Atomic-deficient nanostructurization in water-sorption alumomagnesium spinel ceramics MgAl2O4

Atomic-deficient nanostructurization in alumomagnesium MgAl2O4 ceramics sintered at 1100–1400 °C caused by water sorption are studied employing positron annihilation lifetime spectroscopy. Detected PAL spectra are reconstructed from unconstrained x4-term decomposition, and further transformed to x3-term form to be applicable for analysis with x3–x2-CDA (coupling decomposition algorithm). It is proved that water-immersion processes reduce positronium (Ps) decaying in large-size holes of ceramics (1.70–1.84 nm in radius) at the expense of enhanced trapping in tiny (~ 0.2 nm in radius) Ps-traps. The water sorption is shown to be more pronounced in structurally imperfect ceramics sintered at Ts = 1100–1200 °C due to irreversible transformations between constituting phases, while reversible physical-sorption processes are dominated in structurally uniform ceramics composed of main spinel phase.


Background
Alumomagnesium spinel ceramics MgAl 2 O 4 are known to be an excellent candidate for humidity sensors possessing a row of functional advantages before known prototypes (Kulwicki 1991;Gusmano et al. 1992;Gusmano et al. 1993;Traversa 1995;Kashi et al. 2012).The mechanism of their remarkable sensing ability is related to a great diversity of chemical and physical water-sorption processes occurring in a rich nanoporous structure of these ceramics (Traversa 1995;Kashi et al. 2012).
At a nanospace, this functionality directly relates to wellknown host-guest chemistry problems, dealing with filling of some open nanospaces in host matrix, which can be occupied by guest entities such as embedded atoms, molecules, atomic groups and clusters, distinct particles (Groen et al. 2003;Kobayashi et al. 2007;Hill et al. 2005;Kullmann et al. 2012). To identify such nanometer length-scale inhomogeneities, the method of positron annihilation lifetime (PAL) spectroscopy probing space-time continuum correlations for electron interaction with its antiparticle (positron), i.e., dependence between averaged positron lifetime and available free volume, was recognized recently as one of most promising non-destructive tools (Krause-Rehberg and Leipner 1999;Jean et al. 2003).
But possibilities of this method are essentially restricted, when dealing with substances with nanoscale atomic-deficient imperfections, i.e., free-volume elements in nanosubstances possessing simultaneously contributions from positrons annihilating in (1) defect-free bulk state, (2) deep ground state of positron-capturing sites (positron traps) and (3) bound positron-electron (positronium, Ps) state. In our preliminary works (Klym et al. 2016a, b), these channels were studied in MgAl 2 O 4 ceramics separately due to the PAL spectra reconstructed through unconstrained x4-term decomposition. When nanostructurization takes place as modification of atomic-deficient space, these processes can be tightly interconnected changing ratio between positrontrapping sites and Ps-decaying sites (Ps-traps). In such case of tightly coupling positron-and Ps-related traps, an important information can be gained from additional algorithms, developed to parameterize the PAL spectra under condition of known interconnection between positron-and Ps-related inputs. One of such resolutions referred to as x3-x2-CDA (coupling decomposition algorithm) was proposed recently (Shpotyuk et al. 2015).

3
In this work, we check the possibilities of this approach to identify changes in atomic-deficient structure of alumomagnesium spinel ceramics MgAl 2 O 4 responsible for watersorption processes.

Ceramics preparation route
The alumomagnesium MgAl 2 O 4 spinel ceramics were sintered at different temperatures (T s ) of 1100, 1200, 1300 and 1400 °C during 2 h, which are deterministic in their microstructure perfectness, the more detailed description of technological route being presented in Klym et al. (2014Klym et al. ( , 2016b. In respect to X-ray diffraction measurements, the ceramics prepared at lower T s = 1100-1200 °C are composed of main spinel phase and large amount of additional MgO and Al 2 O 3 phases (up to 12%), while the ceramics sintered at high T s = 1300-1400 °C contain additionally only MgO phase in the amount of 3.5 and 1.5%, respectively.

