o e r f i c i e n t s of thermal expmsion may appear i n t h e - t e s t - p i e c e s . ) I~nmediately below t h e i r o n p l a t e s and a t a d i s t a n c e of about 5 nun t h e r e a r e two electroma@ets C1 and C2. P1 and P2 a r e each supported i n a l e v e l p o s i t i o n , a t t h e i r o s c i l - l a t o r y nodes, by two f i n e sillr t h r e a d s s t r e t c h e d between t h e two metal U-brackets B. The b r a c k e t s B and t h e rmgnets C1 and C z a r e mounted on a

s t u r d y metal base. Their p o s i t i o n s a r e f r e e l y a l t e r a b l e t,o s u i t t h e dimensions of t h e experiment. The whole apparatus, i n advance of t h e experiment, i s s e t up i n t h e c o l d room, ana enclosed i n t h e cold-box L which i s r e f r i g e r a t e d by c i r c u l a t i n g l i q u i d oxygen o r n i t r o g e n . The o u t s i d e of t h e box i s packed with styrofoarn, a good thermal i n s u l a t o r .

The i d e a l procedure would be t o measure t h e specimen temperature by a

thermocouple d i r e c t l y i n c o n t a c t with P2, but s i n c e t h i s would a f f e c t t h e . damping of t h e v i b r a t i o n s , we decided t o t a k e a s equivalent t o t h e temperature of

P2

t h e temperature measured by a thermocouple i n c o n t a c t with t h e i c e - b a r P1, which i s shaped t o t h e same dimensions and l o c a t e d i n a p o s i t i o n where t h e thermal c o n d i t i o n s a r e about t h e same as f o r

P2.

Since a mobile regula- t i o n of t h e temperature i n t h i s apparatus would be d i r f i c u l t , our procedure was t o prolong t h e c i r c u l a t i o n of l i q u i d oxygen o r n i t r o g e n , c o o l i n g t h e system u n t i l t h e temperature of P1 stood equal t o t h e b o l l i n g p o i n t of t h e r e f r i g e r a n t ; t h e n t h e supply was shut off and t h e measurements were conducted d u r i n g t h e subsequent f r e e r i s e of t h e ten~pera-Lure. The r a t e of rise was s a t i s f a c t o r i l y slow; it took about e i g h t hours f o r .the temperature i n t h i s apparatus t o come up from t h a t of l i q u i d oxygen t o - 3 O C . The cold-box was nnde i n t h r e e s i z e s , 45 x 1 6

x

12 cm3, 24 x 13

x

12 cm3, and 1 5

x

1 3

x

12

cm3,

t o s u i t t h e s i z e of t h e t e s t - p i e c e s .

If a l t e r n a t i n g c u r r e n t i s supplied t o t h e nTagnet c o i l C1 and i t s f r e - quency continuously v a r i e d ,

P2

w i l l begin t o v i b r a t e , and a t resonance, when

*

For d e t a i l s of t h e method s e e r e f e r e n c e s 1, 2, 3 and 4.

t h e impressed frequency matches t h e n a t u r a l v i b r a t o r y frequency of

P2,

t h e induced c u r r e n t i n c o i l C z r r i l l reach i t s maximum. A t t h i s p o i n t we s h o r t - c i r c u i t t h e c u r r e n t i n C1, l e a v i n g

Pg i n f r e e o s c i l l a t i o n , with a g r a d u a l l y

decaying amplitude. If f i s t h e n a t u r a l v i b r a t o r y frequency of

P2

and i s t h e measured time r e q u i r e d f o r t h e amplitude t o f a l l t o l/nth of i t s o r i g i n a l value, t h c n Young's modulus E and t h e q u a n t i t y t a n 6, p r o p o r t i o n a l t o t h e i n t e r n a l f r i c t i o n , a r e given by t h e formulae

logen t a n 6 =

n * f ( 2

1

Here m i s a c o n s t a n t d-etermined by t h e mode of v i b r a t i o n ,

&

i s t h e l e n g t h of specimen

P2,

-

a i s i t s t h i c l m e s s , and p i s t h e d e n s i t y .

111. E x ~ e r i m e n t a l R e s u l t s

In Figure 2 we show photographs, i n p o l a r i z e d l i g h t , of r e p r e s e n t a t i v e specimens of t h e kinds of i c e used i n t h e experiments. (A) and ( B ) a r e com- mercial i c e of p o l y c r y s t a l l i n e s t r u c t u r e . ( A ) i s c u t from a l a r g e block of i c e , with t h e f a c e n o r i n % l t o t h e d i r e c t i o n of f r e e z i n g ; i n ( B ) t h e f a c e i s p a r a l l e l t o t h e d i r e c t i o n of f r e e z i n g . (A) i s 1 7 cm i n l e n g t h , s o t h a t t h e c r y s t a l g r a i n s i n t h e photograph a r e 1 0 nm t o 5 mn i n s i z e . ( C ) and ( D ) a r e a r t i f i c i a l s i n g l e - c r y s t a l i c e prepsred i n t h e l a b o r a t o r y . In

( c ) ,

however, t h e r e was a sudden change of c o n d i t i o n s midway i n t h e f r e e z i n g process, w i t h t h e r e s u l t t h a t t h e sample came o u t d i v i d e d i n t o two s i n g l e c r y s t a l s , with a d i s c o n t i n u i t y i n t h e o r i e n t a t i o n . That i s t o say, t h e r e a r e two s i n g l e

c r y s t a l s Joined t o g e t h e r a t a s i n g l e g r a i n boundary. (D) i s a p e r f e c t s i n g l e c r y s t a l ,

show in^

no g r a i n boundary s t r u c t u r e . I?.'hat i s tlleant h e r e by " p e r f e c t " i s t h a t no r m t t e r how t h e p o l a r i z e r i s r o t a t e d no d i s t o r t i o n whatever can be d e t e c t e d i n t h e i n t e r i o r of t h e crys-l;al. A f t e r compl-etion of t h e experiments, ethylene d i c h l o r i d e s o l u t i o n of fonnvar (used f o r r e p l i c a s ) was a p p l i e d t o t h e s i n g l e - c r y s t a l i c e , producing p i t s , and from t h e d i r e c t i o n of t h e c r y s t a l s u r f a c e s as revealed b y t h e p i t s t h e o r i e n t a t i o n w a s determined. Tlie c r y s t a l axes werc determined by Higuc h i

'

s me thod

.

