HAL Id: jpa-00215450
https://hal.archives-ouvertes.fr/jpa-00215450
Submitted on 1 Jan 1973
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
DEFECT ASSOCIATION IN Cd2+ DOPED NaCl CRYSTALS
E. Laredo, D. Figueroa
To cite this version:
E. Laredo, D. Figueroa. DEFECT ASSOCIATION IN Cd2+ DOPED NaCl CRYSTALS. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-449-C9-454. �10.1051/jphyscol:1973974�. �jpa-00215450�
JOURNAL DE PHYSIQUE C0ll0que C 9 , 5~pp/&tnet7t au no 11-12, Tome 34, Novernbl.e-Dkcembre 1973, page C9-449
DEFECT ASSOCIATION IN Cd2+ DOPED NaCl CRYSTALS
E. L A R E D O a n d D. F I G U E R O A
C e n t r o d e Fisica, I n s t i t u t o Venezolano d e Investigaciones Cientificas A p a r t a d o 1827 Caracas, Venezuela
RCsumC. - Des monocristaux de NaCl fortement dopes par Cd . (5 ;., 10-6 < c < 7 x 10-3) ont etC etudies par conductivite. Des mesures anterieures de rayons X a temperature ordinaire avaient rnontre, dans les echantillons les plus dopes, I'existence d'une phase precipitee identifiee telle une superstructure de composition Nac,CdClr;. Un diagra~nme de O T en fonction de 1 / T pour tous les cristaux, et pour les temperatures comprises entre 300 et 1 050 K, montre plusieurs zones repro- ductibles. La dissolution des precipites en superstructure se produit entre 500 et 700 K. L'entropie et I'enthalpie de dissolution sont : (1,2 ::0, I ) 1 0 - eV. K-I et 1,40
+-
0,06 eV. La zone entre 600 et 700 K pour les cristaux les moins dopes est interpretee en termes de dissolution des complexes neutres en lacunes cationiques et ions cadmium libres. Les interactions a longue distance entre ces deux types de defaut isoles sont prises en consideration. Le modele de Lidiard est utilise pour calculer le degre d'association et la conductivite resultante. Pour des concentrations aussi elevees que 10-3, l'knergie dc Debye-Hiickel est egale a 50 ::, de I'energie d'association et ne pourrait pas Ctre negligee. E n consequence. I'energie de liaison du dipble est trouvee egale a 0,37 eV. Celle-ci est a rapprocher de la valeur theorique de Bassani de 0,38 eV. La niobilitk limite des lacunes cationiques en I'absence d'interactions est aussi evaluee.Abstract. - NaCl single crystals highly doped witli C d 2 . (5 :- 10-6 i c i 7 x 10-3), were studied by ionic conductivity techniques. Previous X-ray experiments at room temperature had shown, in the most doped samples, the existence of a precipitated phase identified as a super- structure of c o m p x i t i o n Nac,CdCIs. A plot of csT as a function of l I T for all tlie crystals, and for temperatures betwcen 300 and 1 050 K , shows several reproducible zones. The dissolution of the superstructure precipitates takes place from 500 to 700 K. The dissolution entropy and enthalpy were determined, A S , !
-
(1.2 !I 0.1) 10 3 eV. K - 1 , W,I = 1.40 .- 0.06 eV. The zone between 600 and 700 I< for the less doped crystals is interpreted in ternis of the dissolution of neutral complexes into unassociated positive vacancies and Cadmium ions. Long range Coulomb interactions bet- ween the two kinds of isolated defects is taken into account. Lidiard's model is used to calculate tlie degree of association and the resulting conductivity. For concentrations as high as 10-3, the Debye-Hiickel energy is 50 j'/, of the association energy and could certainly not be neglected.Consequently, the binding energy o f the dipole is found to be equal to 0.37 eV. This is to be conipa- red with Bassani and Fumi's theoretical estimate of 0.38 eV. The limiting mobility of positive vacancies in the absence of interactions is also evaluated.
