ELECTRIC CHARACTERISTICS OF POINT DEFECTS IN HCl-DOPED ICE

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ELECTRIC CHARACTERISTICS OF POINT DEFECTS IN HCl-DOPED ICE

I. Takei, N. Maeno

To cite this version:

I. Takei, N. Maeno. ELECTRIC CHARACTERISTICS OF POINT DEFECTS IN HCl-DOPED ICE. Journal de Physique Colloques, 1987, 48 (C1), pp.C1-121-C1-126. �10.1051/jphyscol:1987118�.

�jpa-00226262�

JOURNAL DE PHYSIQUE

Colloque C1, suppl6ment a u no 3, Tome 48, mars 1987

ELECTRIC CHARACTERISTICS OF POINT DEFECTS IN HC1-DOPED ICE

I. TAKE1 and N. MAENO

The Institute of Low Temperature Sciences, Hokkaido University, Sapporo 060, Japan

RQsum6 - Les charges effectives des d6fauts de Bjerrum et ioniques ont 6th estim6es

$a partir de la variation du courant avec la temp6rature dans le cas de la glace pure : DL = 0.374e and e f = 0,626 e. A partir de ces charges effectives et des conductivit6s mesur6es pour la glace dop6e avec HC1, les composantes de la conductivit6 due aux d6fauts ponctuels ont 6th obtenues ; elles montrent l'existence d'une zone de recouvrement dans le comportement des d6fauts avec un 6change des r8les entre les deux types de d6fauts ponctuels. Les analyses ont donne 1'6nergie de dissociation de HC1 dans la glace 0,65 2 0,018 eV et les Bnergies de migration des d6faut.s L et des d6fauts ioniques positifs sont respectivement 0,190 1: 0,017 et pratiquement 261-0.

Abstract - Effective charges of Bjerrum and ionic defects were estimated from temperature dependences of the dispersion strength of pure ice: eDL=0.374e and ef=0.626e. From those effective charges and measured conductivities of HC1-doped ice, conductivity components of point defects were derived, showing the existence of a crossover behavior, which is an exchange of roles between two types of point defects. Analyses gave the dissociation energy of HC1 in ice 0.65f0.018 eV and migration energies of L and positive ionic defects are 0.190f0.017 eV and nearly zero respective1 y.

I. I m O D u m I o N

Electrical properties of ice have been explained in terms of two kinds of point defects which are ionic defects (OH-, ~ ~and Bjerrum defects 0 ~ ) ( D and L).E11 The present authors[21 showed that electrical properties of single crystals of ice are affected by small amounts of HC1, and suggested a complete dissociation of HC1 at higher temperatures and that with some

activation energy at lower temperatures; but the relation of HC1 and point defects was

not sufficiently clear. ₁₀

In this work, effective charges of p o i n t d e f e c t s a r e d e t e r m i n e d f r o m temperature dependences of the dispersion strength of pure ice and conductivity components of each point defect are 2

estimated from electrical parameters of HC1- doped ice measured in a wide temperature

$

range. A detailed description of samples a n d m e a s u r i n g a p p a r a t u s i s g i v e n elsewhere.[2,31

11. EFFECTIVE CHARGES OF POINT DEFECTS IN 0

I I I I

A d -

- AK = A

T -To -

- A : C = 2 . 4 1 ~ 1 0 ~ ~ ^{A .&} ,&"'& -

T,= 2.2K e A @'

- o : C = 2 . 3 0 ~ 1 0 ~ ~ " &@ - b = 4 8 . 7 K A,A ,y do'

,,o' -

pure ice -

, ,fl A A : c L -

o * : C i , -

..'" I..'. I I I I

ICE 0 100 2 0 0

A. Dispersion strength of pure ice temperature ( K ) The temperature dependence of the FIG. 1. Temperature dependences dispersion strength of ice has been measured of the reciprocal of dispersion by many workersC4-81 but their results are strength of pure ice (circle:cu n o t s i m i l a r p r o b a b l y b e c a u s e m o s t and triangle: CL ).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987118