\:hen we measure t h e i n t e r n a l f r i c t i o n of a s o l i d by t h e v i b r a t i o n method, t h i s q u a n t i t y i s not a f u n c t i o n of t e u p e r a t u r e and v i b r a t i o n f r e - quency alone, b u t w i l l a l s o , depending on t h e causes t h a t produce t h e

i n t e r n a l f r i c t i o n , v a r y greatl-y with t h e amplitude of t h e v i b r a - t i o n s

.

S i n c e i n t h e c a s e of our experic!anl;s t h e s p e c i n i ~ n s were enclosed i n t h e t i g h t l y s e a l c d cold-box of Figure 1, -[;he v i b r a t o r y a r ~ ~ p l i t u d e could not e a s i l y b e determined. Therefore with i c e t h e n e c e s s i t y a r i s e s of i n v e s t i t a t i n g i n advance how much t h e i n t e r n a l f r i c t i o n a l t e r s v i t h t h e v i b r a t o r y amplitude. Figure 3 shows t h e changes of i n t e r n a l f r i c t i o n o c c u r r i n g i n i c e - b a r s of t h e dinznsions shown when, i n t h e cold rooln, t h e y were caused t o v i b r a t e with

an

aclplitude t h a t was v a r i e d from 10 p t o 8CO p. Tlle v i b r a t o r y ~implitude i s

p l o t t e d as a b s c i s s a , i n microns. The ice-specimens used i n t h e experiments were of commercial p o l y c r y s t a l . l i n e i c e <and, as sh~~hl11 schenzatically i n t h e Figure, were c u t w i t h t h e i r [broad] f a c e s perpen4icula.r t o and p a r a l l e l . t o t h e d i r e c t i o n o f f r e e z i n g . The v i b r a . t o r y a n ~ p l i t u d e s were determined b y observing, with a h o r i z o n t a l microscope, t h e d e f l e c t i o n s of a snr111 boss on t h e s u r f a c e of t h e i c e , i l l u m i n a t e d o b l i q u e l y by a s t r o n g l i g h t . The b o s s ,

s h i n i n g i n t h e f i e l d o f t h e microscope, c o u l d be observed when t h e b a r w a s se-t v i b r a t i n g . ( C f . Teion K:~.gaku, 15, p.44.) F i g u r e 3 shows t h a t a l t h o u g h t h e amplitude o f t h e v i b r a t i o n s c h a n ~ t e s g r e a t l y , t h e q u a n t i t y t a n 6 does n o t a p p e a r t o a l t e r v e r y mrked1.y. Ln o u r subsequent measurements, a l l v i b r a t o r y amplitudes were kept as s m a l l a s p o s s i b l e

---

w i t h i n limits of a few microns.

i ) The i n t e r n a l f r i c t i o n of p o l y c r y s t a l l i n e i c e . F i g u r e 4 shows o u r e x p e r i m e n t a l r e s u l t s on p o l y c r y s t a l l i n e commercial i c e . Curves (1.-5) _- - are a s e r i e s o f measurements a t v a r y i n g v i b r a t i o n - f r e q u e n c y made on t e s t p i e c e s c u t w i t h t h e i r f a c e s normal t o t h e d i r e e c t i o n of f r e e z i n g , while curve ( 6 ) i s f o r a specimen c u t p a r a l l e l t o t h e d i r e c t i o n of f r e e z i n g . In c u r v e ( I ) , a bar of l e n g t h 38.7 cm, width 1 9 . .'; crn and thiclcness 0.7 cyn i s measured a t i t s funda- mental frequency. The r e a d i n g s were begun a t t h e l o w - t e m p e r a a r e end. A s t h e t e m p e r a t u r e r i s e s , t a n 6 e x h i b i t s , a t - 1 . 4 5 0 ~ , a peak of h e i g h t 0.005. With f u r t h e r r i s e of t e m p e r a t u r e t m 6 d e c r e a s e s , 01-ily t o e x h i b i t , a t - 7 5 O ~ , i t s s h a r p maximum peak of h e i g h t 0.01. Again t a n 6 d i m i n i s h e s as t h e t e m p e r a t u r e r i s e s , and i n th.e n e i w o o r h o o d o f -30°C r e a c h e s a minimum; t h e n as t h e tem- p e r a t u r e approaches t h e mel-ting p o i n t t a n 6 i n c r e z s e s e x p o n e n t i a l l y . Curve

( 2 ) i s measured on t h e same specimen a t t h e f i r s t harmonic overtone, c o r - responding t o about 2.73 tinies t h e fundamental frequency of v i b r a t i o n . I n t h i s c a s e , t h e s u p p o r t i n g p o i n t s of t h e i c e - b a r were t r a n s f e r r e d from t h e n o d a l pol.nt of t h e fundamental v i b r a t i o n t o t h a t of f i r s t harmonic o v e r t o n e . The whole p i c t u r e rernains about t h e same: t:vo peaks a p p e a r i n t a n 6, and t h e r e i s a r a p i d r i s e a s t h e m e l t i n g p o i n t is approached. But t h e r e a r e a l s o d i f f e r e n c e s from c u r v e ( 1 ) . The low-temperature t:in 6 peak i n t h e v i c i n i t y o f -145OC i s t e n d i n g t o d e c r e a s e , w h i l e t h e -temperature a t which t h e peak i n t h e middle range a p p e a r s has been d i s p l a c e d t o t h e h i g h s i d e ( - 6 3 O ~ ) as

compared w i t h t h e fundamental-frequency c u r v e . Now l e t us t u r n t o c u r v e ( 3 ) , which r e p r e s e n t s t h e v a r i a t i o n of tam 6 n~easured at; t h e second overtone, corresponding t o about 5 . 4 t i m e s t h e funclanlental frequency. Again we s e e a diminution of t h e peak i n t h e low-terr~pernturc r e g i o n and a displacenlent of t h e mid-range maximum t o a. h i g h e r tempera.ture. Curve ( 4 ) i s measured a t t h e

f o u r t h overtone, about 1 3 . 3 t itnes t h e fundamen-La1 rrequency

.

