Cellular Ceramics / 4

372 Part 4 Properties

Looking at the variable cross sections it becomes obvious that a fixed factor like that used for Eq. (11) of Chapter 1.1 does not give exact conductivity values, since the effect of various cross sections is not regarded. A prediction of the actual electrical resistance needs a mathematical model which is able to take the various modifications of cross-sectional area, density of ligaments, and distribution along the electrical path into account. In Chapter 4.1 some models are given for Young moduli of foam structures which can be applied to electrical conduction as well. Additional models based on MSA, mixing, percolation, and effective-media theories have been published by a number of authors with regard to electrical conductivity [2, 8, 26].

The general effective-media equation (McLachlan) combines effective media and percolation theory, so that it is applicable for a wide range of different composite structures. Since foams are composites consisting of voids and interconnected solid phase their electrical conductivity might be described by the McLachlan equation [26, 27]:

where m is the volume fraction, Uc the critical volume fraction of conducting phase, r the electrical conductivity, s the equation parameter 1 (insulating phase), t the equation parameter 2 (conducting phase), i the the index for insulating phase, c the index for the conducting phase, and M the index for the composite mixture.

The specific features of conductive foam ceramic allow a simplification of Eq. (6). The conductivity of the voids is almost zero in comparison to a semiconducting or conducting ceramic phase. The term of the insulating phase is reduced to Eq. (7):

The modified Eq. (6) for foam ceramic is given by Eq. (8):

If the conductivity of the foam is to be predicted, Eq. (8) can be transformed into Eq. (9):

Equation (9) requires the knowledge of the volume fractions of solid and void phase, the conductivity of the solid phase, and the parameters Uc and t. The parameter t needs to be fitted to the actual foam structure. Published values of t are in the range

4.4 Electrical Properties 373

of 0.8–4.5 [27]. Uc is fairly low for foam structures in which percolation occurs as soon as any foam is consistent (< 0.05).

Figure 6 illustrates the relation of equation parameters rc and mi to the electrical conductivity of foam materials. They are the most important parameters for the alteration of electrical conductivity. The ceramic material which is used for the foam determines rc. The actual conductivity is determined by the volume content of voids, which is represented by mi. This parameter strongly alters the conductivity of foam, as it is shown by Fig. 6 (bottom). However, in contrast to conventional composites the conductivity changes moderately in almost linear relation to the content of

Figure 6 Influence of parameters from Eq. (9) on electrical conductivity of foam material. Top: parameter rc, (Uc = 0.02; t = 0.8;

mi = 0.9, mc = 0.1); Bottom: parameter mi (t = 0.8, Uc = 0.02, mi= 0.9, mc= 0.1, and rc = 100 S cm–1).

374 Part 4 Properties

insulating phase (voids), since the percolation threshold parameter Uc is fairly low (about 0.02) for foam materials. The parameter t can vary in the range between 0.8 and 4.5, which does affect the foam conductivity but to a much lower degree than mi.

Ceramic foams have been manufactured and investigated with regard to their electrical conductivity [28]. The foams were obtained by direct foaming of silicon oxycarbide precursors. The use of the precursor alone leads to low conductivity in the range of 10–5 to 10–4 S m–1. The same precursor was also investigated with various filler materials. The conductivity was increased to 30 S m–1 by applying fillers of about 30 wt % SiC, C, and MoSi2. The use of Cu acetate and oxide can increase the electrical conductivity to about 4500 S m–1 even with relatively low Cu content. The direct electrical heating of precursor-derived foams is demonstrated in this paper up to 1200 C.

The dielectric constant of insulating cellular materials is decreased by dilution of the solid volume by the gas-filled cells. This was already shown for porous ceramics, where the dielectric constant follows the rule of mixtures [8]. Exceptions exist with materials of high dielectric constant [8]. Pore-charging effects can alter the linear dependence of the dielectric constant on porosity. Additional effects of the voids on the solid phase can alter the material, and hence er. The cellular structure does not influence the dielectrical properties with the same complexity as it does for the electrical conductivity. Changes in the dielectric constant of lead zirconate titanate (PZT) were reported in Ref. [29]. The foam material reaches dielectric constants in the range of 50–100, while the dense PZT material shows values above 2300.

