THEORETICAL AND EXPERIMENTAL STUDY OF PURE AND DOPED ICE Ih BY THE METHOD OF THERMALLY STIMULATED DEPOLARIZATION

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THEORETICAL AND EXPERIMENTAL STUDY OF PURE AND DOPED ICE Ih BY THE METHOD OF

THERMALLY STIMULATED DEPOLARIZATION

A. Zaretskii, V. Petrenko, A. Trukhanov, E. Aziev, M. Tonkonogov

To cite this version:

A. Zaretskii, V. Petrenko, A. Trukhanov, E. Aziev, M. Tonkonogov. THEORETICAL AND EX- PERIMENTAL STUDY OF PURE AND DOPED ICE Ih BY THE METHOD OF THERMALLY STIMULATED DEPOLARIZATION. Journal de Physique Colloques, 1987, 48 (C1), pp.C1-87-C1-91.

�10.1051/jphyscol:1987112�. �jpa-00226256�

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JOURNAL D E PHYSIQUE

Colloque C1, suppl6ment au no 3, Tome 48, mars 1987

THEORETICAL AND EXPERIMENTAL STUDY OF PURE AND DOPED ICE I h BY THE METHOD OF THERMALLY STIMULATED DEPOLARIZATION

A.V. ZARETSKII, V.F. PETRENKO, A.V. TRUKHANOV, E.A. AZIEV* and M.P. TONKONOGOV'

Institute of Solid State Physics, The USSR Academy of Sciences, Chernogolovka 142432, USSR, Moscow District

"~olitechnical Institute, Karaganda, Kazakh SSR, 470041 USSR

R6sum6 - Les theories concernant les courants de polarisation et de d6pola- risation stimule thermiquement ont BtB appliquees au cas de la glace 6tudi6e 2 ltaide dtune cellule 2 glectrodes ohmiques. Les resultats obtenus dif- ferent de ceux obtenus de maniere usuelle. De nouvelles donnees experimen- tales pour la glace dopee avec HC1 et NH4OH sont pr6sentBes.

Abstract - TSDC and TSPC theories have been proposed for ice with ohmic electrodes. The results obtained differ from those derived by a traditional approach. New experimental data for HC1 and NH40H doped ice are presented.

1. INTRODUCTION

The methods based on field induced thermally stimulated currents (FITSC) are deservedly well known and are widely used for studying many electronic and ionic conductors /2.3/. This is due to the high sensitivity of these methods and the com- paratively simple experimental equipment required. However, for analyzing the expe- rimental data it is necessary that the theory should be well developed allowing for both the subject of research and the conditions of .experiment. The list of papers devoted to the development of the theory is long, starting with the classical pioneering work of Bucci and Fieschi /4/. Insulators and dielectrics with electronic and ionic conductivities have been investigated. The first theoretical models for thermally stimulated depolarization currents (TSDC) (/5,6/ and for thermally polarization currents (TSPC) /5/ in ice have been worked out on the basis of the principles developed for standard conductors. It is commoun knowledge, that ice has specific electrical properties, (e.g. an electrical current passing through ice causes polarization of the lattice)/7/. In the first part of our work we propose the TSDC and TSPC theories for ice crystals with ideally ohmic electrodes, in the former case the peculiarity of ice being taken into account. Doped ice should be studied to compare theory and experiment. Though the experimental data obtained are in abundance /8,5,9/, there are still many discrepancies and even contradictions. One of the reasons for this is the study of a small number of concentrations, which sometimes differ much from each other. It is presumably this fact that results in the peak "tangling up". Thus we consider it extremely reasonable to analyze in detail the effect of doping on the FITSC spectra. This paper is assumed to present such an analysis and deals with the spectra of the TSDC in HC1-doped ice.

2. FITSC IN THE ICE WITH OHMIC ELECTRODES

Let us consider a plane ice capacitor (fig.

1).