Here, however, t h e specimen had been planed dovm t o a t h i c k n e s s of 0 . 5 1 cm, because a f t e r c o ~ n p l e t i o n of curve ( 3 ) i t s d i n e n s i o n s had become r a t h e r i r r e g u l a r as a r e s u l - t o f s u b l i m a t i o n . Consequently t h e f undu.rnenl;al frequency w a s s l i g h t l y lower

---

about 99.5 c y c l e s

-- -

t h a n t h e o r i g i n a l v a l u e , s o t h a t t h e frequency o f t h e f o u r t h overtone, i n curve (4), w a s 1316 c y c l e s . In t h i s cu.rve t h e low- t e m p e r a t u r e t a n 6 peak has p r a c t i c a l l y d i s a p p e a r e d , w h i l e t h e mid-range peak has s h i f t e d t o a s t i l l h i g h e r t e m p e r a t u r e ; 1;he peaks themselves Ymve become c o n s i d e r a b l y lower as conlpared w i t h t h e i r i n i t i a l h e i g h t s i n c u m e ( 1 ) .

A t t h i s p o i n t i n t h e experiment, t h e specimens had been s u b j e c t e d t o f o u r s u c c e s s i v e t h o r l i ~ a l v a r i a t i o n s o v e r

a

wide range o f t e m p e r a t u r e s , from n e a r t h e nielting p o i n t t o t h e 1-ow t e m p e r a t u r e oC l i q u i d oxygen. I f t h e r e were any h y s t e r e s i s involved i n t h e thermal. c l l a r n c t e r i s t i c s of t a n 6 i n i c e , t h e n i f we rt~oved back t o t h e fundamental. P r e c ~ ~ ~ e n c y a n d r e p e a t e d t h e measure- ments, t a n 6 woul4 n o t be l i k e l y t o reproduce i t s o r i g i n a l v a l u e s . To

i n v e s t i g a t e t h i s m a t t e r we now p l o t t e d t a n 6 curve ( 5 ) a t t h e fundamental frequency. A s w e have explained, t h e t e s t - p i e c e t h i c l u l e s s had nreanwhile been changed i n t h e t r u i n g - u p o p e r a t i o n , s o t h a t t h e frequency w a s smnller than i n t h e c a s e of curve (1). The low-temperature peak of ttul 6 was n e v e r t h e l e s s

s t i l . 1 i n t h e same place, but t h e peak i n t h e middle region, a s one viould expect with t h e reduced frequency, appeared a t a lower temperature ( - 7 0 " ~ ) t h a n i n curve ( 1 ) . No n o t i c e a b l e h y s t e r e s i s e f f e c t i s seen i n t h e o v e r - a l l form of t h e curve nor i n t h e peak v a l u e s .

Curve ( 6 ) r e p r e s e n t s v a l u e s of t a n 6 measured a t t h e fundamental f r e - quency of v i b r a t i o n i n a p o l y c r y s t a l l i n e specimen of almost t h e same s i z e , c u t

w i t h i t s f a c e s p a r a l l e l t o t h e d i r e c t i o n of f r e e z i n g . Although t h e d i s t r i - b u t i o n of t h e c r y s t a l gra.ins i s 11nrkedly d i f f e r e n t as compared w i t h t h e former specimen, t h e r e i s p r a c t i c a l l y no change i n t h e temperature-behavior of t a n 6.

The t o p part of Figure 4 shows Young's modulus f o r i c e , measured i n t h e same range of t e m p e r a t u r e s . The numbers on t h e c u r v e s r e f e r t o Ineasure- ments a s foll.ows: curve ( l ) , f o r t h e fundamental frequency; curve ( 2 ) , f o r t h e f i r s t overtone; curve ( 3 ) , f o r t h e second overtone. I n t h e v i c i n i t y of

- 1 0 " ~ ~ Young's modulus has a v a l u e of 7 - 2 x

lo1',

and i n c r e a s e s w i t h d e c r e a s e of temperature; a t -180°C it becomes 8 . 5 X 1 0 l 0 .

The temperature c h a r a c t e r i s t i c s of t a n 6 f o r p o l y c r y s t a l l i n e i c e may be summarized a s f o l l o w s . Over t h e temperature range from O"C t o -180°C, t a n 6 of p o l y c r y s t a l l i n e i c e e x h i b i t s t h r e e d i s t i n c t i v e v a r i a t i o n s . F i r s t , Prom O°C t o -35°C t h e r e i s a r a p i d f a l l o f t a n 6. Second, i n t h e middle range from 35°C t o -120°C a l a r g e maximum of t a n 6 develops, t h e peak value of which d e c r e a s e s with i n c r e a s i n g v i b r a t i o n frequency, w h i l e simultaneously t h e t e m -

p e r a t u r e a t which t h e peak appears i s d i s p l a c e d t o t h e high s i d e . Third, t h e r e i s s t i l l a n o t h e r peak i n t h e r e g i o n around -1.4S°C. I n t h i s c a s e t h e peak val-ues decrease with i n c r e a s i n g v i b r a t i o n frequency, but t h e temperature

a t

which t h e m a x i r n t ~ m occurs does n o t s h i f t with frequency.

