IONIC CONDUCTIVITY MEASUREMENTS OF HEAVILY DOPED AgCl : Cd CRYSTALS

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IONIC CONDUCTIVITY MEASUREMENTS OF HEAVILY DOPED AgCl : Cd CRYSTALS

K. Zierold, M. Wentz, F. Granzer

To cite this version:

K. Zierold, M. Wentz, F. Granzer. IONIC CONDUCTIVITY MEASUREMENTS OF HEAVILY DOPED AgCl : Cd CRYSTALS. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-415-C9-420.

�10.1051/jphyscol:1973969�. �jpa-00215445�

J O U R N A L DE PHYSIQUE

Colloque C9, supplimetlt au t1° 1 1- 12, Tot~c. 34, Novembre-Dkcembre 1973, page C9-415

IONIC CONDUCTIVITY MEASUREMENTS OF HEAVILY DOPED AgCl : Cd CRYSTALS

K. ZIEROLD, M . W E N T Z and F. G R A N Z E R Tnstitut fiir angewandte Physik, D 6 Frankfurt a m Main,

Robert-Mayer-Strasse 2-4, B R D

Resume.

^-

Nous avons mesure la conductivite ionique de AgCI, fortement dopC par Cdz+

(0

a

5 000 ppm). Dans le domaine de temperature 250-400

K,

nous avons Ctudie la solubilite de Cd++ dans AgCI. Pour la discussion des resultats obtenus en mesurant la conductivite ionique au-dessous de 240

K

et pour expliqucr les energies d'Arrhenius tres Clevees dans ce domaine de temperature, nous avons propose les deux modeles suivants

: 1)

Association des dipdles aux agregats plus grands. 2) Precipitations d'une superstructure

:

CdCI2,

6

AgCI.

Abstract.

-

Ionic conductivity measurements

in

heavily doped AgCI

:

Cd crystals (from 0 to 5 000 ppni) were carried out. A solubility curve of Cd? in AgCl for the temperature range 250

K

to 400

K

is presented. Very high Arrhenius energies were measured below 240

K. A

dipole association model and a superstructure model are discussed to explain the obtained conductivity data.

I t

is shown that the experimental results can appropriately be described by the assumption of the precipitation of this superstructure (CdC12.6 AgCI).

I . Introduction.

-

Ionic conductivity measurements in AgCl doped with divalent metal ions have been performed by many authors [ l ] to [ 5 ] . Mainly crystals with small impurity concentrations were used, which have been investigated extensively over the whole temperature range. Examinations of heavily doped samples were usually limited t o temperatures between r o o m temperature and melting point. Therefore a lack of information exists, concerning all properties related to transport phenomena in heavily doped ionic crystals below room temperature. It is the aim o f this contribution to present some preliminary results obtained by ionic conductivity measurements o f AgCl Crystals containing between 0 and 5 000 ppm cadmium.

2. Experimental.

-

2 . 1 CRYSTAL PREPARATION.

-

T w o different shapes of crystals were used in the experiments (Fig. 1)

:

a) Plate-like crystals about 200

¹¹

thick, individually doped u p to 5 000 ppm C d Z + and grown by the sandwich method. This method was introduced by Clark and Mitchell [6] and improved by Zorgiebel a n d Wendnagel [S].

b) Discs of about

3

nim thickness cut from

a

cylin- drical crystal of 15 mni in diameter grown by the Bridgman method.

The second were used for comparison and to exclude surface ell'ects. The impurity concentration of the Bridgmnn-samples was determined by the distribution coefficient

[9].

T o achieve smooth surfaces, all samples were polished with KCN

^- 01- NaZS,O, -

solutions. T o avoid

1. p l a t e l e t s

evaporated Ag-electrodes

/ I

quarzglas

2 . Bridgman crystals

,evaporated Ag-electrodes

FIG. 1 . - Measuring arrangement.

polarization effects silver electrodes were evaporated on [lo].

2 . 2 MEASUREMENTS.

^-

The electrical resistance of the samples was measured with an ohmmeter (Knick company), which has an input resistance up to 10" 52 and an accuracy ol

3

to 10 '%, dependent on sensitivity range.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973969

C9-416 K . ZIEROLD, M . WENTZ A N D F. GRANZER

First the samples were cooled down in a cryostat to a temperature of about 170 K and kept thus at least for 2 h. During the measuring procedure the samples were warmed up with a heating rate of 0.5 K/min. The electrical resistance was measured at intervals of 2 t o 10 K. We have checked

a t

different temperatures, that a storage time up to one hour did not affect the results.

