Cellular Ceramics / 4

361

4.4

Electrical Properties

Hans-Peter Martin and Joerg Adler

4.4.1

Introduction and Fundamentals

Cellular ceramic solids can be of various types:

The common feature of all the above cellular materials is a combination of solid and gaseous elements which are structured by more or less defined regular geometric shapes and positions.

Cellular materials differ from the “conventional” materials by the combination of a solid phase with closed or open regularly structured voids, tubes, or any other type of inhomogenities, such as pores. These inhomogenities change the electrical properties of cellular materials drastically if they differ from the ceramic. The most common inhomogenities are pores in a great variety of shapes and sizes. The general effects of porosity, such as dilution of one material, and the specific effects of porosity, which include effects determined by shape and distribution, are interlinked. This is of interest if electrical insulation or dielectric effects are aimed for an application. As long as no extreme temperature or high voltage is applied, the gaseous phase is just a passive component of the cellular material for electrical conduction or electrical capacity. The influence of the gaseous phase on the conduction mechanism is more complicated, while the influence on the dielectrical properties almost completely depends on the volume fraction of the gaseous phase.

The solid phase determines whether the material is electrically conducting, semiconducting, or insulating. It holds the electrical carriers and governs the electrical phenomena of the cellular materials in the vast majority of cases. The only exception could be a cellular material which is filled by an electrically conductive component which partly or completely substitutes the gaseous phase.

An obvious idea is that the electrical properties of the solid phase are identical with those of the same bulk material. However, manufacture of foam ceramics and conventional bulk ceramics can differ. Figure 1 presents the microstructure of conventional sintered silicon carbide and an SiC microstrut of a foam ceramic. There

Cellular Ceramics: Structure, Manufacturing, Properties and Applications.

Michael Scheffler, Paolo Colombo (Eds.)

Copyright 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31320-6

362 Part 4 Properties

Figure 1 Micrographs of dense S-SiC (left) and S-SiC ligament from foam (right).

are significant differences in materials structure between the conventional and the ceramic foam material.

On the macroscopic scale of products made of cellular ceramics the electrical properties are influenced by the way in which the solid network is joined, the shape and geometry of the solid material, and interactions of the solid with the gaseous phase. A more detailed discussion is given below.

Since electrical applications have not been the driving force for the development of cellular materials, the electrical properties have not yet been investigated to the same extent as properties like permeability, mechanical strength, and thermal properties [1]. Nevertheless, several publications mention electrical data or report experiment results for cellular materials [1–7]. Moreover, there are links to mechanical and thermal behavior which are influenced by porosity or cellular effects. Changes in mechanical properties like Young’s modulus and thermal conductivity are related to the electrical properties. This opens the opportunity to use models or considerations which were made for other properties. But care is needed in applying these models to electrical properties, since the physical character of the conduction or dielectric processes might require alteration or even exclude certain models of other physical phenomena. Chapters of this book on mechanical (4.1) and thermal properties (4.3) discuss a number of models which can be applied to electrical properties, for example, Minimum Solid Area (MSA) models. Furthermore, some aspects of porous materials which are related to cellular materials or even identical to them are discussed in [8]. In addition to the consideration of mechanical properties in relation to the porosity, electrical properties are also discussed in this book. It is stated that MSA models are consistent for the relation of porosity and electrical conductivity of different ceramic materials [8]. One should always be aware of the influence of pore size, pore shape, and other pore characteristics which could be significant for conduction. Even dielectric properties could be influenced by the character of the pores, particularly if the base materials are piezoelectric or ferroelectric [8].

The specific issue of cellular ceramics is the existence of large-scale “pores” such as tubular pores of honeycombs or macroscopic voids of foams. The “conventional” pores of ceramics are built up by ceramic grains. The maximum size of these pores

4.4 Electrical Properties 363

depends on the grain size of the ceramic powder. The cellular pores are built up by macroscopic ceramic elements like walls of honeycombs or struts of foams, which consist of a number of grains. These pores can be manufactured in any size which is achievable by the applied technology. These ceramic elements may contain microscopic pores themselves. Ultimately, the porous effect is more complex than that known for “conventional” porous ceramics, and this must be considered in modeling cellular materials.