Next we s h a l l show how t h e temperature c h a r a c t e r i s t i c s of t a n 6 f o r s i n g l e - c r y s t a l i c e d i f f e r from t h o s e f o r p o l . y c r y s t a l l i n e i c e .

ii) The temperature c h a r a c t e r i s t i c s of s i n g l e - c r y s t a l i c e . Figure 5 shows measurements of t a n 6 f o r an a r t i f i c i a l s i n g l e - c r y s s a l i c e produced i n t h e c o l d chamber by f r e e z i n g o r d i n a r y t a p water. The s i n g l e c r y s t a l s , flaw- f r e e parts of t h e i c e e x h i b i t i n g no d i s t o r t i o n under c r o s s e d p o l a r o i d s , were c u t o u t and shaped i n t o ~ * e c t y g u l a r t e s t - b a r s . Vie were a b l e t o o b t a i n them q u i t e l a r g e , t h e b i g g e s t b e i n g 17 cm long, t h e s r m l l e s t 13 cm.

he

c r y s t a l s were p r d u c e d by M r . Waltnhan~ of our I n s t i t u t e [ 6 ] . ) C~u-ves ( l ) , ( 2 ) and ( 3 ) r e s p e c t i v e l y r e p r e s e n t measurer~ients of t a n 6 a t 51-0, 870 and 2350 c y c l e s , made on s i n g l e - c r y s t a l . specimens having t h e C-axis lengthwise of t h e r e c t a n g u l a r b a r ; t h a t i s , britn t h e i r slip-pl-anes p a r a l l e l t o t h e d i r e c t i o n of v i b r a t i o n . The o r d e r of t h e measurements was a s f o l l o w s . F i r s t we t o o k curve ( 2 ) a t t h e fundarilental frequency of 870 cycl-es, then curve ( 3 ) a t t h e f i r s t harmonic overtone, and f i n a l l y , a f t e r trimming down t h e t h i c l m e s s of t h e specimen,

curve ( 1 ) . The values of t a n 6 a r e pl-otted a.s o r d i n a t e s on a s c a l e ~ n a p i f i e d f i v e times a s compared w i t h t h e s c a l e of F i g m e 4. To show how s m a l l t h e i n t e r n a l f r i c t i o n of t h e s e c r y s t a l s i s i n cou!parison with t h a t of t h e poly-

i c e measurements from Figure 4. Branch b of curve ( 5 ) , a f t e r pz~ssing through t h e peak value a t 0.008 (not shovm i n t h g Figure), connects t o branch b 1

.

Since curve (5) i s f o r frequency 842 cycles, t h e s i n g l e - c r y s t a l v a l u e s T o r nearly the same frequency, a s seen in curve (2), a r e indicative of t h e reduc- t i o n i n t h e i n t e r n a l f r i c t i o n of single-crystal i c e a s compared with poly- c r y s t a l l i n e ice. A f u r t h e r f a c t i s t h a t t h e curves of t a n 6 f o r single- c r y s t a l i c e do not show a rapid increase a s t h e temperature approaches -the melting point, a s they do i n t h e case of polycrystalline ice, but on t h e contrary they f a l l steeply toward t h e meltinc point. Moreover t h e r e i s probably no low-temperature peak of t a n 6 a s observed around -145°C i n poly- c r y s t a l l i n e i c e ( o r i f a peak does e x i s t ,

it

i s f a r smaller than in poly- c r y s t a l l i n e i c e ) . We have only t h e tan 6 peak i n t h e middle range, t h e peak t h a t exhibits a frequency-dependent displacement toward t h e higher temperatures.

The rapid r i s e of t a n 6 in polycrystalline i c e a s t h e melting point

i s

approached, i n c o n t r a s t t o t h e experimentally established decrease toward t h e melting point in single-crystal ice, m y no doubt be ascribed t o i n t e r n a l f r i c t i o n a r i s i n g a t t h e grain boundaries. To support t h i s t h e r e i s another experimental. f a c t ; it appears from curve (4) of Figure 5. This curve repre- s e n t s measurements m d e on a specimen comprising two s i n g l e c r y s t a l s separated by one grain boundary, a s shown i n t h e polarized-light photograph C of Figure 2. Branch a of curve ( 4 ) , a f t e r passing through a maximum of height 0.01 (not

shown

i K

t h e Figure), joins t h e other branch a ' .

In

t h i s curve, then, a s t h e Figure shows, t h e r e

i s

a r i s e of t a n 6 when

tz

t e m p e r a t ~ r e exceeds - 2 0 " ~ .

In

other words, t h e presence of even a s i n g l e c r y s t a l boundary

in

t h e specimen causes t h e temperature c h a r a c t e r i s t i c s of t a n 6 t o resemble those of poly- c r y s t a l l i n e i c e

.

In

Figure 6 we show other examples of measurements of t a n 6 on single- c r y s t a l i c e . Curves ( 3 ) and ( 4 ) of Figure 6 exhibit .the temperature charac- t e r i s t i c s of t a n 6 f o r a s i n g l e c r y s t a l which, l i k e t h e previous specimens, has t h e C-axis more or l e s s coinciding with t h e lengthwise a x i s of t h e bar.

The vibration frequencies a r e 715 and 1950 cycles respectively.

In

both cases

t h e peak i s swll, about of t h e same s i z e a s i n Figure 5, and t h e temperatures a t which t h e peak appears a r e -40°C and -22°C. Curves ( 1 ) and ( 2 ) a r e

an

example of a single-crystal i c e having a t a n

6

mxbnurn of t h e same height a s t h a t of p l y c r y s t a l l i n e ice.

In

t h i s s i n g l e c r y s t a l t h e C-axis

i s

o r i e n t a t e d

i n t h e d i r e c t i o n of t h e thickness of t h e test-bar. Curve (1) i s a t 510 cycles, curve ( 2 ) a t 1390 cycles. These two curves lack t h e rapidly r i s i n g

part

of t a n

6

i n t h e v i c i n i t y of the melting point; t h e peak i n t h e v i c i n i t y of

- 1 4 5 " ~

i s

a l s o missing. The middle-range peak, t h e peak which with increasing frequency s h i f t s toward higher temperatures, i s markedly higher a s compared with t h e single c r y s t a l of curves ( 3 ) and ( 4 ) . This specimen, examined between crossed p l a r i z e r s , shows up a s e n t i r e l y a s i n g l e c r y s t a l , but t h e r e

i s a v i s i b l e pattern of i n t e r n a l d i s t o r t i o n (Figure 7). Such d i s t o r t i o n

i s

q u i t e absent from t h e s i n g l e c r y s t a l of curves (3) and ( 4 ) , o r from t h e s i n g l e c r y s t a l of Figure 2. One may perhaps imagine t h e d i s t o r t i o n p a t t e r n a s

an

a r r a y of very s l i g h t l y inclined faces of microscopic c r y s t a l s , t h a t is, of