PAL spectra measurement procedure
The PAL spectroscopic measurements were performed using ORTEC instrument equipped with 22 Na source placed between two identical sandwiched ceramics samples. The measurements were conducted at 22 °C and relative humidity RH = 35% for ceramics samples taken just after initial drying and 7-days water-vapor exposure in desiccator (RH = 100%). To analyze both short and more prolonged PAL components, the spectra were collected within 6.15 and 61.5 ps channel widths, and further analyzed with LT software (Kansy 1996).
In our previous works (Filipecki et al. 2007;Klym et al. 2011), the MgAl 2 O 4 ceramics were studied using x3-term fitting procedure under normal statistical analysis of PAL spectra accumulated near 1 M of elementary positron annihilation events. This decomposition route allows studying only one annihilation channel directly related to watersorption processes, namely the catalytic effect revealed due to preferential Ps decaying in open pores filled with adsorbed water (Filipecki et al. 2007). At high-statistical measurements (more than 1 M counts), the best results were obtained with unconstrained x4-term decomposition (Klym et al. 2016a;Klym et al. 2016b), which allow to study nanopores of more extended sizes, responsible for o-Ps decaying. Each PAL spectrum was processed multiple times owing to slight changes in the number of channels, annihilation background and time shift of the 0-th channel. In such a way, we obtained fitting parameters (positron lifetimes τ 1 , τ 2 , τ 3 , τ 4 and corresponding unity-normalized intensities I 1 , I 2 , I 3 , I 4 ), which correspond to annihilation of positrons in the samples of interest within a quite reliable error-bar.
The decaying of bound positron-electron positronium (Ps) states forms important channel of PAL spectrum in substances possessing long-lived lifetime components (Krause-Rehberg and Leipner 1999; Jean et al. 2003). Basically, the Ps exists as para-Ps (p-Ps) with antiparallel positron-electron spins, decaying intrinsically with two γ-quanta and lifetime of 0.125 ns (in a vacuum), as well as ortho-Ps (o-Ps) with parallel positron-electron spins, decaying with three γ-quanta and lifetime of 142 ns (these states are occupied as 1:3). In a matter, since positron wave function overlaps with electron outside, the annihilation with such electron decreases lifetime to 0.5-10 ns (two γ-rays "pick-off" annihilation). Correspondingly, the Ps localized in free-volume spaces gives indication on their mean radii R in terms of long-lived τ 3 lifetime (the relative intensity of this component I 3 correlates with density of Ps sites) in respect to Tao-Eldrup equation: where ΔR = 0.166 nm is fitted empirical layer thickness (Jean et al. 2003).
By fitting Eq. (1) with measured τ 3 values, the R 3 and spherical free volumes V f can be determined.

Ps-to-positron-trapping conversion processes by x3-x2-CDA
For inhomogeneous solids, where annihilation is expected through mixed interconnected positron-Ps channels, the formalism of Ps-to-positron trapping conversion (Shpotyuk et al. 2015) can be applied to identify the changes occurring in atomic-deficient structure. The embedded guest entities (GEs) like water molecules, for instance, occupy some open spaces of Ps-decaying sites in host ceramics matrix, resulting in increased annihilation contribution from remnants of these traps.
Within this approach (which is valid only for substances allowing one type of trapping changes, when Ps-decaying sites are substituted by the same positron-trapping sites), we deal with x3-term decomposed PAL spectrum transformed to the generalized x2-term form for both reference and GEmodified substances. The second component in this generalized x2-term spectrum involves all possible contributions, arising from positron trapping, o-Ps decaying and p-Ps selfannihilation. Such simplification allows resolving additional input with defect-specific τ int lifetime and I int intensity in the second component of the reconstructed x2-term PAL spectrum for GE-modified matrix, provided compensating (τ n , I n ) input in first component obeys complete interchannel balance. Parameterization of Ps-to-positron trapping conversion in modified matrix (caused by GEs embedded in Ps-decaying sites) can be performed accepting (τ n , I n ) and (τ int , I int ) as corresponding first and second components of x2-term PAL spectrum employing conventional two-state simple trapping model (West 1973;Krause-Rehberg and Leipner 1999;Tuomisto and Makkonen 2013;Saarinen et al. 1998). The trapping modes derived within this approach are signatures of hypothetical GE-modified (nanostructurized) matrix evolving Ps-and positron-trapping sites, these being defect-specific τ int and defect-free bulk GE b lifetimes, trapping rate in defects GE b , and some derivative characteristics, such as signature of trap size in terms of equivalent number of vacancies defined by (τ int-GE b ) difference and nature of these traps defined by τ int / GE b ratio (Krause-Rehberg and Leipner 1999).