The electric properties of ice are conditioned by the motion of four kinds of proton defects ionic (H30+ and O H ' ) and orientational (L and D) defects. To find FITSC it is necessary to write out a closed system of equations for all the quantities responsible for the current upon heating.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987112

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CI-88 JOURNAL DE PHYSIQUE

Fig.1. An i c e s a m p l e w i t h o h m i c e l e c t r o d e s .

OUMIC

I

^{I C E}

Assuming the electrodes to be ideally ohmic, we can believe that all the quantities are independent of the coordinates. We suppose here that ei and si are the effective charge and the conductivity of i-th defect (el = -e2, e3 = -e4, el+e3 = e ; e being the proton charge)

;

ji( t) is the projection of the flux density on x axis ; fi (t) and E are corresponding projections of the configuration vector and of the electric field strength on x axis. The values of i = 1.2.3.4 are associated with ionic H30+

and OH' defects and with orientational D and L defects : 1

_:

,

2 : ^f'-fl,

3

: IIDII,

4

:

"L". For the configurational vector from /7/ we have

:

where a1 = 1, a2 = -1, a3 = -1, a4 = 1. For the four phenomenological equations relating fluxes and thermodynamical forces we can write

:

Here: $ = 3.85 kg T roo /lo/; ro9 = 0.276 nm is the distance between Oxygen atoms, kg is the Boltzmann constant, T

1s

the temperature. fi (t =

0)

= 0 will be the initial condition for finding TSTP, and n ( t = 0) = no (in this case E = 0) -

for finding TSDC.

Assuming the heating linear proceeding at the rate H and using standard methods of calculation, we get for the bulk current density /7/

:

e~ '6")

JTSPC(T)/F = , s - - ^exp

^(-

-

H tD H

0

tD

SI SB

- ^-

^-)

^{exp (+} -

e1 eB

Heating starts with the temperature TO, t~ is the Debye time of relaxation, SI and sg are accordingly, partial conductivities of ionic and orientational defects and sO0 the high frequency conductivity of ice ; ep is the polarization charge

:

Regarding ice as an standard substance (i.e. , the configuration vector is neglec-

ted) with static conductivity SST and dielectric permittivity EST one could obtain:

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and also the following equations

:

Po

JTs~c(T) = - ^exp

^(-

- ¹

t~

JTSPC(T)/E = soo - - ^exp

^(-

^-1

FI t~ TI ^To ^t~

instead of eqs. (3) and (4).

A detailed comparative analysis of equations (3), (41, (7) and (8) has been done elsewhere. In this paper we would like to emphasize the following

:

1. Equations (31, (4) on the one hand and equations (4), (8) on the other coincide completely only in the presence of single type proton charge carriers.

2. The presence of defects of two types (for instance, H30+ and L) may give rise to quite different, sometimes extremely differing contrasting FITSC spectra calculated by the traditional theory (7), (8) aed by that proposed in this paper

( 3 1 , (4).

3. Even very low doping levels may considerably affect the type of the TSDC and TSPC speotra.

As is seen from eqs. (3) and (4), the current released on warming may be reversed in sign and flow in the direction opposite to that of the electric field. The physical sense of this inversion lies in the fact that unlike standard conductors, the flow of carriers in ice is defined both by the magnitude and direction of the electric field and by those of the configuration vector

(2).

To summarize it should be noted that creation of an ohmic contact on ice is a very complicated problem. For practical purposes the FITSC theory with partially or com- pletely blocking electrodes is undoubtedly more important. A certain success in the development of that theory accounts for much richer pattern of experimental TSDC and TSPC spectra as compared to those obtained on the basis of the theory suggested.

However the scope of the present publication does not permit us to consider this problem in detail.

3. EXPERIMENTAL STUDY OF THE HC1 - ^{DOPED ICE}

The ice samples with stainless steel electrodes were normally subjected to the ac- tion of an electric field of 1.105 ~ m - l (240 K) for 15 min. The cooling down to the temperature of liquid nitrogen was done at the rate of

rr/

20K min.-l. After the polarising field was switched off, the sample was heated at the rate of 2.4 ~min-l.

