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Electrical measurements on ice thin films near the cubic → hexagonal phase transformation
Thin Solid Films, 112 (1984) 17-28
17
ELECTRONICS AND OPTICS
ELECTRICAL MEASUREMENTS ON ICE THIN FILMS NEAR THE CUBIC ~ HEXAGONAL PHASE TRANSFORMATION JANUSZ CHRZANOWSKI AND BOGDAN SUJAK
Institute of Experimental Physics, University of Wroctaw, ul. Cybulskiego 36, 50-205 Wroclaw (Poland) (Received March 31, 1983; accepted November 9, 1983)
A correlation between the known phase transition in ice, from the cubic to the hexagonal modification, and the temperature range in which the activation energy for d.c. electrical conduction changes its value is shown. This change in the activation energy is discussed in relation to molecular rotation in ice. The results presented reveal a possible influence of orientational Bjerrum defects on the d.c. electric conduction in ice at low temperatures. It is also suggested that the temperature range in which the recrystallization process takes place in an ice layer depends on the thickness of the deposited layer.
1. INTRODUCTION Ice in various modifications is still studied for its special properties which appear under various conditions. The appearance of allotropic forms of molecular crystals is also of great importance from the point of view of studies on the natural electret effect in polar molecule condensates. As has been shown t, phase transformations in cryocondensed thin films of polar molecules may, at least in some cases, significantly affect the observed surface charges. Also, there are most probably close relations between the generation of surface charges on the free surface of the condensate layer and such phase transformations as the a--,13 phase change in solidified films of methanol 2. Therefore, information concerning phase transformations in polar molecule cryocondensates is also of importance in understanding the nature of the electret effect observed in water vapour condensates. As is known a-7, ice layers prepared in various temperature ranges may exist in different modifications. Below about 120K ice layers obtained by vacuum deposition onto a cold substrate are mainly amorphous, At higher temperatures two crystalline forms have been observed: a cubic phase (Ic, sphalerite structure) and a hexagonal phase (Ih, wurtzite structure). The temperature ranges in which these phases can exist were found to be rather wide but the temperatures of the phase changes are not strictly fixed6. The cubic ~ hexagonal transformation in ice has a relatively higher rate than that for the conversion from the amorphous to the crystalline (cubic) modification and usually occurs rapidly above 193 K. If the temperature of a sample of cubic ice is 0040-6090/84/$3.00
© Elsevier Sequoia/Printed in The Netherlands
18
J. CHRZANOWSKI, B. SUJAK
raised at the rate of a few kelvins per minute the conversion takes place near 203 K. The transformation to the hexagonal phase begins spontaneously and the crystallites grow rapidly, attaining a few micrometres in diameter 6. Although hexagonal ice is the only energetically stable modification of ice, several of its physical parameters (e.g. the dielectric permittivity) alter their values significantly when it is heated or cooled. It is thought that these changes correspond to the rotational movement of some water molecules or the displacement of some protons in relation to neighbouring atoms. The fact that the dielectric permittivity and the electrical conductivity of hexagonal ice are of the same order of magnitude as those of water (at the same temperatures) indicates that the molecules in an ice crystal have a definite degree of freedom. In hexagonal ice crystals cooled below about 200 K some degree of disorder remains frozen. Such a crystal does not attain a completely ordered structure even at 0 K and has an excess entropy S(0 K) = R in(2~) where R is the gas constant. The low value of the melting entropy of ice (S = 5.3 cal mol - i K - 1) supports the hypothesis that well below the melting point a number of hydrogen bonds are broken. A rapid acceleration in this process takes place close to the cubic ~ hexagonal phase change and is usually observed at about 200 K. In crystals constructed of polar molecules the molecules are oriented at low temperatures along certain distinct crystallographic directions. Heating of the crystal to a specific temperature TO leads to a rapid increase in the dielectric permittivity. The long-range order vanishes and for T > TO the behaviour of the molecular crystal is very similar to that of the polar liquid. This effect (so-called rotation melting) is often observed in a number of molecular crystals, e.g. CH4, C H 3 O H and H2S 8,9. Such a phase transition is often identified with the k-type second-order phase change a. However, there are some divergences in such an approach to the "refreezing" of molecular rotation in solids t°. The process of rotation melting in substances with hydrogen bonds is often related to the transition from the ferroelectric to the paraelectric phase as has been observed, for example, in HCI crystals at 98 K 11. A ferroelectric response for ice was first reported at 100 K ~z and later near 200 K ~3. Nevertheless, this problem is still not resolved ~4. As can be concluded on the basis of the temperature dependence of the dielectric permittivity of ice at low frequencies 9, the breaking of hydrogen bonds in hexagonal ice during heating of the crystal is a continuous process and shows a local maximum rate near 240 K. At the same temperature an intense sublimation of ice is usually observed. Hence, the appearance of molecular rotation in ice (at 200 K) should be considered in terms of a hindered rotation for which the height of the potential barrier depends on the temperature. Our recent observations concerning thermally stimulated currents in condensates of polar molecules suggest that the temperature at which the recrystallization process takes place, during the transformation from the cubic to the hexagonal modification in ice layers, depends not only on such factors as the heating rate but also on the thickness of the deposited film. In this paper the results of d.c. measurements on ice thin films near the cubic hexagonal phase change are reported. They show that the temperature of this phase change depends on the thickness of the deposited ice layer. Also, they suggest an important role for orientational Bjerrum defects in the mechanism of d.c. electrical conduction in ice at low temperatures.
ELECTRICAL MEASUREMENTS ON ICE FILMS
2.
19
EXPERIMENTAL DETAILS
As is known (see for example ref. 15), measurement of the d.c. electrical conductivity (or current) is a very convenient method of studying polymorphic phase transformations. It is always assumed (see for example ref. 16) that the temperature at which the particular recrystallization occurs is indicated by the change in the thermal activation energy EA for d.c. electric conduction. In our experiment a d.c. electric current through the measurement cell covered with the ice condensate under investigation was measured with a vibrating reed electrometer in the temperature range 180-240 K. The measurement cell contained double comb-shaped silver electrodes deposited onto a high resistance substrate. The preparation of the measurement cell used in our experiment has been described in detail elsewhere 2. Descriptions of such a cell are also available in older papers dealing with the electrical conductivity of thin films of organic solids 17,1a. The ice films were deposited from the gas phase by condensation onto the surface of a deeply cooled measurement cell in a vacuum of the order of 10- 4 Pa. The measurement cell was attached to a cryofinger of a continuous flow cryostat in such a way that the water vapour could be condensed onto the measurement cell surface only. Thus the thickness of the ice layer could be calculated from the total mass of the condensed substance. In separate measurements variations in the capacitance of a comb-shaped capacitor confirmed the linear increase in thickness of the deposited layer with increasing time of condensation. The layers studied were usually 1-10 ttm thick but in some cases 30 ttm layers were also examined. Doubly distilled and demineralized water was used as the source of the gaseous phase to be condensed onto the measurement cell. In all parts of the experiment the layers studied were deposited at 80 K (amorphous form) and heated at a constant rate of 3 K m i n - 1. This heating rate allowed us to compare some of our observations with recently published results on thermally stimulated depolarization currents in ice 14'19. Such a heating rate is also typical for other experiments on ice, e.g. in structural investigations 6. In the temperature range of 180-240 K that we used the thickness of the examined layers was almost constant if we ignore the decrease of a few per cent caused by the slow process of ice sublimation. 3.
