Keywords

1 Introduction

A long time nanostructured MgAl2O4 ceramics are interesting materials for humidity sensors due to their inner nanoporous structure and surface porosity, which promotes effective cooperative adsorption of water molecular [1,2,3,4]. The humidity-sensing application of these ceramics is known to be determinant of chemical and physical water–adsorption processes occurring within inner pores in ceramics bulk [5,6,7]. The presence of open porosity permits greater conductivity due to the enhancement of the specific surface area available for water–adsorption [8,9,10]. Recently, it was shown that amount of adsorbed water in these ceramics affects not only their electrical conductivity, but also other physical–chemical parameters [10, 11]. Such parameters can be the positron trapping modes of free volumes (or nanovoids) studied by positron annihilation lifetime spectroscopy (PALS)—one of the most informative experimental methods for studying of structurally intrinsic nanovoids in solids such as ceramics [12,13,14,15], thick films based on ceramics [15,16,17], and nanocomposites [18, 19] in the form of different modifications (clusters, agglomerates, nanopores, etc.) [20, 21].

We have achieved significant success in the study of spinel MgAl2O4 ceramics by the PALS method [8, 10, 11, 21]. It was shown that positrons injected in the studied MgAl2O4 ceramics can undergo two different processes such as positron trapping and ortho-positronium o-Ps decaying. The latter process (so-called “pick-off” annihilation) resulting from Ps interaction with electron from environment (including annihilation in liquid water) is ended by emission of two γ-quanta [20, 22]. In general, these two channels of positron annihilation are independent. However, if trapping sites will appear in a vicinity of grain boundaries neighboring with free-volume pores, these positron-positronium traps become mutually interconnected resulting in a significant complication of PALS data.

We have developed several approaches to the analysis of PALS spectra for the humidity-sensitive MgAl2O4 ceramics using different numbers of fitting parameters and algorithms to justify the obtained results [21, 23,24,25]. The goal of this work is to generalize in one work the previously presented approaches to the analysis of the PALS spectra of nanostructured spinel-type MgAl2O4 ceramics at adsorption of water. The trapping of PALS spectra is presented at the analysis on three and four components and also at the fixed values of some positron trapping parameters.

2 Sample Preparation and Experimental

The studied spinel-type MgAl2O4 ceramics were sintered from fine-dispersive Al2O3 and MgO powders using a special regime with maximal temperatures Ts of 1400 °C, the total duration being 2 h [21, 23]. In a result, the humidity-sensitive ceramics with a so-called trimodal pore size distribution and character values of pore radiuses centered near ~0.003, 0.09 and 0.4 μm were obtained [21]. The phase composition of ceramics obtained with X-ray diffraction [21, 23] was established that the studied ceramics contained the main spinel phase and small quantity of MgO phase (1.5%).

PALS measurements were performed using an ORTEC spectrometer [20, 26]. The 22Na isotope was used as positron source, placed between two identical samples. The obtained PALS spectra were decomposed by LT computer program of Kansy [27]. In this work, three experimental and analysis approaches were presented to study of water–adsorption processes in the nanostructured MgAl2O4 ceramics using PALS method.

The first approach: analysis of PALS spectra by three-component fitting procedure in MgAl2O4 ceramics before and after water–adsorption. PALS measurements were performed at 20 °C and ~35% relative humidity [21]. We used three measured PALS spectra for each investigated pair of samples, the best results being chosen by comparing statistically weighted least-squares deviations between experimental points and theoretical curve. In order to change interrelation between positron trapping and Ps decay modes in the deconvoluted PALS spectra, we placed the samples into distillated water for 12 h. Then, the PALS measurements were repeated once more with water-immersed MgAl2O4 ceramics at the same conditions. We used three-component fitting of PALS spectra and obtained fitting parameters (positron lifetimes τ1, τ2, τ3 and corresponding unity-normalized intensities I1, I2, I3). Typical PALS spectra decomposed on three components using LT program (with τ1, τ2 and τ3 lifetimes as well as I1, I2, and I3 intensities) are shown in Fig. 1.

Fig. 1
figure 1

Fitting of PALS spectra for MgAl2O4 ceramics on three components using LT computer program [28]

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The second approach: analysis of PALS spectra by three-component fitting procedure in the MgAl2O4 ceramics at fixation of the lifetimes of the first and the second PALS components within row of relative humidity (RH). PALS measurements were performed at 20 °C. The selection of corresponding values for measuring chamber permit to investigation of samples at constant values of relative humidity in the range of 25–60% and 25–98% [24, 28].