microscopic sub-grain boundaries. This i s no

nnre

than simple speculation,

thou&

it

i s c r e d i b l e t h a t t h e markedly greater s i z e of t h e peak i n curves (1) ,and ( 2 ) , a s compared with t h a t i n curves ( 3 ) and ( 4 ) , should be due t o i n t e r n a l d i s t o r t i o n of t h e c r y s t a l . A f i n a l decision i n t h i s matter must

w a i t

I n t e r n a l f r i c t i o n i n s i n d e - c r y s t a l i c e tnay be s u m m r i l y d e s c r i b e d as

fo1lor.r~. The t a n 6 curve of s i n g l e - c r y s t a l i c e does not show t h e r i s e i n the high-temperature range, t h e r i s e t h a t i s caused by c r y s t a l boundaries. The peak i n t h e v i c i n i t y o r -145O~ i s p r a c t i c a l l y absent ( o r i f p r e s e n t , i s v e r y s ~ n a l l ) . The t a n 6 peak t h a t appears i n t h e middle range of tenlperatures m y be small, a few o r a t e n t h of' t h a t of p o l y c r y s t a l l i l : ~ ic e , o r it may be of about t h e same h e i g h t a s i n p o l y c r y s t a l l i n e i - e

.

iii) Change i n t a n 6 due t o Tyndall f i g u r e s o r i n t e r n a l s t r a i n s pro- duced i n t h e i c e by t h e m l i r r a d i a t i o n . It i s w e l l known t h a t i n t e r n a l f r i c t i o n i n metals a l t e r s with working

_-

---

t h a t i s , it i s n o d i f i e d by com- p r e s s i o n s and extensions. I n t h e c a s e o f i c e a l s o it m y be v e r y i n f o n m t i v e t o i n v e s t i g a t e how t h e i n t e r n a l f r i c t i o n , as discuss?d above, w i l l a l t e r with working, i f t h e p r o p e r t i e s of i c e c r e considered i n a n a 7 . 0 ~ with metals. But s i n c e i c e i s c h a r a c t e r i s t i c a l l y fran[:ible, it would be d i f f i c u l t t o work it f r e e l y i n t h e same way as a metal. Therefore we t r i e d thermal i r r a d i a t i o n of t h e i c e , producing Tyndall f i g u r e s bj i n t e r n a l melting; t h e n , a f t e r r e - f r e e z i n g , we made measure~ilents of t a n 6 _{and con~pared them wil;h tlre p r i o r values.'}

tlhen i c e i s s u b j e c t e d t o t h e m l i r r a d i a t i o n , m e l t i n g begins a t t h e c r y s t a l boundaries, while a t t h e same time t h e r e occurs, i n t h e i n t e r i o r of t h e c r y s t a l . g r a i n s , an i n t e r n a l m e l t i n g i n %he form kaown a s Tyndall f i g u r e s o r T y n d n l l ' s flowers [ 7 ] . Upon c e s s a t i o n of t h e i r r a d i a t i o n , t h e s e melted regions recongeal i n t o i c e , and '!~'nen t h i s happens t h e i n t e r n a l melt-water does n o t f r e e z e i n t h e same way a s b e f o r e : t h e r e rennin vacuous bubbles, due t o d i f f e r e n c e i n t h e s p e c i f i c volumes of i c e and water. Thus f i s s u r e s a r e opened a l o n g t h e b a s a l planes and d i s t o r t i o n i s produced. When examined i11 a d.ark room under oblique i l l u ~ n i n a t i o n , th e Tyndall f i g u r e s o r t h e f i n e c r a c k s i n t h e b a s a l planes s h i n e stronpJy by r e f l e c t e d l i g h t . ??he l'yndall f i g u r e s o r f i n e c r a c k s i n t h e s i n g l e - c r y s t a l i c e of P i ~ u r e 8 , which has t h e C-axis i n t h e lengthwise d i r e c t i o n of t h e rod, a r e v i s i b l e as a m u l t i t u d e of p a r a l l e l l i n e s .

In t h i s way, then, we can produce .m interna.1 d i s t o r t i o n i11 i c e .

Figure 9 shows t h e ter~~perature-be11avi.or of t a n 6 as measured i n poly- c r y s t a l l b e and i n s i n { ; l e - c r y s t a l i c e b e f o r e uld a f t e r exposure t o t i l e r ~ n a l r a d i a t i o n . Cul-ve 1- i s f o r p o l y c r y s t a l l i n e i c e b e f o r e i r r a d i a t i o n and i s

measured a t t h e fundamen-tal vi.bration frequency of 460 c y c l e s ; curvc 2 i s f o r t h e same specimen a f t e r i r r a d i a t i o n and d e v e l ~ p l l e n t of t h e l?yndall f i g u r e s . Let us f i r s t loolr a t t h e t a n G peak i n t h e middle range of temperatures. The graph shows t h a t t h i s peal< i s q u i t e u n a f f e c t e d by t h e i r r a d i a t i o n . The peak i n t h e v i c i n i t y of -140°C, however, has become stnaller i n conlparison t o i t s h e i g h t before i r r a d i a t i o n . And t h e grain-boundary i n t e r n a l f r i c t i o n t h a t develops i n t h e high-temperature range has, after i r r a d i a t i o n , become m r k e d l y g r e a t e r t h a n b e f o r e i r r a d i a t i o n .

Curves ( 3 ) and (1) r e p r e s e n t t h e r e s u l t of similar experiments on s i n g l e - c r y s t a l i c e . Curve ( 3 ) i s tlle v n r i a t i o n of t a n 6 b e f o r e i r r a d i a t i o n ; curvc ( 4 ) a f t e c i r r a d i a t i o n . 'The t \ . ~ o c o i n c i d e alnlost p e r f e c t l y ; t h e i n t e r n a l f r i c t i o n of s i n , y l e - c ~ y s t a l i c e i s qui-te &?affected by d i s t o r t i o n s o r Tjndrzll f i ~ t c l r e s art; i f i c i a l . 1 ~ produced w i t h i n i t .

Fro% t h e s e L~;JO e:ry;erin!ents, we niiy say a s f o l l o v ~ s

.