RI~SULTS AND DISCUSSION
Typical plots of the logarithm of the measured current density J versus the reciprocal temperature 1/T are presented in Fig. 1. To show all the typical dependences of log J versus 1/T observed for ice layers of various thicknesses the units on the vertical axis have been omitted. The measured thermally dependent current through the measurement cell covered with the ice film depends linearly on the thickness of the deposited layer (Fig. 2) in the examined thickness range of 1-30 ttrn. Such a dependence l(d) was always observed for the layers studied provided that the temperature of the cell covered with ice did not exceed about 245 K. Above this temperature the surface conductivity rises rapidly leading to a marked increase in the current density irrespective of the thickness of the ice layer. Below 240 K the conductivity of bulk ice
20
J. CHRZANOWSKI, B, SUJAK
~o ~4o
230
220
210
200
>~10 ,am \.
6-8pro
190 T [.K] --
[g]
A
i
i
¢ &E=E~ EA '~ O6eV
!
~
\
Lg.~
[A]
10~/'T
~055ev ~032eV
\ \\\" 1 - 21 pm
~.o
~.2
~
/.6
~s
s'o --si2
si~
Fig. 1. TypicallogJvs. 1/T dependences observed for theicecondensatesofvariousthicknesseslapplied voltage, 150 V): - -, extension of the main segments of the observed dependences.
z[~]i
i
d [~m] Fig. 2. Current through deposited ice layers of various thicknesses (T = 235 K).
21
ELECTRICAL MEASUREMENTS ON ICE FILMS
was usually observed. This is in good agreement with the results of d.c. electrical conductivity studies on ice crystals reported by Maidique et al. 2° The silver electrodes used ensured good ohmic contacts and allowed a linear relation between the measured current and the applied voltage to be obtained (Fig. 3). Deviations from the ohmic regime were usually observed only when the surface conductivity was the result of an increase in the pressure above the free surface of the layer and always when the applied voltage exceeded 250 V (electric field, about 5000 V cm- 1).
×I[A~ 10-10I
/ A A
×10-8
I
Aj
/
4
/ 3
/ ~ Z _ ~
/
100
!3
°/
200
300
400
500
U IV]
Fig. 3. Current-voltagecharacteristics for ice layers of various thicknesses and at various temperatures: Q , d = l~tm, T = 2 0 5 K ; A , d = 10Bm, T = 2 0 5 K ; O , d = I~m,T=235K.
Recooling of an ice layer warmed above the range 200-220 K led to the condensation (resublimation) of a very thin film of water molecules onto the ice layer examined, with a consequent marked change in the surface conductivity which significantly affected the measured current. To remove this interfering effect rather intense pumping was applied. However, this resulted in large changes in the ice layer thickness and substantially influenced the measured current densities, especially for the thinner layers studied. Also, the pumping procedure led to an uncontrolled decrease in the temperature of the condensate layer. Hence, the presented log J versus l I T curves concern only current measurements recorded during heating of the layers examined which were maintained in dynamic equilibrium with their saturated vapour. We consider that the range of temperatures employed, which was below that causing intense sublimation of ice, and the relatively high electric field applied (about 3000 V cm- 1) made our results free of the restrictions listed in ref. 20. If it is assumed that a change in the activation energy for electrical conduction takes place at the phase transition, the temperature at which this transition occurs may be estimated. The observed dependence of log J on l I T may be approximated by two linear segments with different slopes. Hence, the current density through the measurement cell covered with the ice condensate layer may be described by an exponential function: J Qcexp(-EA/kBT) where J is the measured current density, E^ is the thermal activation energy for d.c. electrical conduction, kB is Boltzmann's constant and T is the absolute temperature.
22
J. CHRZANOWSKI, B. SUJAK
It was also observed for the thicker layers studied (5-10 ~tm) that within the temperature range 193-205 K a third activation energy EA" could appear. Its value of about 0.6 eV is very close to the mean arithmetic value EA"' = ½(EAc+ EAh) where EAc and EAh are the thermal activation energies for the cubic and the hexagonal modifications respectively. It is reasonable to assume that this third activation energy, appearing in the vicinity of 200 K, is an activation energy for the cubic and hexagonal mixture present in such layers. Further, more detailed considerations on the nature of the process corresponding to EA", presented in the next pages, do not exclude such a possibility. We should like to point out that irrespective of the ice layer thickness the difference AE between the activation energy for the hexagonal form (EAh) and that for the cubic form (EA c) is constant. The value of AE = EA h - EA c is about 0.6 eV (Fig. 1). Careful analysis of the observed log J versus 1/T curves shows that both the activation energies EA h and EA c decrease, attaining 0.84 eV and 0.23 eV for the hexagonal and the cubic modifications respectively, when the thickness of the deposited ice layer increases from 1 to about 30 ~tm (Fig. 4). Extrapolation of the
12o I EA
[~v] i x \e
too
o~. 09o
08o I I
07o I
060
~E~O.6eV
05o i
o~o I
O3O 020
d [~]
Fig. 4. Activation energies EAc and EAh for d.c. conduction plotted against the thickness of the deposited ice layer: O, 0, mean values of the observed activation energies for ice layers of various thicknesses in the cubic and the hexagonal modifications respectively.
ELECTRICAL MEASUREMENTS ON ICE FILMS
23
thickness dependences EA(d) presented in Fig. 4 to zero thickness of the condensate layer gives for both activation energies determined EAc - 0 . 5 8 e V and EAh = 1.15 eV. The mean error in the evaluation of the activation energies is about _ 0.05 eV. The liberation of additional degrees of freedom which is observed in ice crystals near 200 K coincides with a considerable change in the thermal activation energy for d.c. conduction. Measurements of the a.c. electrical conductivity in polycrystalline ice samples also show significant variations in this conductivity close to the temperatures at which the known phase transformations in ice take place 21. The a.c. conductivity of fine-grained polycrystalline ice at 104 Hz very often shows a rapid variation close to 240 K. In some cases even a high "step" in this conductivity was observed at about 240 K while the peak of the conductivity was reported to occur at 193 K 21. Each H 2 0 molecule in the ice lattice is held by four hydrogen bonds. For a reorientation of the H 2 0 molecule three of the hydrogen bonds have to be broken while the oxygen position is maintained. This requires about 0,6eV per H 2 0 molecule22.23. The occurrence in solids with hydrogen bonds of molecular rotation at temperatures close to that at which a change occurs in the activation energy for electrical conduction suggests a protonic mechanism for the conduction. This electrical conduction has been ascribed to an increase in the probability of proton transfer as a consequence of the rotation of the molecular fragments. This rotation effect has been considered in terms of protonic hopping between two stable intermolecular sites, i,e. the double-well approach (see for example ref. 24). Therefore the change in activation energy of about 0.6 eV, as observed in our experiment, takes place at temperatures very close to that for the cubic --* hexagonal phase change. One of the possible explanations for the observed changes in EAc and EAh when the thickness of the deposited ice layers are altered may be as follows. There are two significant mechanisms of d.c. electrical conduction in the ice modifications that we studied. These are a consequence of the existence and migration of the two types of defects: ionic (H30 ÷ and O H - ) and orientational (Bjerrum L and D defects) 24. The latter defects are produced by a rotary motion of a proton from one position between two oxygen atoms ( O H . . ' O ) to another interoxygen position, producing a doubly occupied bond (D defect) and a vacant bond (L defect)22'24. It is usually assumed that the d.c. electrical conduction in hexagonal ice occurs mainly by the ionic mechanism in which the protons jump between two alternative sites in an O . " O bond. However, there are some suggestions 2s that the mechanism of the d.c. electrical conduction in ice at low temperatures may be other than ionic and may be governed by the Bjerrum orientational defects. Let us again consider Fig. 4. The extreme values of the activation energies EA° and EAh which are evaluated from this figure are characteristic of a number of processes that take place in ice. Thus the energy E^ ~ = 0.23 eV is very close to that for the migration of the orientational Bjerrum defects; EA~ = 0.58 eV is close to the activation energy for the motion of H + (H30 +) ions in ice; EAh = 1.15 eV is typical of the energy for the creation of a pair of ions (H 30 ÷ + OH-)22' 24. As mentioned earlier, the restrictions described in ref. 20 concerning studies of the d.c. electrical conductivity in ice are probably invalid for our experiments.
