CALCULATIONS OF POINT DEFECT PROPERTIES.Disorder in Pure and Doped Strontium Chloride

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CALCULATIONS OF POINT DEFECT

PROPERTIES.Disorder in Pure and Doped Strontium Chloride

P. Bendall, C. Catlow

To cite this version:

P. Bendall, C. Catlow. CALCULATIONS OF POINT DEFECT PROPERTIES.Disorder in Pure and Doped Strontium Chloride. Journal de Physique Colloques, 1980, 41 (C6), pp.C6-61-C6-63.

�10.1051/jphyscol:1980616�. �jpa-00220054�

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JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 7, Tome 41, Juillet 1980, page C6-61

CALCULATIONS OF POINT DEFECT PROPERTIES.

Disorder in Pure and Doped Strontium Chloride

P. J. Bendall (*) and C . R. A. Catlow (**)

(*) Inorganic Chemistry Laboratory, Oxford (**) Dept. of Chemistry, University College, London

RCsumC. - Nous prtsentons une etude thtorique sur les proprietts des dtfauts dans le chlorure de strontium pur et dope par cations monovalents. Nous examinons les defauts intrinskques trouvant que l'energie de formation d'un defaut du type Frenkel anionique est en bon accord avec les valeurs experimentales. Nous montrons que les defauts du type cation alkalin interstitiel sont importants aux basses temperatures dans des cristaux dopes par chlorides alkalins.

Abstract. - We present a theoretical study of the defect properties of pure and anion deficient strontium chloride.

We examine intrinsic defects obtaining an anion Frenkel enthalpy in good agreement with experimental values.

We show that alkali cation interstitials are important at low temperatures in monovalent doped crystals.

1. Introduction. - The nature of defects in pure and doped compounds with the fluorite structure at low defect concentrations have been principally determined from conductivity data [l-61. In common with other fluorites the predominant intrinsic defects in strontium chloride are of the anion Frenkel type.

Doping with monovalent cations leads to an enhance- ment of ionic conductivity and has led to proposals that alkali cations occupy regular cation sites with charge compensation by anion vacancies. Recently, however, it has been suggested that alkali cations on interstitial sites must also be considered [5].

In this paper we report a general survey of defect energetics in pure and anion-deficient strontium chloride using defect energy calculations, with parti- cular emphasis on the question of the mode of solution of monovalent dopants.

2. Technique. ^-In our calculations of defect energies we have used the HADES program 17, 81. As in earlier work on alkaline-earth fluorides [9] our lattice potential is based on the ionic model, short- range interionic interactions are described by a Born-Mayer potential and ionic polarization is treat- ed using the shell model. The parameters for this model (Table I) were derived from experimental data (see [lo]) using the same techniques as those employed for the alkaline-earth fluorides [9]. For interactions between alkali cations and anions we have used potentials derived by Catlow et al. [I 11.

3. Results and discussion. - 3.1 INTRINSIC

111 I I ( I S . - The calculated energies clearly confirm

the anion Frenkel model, with intrinsic enthalpies of anion Frenkel 2.06 eV, cation Frenkel 5.85 eV, Schottky 4.00 eV. The anion Frenkel enthalpy is

Table I. - Potential parameters for Strontium Chlo- ride.

Cation-anion interaction

Anion-anion interaction

Cation and anion shell charges are Y + and Y - and spring constants K + and k -

.

Al 2 (eV) 2 250.30

P I z

(4

0.339 7

A22 (eV) 1227.18

P 1 2

(4

0.321 4

C 2 , ( e v .

W6)

^0.0

y+ (1 e 1) 5.038

in good agreement with recent experimental values e.g. 2.0 ⁾0.2 eV [3] and 2.02 eV (Chadwick et a[., this conference).

The results for defect migration mechanisms (Table 11) resemble those for the alkaline-earth fluorides [9]. We find that the activation energy for anion vacancy migration is lower than those for anion interstitial migration and that, for the latter, the interstitialcy mechanism has a lower activation energy than a direct ( 110 ) jump even when relaxa- tion of adjacent anions is taken into account. The calculated value for vacancy migration is in good agreement with experimental values but that for interstitial migration is underestimated - a feature

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980616

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C6-62 P. J . BENDALL AND C. R . A. CATLOW

Table 11. ^-Intrinsic defect migration-activation ener- gies.

