Title

Electrical Properties of Ice Doped with Different Electrolytes

Author(s)Levi, Laura

Citation

Physics of Snow and Ice : proceedings, 1(1), 159-172

Issue Date

1967

Doc URL

http://hdl.handle.net/2115/20294

Typebulletin (article)

Note

International Conference on Low Temperature Science. I. Conference on Physics of Snow and Ice, II. Conference on
Cryobiology. (August, 14-19, 1966, Sapporo, Japan)

File Information1̲p159-172.pdf

Instructions for use

Hokkaido University Collection of Scholarly and Academic Papers : HUSCAPElectrical Properties of Ice Doped with Different Electrolytes
Laura LEVI*
Instituto de Ffsica de la Atmosfera Departamento de Meteorologia
Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina

Abstract
The electrical properties of ice doped with the series of hydracids from HF to HI, with NH3
and with NH3 and HF in different ratios were studied.
In most cases the ,DC conductivity was measured. The similarity of the results obtained underthese conditions for ice doped with different hydracids indicates that these monovalent anions playa similar role in the ~;ystal lattice in spite of their different diameters.
A comparison of the behaviour of the ice+HF+NH3 system with that of ice+HF and ice+NH3
shows that, as a first approximation, the general laws of electrolytes may be applied to doped ice.
An estimation is obtained of the dissociation constants involved and of the ratio p_Ip+ between
the mobility of OH- and H 30+ ions.
Ice doped with NH3 and, in a few cases, ice doped with NH4F were also studied by an AC
method. The results indicate that the concentration in the lattice of Bjerrum defects of D type isslightly increased by the presence of NH3. An estimation was obtained of the corresponding dissociation constants and of the ratio PDI PL, between the mobility of D and L defects. The estimationshows that PDI PL < 1. This may be caus~d by the higher formation energy of the D defects thanthat of the L defects.

I. Introduction
The electrical properties of ice are related to the presence of certain types of latticedefects, i.e. of ions H30+, OH- and of Bjerrum defects D, L (doubly occupied and vacantbonds) and it was established that the proton mobility is several orders higher than theusual mobility of ions in solids. Thus, the presence of electrolytes may substantiallymodify the electric properties of the crystals only if it modifies the concentration ofthese defects.
The most thorough studies of the electric behaviour of doped ice were performed
with HF as the dopant (Griinicher, 1963; Jaccard, 1959) .. This electrolyte has been accepted to be one of the most suitable lattce modifiers because of the similarity in diameterand number of electrons between F and 0 atoms. Thus HF may be considered to replace
H 20 molecules in the lattice, increasing the concentration of H30+ ions and L defects
in accordance with the following processes HF+H 20";' H30+ +F-(1)

HF=HFD+L .

(2)

In eq. (2) we have used Onsager's notation (Onsager and Dupuis, 1960; Onsager,* Present address:

Carrera del Investigador, Consejo Nacional de Investigaciones, Rivadavia
1917, Buenos Aires, Argentina.

160

L. LEVI

1962) for the association of HF with a D defect and the corresponding dissociation of
the vacant hydrogen bond created in the' lattice by ~he structure of this molecule.
A symmetrical behaviour could be expected for ice doped with NH3 ; actually also N
and 0 atoms are similar in diameter and NH3 molecules (or NH: ions) may be assumed
to enter the ice lattice substitutionally with respect to H 20, giving place to the processes
analogous to eqs. (1) and (2):NH3+H20~NH: +HO-(3)

NH3 = NH3L+ D .

(4)

On the other hand, studies of impurity segregation of ice growing from different
electrolytic solutions (Jaccard and Levi, 1961; De Micheli and Iribarne, 1963) have shownthat neither the ratio between the solid and ~ liquid concentration (segregation factor S)
nor the value of maximum concentration which may be obtained in ice, are mainly determined by the diameter of the impurity atoms. Actually the factor S has the sameorder of magnitude for all the hydracids from HF to HI (Levi and Arias, 1964) (between
50 and 500 according to concentration, with a maximum near 103 for ice doped with HI)
though the atomic diameter of the anion increases from 1.36 to 2.16 A; on the contrary,
the segregation is much higher for NH3 (up to 104) in spite of the observed similarity
III diameter between Nand O.
In the present work the electric behaviour of doped ice is discussed in the following
cases:
1) Ice doped with the series of the hydracides, from HF to HI, to investigate theimportance of the atomic diameter in the role played by the impurity molecules in thelattice;2) Ice doped with NH3 to obtain information on the processes given by eqs. (3) and(4) and on the mobility of OH- ions and D defects;3) Ice doped with HF and NH3 in different ratios, which was assumed to allow
a direct comparison between the values of the three dissociation constants involved (ofthe acid, the base and of ice considered as a solvent) and between the mobility of defects
of opposite sign, i. e. of ions H30 + and OH- and of Bjerrum defects D and L.