3. Theory.

-

The theoretical backround is well established [l I], 1121. It follows a short repetition of the final equations. The conductivity

a

is given by

:

Arrhenius energies as a function of activation energies in the region I to IV.

(HF

=

Frenkel enthalpy,

Uo,

UD resp. migratiorz energy for interstitials resp. vacalicies

;

U ,

=

activation energy for association of impurity- vacancy-dipoles

;

U p

=

activation energy for oacancies in the

cr

preci- pitation region

^)).

Region I : intrinsic region El = H F / ~ -I- UO Region I1 : vacancy region EII = Un

Region 111 : dipole association region EIII = Un

+

^{U A / ~}

Region 1V : (( precipitation region )) Erv = UiIi

+

^Ul,

( x = ;

L1

=

mobility

;

q

=

ion charge). Regions 111 alld IV are liere of special interest, espe-

The summation runs over all possible kinds of charge cially because region I V is assumed to be a rather carriers i. The mobility is given by

:

unknown

⁽⁽

precipitation region

D.

B

p = -

T . e i p j - $1 ^{4. Results.}

^-

^{4 .}

¹

DESCRIPTION

^OF THE CONDUC- TIVITY

PLOTS.

-

Figure 3 and figure 4 show the Arrhe- ( U

=

activation energy

;

T

=

Kelvin temperature

;

nius plots of the two types of crystals with various k

=

Boltzmann's constant

;

B

=

constant). impurity concentrations. Let us first consider the Whence follows the final equation

:

curves of the

⁽⁽

pure

⁾⁾

crystals

i n

both graphs. We can distinguish the regions I, 11 and 111. It is well known o~ - ^exp (

^-

⁽³⁾ from theory e. g. [ I 11, [I21 that the transition tem- perature between region I and I1 depends on the impurity concentration, namely the lower the transi- E being a sum of different activation energies depending

tion temperature the lower the impurity concentra- on the temperature range.

tion. Consequently the undoped Bridgman crystals Figure 2 shows the typical Arrhenius-curve obtained

are

((

purer

⁾⁾

than the platelets. In the other curves from the conductivity of an ionic crystal doped with

divalent metals.

r e g i o n

1

1 1

FIG. 2. - Typical Arrhenius plot of ionic conductivity.

1.. Ag CI "pure"

2.0 4 CI + 5 0 p p m Cd 3.0 Ag C l * 5 0 0 p p m C d L.fiAgCI 5 0 0 0 ppm Cd

Generally 4 well defined slopes will be observed

with different corresponding Arrhenius energies E.

' 5 . 4 ^I 5.0 ^I 4.6 4.2 3.8 ^I 3.4 ^I 3.0 ^I 2.6 ^I 2.2 ^I

Table I shows the functions between the Arrhenius

c - 1000

energies and the different activation energies, i. e.

^T

the dominating conductivity process in these regions.

FIG. 3. - Ionic conductivity of AgCI : Cd (platelets).

IONIC CONDUCTIVITY MEASUREMENTS O F HEAVILY DOPED AgCI : Cd CRYSTALS C9-4 1 7

FIG. 4. onic condi~ctivity of AgCI : Cd (Bridgman).

different slopes of region 111 and IV type as well as their transition regions are well discernible. The measured curves could be satisfactorily reproduced with one and the same sample. Different samples with the same impurity concentration showed good agreement in Arrhenius energies of region I, 11 and I11 ( A E

=

1 5 x).

On the other hand the transition temperature between region IT1 and IV and the Arrhenius energies of region 1V showed great differences. There was no relation to be found between the impurity concen- tration and the slope of region 1V.

The differences in slope of region IV between the two types of crystals may be due to an enhanced surface conductivity originating from the measuring arrangement of the platelets. The transition region occurs in 3 difl'erent types.

1)

A slow nlonotonous transition.

2) A n abrupt change.

3) A vague step-like change (Fig. 3, curve 3).

