Study of nanoporous in humidity-sensitive MgAl₂O₄ ceramics with positron annihilation lifetime spectroscopy
It has been shown that positron annihilation lifetime spectroscopy is a quite
 promising tool for nanostructural characterization of humidity-sensitive spinel-type
 MgAl₂O₄ceramics. The results have been achieved using the four-component fitting
 procedure with arbitrary l...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2011
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| citation_txt | Study of nanoporous in humidity-sensitive MgAl₂O₄ ceramics with positron annihilation lifetime spectroscopy / H. Klym // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 109-113. — Бібліогр.: 23 назв. — англ. |
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| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | It has been shown that positron annihilation lifetime spectroscopy is a quite
promising tool for nanostructural characterization of humidity-sensitive spinel-type
MgAl₂O₄ceramics. The results have been achieved using the four-component fitting
procedure with arbitrary lifetimes that is applied to mathematically treat the measured
spectra. It has been shown that the Tao-Eldrup model is adequate to calculate the
nanopore size in MgAl₂O₄ ceramics if using the lifetime values of the third and fourth
components.
|
| first_indexed | 2025-12-07T18:38:17Z |
| format | Article |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 109-113.
PACS 82.45.Xy, 92.60.Jq
Study of nanoporous in humidity-sensitive MgAl2O4 ceramics
with positron annihilation lifetime spectroscopy
H. Klym
Scientific Research Company “Carat”, 202, Stryjska str., 79031 Lviv, Ukraine
Lviv Polytechnic National University, 12, Bandera str., 79013 Lviv, Ukraine
Phone: 8-0322-638303 ; e-mail: klymha@yahoo.com, scigroup@novas.com.ua
Abstract. It has been shown that positron annihilation lifetime spectroscopy is a quite
promising tool for nanostructural characterization of humidity-sensitive spinel-type
MgAl2O4 ceramics. The results have been achieved using the four-component fitting
procedure with arbitrary lifetimes that is applied to mathematically treat the measured
spectra. It has been shown that the Tao-Eldrup model is adequate to calculate the
nanopore size in MgAl2O4 ceramics if using the lifetime values of the third and fourth
components.
Keywords: nanopore, humidity-sensitive ceramics, sensor, spectroscopy.
Manuscript received 28.04.10; accepted for publication 02.12.10; published online 28.02.11.
1. Introduction
Nowadays, an adequate understanding the correlation
between structure and physical-chemical properties of
functional ceramics, one of the typical representatives of
the so-called topologically disordered substances having
wide application, is still in a sphere of sharp scientific
and commercial interests for scientists and numerous
known electronic firms all over the world [1-4]. The
atomic-species structure or spatial order arrangement in
atomic positions is typically taken as a main determinant
for their properties. In bulk ceramics, in dependence on
the sintering temperature, a significant shrinkage of the
atomic structure occurs, which leads finally to more or
less complicated pore topology [5]. These pores along
with specific vacancy-type defects within individual
crystalline grains and intergranual boundaries represent
free-volume structure of ceramics.
Humidity-sensitive nanoporous MgAl2O4 ceramics
with the spinel structure are one of the most promising
materials in view of their application in microelectronics
as active elements for humidity sensors [6-9]. Because of
significant complications in the microstructure of these
ceramics revealed at the levels of individual grains,
intergranual boundaries and pores, the further progress in
this field depends on the development of new
characterization techniques that can be used in addition to
the traditional ones. This concerns the positron anni-
hilation lifetime spectroscopy (PALS), the method really
applied to ceramics because of significant complications
in correct interpretation of the obtained data [9].
Positrons injected to the studied MgAl2O4 ceramics
undergo two positron trapping with two components in
positron lifetimes and ortho-positronium o-Ps decaying,
these parameters being obtained with the so-called three-
and four-component mathematical fitting procedure.
Within this approach, the shortest component of the
deconvoluted PALS spectra with the positron lifetime τ1
reflects mainly microstructure specificity of the spinel
ceramics, and the middle component with the positron
lifetime τ2 corresponds to extended defects located near
intergranual boundaries. The third and fourth
components with the lifetimes τ3 and τ4 are related to
“pick-off” annihilation of o-Ps in nanopores. It is
established that the adsorbed water molecules act
catalytically on positron trapping in MgAl2O4 ceramics,
and do not change significantly o-Ps decaying
modes [10]. This work is aimed at the study of
application possibilities of the PALS technique to
characterize nanoporous features of humidity-sensitive
spinel MgAl2O4 ceramics.