II. Results and Discussion
EXPERIMENTAL METHODS

Ice was grown in polyethylene tubes approximately 2.4 cm in diameter by immersion
III a bath of cold alcohol, at a speed of 0.5 to 4p/sec.
In mosi: cases the solution was
gently stirred during growth to maintain a homogeneous concentration. Ice doped with
NH3 was better obtained without stirring.
The actual concentration of the electrolyte in the samples was measured after melting.
Generally the concentration was determined by the measurement of electrical conductivityof melted ice, using a calibrated conductivity c~ll. In the case of ice doped with HF
and NH3 in different ratios, the amperometric titration and the Nessler method wereused for the determination of the concentrations of F- and NH: respectively. As an
auxiliary method, pH measurements were also performed.
For the electrical measurements in ice, Pt electrodes were mounted on the surface

161

ELECTRICAL PROPERTIES OF DOPED ICEof the sample by heating in such a way as to allow the surface to melt slightly andrefreeze.
To reduce the errors due to the formation of the space charges near the electrodes,
the DC measurements were usually made by an oscillograph used as a voltmeter, so thatthe instantaneous voltage, when the field was applied, could be determined on a known
resistance connected in series with the ice. In high concentrations of the electrolytes,
especially for ice doped with NH3, the transient effects were negligible and a galvanometercould be used for the measurements.
Potential differe~tes of 45 to 90 V were applied on samples usually about 1 cm thick.
In the special case of ice doped with HF + NH3 samples up to 3:"'4 cm of thickness wereused to make possible the more complex analysis of the melted ice.
For the AC measurements we used a General Radio Capacitance Bridge (model
1610-3) including a guard circuit which eliminates the capacitance of the enclosure andleads connected to the ui:J.known capacitor. Owing t~ the low capacitance 'and highdissipation factor of the ice samples, the "substitution method" was used, where theunknown capacitor is connected across the precision capacitor of the bridge.
Before beginning the measurements, the samples, were maintained for several hours
at the desired temperature.
RESULTSa)

Ice doped with hydracids

The results obtained in ice doped with hydracids (Levi and Arias, 1964) are plottedin Fig. 1, curve (1). In Fig. 1, the logarithm of the conductivity (} of different samples
is plotted against the logarithm of the concentration C, at t= -17°C. It may be notedthat all of the experimental values corresponding to the different hydracids are distributed
along the same curve.
In low concentrations, the curve may be considered as a straight line with a slop~
equal to 1/2. In this range, the conductivity may be expressed by(} = rCl/2 ,(5)where r=5 X 10- 15 ohm-I cml / 2 • For concentrations between 5 xlO- 4 and 10- 2 N, the experimental points deviate from the straight line and are scattered along the inferior branchof the curve, which seems to tend to have a constant value. In the range of higher
concentrations, the conductivity increases again, showing the distribution expressed by
the eq. (5). However, the results are more dispersed in this region and the ice begins
to loose its transparency.
Some experiments were also performed using acids of more complex molecules anddifferent valence, such as HN0 3, H 2S0 4, H 3B03. It was observed that the behaviour of
ice doped with HN0 3 was similar to that of ice doped with hydracids. The concentration
obtained in ice grown from solutions of H 2S0 4 was less reproducible and the values ofconductivity of doped ice was lower and more dispersed than that of hydracids. As for
H 3B03, its dissociation in water is low and it does not change the conductivity of ice
in-a measurable way.
These results indicate that monovalent anions of very different structure and diameter,
such as F- and NO; may playa similar role in the crystal lattice. As for H 2S0 4, probably