24
J. CHRZANOWSKI, B. SUJAK
Hence, it can be assumed that the energy EA c = 0.23 eV observed for thick cubic ice layers is the activation energy for the migration of orientational Bjerrum defects. For the thinner films examined the activation energy for d.c. electrical conduction rises. Since the low temperature electrical conductivity is as a rule very sensitive to structure, this increase in EA c may be a result of the structural disorder which develops when the deposited layer is very thin. However, the extrapolated EA c value of 0.58 eV for very thin films (less than 1 tam) does not seem to be accidental and suggests that another mechanism of charge transport may dominate in this thickness range. The smooth transition in EA c from 0.23 to 0.58 eV supports the supposition that there is a real and continuous change in the charge transport mechanism. Therefore, depending on the deposited layer thickness, one of the mechanisms, ionic or Bjerrum defect migration, may make the dominant contribution to the observed activation energy in cubic ice films. The change in the d.c. conduction mechanism in thin ice films indicates a significant decrease in the rate of the diffusion processes in which Bjerrum defects play an important role. As mentioned earlier, in some cases during warming of the ice layer a third activation energy EA"' c a n appear (Fig. 1). EA'" also depends slightly on the thickness of the ice layer examined. The difference AE = EA"' - EA c of 0.32 eV is close to onehalf of the energy required for the creation of a pair of Bjerrum defects: E o = 0.68 eV 24. Thus, the third activation energy E A " of 0.55 eV observed in some cases corresponds to the creation and migration of Bjerrum defects with an activation energy E A " = 1E O-q-E~, of 0.55 eV, where E~ = 0.23 eV is the activation energy for Bjerrum L defect migration. This EA'" value is close to the theoretically predicted value of 0.575 eV 24. At the temperature of the cubic--, hexagonal phase change the activation energy rises by about 0.6 eV. This leads to an activation energy EAh in the hexagonal modification of 1.15 eV for very thin films and of 0.84 eV for thick films. Considering these changes in the activation energy in terms of defect creation and migration, it can be inferred that the "jump" of about 0.6 eV at the phase transition is caused by a process in which ionic defects are produced within the condensate layer. The activation energy for d.c. conduction in very thin ice films of hexagonal structure would therefore be EA h -----½Eoi°n+Em i°n where Eo i°n is the energy needed for the creation of a pair of ionic defects and Emi°n is the energy for the migration of the defect of greater mobility (H sO +). It can be expected that for the thicker ice layers deposited the structure of the condensate becomes more ordered (weakly imperfected) and the diffusion of Bjerrum defects may be greater than that in very thin films. Since above the phase change thermal excitations are energetically sufficient for the creation and migration of both types of defect, the activation energy for d.c. electric conduction will be determined by contributions from both these processes, i.e. the creation and migration of both ionic and orientational defects. Hence, if both types of the defect make similar contributions to the charge transport in thick ice layers (about 30 tam) just above the phase change, the activation energy should be given by /~ = l172.t~,2L, S i l oiOn + EmiOn) + (½Eo + Era)} ~ 0.86 eV
This value agrees quite closely with the experimentally determined value of about 0.84 eV (Fig. 4).
25
ELECTRICAL MEASUREMENTS ON ICE FILMS
As seen in Fig. 1, some of the observed log J versus 1/T curves seem to consist of a number of segments of various slopes. This was observed mainly for the layers 4-8 lain in thickness. It can be assumed that this is due to the very complicated processes of nucleation in a layer whose thickness is equal to the mean size of the microcrystallite grains present in ice films in the temperature range employed6. The especially wide dispersion in the experimental points (Fig. 5) for the layers 4-8 I~min thickness suggests that the relation between the thickness of the deposited layer and the mean diameter of the microcrystallites in the layer is an important factor. This seems to support our supposition that structural disorder has a marked influence on the mechanism of d.c. conduction in the layers studied. For layers thinner than about 5 ttm, only the two activation energies EA¢ and EAh were found. The appearance of a temperature transition region in which the cubic and hexagonal modifications can coexist with a corresponding activation energy of about 0.6 eV seems only to be possible when the thickness of the layer exceeds the mean size of the microcrystalline grains. The sharp transition above 200 K in the thinner layers studied may be considered as a rapid relaxation of the "superheated" cubic layer to the hexagonal modification. In many experimental runs, however, the observed dependence of log J on l I T consisted of two segments for all thicknesses of the layers studied (1-30 ~tm). For thicker layers the temperature range in which the change in slope of the log J versus 1/T curve was observed showed a tendency to shift towards lower temperatures, indicating a reduction in the superheating effect. This is presented in Fig. 5. Experimental points in this figure indicate the temperatures at which the change in the activation energy EA was observed. The points of intersection of the extended main linear segments for the log J versus l I T curves that comprise many segments are also included. These points of intersection exhibit the same tendency to temperature shifting as do the data for thicker films mentioned above. As seen in Fig. 5 the temperature at which the change in E A occurs is shifted from 225 K for thin films (1 ~tm) to about 200 K for thick layers (30 ~tm). An extrapolation to zero film thickness gives a temperature of about 235 K, which is T [K]
230
L• 220
210
|
•
:
"
•
•
:
"
~1OsJm
200
d [;Jm]
Fig. 5. Temperature at which the activation energy for d.c. conduction changes its magnitude as a function of the thickness of the deposited ice layer: _~g~, temperature ranges in which the cubic --* hexagonal transformation was usually observed in ice specimens of various thicknesses.