2. Theoretical approach within the frames
of the Tao-Eldrup model
To study o-Ps “pick-off” annihilation processes in
MgAl2O4 ceramics, the mathematical model is needed
for adequate description of nanostructured pores in these
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
109
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 109-113.
humidity-sensitive materials. As this model, the Tao-
Eldrup one can be applied.
In recent 20 years, the relation between the o-Ps
lifetime and free volume size has been determined using
the Tao-Eldrup model [11, 12]. It assumes that o-Ps
trapped inside the spherical free volume (represented by
rectangular potential well) may decay spontaneously via
three-quantum annihilation or “pick-off” process. In this
case, the o-Ps decay constant is
)1( PP TbET −λ+λ=λ − , (1)
where TSb λ+λ=λ
4
3
4
1
is the decay rate of ortho-
positronium in bulk material ( = 7.9895 ns and =
7.0410 ns are the decay rates of para- and o-Ps in
vacuum), P is the probability to find o-Ps outside the
potential well.
Sλ Tλ
The Tao-Eldrup model was elaborated for small
free volumes, like vacancies in solids, voids in polymers,
bubbles forced by Ps in liquids. In that case, the spacing
of energy levels in small voids is much larger than
thermal energy, and thus only the lowest level is
populated; Ps wavefunction for this state is the spherical
Bessel function. In order to simplify the calculations, the
well of finite depth is substituted by infinitely deep one
but broadened Δ (nm), which is needed to reproduce the
value of P in finite well depth and radius R (nm)
[11, 12]. Then,
⎟
⎠
⎞
⎜
⎝
⎛
Δ+
π
π
+
Δ+
−=
R
R
R
RP 2sin
2
11 . (2)
The results of calculation for cubic geometry can be
compared to spherical (or cylindrical) side length
a (nm):
)(2 Δ+= Ra . (3)
The square of o-Ps wavefunction in an infinite
potential well is adduced in [11].
3. Experimental
The studied ceramics were prepared from Al2O3 with
specific surface area of 67 m2/g and
4MgCO3⋅Mg(OH)2⋅5H2O with specific surface area of
12.8 m2/g. The obtained powder is mixed with an
organic binder to prepare green body billets. Then, these
pellets are sintered using a special technological regime
with the maximal temperatures Ts of 1200, 1300 and
1400 °C for 2 h.
Phase composition of MgAl2O4 ceramics was
determined using the X-ray diffractometry (XRD)
method. The XRD patterns were recorded at room
temperature using HZG-4a powder diffractometer with
CuKα radiation. This equipment was attested with NIST
SRM-1976 and Si standards. The measurements were
carried out in 2θ step of 0.05° with variable scanning
rate, depending on sample quality. The profile analyses
were performed using the method of approximation of
X-ray reflections by the pseudo-Voigt function. The
lattice parameters and crystal structures of phases were
refined using the Rietveld method with FULLPROF.2k
program [13] from WinPLOTR software [14, 15].
Results obtained with XRD method testify that
ceramics sintered at Ts = 1200-1400 °C contain two
phases: the main spinel MgAl2O4 phase (space group
Fd 3m) and some additives of MgO (space group
Fm 3 m). The phase composition of MgAl2O4 ceramics
obtained with XRD method is shown in Table 1.
PALS measurements were performed with an
ORTEC spectrometer based on 22Na source placed
between two ceramic samples (Fig. 1) at 20 °C and
relative humidity of 35%, as it was described in more
details elsewhere [16, 18].
The obtained spectra were mathematically treated
with the LT computer program [20]. In general, we used
4 to 5 measured spectra for each pair of samples differed
by a total number of elementary annihilation events in
the range of 0.9-1.2 millions. Each of these spectra was
multiply treated owing to slight changes in the number
of final channels, annihilation background and time shift
of the spectrum. Then, the variance of statistically
weighted least-squares deviations between experimental
points and theoretical curve was taken into account to
compare the obtained results. Only results with
deviations quite close to 1.0 (the optimal deviation
ranges from 0.95 to ∼1.1-1.2) were left for further
consideration. In such a way, we obtained the numerical
PAL parameters (positron lifetimes τ1, τ2, τ3 and τ4 as
well as intensities I1, I2, I3 and I4), which correspond to
annihilation of positrons in the samples of interest.
ln = f(U)
LT
τ1τ2
Fig. 1. Block-scheme of conventional sample-source
“sandwich” arrangement for PALS measurements using the
ORTEC apparatus [17, 19]: 1 – foil-covered 22Na source, 2 –
two identical samples, 3.1 and 3.2 – scintillators of γ-quanta
(plastic KL detectors), 4.1 and 4.2 – photomultipliers (model
RCA 8575), 5.1 and 5.2 – constant fraction discriminators
(model 473A), 6 – delay line (model 425A), 7 – time-pulse
height converter (model 467), 8 – preamplifier (model 113),
9 – amplifier (model 471), 10 – single channel analyzer (model
455), 11 – multichannel analyzer (model 6420B), 12 – personal
computer.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
110
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 109-113.
