ELECTROMIGRATION OF Ca2+ IN NaCl

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ELECTROMIGRATION OF Ca2+ IN NaCl

G. Brebec

To cite this version:

G. Brebec. ELECTROMIGRATION OF Ca2+ IN NaCl. Journal de Physique Colloques, 1973, 34

(C9), pp.C9-421-C9-423. �10.1051/jphyscol:1973970�. �jpa-00215446�

JOURNAL DE PHYSIQUE

Co//oque C9, supp/&ent au no 1 1-1 2 ,

Torlze

34, Novenrbre-Dicembre 1973, page C9-421

ELECTROMIGRATION OF Ca2+ IN NaCl

G . BREBEC

Section d e Recherches de Mitallurgie Physique,

Centre dYEtudes NuclCaires de Saclay, BP 2, 91190 Gif-sur-Yvette, France

RCsume. -

Nous decrivons une methode nouvelle pour l'etude de l'electromigration. Cette mkthode a Cte utilisee pour etudier l'electromigration du Cal- dans NaCI.

La charge efficace du calcium en solution dans NaCl a Cte trouvee egale

a 0,08

1 e I.

A

partir de nos resultats et en utilisant les vapeurs obtenues anterieurement sur la diffusion, la conductivite electrique et la relaxation dipolaire, nous avons pu calculer les cinq frkquences de saut de la lacune autour du calcium.

Abstract. - We describe a new method for studying electromigration. This method has been used to investigate the electromigration of Cazi in NaCI.

We found that the effective charge of solute calcium in NaCl is about

0.08

je I.

We have calculated the vacancy jump frequencies around a calcium ion from the present work and other data relative to diffusion, electric conductivity and electric relaxation.

As it can be seen o n the figure 1 five vacancy jump and pure crystals allow us t o calculate

w ,

a n d the frequencies are classically defined in a fcc dilute ratio

w,/1v3.

We have, indeed,

alloy [I].

w ,

is the jump frequency for the free vacancy

far from the impurity a n d w , t o

w ,

are the different I ,

D d o p e d crystal = - a - W 2

jump frequencies for the bounded vacancy. 3

where a is the anion - cation separation and

C,,

the equilibrium vacancy concentration.

-

F o r divalent impurities in NaCl reorientation dipoles experiments [2] showed that

w ,

is nearly equal to

w,.

-

Finally the generalized Nernst-Einstein equation derived by Manning [3] gives us a relation between

w , / M ~ ~

and

w o / w 4 .

For a divalent impurity in NaCl we have

:

This model is, of course, quite rough

;

firstly it does not take into account the solute vacancy inter- actions beyond the first neighboring positions and secondly it is assumed that there is only one kind of dissociative o r associative jumps. In metals by combin- ing the self diffusion, impurity diffusion and isotope effects data

it

is possible to get the three ratios

H , ~ / I ~ . , ,

w , / w , and

n~,/n~,.

I n ionic crystals

we

can obtain, in principle, the five jump frequencies as following

: - w10

can be determined by measuring the electric conductivity.

-

Impurity dify~~sions experiments in heavily doped

F is a function of only the ratio

wo/w4

(it varies from

217

to I when

M ] , / M ~ ~

varies from

0

to a), e is the charge of the electron and

p

the electric mobility.

We have, then, five unknowns (the five jump fre- quencies) and five relations thus in principle, we can calculate the frequencies.

We have chosen the system CaCI, in NaCl because

II.,,

and C,, have already been measured [4] and also

Dd

,,,, and D ,,,,, [5] so that the ratio

M , , / ) v ~

and

^{1 0 ,}

were knowns.

According to [4]

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973970

C9-422 G. BREBEC

and The solution with our conditions is

:

CLO

=

258 exp ( -

-

2;) .

According to [5]

and

D,,,,

Ca =

0.13 exp

We have then measured the electric mobility of c a 2 + in NaCl to get the fifth relation.

1 . Experimental techniques.

-

The classical techni- que [6] which consists of depositing a thin layer of CaCI, between two NaCl blocks was disappointing

;

the most part of the CaCI, was blocked up at the interface so that the penetration curves could not be utilized. We have then developed an other method whose principle is sketched on figure 2.