26
J. CHRZANOWSKI, B. SUJAK
close to the temperature range in which a considerable increase in hydrogen bond breaking in ice probably occurs. In contrast, for thick layers the temperature of the activation energy change is shifted towards the range in which the cubic -~ hexagonal transformation is usually observed in bulk ice, i.e. 190-200 K, and where various electric and mechanical phenomena are often observed. It is worth remarking that von Hippel et al. 26 found for a polycrystalline rapidly grown ice sample relaxation spectra which showed a local maximum near 235 K, in contrast with the behaviour of pure ice crystals. Also, the time constants for the various relaxation processes increased by a factor of about 10. This was probably due to the presence of a number of dislocations in the polycrystalline ice samples examined 26. If the assumption made above that the structural disorder in ice thin films formed by vacuum deposition is responsible for the change in the d.c. electric conduction mechanism, by blocking the diffusion processes in ice films, is correct, then an influence of the structural disorder should also be seen in the rate of conversion of cubic ice to the hexagonal form and should result in a shifting in the phase change temperature to the higher temperature region. We consider that exactly this effect is presented in Fig. 5. Above a temperature of about 235 K cubic ice cannot exist under the conditions employed in our experiment. The connection between structural disorder in ice films and the cubic --, hexagonal phase change seems to be more important than it did initially. As seen in Fig. 5 the greatest superheating effect appears for the thinnest films examined, which most probably show considerable structural imperfection. In particular, a number of dislocations and point defects are probably created. A high concentration of dislocations which can induce an increase in internal friction in such fine-grained polycrystalline films seems to be rather obvious at least, because of the known mechanism of growth of the crystals through the development of screw dislocations. The concentration of dislocations probably decreases as the thickness of the deposited film increases, similar to the behaviour observed in thin films of other substances 27. The large number of dislocations in thin ice films and the strong interaction between the dislocations and Bjerrum defects can lead to significant lowering of the rates of diffusion processes at low temperatures. It is known that the movement of a dislocation requires a large number of Bjerrum defects to reorient the bonds 28. Therefore, most of these point defects may interact with the dislocations which are attracted to their cores. Such a process, leading to "immobilization" of a large number of Bjerrum defects, would involve a relative increase in the importance of ionic defects and would result in a weak ionic current in cubic ice films with an activation energy for d.c. electrical conduction of 0.6 eV because of the dominance of the ionic charge transport process. If these considerations are correct, then the conversion process of cubic ice to the hexagonal modification may be closely related to the existence and motion of dislocations, as suggested in some papers 29. It can be expected that the cubic ~ hexagonal conversion process in ice may be induced by appropriate reactions between certain types of dislocations in cubic ice or by dissociation of the dislocations. Such reactions which obey the rules of Frank 3° and lead to a reduction in the free energy of the cubic ice layer would stimulate the conversion process. The stacking faults created by reaction between the dislocations (or dissociation of the dislocations) in ice of the sphalerite structure
ELECTRICAL MEASUREMENTS ON ICE FILMS
27
would form elements of the wurtzite structure (h.c.p.) basal plane (0001), as occurs in several phase transformations for other substances 31. The stacking faults created would be incipient crystals of the new hexagonal phase. The close geometrical similarity of the two structures, which include some planes with identically packed atoms ((111) and (0001)), would be an important factor facilitating the transition under consideration. Since the phase change should proceed at the diffusion rate, the rate of conversion should obey an exponential dependence of the type exp(-Ec/kBT) where Eo is the energy required for the conversion. The drift velocity of dislocations in bulk ice is rather low on account of the strong Peierls forces in ice, among other factors 32. At 223 K this drift velocity is estimated2s to be of about 50 .~ s- 1 and it is probable that this value falls with decreasing temperature in cubic ice also. Since the drift velocity of a dislocation also depends on the structural disorder in the substance 3° the movement of a dislocation in cubic ice films may also be significantly affected by a considerable structural imperfection and by interaction with other dislocations. This would lead to a slowing down of the motion of the dislocation and consequently to a reduction in the rate of conversion from the cubic to the hexagonal modification. Thus, the decrease in velocity of the dislocations would give rise to the possibility of the existence of the superheated cubic phase above 200 K up to a temperature at which thermal excitations would unblock the diffusion processes. 4. CONCLUDING REMARKS
In this paper we presented our experimental results of studies on direct electrical currents in thin films of polycrystalline ice which were undertaken in the vicinity of the phase transition from the cubic to the hexagonal modification. Our results suggest that near this phase change both types of points defects, ionic and orientational, can participate in the d.c. electrical conduction in thin ice films. Also, the structural disorder in the thin ice films examined seems to be of importance to the d.c. conductivity. The relation between the charge transport processes in the ice films studied and the diffusion rates for these processes seems to be responsible for the change in the conduction mechanism in the vicinity of the phase transformation. The existence and physical properties of dislocations in ice also seem to have a considerable influence on the electrical properties of ice. Perhaps it is worth mentioning that, to explain the results of our recent optical investigations on spontaneously electrically polarized ice thin films at about 90 K 33, we had to make an assumption that the elementary dipoles in the films examined, which interacted with a light wave, are aligned along the screw lines surrounding the normal direction to the condensate surface (the direction of the spontaneous polarization vector P). Our observations concerning the shift in the phase change temperature towards the range above 200 K seem to have a few indirect confirmations. For example, Cubiotti and Geracitano 13 have shown that the suggested Curie point of ice shifts to lower temperatures when the thickness of vapour-deposited ice layers is increased. Also Dowell and Rifert6 found from X-ray studies that the intensity of the recrystallization processes in ice layers depends on the thickness of the deposited layer.
28
J. CHRZANOWSKI, B. SUJAK
ACKNOWLEDGMENTS
The authors are grateful to Dr. Malcolm Mellow from the Cold Regions Research and Engineering Laboratory, Hanover, NH, U.S.A., for his constructive criticism and many helpful suggestions. This work was supported by the Polish Academy of Sciences within the Main Scientific Project 05.13. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
J. Chrzanowski and B. Sujak, Acta Phys. Pol. A, 64 (1983) 107. J. Chrzanowski and B. Sujak, Thin Solid Films, 101 (1983) 123. J.A. Pryde and G. O. Jones, Nature (London), 170 (1952) 685. M. Blackman and N. D. Lisgarten, Proc. R. Soc. London, Ser. A, 239 (1957) 93. F.V. Schalcross and G. B. Carpenter, J. Chem. Phys., 26 (1957) 782. L.G. DowellandA. P. Rifert, Nature(London),188(1960)l144. C.G. Venkatesch, St. Rice and J. B. Bates, J. Chem. Phys., 63 (1975) 1065. K. Pigofi and Z. Ruziewicz, Physical Chemistry, Polish Scientific Publishers, Warsaw, 1980 (in Polish). Ch. Kittel, Introduction to Solid State Physics, Wiley, New York, 3rd edn., 1966. L. Landau and E. M. Lifshitz, Statistical Physics, Nauka, Moscow, 1964. S. Hoshino, K. Shimaoka and N. Niimura, Phys. Rev. Lett., 19 (1967) 1286. B. Dengel, U. Eckner, H. Plitz and N. Riehl, Phys. Lett., 9 (1964) 291. G. Cubiotti and R. Geracitano, Ph3s. Lett. A, 24 (1967) 179. G.P. Johari and S. J. Jones, J. Chem. Phys., 62 (1975) 4213. W. Wendlandt, Thermal Methods of Analysis, Wiley, New York, 1974. M. Kryszewski, Polvmolecular Semiconductors, Polish Scientific Publishers, Warsaw, 1968 (in Polish). G. Tolin, D. R. Kearns and M. Cavin, J. Chem. Phys., 32 (1960) 1013. F. Gutman and L. E. Lyons, Organic Semiconductors, Wiley, New York, 1967. P. Pissis, G. Boudouris, J. G. Carson and J. L. Leveque, Z. Natur]brsch.. 36a ( 1981 ) 321. M . A . Maidique, A. von Hippel and B. Westphal, J. Chem. Phys., 54 (1970) 150, M. Mellor, CRRLab Res. Rep. 292, 1970, and references cited therein (Cold Regions Research Laboratory, Hanover, NH, U.S.A.). A. Bielafiski, K. Gumifiski, B. Kamiefiski, K. Pigofi and L. Sobczyk (eds.), Physical Chemisto', Polish Scientific Publishers, Warsaw, 1980 (in Polish). L. Sobczyk (ed.), The Hydrogen Bond, Polish Scientific Publishers, Warsaw, 1969 (in Polish). C. Jaccard, Helv. Phys, Acta, 32 (1959) 89. H. Graenicher, in N. Riehl, B. Bullemer and H. Engelhardt (eds.), Physics oJlce, New York, 1969, after ref. 19. A. yon Hippel, R. Mykolajewycz, A. H. Runck and B. Westphal, J. Chem. Phys., 57 (1972) 2560. T . D . Dzhafarow, Imperfections and Diffusion in Epitaxial Structures, Nauka, Leningrad, 1978 (in Russian). S. J, Jones and J. W. Glen, Philos. Mag., 19 (1969) 13. U. del Penino, A. Loria, S. Mantovani and E. Mazzega, Nuovo Cimento B, 24 (1974) 108. J. Weertman and J. R. Weertman, Elementary' Dislocation Theory, Collier-Macmillan, London, 1967. S. Amelinckx, The Direct Observation of Dislocations, Academic Press, New York, 1964. J. Perez, J. Tatibouet, R. Vassoille and P. Goben, in Mechanisms of Internal Friction in Solids, Nauka, Moscow, 1974 (in Russian). J. Chrzanowski and B. Sujak, Proc. Int. Conf. on Cryogenic Fundamentals, Cracow, Wroctaw, April 8-14, 1983, in the press.