4.4.2.4

Ceramic Fibers

Ceramic fibers have became widely used as a consequence of developments of the last few decades which have made them commercially available. Particularly electrically insulating fibers like alumina and silicate fibers have been widely used for thermal insulation and furnace construction. Electrical insulation has not been the main focus for these materials, but it is usually considered an advantage because there are no problems with touching electrical heating elements. Kamimura et al. [7] discuss the development of a Si3N4 fiber material which may be useful as highly temperature resistant material for electrical insulation of cables and electrical connections. More interesting here is the comparison given of electrical resistance with other fiber products made of alumina, quartz, and silicon carbide. As one would expect, woven or mat products made of the above materials show fairly high electrical resistivity at room temperature. Even the silicon carbide mat has an electrical resistivity of 106 X m. Except for the quartz fiber product all fiber tapes show almost constant electrical resistivity with increasing temperature. This behavior demonstrates that the electrical resistivity is not really dominated by the bulk ceramic material but by the resistance of the fiber-surface contacts in the mat. This is a specific effect of this class of cellular materials. The silicon carbide fiber product should show a drastic decrease in electrical resistivity if the semiconductive mechanisms becomes effective at high temperature. However, the electrical resistivity does not

4.4 Electrical Properties 375

change. A slight increase could even be noted due to the growing thickness of the oxide layer around the silicon carbide fibers.

If a continuous fiber strand is used the effect of oxide layers does not influence electrical conduction as long as the ratio of the oxide volume is small compared to that of the conductive fiber. In this case the electrical resistance is derived from the total cross-sectional areas of the single fibers. The resistance or conductivity can be considered reciprocal to honeycomb materials, since there are long continuous fibers (tubes) and insulating space between them. Continuous silicon carbide fibers can differ in microstructure to conventional silicon carbide materials, since they are either precursor-derived [30, 31] or CVD-derived. CVD fibers can be controlled rather precisely with regard to their chemical composition and microstructure. Depending on the preferences of the application electrical properties can be tailored.

If fibers are interconnected by sintering, their structure resembles foam ceramics. But the cross-sectional area and the electrical properties are more homogeneous. An illustration of fiber contact is given in Fig. 7 (top) and shown for a Tyranno fiber mat in Fig. 7 (bottom).

Precursor-derived SiC fibers have been commercially available for more than 20 years and have been improved considerably since electron-beam curing was used for manufacture [30]. These precursor-derived fibers have rather high electrical resistance since they either include oxygen or exhibit an amorphous structure. Properties of cellular materials like tapes and networks will correspond to the fiber properties.

Figure 7 Principal structure of connected-fiber mat (top) and

SEM image of Tyranno fiber mat (bottom).

376 Part 4 Properties

The direction of the fiber axis, the length of the fibers, and the kind of fiber interconnections need to be considered to estimate or calculate the electrical resistance of fibrous materials. The general tendency is that a higher packing density of fibers increases the electrical conductivity and the dielectric constant of the connected fiber material. While the dielectric constant depends almost completely on the volume content of fiber material and the kind of the ceramic, the electrical conductivity is governed by further parameters such as length of fibers, interconnection of single fibers, and the fiber arrangement. Since the fibers are of uniform diameter and length the creation of a mathematical description is easier than for foam materials.

4.4.3

Electrical Applications of Cellular Ceramics

4.4.3.1

Foam Ceramic Heaters

Foam ceramics are interesting materials for electrical heating. Silicon carbide foams are available from different producers. Because of the semiconductivity of silicon carbide it can be directly heated by applying electrical power. The specific advantages by using foam ceramics as heater material are shown by Table 4.

Silicon carbide foam materials can be produced by a number of technological procedures:

Table 4 Some advantages of ceramic foam heating elements.

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All manufacturing procedures can be used for foam production. The electrical properties are rather different for the different SiC material types with the same trends as observed for the related bulk materials (Table 1).

SiC foam ceramics for direct electrical heating have been developed and produced by Fraunhofer IKTS [32–34]. Cylindrical foam bodies made of Si-SiC (LigaFill) are used for demonstration of some principal heating features. The foam was manufactured according to the replication technique [31, 33]. Because of the good wetting of liquid silicon the small pores of the ligaments are filled with silicon during infiltration (Fig. 8). The resulting Si-SiC material contains about 20–40 wt % of free silicon. The foam cells are still open and unfilled.

Figure 8 Micrographs of unfilled (top) and Si-filled (bottom) ligament of SiC foam.

Silicon is a better electrical conductor than silicon carbide. The rather high content of elemental silicon in combination with effects which have been discussed above means that the final LigaFill foam material exhibits outstanding electrical conductivity with an electrical resistance of less than 0.01 Xcm [34]. Typical of bulk SiSiC materials reach specific electrical resistance of around 0.03 Xcm according to our experience. The LigaFill structure consists of Si-SiC coating and internal bulk silicon ligaments because of filling of the out-burned polymer ligaments.

