Transport in electroceramics: micro- and nano-structural aspects

doi:10.1016/S0955-2219(03)00507-7

Journal of the European Ceramic Society

Volume 24, Issue 6, 2004, Pages 1251-1257

https://doi.org/10.1016/S0955-2219(03)00507-7 Get rights and content

Abstract

Point defects are of paramount importance for electroceramics. They are key structure elements as regards materials functionality; but, in addition, they are also decisive for chemical kinetics, hence for preparation, conditioning, annealing and degradation phenomena. Concentrations and mobilities of these charge carriers are significantly changed at or near interfaces (or more generally higher dimensional defects) giving rise to depletion, accumulation, and inversion layers with respect to ionic and electronic carriers and hence to distinct electrical and chemical effects. It is discussed how these effects can be explained and how such knowledge can be used to design electroceramics purposefully. Examples refer to ionically or mixed conducting oxides and halides. Finally, in nano-structured materials the spacing of interfaces becomes relevant in that local properties can be severely affected. Such size effects do not only lead to confinement effects in the case of electronic carriers but also to anomalies with respect to ion conduction and mass transport. The potential of the nano-regime for electrical and chemical properties of electroceramics is discussed in the framework of a “soft materials science”.

Introduction

Defects are of paramount significance for electroceramics. While the number of defects increases with dimensionality, their mobility decreases. As a consequence, point defects are even present under equilibrium conditions and in fact are often in local equilibrium under operational conditions, whilst interfaces as two-dimensional defects are typical frozen-in structure elements, introduced and shaped by the preparation. Nonetheless, and this will be largely the scope of this paper, they set important boundary conditions for the point defect concentrations. One-dimensional defects such as (isolated) dislocations play an intermediate role, they are also typical non-equilibrium phenomena but often mobile enough to be healed out at operation temperatures. If we distribute N_D zero-, one- or two-dimensional defects (dimensionality D) randomly within a cubic crystal containing N uncharged atoms of the same kind, the equilibrium concentration (arc denotes equilibrium value) is (1, 2) $N_{D} ∼ N^{1−D3} exp − Δ G_{D}^{∗} kT .$

The reduction of $N_{D}$ with increasing D is due to the decreased number of available states $N^{1−D3}$ but more importantly due to the increased free formation enthalpy per defect. As a consequence, realistic numbers for ΔG_D* lead to an equilibrium number of defects, much less than unity (i.e. virtually zero) if D=2 or 3. This is even more so if the crystal size (i.e. N) is small. Owing to a perceptible mobility of dislocations, it is often assumed that free dislocations are absent in nanocrystalline matter. Hence in this paper we ignore dislocations, while we consider interfaces as metastable frozen-in structure elements. Point defects are considered to be in local equilibrium (usually in one sublattice) or (as dopant defects or defects in other sublattices) totally frozen.

The role of point defects in solids as decisive mobile atomic/ionic excitations and hence as charge carriers is analogous to that of H₃O⁺ (excess proton) and OH⁻ (lacking proton) in water, which highlights the significance not only for the electrical transport but also for mass transport and chemical kinetics.

Point defects—in a wider sense, also including the electronic carriers (excess electron, and lacking electron=electron hole)—play a direct prime role for the function of many electroceramics, as typically used in electrochemical devices such as batteries, fuel cells, ceramic membranes, electrochemical sensors and electrochromic windows. In addition to that—as they are indispensable for the chemical kinetics—they play a decisive role in preparation, processing, conditioning and degradation of electroceramics even if they are not very relevant for the function.

Consequently, it is of high priority to know the control parameters for tailoring the defect chemistry in a given electroceramic material. This will be briefly discussed.

Section snippets

Parameters controlling point defect chemistry

Let us first consider the bulk of a binary MX under equilibrium conditions. Under Brouwer conditions (only two majority carriers), the solution for the defect concentration (c_j) reads $c_{j} =α_{j} P_{X_{2}}^{N_{j}} C^{M_{j}} ∏ r K_{r}^{γ_{rj}} T,$ revealing the control parameters, component potential (P_X₂), doping content (C) and temperature (α being a constant). Note that the boundaries of the windows in which Eq. (2) holds—and hence the characteristic exponents (being rational numbers) N_j; M_j; γ_rj—depend unambiguously on P, C, T (we

Interfacial effects on defect chemistry and transport

It has been shown in detail that internal boundaries also lead to severe changes in the defect chemistry via space charge effects (cf. role of heterogeneous doping).⁷ In that sense they are also ex situ parameters. However, now the calculation cannot resort on electroneutrality. In addition, the structurally modified part of the interface (compared to the bulk)—the interfacial core—will exhibit its own defect chemistry and special mobilities, and can hence, provide fast pathways or obstacles

Examples of accumulation and depletion layers

A striking example for the efficacy of heterogeneous doping is the admixture of insulating but surface active second phase particles, e.g., Al₂O₃ to AgCl, the positive surface charge due to Ag⁺ adsorption is equivalent to a drastic increase of silver vacancies in the adjacent boundary regions.⁷ At the contact of two ionic conductors (apart from phase equilibration) a redistribution of ions over both space charge regions [and of course also of electrons, see Eq. (4)], occurs; this explains

Nano-structured materials: the spacing of interfaces as control parameter

Nano-structured materials necessarily possess a high proportion of interfaces (ϕ_bg),typically more than 10% of the atoms sit in what can be called interfacial core. Hence we expect pronounced size effects. In this context it proves worthwhile (even though a clear distinction is not always feasible) to distinguish between “trivial size effects” whereby the same effects as described above, are realised but appear in an augmented way owing to the increased ϕ_bg, and “true” size effects whereby also

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Transport in electroceramics: micro- and nano-structural aspects

Abstract

Introduction

Section snippets

Parameters controlling point defect chemistry

Interfacial effects on defect chemistry and transport

Examples of accumulation and depletion layers

Nano-structured materials: the spacing of interfaces as control parameter

Solid State Ionics

Solid State Ionics

Solid State Ionics

Phys. Chem. Chem. Phys.

Solid State Ionics

Phys. Rev. A

J. Electrochem. Soc.

Defect chemistrycomposition, transport, and reactions in the solid state; part I: thermodynamics

Angew. Chem., Int. Ed. Engl.

Festkörper—Fehler und Funktion: Prinzipien der Physikalischen Festkörperchemie

Partial conductivities in SrTiO3bulk polarization experiments, oxygen concentration cell measurements, and defect-chemical modeling

J. Am. Ceram. Soc.

Controlled conductivity in cadmium sulfide single crystals

Z. Phys. Chem.

Defect chemistry of relaxor ferroelectrics and the implications for dielectric degradation

J. Am. Ceram. Soc.

J. Am. Ceram. Soc.

Low-temperature defect chemistry of oxides. I. General aspects and numerical calculations

J. Appl. Phys.

Low-temperature defect chemistry of oxides. II. Analytical relations

J. Appl. Phys.

Ionic conduction in space charge regions

Prog. Solid St. Chem.

Point defect thermodynamics: macro- vs. nanocrystals

Electrochemistry

Partial conductivities in SrTiO₃bulk polarization experiments, oxygen concentration cell measurements, and defect-chemical modeling