The application of cellular ceramics for electrical functions offers a number of unique features, such as tailoring of electrical resistance by the kind of cellular structure, anisotropic behavior of electrical conduction, combination of various types of cellular structures, modification of the electrical performance by using the properties of the gaseous phase, excellent transfer of energy from the cellular product into the surroundings (electrical heaters), and combination of excellent electrical conductivity with moderate thermal insulation.

Table 1 Electrical properties of bulk ceramic materials.

* Ref. [10]. ** Experimental data from the authors.

The data in Table 1 are intended to give a basic idea about the range of a few electrical properties of ceramic materials. Unfortunately, almost no proper data are available for porous ceramic materials, so that the given data can not be applied directly for cellular materials.

A very important parameter is the specific electrical resistance. It is a materials constant which changes with temperature. It is the reciprocal of the specific electri-

364 Part 4 Properties

cal conductivity, which depends on the mobility, charge, and number of the electrical carriers per unit volume. Since the mobility and number of free electrical carriers depend on temperature, the specific electrical resistivity is also temperature-depen- dent. The specific resistivity can be obtained by measuring the electrical resistivity, the cross-sectional dimensions, and the length of a material sample, and finally calculated for practical use by Eq. (1)

where el is the specific electrical resistance, R is the electrical resistance of the sample, A the cross-sectional area, and l the sample length.

The specific electrical resistivity data of Table 1 show that most of the ceramic materials are insulators ( el > 108 X m). This is due to the dominant ionic and covalent binding between the ions or atoms of ceramic compounds. In most cases no free electrical carriers are available for electrical transport through the ceramic material. Some of the materials become electrically conductive at high temperatures. For instance, the specific electrical resistivity of zirconium dioxide drops from 106 X m at 20 C to about 10–2 Xm at 1000 C because of the activation of oxygen ions, which become able to move by diffusion through the material.

Some ceramic materials are semiconductive, for example, B4C and SiC. The conductivity of SiC is due to the much smaller band gap between valence band and conduction band of the electrons. It reaches about 2.2 eV for b-SiC [11]. The resistance of these semiconducting materials decreases with increasing temperature because more free carriers (electrons and electron holes) are mobilized by thermal energy. Silicon carbide materials can have quite different electrical resistance depending on the type of manufacture. Even the same SiC material type, for example, sintered SiC (S-SiC), can differ by several orders of magnitude in resistivity just by slight variation of the sintering aid, sintering temperature, or other technological parameters. The porosity of cellular materials changes the parameters A, l, and el of Eq. (1), and this results in considerable changes in electrical resistance.

The insulators (specific electrical resistivity > 108 Xm) are known as dielectric materials. When an electric field is applied to these materials polarization of electrons or ions occurs inside the material. This effect leads to an increase in the capacitance of a capacitor on filling it with the dielectric material. The dielectric constant er gives the ratio of the capacitance between a capacitor filled with material Cm and one filled with vacuum C0 (Eq. (2)):

In most cases the cellular effect on the dielectrical constant is the dilution of the material by air-filled pores or cellular elements. Additional effects which may change the character of the ceramic material are particularly observed for ferroelectric or piezoelectric materials.

4.4 Electrical Properties 365

The complexity of the solid–gaseous interaction is illustrated by porous liquidphase sintered SiC (LPS-SiC), which demonstrates the influence of a porous structure on the electrical resistance (Fig. 2).

Figure 2 R–T characteristics of dense (top) and porous (bottom) LPS-SiC.

The electrical resistance can be modified by porosity in various manners:

366 Part 4 Properties

The first effect is a trivial one which needs no further discussion. The other effects can be caused by a number of specific reasons which can not be discussed in general. The electrical resistance of porous LPS-SiC (pore volume of 40 %) serves as an example to illuminate the above mentioned effects.

