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Conductivity of ice by a guarded potential probe method
Solid State Communications, Vol. 6, PP. 663-664, 1968. Pergamon Press.
Printed in Great Britain
CONDUCTIVITY OF ICE BY A GUARDED POTENTIAL PROBE METHOD B. Bullemer, I. Eisele, H. Engelhardt, N. Riehi and P. Seige Physik-Department der Technischen Hochschule Mtinchen, Germany (Received 24 April 1968; in revised form 6 June 1968 by G. Busch)
Bulk and surface potentials have been determined separately. They are different in most cases. Bulk conductivity of pure ice is 1.5 x 10_ic (~.cm)~at -10°C, with an activation energy of 8. 5 ~ 0. 5 kcal/mole.
ELECTRODES that inject only limited quantities of charge carriers cause a major part of the difficulties encountered in conductivity measurements. This is especially the case In ice where the carriers to be injected are protons (and/or possibly OW by -ions). If the intrinsic carried away the electric field are protons not replaced by a sufficient number of protons injected from the anode the intrinsic OH- (~~+ ~ ~.i. ) form a negative space charge giving a drop of potential near the anode. On the other hand protons not readily discharged or absorbed can yield a drop of potential near the cathode. Potential probe measurements are widely used to assign electric
into cylinders (15 cm long and 4. 4 cm dia. with c-direction along the axis). These stood on a palladium coated cathode with a guard ring and supported a heating ring on top to melt the top centimeter of Ice. An immersed palladium sheet served to contact the water anode. (10 cm2) Three probes (Pd-wire 0. 5 mm) and their guard rings (Pd-coated copper tubes 3 mm long, 10 mm dia. were Introduced radially into the crystal reaching the cylinder axis (drilled holes, “water solder” or tight fit, longitudinal spacing of probe wires 1.5 cm, radial spacing 120°C, symmetrical position between anode and cathode). Only for an applied voltage V 1 of below 10 V are potentials along the cylinder axis strictly linear from anode to cathode. Large potential drops are found at both electrodes as V1, increases to larger than 10 V (Fig. 1). The slopes of potential profiles yield the bulk electric field: Eb (V,) < V. /d (= for V. < 10 V only). Surface potentials were determined with guard rings disconnected from the unity gain amplifier. For all voltages applied in these experiments (V1 = 108V maximum) the results show a linear variation of the surface potential from anode to cathode; i. e. surface field E1 does not depend on distance from the electrodes: E1 = V1 /d. It is easily seen that the electric field may have a radial component everywhere in the crystal except along the axis and in a plane parallel to the electrodes, where surface and bulk potentials are equal. In other words the bulk current lines form a bottle neck for V1 of above 10 V. This is expressed in the bulk current versus field plot by an ohmic behaviour up to 0. 65 V/cm. The slope is proportional to the square root of Eb after the bottle neck is formed. It saturates above 3 V/cm, the
fields correctly to their currents. In ice surface currents, due to the “waterlike” surface layer, are so importanti that conventional potential probe experiments primarily yield information on surface potentials (different from the bulk values in general). Using a sample geometry such that the surface resistance between the electrodes is as large as possible compared with the bulk resistance, it should be possible to filter bulk potential drop and bulk conductivity from the data. 2 That means in any case to separate a small effect (bulk) from a large one (surface), Instead we preferred a direct method: Each potential probe is protected by a guard ring. The probe drives a unity gain amplifier (Keithley 610 B, max. 100 V, 100 ~A secondary) which applies the bulk potential to the guard ring. Consequently the probe is prevented from “seeing’ the surface potential. Our method was first used to test a water anode, which has been assumed to be an ideal proton injector (compare reference 3). The samples were pure Co2-free ice single crystals (compare reference 4) cut on a lathe 663
664
CONDUCTIVITY OF ICE
plot becoming linear gain. To calculate the 1c f-ri cm_i at bulk conductivity (o = section 1. 5 x 1O_ 10°C), the low field should be used, as only there does the simple relation between electrode area and current density hold. Temperature dependence of bulk conductivity is 8. 5 ± 0.5 kcal/mole (between -9 and -20°C), a value determined earlier by two of the present authors 1 and verified since by Durand, Deleplanque and Kahane for temperatures ranging from -30 to -70°C.5
Vol. 6, No. 9
V ~(Vo~ts) Water
-
Ice
£0
Surface currents are known to surpass bulk currents in the temperature range considered here 1 Using water electrodes the effect is even more pronounced due to an almost ideal coupling between electrode and the “waterlike” surface layer. (I,~ 100. lb at 13°C; and by extrapolation L = lb at -25 °C). Surface current activation energies from 26 to 30 kcal/ mole were found for different samples.