Details of the experimental procedure are described elsewhere.

Fig. 2 shows the TSDC speotra of the HC1-doped ice. The typical influence of NH40H doping on the TSDC spectra is shown in Fig. 3.

In Fig. 2 one can see that in HC1-doped crystals the TSDC exhibits a low-temperature (LT) peak, which changes appreciably with concentration. Peak 2

(

d l 2 0 K) is sub- jected to much less change. (To avoid misunderstanding it should be noted that our notation for TSDC peaks, as LT-peak and peak 2, may not coincide with the notation adopted by other authors). With changing of HC1 concentration, the peaks come closer and closer together (fig. 4) and the LT peak amplitude not only equals but even exceeds that of peak 2 (fig. 5).

Such an effect of doping on the TSDC spectra may be responsible for certain discrepancies between the data obtained by different authors and for widely different interpretations based on the nature of these peaks (see the analysis by Johari and Jones /6/).

We believe that peak 2, existing in a predominantly undoped (pure) and in weakly

doped ice is most likely caused by motion of L defects, responsible for the Debye

dispersion in this temperature range. This concept is confirmed by both the weak

dependence of the amplitude and peak location on the HC1 concentration (Figs 4 and

51, and shift of the peak to the low-temperature region when doped with HC1, and to

the high-temperature region, when doped with NH40H (Fig. 3).

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80 100 120 140 160 180

TEMPERATURE, K

UNWPED

Fig.3 'TSDC s p e c t r a of undpped a n d HC1- a n d NH OH- doped

ice. ⁴

Fig.2 TSDC s p e c t r a of HC1- doped ice. T h e s c a l e o n t h e current a x i s i s given for the lower graph. T h e shift of other s p e c t r a i s denoted by the correspondin.g horisontal sections.

LT Peak

Fig.4 Effect of HCl doping o n the temperature of the maxima of I/r p e a k and p e a k 2.

I t , , , , , ,

10%

lom

1022 1024

HCI Concentration,

m3

m -

D

9 E

0 U

go-

-7 I

U

1o18

loz0 loz2

1024

Hcl ~oncentrot1on.6~

i'-pk'

^L^{LT Peak}^I ^, ^, ^I ^, ^, Fig.5 E f f e c t of HCl doping o n the magnitude of L T p e a k and p e a k 2.

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The close to root growth of the LT peak amplitude with HC1 concentration is likely to be attributed to an increase in the ionic concentration upon doping. Indeed the HC1 doping of ice gives rise, as is show by Takei and Maeno /11/, to the root growth of H30+ ions in the temperature range under consideration. The ions may affect volume conductivity processes and also the formation of the space charge adjacent to electrode /12/.

Which of the processes affects the TSDC spectra the most remains to be investigated.

References

/1/ Vanderschueren J. and Gasiot J., in ttTherrnally Stimulated Relaxation in Solidstt, edited by P. Braunlich, Springer Verlag, Berlin, (1979), p. 135.

/2/ Braunlich P. (editor), "Thermally Stimulated Relaxation in Solids", Springer Verlag, Berlin, (1979).

/3/ Sessler G.M. (editor), "Electrets", Springer Verlag, Berlin

(

1980).

/4/ Bucci C. and Fiechi R., Phys. Rev. Lett., l2, (1964), 16.

/5/ Chamberlain J. and Fletcher N.H., Phys. Kondens. Mat., 2 (1971), 193.

/6/ Johari G.P. and Jones S.J., J. Chem. Phys., 62, (19741, 4213.

/7/ Jaccard C., Helv. Phys. Acta, 2, (1959), 89-128.

/8/ Pissis P., Apekis L. and Boudouris G., Nuovo Cimento, %, (19811, 365.

/ 9 /