Cellular Ceramics / p3

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3.1

Characterization of Structure and Morphology

Steven Mullens, Jan Luyten, and Juergen Zeschky

3.1.1

Introduction and Theoretical Background

3.1.1.1

The Importance of Foam Structure Characterization

Ceramic foams, also named cellular ceramics or porous ceramics, offer a series of unique properties because of their combination of a highly porous cellular structure and a tailored composition of the strut material. Porous ceramics are promising candidates for a wide range of engineering applications. As the internal structure of these materials can vary widely, there is a diversity of fields in which these products are already being used or in which they can be of substantial benefit [1].

When considering the internal, three-dimensional architecture of foam materials, one can use a number of characterization parameters such as cell size distribution and cell morphology (for example anisotropy), window opening, strut thickness, shape and length, interconnectivity, porosity, and type of porosity (open versus closed). Figure 1 shows some of these structural parameters for the open and closed cell units.

In the last few years, several innovative manufacturing routes have led to a wide diversity of ceramic foam materials, with respect to the materials of which they are composed, specific structure, and mechanical strength. The window of properties and characteristics for each technology can be tailored to some extent by means of

edge / strut

vertex

Figure 1 Some components of the structure of a cell unit in a) open and b) closed foams.

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

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the experimental conditions during processing, depending on the desired properties for a specific application.

The ability to tailor the pore structure is exemplified by comparing the strut morphology of ceramic foams produced by replication of reticulated polyurethane and by direct foaming of a ceramic suspension with a gelling agent [3]. Figure 2a shows the triangular-shaped strut with a hole in the center that results from pyrolysis of the polymer skeleton. Clearly, this feature will affect properties such as the mechanical behavior of the foam. In contrast, direct foaming of a ceramic suspension produces a material with dense struts (Fig. 2b).

Figure 2 Strut morphology for a foam made by a) replication of reticulated polyurethane foam and b) direct foaming of a ceramic suspension.

As the manufacturing and processing parameters determine the ultimate properties of the foam structure and thus its domain of application, accurate and quantitative characterization of the morphology and the internal architecture of the foam is essential both for product development, manufacturing, and end-use.

3.1.1.2

Structure-Dependent Properties

Ceramic foams significantly extend the range of properties of materials that are available to engineers, because they have an unique combination of characteristics. Table 1 lists some of the properties of ceramic foams directly related to their typical microand macrostructure [1].

The relative density, defined as the foam density divided by the density of the solid material, is one of the most important structural properties that governs the general behavior of a ceramic foam. The relative density of common foams usually ranges between 0.5 and 0.30.

The thermal conductivity varies from 0.1 to 1 W m–1 K–1. Heat transfer can be further reduced by decreasing the cell size while maintaining a low density [4]. The electrical resistivity increases when an electrically conductive material is foamed [5], and the dielectric constant of dielectric foams increases with increasing density [6].

3.1 Characterization of Structure and Morphology 231

mechanical analysis is substantially simplified by this cell geometry, and this allows the derivation of a general set of expressions for the mechanical behavior. However, assigning a single unit cell to these complex macrostructures may be a major oversimplification [14, 15]. Gibson and Ashby have shown that by using this unit cell the relative density of most three-dimensional cellular solids can be related to the macrostructure by the following expressions for openand closed-cell foams:

These expressions should be accurate for relative densities less than 0.3. The parameters C1 and C2 are constants characterizing the cell geometry. Ashby and Gibson derived 0.333 and 0.766 for C1 and C2, respectively.

During the foaming process, cell elongation in the direction of foam expansion can occur. Therefore, in many cases, characterization in three dimensions is necessary for an accurate description of cell size. Zhang and Ashby [16] argued that the cell geometry best representing isotropic foams, and at the same time capable of filling space, is a tetrakaidecahedron, also known as the Kelvin cell. This truncated octahedron was considered the best unit cell for partitioning space into cavities of equal volume while minimizing the interfacial area (Fig. 5a) until in 1993 Weaire and Phelan discovered a foam structure containing two different types of cavities of equal volume and with a smaller surface area than the Kelvin foam [17]. The unit cell consists of eight polyhedra (two dodecahedra and six 14-hedra) and is replicated in a cubic lattice. Figure 5b shows a dodecahedron at the front upper right; the other visible cells are 14-hedra.

Figure 5 Foam structure composed of a) tetrakaidecahedra (Kelvin cells) and b) the Weaire–Phelan unit cell consisting of eight polyhedra.

At high relative densities (> 0.3), the cellular structure is lost and identification of a repeating unit cell becomes more problematic.

A theoretical model by Peng et al. [18] correlates the overall porosity with the structural parameters of a single cell. Under the condition of equally sized spherical foam cells having a dense packing and thus a mean pore coordination number of

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12, the pore volume fraction Vp can be expressed in terms of the ratio of window size to cell size k

This equation holds for fractional porosities above a critical value of Vp= 0.74. However, the model assumptions are rarely found in practice. For example, the window diameter strongly depends on the fabrication method and varies over a wide range for foams with the same fractional density.