The size of the produced foam ceramic heaters is 30 mm in diameter and a 60 mm in length. The cell size was varied from 10 to 60 ppi and the relative density was about 15 %. The side ends of the cylinders were closed by disks of dense Si-SiC

378 Part 4 Properties

material. Graphite electrodes were mounted onto the Si-SiC ends to provide good electrical contact to the ceramic foam.

The foam could be heated up to 900 C within 4 min by applying about 15 V/50 A. The inside and the middle of the sample are the hottest regions because of the temperature coefficient caused by cooling effects in the outer region of the foam. Table 4 gives some electrical data for direct electrical heating of the described samples.

Table 5 Heating behavior of Si-SiC foam ceramic in dependence on ppi and silicon content.

The observations show that the temperature does not have a drastic effect on the electrical resistance of the ceramic foam. Given the characteristics for bulk Si-SiC materials, it conforms to the expectation of a slight positive temperature coefficient of the electrical resistance.

The size of cells affects the electrical resistance indirectly by causing different infiltration behavior of the ligaments and changing the composition of the materials. The small-diameter ligaments of fine foam materials are infiltrated by silicon more efficiently than large-diameter ligaments because of the resulting capillary force, which promotes the infiltration process. Consequently the ratio of silicon to silicon carbide is greater for fine foams, which results in lower electrical resistance.

A comparison of the heating procedure of foam ceramics and bulk ceramics was performed in addition to the above experiments. An Si-SiC sample with the same effective cross section and hence similar electrical resistance was chosen. Heating was quite different compared to the foam material. A significant decrease in the original resistance is observed with temperature increase. When the sample reached about 550 C it cracked due to high energy load, so that a further heating up to 900 C was impossible.

This experiment illuminates the outstanding performance of foam ceramics with regard to heating rate (ca. 200 K min–1 was tested) and thermal loading. Particularly the high ratio of surface to mass results in the above advantages, which are directly related to the cellular structure of the foam ceramics.

4.4.3.2

Electrically Conductive Honeycombs

The manufacture of electrical conductive honeycomb materials from a porcelain ceramic and coal tar pitch is reported by Alcaniz-Monge et al. [6]. The honeycomb ceramic is impregnated by the molten carbon precursor and then pyrolyzed up to 1073 or 1273 K under nitrogen atmosphere. A layer of carbon is formed which enables electrical conduction. The conductivity can be controlled by the temperature of carbonization, as demonstrated by the experimental results [1073 K (800 C) –

4.4 Electrical Properties 379

30 (Xm)–1 and 1273 K (1000 C) – 160 (Xm)–1]. The aim of this development is the manufacture of electrodes for electrochemical applications.

A similar approach is reported in Ref. [4]. Cordierite honeycombs are impregnated with carbonaceous precursors. The electrical conductivity of the impregnated honeycomb reaches 0.31–110 (Xm)–1, depending on precursor and pyrolysis temperature.

Electrical conductivity can be achieved by using conductive ceramic materials like silicon carbide. This is demonstrated in Refs. [35–37], which describe silicon carbide honeycomb materials which are used as soot filters for diesel engines. Regeneration can be performed by direct electrical heating of the filter. The electrical assembly and the resistance are shown in Ref. [37]. Heating ignites the settled soot particles at about 650 C and regenerates the filter. Regeneration takes approximately 4 min and consumes 1.5 kW (24 V).

4.4.4

Summary

The electrical properties of cellular ceramic materials have not been the main focus of the development so far. Nevertheless, there are some specific effects which are unique to these materials.

The electrical behavior of cellular materials is determined by the type of ceramic material, the amount of pores/cells, the specific pore features, and the general cellular structure. The dielectric properties mainly depend on the volume fraction of pores and cells and the type of ceramic material. This causes exclusively a decrease in the dielectric constant in comparison to dense materials. The electrical conduction of cellular materials can be changed by the alteration of cross-sectional area, shape and size of cells and pores, surface composition, grain boundary character, and/or electronic properties of the material itself. Although this behavior is more complex the main trend leads to a decrease of the electrical conductivity of the cellular material in comparison to a dense material of the same kind. Because of the character of the used manufacturing procedures cellular ceramic material are different to the well-known bulk ceramic materials with regard to electrical properties.

Models of electric properties are related to models of other properties like Young’s modulus or thermal conduction, which are based on more extensive work than those of electrical phenomena. Since the manufacture of cellular materials often differs from conventional ceramics (foam, connected fibers, etc.) the material properties have to be considered specifically for modeling.

Honeycombs, foams, and biomimetic materials can be used for numerous specific applications which include electrical features. Some examples were given in this chapter.

Acknowledgement

We acknowledge R.W. Rice for fruitful and critical discussion during the reviewing process, which was a valuable contribution to this chapter.

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References