162

L. LEVI

similar mechanisms may exist which bring about the dispersion of the results, both insegregation and conductivity.
It is interesting to note that these results have been recently confirmed by Gross(1965) who obtained, for ice doped with HF, a curve of conductivity at :""15°C, which
nearly coincides with the curve of Fig. 1 for concentrations < 10- 2N. Gross is of
the opinion that only the straight part of the curve is significant and represents his
results by a law of the type (5) with r=1xlO-4(mol/I)--1/2ohm-lcm-l=4xlO-150hm-1
cm 1/ 2. This author considered that the divergence of data from the straight line observedin high concentrations resulted from intergranular precipitation of the electrolyte, whichcaused the opacity of the samples. However, a careful analysis of the experimental
results given by Gross indicates that the change of slope of the curve begins, as in ourcase, in concentrations near 5 X 10- 4N, where ice generally is observed to be transparent.
This behaviour will be discussed later. In the present paragraph, we suggest that the
reproducibility of results in crysta.ls obtained in different growth conditions may indicate
the possibility that the increase of conductivity in high concentrations could be limited
by some effects closely related to the structure of the lattice.
b)

Ice doped with NHa

The electrical behaviour or Ice doped with NH3 has been studied by AC (Arias etat., i966) and DC (Levi and Lubart, 1961) methods.

lOll' u(ohm~cm.')
+-HF

A-HCl
e-HBr

x-HI

0+

+

+

lo~. G(ohm~' c.ni~]

Fig. 1.

DC conductivity of ice doped with hydracids (curve 1) and withNH3 (curve 2) as a function of concentration

ELECTRICAL PROPERTIES OF DOPED ICE

163

JOQU
7

3

2

9

io
o

\

IT

\
\

\

1~------2L------L------L---~~--'lO-Q~V
Fig. 2.

Ice doped with NH3, C=8xlO- 5 N. Curves (a) and (b), dielectric constantand curves (a ') and (b / ), conductivity at -10 and -25°C, respectively

log (e.-Coo)

LogG

.3

9

10

Fig. 3.

Ice doped with NH 3, C=5xlO- 4 N. Curves (a) and (b), dielectric constantand curves (a / ) and (b / ), conductivity at -10 and -25°C, respectively

164

L. LEVIl09(£ -£0»

(0')

--~

--~
(c')
__
~

_ _

J!

X

J

3

)1

V

)

,I: X

3

2

o

\

-,

IT

,
\

\

,

\
\
\

\

T~------~----~~----~-L__~~~'~~

ogl!

Fig. 4.

Ice doped with NH3, C=6x1O- 2 N. Curves (a), (b) and (e), dielectric constantand curves (a'), (b') and (e'), conductivity at -10, -25 and -40°C, respectively

Figure 1, curve (2) shows the logarithmic curve of the DC conductivity, as a functionof the concentration, obtained at t= -10°C. The general behaviour is similar to thatobserved for ice doped with hydracids, though the values of conductivity are lower andthe inflection of the curve, at a concentration near 10- 3 N, is more obvious than thatof curve (1). Actually the conductivity attains at this concentration a value of about
10- 7 ohm- 1 cm- 1 and then remains constant for a further increase of the concentration.
In tl;1e concentrations C<10- 3 N, the eq .. (5) may be applied with r=8xlO- 17 ohm- 1
1 2
cm / • It must be noted that the conductivity is about two orders of magnitude lower
than that of ice doped with hydracides in the same concentrations.
The frequency dependencies of the dielectric constant and conductivity for ice samples
doped with different concentrations of NH3 are shown in Figs. 2 to 4. In each figure,curves a, b, c, and a', b', c', represent the real dielectric constant (e(w)-e oo ), and conductivity a(w) measured as a function of the frequency, at different temperatures (-10,-25 and -40°C). It may be noted that at t= -10°C, the curves of the dielectric constantnearly coincide with that of pure ice (Figs. 2 to 4). For all the concentrations the static
dielectric constant is es = 100 and the main inflection may be seen near the Debye frequency, liD =4 X 103 c/sec. However, for concentrations C> 10- 4 N, some divergence fromthe Debye dispersion is observed, marked by a secondary inflection at about 104 c/sec(curves (a) in Figs. 3 and 4). This divergence increases with the decreasing temperature.
At t= -25°C and C;;;: 10- 4 N, the dielectric constant tends to a static value of about 50-