It is remarkable that sometimes

a n

effect occurs in region 111 which is eminent for the interpretation of region IV, illustrated i n figure 4, curve 4. The slopes of the longer parts correspond to the usual slopes of region

111,

that is [he Arrhenius energy of the dipole association region. The edges

in

the curve :ire inter- preted to

be

spontaneous increments of the silver vacancy concentration, which may be due to

a

sudden solution process of

a

precipitated phase

in

the crystals caused by heating. From

t h i \ very

I;lst running process

a hint can be taken to

a

precipitated superstructure of CdC1, . 6 AgCl which will be discussed later on.

In some other crystals a slightly larger Arrhenius energy was observed which can be interpreted as many small indistinguishable solution processes.

4 . 2 ACTIVATION

ENERGIES.

-The activation energies for the intrinsic region E,, the vacancy migration

U,

and the association to dipoles

UA

are calculated from the Arrhenius energies with the formulae of table I.

In table I1 these results are compared with those of

Values for defects paran~eters

in AgCl

:

Cd Abbink

and Miiller Martin

(1965) (1966)

- -

El (eV) 0.785 0.725 U , (eV) 0.35 0.27 U , (eV) 0.27 0.47

Corish and

Jacobs Present (1 972) work

- -

0.74 0.78 0.29 0.30 0.29 0.30

other authors. Our value for the intrinsic region is in good accordance with that found by Miiller (31, the values for the vacancy migration and the asso- ciation agree well with those of Corish and Jacobs (51.

4.3 SOLUBILITY LIMIT.

-

Isotherrnes of the conduc- tivity versus the Cadmium-ion concentration are plotted in figure 5.

FIG.

5. - lonlc conductivity isothermes of AgCl : Cd (platelets) Alg ( u T ) = ' 0.15.

C9-418 K . ZIEROLD, M . WENTZ A N D F. GRANZER

It can be seen that the conductivity reaches a

saturation at relatively low concentrations. From these saturation values the concentrations of the free Silver vacancies xu depending on temperature can be computed by eq. (1) to (3). The concentrations of free vacancies and free Cd-ions must be equal for electroneutrality. The total number of nonpreci- pitated Cd2+-ions

ys

is given by

:

where a denotes the degree of association

:

( x ,

=

concentration of dipoles), K A ( T ) is tlie equi- librium constant of the reaction for the association of dipoles

:

(U,

=

activation energy for the association),

y

equals the activity coefficient of the Debye-Hiickel-Theory for long range ionic interaction

[ l l ] :

- z2 e2 X

Iny

=

2 &kT(1 + ^XR)

where X, the Debye-Hiickel screening constant, is given in the case of AgCl by

:

( E =

dielectric constant, R

=

closest distance of inter-

acting ions, V

=

volume per ion pair).

I

260 2 i 0 300 3 $ 0 3 4 0 3k0 3 b 0 400

.

FIG.

6.

-

Solubility curve of Cd2+ in AgCl ; calculated from the measured saturation values.

Errnftit~l : On the top of the figure please read : Y S = X n -1- XA instead of Y = X u

+

XA.

Using eq. (4) to (8) the solubility limit of Cd2'-ions in AgCl as a function of temperature is shown in figure 6. A solubility limit of 200 ppm was found at room temperature, which is in good accordance with observations of the turbidity limit in doped AgCl

:

Cd crystals.

5. Discussion.

^-

5.1 PRELIMINARY REMARKS.

-

The most striking effect of the conductivity measu- rements is the existence of tlie region I V below 240 K, the

tt p~.c'cil~itation r ~ g i o n D.

In this region the conduc- tivity mechanism is assumed to be determined by vacancies too. Therefore the changed slope in region 1V can be explained in two different ways

:

I ) Enhanced binding energy for vacancies by dipole agglomeration.

2) A new mechanism dominates for the generation of vacancies, because the ili~purity-vacancy-pairs have disappeared by precipitation.

Independently of the detailed mechanism both processes are controlled by diffusion. On the other hand it is well known from diffusiori data in AgCl [I 81, [I91 that the diffusion coefficients D of Cadmium-ions and Silver vacancies are small at temperatures below 240 K

:

Da

=

cm2/s,

DCd2+ =

10-'a cm2/s.

