ELLIPSOMETRIC STUDY OF THE ICE SURFACE STRUCTURE JUST BELOW THE MELTING POINT

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ELLIPSOMETRIC STUDY OF THE ICE SURFACE STRUCTURE JUST BELOW THE MELTING POINT

Y. Furukawa, M. Yamamoto, T. Kuroda

To cite this version:

Y. Furukawa, M. Yamamoto, T. Kuroda. ELLIPSOMETRIC STUDY OF THE ICE SURFACE

STRUCTURE JUST BELOW THE MELTING POINT. Journal de Physique Colloques, 1987, 48

(C1), pp.C1-495-C1-501. �10.1051/jphyscol:1987168�. �jpa-00226314�

JOURNAL DE PHYSIQUE

Colloque C1, supplbment au n o 3, Tome 48, mars 1987

ELLIPSOMETRIC STUDY OF THE ICE SURFACE STRUCTURE JUST BELOW THE MELTING POINT

Y. FURUKAWA, M. YAMAMOTO* and T. KURODA

The Institute of Low Temperature Sciences, Hokkaido University, Sapporo 060, Japan

"~esearch Institute for Scientific Measurements, T0h0ku University, Sendai 980, Japan

&sum6 - ^{L'indice de} rdfraction nl et lldpaisseur de la couche de transition (Q.L.L.) h la surface dlun cristal de glace h tdrature juste en-dessous du point de fusion (O°C) ont 6th mesurds h 116quilibre en utilisant une m6thode d'ellipscnn6trie in-situ. Les couches de transition ont dtd-observ6es h des tdratures sdrieures h -2 et -4OC pour les faces f 0001fet ~ 1 0 1 0 ~ respectivement et n1 = 1,330 pour les deux faces. Cette valeur est tres proche de celle de l'eau en volume h 0°C. ~ssoci6 h des observations sur les formes des cristaux de glace prbs du point de fusion, on doit s1attendre h ce que 13 structure de llinterface entre la couche de transition et la glace sur la face {lolo! varie brutalement au-dessous de -Z°C pour devenir plus rugueuse.

Abstract : The r e f r a c t i v e index n l and the thickness d of the t r a n s i t i o n layer ( q u a s i - l i q u i d layer) on the surface of an ice crystal a t temperatures j u s t below the me1 ting point (0°C) were measured in equilibrium, using an in-situ method of el lipso- metry. The t r a n s i t i o n layers were observed a t temperatures above -2 and -4°C f o r (0001)- and {1010}-faces, respectively, and n was 1.330 f o r both faces, which i s very close t o the r e f r a c t i v e index of bulk w a k r a t O°C (nw=1.333). Combined with the observational r e s u l t s about the ice crystal shapes near the melting point, i t was expected t h a t the interface structure between t r a n s i t i o n layer and i c e on the (1010)-face changes from smooth t o rough a t -2°C.

1. Introduction

I t i s known t h a t the ice crystal surface i s covered with a t r a n s i t i o n layer (so-called quasi-liquid layer, hereafter QLL) a t temperatures j u s t below i t s bulk melting point (0°C) in equilibrium. The surface s t r u c t u r e l i k e t h i s i s intimately related t o the physical phenomena such a s the mechanical adhesion[1,2], sintering[3], gas adsorption[4,5], d i e l e c t r i c constant[6], surface e l e c t r i c a l conductivity[7,8], NMR[9], Vol t a effect[lO], photoemission[ll] and surface disorder[12]. A1 though these experimental r e s u l t s show the existence of the t r a n s i t i o n layer on the ice surface, conclusions d i f f e r each other on the physical properties of the layer, i t s thickness and t h e temperature range f o r which i t i s stable. Recently, Beaglehole and NasonC13l showed, by the measurements of the e l l i p t i c i t y c o e f f i c i e n t f o r the reflected l i g h t from the ice surface, t h a t the layer thickness depends on the surface orientations. We consider, however, t h a t there were some problems in t h e i r measure- ments; f i r s t they assumed t h a t the r e f r a c t i v e index of the t r a n s i t i o n layer was equal1 t o t h a t of bulk water, and second the i c e surfaces used were prepared dest- ructively. Consequently, we do not know yet whether the t r a n s i t i o n layer on the i c e surface i s "water-like" indeed and how thick i t i s .

