HAL Id: jpa-00216948
https://hal.archives-ouvertes.fr/jpa-00216948
Submitted on 1 Jan 1976HAL 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.
POINT DEFECT IN SILVER
HALIDES.DETERMINATION OF IONIC
TRANSPORT PROCESSES IN SILVER HALIDES
R. Friauf
To cite this version:
POINT DEFECTS IN SILVER HALIDES.
DETERMINATION OF IONIC TRANSPORT PROCESSES
IN SILVER HALIDES
R. J. FRIAUF
University of Kansas, Department of Physics, Lawrence, Kansas 66044, U. S. A.
Résumé. •— On présente une revue des techniques expérimentales et des conceptions de modèles qui sont employées pour élucider la nature des processus de transport ionique dans ces matières intéressantes. AgCl et AgBr sont des cristaux ioniques simples montrant une conductivité et une diffusion inhabituellement grandes près du point de fusion, comparables à celles de plusieurs conduc-teurs superioniques. Les mesures de conductivité sur les cristaux purs et dopés montrent que les défauts de Frenkel sont dominants, avec des cations interstitiels beaucoup plus mobiles que les trous cationiques. La comparaison de diffusion des traceurs d'argent avec les facteurs de corréla-tion théoriques montre que les cacorréla-tions interstitiels se déplacent avec au moins deux sortes de sauts indirects interstitiels. Cette image est confirmée par les mesures de l'effet isotopique, qui indiquent que le saut interstitiel indirect oblique est très compliqué. Une analyse plus soignée de la conductivité à l'aide d'un calculateur, en tenant compte des interactions coulombiennes à courte et longue portée et en employant des tests statistiques, produit une anomalie importante pour les températures plus élevées, qui ne peut s'expliquer que partiellement par le traitement de Debye-Hùckel-Lidiard. Des mesures nouvelles de la conductivité par des techniques expérimentales per-fectionnées explorent l'anomalie très importante pour AgBr, et les résultats sont comparés avec les observations récentes de la diffusion de Na dans ces matériaux. Toutes les indications suggèrent fortement qu'il y a une croissance anormale des concentrations de défauts à cause d'un relâche-ment général du réseau cristallin.
Abstract. — A review is given of the many experimental methods and theoretical concepts used to elucidate the nature of ionic transport processes in these interesting materials. AgCl and AgBr are simple ionic crystals displaying unusually large conductivity and diffusion near the melting point, comparable to many superionic conductors. From conductivity in pure and doped samples it is established that Frenkel defects are dominant, with interstitial cations appreciably more mobile than cation vacancies. Comparison of silver tracer diffusion to theoretical correlation factors shows that interstitial silver ions move by at least two kinds of interstitialcy or knock-on processes. This picture is confirmed by isotope effect measurements, which indicate that the non-collinear interstitialcy jump is quite complicated. More elaborate computer analysis of conductivity results, taking into account short and long range coulomb interactions and using chi-square statistical tests, yields a large high temperature anomaly that is only partly accounted for by the Debye-Htickel-Lidiard treatment. New conductivity measurements with improved experimental techniques explore the very large anomaly in AgBr, and the results are compared to recent observations for diffusion of sodium in these crystals. All evidence strongly suggests an anomalous rise in defect concentration caused by a general softening of the lattice.
DISCUSSION
A. B. LIDIARD. — The increase in defect formation energy at high temperatures as inferred from your measurements can, I think, be represented as a term which is proportional to the number of defects. Though one might suppose this to be a defect interaction term, it is likely that it actually derives from the effect of defects upon those physical properties of the crystal which enter into the formation energy of the defects (e. g. lattice expansion). Such an effect would give a term in the defect formation energy which is linear in
defect concentration, whereas the actual electrostatic defect interaction gives a term closely proportional to the square root of the defect concentration.
R. J. FRIAUF. — This is an intriguing, and I believe basically sound, approach to a phenomenological description. I also agree fully with your physical description of the origin of the effect. Such an approach is especially provocative because it involves some fea-tures of a cooperative process. This picture can
C7-394 R. J. FRIAUF tainly provide a good qualitative description of the
observations and I hope soon to develop a semi- quantitative fit along these lines.
R. BAUER. - In the silver halides, the force cons- tants decrease sizeably with increasing temperature, as it is seen from the strong decrease of the elastic constants c,, and c,,. This leads to an intrinsic reduc- tion of the defect formation energies and affects pro- bably also the formation entropies. Work on this subject is in progress.
A. L. LASKAR.
-
It is indeed very satisfying that the classical high temperature anomaly in Ag-halides is excellently settled. We may be coming to the truth finally !One of the slides shown in the presentation shows
f,, us T for Cd-doped AgC1. It is found to be mostly temperature independent and shows the proper corre- lation factor for the vacancy mechanism. However, at higher temperature, there is a lowering of the value off,,.
Since the high temperature anomaly is due to the temperature dependence of defect formation energy, as you have shown, and this affects diffusion and con- ductivity in the same way, will you not expect f,, to be constant ?
R. 5. FRIAUF.
-
The effect seen in figure 6 for Cd-doped AgCl is caused by a small amount of interstitial diffusion. At temperatures between 200 and 250 OC the intrinsic Frenkel defect contribution starts to become comparable to the divalent impurity concentration of several hundred ppm : the mass action laws then allow a small number of interstitial defects, which have a disproportionately large influence because of the large mobility ratio at these tempera- tures (q = pi/p,--
20 in figure 2). Since the correla- tion factor is considerably smaller for the interstitialcy mechanisms than for vacancy diffusion, the overall value of f,, is lowered slightly by this admixture.At higher temperatures in the pure crystal the compo- site value off,, is temperature dependent because of the continuously changing contributions of vacancy, collinear interstitialcy, and noncollinear interstitialcy jumps to the diffusion of Ag (see figure 9). The changes
in the relative contributions depend, of course, on the migration energies for each of the three mechanisms. A simple enhancement of the defect concentrations, which appears to explain most of the conductivity anomaly, would not lead to any additional changes in