Results and discussion
The raw PAL spectra for initially dried and water-immersed MgAl 2 O 4 spinel ceramics (obtained at different sintering temperatures T s ) were reconstructed from constraint-free x4-term decomposition (Klym et al. 2016a), the corresponding fitting parameters being gathered in Table 1. These data clearly indicate that positrons are trapped more strongly in spinel ceramics prepared at lower T s , as it reflected in the increased values of second component intensity I 2 (see Table 1). Preferential decrease of defect-specific τ 2 lifetime and increasing I 2 intensity in water-immersed MgAl 2 O 4 ceramics is due to intensification of positron trapping processes in free-volume defects near grain boundaries filled with water (Filipecki et al. 2007).
The water-vapor sorption in ceramics results also in essential evolution of third and fourth Ps-decaying components. The radii of Ps-sites corresponding to third component calculated with known Tao-Eldrup Eq. (1) using τ 3 = 2.24-2.50 ns for MgAl 2 O 4 ceramics in growing T s sequence (Table 1) are only slightly changed under water sorption being in the range of 0.31-0.33 nm. In contrast, the radii of Ps-sites corresponding to fourth component are decreased substantially under water sorption from 1.70-1.84 nm (equivalent of τ 4 = 62-70 ns for alumomagnesium ceramics in decaying T s sequence) to 1.54-1.64 nm (equivalent of τ 4 = 53-59 ns). Under water sorption, the intensities I 3 reveal the same growing tendency as I 2 , while intensities I 4 demonstrate an opposite dropping trend. These findings confirm Ps annihilation in water-filled pores of ceramics due to "bubble" mechanism (Klym et al. 2016a) with third PAL spectrum component responsible for these changes, whereas the fourth component can be undoubtedly ascribed to formation of thin layers of water molecules covering walls of inner pores with larger radii of ~ 60-70 nm (Golovchak et al. 2012).
In such presentation as given in Table 1, these results cannot be treated unambiguously with x3-x2-CDA, because of additional Ps-decaying component in the detected PAL spectra. The resolution occurs to be very simple accepting that second and third components in the x4-term decomposed PAL spectra behave in a similar way that may be due to catalytic effect of positron annihilation in water-immersed medium, while fourth component reflects annihilation of positrons in water-free spaces of larger voids. With this in mind, it is possible to transform the unconstrained x4-term decomposed PAL spectra in modified x3-term form with unchanged first component (τ ** 1 , I ** 1 ) = (τ 1 , I 1 ), third component (τ ** 3 , I ** 3 ) taken as previous fourth (τ 4 , I 4 ), and second component (τ 2 ** , I ** 2 ) determined as averaged value from previous second (τ 2 , I 2 ) and third (τ 3 , I 3 ) components: The results of such transformation are presented in Table 2.
With these data, the x3-x2-CDA procedure (Shpotyuk et al. 2015) can be applied, accepting dried MgAl 2 O 4 ceramics as reference and water-immersed ceramics as modified, the calculated trapping modes being given in Table 3.
Thus, the water-induced trapping conversion in spinel MgAl 2 O 4 ceramics occurs between large-size (1.70-1.84 nm in radius) and tiny (~ 0.2 nm in radius) Ps-trapping sites. This process is captured in the nearest environment of spinel phase, as it follows from τ b GE = 0.195-0.235 ns, the values approaching defect-free bulk positron lifetimes in MgAl 2 O 4 ceramics sintered at different T s (Klym et al. 2014;Klym et al. 2016b). The water sorption is more pronounced in structurally imperfect ceramics sintered at T s = 1100-1200 °C due to irreversible transformations within inner pores between constituting MgO and Al 2 O 3 phases (resulting in increased GE b ~ 1.3-1.5 ns −1 ). In contrast, the reversible physicalsorption processes are dominated in more structurally uniform alumomagnesium ceramics prepared at higher sintering temperatures T s = 1300-1400 °C, which are composed preferentially of main spinel phase.

Conclusions
Atomic-deficient nanostructurization in alumomagnesium spinel ceramics MgAl 2 O 4 sintered at 1100-1400 °C caused by water sorption are studied by employing the method of positron annihilation lifetime (PAL) spectroscopy. The PAL spectra are reconstructed from constraint-free x4-term decomposition, and further transformed to x3-term form to be applicable for analysis with x3-x2-CDA (coupling decomposition algorithm). It is proved that water-immersion processes reduce Ps decaying in large-size holes of MgAl 2 O 4 ceramics (having 1.70-1.84 nm in radius) at the expense of enhanced trapping in tiny (~ 0.2 nm in radius) Ps-traps. The water sorption is more pronounced in structurally imperfect ceramics sintered at T s = 1100-1200 °C due to irreversible transformations between constituting phases, while reversible physical-sorption processes are dominated in more structurally uniform ceramics (T s = 1300-1400 °C) composed preferentially of main spinel phase. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creat iveco mmons .org/licen ses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.