Q

^{y 2}

~ ( x , y , r )

= -,

exp j- --)

^x

2 . J n ~ t 4 Dt

x - v t + I x - v t - 1

x [erf( _{2 JDt} )

^-

^erf( _{2 JDt} -)I ⁽²⁾

One sees that for a given value of

y,

the concentration is maximum if s

=

,~iEt

=

ut so if it is possible to determine the

^s

value for whicli C is maximum it is possible to obtain

^{/ I .}

In practice we used a sample shaped like a U (.Fig. 3). The radioactive calcium chloride (we used Ca 45 which is a /I emitter) is evaporated following the black strip. Electric field is applied between faces A and C. After the run we determine by autoradiograph and optical densito~netry measurements the position of the maxima of concentration for each part ofthe U.

On the figure 4 we can see autoradiographs before and after the run (the sample is sketched in over- printing) and the corresponding optical density curves. The distance 0 between the two maxima is equal to 2

pEt.

anode cathode

More experimental details can be found in [7].

At the sample surface we deposit by evaporation a strip of CaCI, in the striped part EFGH (EF

=

2 1).

The electric field is applied between the faces

1

and 2 in the x direction. If we neglect the surface effects the flux equations are

:

ac ac

J,,,

=

- D - + vC and Je,

=

- D

-

ax JY

so that

:

where

o

is the drift velocity due to the electric field

t' =

!iE ( E is the electric field).

2. Results and discussion.

-

Data are gathered in table I. The quantity

2,

the effective valency, is equal to

:

-

kT

u

NO p x 109 cmz

Run T o C T (s) 6(p)

x

s-1

x

v-1

Z

In using Manning relation (eq. (1)) with our

experimental values of

^,LL

we have drawn the curves

w , / w , like a function of w,/w4 (Fig. 5). The two

ELECTROMIGRATION O F Ca'f I N NaCl _C9-423

FIG.

4. - Autoradiographs before n) and after b) and the corresponding optical density curves.

curves correspond to the two temperatures studied (656 and 697

^{O C ) .}

On the other hand we can write w1/w3

=

( w , / M J ~ ) (w4/W3) ( W ~ / W ~ ) but we know wo/w,

E 1

and we have measured by diffusion expe- riments w4/~v3

;

iv4/w3

⁼

224 at 656

^{O C}

and 166 at 697 OC.

So that our ratios are at the intersection of the curve and of the straight line

:

at 656

O C

intersection between curve Z

=

0.06 and wl/w3

=

224 wo/w4

and for 697

^{O C}

intersection between curve Z

=

0.085 and wl/w3

=

166 wo/w4.

In fact there are always two intersections but we have eliminated the one which corresponds to the very small value of w,/w4 because the frequency

^MJ,

would be in this case, much greater.

Data are gathered in table 11.

We see that w, is the smallest frequency which is reasonable for a divalent impurity

; M I , & ^lzl,

and w,

9 w,

means the complex impurity (Ca2+)- Vacancy is very stable. This is the reason why the effective valency Z is so small. This method can be used only if surface effects are negligible. If any superficial effects would be operating one would expect a dependence of 0 (which is the distance between the maxima)

011 j3

(which is the distance from the surface). We never found such a dependence so we think that for these experimental conditions the surface effects were negligible.

References

[l] LIDIARD, A. B., P l ~ i l . Mag. 5 (1960) 1171. [4] B E N I ~ R E , F.,

BENI~RE,

M.,

CHEMLA,

M., J. PIrys. & CIICIII.

[2] BARR, L. W., LIDIARD, A. B., P I I ~ s . Cljerz~. 10 (Academic Solids 331 (1970) 1205.

Press). ^[5]

SLIFKIN,

L.,

BREBEC,

G., Rapport CEA R 3770 (1969).

[3]

MANNING,

^{J .} R., DifJiil~iolj Kil~etics for. Afa1l1.s Crj.strrls [6]

CHEMLA,

M., Ar~rl. P f r i ~ ~ . 1 (1956) 959.

(Van Nostrand) 1970, p. 165. [7] BRFBEC, G., BEVENOT, J., Acto Met. 21 (1973) 585.