- Email: [email protected]
The diffusion of helium through ice
Solid State Communications, Vol.8, pp.1459—l46l,197O.
Pergamon Press.
Printed in Great Britain
ThE DIFFUSION OF HELIUM ThROUGH ICE
J.
Gordon Davy
*
and Keith W. Miller t
Department of Chemistry, University of California, Berkeley, California 9473). (Received 24 June 1970 by C.W. McCombie)
The diffusion coefficient of helium along the c-axis of single crystals of ice has been found to be of the order of 10 cm2sec’ at —10°C. This result is discussed in the light of current theories of the diffusion of H 20 in ice.
ThE DIFFUSION of helium through a number of crystalline solids at elevated temperatures has been reported. These studies have included diamond, silicon, germanium,’ beryl, aquamarine, 2 tridymite and crystobalite.3 All these quartz, have relatively open structures leaving crystals considerable interstitial space, a property they share with ice. It seemed possible therefore that helium might diffuse along the open channels of ice that have a diameter of about 2.4A and run parallel to the c-axis, but the limitations imposed by the low melting temperature of ice appear to have discouraged experimental investigations, The present study confirms that helium does indeed diffuse through ice.
anisms involved. The results of exploratory experiments designed to test the feasibility of such investigations are reported here. Single crystals of ice were grown in cylindrical stainless steel tubes, 1 cm long x 1 cm diameter, by a method previously described. The crystals grew with the c-axis aligned axially in the tube, and the crystallographic orientation and homogeneity were checked between crossed polaroids. Stainless steel probe tubes, co-axial with the tube surrounding the ice crystal, were frozen into the two flat surfaces of the ice crystal. An outer jacket, concentric with these probe tubes, was sealed onto them and the cylinder surrounding the ice crystal by buna-N ‘0’ ring compression seals. The two outer jackets thus ~
Recently, self-diffusion in ice has been studied with the conclusion that whole H 20 4 molecules are involved in the diffusion process. Several mechanisms have been invoked to explain this result. That of Onsager and Runnels5 postu lates that molecules diffuse several steps in the interstitial space before occupying a new lattice site; others propose vacancy or defect mechanisms.6 The study of the diffusion of small gas molecules through the interstitial space of ice may lead to a further understanding of the mechanisms involved. The results of explanatory
formed supported probes A gas burette containingthe helium at securely. atmospheric pressure was connected to one probe tube. It was verified that the helium collected in the other probe tube had not leaked around the ice crystal by measuring the helium partial pressure in the outer jackets as well as in the receiving probe. The whole apparatus was kept in a cold room maintained at 10°C.In general, experiments lasted several weeks. From time to time, samples were taken by connecting a sampling vessel of known volume to one or other of the three sampling —
Present address: David Sarnoff Research Center, RCA, Princeton, N.J. 08540. ~Present address : Physical Chemistry Laboratory, South Parks Road, Oxford. *
ports (i.e. the receiving probe and two outer jackets). The partial pressurethe of helium present was estimated by connecting sampling vessel 1459
1460
THE DIFFUSION OF HELIUM THROUGH ICE
via a standard leak to a suitably calibrated mass spectrometer. Consistent and reproducible results were obtained for two different single crystals, giving a permeability coefficient of 3.0 ±0.3 x 1O~’atoms cm~sec~’ atm~.We would expect the absolute accuracy to be lower than indicated by the variation between experiments, and the main source of error is ~robably an inevitable loss of helium from the receiving probe during such a long experiment.
Vol.8, No. 18
An alternative, and perhaps better approach, is to compare the diffusion coefficients of helium through various solids at their melting poi nts when lattice motions are more closely equivalent. Results for single crystals of silicon (m.p. 1683K) and germanium (m.p. 1220K) have been obtained close to the melting point. Short extrapolation of these data yield helium diffusion coefficients of the order of lO5cm2sec1. Data for a-crystobalite (m.p. 1968K) and a-tridymite (m.p. 1976K) require rather long extrapolation to the melting point, but nonetheless also yield values of the order of 105cm2sec~. Considering the large difference in absolute temperature these results are remarkably close to our value for helium in ice just below the melting point.