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ELECTRONICS AND OPTICS
ELECTRICAL MEASUREMENTS ON ICE THIN FILMS NEAR THE CUBIC ~ HEXAGONAL PHASE TRANSFORMATION JANUSZ CHRZANOWSKI AND BOGDAN SUJAK
Institute of Experimental Physics, University of Wroctaw, ul. Cybulskiego 36, 50-205 Wroclaw (Poland) (Received March 31, 1983; accepted November 9, 1983)
A correlation between the known phase transition in ice, from the cubic to the hexagonal modification, and the temperature range in which the activation energy for d.c. electrical conduction changes its value is shown. This change in the activation energy is discussed in relation to molecular rotation in ice. The results presented reveal a possible influence of orientational Bjerrum defects on the d.c. electric conduction in ice at low temperatures. It is also suggested that the temperature range in which the recrystallization process takes place in an ice layer depends on the thickness of the deposited layer.
1. INTRODUCTION Ice in various modifications is still studied for its special properties which appear under various conditions. The appearance of allotropic forms of molecular crystals is also of great importance from the point of view of studies on the natural electret effect in polar molecule condensates. As has been shown t, phase transformations in cryocondensed thin films of polar molecules may, at least in some cases, significantly affect the observed surface charges. Also, there are most probably close relations between the generation of surface charges on the free surface of the condensate layer and such phase transformations as the a--,13 phase change in solidified films of methanol 2. Therefore, information concerning phase transformations in polar molecule cryocondensates is also of importance in understanding the nature of the electret effect observed in water vapour condensates. As is known a-7, ice layers prepared in various temperature ranges may exist in different modifications. Below about 120K ice layers obtained by vacuum deposition onto a cold substrate are mainly amorphous, At higher temperatures two crystalline forms have been observed: a cubic phase (Ic, sphalerite structure) and a hexagonal phase (Ih, wurtzite structure). The temperature ranges in which these phases can exist were found to be rather wide but the temperatures of the phase changes are not strictly fixed6. The cubic ~ hexagonal transformation in ice has a relatively higher rate than that for the conversion from the amorphous to the crystalline (cubic) modification and usually occurs rapidly above 193 K. If the temperature of a sample of cubic ice is 0040-6090/84/$3.00
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J. CHRZANOWSKI, B. SUJAK
raised at the rate of a few kelvins per minute the conversion takes place near 203 K. The transformation to the hexagonal phase begins spontaneously and the crystallites grow rapidly, attaining a few micrometres in diameter 6. Although hexagonal ice is the only energetically stable modification of ice, several of its physical parameters (e.g. the dielectric permittivity) alter their values significantly when it is heated or cooled. It is thought that these changes correspond to the rotational movement of some water molecules or the displacement of some protons in relation to neighbouring atoms. The fact that the dielectric permittivity and the electrical conductivity of hexagonal ice are of the same order of magnitude as those of water (at the same temperatures) indicates that the molecules in an ice crystal have a definite degree of freedom. In hexagonal ice crystals cooled below about 200 K some degree of disorder remains frozen. Such a crystal does not attain a completely ordered structure even at 0 K and has an excess entropy S(0 K) = R in(2~) where R is the gas constant. The low value of the melting entropy of ice (S = 5.3 cal mol - i K - 1) supports the hypothesis that well below the melting point a number of hydrogen bonds are broken. A rapid acceleration in this process takes place close to the cubic ~ hexagonal phase change and is usually observed at about 200 K. In crystals constructed of polar molecules the molecules are oriented at low temperatures along certain distinct crystallographic directions. Heating of the crystal to a specific temperature TO leads to a rapid increase in the dielectric permittivity. The long-range order vanishes and for T > TO the behaviour of the molecular crystal is very similar to that of the polar liquid. This effect (so-called rotation melting) is often observed in a number of molecular crystals, e.g. CH4, C H 3 O H and H2S 8,9. Such a phase transition is often identified with the k-type second-order phase change a. However, there are some divergences in such an approach to the "refreezing" of molecular rotation in solids t°. The process of rotation melting in substances with hydrogen bonds is often related to the transition from the ferroelectric to the paraelectric phase as has been observed, for example, in HCI crystals at 98 K 11. A ferroelectric response for ice was first reported at 100 K ~z and later near 200 K ~3. Nevertheless, this problem is still not resolved ~4. As can be concluded on the basis of the temperature dependence of the dielectric permittivity of ice at low frequencies 9, the breaking of hydrogen bonds in hexagonal ice during heating of the crystal is a continuous process and shows a local maximum rate near 240 K. At the same temperature an intense sublimation of ice is usually observed. Hence, the appearance of molecular rotation in ice (at 200 K) should be considered in terms of a hindered rotation for which the height of the potential barrier depends on the temperature. Our recent observations concerning thermally stimulated currents in condensates of polar molecules suggest that the temperature at which the recrystallization process takes place, during the transformation from the cubic to the hexagonal modification in ice layers, depends not only on such factors as the heating rate but also on the thickness of the deposited film. In this paper the results of d.c. measurements on ice thin films near the cubic hexagonal phase change are reported. They show that the temperature of this phase change depends on the thickness of the deposited ice layer. Also, they suggest an important role for orientational Bjerrum defects in the mechanism of d.c. electrical conduction in ice at low temperatures.
ELECTRICAL MEASUREMENTS ON ICE FILMS
2.
19
EXPERIMENTAL DETAILS
As is known (see for example ref. 15), measurement of the d.c. electrical conductivity (or current) is a very convenient method of studying polymorphic phase transformations. It is always assumed (see for example ref. 16) that the temperature at which the particular recrystallization occurs is indicated by the change in the thermal activation energy EA for d.c. electric conduction. In our experiment a d.c. electric current through the measurement cell covered with the ice condensate under investigation was measured with a vibrating reed electrometer in the temperature range 180-240 K. The measurement cell contained double comb-shaped silver electrodes deposited onto a high resistance substrate. The preparation of the measurement cell used in our experiment has been described in detail elsewhere 2. Descriptions of such a cell are also available in older papers dealing with the electrical conductivity of thin films of organic solids 17,1a. The ice films were deposited from the gas phase by condensation onto the surface of a deeply cooled measurement cell in a vacuum of the order of 10- 4 Pa. The measurement cell was attached to a cryofinger of a continuous flow cryostat in such a way that the water vapour could be condensed onto the measurement cell surface only. Thus the thickness of the ice layer could be calculated from the total mass of the condensed substance. In separate measurements variations in the capacitance of a comb-shaped capacitor confirmed the linear increase in thickness of the deposited layer with increasing time of condensation. The layers studied were usually 1-10 ttm thick but in some cases 30 ttm layers were also examined. Doubly distilled and demineralized water was used as the source of the gaseous phase to be condensed onto the measurement cell. In all parts of the experiment the layers studied were deposited at 80 K (amorphous form) and heated at a constant rate of 3 K m i n - 1. This heating rate allowed us to compare some of our observations with recently published results on thermally stimulated depolarization currents in ice 14'19. Such a heating rate is also typical for other experiments on ice, e.g. in structural investigations 6. In the temperature range of 180-240 K that we used the thickness of the examined layers was almost constant if we ignore the decrease of a few per cent caused by the slow process of ice sublimation. 3.