Calc. Expt.

- -

Anion vacancy 0.24 eV 0.35

Anion interstitial : 0.86

direct ( 110 ) jump 1.76 relaxed ( 110 ) jump 0.87

interstitialcy 0.46

(Experimental values ; Chadwick et al. ; this conference.)

found with similar calculations on the alkaline-earth fluorides [9].

3.2 MONOVALENT DOPANTS. - The five possible modes of solution of monovalent cations in the fluorite lattice are as : cation and anion interstitials;

the monovalent cation entering as a substitutional with compensation by either an anion vacancy or a monovalent cation interstitial ; monovalent cation interstitial with cation vacancy compensation ; monovalent cation substitutional with cation interstitial compensation (I) :

Mode A MCI + -M:

+

C1;

Mode B MCl ⁺ M:

+

C1; (+ SrCl,) Mode C MCl + ) M:

+

^$^M+⁽⁺

*

^SrC1,)

Mode D MC1 -+ M:

+

^$^Sr?+⁽⁺⁾^SrCl,)

Mode E MCl -+ M:

+ 3

^Sri2+⁽⁺

4

SrC1,)

.

The calculated point defect energies are given in table I11 and calculated cohesive energies are - 21.4 eV

Table 111. ^-Calculated point defect energies.

Anion vacancy 3.53 eV

Cation vacancy 18.34

Anion interstitial - 1.47 Cation interstitial - 12.49 Na ⁺substitutional 11.26 Na+ interstitial - 4.10

for SrC1, and - 7.93 eV for NaCl [Ill. We can use these values to calculate the energies of the modes of solution outlined above using the equations :

( I ) Subscripts i, s and v refer to interstitial, substitutional and

vacancy respectively.

where Ecoh is the cohesive energy. The values that we obtain are given in table IV.

Table 1V. ^-Energies of modes of solution of NaCl in SrCl,.

Mode Energy (eV)

- ^-

A 2.36

B 1.32

C 0.81

D 2.30

E 2.25

The most favourable mode (C) is that in which M f enters the lattice both as a substitutional and an interstitial. This would seem to be in contradiction with the results of conductivity studies which indicate that the predominant defects are cation substitutional~ and anion vacancies, i.e. mode B. However we need to consider equilibria between the various point defects. The simplest equilibrium that we might expect is that between defects formed by modes B and C,

Gervais e t al. [5] (see also [12]) suggest that an equili- brium of the type

may occur at high dopant concentrations. We find that for NaCl the formation of an alkali cation interstitial and a strontium vacancy is unfavourable by 2.98 eV. Elimination of the cation vacancy and two anion vacancies leads to the gain of the Schottky energy and the overall reaction corresponds to our mode C.

A satisfactory thermodynamic model for the distribution of point defects must include defect pair formation and entropy terms. In addition, kinetic factors associated with the mobility of alkali cations may prevent thermodynamic equilibrium to be attained. We have therefore used the calculated defect-pair binding energies (Table V) with those reported above in a simple mass action treatment of the defect equilibria [13] to obtain the distribution of defects as a function of dopant concentration and temperature.

Table V. - Defect-pair binding energies.

Binding energy (eV)

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DISORDER IN PURE AND DOPED STRONTIUM CHLORIDE C6-63

The following mass-action equations have been considered :

k, = [(M,+ Cl;)I/[M,+l [C1;1 k2 = [(M,+ Mi+)l/[M,fl [M;1 k3 = [MBI [C1;12/[Mi+I k4 = [Cl;] [Cl;]

.

1 2 3

T-l. lo3 K

Fig. 1. - Logarithm of calculated number of unbound vacancies (x,) versus 1/T for : A 1 ppm, B 10 ppm, C 100 ppm. Na'.

The results for Sr(Na)C12-, are plotted in figure 1 as the log of the number of unbound vacancies versus 1/T for three dopant levels. Four distinct regions can be identified :

1) At high temperatures the number of vacancies is determined mainly by the Frenkel energy and in this region the defects are predominantly intrinsic.