1. Introduction. - T h e electric conductivity o f alkali halides crystals h a s been widely used in t h e l a s t years t o d e t e r m i n e t h e energy parameters f o r t h e migration a n d creation of lattice defects. In alkali halides, t h e isolated positive vacancies a r e m a i n l y responsible f o r t h e current transport. These c h a r g e carriers c a n be created thermally ( S c h o t t k y defects), o r as c h a r g e c o m p e n s a t o r s t o maintain the electrical neutrality o f t h e crystal d o p e d with divalent positive ions. T h e s e d o u b l y charged cations a r e in different states d e p e n d i n g o n their total concen- t r a t i o n a n d the tempel-aturc. T h e y c a n be in substi- tutional position b o u n d t o t h e vacancy, t l i ~ ~ s forming d i p o l a r complexes, o r isolated in the host lattice.
F o r highly d o p e d crystals t h e impurity ions. Me'
'.
f o r m precipitates in t h e N a C I matrix. With very few exceptions, these precipitates Iia\lc t h e s a m e crystalline s t r u c t u r e a s t h e McCI, salt introduced in t h e melt d u r i n g t h e cryst:il g r o w t h . In s o m e o t h e r cases t h e impurity f o r m s precipilates which a r c a
superstructure o f tlie host lattice. T w o kinds o f supel-structures have been f o u n d by m e a n s o f X-ray diffraction techniques : A n inverse spinel in tlie L i F : NiF, [ I ] system. a n d a N a C l s t r u c t u r e witli a paranieter twice t h a t o f the alkali halide i n L i F : M g F , [ 2 ] a n d NaCI : CdCI,. In this last case, this superstructure was found t o be a metastable phase by Suzuki [3]. I n this work, we report t h e results o f the ionic conductivity studies o n N a C l crystals doped with C d C I 2 . T h e c a d m i u m concentration (expressed in molar fractionj present in o u r samples ranges from t h e (( pure )) crystal, with a b a c k g r o u n d impurity concentl-ation o f 6 p p m t o 7 x T h i s value is ten times higher t h a n t h e u p p e r limit reported i n the previous study o n this system, a s we needed high defect concentrations t o obtain measurable e r e c t s by X-rav difrl-:~ction techniques.
Etrel a n d M : ~ ~ i r e r [4]. in a now classic article o n thc ionic conducti\.ity of NaCI : C d C l z cryst;~ls, c:~lculated se\,er:il energy parameters using a sini-
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973974
C9-450 E. LAREDO A N D D. FIGUEROA
ple association theory and graphic determinations.
Lidiard [ 5 ] , using a theory which takes into account the long-range Coulomb inleractions of unassociated defects, calculated the binding energy of the cadmium ion-vacancy complex and the mobility of the cation vacancy after Etzel's experimental data. In the same system, studies of N a nuclear magnetic relaxation by Satoh [6], cation self-diffusion and conductivity by Trnovcova [7] and C d 2 + diffusion by Allen et al. [8], have been performed.
The determination of the energy parameters that we report here was made using Lidiard's theory where the Debye-Hiickel approximation describes the long range Coulomb interactions. Non linear least squares computer fitting has been used in several occasions.
2. Theory. - We will resume here the Lidiard's theory. The concentration of positive cation vacancies of mobility p,, is x , at a temperature T. In pure crystals the Schottky defects are the only source of cation vacancies. If x, is the concentration of anion vacancies, for thermodynamic equilibrium we can write
H A S s, x, = exp - "exp-"
kT k
where H, and AS, are the enthalpy and entropy for the formation of a Schottly pair. In the case of a C d 2 + doped crystal, the number of cation vacancies is increased because of the positive vacancies intro- duced in the lattice for charge compensation by the substitutional C d 2 + ions. These vacancies can be either isolated in the lattice, or bound t o the impurity cation, forming thus neutral complexes. The equi- librium constant can be expressed as
where p is the degree of association ( - i) the asso- ciation energy of the dipole and c is the total cadmium concentration in the lattice.
