PHYSICAL REVIEW B VOLUME 52, NUMBER 2 1 JULY 1995-II Electrophysical properties of metal-solid-electrolyte composites S. Gluzman Institut fiir Energieverfahrenstechnik, Forschungszentrum Jiilich GmbH (KFA), D 5242-5 Julich, Germany A. A. Kornyshev Institutfiir Energieverfahrenstechnik, Forschungszentrum Ju lich 'GmbH (KFA), D-52425 Jiiiich, Germany and The A. N. Frumkin Institute of Electrochemistry of the Academy of Sciences, 117071 Moscow, Russia A. V. Neimark Institut fiir Anorganishe and Analytishe Chemic, Iohannes Guten-berg Universitat Mainz, D 55099 -Germany and Laboratorie Phenomenes de Transport dans les Melanges, C.N. R.S. , F-86360 Chassenenil du Poitou, France (Received 31 May 1994; revised manuscript received 20 December 1994) An e6'ective-medium theory of a random mixture of metal and solid electrolyte particles is developed to describe the bulk ac conductance of the composite. It predicts a 4 to 6 orders of magnitude enhance- ment of the dielectric permeability of the composite near the percolation threshold for electronic con- ductivity. As the frequency increases, the enhancement falls to the level of a metal-dielectric composite, as the role of the double-layer capacitance of the blocking interfaces between metal and electrolyte grains diminishes. Analytical expressions are obtained for the conductivity and dielectric function over the whole range of relative concentrations and in a broad frequency range. I. INTRODUCTION A. Metal-solid electrolyte composites There is presently great interest in dual-phase compos- ites of electronic and fast ionic conductors. These are, in particular, membranes with solid electrolyte components in which oxygen anions or protons are the conducting species used for separations and heterogeneous chemical reactions. ' In such systems the metal component plays the role of an electronically conductive catalyst or sup- porter that provides a smooth contact of the membrane with the bulk metal electrodes. Typical examples are ceramic mixtures of yttria-stabilized zirconia (YSZ) and nickel or palladium granules, the systems regarded as promising materials for hydrogen electrodes in solid ox- ide fuel cells. ' On the other hand, systems of this kind could be of interest as materials with unusual dielectric properties. The electrophysical properties of composite materials are frequently described in terms of percolation theory. Single- and dual-component systems have been considered, including clusters of conducting granules and mixtures of a conductor and superconduc- tor, an ionic conductor and insulator, and metal and insu- lator particles. ' A mixture of conductors of the first and second kind, such as a metal — solid-electrolyte corn- posite, contains some features which other composites do not possess, which makes these composites interesting from the fundamental point of view, as well. These features are as follows. (i) Solid electrolyte granules are ionic conductors, the conductivity being, usually, a few orders of magnitude smaller than the electronic conductivity of the metal. (ii) There is no dc current across the interface of the electronic conductor and ionic conductor, unless some Faraday process (electrochemical reaction) takes place at the interface. (iii) An electric double layer of microscopic dimensions is formed at the blocking metal/solid-electrolyte contact with the double-layer capacitance ~ 10 pF/cm, a value some 10 — 10 times greater than the geometrical capaci- tance of insulator particles of the same size (in the range of micrometers and greater). (iv) While the metal/solid-electrolyte contact is block- ing for dc, it can conduct ac current in the same way as a metal/dielectric interface, but the characteristic frequen- cies for the former are much lower. These frequencies are determined by the relaxation time needed to charge the double layer via the migration of ions through the bulk of the electrolyte to the interface. ' This time is -l41/D, where D is the difFusion coefficient of mobile ions, I& is the Debye length in the solid electrolyte, while l is the thickness of the solid electrolyte particles. ' In composites, the size of the grain will stand for l, i.e. , the relaxation time will be proportional to the size of the grain. For a particle of 1 pm size the typical relaxation time — 10 — 10 s. The relaxation should give rise to a pronounced frequency dispersion of dielectric permittivi- ty in the MHz range, at frequencies the lower the larger the granules. B. Metal/composite/metal structures There is, however, a principal di6'erence between metal-insulator and metal — solid-electrolyte mixtures due to electric double-layer formation at the metal/solid- electrolyte interface. The latter does not let a static elec- tric field penetrate into the bulk of the composite below the percolation threshold in the metal component. 0163-1829/95/52(2)/927(12)/$06. 00 52 927 1995 The American Physical Society