J. Phys. Chem. 1983,87,4139-4142
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Growth Rate of Recrystallization in Ice Mutsuml Ohtomo and Gorow Wakahama’ The Instirote of Low Temperature Science, Hokkaido Unlversi~,Sapporo, 060 Japan (Received August 23, 1982; In Final Form: April 19, 1983)
It was found that the growth rate of a recrystallized grain, grown in a deformed single crystal of ice, depended linearly on the strain of the deformed matrix, and also that a change occurred in activation energy at about 215 K to indicate a transformation in the structure of the grain boundary. The diffusion coefficient of recrystallization growth (namely,the grain boundary diffusion coefficient)at 272.7 K, estimated from the growth rate, was in good agreement with the value deduced from a model of the melting grain boundary. 1. Introduction Despite the fact that extensive studies have been made of recrystallization in ice,’* the knowledge of it is far from complete. Most of the past studies1+ used polycrystalline ice samples and paid attention mainly to a change, before and after recrystallization, in the distribution of the crystallographic orientation of the axes. though they are advantageous, of course, in obtaining a total picture of the phenomenon of recrystallization in polycrystalline ice, they are not suitable for looking into the problems about how the crystallographic orientation of axes of a recrystallized grain is characterized in the matrix. Ohtomo and Wakahama’ grew a recrystallized grain using a single crystal of ice by the strain annealing method, and revealed that the orientation of the c axis of the recrystallized grain is dependent on that of the deformed matrix. They interpreted the dependence from a kinetic point of view. Now, for the total picture of the formation mechanism of preferred orientation in polycrystalline ice by recrystallization the growth rate is as important as its crystallographic orientation. The present study aims at examining the dependence of the growth rate of the recrystallized grain on the temperature and the driving force. In this connection, the value of the diffusion coefficient estimated from the obtained growth rate was found considerably larger than that of volume diffusion coefficient in ice, and was found rather comparable to that of water. Besides, a change in activation energy for recrystallization growth was found. So a nuclear magnetic resonance (NMR) test was conducted to check the structure of the growth interface of recrystallization (i.e., grain boundary). On the basis of these results, a model of the grain boundary in ice near the melting point is proposed; then the thickness and free energy of it are discussed.
2. Experimental Method a. Driving Force Dependence of Recrystallization Growth. A rectangular solid sample about 4 X 5 X 5 cm3 was cut from a large-sized single crystal from Mendenhall Glacier8 in such a manner that its c axis was parallel to its top face. Then, after the sample was compressed uniaxially normal to its top face, it was sliced to a thickness of 3 mm normal to the stress axis. A pick with a pin on the surface of a sliced test piece usually caused nucleation in it. It was annealed for 3 h at 272.7 K in an annealing (1) G . P. Rigsby, J. Glackl., 3, 589 (1960). (2) 0. Watanabe and H. Oura, Low Temp. Sci., Ser. A, 26, 1 (1968). (3) H. Tanaka, J. Geol. SOC.Jpn., 37, 659 (1972). (4) A. Higashi, A. Fukuda, H. Shrjji, and N. Kiso, Seppy6,35,3 (1973). (5) B. Kamb, Geophys. Mon., 16, 211 (1973). (6) C. J. L. Wilson and D. S. Russel-Head, J. Glaciol., 28, 145 (1982). (7) M. Ohtomo and G . Wakahama, Low Temp. Sci., Ser. A , 41, 1 (1982). (8) A. Higashi, M. Matsuda, H. Shoji, and M. Ohtomo, unpublished. 0022-3654/83/2087-4~39$01.50/O
box set under a polarizing microscope. The growth process of the nuclei during the annealing was recorded with a series of time-lapse photographs. Data obtained from the first 30 min were omitted so that the effects of the stress-concentrated area as a result of the picking was avoided. In addition to this, as the growth rate decreases with a lapse of time due to the recovery process of the test piece, the obtained value of growth rate is the mean value for 2.5 h. As the recrystallized grain showed anisotropy in growth rate, the growth rate of the fastest migrating grain boundary was measured for each grain. The dislocation density of the deformed matrix was determined by the etch pit density methodg after annealing. b. Temperature Dependence of Recrystallization Growth Rate. A recrystallized grain was also grown by the strain annealing method. However, a somewhat different procedure from the previous section was adopted. The c axis of a sample was chosen for the top face, as described in the