3.1.2

Characterization of Foam Pore Structure

Although resolving the structure of cellular foams has been the subject of scientific research for some time, no simple standard experimental technique or procedure to determine some of the most common structural parameters has been identified so far. Although most of the characterization techniques have proven their value in different fields of scientific research for several years, their potential in investigating the parameters that describe the shape, isotropy, and interconnectivity of single cells, as well as the isotropy and fractional density of the whole component, in highly porous materials has yet to be explored.

The following section of this chapter describes a series of analytical characterization techniques commonly used in the determination of some of the most relevant structural parameters of porous materials. For each technique, both the underlying principle and a general interpretation of the measured data are briefly reviewed. Also, the experimental specifications are listed in greater detail.

For comparing the various techniques, a set of porous alumina samples was manufactured. More details on the manufacturing route are given in Section 3.1.2.1. Because of the nondestructive nature of some characterization techniques, the same set of samples could be applied for different techniques. The bar-shaped ceramic foam samples were cut in half: one part was sliced and analyzed by image analysis, and the other was successively used for the Visiocell measurements, permeability measurements (capillary flow porometry), and micro computer tomography. As all the reported measurements originate from the same batch of samples, the influence of process variations is eliminated. This approach enables a more reliable comparison of the techniques discussed below. Section 3.1.2.2 ends with a short overview of other techniques that are either well known for characterizing porous samples or are relatively new in this research field. Section 3.1.2.3 summarizes the various techniques and the corresponding pore sizes for this set of samples.

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3.1.2.1

Sample Preparation

Most of the analytical techniques were applied to a series of porous alumina samples, which were all produced by replication of reticulated polyurethane foam. The advantages of this method include the wide diversity in mean cell size of the polyurethane sponges, the narrow pore size distribution, and the relatively large window of processing parameters, which enable a broad range of structures for the ceramic foams. Processing is described in Chapter 2.1 and detailed in Ref. [2].

Four polyurethane foams were selected (kindly supplied by Recticel Co., Belgium). The reaction-bonded aluminum oxide suspension used to coat the polymeric sponges contained a high concentration (30–35 vol %) or a low concentration (20 vol %) of ceramic/metal powder. After drying, the polyurethane was pyrolyzed at 600 C in air, and the resulting samples were sintered for 1 h at 1750 C. This procedure resulted in eight ceramic foam samples, with expected mean pore sizes ranging from 400 to 1800 mm.

Table 2 lists information about the samples that were investigated. The sample identification contains the approximate mean cell size of the polyurethane foam and the concentration of reaction-bonded suspension used to coat the polyurethane foam (e.g., PU-620-20: sample made starting from a polyurethane foam with an approximate pore diameter of 620 mm and coated with a suspension containing 20 vol % of aluminum/alumina powder).

Table 2 Overview of the investigated samples.

* Pore size determined by Visiocell (see Section 3.1.2.2).

** Volume shrinkage measured by geometry difference after sintering.

3.1.2.2

Characterization Methods

The different methods can be classified according to some inherent aspects of the technique itself:

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1)Nondestructive and destructive methods are distinguished according to whether the foam is irreversibly modified by the test itself (e.g., mercury intrusion porosimetry) or by sample preparation (e.g., thin slices used in image analysis). Capillary flow analysis, liquid extrusion porosimetry, and micro computer tomography are examples of nondestructive characterization techniques.

2)Microscopic or macroscopic techniques according to the size of the area of interest.

3)The dimensionality of the analysis: transferring two-dimensional data to the representation of the three-dimensional internal structure is problematic for geometrically complex pore shapes and requires in many cases foreknowledge and assumptions on shape, distribution, and isotropy. The step from spatial morphology to planar sections, as in two-dimensional characterization techniques like image analysis, involves a great loss of information.

Ideally, because many properties of the cellular material are directly related to the architecture of the sample, a direct, noninvasive investigation of the three-dimen- sional internal structure of the material is preferred. However, because no single characterization technique can provide a complete overview of all structural parameters, a combination of methods is in many cases necessary. Prior knowledge of the sample structure can help in selecting the appropriate technique or combination of complementary techniques to give a realistic description of the sample, depending on the desired information for a specific application.

3.1.2.2.1The PPI Method

Principle

The size of a cell is one of the key parameters in the design of a foam. For many applications, foam performance is directly influenced by cell size. For more than 25 years, the cellular structure and the cell size have been defined by the unit ppi (pores per inch) [19]. The number of pores is counted over a standard length of one inch. The linear intercept method was primarily used when manual measurements were required to obtain data, because they could be performed by drawing random lines on images of sections. Figure 6 examplifies this method on a micrograph of a polyurethane foam. With modern computer-based instruments, it is usually easier to measure the intersection areas which are made by a sampling plane with the object.

Interpretation of measured characteristics

This unit can be a little confusing and subjective because of:

1)The unclear definition of a “pore”: it can be a window or the full section of the cell.

2)The size of the pore: in case of a cell window, the size depends on the viewing angle. For the cell section, the size depends on the location of the section (top, middle, or bottom).