Keywords

1 Introduction

It is known that among a large number of porous materials used for humidity sensors [1,2,3,4,5,6], spinel ceramics is one of the best. Functional ceramics, in particular MgO-Al2O3 ceramics, are thermally and chemically more stable compared with other types of porous materials with a short reaction time to change humidity [7,8,9]. In addition, the materials of active elements of humidity sensors based on ceramics do not require additional processes after technological optimization.

As noted in [10,11,12,13,14,15], the functionality of ceramic materials is determined by the microstructure of their grains, intergranular boundaries, and pores of different sizes and shapes. These elements, in general, depend on the characteristics of sintering ceramics and significantly affect its nanostructure [16,17,18,19]. In addition, the operational electrical properties of humidity-sensitive elements depend on the sorption processes, the surface area, and the sufficient amount of nanopore in the material [20,21,22]. Therefore, it is important to study the processes of nanostructured materials with developed porosity and optimal pore size distribution [19, 23, 24]. It is the void inclusion in ceramic materials that significantly affects their exploitation properties [19, 25].

Traditionally, microstructural features of materials are studied using X-ray diffraction, electron microscopy, porosimetric equipment, etc. [26,27,28]. However, methods for Hg and N2 porosimetry are limited in use, since it provides information about open nanoscale pores with radius of >5 nm and >2 nm, respectively. It is known that physical processes in ceramics depend not only on the amount and nature of large open pores but also on nanoporous and free-volume vacancies, vacancy clusters, defects, etc. [29]. Therefore, in order to obtain more information about these structural inhomogeneities and their influence on the properties of ceramics MgO-Al2O3, it is also helpful to use additional structural research methods that allow studying pores and volumetric inclusion at the nanoscale level. In this case, positron annihilation lifetime (PAL) method is one of the most powerful experimental methods for studying internal structural voids in solids [30,31,32].

Previously, in studying the structural features of the MgO-Al2O3 ceramic by the PAL method, it was shown that two processes can take place in this material: the positron trapping in defects (two components) and ortho-positronium (o-Ps) decaying (one component) obtained in the expansion of three components [20,21,22,23, 33]. Within the framework of this approach, the short-term component of the PAL spectrum with the lifetime τ 1 reflects the microstructural features of the spinel, the mean component with lifetime τ 2—defects near the intergranular boundaries. The third component with lifetime τ 3 is related to the “pick-off” annihilation of o-Ps in intergranular nanoporous filled with adsorbed water [20,21,22, 33, 34]. Using the lifetime of the third component, it was possible to calculate the radii of nanopores according to the Tao-Eldrup model [35,36,37]. However, for such a material as humidity-sensitive ceramics MgO-Al2O3, there are nanopores of different sizes and different natures [17, 23, 24, 38], the study of which by PAL method requires its modification and optimization.

The aim of this work is nanoscale investigation of pores in adsorption-desorption cycles in the MgO-Al2O3 ceramics sintered at 1400 °C for 2 hours using the modified PAL method at four-component spectrum decomposition procedure.

2 Experimental Details

The PAL study was performed using the ORTEC spectrometer (full width at half the maximum was 0.27 ns, a separation of 230 ps) at a temperature of 22 °C and an initial relative humidity of 35% [39,40,41]. Two identical test specimens were placed on both sides of the positron source (22Na isotope, activity ~ 50 kBq) from an aqueous solution of 22NaCl wrapped in a special Kapton® foil with a thickness of 12 μm.

The scheme of the experimental setup for obtaining lifetime spectra is depicted in Fig. 14.1. The signal of an initial 1.27 MeV γ-quantum recorded by the γ-scintillator is converted into an analog electrical pulse in a photomultiplier connected to this scintillator. The signal emitted from the anode of this photomultiplier and gets through a constant discriminator serves as the initial signal for the time pulse converter [42].

Fig. 14.1
figure 1

Measuring PAL system based on ORTEC spectrometer [42]

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The second scintillator registers one of two γ-quanta with an energy of 0.511 MeV. The corresponding signal from the photomultiplier anode is compared in a time pulse converter with a signal from the dynode of this photomultiplier, previously processed by the amplifier of the signal, an amplifier, and a one-channel analyzer. When changing the electrical parameters of the delay line, the initial zero-time position of the measured spectrum is selected.

The amplitude of the output signal obtained from the converter is proportional to the difference between the occurrence of the initial and final γ-quanta or the residence time of the positron. Analog-digital signal is recorded in the memory of the multichannel analyzer; the data is fed to a personal computer. Thus, a complete spectrum of the lifetime of a positron is obtained (the dependence of the number of channels or the number of counts from the positron lifetimes).