C1-122 JOURNAL DE PHYSIQUE

measurements were conducted in higher temperature ranges. Our data, Fig.1, show that Curie-Weiss law and Curie law are applied respectively in d~rections parallel and perpendicular to the c-axis. The Curie constant and Curie point in the Curie- Weiss law are respectively 2 . 3 0 ~ 1 0 ~ K and 48.7 K. The Curie constant in the Curie law is 2 . 4 1 ~ 1 0 ~ K. The anisotropy amounts to 14% at -lo°C, which increases with decreasing temperature, e.g. 22% at -90°c.

B. Effective charges of point defects

Effective charges of point defects were estimated with Onsager and Dupuis' method 191 from the temperature dependence of the dispersion. Values of effective dipole moment and charge were respectively VM=2.87D and eDL=0.374e in the c-axis, and+,=2.93D and eDL=0.383e in the perpendicular direction. Here e is the elementary charge ( l . 6 x l 0 - ~ ~ C). From the definition of effective charges, e=eDL+e+, w e get e+=0.626e and 0.617e in the directions parallel and perpendicular to the c-axis respectively. The results are summarized in Table I.

Table I. Effective charges of point defects.

Investigators Date eL/e

e ~ ~ / e

Jaccard [I51 1959 0.565 0.435

Onsager & Dupuis [91 1962

. .

. . . ^0.48

Jaccard 110 1 1964 0.45(c,,) 0.55(c,,)

0.49(cs) 0.51(cz)

Worz & Cole 141 1969

...

B~lgram & Granicher [I91 1978 0.75 0.25

Camplin et al. [I61 1978 0.730 0.438

Hubmann [I81 1979 0.62+0.01 0.3810.01

Scheiner & Nagle [201 1983

...

Takei & Maeno 1986 0.626(c11) 0.374(c,)

(present work) 0.617(~r) 0.383(~~)

111. BEHAVIORS OF W I N T DEFECTS IN HC1-DOPED ICE A. Conductivity components of point defects

According to the Jaccard theory [ 10 I, electrical parameters of ice are approximately described by the following equations:

~ , - o ~ = ( ~ , / e , - ~ ~ ~ / e ~ ~ ) ~ / ( u + / e + ~ + a - - D L / ~ D L 2 , (3) and A ~ ~ = ( o , / e , - o ~ ~ / e ~ ~ ) 2 / ( ~ O @ ( ~ + / e - ? '+aDL/e 2 , ) (4)

D L Here a+= 5+ + 5 -, ODL= OD +OL and

where ni and ui are respectively the concentration and mobility of each defect, and om and G o are high-frequency and dc conductivities respectively, A K ~ is dispersion strength, and $ i s a product of a constant and absolute temperature.

From Eqs. (1) and ( 2 ) , 5 DL and 5* are given as follows:

and (0.,-5, )+2o0e, /ei{(o,-0,) (5,-50+400eDLek/e2))t] ( 7 ) These equations give two values for each conductivity component.

Figure 2 shows the temperature dependence of 0, and G O for HC1-doped ice (sample B: grown from 4x10-~ mol/l HC1 solution) in the temperature range from -loOc

FIG. 2. Temperature dependences of high-frequency (triangle) and dc (circle) conductivities of HC1-doped ice (sample B, grown from 4x10-~ mol/l HC1 solution) in the c-axis direction.

FIG. 3. Temperature dependences of conductivity components of Bjerrum (triangle) and ionic (circle) defects. Sample B.

to - 1 5 0 ~ ~ . Owand DO are respectively limiting values of Debye dispersion. Above -30°c, O m decreases and G o is constant with decreasing temperature; in the range from -30°C to - 1 1 0 ~ ~ 0, and u 0 are nearly equal to each other and decrease with decreasing temperature; below - 1 1 0 ~ ~ 0,becomes larger than GO.