The i n t e r n a l f r i c t i o n a r i s i n c ; a t cl-ystal g r a i n b o ~ m d a r i e s i s mmrltecily i n c r e a s e d by thermal i r r a d i a t i o n ; t h e c r y s t a l p a i n bound.aries a r e ski-ong1.y n o d i f i e d 'uy n e l - t i n g ciue .to t h e

i r r a d i a t i o n . But t h e frequency-dependent peak of t a n 6 i n t h e i n t e n n e d i a t e temperature range i s unchanged, both in polyc r y s t a l l i n e cvld i n single-c r y s t a l i c e . Consequently t h e mechanism here causing t h e i n t e r n a l f r i c t i o n i s unre- l a t e d t o macroscopic s t r u c t u r e s such as Tynilall f i g u r e s o r i n t e r n a l cra,cks; we m y t a k e it that t h e cause l i e s i n a. microscnpic s t r u c t u r e i n t h e i c e c r y s t a l . I n p o l y c r y s t a l l i n e i c e t h e t a n 6 peak a t t h e low-temperature end i s reduced t o about h a l f - s i z e by t h e thermal i r r a d i a t i o n . The reason f o r t h i s i s not c l e a r , b u t it i s d i f f i c u l t t o s e e i n it a nlechanism of reduction of i n t e r n a l f r i c t i o n by Tyndall f i 6 u e s o r cracks. Rather we mxy t a k e it a s more l i k e l y an annealing e f f e c t ; t h e specimen i s heated t o 0°C by t h e i r r a d i a - t i o n . But t h i s conclusion must wait upon f u t u r e r e s e a r c h .

IV.

Activation Enerm

We have seen t h a t i n t h e i n t e r v a l from O 0 t o -180°C t h e i n t e r n a l f r i c t i o n of i c e e x h i b i t s t h r e e c a u s a l l y d i f f e r e n t c h a r a c t e r i s t i c v a r i a t i o n s . In p o l y c r y s t a l l i n e i c e t h e r e i s a f r i c t i o n a r i s i n g a t t h e c r y s t a l p a i n boundaries; t h e r e i s a f r i c t i o n e x h i b i t i n g t h e c h a r a c t e r i s t i c t h a t i t s peak

i s displaced with i n c r e a s i n g frequency toward t h e hirber-temperature side; t h e r e i s t h e low-temperature f r i c t i o n i n t h e v i c i n i t y of -140° t o -150°C which

e x h i b i t s no frequency-dependent displacement of I t s peak. The i n t e r n a l f r i c - t i o n of s i n g l e - c r y s t a l i c e i s of t h e frequency-dependent t y p e alone; n e i t h e r t h e grain-boundary f r i c t i o n nor t h e low-temperature peak appears. In t h i s

s e c t i o n of our paper we s h a l l d i s c u s s t h e a c t i v a t i o n energies d e r i v a b l e from t h e temperature c h a r a c t e r i s t i c s of t h e s e f r i c t i o n < ? .

I n

Figure 10 w e have t h e values of t a n 6 f o r t h e p o l y c r y s t a l l i n e i c e of Figure 4 i n t h e temperature range from 0" t o -35OC, p l o t t e d a s o r d i n a t e s Dn a logarithmic s c a l e 3l;ainst t h e r e c i p r o c a l s of t h e a b s o l u t e temperatilres a s a b s c i s s a e . The numbers of t h e curves correspond t o t h o s e of Figure 4. I f we look a t t h e low-frequency curve ( l ) , we s e e t h a t between O 0 and -2S°C t h e p l o t t e d p o i n t s l i e on a s t r a i g h t l i n e , s a t i s f y i n g t h e r e l a t i o n s h i p

-El

t a n 6 = t a n 60 exp

-

_m

Here

El i s

a c t i v a t i o n energy, H i s t h e gas constant, T i s . a b s o l u t e temperature, and t a n 60 i s a. c o n s t a n t . A t temperatures below -25OC, however, t h e measure- ments d e v i a t e from t h e s t r a i g h t l i n e onto a curve. This i s because another r e l a x a t i o n mechanism which appears i n t h e middle-temperature range begins t o be superimposed. Curves ( 2 ) t o ( 4 ) r e v e a l t h a t t h i s d e v i a t i o n from l i n e a r i t y due t o t h e superimposition e f f e c t appears a t p r o g r e s s i v e l y higher temperatures as t h e v i b r a t o r y frequency i n c r e a s e s . Thus when we a r e considering only t h e i n t e r n a l f r i c t i o n a r i s i n g a t t h e c r y s t a l g r a i n boundaries, t h e p l o t t e d p o i n t s should n o t b e extended t o o f a r toward t h e lower temperatures. From t h e slope of t h e s t r a i g h t - l i n e p a r t s of t h e family of curves i n Figure 10 we f i n d t h e a c t i v a t i o n enerey

El

f o r t h e grain-boundary i n t e r n a l f r i c t i o n t o be about 17-20 ~ c a l / n l o l .

Next l e t us consider t h e i n t e r n a l f r i c t i o n developed i.n t h e middle

temperature range. In Figure 4 we have shown t h e temperature behavior of

e x h i b i t s

a

s h a r p c e n t r a l peak, from which

it

diminishes s t e e p l y on both t h e hip$-temperature and t h e low-temperature s i d e s . It i s n o t c l e a r what the mechanism i s , but it m y be t h a t on t h e high-temperature s i d e t h e v i b r a t o r y s t r a i n c l o s e l y follows t h e v a r i a t i o n s of t h e e x t e r n a l d r i v i n g f o r c e s , without m y time-lag, while on t h e low-temperature s i d e , on t h e c o n t r a r y , t h e s t r a i n i s

not a b l e t o follow t h e s t r e s s v a r i a t i o n s ; t h e phase-difference between t h e s t r e s s and s t r a i n v e c t o r s m y be

mximum

a t j u s t t h e temperature where t h e nlaximum of t z n 6 _{appears. The phenomenon i s forrnally s i i n i l a r t o t h e c a s e of}

an a l t e r n a t i n g e l e c t r i c f i e l d a p p l i e d t h e ice; t h e d i p o l e s i n t h e i c e , t u r n i n g t o follow t h e d i r e c t i o n of t h e e l e c t r i c f i e l d , do s o with a l a g and

with r e s u l t i n g d i e l e c t r i c l o s s e s .