In order to obtain the diffusion coefficient, the solubility of helium in ice is required. Two estimates are available; one from freezing point data~ the other from direct measurement. 10 These give solubilities of 5 x 107 and 4 x 1017 atoms He/cm~ ice/atm He respectively, yielding a value for the diffusion of helium through ice at 10°C of about 6 x 107cm2 sec-1.
If the diffusion coefficient of neon at the melting point gives a fair indication of the rate
—
Table I
Ice reference 12 He H 20 Ne *
263K
2.63
10~
275 2.78
10h1 —
Dcm2 sec a-Tridymite ~ 263K
m.p.*
101~
10~ —
1020
1o~
Fused Silica13 263K 10~ —
1013
10~ —
io~
Data obtained by long extrapolation
This diffusion coefficient may be compared (Table 1) with those in related solids at 10°C. Ice, which has a root mean square vibrational amplitude of about 0.4 A at 10°C,~ allows more rapid passage of helium than a-tridymite which has channels (2.2— 2.6 A) bounded by six membered rin~ of Si04 tetrahedra; the diffusion coefficient in ice is more comparable to that for fused silica with various sized channels3 bounded We by up similarities to eight S04 tetrahedra. alsorings noteofthe in the ratios of the diffusion coefficients for helium to water in ice and for helium to neon (whose diameter is close to water’s) in a-tridymite and in fused silica, —
—
of interstitial diffusion of whole water molecules, then for H20 in ice interstitial diffusion is faster than that calculated for defect diffusion alone. The contribution of interstitial diffusion would thus lead to an increase in the overall diffusion coefficient in the manner postulated by Onsager and Runnels ~ to account for the low diffusion coefficient predicted by the defect model. On the basis of the present data, such conclusion must be regarded as extremely ten-a tative, but our results do indicate that accurate measurements, including anistropy and temperature dependence, of the diffusion coefficients of He3, He4 and Ne in ice would provide a
Vol.8, No. 18
THE DIFFUSION OF HELIUM THROUGH ICE
useful method of investigating the mechanism of diffusion in ice. Acknowledgements We wish to acknowledge helpful discussions with Professors J.H. Hildebrand and G.A. Somorjai. The work was —
1461
supported by a grant from the National Science Foundation administered by J.H.H. and by the Inorganic Materials Research Division of the Lawrence Radiation Laboratory, which operates under ,the auspices of the U.S. Atomic Energy Commisss
REFERENCES 1.
LUTHER L.C. and MOORE W.J., J. Chem. Phys. 41, 1018 (1964).
2. 3.
BRANDT R.M. and HALTORI M., J. Chem. Phys. 42,, 1826 (1965). BARRER R.M. and VAUGHAN DEW., Trans. Faraday.Soc. 63, 2275 (1967).
4. 5. 6.
KUHN W. and THURKAUF M., Helv. Chim. Acta. 41, 938 (1958). ONSAGER 11. and RUNNELS L.K., Proc. Nat. Acad. Sci. U.s. 50, 208 (1963) and J. Chem. Phys. 50, 1095 (1969). HASS C., Phys. Leit. 3, 126 (1962).
7. 8.
SIKSNA R., Ark. Fyi. 11, 495 (1957). DAVY J.G., University of California Radiation Laboratory Report, UCRL 19133 (1970).
9. 10.
NAMIOT A.Yv. and BUKHGALTER E.B., 3. Struct. Chem. 5, 759 (1967). KAHANE A., KLINGER J. and PHILIPPE M., Solid State Comrnuu. 7, 1055 (1969).
11. 12.
OWSTON PG., Ad~’.Phys. 7, 171 (1958). PIEFcOTTI R.A., J. Phys. Chem. 69, 281 (1965).
13.
SWETS D.E., LEE R.W. and FRANK R.C., J. Chem, Phys. 34, 17 (1961).
Le coefficient de diffusion de l’helium le long de l’axe c d’un seul cristal de glace est reporté etre de l’ordre de 10~cm2sec~ a —10°C. Le résultat est discuté a la lumiére des theories courantes de la diffusion de H20 dans la glace.