Special testing procedure with a set of standard thermally treated non-defected Ni and Al probes was performed to correctly account for source input and other positron trapping channels in the measured lifetime spectra. The obtained data were mathematically treated at three-component fitting procedure with the fixed positron lifetimes of the first and second PALS components (τ1 and τ2). Only results with FIT (short abbreviation originated from “fitting”) values close to 1.0 [24] were left for further consideration.

The third approach: analysis of PALS spectra by four-component fitting procedure in MgAl2O4 ceramics before and after water–adsorption [23]. The PALS measurements were performed at 22 °C and relative humidity RH = 35% after drying (initial samples) and after 7 days of water exposure (water vapor in desiccator at RH = 100%). Each PALS spectrum was collected within 6.15 ps channel width to analyze short and intermediate PALS components. To obtain data on longest-lived PALS components, the same ceramics were studied within a channel width of 61.5 ps as in [23, 29, 30]. At high-statistical measurements (more than ten millions of counts), the best results were obtained with four-term decomposition procedure. Such approach allows us to study nanopores of different sizes, responsible for o-Ps decaying. Each PALS spectrum was processed multiply owing to slight changes in the number of final channels, annihilation background, and time shift of the 0-th channel. In such a manner, we obtained fitting parameters (positron lifetimes τ1, τ2, τ3, τ4 and corresponding unity-normalized intensities I1, I2, I3, I4), which correspond to annihilation of positrons in the samples of interest.

In the all three approaches with using a well-developed formalism for two-state positron trapping model [21, 31, 32], the following parameters describing positron lifetime spectra can be calculated according to Eqs. (1–3):

$$\kappa_{d} = \frac{{I_{2} }}{{I_{1} }}\left( {\frac{1}{{\tau_{b} }} - \frac{1}{{\tau_{2} }}} \right),$$
(1)
$$\tau_{b} = \frac{{I_{1} + I_{2} }}{{\frac{{I_{1} }}{{\tau_{1} }} + \frac{{I_{2} }}{{\tau_{2} }}}},$$
(2)
$$\tau_{av.} = \frac{{\tau_{1} I_{1} + \tau_{2} I_{2} }}{{I_{1} + I_{2} }},$$
(3)

where κd is positron trapping rate in defect, τb—positron lifetime in defect-free bulk, and τav.—average positron lifetime. In addition, the difference (τ2 − τb) can be accepted as a size measure of extended defects where positrons are trapped in terms of equivalent number of monovacancies, as well as the τ2/τb ratio represents the nature of these defects.

3 Results and Discussion

3.1 Water–adsorption Processes in Nanostructured MgAl2O3 Ceramics Studied by Three-Component Fitting Procedure

The obtained PALS characteristics for the MgAl2O4 ceramics sintered at different Ts before and after water-immersion have a peak and region of smooth fading of coincidence counts in time (Fig. 2). Mathematically such curves describe by sum of exponential functions with different indexes (inversed to lifetimes).

Fig. 2
figure 2

Positron lifetime spectra for initial and water-immersed MgAl2O4 ceramics sintered at different Ts [28]

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As has been shown [21, 28], at three-component fitting procedure, the shortest (lifetime τ1 and intensity I1) and middle (lifetime τ2 and intensity I2) PALS components were ascribed to positron trapping modes. By accepting two-state positron trapping model [32], the longer τ2 lifetime can be treated as defect-related one; these positron trapping defects being located near grain boundaries [33].

Obtained fitting parameters and positron trapping modes for initial and water-immersed MgAl2O4 ceramics are shown in Tables 1 and 2, respectively. The radii R3 of spherical nanopores (given in Table 2) were calculated using of o-Ps-related τ3 lifetime in known Tao-Eldrup model [34, 35]:

Table 1 Fitting parameters for initial and water-immersed MgAl2O4 ceramics mathematically treated within three-component procedure [21]
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Table 2 Positron trapping modes for initial and water-immersed MgAl2O4 ceramics mathematically treated within three-component procedure [21]
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$$\tau _{{o - Ps}} = \left[ {2\left( {1 - \frac{R}{{R + \Delta R}} + \frac{1}{{2\pi }}\sin \left( {\frac{{2\pi R}}{{R + \Delta R}}} \right)} \right) + 0.007} \right]^{{ - 1}}$$
(4)

where ΔR is empirically derived parameter (ΔR ≈ 0.1656 nm for polymers [18]), which describes effective thickness of the electron layer responsible for the “pick-off” annihilation of o-Ps in a hole.

As has been shown early [21,22,23,24] and above, the first component of PALS spectra with lifetime τ1 and intensity I1 as well as the second component with lifetime τ2 and intensity I2 are related to positron trapping modes. The lifetime τ2 reflects positron trapping on defects located near grain boundaries on ceramic materials.