The mean diffusion length 1 may be approximated by

:

For T

=

240 K and a diffusion time r

⁼

100 s the resp. diffusion lengths are

:

I , < 5

x

lo4 cm, lCd2+ < 2

x

10-'cm

The diffusion length being extremely small, the preci- pitation from a homogeneous distribution of Cd2+-ions turns out to be very improbable. These inhomogenities may be due to

1) locally enhanced concentration of two or more dipoles which then will form dimers or trimers

;

2) dipoles localized near the surface of precipi- tations.

In both cases only short diffusion lengths are needed, and each of the two ways mentioned above may be used to interprete tlie slope in region IV.

5 . 2 DIPOLE

ASSOCIATION

MODEL.

-

The dipole association mechanism is illustrated in figure 7 [13], [14]. The association energies U D for dimers and U , for trimers were roughly calculated by

a

simple Cou- lomb interaction taking into account the dielectric constant of AgCI.

(zi =

+ I for Cd-ions

; zi = -

1 for vacancies

; r i j =

distance between charges i, j

; E =

12.5).

For an impurity-vacancy-dipole results the binding

energy U ,

= -

0.29 eV, for a dimer U D

= -

0.75 eV

IONIC CONDUCTIVITY MEASUREMENTS OF HEAVILY DOPED AgCI : Cd CRYSTALS C9-419

of

AUD

and

AU,

are very small. Therefore the mea-

+ sured high Arrhenius energies of region 1V cannot be explained by the dipole association model.

5 . 3 SUPERSTRUCTURE

MODEL. -

It is reasonable to

+ ^{- +} discuss a superstructure CdCl, . 6 AgCl with twice

the lattice constant of the host lattice (Fig. 8).

(100) (100)

impurity

-

^vacancy

-

dipole dimer

t r i m e r

FIG. 7. - Dipole association model ; impurity-vacancy- dipole, dimer, trimer [13], [14]

+-

⁼ impurity ion,

n

^{= vacancy,}

+

^{= Ag-ion, - - - CI-ion.}

and for trimer

UT = -

1.18 eV. The effective binding energies

AUD

or

AUT

respectively are the differences between the energies

U D

or

UT

resp. and the sum of the energies of the isolated dipoles.

AUD = U D -

2 UA

= -

0.17 eV (1 1)

AUT = UT -

3

U , = -

0.31 eV

Then the following equation system was used to calculate

x n ( T ) :

2

1

X*

_{x D} ⁼

K D ( T )

=

exp (

^-

$1 ⁽¹⁴⁾

( x , , xT =

concentration of dimers and trimers resp.).

Thence

The values of

x n ( T )

obtained by this equation were used to calculate the Arrhenius energy E I V by eq. (1) to (3). Using the following reasonable seeming para- meters

UIIl =

0.30 eV,

U , =

0.29 eV,

AU, =

0.17 eV.

AUT =

0.31 eV as a typical energy value is obtained

:

E , ,

=

0.52 e\'

It is seen by

a

variation of these paranletel-s that

E,,,

is mainly determined by

U , .

while the contributions

FIG. 8. - Superstructure model of C d C l ~ p . 6 AgCI, model after Suzuki [15].

This superstructure was first found by Suzuki [I51 in NaC1

:

Cd and also reported by Lilley and New- kirk [I61 for LiF

:

Mg. Preliminary interpretations of small angle X-ray measurements confirm the assumption to have such a superstructure in AgCI.

For the reason of simplicity the basis of the super- structure is considered to be composed of 4 Cd-ions and 4 vacancies. The binding energy Us of this basis is calculated by eq. (lo), furnishing

:

A vacancy dissociating from this basis leads to a positively charged configuration with the binding energy

:

US-3

= -

0.90 eV .

The difference energy

U s - n - Us

is the energy for separating one vacancy from the superstructure

:

The dissociation of a second vacancy once more lowers the binding energy US-2D of the remaining configuration and for the activation energy

U 2

of this vacancy follows

:

In analogy dissolving a third and fourth vacancy resp., the activation energies are given by

:

By this simple consideration it is seen that the acti- vation energies for taking off free vacancies from

a

superstructure particle depends on the size and the remaining charge of the precipitated state. By means of this model

i n

comparison witti the dipole associa- tion model the measured high and different Arrhenius

2R

C9-420 K. ZIEROLD, M. WENTZ AND F. GRANZER

energies of region IV can be explained most favou- precipitation. It was shown that the dipole association

rably

:

model cannot explain the high Arrhenius energies

1) The high Arrhenius energies can be understood as functions of averaged activation energies for vacancies from the superstructure lattice.