165

ELECTRICAL PROPERTIES OF DOPED ICE

70 (curves (b) of Figs. 3 and 4); also the inflection near the Debye frequency 1S more
indeterminate than in the pure ice, probably indicating the existence of more than one
relaxation time. Finally, in curve (c) of Fig. 4, obtained at -40°C, the slope of thecurve changes slowly and the value of the dielectric constant at the Debye frequency
for pure ice (vn = 250 c/sec) is still about 10, so that a static dielectric constant es = 20
may be expected.
On the other hand, the average slope of the conductivity curves decreases with theincreasing NH3 concentration, because the high frequency conductivity a"" increases
slower than the low frequency conductivity a (which usually coincides with DC conductivity)*; then aja decreases with increasing concentration of NH3 though the differencea"" -a may be considered as nearly independent of the concentration. For C ~ 10- 3 N,

a and a are of the same order of magnitude. Table 1 gives the average values ofa"", a, (a"" -a)/a "" measured for different samples in concentrations ~ 10- 3 N, and thecorresponding values for pure ice.
Table 1.

Doped ice

Pure ice(J""(J

fIoo-a(Joo-(J°C

ohm-l.cm- 1

ohm-l.cm- 1

ohm-l.cm- 1

(J""

-10
-25
-40

32 x10- 8

10'X10- 822x10- 8

0.68

11 x10- 8

6x10- 85x10- 80.45

3.5x10- 8

2.5

xlO- 81x10- 80.28

-10

20 X10- 8

0.1

X10- 820x10- 8

1

-25

5

x10- 80.03

x10- 8

5X10- 8

1-40

1 X10- 8

0.007X10- 8

1xlO- 8

1

From this table an estimation of the activation energy of conductivity may beobtained; this is approximately Ea~0.35 eV, both for aoo and a. However a small difference between the activation energies of these conductivities is shown by the decreaseof the ratio (a"" -a)/a"" with the diminishing temperature and by the corresponding decrease of the static dielectric constant, observed previously. Actually, according to thetheory (Jaccard, 1964), es may be expressed bywhere a is a constant and T the absolute temperature.
c)

Ice doped with HF and NHa in different ratios

The system ice+HF+NH3 was studied in DC at -17"C. The results are give mcurve (1) of Fig. 5. In this figure, the abcissa shows the logarithm of the concentration
ratio [HF]/[NH3] (where [HF] and [NH3] are the concentrations of the corresponding
electrolyte) and the ordinate the logarithm of the reduced conductivity a/aD, where aD isthe conductivity of pure ice (ao=5X10- 1o at -17°C).

* The DC conductivity is indicated byof pure ice.

(J,

because (Jo will be used to indicate the DC conductivity

166

L. LEVI

Fig. 5.

DC conductivity of the system ice+HF+NH3 as a function ofconcentration ratio; (1), experimental curve; (2) and (3), theoretical curves. Values of the constant in Table 4 was used for
calculation of curve (3)The results indicate (Levi, Milman and Suraski, 1963) that, in the range of 10- 2 .;;;
[HF]/[NH3] ';;;5, the conductivity of the system may be considered as independent of thetotal concentration of the samples, being only a function of the concentration ratio. The
graph shows two ascending branches, the conductivity increasing for F excess (rightbranch) and NH3 excess (left branch). The latter was indicated by a dash line because
the experimental results were more uncertain in this range, due to difficulties in thechemical analysis of the samples. The conductivity is particularly sensitive to small
variations in the concentration around the equivalence point ([HF] = [NH 3]), where a/ap
~50.
The curve passes through a minimum for a small excess of NH3, where somesamples show a conductivity relatively close to that of pure ice. For concentration ratios[HF]/[NH3]';;; 10- 2 or [HF]/[NH3] ;;;'10, the conductivity approximately coincides with thatof ice doped with NH3 or HF alone, in the same total concentrations.
A few experiments were also performed in A~ on samples obtained from NH4F
solutions, in high concentrations. In Table 2, the results obtained for C-1O- 2 N (-20°C)
are compared with the corresponding ones for pure ice. The low frequency conductivity
a coincides with that of the equivalence point in DC, showing that [NH3] = [HF]. Both
Table 2.
(J