20’~~ ----__~
1O_~___ x~rrj
-
The numerous drawbacks inherent in the use of water electrodes (temperature gradients, a limited voltage and temperature range) seem to be complemented by another most serious
FIG. 1 problem: limited proton injecting ability. The method just described will be applied to various types of electrodes, and we hope to report results soon.
References 1.
BULLEMER B. and RIEHL N., 7, 248 (1968).
Solid State Commun. 4, 447 (1966); Phys. Kondens. Materie —
_______________________
2.
JACCARD C., Z. Angew. Math. Phys. 17, 657 (1966).
3.
EIGEN M., DE MAEYER L. and SPATZ H. -Ch.,
4.
ENGELHARDT H. and RIEHL N.,
5.
DURAND M., DELEPLANQUE M. and KAHANE A., Solid State Commun. 5, 759 (1967).
Ber. Bunsenges. Phys. Chem. 68, 19 (1964).
Phys. Kondens. Materie 5, 73 (1966).
Volumen und Oberflächenpotentiale wurden unabhangig von einander untersucht. Sie sind meist deutlich verschieden. Die Volumenleitfahigkeit des reinen Eises betrgt 1,5. 1O~ (Q .cm)1 bei -10°C, die zugehörige Aktivierungsenergie 8, 5 ± 0, 5 kcal/mol.
Printed in Great Britain
CONDUCTIVITY OF ICE BY A GUARDED POTENTIAL PROBE METHOD B. Bullemer, I. Eisele, H. Engelhardt, N. Riehi and P. Seige Physik-Department der Technischen Hochschule Mtinchen, Germany (Received 24 April 1968; in revised form 6 June 1968 by G. Busch)
Bulk and surface potentials have been determined separately. They are different in most cases. Bulk conductivity of pure ice is 1.5 x 10_ic (~.cm)~at -10°C, with an activation energy of 8. 5 ~ 0. 5 kcal/mole.
ELECTRODES that inject only limited quantities of charge carriers cause a major part of the difficulties encountered in conductivity measurements. This is especially the case In ice where the carriers to be injected are protons (and/or possibly OW by -ions). If the intrinsic carried away the electric field are protons not replaced by a sufficient number of protons injected from the anode the intrinsic OH- (~~+ ~ ~.i. ) form a negative space charge giving a drop of potential near the anode. On the other hand protons not readily discharged or absorbed can yield a drop of potential near the cathode. Potential probe measurements are widely used to assign electric
into cylinders (15 cm long and 4. 4 cm dia. with c-direction along the axis). These stood on a palladium coated cathode with a guard ring and supported a heating ring on top to melt the top centimeter of Ice. An immersed palladium sheet served to contact the water anode. (10 cm2) Three probes (Pd-wire 0. 5 mm) and their guard rings (Pd-coated copper tubes 3 mm long, 10 mm dia. were Introduced radially into the crystal reaching the cylinder axis (drilled holes, “water solder” or tight fit, longitudinal spacing of probe wires 1.5 cm, radial spacing 120°C, symmetrical position between anode and cathode). Only for an applied voltage V 1 of below 10 V are potentials along the cylinder axis strictly linear from anode to cathode. Large potential drops are found at both electrodes as V1, increases to larger than 10 V (Fig. 1). The slopes of potential profiles yield the bulk electric field: Eb (V,) < V. /d (= for V. < 10 V only). Surface potentials were determined with guard rings disconnected from the unity gain amplifier. For all voltages applied in these experiments (V1 = 108V maximum) the results show a linear variation of the surface potential from anode to cathode; i. e. surface field E1 does not depend on distance from the electrodes: E1 = V1 /d. It is easily seen that the electric field may have a radial component everywhere in the crystal except along the axis and in a plane parallel to the electrodes, where surface and bulk potentials are equal. In other words the bulk current lines form a bottle neck for V1 of above 10 V. This is expressed in the bulk current versus field plot by an ohmic behaviour up to 0. 65 V/cm. The slope is proportional to the square root of Eb after the bottle neck is formed. It saturates above 3 V/cm, the