In initial ceramic samples obtained at different Ts, the shortest τ1 and middle τ2 positron lifetimes and intensities I1 and I2 reduced with rises of sintering temperature (see Table 1 and Fig. 3). In spate of structural distinction of ceramics sintered at different Ts, positrons are trapped in defects with the same rate of κd = 0.60 ns−1 (Table 2). The radii R3 of spherical nanopores (given in Fig. 3) were calculated using τ3 lifetimes in Tao-Eldrup model.

Fig. 3
figure 3

Nanopore radii R3 in MgAl2O4 ceramics sintered at 1100–1400 °C changed in water–adsorption cycles

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Fig. 4
figure 4

Changes in lifetime components in dependence on sintering temperature of MgAl2O4 ceramics [28]

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The third PALS component with lifetime τ3 is related with o-Ps decaying. In initial ceramic samples, this lifetime reduces from 2.6 to 1.9 ns with Ts, but intensity I3 is closed to 0.02. In water-adsorbed ceramics, lifetime τ3 is closed to 1,84 ns, while τ3 ~ 1.88 ns is related to o-Ps “pick-off” decaying in water at 20 °C. In all cases, intensity I3 rises from 2% to 0.12–0.15 a.u. testifying large amount of adsorbed water in ceramic samples. This change is accompanied by reduced in parameters of the first PALS component, but parameters of the second component are without changes.

3.2 Water–Adsorption Processes in Nanostructured MgAl2O3 Ceramics Studied by Three-Component Fitting Procedure with Fixation of the Lifetimes

To study more considerable changes in positron trapping in the MgAl2O4 ceramics caused by absorbed water, the new algorithm is needed to treatment of PALS data [24]. This task can be permitted due to fixation of τ1 and τ2 parameters because adsorbed water not changes structure of spinel ceramics.

As was described above, the lifetime τ2 is related to extended defects near grain boundaries in ceramic materials. Positrons are trapped in the same defects in MgAl2O4 ceramics independent on amount of adsorbed water by their nanopores. So, the first and second positron lifetimes (τ1 and τ2) can be considered near constant. Therefore, all changes in fitting parameters of these components will be reflected in intensities I1 and I2. The third lifetime τ3 is non-fixed (see Table 3). Treatment of experimental PALS data was carried out at fixed lifetimes (τ1 = 0.17–0.2 ns and τ2 = 0.36–0.38 ns). At that, the best FIT parameters were obtained at constant lifetimes τ1 = 0.17 ns and τ2 = 0.37 ns [24].

Table 3 PALS characteristics for MgAl2O4 ceramics sintered at 1300 °C (RH = 25%–60%–98%–60%–25%)
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The I1 and I2 intensities are changed dependently from amount of adsorbed water in MgAl2O4 ceramics. Thus, rising of RH from 25 to 98% results in reducing of intensity I1 and increasing of intensity I2. The changes of RH from 98 to 25% reflect inverse to previously described transformation in I1 and I2 intensities (Table 3). The positron trapping in water-immersed defects related to the second component is more intensive. The lifetimes τ3 are near 2.3–2.8 ns. The input of this component is not changed, and intensity is near 1% [36].

Fig. 5
figure 5

Dependences of positron intensity I2 and positron trapping rate κd on relative humidity in adsorption–desorption cycles for the MgAl2O4 ceramics sintered at different Ts [28]

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In contrast, most significant changes in positron trapping in MgAl2O4 ceramics caused by water-sorption reflect in positron trapping rate in defect κd (Fig. 5). Thus, the water-sorption effect in the studied spinel ceramics is accumulated in non-direct trapping κd parameter [24].

3.3 Water–Adsorption Processes in Nanostructured MgAl2O3 Ceramics Studied by Four-Component Fitting Procedure

Fitting parameters obtained within four-component treatment of the reconstructed PALS spectra of initial and water vapor MgAl2O4 ceramics sintered at 1100–1400 °C are gathered in Table 4. It is established that τ1 lifetime in the dried ceramics decreases with Ts, while I1 intensity increases in respect to amount of main spinel phase like in [32]. Positrons are trapped more strongly in ceramics prepared at lower Ts, as reflected in the values of the second component of the reconstructed PALS spectra. As it follows from Table 4, the numerical values of this component (τ2 and I2) decrease with Ts.