(J",

IJn

ohm- l cm- lohm- l cm- l

c/sec

Doped ice

1 X 10- 8

5xlO-7100

8X103

Pure ice

3x10- 105xlO- 8

100

8x102

167

ELECTRICAL PROPERTIES OF DOPED ICE(J and ).In (De bye frequency) are about one order of magnitude higher than for pure ice.
DISCUSSION

According to the theory of the electric behaviour of ice (Jaccard, 1964), based on
the mechanism of proton transfer, the AC and h.f. conductivities may be expressed
as functions of partial specific conductivities d± and (JnL of ionic and Bjerrum defects
by the equations:(7)(8)

where e± and enL are the electric charge carried by defects,

e± ,...., enL """ (e*/2) ,(9)and e* is the proton charge.
For pure ice, it has been shown that ((J",,/o)""" ((Jndo±)""" 102 and eqs. (7) and (8) may
be simplified by
(10)
(11)
The ratio (J.,,/(J is generally reduced in doped Ice. However, it has been shown that,with a few exceptions,· the simplified expressions (10) and (11) may be applied, as a first
approximation, in doped .ice, so that (J and (J "" may be considered respe~tively proportional
to the mobility and concentrationof ions and· Bjerrum defects.
,a)Dissociation of hydmcids and NHa in ice

According to the experimental results, it may be considered that the approximate
expressions (10) and (11) are generally valid for ice doped with hydracids, in a wide
range of concentrations and for ice doped with NH 3, in concentrations C <10- 3N. Thus,
the proportionality between conductivity and the square root of concentration given byeq. (5) indicates that the electrolytes are dissociat~d according to the mass action law,and the constant r (which we will indicate by rHA and rNH3 for hydracids and NH3,
respectively) is given byrHA =/1.+'; KHA

rNH3 =/1. _.; KNH3

(12)

,

(13)

'

where /1.+' /1._ are the mobility of H30+ and OH-· ions and K HA , K NH , the dissociation
constants for hydracids and for NH3.
Table 3.
The estimated values of the dissociation constants KHA and K NH , at -17°C
are given in Table 3. In this table, thecomputation of KHA was made by the

8 X 10- 2 cm2/V. sec
1/10 ............. ,. 1

3.6X10- 10 ···1.2X10- 9 mol/1
3.8x 10- 12 ···1.5X 10- 13 mol/l

1at-17°CJ

use of data of the proton mobility (/1.+ .
+/1.J obtained by Eigen De Maeyer and Spatz (1964) a.nd of an estimated value of/1._//1.+, which ranges from 1/10 to 1. (The value of /1._//1.+ will be discussed later). The
value of K NH , at -17°C was calculated taking ,into account the activation energy fordissociation E = 2Eq,....,0.7 eV.

168

L. LEVI

On the other hand, the reduction in ·slope of the conductivity curves for a concentration between 5 X 10- 2 and 10- 1 N, observed both for hydracids and for NH3, suggests
the existance of some effect limiting the number of charge carriers in ice. This phenomenon may be explained by Onsager's hypothesis (1960, 1962) that a fraction of ionsformed by dissociation should combine with Bjerrum defects of the opposite sign, forming
trapped ions which do not take part in the process of the electrical conduction. In thesehigh concentrations, this effect may be important enough to reduce and eventually tostop the increase of the conductivity. However, one mu~t not exclude the possibility ofother effects that might reduce the increase of conductivity such as the formation of
aggregates of impurity molecules in the solid or similar phenomena.
It may be shown that, if the observed effect is mainly due to the trapping effect,the equilibrium constants K HL , and K OIlD , for dissociation of trapped ions in free ions,and Bjerrum defects would coincide with the concentration of the electrolyte, in theregion where the inflection of the conductivity curves is observed (Levi and Arias,
1964). However, if other phenomena were also important, these constants would behigher arid we may put

1
J ;;;. 5 X 10- 4 mol/l
OHD,

KIlL,

K

(14)

It may be noted that according to these results, the fraction of trapped ions in pure ice
would be negligible (,,;;; 1/100 of the totai ion concentration). On the other hand, if theupper limit in eq. (14) is considered, the values of dissociation constants which satisfy theexperimental results would be about three times higher than the values given in Table 3.
b)

Ice doped with HF and NHa in different ratios and dissociation constants involved