fields correctly to their currents. In ice surface currents, due to the “waterlike” surface layer, are so importanti that conventional potential probe experiments primarily yield information on surface potentials (different from the bulk values in general). Using a sample geometry such that the surface resistance between the electrodes is as large as possible compared with the bulk resistance, it should be possible to filter bulk potential drop and bulk conductivity from the data. 2 That means in any case to separate a small effect (bulk) from a large one (surface), Instead we preferred a direct method: Each potential probe is protected by a guard ring. The probe drives a unity gain amplifier (Keithley 610 B, max. 100 V, 100 ~A secondary) which applies the bulk potential to the guard ring. Consequently the probe is prevented from “seeing’ the surface potential. Our method was first used to test a water anode, which has been assumed to be an ideal proton injector (compare reference 3). The samples were pure Co2-free ice single crystals (compare reference 4) cut on a lathe 663
664
CONDUCTIVITY OF ICE
plot becoming linear gain. To calculate the 1c f-ri cm_i at bulk conductivity (o = section 1. 5 x 1O_ 10°C), the low field should be used, as only there does the simple relation between electrode area and current density hold. Temperature dependence of bulk conductivity is 8. 5 ± 0.5 kcal/mole (between -9 and -20°C), a value determined earlier by two of the present authors 1 and verified since by Durand, Deleplanque and Kahane for temperatures ranging from -30 to -70°C.5
Vol. 6, No. 9
V ~(Vo~ts) Water
-
Ice
£0
Surface currents are known to surpass bulk currents in the temperature range considered here 1 Using water electrodes the effect is even more pronounced due to an almost ideal coupling between electrode and the “waterlike” surface layer. (I,~ 100. lb at 13°C; and by extrapolation L = lb at -25 °C). Surface current activation energies from 26 to 30 kcal/ mole were found for different samples.
20’~~ ----__~
1O_~___ x~rrj
-
The numerous drawbacks inherent in the use of water electrodes (temperature gradients, a limited voltage and temperature range) seem to be complemented by another most serious
FIG. 1 problem: limited proton injecting ability. The method just described will be applied to various types of electrodes, and we hope to report results soon.
References 1.
BULLEMER B. and RIEHL N., 7, 248 (1968).
Solid State Commun. 4, 447 (1966); Phys. Kondens. Materie —
_______________________
2.
JACCARD C., Z. Angew. Math. Phys. 17, 657 (1966).
3.
EIGEN M., DE MAEYER L. and SPATZ H. -Ch.,
4.
ENGELHARDT H. and RIEHL N.,
5.
DURAND M., DELEPLANQUE M. and KAHANE A., Solid State Commun. 5, 759 (1967).
Ber. Bunsenges. Phys. Chem. 68, 19 (1964).
Phys. Kondens. Materie 5, 73 (1966).
Volumen und Oberflächenpotentiale wurden unabhangig von einander untersucht. Sie sind meist deutlich verschieden. Die Volumenleitfahigkeit des reinen Eises betrgt 1,5. 1O~ (Q .cm)1 bei -10°C, die zugehörige Aktivierungsenergie 8, 5 ± 0, 5 kcal/mol.