Figure 11 i s a r e p l o t of Figure 4 t o show t h e r e l a t i o n s h i p of

tan

6 t o t h e v i b r a t o r y frequency, with tile temperature a s t h e [ f i x e d ] parameter; t h e a b s c i s s a i s t h e a n w l a r ' frequency 2rrf i n a logarithmic s c a l e .

Tan

8 v e r s u s l o g u, g i v e s us a family of curves with almost symmetrical peaks. I f we put u+,,.~, f o r t h e a.ngu1a.r frequency a t which t h i s

tan

6 pealt occurs, t h e r e l a x a t i o n time i s

1

I - - ; -

%EX ( 4 )

I n

Figure 12, which shows

t m 6

a g a i n s t a l o g a r i t h u ~ i c s c a l e of wr, t h e p l o t t e d p o i n t s a r e n i c e l y d i s t r i b u t e d on e i t h e r s i d e of t h e well-known r e l a x a t i o n

C 11rVe :

I n Fi.e;l~re 1 3 t h e r e l a x a t i o n tirrles T, _{c a l c u l a t e d from equation} ( 4 ) , a r e p l o t t e d a s ordinates, and t h e r e c i p r o c a l a b s o l u t e temperatures a t which t h e peaks appear a r e talcen a s a b s c i s s a e . The s t r a i g h t l i n e ( a ) i s f o r g l a c i e r i c e ; ( b ) i s f o r commercial po.lycrystalline ice; ( c ) and ( d ) a r e f o r s i n g l e - c r y s t a l i c e . I n each c a s e t h e r e l a t i o n between T and

T'~

i s l i n e a r , c a t i s f y i n g

t h e r e l a t i o n s h i p

E2

T = -rO exp

-

RT

Here C 2 i s t h e a c t i v a t i o n energy of t h e r e l z x a t i o n mechmism producing t h e i n t e r n a l f r i c t i o n peak; T, i s :3 c o n s t a n t .

E2

i s c a l c u l a t e d from t h e s l o p e s

of t h e s e straigh-1; l i n e s , and t h e l i n e s al.1 b e i n g p a r a l l e l t o each o t h e r , w e f i n d t h a t

E2

i s about 6 ~:cal/mol.

I f we now compare t h e s e values with t h o s e of o t h e r research-workers, t h e s i t u a t i o n i s as fol1o:rs. ( e ) i n Figure 1 3 shows t h e r e l a t i o n s h i p of r e l a x a t i o n time t o temperature a s obtained by ICnecer e t a l . [8] f o r round rods of s i n g l e - c r y s t a l i c e i n t o r s i o n a l v i b r a t i o n . I n t h i s c r s e t h e a c t i v a - t i o n energy i s 8.45 Kcal/mol. ?.'he teriperature range f o r t h e measurements, ho~,rever, was 0"

-

25°C. On ( f ) a r e p l o t t e d , q a i n s t T ' ~ , t h e v a l u e s found by Ilur~bel e t a l . [ 9 ] and by Auty an(: Cole [lo] f o r t h e r e l a x a t i o n tirne a s d e t e r ~ r ~ i n e d from t h e d i e l e c t r i c l o s s peak i n i c e . The a c t i v a t i o n energy f o r t h e d i e l e c t r i c r e l a x a t i o n , a s ca.lculnteci f r o m t h e s l o p e of t h i s l i n e , i s 113.25 ~<cal/mol, about twice t h e a c t i v a t i o n e n e r a r obtained by us f o r t h e

rnechca,n i c a l r e l a x a t ion. The d i e l e c t r i c r e l a x a t ion phenomenon i s a s c r i b e d t o r o t a t i o n of t h e ice-molecule d i p o l e s . Regarding t h e rneciianism r e s p o n s i b l e f o r t h e mechanical r e l a x a t i o n phenomenon a s obselvcd by us i n t h e range -30 t o 90°C, nothing d e f i n i t e can be s a i d frorrl colllprison o f a c t i v a t i o r i e n e r g i e s al-one, b u t it i s a p o j n t worth n o t i n g t h a t 6 ~ c u l / m o l i s ;)bout h a l f t h e a c t i - v a t i o n energy of evaporation, o r e q u a l t c ) t h e a c t i v a t i o n e n e r a r e q u i r e d t o break one mol.ecular bond i n i c e .

N o w we rrrust mention t h e a c t i v a t i o n energy of t h e i n t e r n a l f r i c t i o n t h a t develops i n t h e v i c i n i t y of -14:0° t o -150°C. T h i s peak diminishes with i n c r e a s e of t h e v i b r a t i o n a l frequency, and w i t h i n t h e range of experimental e r r o r t h e r e i s no v a r i a t i o n of t h e temperature a t which t h e peak occurs. F o r m l l y speaking, t h i s means t h a t t h e a c t i v a t i o n energy i s i n f i n i t e l y g r e a t . In s i n g l e c.qs.Lals p r e p r e d i n t h e 1.aboratol-y, t h e peak i n q u e s t i o n e i t h e r does n o t appear o r i s smzill. It i s n o t obsei-ved a t a l l i n i c e which, l i k e g l a c i e r i c e , has been produced. by s i n t e r i n g under e r e a t p r e s s u r e s a c t i n g over a long space of time.

V . Conclusions

I n measurements of t h e i - n t e r n a l f r i c t i o n 01 p o l y c r y s t a l l i n e and s i n g l e - c r y s t a l i c e i n t h e t e n ~ p e r a t u r e rance 0" t o -lEIO°C,

i t

was found t h a t , i n t h e c a s e of p o l y c r y s t a l l i n e i c e , the t a n

6

[component] a s c r i b a b l e t o t h e c r y s t a l boundaries a t f i r s t e x h i b i t e d

an

abrupt d e c l i n e i n tile range from 0°C t o -30°C. This [component i s completely extinguished a t te~npera,tul-es below

-,?OOc,

and

i n t h e range from -?O°C t o -90°C a f r e c l u e n c - e n d n i n t e r n a l f r i c t i o n develops. Nith f u r t h e r d e c r e a s e of tenlperature t h i s f r i c t i o n d i e s o u t , and another peal< t h e n develops i11 t h e v i c i n i t y of -140°C t o - 1 4 5 " ~ . The temperu-

t u r e a t which t h e l a s t peak a p p a r s i s independent of frequency. In s i n g l e c r y s t a l s and i n g l a c i e r i c e t h i s peak i s n o t obsenreci.