Finally, the behaviour of electrolytes in ice crystals may be discussed taking into
account the results obtained for the system ice+NH3+HF, studied as a function of theconcentration ratio of the electrolytes.
It may be easily shown, using the classic theory of electrolytes (Glasston, 1937), thatthe behaviour of such a system, treated as an electrolytic solution of a weak acid anda weak base, is in a qualitative agreement with the experimental results given by curve(1), Fig. 5 (Levi et al., 1963). The higher dissociation of the hydracid with respect tothe base, obtained by the separate study of ice doped with these electrolytes is confirmedby the following facts:
1) the slope of the conductivity curve is high in the rig ion where [HF]>[NH3] ;2) the value of conductivity at the .equivalence point is more than one order of magnitude
higher than the conductivity of pure ice;3) the position of the minimum of the curve, corresponds to a low excess of NH3 concentration.
Table 4.
According to the theory, the conductivity ofthe system depends on the concentration ratio
Curve (2) Curve (3)[HF]/[NH3] and on the parameters KHF/ K NH , ~nd
KIlF/KNH,
200200
K HF /'; K o , where ffo is the concentration of
KHF/-./ Ko28
90
H30+ and OH" in pure ice. Curves (2) and (3)169ELECTRICAL PROPERTIES OF DOPED ICEin Fig. 5 represent two theoretical approximations of curve (1), calculated for the valuesof the parameters given in Table 4.
On the other hand, KHF(=KHA ) and K NH , were obtained independently in Table 3.
According to the most recent results (Eigen et al., 1964); ..; Ko is(15)
The value of this constant at -l7°C may be calculated within an interval of uncertainty,
due to the different values of the activation energy of pure ice conductivity, given by
the bibliography. As the value of the activation energy varies from E=0.47 e V (Eigen,
De Maeyer and Spatz, 1964) to E = 1 e V (Heinmets and Blum, 1962), the value of ..; Ko
at t= -17°C may range between

8 X 10- 11 ,,;; ..; Ko ,,;; 4.6 X 10- 11(15')

Taking these results into account we obtain, at this, temperature, the values of theparameters given in Table 5. In the first column they were calculated directly from
Table 3, while in columns 2 and 3 the trapping effect was taken into account, withK HL , = K oHD , = 5 X 14 -4 mol/I. In column 3 the special values of the parameters whichcorrespond to tl_/tl+ =1/7 were indicated. Here the uncertainty of the parameter

KHF/ffo depends only on that of ..; Ko given by eq. (15').
Table 5.
No trapping eff.

With trapping eff.

With trapping eff.

p_/ p +

10-1..· 1

10-1.·· 1

1/7

KHF/KNH,
KHFf./ Ko

95

95 ... 8x103

190... 8x103

4.5 ···26

13.5 ···78

15···26

Comparing Table 5 with Table 4, we observe that a good concordance is obtainedfor KHF/KNH" if we assume tl_/tl+ = 1/7. If the highest value of KHFN Ko in Table 5
is taken in these condition, both parameters approximate those of curve (2) in Fig. 5. A
better approximation would be obtained if a higher value could be assigned to the lastparameter, as it is shown by curve (3) in the same figure.
c)

AC measurements zn ice doped with NHa and dissociation constants of Bjerrum
defects

The DC behaviour of ice doped with NH3 has been interpreted in the previous
paragraphs considering for all the concentrations, aDL>a±. The validity of this assumption is not immediately evident, but it results easily from the application of eqs. (6), (7)and (8) to the conditions a",>a and O:s>O, which are valid in all the studied range.
On the other hand, the slow increase of aoo with NH3 concentration shown in Figs. 2 to
4 indicates that the specific conductivity of Bjerrum defects aDL depends slightly on
this concentration, i.e. that the dissociation constant KNH3D corresponding to the process(4) is small. To obtain an estimation of this constant, we have applied eqs. (7) and (8) to
calculate aDL for C_1O- 3N; considering the concentration of L defects to be small
with respect to that of D defects we may write

170

L. LEVI(16)
The mobility ttD has not been evaluated directly, but all the results indicate that it isprobably lower than ttL (Jaccard, 1959; Bryant and Fletcher, 1965). If we assume that(17)

we obtain
1 X 10- 4 ;;;;, KNH,D ;;;;, 1 X 10- 6 mol/l .