Table 1. Phase composition of MgAl2O4 ceramics.
Ts,
°C
MgAl2O4 – weight
fraction, %
MgO – weight
fraction, %
1200 93.63(0.78) 6.37(0.27)
1300 94.12(0.80) 5.88(0.30)
1400 94.05(0.78) 5.95(0.34)
The positron trapping modes in the sintered
MgAl2O4 ceramics were calculated using the known
formalism for the two-state positron trapping model
[17, 21]:
21
2211 ¦У¦У
II
II
av +
+
=¦У , ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
21
2
¦У
1
¦У
1¦К
b
d I
I
, (4)
2
2
1
1
21
¦У¦У
¦У
II
II
b
+
+
= , (5)
where τb is the positron lifetime in defect-free bulk, τav –
average positron lifetime, κd – positron trapping rate of
defect. In addition, the τ2 – τb difference was accepted as
a size measure for extended free-volume defects where
positrons are trapped (in terms of equivalent number of
monovacancies), as well as the τ2/τb ratio was taken in a
direct correlation to the nature of these defects [22].
3. Results and discussion
In accordance with the scanning electron microscopy
data presented in [23], the observed additional phases
are non-uniformly distributed within ceramics bulk,
being more clearly pronounced near intergranual
boundaries. These phase extractions serve as specific
trapping centers for positrons penetrating ceramics. So,
using the PALS method we could study more carefully
structural peculiarities of the MgAl2O4 ceramics sintered
at various Ts.
Taking into account the model described in
[16, 22, 23], the shortest lifetime component in the
studied ceramics reflects mainly the microstructure
specificity of the spinel with character octahedral and
tetrahedral cation vacancies. It is shown (see Table 2)
that the lifetime τ1 of this first component and intensity
I1 are not practically changed with Ts. The second
component with the positron lifetime τ2 corresponds to
extended defects located near intergranual boundaries.
The fitting parameters of this lifetime component
(τ2 and I2) decrease with Ts. Consequently, the
corresponding positron trapping modes of extended
defects near intergranual boundaries will be changed,
too. The third and fourth components with the lifetimes
τ3 and τ4 are caused by “pick-off” annihilation of o-Ps in
nanopores [23].
These changes are related with a more branched
structure of open pores in the ceramics sintered at higher
Ts (1300 and 1400 °C). With Ts growing, the o-Ps “pick-
off” decay occurs preferentially in the nanopores filled
by absorbed water, while the ceramic samples sintered at
relatively low Ts (1200 °C) show this process in both
water-filled and water-free nanopores.
The positron trapping modes such as the average
τav, defect-free bulk τb and difference τ2 – τb are
insignificantly changed with the sintering temperature.
Table 2. PALS Characteristic of MgAl2O4 ceramics mathematically treated with the four-component fitting procedure.
Fitting parameters Positron trapping modes Ts, °C
τ1,
ns
I1,
a.u.
τ2,
ns
I2,
a.u.
τ3,
ns
I3,
a.u.
τ4,
ns
I4,
a.u.
τav,
ns
τb,
ns
κd,
ns-1
τ2–τb,
ns
τ2/τb
1200 0.16 0.65 0.38 0.33 2.03 0.010 48.4 0.011 0.24 0.20 1.07 0.18 1.89
1300 0.15 0.67 0.35 0.32 1.98 0.007 40.8 0.005 0.22 0.19 0.85 0.20 2.03
1400 0.15 0.67 0.35 0.31 1.94 0.008 42.4 0.005 0.22 0.19 0.81 0.21 2.10
Table 3. o-Ps lifetime as a function of the pore size within the range of free volume for sphere, cube and capillaries with
circular and square cross-sections, when assuming the side length a = 2R (T = 293 K).