RI~SULTS AND DISCUSSION
Typical plots of the logarithm of the measured current density J versus the reciprocal temperature 1/T are presented in Fig. 1. To show all the typical dependences of log J versus 1/T observed for ice layers of various thicknesses the units on the vertical axis have been omitted. The measured thermally dependent current through the measurement cell covered with the ice film depends linearly on the thickness of the deposited layer (Fig. 2) in the examined thickness range of 1-30 ttrn. Such a dependence l(d) was always observed for the layers studied provided that the temperature of the cell covered with ice did not exceed about 245 K. Above this temperature the surface conductivity rises rapidly leading to a marked increase in the current density irrespective of the thickness of the ice layer. Below 240 K the conductivity of bulk ice
20
J. CHRZANOWSKI, B, SUJAK
~o ~4o
230
220
210
200
>~10 ,am \.
6-8pro
190 T [.K] --
[g]
A
i
i
¢ &E=E~ EA '~ O6eV
!
~
\
Lg.~
[A]
10~/'T
~055ev ~032eV
\ \\\" 1 - 21 pm
~.o
~.2
~
/.6
~s
s'o --si2
si~
Fig. 1. TypicallogJvs. 1/T dependences observed for theicecondensatesofvariousthicknesseslapplied voltage, 150 V): - -, extension of the main segments of the observed dependences.
z[~]i
i
d [~m] Fig. 2. Current through deposited ice layers of various thicknesses (T = 235 K).
21
ELECTRICAL MEASUREMENTS ON ICE FILMS
was usually observed. This is in good agreement with the results of d.c. electrical conductivity studies on ice crystals reported by Maidique et al. 2° The silver electrodes used ensured good ohmic contacts and allowed a linear relation between the measured current and the applied voltage to be obtained (Fig. 3). Deviations from the ohmic regime were usually observed only when the surface conductivity was the result of an increase in the pressure above the free surface of the layer and always when the applied voltage exceeded 250 V (electric field, about 5000 V cm- 1).
×I[A~ 10-10I
/ A A
×10-8
I
Aj
/
4
/ 3
/ ~ Z _ ~
/
100
!3
°/
200
300
400
500
U IV]
Fig. 3. Current-voltagecharacteristics for ice layers of various thicknesses and at various temperatures: Q , d = l~tm, T = 2 0 5 K ; A , d = 10Bm, T = 2 0 5 K ; O , d = I~m,T=235K.
Recooling of an ice layer warmed above the range 200-220 K led to the condensation (resublimation) of a very thin film of water molecules onto the ice layer examined, with a consequent marked change in the surface conductivity which significantly affected the measured current. To remove this interfering effect rather intense pumping was applied. However, this resulted in large changes in the ice layer thickness and substantially influenced the measured current densities, especially for the thinner layers studied. Also, the pumping procedure led to an uncontrolled decrease in the temperature of the condensate layer. Hence, the presented log J versus l I T curves concern only current measurements recorded during heating of the layers examined which were maintained in dynamic equilibrium with their saturated vapour. We consider that the range of temperatures employed, which was below that causing intense sublimation of ice, and the relatively high electric field applied (about 3000 V cm- 1) made our results free of the restrictions listed in ref. 20. If it is assumed that a change in the activation energy for electrical conduction takes place at the phase transition, the temperature at which this transition occurs may be estimated. The observed dependence of log J on l I T may be approximated by two linear segments with different slopes. Hence, the current density through the measurement cell covered with the ice condensate layer may be described by an exponential function: J Qcexp(-EA/kBT) where J is the measured current density, E^ is the thermal activation energy for d.c. electrical conduction, kB is Boltzmann's constant and T is the absolute temperature.
22
J. CHRZANOWSKI, B. SUJAK
It was also observed for the thicker layers studied (5-10 ~tm) that within the temperature range 193-205 K a third activation energy EA" could appear. Its value of about 0.6 eV is very close to the mean arithmetic value EA"' = ½(EAc+ EAh) where EAc and EAh are the thermal activation energies for the cubic and the hexagonal modifications respectively. It is reasonable to assume that this third activation energy, appearing in the vicinity of 200 K, is an activation energy for the cubic and hexagonal mixture present in such layers. Further, more detailed considerations on the nature of the process corresponding to EA", presented in the next pages, do not exclude such a possibility. We should like to point out that irrespective of the ice layer thickness the difference AE between the activation energy for the hexagonal form (EAh) and that for the cubic form (EA c) is constant. The value of AE = EA h - EA c is about 0.6 eV (Fig. 1). Careful analysis of the observed log J versus 1/T curves shows that both the activation energies EA h and EA c decrease, attaining 0.84 eV and 0.23 eV for the hexagonal and the cubic modifications respectively, when the thickness of the deposited ice layer increases from 1 to about 30 ~tm (Fig. 4). Extrapolation of the
12o I EA
[~v] i x \e
too
o~. 09o
08o I I
07o I
060
~E~O.6eV
05o i
o~o I
O3O 020
d [~]
Fig. 4. Activation energies EAc and EAh for d.c. conduction plotted against the thickness of the deposited ice layer: O, 0, mean values of the observed activation energies for ice layers of various thicknesses in the cubic and the hexagonal modifications respectively.
ELECTRICAL MEASUREMENTS ON ICE FILMS
23
thickness dependences EA(d) presented in Fig. 4 to zero thickness of the condensate layer gives for both activation energies determined EAc - 0 . 5 8 e V and EAh = 1.15 eV. The mean error in the evaluation of the activation energies is about _ 0.05 eV. The liberation of additional degrees of freedom which is observed in ice crystals near 200 K coincides with a considerable change in the thermal activation energy for d.c. conduction. Measurements of the a.c. electrical conductivity in polycrystalline ice samples also show significant variations in this conductivity close to the temperatures at which the known phase transformations in ice take place 21. The a.c. conductivity of fine-grained polycrystalline ice at 104 Hz very often shows a rapid variation close to 240 K. In some cases even a high "step" in this conductivity was observed at about 240 K while the peak of the conductivity was reported to occur at 193 K 21. Each H 2 0 molecule in the ice lattice is held by four hydrogen bonds. For a reorientation of the H 2 0 molecule three of the hydrogen bonds have to be broken while the oxygen position is maintained. This requires about 0,6eV per H 2 0 molecule22.23. The occurrence in solids with hydrogen bonds of molecular rotation at temperatures close to that at which a change occurs in the activation energy for electrical conduction suggests a protonic mechanism for the conduction. This electrical conduction has been ascribed to an increase in the probability of proton transfer as a consequence of the rotation of the molecular fragments. This rotation effect has been considered in terms of protonic hopping between two stable intermolecular sites, i,e. the double-well approach (see for example ref. 24). Therefore the change in activation energy of about 0.6 eV, as observed in our experiment, takes place at temperatures very close to that for the cubic --* hexagonal phase change. One of the possible explanations for the observed changes in EAc and EAh when the thickness of the deposited ice layers are altered may be as follows. There are two significant mechanisms of d.c. electrical conduction in the ice modifications that we studied. These are a consequence of the existence and migration of the two types of defects: ionic (H30 ÷ and O H - ) and orientational (Bjerrum L and D defects) 24. The latter defects are produced by a rotary motion of a proton from one position between two oxygen atoms ( O H . . ' O ) to another interoxygen position, producing a doubly occupied bond (D defect) and a vacant bond (L defect)22'24. It is usually assumed that the d.c. electrical conduction in hexagonal ice occurs mainly by the ionic mechanism in which the protons jump between two alternative sites in an O . " O bond. However, there are some suggestions 2s that the mechanism of the d.c. electrical conduction in ice at low temperatures may be other than ionic and may be governed by the Bjerrum orientational defects. Let us again consider Fig. 4. The extreme values of the activation energies EA° and EAh which are evaluated from this figure are characteristic of a number of processes that take place in ice. Thus the energy E^ ~ = 0.23 eV is very close to that for the migration of the orientational Bjerrum defects; EA~ = 0.58 eV is close to the activation energy for the motion of H + (H30 +) ions in ice; EAh = 1.15 eV is typical of the energy for the creation of a pair of ions (H 30 ÷ + OH-)22' 24. As mentioned earlier, the restrictions described in ref. 20 concerning studies of the d.c. electrical conductivity in ice are probably invalid for our experiments.