On the other hand, several theoretical works about the t r a n s i t i o n layer have been pub1 ished. Fletcher[l4] indicated t h a t the water layer i s energetically favored a t temperatures above - ( 5 2 3)"C and i t s thickness decreases with decreasing temperature. Kuroda and Lacmann[l5] showed t h a t the QCL on the i c e surface i s thermodynamically s t a b l e above a c r i t i c a l temperature and the habit change of snow c r y s t a l s can be explained by the anisotropy of the thickness of QLL.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987168

C1-496 JOURNAL DE PHYSIQUE

The aim of t h i s work i s t o measure d i r e c t l y the physical properties and t h e thickness of the t r a n s i t i o n layer on C0001)- and {10'iOI-faces of i c e s i n g l e c r y s t a l , using an ellipsometry. As a r e s u l t , the temperature dependence and t h e anisotropy of t h e layer thickness a r e c l a r i f i e d and the surface s t r u c t u r e of i c e crystal i s discussed i n connection w i t h the habit change of i c e c r y s t a l s observed j u s t below the melting point.

2. Experimental 2.1 El 1 ipsometry

When the l i n e a r l y polarized l i g h t i s reflected a t t h e surface covered with the t r a n s i t i o n layer l i k e QLL (fig. I ) , i t i s changed t o the e l l i p t i c a l l y polarized l i g h t . Then the complex r e l a t i v e amplitude attenuation p, which i s a r a t i o of amplitude r e f l e c t i v i t i e s ( R and Rs) of p- and s-polarizations, i s given by,

P

p = R / R = tanY exp(iA)

P s (1 1

Where, tanY i s related t o the r e l a t i v e amplitude change and A t o the r e l a t i v e phase change. The value p i s extremely s e n s i t i v e t o the r e f r a c t i v e index nl and the thickness d of t h e layer[l6].

A null ellipsometry was operated f o r t h e He-Ne l a s e r beam (X=633nm) i n a walk-in cold room. To measure p of i c e surface a t maximum s e n s i t i v i t y t o n and d, the angle of incidence (o was s e t t o 52.950". The sample was put in a chamher with two small holes t o admit the l a s e r beam. The inside wall of the sample chamber was covered with a t h i n i c e sheet which works a s a vapor source. Temperatures of sample and vapor source were able t o be controlled separately.

2.2 Sample of i c e surface

The sample of i c e surface used i n t h i s experiment was a s l i c e of a negative crystal ( f i g . 2-a), which i s a hole i n a shape of a sharp hexagonal prism grown a t the end of a hypodermic needle inserted in an i c e s i n g l e c r y s t a l , by continuous evacuation of water vapor through the needle 17,181. The surface prepared in t h i s way has several c h a r a c t e r i s t i c s a s follows; 11) the maximum diameter of surface i s

Fig. 1 Schematic i l l u s t r a t i o n of the reflec- Fig. 2 Negative c r y s t a l s of i c e : t i o n of polarized l i g h t a t the surface ( a ) a negative crystal with a covered with a t r a n s i t i o n layer. hexagonal prism shape (below r e f r a c t i v e indices of the t . r a n s i t i ~ ! i 5 1 % ~ r -2°C); (b) a spherical nega- and i c e , d: thickness of t h e layer. The t i v e crystal with two small p-polarization i s parallel t o t h e plane basal f a c e t s (above -2°C).

of incidence and the s-polarization per- Scale bars indicate 1 nun.

pendicular t o the surface.

3 t o 4 mm, ( 2 ) molecularly f l a t , (3) f r e e from misorientations (exact surface orien- t a t i o n of {00011 and {10TO1), and ( 4 ) f r e e from contaminations. Consequently, these surfaces a r e the best one in the purpose of t h e investigation of crystal surface.