Pore size, nm/geometry
spherical cubic cylindrical cuboidal
o-Ps life-
times, ns
Δ = 0.166 nm Δ = 0.18 nm Δ = 0.18 nm Δ = 0.19 nm Δ = 0.18 nm Δ = 0.18 nm
τ3
2.03
1.98
1.94
0.28 0.31 0.28 0.25 0.2 0.22
τ4
48.4
1.60
1.80
1.70
1.52
1.4
1.35
40.8 1.40 1.55 1.45 1.30 1.2 1.17
42.4 1.45 1.60 1.50 1.36 1.3 1.20
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
111
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 109-113.
In addition, the positron trapping centre (τ2/τb) is formed
on a typical for MgAl2O4 ceramics level of ∼1.9-2.0
[22], which testifies to the same nature of trapping sites,
whatever the content of absorbed water. In contrast,
most significant changes in positron trapping in
MgAl2O4 ceramics are reflected in the positron trapping
rate in defect κd (see Table 2).
In addition, the size of nanopores for MgAl2O4
ceramics in spherical, cylindrical, cubical and cuboidal
approximations can be calculated using the o-Ps “pick-
off” lifetime (third and fourth components with the
lifetimes τ3 and τ4) within the frames of the Tao-Eldrup
model [11, 12]. The size of nanopores for spinel-
structured MgAl2O4 ceramics calculated with the above
model using τ3 has been shown in Table 3.
4. Conclusions
Thus, positron annihilation lifetime spectroscopy can be
successfully used for experimental studies of structural
defects and nanoporosity in humidity-sensitive MgAl2O4
ceramics. The Tao-Eldrup model can be applied to
calculation of the nanopore size in ceramic materials for
sensor electronics.
5. Acknowledgement
The author thanks to Dr. I. Hadzaman (Drohobych Ivan
Franko State Pedagogical University, Drohobych,
Ukraine) for sample preparation and Dr. A. Ingram
(Opole University of Technology, Poland) for assistance
in PALS experiments.
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113
2. Theoretical approach within the frames of the Tao-Eldrup model
|
| id | nasplib_isofts_kiev_ua-123456789-117652 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T18:38:17Z |
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| spelling | Klym, H. 2017-05-25T18:36:54Z 2017-05-25T18:36:54Z 2011 Study of nanoporous in humidity-sensitive MgAl₂O₄ ceramics with positron annihilation lifetime spectroscopy / H. Klym // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 109-113. — Бібліогр.: 23 назв. — англ. 1560-8034 PACS 82.45.Xy, 92.60.Jq https://nasplib.isofts.kiev.ua/handle/123456789/117652 It has been shown that positron annihilation lifetime spectroscopy is a quite
 promising tool for nanostructural characterization of humidity-sensitive spinel-type
 MgAl₂O₄ceramics. The results have been achieved using the four-component fitting
 procedure with arbitrary lifetimes that is applied to mathematically treat the measured
 spectra. It has been shown that the Tao-Eldrup model is adequate to calculate the
 nanopore size in MgAl₂O₄ ceramics if using the lifetime values of the third and fourth
 components. The author thanks to Dr. I. Hadzaman (Drohobych Ivan
 Franko State Pedagogical University, Drohobych,
 Ukraine) for sample preparation and Dr. A. Ingram
 (Opole University of Technology, Poland) for assistance
 in PALS experiments. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Study of nanoporous in humidity-sensitive MgAl₂O₄ ceramics with positron annihilation lifetime spectroscopy Article published earlier |
| spellingShingle | Study of nanoporous in humidity-sensitive MgAl₂O₄ ceramics with positron annihilation lifetime spectroscopy Klym, H. |
| title | Study of nanoporous in humidity-sensitive MgAl₂O₄ ceramics with positron annihilation lifetime spectroscopy |
| title_full | Study of nanoporous in humidity-sensitive MgAl₂O₄ ceramics with positron annihilation lifetime spectroscopy |
| title_fullStr | Study of nanoporous in humidity-sensitive MgAl₂O₄ ceramics with positron annihilation lifetime spectroscopy |
| title_full_unstemmed | Study of nanoporous in humidity-sensitive MgAl₂O₄ ceramics with positron annihilation lifetime spectroscopy |
| title_short | Study of nanoporous in humidity-sensitive MgAl₂O₄ ceramics with positron annihilation lifetime spectroscopy |
| title_sort | study of nanoporous in humidity-sensitive mgal₂o₄ ceramics with positron annihilation lifetime spectroscopy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/117652 |
| work_keys_str_mv | AT klymh studyofnanoporousinhumiditysensitivemgal2o4ceramicswithpositronannihilationlifetimespectroscopy |