Figure 3 shows the temperature dependence of ODL and a + obtained by using Eqs.

( 6 ) and (7). Circles and triangles show a+ and ODL. The temperature dependences a r e rather complicated and suggest an occurrence of a crossover[lll at which two kinds of point defects exchange their roles.

B. C r o s s o v e r p h e n o m e n o n of HC1-doped ice

Figure 4 shows temperature dependences o ~ A for pure ice and samples B and E K ~ (E: grown from 4 x 1 0 - ~ mol/l HC1 solution). Sample B shows small values around -40°C and -80°c, suggesting the occurrence of a crossover.

If conductivity components of defects satisfy the next relation:

0 +/e+= 0 DL/eD,, (8)

then the D;bye dispersion strength and a difference between the high-frequency and dc conductivities vanish:

A K D = 0, a, - 0 0 = 0. ( 9 )

When Omand O 0 are close, A K and Oi/ei are important values for determining major mechanisms. The complex temperature dependence of conductivity components (sample B, Fig.3) can be explained reasonably with using the concept of a crossover.

If we consider that a crossover occurs at the temperatures above mentioned, we get a relation shown in Fig.5: OJe? > uDL/eDL from -3g0c to -84Oc. Here Ui/ei was chosen instead of ui because the crossover condition is suitably described. The conductivity components of Bjerrum defects give activation energies 0.56420.024 eV above -45OC, 0.175L0.017 eV from -45OC to - 1 2 0 ~ ~ . and 0.25420.019 eV below - 1 2 0 ~ ~ . On the other hand, those of ionic defects give nearly zero energy above -45Oc and 0.310+0.009 eV below -45Oc.

IV. DISCUSSION

In general oi/ei is written as

Cl-124 JOURNAL DE PHYSIQUE

where A is a constant, :E the formation energy, E? the migration energy of defect i.

It was shown in Fig.5 that the activation energy of O+/e+ is nearly zero at higher temperatures and 0.310f0.009 eV at lower temperatures; The same result was confirmed for other samples A with a crossover (Fig.6) and E without a crossover (Fig.7). The zero activation energy at higher temperatures can be explained as follows: the concentration of H ~ O + is constant because HC1 at higher temperatures dissociates completely[21 and the migration energy :E is zero. Then we can describe

u+/et of sample B as

0 +/ei = A'/T ( > -40°c) (11)

and 0 +/e+ = (AW/T)exp(-EC1- f 0+/2kT) ( < -40°c) (12)

FIG. 4. Temperature dependences of dispersion strength of pure ice and HC1-doped ice (B and E g r o w n f r o m 4 x 1 0 - ~ mol/l HC1 solution).

FIG. 5. Temperature dependences of c o n d u c t i v i t y - c o m p o n e n t s divided by effective charges (eDL=0.374e a n d e =0.626e). f Sample B. This sample shows two crossover-points at - 3 9 O ~ and -84Oc.

where A' and A" are constants. Using Eq.(12), w e get the dissociation energy ~ ~ 0 ' from HC1 in ice, 0.650+0.018 eV. This value is different from previous values 13.6 kcal/mol (0.59 eV) by Young and Salomonll21, 12.2 kcal/mol (0.53 eV, KC1 doped ice) by Maeno[b31 and 2x6.7 kcal/mol (0.58 eV) by Gross[l4]; these values were directly derived from activation energies of the dc conductivity.