previous section. Next, using a band saw, we cut grooves in a gridiron pattern on the top face. Then, the sample was compressed uniaxially normal to the top surface by about 20% at 263 K. During the deformation the grooves on the top face were closed due to stress concentration in the portion. After deformation, the sample was sliced to a thickness of 3 mm parallel to the stress axis and the sliced test pieces were annealed in an annealing box a t a constant temperature. Some of a large number of recrystallized nuclei, formed at the grooved portion where the stress was concentrated, started growing toward the deformed matrix. The test pieces were annealed in the temperature range from 83 to 272.7 K. The annealing period was 24 h above 253 K; however, below 253 K it was 100-200 h, because otherwise the growth would not be detected. After annealing, a photograph was taken under the polarizing microscope to record the displacement of the grain boundary. Growth rate of the fastest migrating grain boundary of each recrystallized grain was also obtained from photographs taken before and after the annealing. The obtained data for the growth rate are the mean value of the annealing period, as the experiment of the driving force dependence is also. c. An N M R Test for Recrystallized Grains. As mentioned later, it is considered that a transformation in the structure of the grain boundary in ice near the melting point results from grain boundary melting. Hence, we attempted an NMR test for checking the transformation by conducting measurements using a wide-line NMR spectrometer. Test pieces were prepared by the following procedures: A rectangular solid sample of a single crystal (9) D. Kuroiwa and W. L. Hamilton in “Ice and Snow”, MIT Press, Boston, 1962, p 34.
0 1983 American Chemical Society
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Ohtomo and Wakahama
The Journal of Physical Chemistry, Vd. 87, No. 21, 1983
mm/h
0.1
0.01
10 Per ct. Strain Flgw 1. Driving force dependence of qowth rate of the recrystallized grain at 272.7 K. 1
5mm Flgure 3. Photograph of a thin section of an NMR test piece taken under crossed polarizers.
0 : 0 5ev (T>215K) :0.02 e V ( T r . 2 1 5 K ) W
Flgure 4. Signals from an NMR: solid line, at 272.7 K; broken line, at 270 K. The peak is indicated by an arrow.
Flgure 2. Log recrystallization growth rate vs. 1/T (K).
of ice, about 4 x 4 x 10 cm3, was cut from a large-sized single crystal of ice;8 then it was deformed uniaxially by 90% at 263 K; a test piece was cut from it. After cutting, we immediately mounted the test piece on the apparatus. As a large number of recrystallized grains appeared during the deformation, the test piece had a large sum of specific area of the grain boundary in it. Moreover, it had many growing recrystallized grains.
3. Result of Experiments Figure 1shows the dependence of the recrystallization growth rate on the driving force when the sample was deformed within 2-20%. It becomes evident that the growth rate changes linearly with the strain on the matrix, as indicated in the figure. The dislocation density of the deformed matrix was within the order of 106-107 after annealing for the case 5 % deformation. The growth rate of the recrystallized grain a t the strain was within 0.035-0.065 mm/h. Measurements were made of the dislocation density in almost all the samples. For samples deformed by a strain of more than 8%,however, the sensitivities of the microscope and the method made it difficult to measure the dislocation density exactly. The reason why the measured values of the dislocation density were not accepted for the 2% strain deformation is that the measured values of the growth rate deviated from the line as shown in Figure 1.
The temperature dependence of the recrystallization growth rate is indicated in Figure 2. It is revealed that this dependence shows a change near 215 K. The activation energies obtained for the growth rate of the recrystallized grain were 0.5 eV a t temperatures not lower than 215 K and 0.02 eV between 215 and 83 K. Figure 3 shows a photograph of a thin section of a polycrystalline test piece for an NMR study taken under crossed polarizers. The mean diameter of the grain is 0.2 mm, and the specific area of the grain boundary is assumed to be within 0.014.1 m2/g. The result of the NMR tests are indicated in Figure 4. In this figure the solid and the broken line gives the result a t 272.7 and 270 K, respectively. No experiment was conducted above 272.7 K to prevent the test piece from fusing. It is evident from Figure 4 that only at 272.7 K the test piece shows a narrow component denoted by an arrow. The relative intensity of the narrow component in the NMR spectra is 0.3%. No peak appeared, however, below 270 K.