The manufacture of this type of material has been described elsewhere [12]. It is based on the well-known technology of LPS-SiC manufacture. High porosity is obtained by selecting suitable grain size distributions. The oxidic sintering additives form a liquid phase which is able to reprecipitate silicon carbide and thus promote the sintering process. The oxides themselves solidify as isolated aggregates at the triple junctions of the SiC grains without forming an interconnected layer around the silicon carbide grains. The SiC grains are doped by the oxide additives, so that the outer sphere of the SiC grains is highly conductive for electrical carriers, as was already discussed for dense LPS-SiC materials [13]. The porous silicon carbide is sintered according to the same mechanism as dense LPS-SiC, but its silicon carbide grains are completely accessible to the additives because of the high porosity. This shows the alteration of the SiC grains due to the porosity. Furthermore, the formation of intergrown SiC boundaries and segregations of oxide-dominated triple points predetermines the favorable path of electrical conduction and the final resistivity of the material demonstrating the effect of alteration of grain boundaries on the electrical resistivity. The outcome is a silicon carbide material with extraordinary electrical conductivity at room temperature and almost no change in electrical resistivity with increasing temperature. The interaction of the sintering additives and the ceramic grains is promoted by the pores during sintering, and this results in a level of electrical conductivity of a polycrystalline SiC material that has never before been achieved [14]. However, if the porous SiC material is heated under oxidizing atmosphere the resistance increases drastically at temperatures above 500 C. The large surface area and accessibility of the SiC grains to the atmosphere promote oxidation along the grain boundaries. This interaction of the pores with the material again changes the electrical resistance drastically.

4.4.2

Specific Aspects of Electrical Properties of Cellular Solids

Whether a cellular ceramic is electrically conductive or insulating is determined by the solid ceramic in the same way as for other ceramics. The specific aspects of cellular ceramics are derived from the arrangement of the cellular structure. Furthermore, the existence and character of porosity inside the solid ceramic elements of the cellular structure strongly change the resulting electrical properties. Since the electrical properties are a product of the interaction between solid and gaseous phase, honeycombs, biomimetic ceramic structures, foams, and connected fibers must be discussed in different ways.

4.4 Electrical Properties 367

4.4.2.1

Honeycombs

Honeycomb materials are produced by extruding a plastic ceramic mass (Chapter 2.2). They mostly consist of the ceramic material and large gas-filled tubes. Tube diameters as small as 200 mm have been reported [5, 15] in addition to larger sized honeycombs which have been well established for a number of years. The interaction with the gas phase and the ceramic material is limited to the surface as long as the ceramic material is dense. Therefore, consideration of the electrical properties could be performed in a similar manner to the mechanical properties (Chapter 4.1). The MSA model, which gives the relation of the porous to the dense material, is given in that chapter already [E/E0 = (1–P)n, n = 1]. The straight tubular pores of honeycomb structures result in the upper limit of conductivity for porous or cellular structures being reached.

In most cases the cellular effect of a honeycomb ceramic on the electrical resistance is a simple geometrical one. The cross section is reduced by the lack of conductive material, so that the electrical resistance is increased in comparison to bulk material. An illustration is given in Fig. 3. The cross-sectional area of bulk material can be calculated by Eq. (3)

and the cross-sectional area of honeycomb material by Eq. (4)

where x is the number of tubular pores of the honeycomb, c1 the horizontal width of a tubular pore, and c2 the vertical width of a tubular pore.

The resistance can be calculated by Eq. (1) using the honeycomb cross-sectional area according to Eq. (4) by Eq. (5)

where Rh is the electrical resistance of the honeycomb sample, el the specific electrical resistivity of the ceramic material, l the length of the honeycomb sample, and Ah the cross-sectional area of the honeycomb sample.