Table 4 Fitting parameters for MgAl2O4 ceramics sintered at different Ts obtained at four-component decomposition procedure [23]
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As it follows from Table 5, the calculated values of positron trapping modes in MgAl2O4 ceramics (average positron lifetime τav., bulk positron lifetimes in defect-free samples τb and positron trapping rates in defects κd) are decreased with sintering temperature Ts. These parameters are in good agreements with amount of additional MgO and Al2O3 phases in the ceramics [32].

Table 5 Positron trapping modes and radii of nanopores determined from four-component fitting procedure for MgAl2O4 ceramics sintered at different Ts [23]
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At the same time, the principal water–vapor sorption processes in the studied MgAl2O4 ceramics sintered at 1100–1400 °C occur to be mostly determined by o-Ps related components in the PALS spectra reconstructed through four-term fitting procedure. As it was shown earlier [24, 29], the corresponding long-lived lifetimes τ3 and τ4 reflect sizes of nanopores, and their intensities I3 and I4 are directly related to the number of these nanopores.

So, in the initial MgAl2O4 ceramics sintered at 1100–1400 °C, the lifetime τ3 increases with Ts, while intensity I3 decreases (Table 4). These changes are due to the increase in the size of small nanopores with radius R3, and their reduction is caused by increasing contact between grains. The lifetime τ4 and intensity I4 naturally decrease with Ts, indicating reduction in size and number of nanopores with radius R4. The radii R3 and R4 of spherical nanopores (given in Table 5) were calculated using τ3 and τ4 lifetimes in Tao-Eldrup model. It is shown that radius of nanopores R3 increases from 0.309 to 0.331 nm, and R4 remains nearly at the same level (~1.8 nm) in the initially dried ceramics sintered at 1100–1400 °C (Fig. 6).

Fig. 6
figure 6

Nanopore radii R3 and R4 in MgAl2O4 ceramics sintered at 1100–1400 °C changed in water–adsorption cycle

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Preferential decreasing of the lifetime τ2 in water vapor MgAl2O4 ceramics and increasing of their intensity I2 demonstrate intensification of positron trapping in defects near grain boundaries filled with water. Thus, the water–adsorption processes in MgAl2O4 ceramics are accompanied by fragmentation of positron trapping sites near grain boundaries [23].

Water–vapor sorption processes in the studied ceramics result in essential evolution of third and fourth o-Ps-related components. The intensity I3 increases in all initial samples after water–vapor exposure, thus confirming o-Ps annihilation in water-filled nanopores through a “bubble” mechanism (with corresponding o-Ps lifetime close to 1.8 ns) [37,38,39]. At the same time, the lifetime τ3 decreases in more defective ceramics sintered at 1100 and 1200 °C, but increases in more perfect ceramics sintered at 1300 °C and 1400 °C.

Other mechanism of water–vapor sorption processes similar to one reported in [40] is realized in the studied MgAl2O4 ceramics through fourth component of the PAL spectra. Unlike the third component, the intensity I4 decreases in water–vapor exposure ceramics samples. Since this intensity does not drop to zero being within 0.4–0.9% domain, it should be assumed that there exists a fraction of closed nanopores, where o-Ps are trapped [29].

4 Conclusions

Peculiarities of water–adsorption processes in nanostructured humidity-sensitive MgAl2O4 ceramics studied by positron annihilation lifetime at three- and four-component fitting procedures were generalized. The mathematical treatment of experimental PALS data at constant values of reduced bulk and defect-related lifetimes allows to refine the most significant changes caused by absorbed water in the functional ceramics.

It is shown that positrons are trapped more strongly in the ceramics obtained at lower Ts, which was reflected in the second component of the four-term decomposed PALS spectra. The positron trapping in defects occurs more efficiently in water-immersed ceramics due to increase in positron trapping rate of extended defects. The more perfect structure of ceramics, the more considerable changes occur in the water-absorbing pores.

The third and fourth longest-lived components in PALS spectra are due to annihilation of o-Ps atoms in the nanopores, the corresponding radii being calculated from τ3 and τ4 lifetimes using known Tao-Eldrup model. The Ps annihilation in nanopores with adsorbed water vapor is shown to occur via two mechanisms: o-Ps decaying in nanopores including “pick-off” annihilation in the “bubbles” of liquid water and o-Ps trapping in free volume of nanopores with physisorbed water molecules at the pore walls. The water vapor modifies defects in ceramics located near grain boundaries, and this process accompanied by void fragmentation at water–adsorption.

The fixation of all water-dependent positron trapping inputs allows to refine the most significant changes in positron trapping rate of extended defects located near grain boundaries. The water–adsorption processes in MgAl2O4 ceramics leads to corresponding increase in positron trapping rates of extended defects located near grain boundaries.