24
J. CHRZANOWSKI, B. SUJAK
Hence, it can be assumed that the energy EA c = 0.23 eV observed for thick cubic ice layers is the activation energy for the migration of orientational Bjerrum defects. For the thinner films examined the activation energy for d.c. electrical conduction rises. Since the low temperature electrical conductivity is as a rule very sensitive to structure, this increase in EA c may be a result of the structural disorder which develops when the deposited layer is very thin. However, the extrapolated EA c value of 0.58 eV for very thin films (less than 1 tam) does not seem to be accidental and suggests that another mechanism of charge transport may dominate in this thickness range. The smooth transition in EA c from 0.23 to 0.58 eV supports the supposition that there is a real and continuous change in the charge transport mechanism. Therefore, depending on the deposited layer thickness, one of the mechanisms, ionic or Bjerrum defect migration, may make the dominant contribution to the observed activation energy in cubic ice films. The change in the d.c. conduction mechanism in thin ice films indicates a significant decrease in the rate of the diffusion processes in which Bjerrum defects play an important role. As mentioned earlier, in some cases during warming of the ice layer a third activation energy EA"' c a n appear (Fig. 1). EA'" also depends slightly on the thickness of the ice layer examined. The difference AE = EA"' - EA c of 0.32 eV is close to onehalf of the energy required for the creation of a pair of Bjerrum defects: E o = 0.68 eV 24. Thus, the third activation energy E A " of 0.55 eV observed in some cases corresponds to the creation and migration of Bjerrum defects with an activation energy E A " = 1E O-q-E~, of 0.55 eV, where E~ = 0.23 eV is the activation energy for Bjerrum L defect migration. This EA'" value is close to the theoretically predicted value of 0.575 eV 24. At the temperature of the cubic--, hexagonal phase change the activation energy rises by about 0.6 eV. This leads to an activation energy EAh in the hexagonal modification of 1.15 eV for very thin films and of 0.84 eV for thick films. Considering these changes in the activation energy in terms of defect creation and migration, it can be inferred that the "jump" of about 0.6 eV at the phase transition is caused by a process in which ionic defects are produced within the condensate layer. The activation energy for d.c. conduction in very thin ice films of hexagonal structure would therefore be EA h -----½Eoi°n+Em i°n where Eo i°n is the energy needed for the creation of a pair of ionic defects and Emi°n is the energy for the migration of the defect of greater mobility (H sO +). It can be expected that for the thicker ice layers deposited the structure of the condensate becomes more ordered (weakly imperfected) and the diffusion of Bjerrum defects may be greater than that in very thin films. Since above the phase change thermal excitations are energetically sufficient for the creation and migration of both types of defect, the activation energy for d.c. electric conduction will be determined by contributions from both these processes, i.e. the creation and migration of both ionic and orientational defects. Hence, if both types of the defect make similar contributions to the charge transport in thick ice layers (about 30 tam) just above the phase change, the activation energy should be given by /~ = l172.t~,2L, S i l oiOn + EmiOn) + (½Eo + Era)} ~ 0.86 eV
This value agrees quite closely with the experimentally determined value of about 0.84 eV (Fig. 4).
25
ELECTRICAL MEASUREMENTS ON ICE FILMS
As seen in Fig. 1, some of the observed log J versus 1/T curves seem to consist of a number of segments of various slopes. This was observed mainly for the layers 4-8 lain in thickness. It can be assumed that this is due to the very complicated processes of nucleation in a layer whose thickness is equal to the mean size of the microcrystallite grains present in ice films in the temperature range employed6. The especially wide dispersion in the experimental points (Fig. 5) for the layers 4-8 I~min thickness suggests that the relation between the thickness of the deposited layer and the mean diameter of the microcrystallites in the layer is an important factor. This seems to support our supposition that structural disorder has a marked influence on the mechanism of d.c. conduction in the layers studied. For layers thinner than about 5 ttm, only the two activation energies EA¢ and EAh were found. The appearance of a temperature transition region in which the cubic and hexagonal modifications can coexist with a corresponding activation energy of about 0.6 eV seems only to be possible when the thickness of the layer exceeds the mean size of the microcrystalline grains. The sharp transition above 200 K in the thinner layers studied may be considered as a rapid relaxation of the "superheated" cubic layer to the hexagonal modification. In many experimental runs, however, the observed dependence of log J on l I T consisted of two segments for all thicknesses of the layers studied (1-30 ~tm). For thicker layers the temperature range in which the change in slope of the log J versus 1/T curve was observed showed a tendency to shift towards lower temperatures, indicating a reduction in the superheating effect. This is presented in Fig. 5. Experimental points in this figure indicate the temperatures at which the change in the activation energy EA was observed. The points of intersection of the extended main linear segments for the log J versus l I T curves that comprise many segments are also included. These points of intersection exhibit the same tendency to temperature shifting as do the data for thicker films mentioned above. As seen in Fig. 5 the temperature at which the change in E A occurs is shifted from 225 K for thin films (1 ~tm) to about 200 K for thick layers (30 ~tm). An extrapolation to zero film thickness gives a temperature of about 235 K, which is T [K]
230
L• 220
210
|
•
:
"
•
•
:
"
~1OsJm
200
d [;Jm]
Fig. 5. Temperature at which the activation energy for d.c. conduction changes its magnitude as a function of the thickness of the deposited ice layer: _~g~, temperature ranges in which the cubic --* hexagonal transformation was usually observed in ice specimens of various thicknesses.