For statistical surveys with a high number of measurements, investigation was made using the PAL-modified hardware complexity with a modernized digital analog converter KC/A and a multichannel (8000 channels) WAA amplitude analyzer. This is possible to simultaneously register two annihilation spectra: up to 50 ns with a resolution of 6.15 ps and up to 500 ns with a resolution of 61.5 ps [42, 43]. The modified circuit for measuring the PAL spectra is shown in Fig. 14.2.

Fig. 14.2
figure 2

Modified PAL system using ORTEC [43]

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Such studies make it possible to obtain information in the expansion of the spectrum into three and four components for a material with advanced nanoporosity (humidity-sensitive MgO-Al2O3 ceramics). For the pairs of samples, three measurements of the PAL spectrum were used, which differed in the total number of simple annihilation events [24]. Each spectrum was repeatedly processed due to minor changes in the number of final channels, the background of annihilation, and the time of change in the spectrum. The best results were selected on the basis of the fit, defined as the lowest mean deviation between the experimental points and the theoretical curve [42]:

$$ \mathrm{FIT}=\frac{\sum \limits_{k=1}^N{\left(\frac{T_k-{E}_k}{\sqrt{E_k}}\right)}^2}{N-m}\approx \frac{1}{N}\sum \limits_{k=1}^N{\left(\frac{T_k-{E}_k}{\sqrt{E_k}}\right)}^2, $$
(14.1)

where N is the number of channels (or number of experimental points), E k experimentally measured number of counts in the kth channel, T k theoretical number of counts in kth channel, \( \sqrt{E_k} \) mean square deviation of the number of counts in the kth channel, m number of fitting parameters.

Thus, in the final result several groups with different numbers of experimental points N were formed in the middle of the chosen procedure of mathematical fitting. Only results with FIT values close to 1 (from 0.95 to 1.1–1.2) were considered to be absolutely relevant. In the next step, these values and the specific characteristics of the PAL were monitored, depending on the annihilation background and the time of change in the spectrum. It should be noted that the correction for the source and the spectrometer solution function remained constant for the entire spectrum [23, 24, 44].

By working out the PAL spectra by the LT program [45,46,47,48], it is possible to obtain the values of the fitting parameters (lifetimes and intensities). Positron trapping parameters in ceramic MgO-Al2O3, such as bulk lifetime τ b, average lifetime τ av, and the rate of positron trapping in defects κ d, were calculated in accordance with the two-state positron trapping modes [49,50,51]. The difference (τ 2 − τ b ) was evaluated as the size of bulk defects, which occupy positrons.

3 Results and Discussion

Since MgO-Al2O3 ceramics are humidity-sensitive materials, the main structural component is open nanoscale pores. Using the modified PAL method and performing additional adsorption-desorption procedures [20,21,22, 42], the processes in nanopores of this material can be studied. So, PAL experiments were carried out in the MgO-Al2O3 ceramics sintered at 1400 °C using high-statistical measurements.

Initial measurements were performed in ceramics dried in a vacuum at 120 °C for 4 hours. To study the interconnection of porous structure of ceramics, the same specimens were immersed in water (placed in the distiller, relative humidity was 100%) for 8 hours (1 day) at a temperature of 22 °C. Measurement of the PAL spectra was repeated 7 days after this procedure. At the last stage, samples of ceramics were again dried in vacuum at 120 °C for 4 hours, and measurements by the PAL method were repeated to determine the reversibility of the physical sorption of water molecules [24, 33, 44].

For the maximum estimation of free volume in ceramic samples and calculation of the nanopore size, the PAL spectra were decomposed by the LT program into four components with lifetimes τ 1 , τ 2, τ 3, and τ 4, as well as intensities I 1 , I 2 , I 3, and I 4 [24, 44]. The third and fourth components of the spectrum reflect the annihilation of o-Ps through the “pick-off” process, including water-immersed nanopores. The PAL spectrum treatment using four-component treatment due to the application of modified measurement method, which allows to expand the research area, is depicted in Fig. 14.3.

Fig. 14.3
figure 3

PAL spectra for the MgO-Al2O3 ceramics decomposed into four components [42]

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The o-Ps lifetime (τ o-Ps) in ceramic materials (the lifetime of the third and fourth components of PAL spectrum) can be related with average radius of nanopores (R) and calculated by the semiempirical Tao-Eldrup model [36, 37]:

$$ {\tau}_{o- Ps}={\left[2\left(1-\frac{R}{R+\Delta R}+\frac{1}{2\pi}\sin \left(\frac{2\pi R}{R+\Delta R}\right)\right)+0.007\right]}^{-1}, $$
(14.2)

where ΔR is an empirically determined parameter (in the classical case ΔR ≈ 0.1656 nm) which describes the effective thickness of electronic layer responsible for “pick-off” annihilation of o-Ps in voids.

