Elsevier

Optics Communications

Volume 168, Issues 1–4, 1 September 1999, Pages 237-250
Optics Communications

Full length article
Characterization of the pore structure of alumina ceramics by diffuse radiation propagation in the near infrared

https://doi.org/10.1016/S0030-4018(99)00347-8Get rights and content

Abstract

Light scattering by pore/particle interfaces causes diffuse light propagation in ceramics. The diffuse light transmission is highly sensitive to structural changes in the last sintering state. The transmission increases more than one order of magnitude between 93% and 99% of the theoretically possible density. By using diffuse transmission and reflection measurements, a quantitative analysis of the pore size distribution can also be made. The directional-hemispherical transmittance and reflectance of partially sintered Al2O3-samples were measured at room temperature in the wavelength range from 700 nm to 2500 nm. A three-flux solution of the equation of radiative transfer is shown to be an adequate tool to derive the extinction coefficients from the directional-hemispherical transmittances. The pore size distribution was determined by fitting theoretical light scattering of spherical pores, which was calculated by the Mie theory, to the experimental extinction data.

Introduction

In materials manufacturing, sintering processes play an important role for the adjustment and optimization of properties. Energy and money can be saved by lowering the sintering temperature and by reducing the sintering time [1]. For different raw materials and applications specially adapted sintering conditions are necessary. The costs for empirical optimization of the sintering conditions by trial-and-error are high as several parameters have to be varied: e.g. sintering temperature, cooling and heating rates as well as the sintering atmosphere in the furnace. In addition, in sintering experiments, results are usually available only after the specimens have cooled down. Thus new methods are desirable which allow to extract results in situ during the sintering process. For chemical reactions, crystallization and melting processes in situ measuring methods are already in use 2, 3.

Until now changes of the microstructure of the material during sintering can only be detected by measuring the shrinkage of the material via dilatometry. The latter allows to determine the pore volume which is an important parameter for the sintering process. Dilatometry is used for process-control during rate-controlled sintering. It is a difference method, however, which depends on the exact determination of the density before or after sintering.

The sensitivity of dilatometry decreases strongly towards the end of sintering, when the shrinkage becomes small. The sintering process is most interesting at this state, however. If sintering is stopped too early, the mechanical properties may be poor, because of still existing pores. When the sintering is stopped too late, the strength may be reduced because unwanted grain growth had occurred.

Light scattering is an additional method for detecting changes in porosity. Light scattering methods at room temperature are already in use to monitor the pore size distribution in ceramics 4, 5, 6. Until now usually highly dense ceramics with pore volumes below 0.5% have been investigated, as in most cases only the directly transmitted (in-line) beam, which decays exponentially with sample thickness, was measured.

In the case of negligible absorption in the sample, the intensity of the diffuse, multiply scattered radiation, however, decreases essentially inversely with the optical thickness of the sample, instead of exponentially. Predominant forward scattering enhances diffuse transmission. The measurement of the diffuse transmission (instead of the in-line transmission) thus allows to cover a porosity range between 0.1% and 5% which is of importance for applications. The directional-hemispherical transmittance of the scattered radiation can be measured with an integrating sphere. In our experimental set-up it also includes the transmitted, non-scattered beam. The transmittance then is converted into an effective extinction coefficient by applying radiative transfer theory.

From the spectral variation of the effective extinction coefficient, the pore structure can be determined by applying the Mie theory. It is also possible to measure the directional-hemispherical transmittance of a laser beam during the sintering process and hence monitor the sinter process in situ.

Experimental results of the measurements of the directional-hemispherical transmittance and reflectance on partially sintered Al2O3-samples and a detailed description of the analysis of such data is presented. For the solution of the equation of radiative transfer we use a three-flux approximation, which mathematically has the same complexity as a two-flux calculation, but provides a far better accuracy.

Section snippets

Determination of extinction coefficients from the directional-hemispherical transmittance

The magnitude of the directional-hemispherical transmission Tdh (including the non-scattered beam) through a sample with independently scattering (and generally also absorbing) pores depends on the internal and external reflection at the sample surface, the porosity, the pore diameter and structure, the index of refraction of the matrix material and the wavelength of the transmitted radiation. If one assumes spherical pores the radiation cross-section and the phase function p(ϑ) of the

Sample production and experimental set up

The measured samples had been made from highly pure Al2O3-powder. The samples were produced by the Fraunhofer-Institut für Silicatforschung (ISC) as follows: Al2O3-powder (Premalox 10-powder from ALCOA) was filled into a cylindrical silicone vessel (∅inside=13 mm, length=30 mm). The silicone vessel was compressed isostatically with 250 MPa for 15 min. Afterwards the green body had an average density of 2230 kg/m3 which corresponds to 56% theoretical possible density (t.d.=3985 kg/m3). The green

Results and analysis

Fig. 7 shows the measured directional-hemispherical transmittance Tdh of the three samples. The sums of Tdh and Rdh are nearly one for λ=700 nm to 2500 nm (Fig. 7). Therefore the directional absorbance Ad=1−(Tdh+Rdh) is negligible in this wavelength range. Values larger than one in Fig. 7 are caused by measurement inaccuracies.

If the absorption is negligible, the effective optical thickness τ0* or the effective extinction E* can be calculated from the known directional-hemispherical

Conclusions

The analysis carried out at our institute have shown that it is possible to determine the pore structure of ceramics by measuring the spectral variation of diffuse transmission in the near infrared where no absorption occurs.

This opens the possibility to use a laser beam as a radiation source for the measurement of the diffuse transmittance in situ during the sintering process. However, in this case one obtains only information about one unknown quantity, in contrast to the spectral

Abbreviations used

ϑscattering angle
θangle relative to the surface normal
ϕazimuth angle
μdirection cosine
τoptical depth
τ0optical thickness
Πporosity
Ωsolid angle
λwavelength
ω0albedo
θccritical angle
σggeometric mean standard deviation
Aabsorption coefficient
aweight factor
Addirectional absorbance
b, Cconstants
Dthickness
d, ∅diameter
dMmodal value
Eextinction coefficient
ffrequency
F, qradiative flux
ganisotropy factor
Iintensity
Lpenetration depth
mindex of refraction
pphase function
Qrelative scattering cross-section
rrandom variable

Acknowledgements

This work is supported by the German Science Foundation (DFG, grant number: CA196/1-1, RA614/2-1) Bonn.

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