The electroneutrality condition in the matrix is given by
x, - x, = c(1 - p ) . (3)
This theory of simple association does not include any term for the long range interactions between unassociated defects. Lidiard has shown that in the Debye-Hiickel approximation this could be done very simply by modifying the preceeding equations as follows :
A S
x, x 2 = exp 2 exp -
k (4)
and
The Debye-Hiickel energy can be expressed as e2 r i
ED, =
& ( I -i ria)
where r i is a screening constant, which is a function of x, and T, a is the lattice parameter a n d E the die- lectric constant of the crystal.
The unassociated defects are supposed t o be unable to approach each other closer than a distance a.
There is also in Lidiard's theory the introduction of a correction factor for the mobility of cation vacancies wl-iich represents the hindrance to ion motion by the Debye-Hiickel cloud :
T o compute To, the association energy expressed in Boltzman constant units, from the ionic conduc- tivity experimental results, we can write equation (5) as
x exp
[$
- 2(2 TCJ2)'I2
( T ~ / T ) ~ / ~ [(I - p) cI]'/'I .
{ 1
+
~ ( T C ,/Z)'l2 [ ( 1 - p) C T ~ / T ] )(7) This equation can be rearranged t o obtain TITo as a function of p :
If we compare a t a given temperature the ionic conductivity of a doped crystal, o, t o the conductivity, a,, of a (( pure )) crystal, with a background concen- tration of divalent impurity co, we can write
where p is the solution of eq. (8) at the considered temperature T.
The theoretical estimate of o/ao was made for various concentrations and temperatures. Values for To were tried and the deduced values of p from eq. (8) were introduced in (9). The program was stopped when the relative difference between the theoretical and the experimental value of ~ x t i o g/o0 was less than 5 x
Tt must be noted that the cadriiium concentration c
we have been using until now is the concentration
DEFECT ASSOCIATION IN CdZ+ DOPED NaCl CRYSTALS C9-45 1
C9-452 E. LAREDO AND D. FIGUEROA of substitutional cadmium ions either bound or
isolated in the NaCl matrix. This concentration c may differ from the amount of C d 2 + determined by chemical analysis if there are precipitates present in the crystal.
The complete dissolution process of these preci- pitates in the matrix into free C d 2 + and free cation vacancies is described by
c = exp eASd x p - - 2 k 2 kT Hd
+
+
12 exp (A& - AS=)k exp
;
H d ) . (LO)3. Experimental. - Tlie crystals were grown from a molten mixture of NaCl and CdCI,, through a temperature gradient (100/cm) in a pure helium atmosphere, with a very low rate for the temperature decrease from the melting point (30/h). The blocks obtained were single crystals, and for the most highly doped blocks tlie impurity distribution was not homogeneous. The total cadmium concentration in our samples was determined by atomic absorption analysis. Both the cadmium and the sodium absorp- tion were measured. The precision on tlie atomic concentrations, c d 2 + / ~ a + , was better than 2.5 "<.
The concentrations lay between 6 ppm and 7 x For some samples, neutron activation analysis was also performed. Tlie crystal used for tlie conductivity was analyzed as well as parallel blocks cleaved before the experiment.
The conductivity cell has been described already 191.
Pure helium gas was used instead of nitrogen. Tlie large faces of tlie crystal were silver painted. The AC measurements (I kHz) used at high temperatures were improved by tlie utilization of a General Radio automatic capacitance bridge which gave a fast digital output. Measurements were taken every 50 while the temperature was increased at a rate of 600/1i.
For the X-ray diffraction experiments, the rotating crystal technique was used. CuKx radiation was diffracted by a small crystal at room temperature.
The crystal was submitted to thermal treatments in order to observe the beliaviour of the precipitates in the matrix. The quencliings were made from high temperature on a copper plate kept at 0 OC.
4. Results and anaIysis of data. - Tlie conductivity results in figure I are plotted as Log a T versus 1 0 3 / ~ , for the different crystal concentrations. For the less doped crystals (c < 5 x lop4) the high temperature intrinsic zone is clearly visible. From its slope tlie enthalpy of creation for Schottky defects can be deduced if we know tlie entlialpy for the migration of a cation vacancy. At lower temperatures all tlie crystals present a zone where the number of carriers is constant arid equal to tlie C d 2 + concentration found by chemical analysis. The slight increase i n a is only due here to the variation of the carriers'
mobility with temperature. From these plots tlie enthalpy of migration of cation vacancies was deter- mined by a least squares fitting in this zone and was found to be equal to 0.75 i 0.03 eV. The limiting mobility in the absence of interactions will be calcu- lated later on, following Lidiard's procedure.