26
J. CHRZANOWSKI, B. SUJAK
close to the temperature range in which a considerable increase in hydrogen bond breaking in ice probably occurs. In contrast, for thick layers the temperature of the activation energy change is shifted towards the range in which the cubic -~ hexagonal transformation is usually observed in bulk ice, i.e. 190-200 K, and where various electric and mechanical phenomena are often observed. It is worth remarking that von Hippel et al. 26 found for a polycrystalline rapidly grown ice sample relaxation spectra which showed a local maximum near 235 K, in contrast with the behaviour of pure ice crystals. Also, the time constants for the various relaxation processes increased by a factor of about 10. This was probably due to the presence of a number of dislocations in the polycrystalline ice samples examined 26. If the assumption made above that the structural disorder in ice thin films formed by vacuum deposition is responsible for the change in the d.c. electric conduction mechanism, by blocking the diffusion processes in ice films, is correct, then an influence of the structural disorder should also be seen in the rate of conversion of cubic ice to the hexagonal form and should result in a shifting in the phase change temperature to the higher temperature region. We consider that exactly this effect is presented in Fig. 5. Above a temperature of about 235 K cubic ice cannot exist under the conditions employed in our experiment. The connection between structural disorder in ice films and the cubic --, hexagonal phase change seems to be more important than it did initially. As seen in Fig. 5 the greatest superheating effect appears for the thinnest films examined, which most probably show considerable structural imperfection. In particular, a number of dislocations and point defects are probably created. A high concentration of dislocations which can induce an increase in internal friction in such fine-grained polycrystalline films seems to be rather obvious at least, because of the known mechanism of growth of the crystals through the development of screw dislocations. The concentration of dislocations probably decreases as the thickness of the deposited film increases, similar to the behaviour observed in thin films of other substances 27. The large number of dislocations in thin ice films and the strong interaction between the dislocations and Bjerrum defects can lead to significant lowering of the rates of diffusion processes at low temperatures. It is known that the movement of a dislocation requires a large number of Bjerrum defects to reorient the bonds 28. Therefore, most of these point defects may interact with the dislocations which are attracted to their cores. Such a process, leading to "immobilization" of a large number of Bjerrum defects, would involve a relative increase in the importance of ionic defects and would result in a weak ionic current in cubic ice films with an activation energy for d.c. electrical conduction of 0.6 eV because of the dominance of the ionic charge transport process. If these considerations are correct, then the conversion process of cubic ice to the hexagonal modification may be closely related to the existence and motion of dislocations, as suggested in some papers 29. It can be expected that the cubic ~ hexagonal conversion process in ice may be induced by appropriate reactions between certain types of dislocations in cubic ice or by dissociation of the dislocations. Such reactions which obey the rules of Frank 3° and lead to a reduction in the free energy of the cubic ice layer would stimulate the conversion process. The stacking faults created by reaction between the dislocations (or dissociation of the dislocations) in ice of the sphalerite structure
ELECTRICAL MEASUREMENTS ON ICE FILMS
27
would form elements of the wurtzite structure (h.c.p.) basal plane (0001), as occurs in several phase transformations for other substances 31. The stacking faults created would be incipient crystals of the new hexagonal phase. The close geometrical similarity of the two structures, which include some planes with identically packed atoms ((111) and (0001)), would be an important factor facilitating the transition under consideration. Since the phase change should proceed at the diffusion rate, the rate of conversion should obey an exponential dependence of the type exp(-Ec/kBT) where Eo is the energy required for the conversion. The drift velocity of dislocations in bulk ice is rather low on account of the strong Peierls forces in ice, among other factors 32. At 223 K this drift velocity is estimated2s to be of about 50 .~ s- 1 and it is probable that this value falls with decreasing temperature in cubic ice also. Since the drift velocity of a dislocation also depends on the structural disorder in the substance 3° the movement of a dislocation in cubic ice films may also be significantly affected by a considerable structural imperfection and by interaction with other dislocations. This would lead to a slowing down of the motion of the dislocation and consequently to a reduction in the rate of conversion from the cubic to the hexagonal modification. Thus, the decrease in velocity of the dislocations would give rise to the possibility of the existence of the superheated cubic phase above 200 K up to a temperature at which thermal excitations would unblock the diffusion processes. 4. CONCLUDING REMARKS
In this paper we presented our experimental results of studies on direct electrical currents in thin films of polycrystalline ice which were undertaken in the vicinity of the phase transition from the cubic to the hexagonal modification. Our results suggest that near this phase change both types of points defects, ionic and orientational, can participate in the d.c. electrical conduction in thin ice films. Also, the structural disorder in the thin ice films examined seems to be of importance to the d.c. conductivity. The relation between the charge transport processes in the ice films studied and the diffusion rates for these processes seems to be responsible for the change in the conduction mechanism in the vicinity of the phase transformation. The existence and physical properties of dislocations in ice also seem to have a considerable influence on the electrical properties of ice. Perhaps it is worth mentioning that, to explain the results of our recent optical investigations on spontaneously electrically polarized ice thin films at about 90 K 33, we had to make an assumption that the elementary dipoles in the films examined, which interacted with a light wave, are aligned along the screw lines surrounding the normal direction to the condensate surface (the direction of the spontaneous polarization vector P). Our observations concerning the shift in the phase change temperature towards the range above 200 K seem to have a few indirect confirmations. For example, Cubiotti and Geracitano 13 have shown that the suggested Curie point of ice shifts to lower temperatures when the thickness of vapour-deposited ice layers is increased. Also Dowell and Rifert6 found from X-ray studies that the intensity of the recrystallization processes in ice layers depends on the thickness of the deposited layer.
28
J. CHRZANOWSKI, B. SUJAK
ACKNOWLEDGMENTS
The authors are grateful to Dr. Malcolm Mellow from the Cold Regions Research and Engineering Laboratory, Hanover, NH, U.S.A., for his constructive criticism and many helpful suggestions. This work was supported by the Polish Academy of Sciences within the Main Scientific Project 05.13. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
J. Chrzanowski and B. Sujak, Acta Phys. Pol. A, 64 (1983) 107. J. Chrzanowski and B. Sujak, Thin Solid Films, 101 (1983) 123. J.A. Pryde and G. O. Jones, Nature (London), 170 (1952) 685. M. Blackman and N. D. Lisgarten, Proc. R. Soc. London, Ser. A, 239 (1957) 93. F.V. Schalcross and G. B. Carpenter, J. Chem. Phys., 26 (1957) 782. L.G. DowellandA. P. Rifert, Nature(London),188(1960)l144. C.G. Venkatesch, St. Rice and J. B. Bates, J. Chem. Phys., 63 (1975) 1065. K. Pigofi and Z. Ruziewicz, Physical Chemistry, Polish Scientific Publishers, Warsaw, 1980 (in Polish). Ch. Kittel, Introduction to Solid State Physics, Wiley, New York, 3rd edn., 1966. L. Landau and E. M. Lifshitz, Statistical Physics, Nauka, Moscow, 1964. S. Hoshino, K. Shimaoka and N. Niimura, Phys. Rev. Lett., 19 (1967) 1286. B. Dengel, U. Eckner, H. Plitz and N. Riehl, Phys. Lett., 9 (1964) 291. G. Cubiotti and R. Geracitano, Ph3s. Lett. A, 24 (1967) 179. G.P. Johari and S. J. Jones, J. Chem. Phys., 62 (1975) 4213. W. Wendlandt, Thermal Methods of Analysis, Wiley, New York, 1974. M. Kryszewski, Polvmolecular Semiconductors, Polish Scientific Publishers, Warsaw, 1968 (in Polish). G. Tolin, D. R. Kearns and M. Cavin, J. Chem. Phys., 32 (1960) 1013. F. Gutman and L. E. Lyons, Organic Semiconductors, Wiley, New York, 1967. P. Pissis, G. Boudouris, J. G. Carson and J. L. Leveque, Z. Natur]brsch.. 36a ( 1981 ) 321. M . A . Maidique, A. von Hippel and B. Westphal, J. Chem. Phys., 54 (1970) 150, M. Mellor, CRRLab Res. Rep. 292, 1970, and references cited therein (Cold Regions Research Laboratory, Hanover, NH, U.S.A.). A. Bielafiski, K. Gumifiski, B. Kamiefiski, K. Pigofi and L. Sobczyk (eds.), Physical Chemisto', Polish Scientific Publishers, Warsaw, 1980 (in Polish). L. Sobczyk (ed.), The Hydrogen Bond, Polish Scientific Publishers, Warsaw, 1969 (in Polish). C. Jaccard, Helv. Phys, Acta, 32 (1959) 89. H. Graenicher, in N. Riehl, B. Bullemer and H. Engelhardt (eds.), Physics oJlce, New York, 1969, after ref. 19. A. yon Hippel, R. Mykolajewycz, A. H. Runck and B. Westphal, J. Chem. Phys., 57 (1972) 2560. T . D . Dzhafarow, Imperfections and Diffusion in Epitaxial Structures, Nauka, Leningrad, 1978 (in Russian). S. J, Jones and J. W. Glen, Philos. Mag., 19 (1969) 13. U. del Penino, A. Loria, S. Mantovani and E. Mazzega, Nuovo Cimento B, 24 (1974) 108. J. Weertman and J. R. Weertman, Elementary' Dislocation Theory, Collier-Macmillan, London, 1967. S. Amelinckx, The Direct Observation of Dislocations, Academic Press, New York, 1964. J. Perez, J. Tatibouet, R. Vassoille and P. Goben, in Mechanisms of Internal Friction in Solids, Nauka, Moscow, 1974 (in Russian). J. Chrzanowski and B. Sujak, Proc. Int. Conf. on Cryogenic Fundamentals, Cracow, Wroctaw, April 8-14, 1983, in the press.