In addition to the radii of nanopores (R 3 and R 4) calculated from the Tao-Eldrup model, the contribution of the corresponding nanopores by semiempirical relation is determined as [42]:

$$ {f}_v=C\cdot {V}_f\cdot {I}_{o- Ps}, $$
(14.3)

where V f = 4/3 ⋅ π ⋅ R o − Ps is free volume calculated using the lifetime of the o-Ps-related components in spherical approximation, I o-Ps is the intensity of the o-Ps-related components, and C is an empirical parameter equal to 0.0018.

As can be seen from Table 14.1, after water immersion of the MgO-Al2O3 ceramics, the lifetime of the second component τ 2 and the intensity of I 2 increase, which shows the intensification of positron trapping in defects near intergranular boundaries [20,21,22]. After drying, the intensity values are virtually returned to their initial values, while the lifetime exceeds the initial value. Thus, adsorption processes of water in the MgO-Al2O3 ceramics are accompanied by fragmentation of voids and desorption—their agglomeration. The change in the positron capture parameters correlates with changes in the parameters of the first and second components of PAL spectra.

Table 14.1 PAL parameters and size of free volumes in the MgO-Al2O3 ceramics sintered at 1400 °C in adsorption-desorption cycles: initial ceramics (1), after immersion (2), final dried (3)
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At water immersion of ceramics, the lifetime of the fourth component τ 4 is accompanied by a decrease in the intensity I 4, while a decrease of lifetime τ 3 leads to an increase in the intensity I 3. In the first case, the decrease of the lifetime τ 4 and the intensity I 4 is due to the arrangement of the layer of water molecules along the walls of the nanopores, which is accompanied by a decrease in the size of the free volume, where the o-Ps atoms are captured. In the second case, the o-Ps annihilation mechanism is more complicated. The decay of o-Ps atoms can occur both in dry nanopores and in the bubbles of water by the “pick-off” process. The last process leads to an increase in the intensity I 3. The contribution of the nanopore with size R 4 is much higher than the pore with radius R 3 (Fig. 14.4). Consequently, the modified multichannel positron annihilation model in the MgO-Al2O3 ceramics [44] besides the positron trapping channel contains a decay channel of o-Ps atoms, which reflects two different annihilation processes in two types of nanopores: “pick-off” annihilation o-Ps in water adsorbed by small nanopores due to “bubble” mechanism and in a free volume of larger nanopores filled by water [52].

Fig. 14.4
figure 4

Dependences of the radii of nanopores R 3 and R 4 (a) and fraction f 3 and f 4 (b) on the conditions of watering and drying

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Thus, PAL method gives information about nanoscale pores in addition to Hg-porosimetry data [23] (Fig. 14.5).

Fig. 14.5
figure 5

Pore size distributions of MgO-Al2O3 ceramics sintered at 1400 °C: Hg-porosimetry [23] and PAL data (for initial ceramics)

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In addition, water also affects the parameters of positron trapping in defects near intergranular boundaries (the second component of the PAL spectrum). Changes in the parameters of the second and third components under the influence of water are the same. With regard to the use of the fourth component, two different approaches can be applied. Within the framework of the first one, it is possible to estimate the influence of physically and chemically adsorbed water [22] on the modification of intergranular boundaries in ceramics during immersion. In accordance with the second approach, one can study the patterns of nanostructured MgO-Al2O3 ceramics under influence of absorbed water by all nanoporous of ceramics. The second and third components of the PAL spectra are interconnected; for ceramics positronium positrons (the second component) can replace traps (the third component). The fourth component reflects completely different processes in larger nanopores during their immersion. Therefore, in the first approach, we can assume that this component does not affect the positron trapping in defects near intergranular boundaries.

4 Conclusions

It is shown that using PAL method for the investigation of nanoscale pores in the MgO-Al2O3 ceramic, it is possible to obtain information on size of nanopores of ceramics (according to Tao-Eldrup model) and to study the processes occurring in these ceramics. The spectrum schedule for the four components also allowed modifying the multichannel positron trapping model, which combines two channels: positron trapping channel and decay of the o-Ps atoms. The third component describes “pick-off” process of o-Ps annihilation in small nanopores and in water, and the fourth component is related to annihilation of o-Ps in the volume of larger nanopores not filled by water.