2) At intermediate temperatures the number of vacancies is equal to the number of dopant cations.

The dopant cations exist in the form of substitutio- n a l ~ with anion vacancy compensation i.e. mode B without defect pair formation.

3) At lower temperatures the formation of defect

pairs and the equilibrium between modes B and C become important. Vacancy compensation of the substitutional is replaced by dopant interstitial compensation. The pronounced curvature of the plot reflects the departure from simple Arrhenius-type behaviour.

4) The curves for all dopant concentrations tend to a common straight line at lower temperatures; in this region the dopant is in the form of approxima- tely equal numbers of cation substitutionals and cation interstitials, i.e. mode C.

Two approximations that we have used will alter the detail of our results. Firstly the potentials used for the calculations were obtained from experimental data appropriate to low temperatures. e.g. the elas- tic constants were values extrapolated to 0 K. We would expect defect energies to change with temperature. Secondly, we have assumed that, for a particu- lar temperature, all the point defects and point defect pairs are in thermodynamic equilibrium. However a factor which is of importance at low temperatures is the activation energy for alkali cation migration.

Our calculations show that such activation energies are high (- 1.8 eV) so equilibrium conditions might not be attained and the level of neutral pairs of alkali substitutionals and interstitials may not be as large as equilibrium values. Thus we would expect mode B to persist to lower temperatures than our results suggest.

4. Conclusion. - Our calculated energies of point defects in strontium chloride show that the intrinsic defect parameters closely resemble those of other fluorites with an anion Frenkel energy of 2 eV. For monovalent doped crystals at high temperatures vacancy compensation dominates but at lower temperatures the vacancies are replaced by dopant interstitial~ as the dominant charge compensator. The cation interstitials, as well as playing a significant role in transport properties, are also important in stabilizing colour centres [14, 151.

Acknowledgment. - We would like to thank Theo- retical Physics Division, Harwell for provision of computing facilities and Dr. A. V. Chadwick for communicating some of his unpublished results.

References [I] BARSIS, E. and TAYLOR, A,, J. Chem. Phys. 45 (1966) 1154.

[2] HOOD, G. M. and MORRISON, J. A,, J. Appl. Phys. 38 (1967) 4796.

[3] PAILLOUX, M., GERVAIS, A,, JACQUET, M. and BATHIER, M., C . R . Hebd. Sian. Acad. Sci. 274B (1972) 991.

[4] JACQUET, M., GERVAIS, A. and BATHER, M., C.R. Hebd. Sian.

Acad. Sci. 278B (1974) 709.

[5] GERVAIS, A,, JACQUET, M. and BATHIER, M., J. Physiquo Colloq. 37 (1976) C7-281.

[6] LIANG, C. C., REA, J. R., JOSHI, A. V. and FOSTER, D. L., J . Solid State Chem. 22 (1977) 171.

[7] CATLOW, C. R. A. and NORGETT, M. J., J. Phys. C : Solrtl St. Phys. 6 (1973) 1325.

[8] NORGETT, M. J., UKAEA report AERE-R7650 (1974).

[9] CATLOW, C. R. A,, J. Phys. C : Solid St. Phys. 9 (1976) 1845.

[lo] HAYES, W. and STONEHAM, A. M., in (( Crystals with the Fluorite Structure ⁾⁾ed. W . Hayes (Oxford : Clarendon).

[l I] CATLOW, C. R. A., DILLER, K. M. and NORGETT, M. J., J. Phys.

C : Solid St. Phys. 10 (1977) 1395.

[12] LIDIARD, A. B., in (( Crystal with the Fluorite Structure D,

ed. W . Hayes (Oxford : Clarendon).

[13] LIDIARD, A. B., Hand. Phys. 20 (1957) 246 (Springer-Verlag).

[14] BENDALL, P. J. and CATLOW, C. R. A., J. Phys. C : Solid St.

Phys. 11 (1 978) L-903.

[15] LEFRANT, S., HARKER, A. H. and TAUREL, L., J. Phys. C : Solid St. Phys. 8 (1975) 11 19.