At lower temperatures, 523 < T < 673 K, ;lnd for concentrations c > 8 x we can note a steep increase in the number of carriers. The X-ray diagrams taken with tlie sanie crystals show the existence of precipitates in the same temperature range. If the crystal is quenched from high tempe- rature, the diffraction peaks due to the precipitated phase disappear showing thus a dissolution of the impurity in the matrix. Annealing on these quenched crystals followed by quencliings at increasing tem- peratures show the reappearance of tlie precipitated phase. This phase presents the sanie relative intensities and periodicity as the CdCI2. 6 NaCl metastable phase found by Suzuki in NaCl : CdCI, mixed crystals.
It is a superstructure of NaCI, with C d 2 + ions and vacancies alternatively located at tlie corners of tlie original NaCl cell. The C1- ions keep their original positions, slightly displaced towards the doubly charged c;idmiuni ions.
Suzuki found the co-existence of this metastable phase with a stable hexagonal one of composition CdCI2.2 NaCI. In our crystals this phase never appeared xnd the cubic superstructure seemed to be the stable one at room temperature. The parameters for the super-structure dissolution process were calcu- lated in a previous paper and were found to be AS, = (1.2
+
0.1) e V . K - ' andFor the less doped crystals ( c < 5 x there is a n intermediate zone between the dissolution and the constant carrier number zone. This zone is detailed in figure 2. I n this zone the variation of the conduc- tivity is attributed to tlie dissociation of dipoles wliicli causes an increase in tlie number of isolated vacancies. This is an adequate zone for determining tlie dipole association energy because the concen- tration c wliich appears in our equations is tlie total concentration of cadmium in tlie crystal.
I n figure 3 we have drawn a set of smooth curves through our experimental points of ( c
+
c,)/a versus a, at four temperatures (606 K, 625 K, 645 K, 667 K).With these curves we can obtain values of o for choosen c
+
co values. Then the experimental ratio ole, was calculated for the four temperatures and concentration values (5 x lo-', 5 xlo-',
1 0 - 7 with the help of a computer program, we tried values of To, calculated thc subsequent p and deduced the tlieoreticnl value of the o / a , ratio, knowing the total concentration of impurities and tlie working temperature. When the agreement bet- ween tlie theoretical and experimental values ola, was considered satisfactory (relative difference better
DEFECT ASSOCIATION 1N Cdzf DOPED NaCl CRYSTALS 0 - 1 5 3
FIG. 2. - The high temperature association region of the conductivity of Cd2+ doped NaCl crystals.
"
(( pure crystal )) ;c = 1.01 x 10-5 ;
n
c = 1.75 x 10-5 ; c = 4.2 x 10-5 ; c = 8.2 X 10-5; X c = 1.63 x 10-4 ; V C = 5.53 x 10-4.FIG. 3. - Experimental data for NaCI : CdCI2 at four tempe- ratures.
than 5 x the To was retained. At each tem- perature the average value of To was calculated.
The To mean value obtained from these four values 4 = 20T was r59 K nad AT,/T,, was less than 61. per
cent. The binding energy for the dipole is then 0.37 0.01 eV. Lidiard found for this same complex, starting from the experimental ionic conductivity results of Etzel and Maurer 0.34 eV. Murin et a/. [ I I ] obtained 0.23 eV in analyzing the curvature of the 344 OC isotherm published by Lidiard. Other expe- rimental techniques have been used for the
<
deter-mination. Allen ct al., with diffusion experiments of C d 2 + ions in NaCI, drew the variation of ( in function of temperature. ( varies between 0.52 and 0.55 eV in the temperature range we are interested in. Satoh.
using Na nuclear magnetic resonance experiments, reports a value of 0.4 eV.