3. Experimental r e s u l t s

A s e r i e s of experiments were carried out a t various conditions. For a l l experiments, the surface temperature T was s e t f i r s t below -lO°C, and increased a t the constant r a t e of O.l0C/min o r l e s s ?

Figure 3 shows the typical change of observed (Y, A) a t t h e condition close t o the equilibrium, which i s plotted in a polar coordinate ( Y , A). The thin s o l i d curves show simulated changes in p f o r thickening a s i n g l e layer of various refrac- t i v e indices. When the t r a n s i t i o n layer does not e x i s t on the surface, (Y, A) i s plotted a t the point S. Since the r e f r a c t i v e index of bulk water i s 1.333 a t O°C, a change in n l appears mainly in I, whereas d appears in A? i f the layer i s water- like. The observed changes of (Y, A) f o r (0001)- and (1010)-faces show t h a t the r e f r a c t i v e index of t h e t r a n s i t i o n layer i s around 1.330, which is quite close t o t h a t of water. I t a l s o means t h a t the properties of the t r a n s i t i o n layer a r e water- l i k e and the s i n g l e layer model i s acceptable f o r the model of i c e surface structure.

Figure 4 shows the change i n A with respect t o Ts f o r both faces.

Under the conclusion t h a t t h e r e f r a c t i v e index of the t r a n s i t i o n layer i s 1.330, the change of A can be read a s the change of t h e layer thickness a s shown in

fig. 4. This r e s u l t s show t h a t the temperature Tw, a t which the QLL appears on the i c e surface, i s -2°C and -4°C f o r {00011- and (10TO1-faces, respectively. Although the temperature dependence of d and the temperature Tw f o r {1010)-faces f a i r l y scattered from sample t o sample, systematic differences in d and Tw between both faces were confirmed by a s e r i e s of experiments.

nrn .o

- basal f0001>-face

---- prism ~ ~ ! ~ ) - f a c e

Fig. 3 Observed changes of p= tany e x p ( i ~ ) in a polar coordinate ( Y , A ) f o r

(0001 )-face (sol id 1 ine) and (10?O}-face (broken 1 ine) with increasing tem-

perature, and simulated changes of p f o r thickening layer ( t h i n s o l i d curves)

with various r e f r a c t i v e indices nl on ice. Crossed marks show the s t a r t i n g

points of experiments.

JOURNAL D E PHYSIQUE

Ts: TEMPERATURE ("C)

0 -5 ^{-10 -15}

d A l n t n B

-basal ( 0 0 0 ll-face

--- prism (10TOl-face

Fig. 4 Temeprature dependence of A and t h e t h i c k n e s s change o f t h e t r a n s i t i o n l a y e r under t h e conclusion o f nl=1.330.

4. Discussion

Kuroda and Lacmann[l5] t h e o r e t i c a l l y discussed t h e temperature dependence and a n i s o t r o p y o f t h e t h i c k n e s s o f QLL as f o l l o w s .

The existence o f QLL on t h e i c e surface i s disadvantageous due t o t h e b u l k f r e e energy o f t h e l i q u i d phase. However, i t lowers t h e surface f r e e energy o f t h e system, so t h a t i t i s t o be p o s s i b l e t h a t t h e QLL s t a b l y e x i s t s on t h e surface.

For i c e surface covered w i t h QLL, t h e y i n d i ~ a t e d t h a t t h e w e t t a b i l i t y parameter Aam becomes p l u s value. That i s ,

where oI, ow and aOI,W a r e t h e s u r f a c e f r e e energies p e r u n i t area ( s u r f a c e t e n s i o n ) f o r t h e - i n t e r f a c e of vapor/ice, vapor/water and ice/water, r e s p e c t i v e l y . Consequ- e n t l y , t h e e q u i l i b r i u m thickness o f QLL de i s determined by t h e balance between t h e disadvantage o f t h e b u l k f r e e energy a4d t h e f a l l o f t h e surface f r e e energy.

where n and A a r e parameters connected t o t h e i n t e r a c t i o n between water molecules, Vm t h e molecular volume, Tm t h e m e l t i n g temperature o f i c e , AT t h e supercooling and Qm t h e l a t e n t heat o f f u s i o n per molecule.