The cross section of honeycomb materials differs according to the direction of current flow. Figure 3 shows the cross section viewed parallel to the axis of extrudation. Current flow perpendicular to the extrudation axis is even more limited by a more reduced cross section. Consequently, the resistance of honeycomb materials depends on the direction of current flow. As long as the wall thickness of the honeycomb is thick enough that the specific surface area is in the range of that of bulk material, the honeycomb products can be considered like bulk ceramic material with regard to their electrical properties.

368 Part 4 Properties

Figure 3 Cross section of bulk (left) and honeycomb (right) materials.

The effect of the honeycomb structure on the dielectric constant is very similar to the effect on the electrical resistance. The mass of the honeycomb material is reduced by the extent shown in Fig. 3. This leads to a proportional reduction in er because of the substitution of ceramic material by air. In contrast to the electrical resistance, the dielectric behavior does not depend on the direction of the applied electrical field.

4.4.2.2

Biomimetic Ceramic Structures

Biomimetic ceramic materials have gained considerable attention in recent years. Their features can vary over a wide range depending on the biological structures which were used to produce the ceramic material [16–18]. Well-described types of biomimetic ceramics are wood-derived carbon materials and silicon carbide (Chapter 2.5) [19,20]. To our knowledge there is no extensive work published on investigations of biomimetic ceramic materials and their electrical properties. Therefore, just few general statements and predictions are given here.

Silicon carbide materials derived from different wood species could behave in various manners with regard to their electrical properties:

The biomimetic structure has a simple geometric effect on the cross-sectional area, as was described for honeycomb materials. The prediction becomes more difficult because the reduction of the cross section area is not constant along the axis of the products, as is illustrated in Fig. 4.

If the wood-derived ceramic is produced by liquid-silicon infiltration all pores can be filled by silicon. The material is no longer a real cellular material in this case. The electrical situation is completely changed because the former voids become conductive. If silicon infiltration is performed by gas-phase reaction the pores can stay open after reaction and sintering, and a honeycomblike material is obtained. The electrical conductivity decreases with increasing amount of pores.

4.4 Electrical Properties 369

Figure 4 Principal structure of honeycomb (left) and woodderived ceramic (right).

The biological template which was used to manufacture the biomimetic ceramic determines the resulting cellular structure. If wood is used as template for siliconinfiltrated silicon carbide or carbon materials the amount of free silicon and free carbon and the structure of the ceramic (pore size, pore shape, silicon distribution, etc.) are predetermined [18, 19]. The difference between wood-derived Si-SiC and conventional Si-SiC is a hierarchic arrangement of the carbon residues or of the free silicon. This can lead to favorable electrical paths along the conductive silicon or carbon structures. A tendency to decreasing conductivity can be expected if the pore volume of the biotemplate increases. The shape, structure, and arrangement of the tem- plate-derived pores govern the degree of modification of conduction. If dielectric materials like alumina or mullite are used for material production the dielectric constant decreases with increasing pore volume, but the dependence on the kind of pores is much less pronounced than for conductivity phenomena.

During sintering and application the silicon carbide material may undergo an interaction with the gaseous phase [20]. Since the wall thickness is in the range of several micrometers a strong interaction with the pores is enabled. The occurring gases depend on the sintering technology and the used raw materials. Doping of the silicon carbide, oxidation of the silicon carbide surface, or even a nitridation could alter the final product. This offers the opportunity to increase or decrease the electrical conductivity or dielectric constant of the ceramic material, depending on the kind of interaction and modification.

4.4.2.3

Ceramic Foams

Foams can be produced by different techniques and from a number of materials (see Part 2 of this book). Alumina, zirconia, glass, carbon, and silicon carbide are the major material types from which ceramic or ceramiclike foams have been made up to now [21–23]. Foams can be open-cell or closed-cell structures. In each case the solid phase is an interconnected matrix and allows transport of electrical carriers. A comparison of electrical properties of different foam types always requires a careful consideration of specific properties like foam density, ligament density, foam material type, and specific structure and composition of the material. Therefore, a straightforward comparison of different foams with regard to their electrical properties is rather vague. General parameters are given below for the estimation of the electrical resistance of ceramic foams.