2) The scattering range of the measured energies from 0.61 eV to 1.8 eV may be due to superstructure particles of different size and

⁽⁽

ionizatiorz

degree D.

6. Conclusion.

-

Ionic conductivity measurements in heavily doped AgCl

:

Cd crystals within a tempe- rature range from 170 K to 470 K were carried out.

The solubility curve (Fig. 6) and the existence of the region IV below 240 K indicate the presence of

measured in region IV. But the superstructure model of CdCl,. 6 AgCl satisfactorily describes all measured results. An exact prove however for this kind of precipitation cannot be obtained by ionic conductivity itself; other measuring methods [I71 like ITC-mea- surements, X-ray experiments, and electron micro- scope investigations will be used for getting more detailed information about the precipitation mecha- nism observed in AgCl

:

Cd.

Acknowledgement.

-

This work has been supported by the Deutsche Forschungsgemeinschaft.

References

[I] KOCH, E. and WAGNER, C., Z . P11ys. Cller?~ie B 38 (1937) 295.

121 EBERT, I. and TELTOW, J., A I I I I ~ I I der Pllys. 5 (1949) 63, 71.

[3] M ~ L L E R , P., P I I ~ s . Srar. Sol. 12 (1965) 775.

[4] ABBINK, H. C. and MARTIN, D. S., J. Phys. & Cl~c,r,~. Solids 27 (1966) 205.

[5] CORISH, J. and JACOBS, P. W. M., J . P11y.s. & Chern. Solids 33 (1972) 1799.

[6] CLARK, P. V. MC D. and MITCHELL, J. W., J. Photogr.

Sci. 4 (1956) 1.

[7] ZORGIEBEL, F. et al., Z. Angew. Plzys. 30 (1970) 316.

[8] GRANZER, F., HENIG, G., SCHOTT, U., DARDAT, K., WENDNAGEL, Th., HAASE. G., Z ~ ~ R G I E B E L , F., in :

(( 8th Int. Conference on Nuclear Photography and Visual Detectors, Bukarest (1972) ^D.

[9] SCHILDKNECHT, H., (( Zo~~er~schn~elzeiz )) (Verlag Chemie, Weinheim) 1964.

[lo] MATEJEC, R., Z. Phys. 148 (1957) 454.

[I I ] LIDIARD, A. B., in : Handbuch der Physik XX, 246 (Springer- Verlag, Berlin) 1957.

[12] BARK, L. W. and LIDIARD, A. B., in : Physical Chemistry, An advanced Treatise, Vol. X, 152 (Academic Press, New York/London) 1970.

[I31 COOK, J. S. and DRYDEN, J. S., J. Pkys. C. 2 (1969) 603.

[I41 CRAWFORD, J. H., J. P I I ~ J s . & Chern. Solids 31 (1970) 399.

[I51 SUZUKI, K., J. Pl~ys. Soc. Japar~ 16 (1961) 67.

[I61 LILLEY, E. and NEWKIRK, J. B., J. Materials Sci. 2 (1967) 567.

[17] HARTMANOVA, M., P/IJJS. Stat. Sol. ( a ) 7 (1971) 303.

[IS] SAWYER, E. and LASKAR, A., J. Phys. & Chern. Solids 33 (1972) 1149.

[I91 S ~ ~ P T I T Z , P. in : Reactilji/y of Solids (John Wiley and Sons, Tnc.) 1969.

DISCUSSION A. KESSLER.

-

If your crystals were not in perfect

equilibrium, one could expect some hysteresis in the data goinp up and down with temperature. Have you observed something of this kind

?

K. ZIEROLD. -Yes. By cooling from room tem- perature or any other temperature in region I11 the conductivity is lower than by heating. The contrary effect is observed by cooling (or quenching) from the intrinsic region.

R. CAPELLETTI.

-

Which is the heating rate during the ionic conductivity measurements

?

If it is high you are actually measuring non-thermo- dynamical equilibrium situation and the activation energy in region IV experimentally obtained is expect- ed to be higher than the real one.

Generally the accomplishment of thermodynamical

equilibrium between simple defects and precipitated

phase requires long time, for instance in alkali halides

doped with divalent cation impurities.