From the equation (2) and (3), deq increases w i t h i n c r e a s i n g Aa .

As t h e s u r f a c e energy p e r u n i t area i s p r o p o r t i o n a l t o t h e number d e n s i t y o? broken hydrogen bonds along t h e surface (broken bond model ), oI(OOO1 ) < a I (1010).

Consequently, t h e f o l l o w i n g r e l a t i o n i s expected,

In the present experiment, i t i s c l a r i f i e d t h a t Tw(OOO1) > ~ ~ ! 1 0 i 0 ) and the thickness increases with increasing temperature. These r e s u l t s q u a l i t a t i v e l y coincide with the theoretical explanation by Kuroda and Lacmann[15].

The temperatures when the QLL appears on the i c e surface a r e higher than those temperatures which have been obtained by other experiments. This reason i s considered t h a t the surfaces used in the present experiment were molecularly f l a t and f r e e from misorientations and contaminations, compared with t h e rough and high index surfaces used in other experiments, Because a I f o r the rough and high index surface i s higher than a (0001) or a ( l o l o ) , surfaces l i k e t h i s a r e more wettable than 100011- and ( 1 0 i 0 ) - ~ f a c e s (namefy, Tw(OOO1) > Tw(lO1O) > Tw(high index)).

On the other hand, i t has been c l a r i f i e d t h a t the conspicuous habit change of i c e crystal occurs a t the temperature of -2°C ( f i g . 5 ) . Kohata e t a l . [I81 showed t h a t the shape of negative crystal (evaporation form) changes t o the sphere which i s truncated with only small {0001)-facets above -2°C-(fig. 2-b), compared with the hexagonal prism surrounded by both (0001)- and (1010)-facets below -2°C

( f i g 2-a). Yamashita and Asano[19] showed t h a t the shape of snow crystal (growth form) also changes from the hexagonal p l a t e t o the c i r c u l a r disk above -2°C. These observational r e s u l t s mean t h a t the anisotropy of growth o r evaporation r a t e s with respect t o a l l surfaces with crystallographic orientations excepting (00011 dis- appears a t temperatures above -2°C. The disappearance of anisotropy l i k e t h i s may occur when the differences of surface s t r u c t u r e s are vanished by the occurence of surface roughening.

The present experimental r e s u l t s showed t h a t the (10i0)-face i s covered with QLL a t temperatures above -4 "C. Consequently, we should consider t h a t the interfgce structure between QLL and i c e changes from smooth t o rough above -2°C f o r t h e (1010) -face, though t h e i n t e r f a c e on (0001)-face i s kept smooth a t whole temperature range (0 t o -2°C). That i s , the surface roughening occurs f o r the i n t e r f a c e on the (1010)-face a t t h i s temperature.

m.

P. TEMPERATURE ("C)

0 -1 -2 -3 -4 - 5

I i ^I

Spherical negative : Hexagonal prismof with basal I negative crystal

0 F

^I

ICE CRYSTAL

SURFACE STRUCTURE 0 F ICE CRYSTAL

Circular-disk I I Hexagonal plate of snow Crystal 1 snow crystal

I I

? ^I _I

I

I

;3gzjI I ^{1 I} rn ^{I C E}

Tr T w ( O 0 0 ~ 1

-.-.-

I I " '

I ICE

T.

oio)

Type I : smooth interface. Type I 1 : rough interface

Fig. 5 Schematic diagram t o show the r e l a t i o n between the microscopic surface

s t r u c t u r e and the i c e crystal morphology. Tr i s the temperature a t which the

surface roughening t r a n s i t i o n occurs.

(21-500 JOURNAL DE PHYSIQUE

5. Conclusions

The conclusions obtained in t h i s study a r e summarized a s follows:

1 ) The r e f r a c t i v e index of t h e t r a n s i t i o n l a y e r i s 1.330 f o r (0001)- and (10T0)- faces, which means t h e properties of t h e t r a n s i t i o n l a y e r a r e very c l o s e t o those of bulk water(nw=l .333) ; t h a t i s t o say, t h e t r a n s i t i o n l a y e r i s QLL.