4. Discussions a. Growth Rate of the Recrystallized Grain. As given in Figure 1, the growth rate of recrystallization in ice a t 272.7 K linearly depends upon the total strain of the deformed matrix. This result implies that the growth rate is characterized not by growth kinetics,l0 but by diffusion of water molecules which contributes to the growth. The dislocation density of the deformed matrix obtained by the etch pit density methodg is of the order of 106-107 cm-2,which gives a driving free energy of recrystallizationl1 in a range from 6 X 10 to 6 X lo2erg.~m-~ or from 2 X (10) N. H. Fletcher in "The Chemical Physics of Ice", Cambridge University Preas, London, 1970, p 106. (11) H. Gleiter and B. Chalmers ina'High-Angle Grain Boundaries", Pergamon Press, New York, 1972, p 133.
Rate of Recrystallization in Ice
Grain Boundary Figure 5. A model of the grain boundary in ice near the melting point.
to 2 X erglatom. For the growth rate of 0.05 mm/h and the free energy in this range, the diffusion coefficient for recrystallization growth (the grain boundary diffusion coefficient),12DR,at 272.7 K was calculated as 1 X 10*-1 X cm2/s, where the jump distance of a water molecule is assumed to be 4.5 X cm. It should be noted that this value of DR is very different from the value of the volume diffusion coefficient of ice,13and is rather similar to that of water, which is of the order of cm2/s.14 It means that the recrystallized grain grew as if from the melt phase. The growth interface of recrystallization (grain boundary) must have a large number of mobile water molecules as assumed in the theory of grain boundary melting.15 The change in value of activation energy for the growth of recrystallization near 215 K ( T / T , N 0.79, T,, is the melting point) as shown in Figure 2 suggests that the structure of the grain boundary underwent a transformation below near OAT,, as indicated in some materials.16J7 b. The Mobile Water Phase in the Grain Boundary. The existence of a quasi-liquid layer at the surface of ice has been already revealed experimentally by an NMR study18 and other methods.lg Kvlividze et a1.18already showed the existence of the mobile water phase in the polycrystalline ice; however, they concluded that it does not exist in the grain boundary, but only at the surface. The peak, which is considered to have originated from the mobile water phase, was also detected in the present experiment. Because the sample used here contained few bubbles (i.e., surfaces), the mobile water phase might be considered to have existed in the grain boundary (grain boundary melting). This possibility further supports the discussion in the previous section. It is supposed as the reason why the peak did not appear at 270 K that the total amount of the specific area of mobile water molecules was too small to be detected because the test piece had a much smaller specific area of the grain boundary than that of Kvlividze.ls It is an unsolved problem for us to find a temperature a t which the mobile water phase can exist, as well as the nature of it. c. A Model of the Grain Boundary in Ice near the Melting Point. We propose in this section a model of the (12)D. Turnbull, Trans. Metall. SOC.AIME, 191, 661 (1951). (13)N. H.Fletcher, ref 10,p 160. (14)D. Eisenberg and W. Kauzmann in "The Structure and Properties of Water", Oxford University Press, London, 1969,p 218. (15)H.Gleiter and B. Chambers, ref 11, p 113. (16)D. W. Demianczuk and K. T. Aust. Acta Metall., 23,1149(1975). (17)K. T. Aust, Can. Metall. Q., 8,173 (1969). (18)V.I. Kvlividze, V. F. Kiselev, A. B. Kurzaev, and L. A. Ushakova, Surf. Sci., 44, 60 (1974). (19)D. Beaglehole and D. Nason, Surf. Sci., 96, 357 (1980).
The Journal of Physical Chemistry, Vol.