Pergamon Press.
Printed in Great Britain
ThE DIFFUSION OF HELIUM ThROUGH ICE
J.
Gordon Davy
*
and Keith W. Miller t
Department of Chemistry, University of California, Berkeley, California 9473). (Received 24 June 1970 by C.W. McCombie)
The diffusion coefficient of helium along the c-axis of single crystals of ice has been found to be of the order of 10 cm2sec’ at —10°C. This result is discussed in the light of current theories of the diffusion of H 20 in ice.
ThE DIFFUSION of helium through a number of crystalline solids at elevated temperatures has been reported. These studies have included diamond, silicon, germanium,’ beryl, aquamarine, 2 tridymite and crystobalite.3 All these quartz, have relatively open structures leaving crystals considerable interstitial space, a property they share with ice. It seemed possible therefore that helium might diffuse along the open channels of ice that have a diameter of about 2.4A and run parallel to the c-axis, but the limitations imposed by the low melting temperature of ice appear to have discouraged experimental investigations, The present study confirms that helium does indeed diffuse through ice.
anisms involved. The results of exploratory experiments designed to test the feasibility of such investigations are reported here. Single crystals of ice were grown in cylindrical stainless steel tubes, 1 cm long x 1 cm diameter, by a method previously described. The crystals grew with the c-axis aligned axially in the tube, and the crystallographic orientation and homogeneity were checked between crossed polaroids. Stainless steel probe tubes, co-axial with the tube surrounding the ice crystal, were frozen into the two flat surfaces of the ice crystal. An outer jacket, concentric with these probe tubes, was sealed onto them and the cylinder surrounding the ice crystal by buna-N ‘0’ ring compression seals. The two outer jackets thus ~
Recently, self-diffusion in ice has been studied with the conclusion that whole H 20 4 molecules are involved in the diffusion process. Several mechanisms have been invoked to explain this result. That of Onsager and Runnels5 postu lates that molecules diffuse several steps in the interstitial space before occupying a new lattice site; others propose vacancy or defect mechanisms.6 The study of the diffusion of small gas molecules through the interstitial space of ice may lead to a further understanding of the mechanisms involved. The results of explanatory
formed supported probes A gas burette containingthe helium at securely. atmospheric pressure was connected to one probe tube. It was verified that the helium collected in the other probe tube had not leaked around the ice crystal by measuring the helium partial pressure in the outer jackets as well as in the receiving probe. The whole apparatus was kept in a cold room maintained at 10°C.In general, experiments lasted several weeks. From time to time, samples were taken by connecting a sampling vessel of known volume to one or other of the three sampling —
Present address: David Sarnoff Research Center, RCA, Princeton, N.J. 08540. ~Present address : Physical Chemistry Laboratory, South Parks Road, Oxford. *
ports (i.e. the receiving probe and two outer jackets). The partial pressurethe of helium present was estimated by connecting sampling vessel 1459
1460
THE DIFFUSION OF HELIUM THROUGH ICE
via a standard leak to a suitably calibrated mass spectrometer. Consistent and reproducible results were obtained for two different single crystals, giving a permeability coefficient of 3.0 ±0.3 x 1O~’atoms cm~sec~’ atm~.We would expect the absolute accuracy to be lower than indicated by the variation between experiments, and the main source of error is ~robably an inevitable loss of helium from the receiving probe during such a long experiment.
Vol.8, No. 18
An alternative, and perhaps better approach, is to compare the diffusion coefficients of helium through various solids at their melting poi nts when lattice motions are more closely equivalent. Results for single crystals of silicon (m.p. 1683K) and germanium (m.p. 1220K) have been obtained close to the melting point. Short extrapolation of these data yield helium diffusion coefficients of the order of lO5cm2sec1. Data for a-crystobalite (m.p. 1968K) and a-tridymite (m.p. 1976K) require rather long extrapolation to the melting point, but nonetheless also yield values of the order of 105cm2sec~. Considering the large difference in absolute temperature these results are remarkably close to our value for helium in ice just below the melting point.