2) Tw(OOO1) = -2°C and T,(IOTO) = -2%-4°C. The thickness of t h e t r a n s i t i o n l a y e r increases with increasing temperature and deq(OOO1) < deq(lO1O) a t temperatures above -4°C.

3 ) These experimental r e s u l t s a r e q u a l i t a t i v e l y explained by t h e theory of Kuroda and Lacmann[l 51.

4 ) The h a b i t change observed f o r t h e negative c r y s t a l and t h e snow c r y s t a l i n d i c a t e s t h a t t h e surface roughening occurs a t t h e i n t e r f a c e between QLL and i c e c r y s t a l on t h e (10i0)-face a t the temperature of -2°C.

6. Acknowledgements

The authors a r e indebted t o Professor Oguro of Hokkaido Kyoiku University f o r h i s kind o f f e r of an i c e s i n g l e c r y s t a l which was used in p a r t of experiment.

This work was supported by t h e S c i e n t i f i c Grant of Japanese Education Ministry.

7. References

U. Nakaya and A. Matsumoto, J. Colloid Sci. 9 1954)41-49. 4

H. H. G. J e l l i n e k , J . Colloid Sci. 14(1959)26 -280;J. Colloid I n t e r f a c e Sci. _{- ,} 25(1967)206-217.

[3] W. D. Kingery, J . Apll. Phys. 31 (1960)833-838.

[4] A. W. Adamson, L. W. Dormant and M. Orem, J . Colloid I n t e r f a c e Sci. 25(1967)206-

9 7 7 L I I .

[5] I. Watanabe and T. Okita, Bull. Inst. Pub. Health 25(1976)67-72.

[6] B. Lagourette, C. Boned and R. Royer, J . Physique 37(1976)955-964.

[7] C. Jaccard, in: Physics of Snow and Ice, Vol. 1 (Hokkaido Univ., Sapporo 1967) 173-179.

[8] N. Maeno and H, Nishimura, J. Glaciology 21(1978)193-205.

[9] V . I. Kvlvidze, U. F. Kiselev, A. B. Karaev and L. A. Ushakova, Surf. Sci.

44(1974)60-68.

[lo] E. Mazzega, V. del Penino, A. Loria and S. Mantovani, J . Chem. Phys. 64(1976) 1028-1 031.

[11] D. Nason and N. H. Fletcher, J . Chem. Phys. 64(1975)4444-4449.

[12] I . Golecki and C. Jaccard, Phys. Lett. 63A(1977)374-376.

[I31 D. Beaglehole and D. Nason, Surf. Sci. 96(1980)357-363.

14 N . H. Fletcher, Phil. Mag. 7(1962)255-269; 18(1968)1287-1300.

15 T. Kuroda and R. Lacmann, J . Crystal Growth 56(1982)189-205.

1 1

[16] M. Yamamoto, Y. Furukawa and T. Kuroda, in preparation.

1171 C. A. Knight and N. C. Knight, Science 150(1965)1819-1821.

1181 S. Kohata, Y. Furukawa and T. Kobayashi, i n preparation.

[I91 A. Yamashita and A. Asano, J. Meteor. Soc. Japan 62(1984)140-145.

COMMENTS V . F . PETRENKO

When you c a l c u l a t e t h e t h i c k n e s s o f a l i q u i d l a y e r you imply t h a t i t i s a homogeneous one. But i f it is n o t , does t h i s change your r e s u l t s ?

Answer :

We can a l s o o b t a i n t h e s i m u l a t e d diagram o f (q.6) f o r t h e inhomogeneous o r

m u l t i l a y e r s model. But t h e i r diagrams c o m p l e t e l y d i f f e r from t h a t f o r t h e

homogeneous s i n g l e l a y e r model. Experimental d a t a o b t a i n e d i n t h i s experiment show

t h e b e s t f i t t i n g t o t h e d i a g r a m f o r t h e h o m o g e n e o u s s i n g l e l a y e r m o d e l .

Consequently, we s h o u l d c o n s i d e r t h a t t h e QLL i s t h e homogeneous s i n g l e l a y e r .