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grain boundary of ice near the melting point according to the discussion in section 4a, that is, a model of wide grain boundary20,21instead of a narrow one, as shown in Figure 5. The existence of the melt phase below the melting point brings about a disadvantage in stability because of the bulk free energy of a system. The factor which contributes to making the water phase thermodynamically stable despite this disadvantage can be explained by a decrease in the free energy of the interface due to the existence of such a phase in the grain boundary of an ice crystal. Discussions on a quasi-liquid layer existing on the ice surface which were made by Kuroda and Lacmann22are expanded to treat the water phase which exists in the grain boundary as follows: The wettability parameter, Aym,is defined in this case by the following expression: Aym =
-
~ c c (~lc")
+ ~lc@)I
(1)
where ycc,ylC(l), and ylc(2) are respectively the amount of free energy of the grain boundary between ice (1)and ice (2), that between ice (1)and water, and that between ice (2) and water. If Aym > 0, a melt layer is capable of existing stability in the grain boundary. The total free energy Af(6) of the grain boundary is given by the following as a function of the thickness 6 of the water layer: f(6) =
+ ylc(2)+
~
A" 6 Qm A y m + - -AT ( A + 6)n Vm T m
(2)
where T , is the melting point of ice; Q, is the molecular heat of melting of ice; Vm is the molecular volume of water in the grain boundary layer; AT = Tm- T represents the degree of supercooling; A and n are parameters which should be determined by microscopic studies or further experiments.22 Equilibrium is attained between the ice and the water layer when Af is at its minimum (6 = 6,J. The equilibrium thickness 6,, is given by
The chemical potential, pgb, of the grain boundary referred to that of ice is given by partially differentiating Af(6) by the number of molecules as follows:
Then, we can estimate the thickness and free energy of the grain boundary in ice near the melting point as follows: If we assume here that the interfacial free energy, ylc, is proportional to the surface energy, yo and the proportion, ylc/yc, is equal to the ratio of heat of fusion to heat of sublimation,22we can obtain, ylc,between ice and water. As Akutsu and OokawaZ3calculated the anisotropy in the surface energy of ice using the broken bond method, we utilize it for estimating the thickness and free energy of the grain boundary. For example, we discuss the case of the grain boundary which is constructed by two (1123) planes as follows: As ~ ~ ( 1 1 2=3 1191.0 e r g / ~ m and~ ycc ~ ~ = 27, = 382 erg/cm2,then ylC(1123)= 22.4 erg/cm2. The grain boundary free energy at 272 K is 60 erg/cm2 from (20)K. Liicke, R. Risen, and F. W. Rosenbaum in "The Nature and Behavior of Grain Boundaries", Plenum Press, New York, 1972,p 245. (21)G. F.Bolling, Acta Metall., 16, 1147 (1968). (22) T.Kuroda and R. Lacmann, J. Crystal Growth, 56, 189 (1982). (23)N.Akutsu and A. Ookawa, unpublished.
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J. Phys. Chem. 1983, 87, 4142-4146
*
eq 2, which is close to the experimental value, 65 3 erg/cm2,at the melting where, A = 1.5 X cm; n = 1; V , = 3.0 X cm3; Q, = 1 X erg/atom;22 and T, = 273.15 K. From eq 3, the resultant value of the equilibrium thickness of the grain boundary, ast, is 6.3 X cm at 272 K. I t decreases with falling temperature to the thickness of 7.0 X cm at 215 K (0.79Tm),that is almost of the order of the lattice space of the ice crystal. Although the experimental knowledge of the grain boundary of ice is very unsatisfactory now, the thickness,
free energy, and anisotropy are obtainable by the present method.
Acknowledgment. We express our gratitude to Professors K. T. Aust and H. Gleiter for their comments and suggestions on this paper. We are also indebted to Professor Y. Suzuki and Dr. T. Takahashi for helpful discussions. We thank Mr. F. Ishii for the use of the NMR apparatus. We also express thanks to Professor A. Higashi and Mrs. N. Akutsu for making single crystals available and for providing unpublished data, respectively. Registry No. Water, 7732-18-5.
(24) W. M. Ketcham and P. V. Hobbs, Phil. Mag.,19, 1161 (1969).