Finally. theoretical estimates of this enthalpy have been made by Reitz and Galnmel [I21 ( H a = 0.44 eV) and by Bassani and Fumi (131 in a more refined way ( H u = 0.38 eV). Our experimental value is in good agreement with the calculation of Bassani and Fumi.
With this value of i, the limiting mobility, /I,, in the absence of interactions can be calculated.
The conductivity CJ can be expressed in function of g, the correction factor, of the mobility / l o , of the concen- tration c of isolated vacancies, of the inter ionic distance a,, and of the electronic charge e
A plot of po T as a function of 1/T for a concen- tration of 5 x lo-', and the four temperatures considered here is represented in figure 4.
FIG. 4. - The limiting mobility po T (cm2.K/statvolt.seg) versus 103/T for a total concentration c
+
co = 5 x 10-5.The least squares fitting in this case gives for the mobility equation
pa 7 =?.43? x
lo6
(exl) - kT statvolt. s cm2E. LAREDO AND D. FIGUEROA
Basic energy parameters for C d 2 + doped NaCl crystals Authors
-
Etzel and Maurer Lidiard
Trnovcova Satoh Allen et al.
Murin et al.
This work Bassani et al.
Dreyfus et al.
Laredo and Dartyge
and the frequency factor v , , can be deduced
In table I all the energy parameters determined here together with other author's results are reported.
We can conclude that Lidiard's theory applied to our experimental data, gives for the energy para- meters values in agreement with those published by other authors using different techniques. However, several other types of defects can be present in our crystals and have not been taken into account in our four defect model. Those are divacancies, triva-
cancies, electrons originating either at the electrode or at the impurity traps present in the crystal. Allo- wance for the existence of Frenkel defects has been included by Allnatt and Pantelis [I41 in their least squares analysis of the ionic conductivity of a pure NaCl crystal.
Other simplifications introduced in the theory must be recalled here : the enthalpies and entropies are supposed to be temperature independent ; we have neglected the temperature dependence of the static dielectric constant. On the other hand in our crystals where a high impurity concentration is present the Debye-Hiickel approximation may be insufficient to describe the effect of defect interactions.
References
[ l ] JEHANNO, G. and PERIO, P., B~tll. SOC. Fr. 111itlel.. Crist 91 (1969) 5.
[2] LILLEY, E. and NEWKIRK, J . B., J. Mater. Sci. 2 (1967) 567.
[3] SUZUKI, K., J. Pl~ys. Soc. Japan 16 (1961) 67.
[4] ETZEL, H. W. and MAURER, R. J., J. C17e1n. Phys. 18 (1950) 1003.
[5] LIDIARD, A. B., P11ys. Rev. 94 (1954) 29.
[6] SATOH, M., J. Phys. Soc. Japa~r 20 (1965) 1008.
[7] TRNOVCOVA, V., Czecll. J. Pllys. B 19, (1969) 663.
[8] ALLEN, C . A., IRELAND, D. T. and FREDERICKS, W. J., J. Chem. PIIJJS. 47 (1967) 3068.
[9] LAREDO, E. and DARTYGE, E., J. CIICJIII. PIiys. 53 (1970) 2214.
[lo] FIGUEROA, D. and LAREDO, E., Solid State Coiiln/lcll. 11 (1972) 1209.
[ l l ] MURIN, A. N., BANASEVICH, S. N. and GRUSHKO, Y., Sov. Pirys. Solid State 3 (1962) 1762.
[12] REITZ, J. R. and GAMMEL, J. L., J. Cl1et11. Pl~ys. 19 (1951) 894.
[I31 BASSANI, F. and FUMI, F. G., NIIOVO Cil~ietlto 11 (1954) 274.
[14] ALLNATT, A. R. and PANTELIS, P., Solid State Cornt~~rlr~. 6 (1968) 309.
DISCUSSION
K. ZIEROLD. - What is the mechanism of the ionic dissolution process of the Suzuki's phase creates only conductivity, precipitation being present ? dipoles, free vacancies and free Cd2+ ions in the
E. LAREDO. - We have supposed that the complete NaCl matrix.