The temperature dependence of ODL/eDL is more complex than of O*/e*. In a higher temperature region, oDL/eDL glves the activation energy of 0.564i0.024 eV (Fig.5). This value agrees with that of pure and low-concentration samples; oDL/eDL at higher temperatures is attributed to intrinsic DL defects excited thermally. In a temperature range from -40°c to - 1 2 0 ~ ~ oDL/eDL gives the activation energy of 0.175k0.017 eV in Fig.5. Comparing samples A and B (Fig.6), a difference in ODL/eDL at these temperatures corresponds to that in constant values O+/e* at higher temperatures. This suggests that the concentration of extrinsic L deTects liberated from HC1 is proportional to that of HC1 and that the activation energy of ODL/eDL in this range corresponds to that of migration. In a lower temperature range below

-120°c, oDL/eqL gives the activation energy of 0.254+0.019 eV (Fig.5). A similar value was obtalned for ODL/eDL of sample E in a low temperature range below -90°c

(Fig.7).

From Eq.(lO), 0 DL/eDL of sample B can be described as

and ,,/e,,= ( B " / T ) ~ * P ( - ( ( ~ / ~ ) E ~ - ~ + E ~ ) /kT) ( < - 1 2 0 ~ ~ ) (15)

where B, B' and B" are constants. Data analyses by use of Eq.(14) give the migration energy, ,:E of L defect, 0.191+0.017 eV. The value of ( 1 / 2 ) ~ f D ~ + E ; ~ is 0.585+_0.024 eV. Then the formation energy of intrinsic DL defects, EEL, is 0.790+_0.082 eV. If we assume that the temperature dependence of aDL/eDL below

o : Ut/e?

sample A I d "

y~

FIG. 6. Temperature dependences of conductivity-components divided by effective charges (eDL=0.374e and ek=0.626e). Sample A, grown from 1 x 1 0 - ~ mol/l HC1 solution. This sample shows two crossover-points at - 3 2 O ~ and -76O~. Broken lines refer to sample B.

'$ 0.568.0.058eV

5

FIG. 7. Temperature dependences of conductivity-components divided by effective charges (eDL=0.374e and e+=0.626e). S a m p l e E. This sample does not show crossover.

Broken lines refer to sample B.

.,lo"- ?Ji0

7 N '5

5 ^10"-

lo" -

.-

0

$ldO-

109 - a : doL/eoL

- 1 2 0 ~ ~ is caused by some trap mechanism, the liberation energy, EEaX, is 0.152+0.072 eV because (1/2)E; X+~: =0.266+_0.019 eV. These values are summarized in Table 11.

The obtained'migration energy of L defect is smaller. than previous values.

However, Jaccardtl51 obtained his value not from a temperature dependence of a conductivity component of L defects but from that of the whole high-frequency conductivity of HF-doped ice; Camplin et a1.[161 obtained their value from a temperature dependence of conductivity components of L defects of HF-doped ice, but their measurements were carried out above -80°c and they only found a crossover at a high-temperature side.

The highest concentration sample A (grown from l x l ~ - ~ mol/l HC1 solution), gives ~ + / e * = 3 . 5 4 ~ 1 0 ~ ~ m2/vsm3 at -loOc, and its conductivity plateau suggests a complet-e dissociation of HC1. Then the HC1 concentration of sample A is 2.7x10-~

Cl-126 JOURNAL DE PHYSIQUE

mol/l if we assume the mobility is 2.4x10-~ m2/vs 1171; similar procedure shows the HC1 concentration of sample B is 1.0x10-~ mol/l.

Table 11. Activation energies of point defects in ice.

( 1/2 )EiL+EEL 0.585k0.024 eV

Formation energy of DL defects ( EEL ) 0.790k0.082 eV Migration energy of L defects ( !E ) 0.190k0.017 eV Liberation energy of L defects

from unknown trap (E:.~ )

Migration energy of ~ ~ 0 ' ( :E ) =O eV

Dissociation energy of HC1 ( ~ g ~ ) - ~ ~ 0.650f0.018 eV ~ +

ACKNOWLEDGMENTS

The authors thank Prof. Y. Suzuki, Prof. G. Wakahama and Dr. T. Kuroda of the Institute of Low Temperature Science, Hokkaido University, for valuable discussions.

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