Growth Rates and Habits of Iee Crystals Grown from the Vapor Phase W. Beckmann,' R. Lacmann, and A. Bierfreund Institut fur Physikalische Chemie der TU, D 33 Braunschweig, West Germany (Received: August 23, 1982; In Final Form: April 18, 1983)
The scope of this work was to clarify the habit modification with temperature of ice crystals growing from the vapor phase. We carefully measured the growth and evaporation rates of the basal and prism face of ice single crystals in substrate chambers. We worked under pure water vapor conditions as well as under additional pressures of nitrogen. We found isometric growth and evaporation with no habit modifications under pure water vapor conditions (except for the growth at -7 "C, where platelike crystals were observed). The transition to nonisometric crystals occurred upon the introduction of nitrogen with pressures exceeding 350 mbar. With the nitrogen, the interface kinetics was considerably decreased. We suppose the adsorption of nitrogen causes a selective poisoning of growth sites of the two faces. This may entail the occurrence of the habit modifications found under atmospheric conditions.
Introduction If ice crystals are grown from the vapor phase under atmospheric conditions, a modification of the habit (either a column or a plate) is observed a t well-defined temperatures. Plates are observed between 0 and -4 "C and between -10 and -25 OC,whereas columns prevail between -4 and -10 " C and a t temperatures below -25 OC.' This habit variation has drawn a lot of attention and attempts have been made to interpret it in terms of crystal growth t h e ~ r i e s . ~For ! ~ these interpretations, growth rate measurements of individual faces are necessary. Most determinations of the growth rates of the basal and prism face were carried out in cloud4+ or substrate chambers' with 1 atm of air present. The air imposes at least a transport resistance, which may hide interface kinetics effects. Only one investigation so far has worked under pure water vapor conditions.s In order to investigate the transitions more closely, we measured the rates of growth and evaporation of the basal and prism face. To separate interface kinetics and transport effects, we worked in a substrate chamber, which allowed work under pure water vapor conditions as well as under foreign gases. Experimental Section Two different substrate chambers were used for all experiments. The construction principle has been taken from the literature7z8and altered in order to better serve our purposes. Special attention has been paid to the control *Present address: CRMC2-CNRS, Campus Luminy, Case 913, F 13 288 Marseille, France. QQ22-3654/83/2Q87-4142$01.5QIQ
of the parameters (absolute temperature, supersaturation, and residual and foreign gas pressure). The crystals were grown on a substrate made either of copper, aluminum, or stainless steel (V2A). Its temperature was controlled by a Peltier element, which could either cool or heat. The chambers were saturated with water vapor from a large ice surface kept a t constant temperature. The supersaturation, the crucial parameter in experiments under pure water vapor conditions, was derived from the measured temperature difference between the substrate and the ice surface saturating the cell. However, due to the high precision necessary (on the order of some millikelvin), these measurements gave no information about the zero point of supersaturation. This point had to be estimated from rate data. Further details of the chambers have been given e l s e ~ h e r e . ~ J ~ For the nucleation of the crystals, a trick was used. If the substrate is cooled to achieve the high supersaturations necessary for nucleation, the crystals will grow too much while the substrate is reheated to the moderate working (1) For a review see P. V. Hobbs, "Ice Physics", Clarendon Press, Oxford, 1974, Chapter 8. (2) R. Lacmann and I. N. Stranski, J . Cryst. Growth, 13/14, 236 (1972). (3) T. Kuroda and R. Lacmann, J . Cryst. Growth, 56, 189 (1982). (4) B. F. Ryan, E. R. Wishart, and D. E. Shaw, J. Atmos. Sci, 33,842 (1976). (9) N. Fukuta, J. Atmos. Sci., 26, 522 (1969). (6) A. Yamashita, Kisho Kenkyu Noto, 123, 813 (1974). (7) D. Shaw and B. J. Mason, Phil. Mag., 46, 249 (1955). (8) D. Lamb and W. D. Scott, J . Cryst. Growth, 12, 21 (1972); D. Lamb, Disseration, University of Washington, Seattle, 1970. (9) W. Beckmann, Disseration, TU Braunschweis, 1981. (10)W. Beckmann, J . Cryst. Growth, 58, 425 (1982).
0 1983 American Chemical
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