(18)

These results may be compared with the behaviour in AC observed for. ice dopedwith NH4F: Zaromb and Brill (1956) and Camp (1963) have shown in their previous workthat the relaxation time and the corresponding activation energy for ice doped with NH4F
are lower than for pure ice. This behaviour may be confirmed by the results given in
Table 2. They show that, for C"'10- 2 N, both (J"" and )lD increase by a factor 10 withrespect to their value in pure ice. Since previous results indicate that L defects arecompletely dissociated from HF molecules in ice doped' with NH 4F, process (2) must
prevail with respect to process (4). Then, assuming the complete dissociation of L defects
and the dissociation according to the mass action law for D defects, we obtain(19)
where C L is the concentration of L defects and KDL the product of equilibrium concentrations of D and L defects in ice.

Considering the results in Table 2, we may put

CL''' 10'; KDL for CNH ,F"'10-2 N and replacing in eq. (19) we have(20)

If we compare eq. (20) with eq. (18) and we take into account previous results on
L defect mobility, we finally have, for temperatures near "":'10°C:
KNH,D ' " 10-d)

4 mol/I;

ttD ' " (1/10), ttL'" 1 X 10-

5

cm2/V. sec .

(21)

Conclusions

The results given In Table 5 and the comparison of eqs. (18) and (20) indicate thatthe electric behaviour of doped ice may be interpreted by the approximation that theprocesses (1) to (4) take place in the lattice. However, some discrepancy exists in theestimation of some parameters, as e.g. KHFN K o , KNH,N Ko. Actually, if we attempt
to completely justify the shape of the curve (1) in Fig. 5, these parameters should be
about three times higher than those obtained from the experimental results.
At present there is not enough information to discuss the causes of this difference
exhaustively. They could be at least partially related to the uncertainty of measurementsin pure ice. Actually, it has been frequently observed that the complete e.limination of
impurities from distilled water is very difficult, and there is a possibility that the electric
properties of ice may be modified by the existence of minute amounts of chemical impurities. In the most recent works on pure ice conductivity considerable care has beentaken in the purification of water used in these experiments. However, the different
values of activation energy obtained by different authors indicate that some errors could
still exist in the results. On the other hand, the interpretation of the behaviour of doped

ELECTRICAL PROPERTIES OF DOPED ICE

171

ice could be considered to be oversimplified. For instance, the hypothesis that the Impurity molecules can incorporate substitutionally with H 20 molecules in iee crystal lattice
may be only partially correct. Actually, it would be difficult to apply it in a similar
way to molecules similar in diameter to H 20 molecules, as HF, and much bigger andof different features as HNOs. It may also be interesting to note in the present discussionthat recent studies of diffusion in ice made by Camp (1963), Kopp, Barnaal and Lowe(1965), have shown that the diffusion coefficient of HF and NH4F are several orders higher
than the coefficient of autodiffusion of H 20 molecules; this could possibly indicate thatinterstitial molecules play some role in the observed phenomena.
Independently of these considerations, the results show that an asymmetry exists
between the behaviour of ice doped with HF (or hydracids in general) and with NH3 •This assymetry is related to the different values of the dissociation constants and of themobilities of simIlar defects of opposite sign.
It may be especially noted that the results given in eq. (21) support the hypothesisthat fJ.D is lower than fJ.L and probably near to (1/10) fJ.L. A slightly higher value for thismobility has been obtained by Bryant and Fletcher (1965) who measured the thermoelectriceffect in ice doped with HF and with NH3 • They found fJ.D/fJ.L=1/2. At present, none
. of these results may be considered as completely reliable and similar causes of errors in
the theoretical interpretation of the phenomena could be important in both cases.
Considering these different results we will state(1/10) fJ.L ~ fJ.D ~ (1/2) fJ.L

(22)

On the other hand, theoretical calculations of the energy of formation of Bjerrum
defects in pure ice show that a considerable distortion of the lattice must take place,specially around defects of the type D (Cohan et al., 1962; Cohan and Weissmann, 1964).
This would not probably be the case for L defects and could be a cause of the above
asymmetry.
The author wishes to thank D. Arias, L. Lubart, O. Milman and E. Suraski for theircollaboration in different parts of this work and M. Weissmann for valuable discussions.
She also acknowledges the support received from the Consejo Nacional de Investigaciones Cientificas y Tecnicas (Argentina).

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