In order to obtain the diffusion coefficient, the solubility of helium in ice is required. Two estimates are available; one from freezing point data~ the other from direct measurement. 10 These give solubilities of 5 x 107 and 4 x 1017 atoms He/cm~ ice/atm He respectively, yielding a value for the diffusion of helium through ice at 10°C of about 6 x 107cm2 sec-1.
If the diffusion coefficient of neon at the melting point gives a fair indication of the rate
—
Table I
Ice reference 12 He H 20 Ne *
263K
2.63
10~
275 2.78
10h1 —
Dcm2 sec a-Tridymite ~ 263K
m.p.*
101~
10~ —
1020
1o~
Fused Silica13 263K 10~ —
1013
10~ —
io~
Data obtained by long extrapolation
This diffusion coefficient may be compared (Table 1) with those in related solids at 10°C. Ice, which has a root mean square vibrational amplitude of about 0.4 A at 10°C,~ allows more rapid passage of helium than a-tridymite which has channels (2.2— 2.6 A) bounded by six membered rin~ of Si04 tetrahedra; the diffusion coefficient in ice is more comparable to that for fused silica with various sized channels3 bounded We by up similarities to eight S04 tetrahedra. alsorings noteofthe in the ratios of the diffusion coefficients for helium to water in ice and for helium to neon (whose diameter is close to water’s) in a-tridymite and in fused silica, —
—
of interstitial diffusion of whole water molecules, then for H20 in ice interstitial diffusion is faster than that calculated for defect diffusion alone. The contribution of interstitial diffusion would thus lead to an increase in the overall diffusion coefficient in the manner postulated by Onsager and Runnels ~ to account for the low diffusion coefficient predicted by the defect model. On the basis of the present data, such conclusion must be regarded as extremely ten-a tative, but our results do indicate that accurate measurements, including anistropy and temperature dependence, of the diffusion coefficients of He3, He4 and Ne in ice would provide a
Vol.8, No. 18
THE DIFFUSION OF HELIUM THROUGH ICE
useful method of investigating the mechanism of diffusion in ice. Acknowledgements We wish to acknowledge helpful discussions with Professors J.H. Hildebrand and G.A. Somorjai. The work was —
1461
supported by a grant from the National Science Foundation administered by J.H.H. and by the Inorganic Materials Research Division of the Lawrence Radiation Laboratory, which operates under ,the auspices of the U.S. Atomic Energy Commisss
REFERENCES 1.
LUTHER L.C. and MOORE W.J., J. Chem. Phys. 41, 1018 (1964).
2. 3.
BRANDT R.M. and HALTORI M., J. Chem. Phys. 42,, 1826 (1965). BARRER R.M. and VAUGHAN DEW., Trans. Faraday.Soc. 63, 2275 (1967).
4. 5. 6.
KUHN W. and THURKAUF M., Helv. Chim. Acta. 41, 938 (1958). ONSAGER 11. and RUNNELS L.K., Proc. Nat. Acad. Sci. U.s. 50, 208 (1963) and J. Chem. Phys. 50, 1095 (1969). HASS C., Phys. Leit. 3, 126 (1962).
7. 8.
SIKSNA R., Ark. Fyi. 11, 495 (1957). DAVY J.G., University of California Radiation Laboratory Report, UCRL 19133 (1970).
9. 10.
NAMIOT A.Yv. and BUKHGALTER E.B., 3. Struct. Chem. 5, 759 (1967). KAHANE A., KLINGER J. and PHILIPPE M., Solid State Comrnuu. 7, 1055 (1969).
11. 12.
OWSTON PG., Ad~’.Phys. 7, 171 (1958). PIEFcOTTI R.A., J. Phys. Chem. 69, 281 (1965).
13.
SWETS D.E., LEE R.W. and FRANK R.C., J. Chem, Phys. 34, 17 (1961).
Le coefficient de diffusion de l’helium le long de l’axe c d’un seul cristal de glace est reporté etre de l’ordre de 10~cm2sec~ a —10°C. Le résultat est discuté a la lumiére des theories courantes de la diffusion de H20 dans la glace.