A f t e r melting -the i c e specjniens on which w e made o u r i n t e r n a l frequency determinations, t h e e l e c t r i c r e s i s t a n c e of t h e water was measured a t room temperature. The s p e c i f i c r e s i s t a n c e of t h e melt-water from b o t h t h e poly- c r y s t a l l i n e i c e and t h e s i n g l e - c r y s t a l i c e vlss t h e same, narncly 8

-

10 times t h a t of r e p e a t e d l y d i s t i l l e d water, i f t h e s p e c i f i c resist,ance of t h e l a t t e r

i s taken a s 1.3 X

l o e

R-cm. I n o t h e r v~orils, t h e cont.ent of i m p u r i t i e s i n e i t h e r t h e s i n g l e - c r y s t a l i c e o r t h e polycrystnlli.ne i c e i s about 8

-

10 t i m e s t h e c o n t e n t i n r e p e a t e d l y d i s t i l l e d water.

The temperature c h a r a c t e r i s t i c s of t a n G f o r g l a c i e r ice are q u i t e d i f f e r e n t from those of t h e cornn:erzi.al p o l y c q - s t s l l i n e i c e . _It i s very

i n t e r e s t i n g t o cou!Fzre tb.2 expi-rime:_it,zl r c s u 3 . t ~ s e t Yol-th above, a n d w e s h a l l l i l i e l y have more t o s a y ibou-t them i.n a f u t u r e pi.;blication.

The a u t h o r s a r e g r a t e f u l t o Professor Takec 1107.1; a l s o t o P r o f e s s o r l J l ~ i c h i r 6 NAIUYA of HokJcaid6 Universj-ty. The i c e c l y s t a l s used i n t h e e x p e r i - ments were furnished by l41-. Gord I.lNCRiIMpL4 of our I n s t i t u t e , whose c o n t r i b u t i o n t o t h e success of our work we shou1.d l i k e - t o n o t e . !.!e a l s o t a k e t h i s oppor- t u n i t y t o express our grat;i-t~lGc f o r u s e 5 r l clliccussion of . t h i s r e s e a r c h with members of t h e Snow Research Group, m s - t i t i ~ i ; e of Low T e c ~ p e r a t u c Science, and t h e C r y s t a l P l ~ t s t i c i t y Research Group

:

:

t

:.lc!;ka:ic?6 U n i v e r s i t y .

Kenji YAMAJI

und

Daisulce IW,Onl~Z, 1956. V i s c o - E l a s t i c i t y of i c e i n t h e t e m p e r a t u r e range 0"

-

-lOG°C (~orrlnnulic:xtion I ) . Teiun I{ag~tku, A15, 171-183.

[DRB

t i - a n s l a t i o n T 6 3

J.

]

-

Daisuke I(UROI7;IA and ICenji YflP4bU17 1956. Study of t h e v i s c o - e l a s t i c i t y of snow b y a v i b r a t i o n method (11). Teion Kagaku,

-

A 1 5 , 43.

Daisuke RJRODJA and ICenji YMUJI, 1953. I n t e r n a l f r i c t i o n of poly- c r y s t a l l i n e and s i n g l e - c r y s t a l i c e . Kinzolcu R u t s u r i [ P h y s i c s of ~ e t a l s ] ,

-

4, 254.

Ryfkichi IUSHIGUCHI and Maohiro IG'LCIIT, 1955. 2kperimentnl method f o r t h e

measurement

of i n t e r n a l f r i c t i o n . Kinzoltu l3utsuri,

_-

2, 116. K e i j i HIGUCHI, 1957.

A

ne:J nethod f o r r e c o r d i n g t h e g r a i n - s t r u c t u r e

of i c e . J. Glaciology,

3,

131.

Gor6 W A I C h t M , 1958. Pending t e s t s on [ r e c t a n g u l a r p l a t e s o f ] i c e . Teion I(all;alcu,

_-

Al.7, 0 7 .

UkichirS, NM~AY;4, 1956. Physics o f s i n g l e c r y s t a l s

of

i c e . Kagaku

[ s c i e n c e ] ,

-

26, 272.

H.O. 1Cneser e t al., 1955. Iviechanische E e l a x a t ion von e i n k r i s t a l l i n e m E i s . Naturwiss., 15, 437.

F. Ilumbel e t a l . , 1953. I l i e l e l r t r i z i t ~ t s l t o n s t a l t e d e s E i s e s . Helv. Phys. Acta, 26, 17.

_-

R.P. 11uty and H. Cole, 1952. D . i e l e c t r i c p r o p e r t i e s of i c e and s o l i d D20. J. Chen~. Phys., 20, 1309.

_-

Fig. 1. Scheme of experimental apparatus.

Fig. 2. Patterns obtained with ice specimens put between crossed polaroids.

A , B. Polycrystalline ice.

C. Z-single crystal ice.

Fig. 3. Relation between tan 8 and amplitude of vibrating ice bar.

t e m p e r a t u r e

Fig. 4. Temperature dependencies of internal friction and Young's modulus of polyc-e ice.

2 S;nqle crystals

t e m p e r a t v r e

Fig. 6. Internal friction of two kinds of single crystal ice

Fig. 8 . Tyndall's figure produced by heat radiation. (Single crystal ice!

Fig. 7. Single crystal ice having interior distortion. Photogragh was taken under the crossed polaroids.

befor8 ;rrad;at;om

@

before ;rradi a t i o n

.

C femperoture

Fig. 1 0 . Relation between log (tan 6) and reciprocal absolute temperature.

W

Fig. 11. Frequency dependence of internal friction of ice.

w in angular frequency.

o r

J - I

o

-20 -40 -60 -80 -100

co

r e c i p r o c o /

o b t o i u t e

t e m p e r a t u r e

Fig. 13. Relation between relaxation time of ice and reciprocal absolute temperature.