Reststrahlen spectroscopy of MgAl₂O₄ spinel
Using IR reflectance spectroscopy and surface polariton spectroscopy in the reststrahlen region, we investigated Czochralski-grown MgAl₂O₄ spinel. The computer analysis of variance made for spectra enabled us to get a mathematical model for reflection spectra of spinel. In our calculations we used c...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2002
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| Цитувати: | Reststrahlen spectroscopy of MgAl₂O₄ spinel / N.N. Boguslavska, E.F. Venger, N.M. Vernidub, Yu.A. Pasechnik, K.V. Shportko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 1. — С. 95-100. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-1211232017-06-14T03:03:14Z Reststrahlen spectroscopy of MgAl₂O₄ spinel Boguslavska, N.N. Venger, E.F. Vernidub, N.M. Pasechnik, Yu.A. Shportko, K.V. Using IR reflectance spectroscopy and surface polariton spectroscopy in the reststrahlen region, we investigated Czochralski-grown MgAl₂O₄ spinel. The computer analysis of variance made for spectra enabled us to get a mathematical model for reflection spectra of spinel. In our calculations we used consistent data for optical parameters (zero- and high-frequency permittivities, transverse optical phonon frequencies and corresponding damping coefficients) of spinel single crystals that have been obtained from comparison between the measured and calculated spectra. These data were used when studying attenuated total reflection spectra and dispersion curves for surface polaritons in MgAl₂O₄ spinel. 2002 Article Reststrahlen spectroscopy of MgAl₂O₄ spinel / N.N. Boguslavska, E.F. Venger, N.M. Vernidub, Yu.A. Pasechnik, K.V. Shportko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 1. — С. 95-100. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS: 71.36.+c, 78.20.-e, 78.68.+m http://dspace.nbuv.gov.ua/handle/123456789/121123 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Using IR reflectance spectroscopy and surface polariton spectroscopy in the reststrahlen region, we investigated Czochralski-grown MgAl₂O₄ spinel. The computer analysis of variance made for spectra enabled us to get a mathematical model for reflection spectra of spinel. In our calculations we used consistent data for optical parameters (zero- and high-frequency permittivities, transverse optical phonon frequencies and corresponding damping coefficients) of spinel single crystals that have been obtained from comparison between the measured and calculated spectra. These data were used when studying attenuated total reflection spectra and dispersion curves for surface polaritons in MgAl₂O₄ spinel. |
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Article |
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Boguslavska, N.N. Venger, E.F. Vernidub, N.M. Pasechnik, Yu.A. Shportko, K.V. |
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Boguslavska, N.N. Venger, E.F. Vernidub, N.M. Pasechnik, Yu.A. Shportko, K.V. Reststrahlen spectroscopy of MgAl₂O₄ spinel Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Boguslavska, N.N. Venger, E.F. Vernidub, N.M. Pasechnik, Yu.A. Shportko, K.V. |
| author_sort |
Boguslavska, N.N. |
| title |
Reststrahlen spectroscopy of MgAl₂O₄ spinel |
| title_short |
Reststrahlen spectroscopy of MgAl₂O₄ spinel |
| title_full |
Reststrahlen spectroscopy of MgAl₂O₄ spinel |
| title_fullStr |
Reststrahlen spectroscopy of MgAl₂O₄ spinel |
| title_full_unstemmed |
Reststrahlen spectroscopy of MgAl₂O₄ spinel |
| title_sort |
reststrahlen spectroscopy of mgal₂o₄ spinel |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2002 |
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http://dspace.nbuv.gov.ua/handle/123456789/121123 |
| citation_txt |
Reststrahlen spectroscopy of MgAl₂O₄ spinel / N.N. Boguslavska, E.F. Venger, N.M. Vernidub, Yu.A. Pasechnik, K.V. Shportko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 1. — С. 95-100. — Бібліогр.: 8 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT boguslavskann reststrahlenspectroscopyofmgal2o4spinel AT vengeref reststrahlenspectroscopyofmgal2o4spinel AT vernidubnm reststrahlenspectroscopyofmgal2o4spinel AT pasechnikyua reststrahlenspectroscopyofmgal2o4spinel AT shportkokv reststrahlenspectroscopyofmgal2o4spinel |
| first_indexed |
2025-07-08T19:13:49Z |
| last_indexed |
2025-07-08T19:13:49Z |
| _version_ |
1837107281133568000 |
| fulltext |
95© 2002, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2002. V. 5, N 1. P. 95-100.
PACS: 71.36.+c, 78.20.-e, 78.68.+m
Reststrahlen spectroscopy of MgAl2O4 spinel
N.N. Boguslavska1), E.F. Venger1), N.M. Vernidub2), Yu.A. Pasechnik2), K.V. Shportko2)
1) Institute of Semiconductor Physics, NAS of Ukraine, 45 prospect Nauky, 03028 Kyiv, Ukraine
Phone: +380 (44) 265 6205; fax: +380 (44) 265 5430
2) M.Dragomanov National Pedagogic University, 9 Pirogova St., 01030 Kyiv, Ukraine
Phone: +380 (44) 224 6557; fax: +380 (44) 224 2251
Abstract. Using IR reflectance spectroscopy and surface polariton spectroscopy in the
reststrahlen region, we investigated Czochralski-grown MgAl2O4 spinel. The computer analy-
sis of variance made for spectra enabled us to get a mathematical model for reflection spectra
of spinel. In our calculations we used consistent data for optical parameters (zero- and high-
frequency permittivities, transverse optical phonon frequencies and corresponding damping
coefficients) of spinel single crystals that have been obtained from comparison between the
measured and calculated spectra. These data were used when studying attenuated total reflec-
tion spectra and dispersion curves for surface polaritons in MgAl2O4 spinel.
Keywords: reflectance spectroscopy, surface polaritons, spinel, reststrahlen, attenuated total
reflection spectra.
Paper received 27.11.01; revised manuscript received 18.01.02; accepted for publication 05.03.02.
1. Introduction
Both natural and synthetic spinelides are promising
materials for use in micro- and optoelectronics. That is
why they often draw attention of researchers. However,
investigation of their physico-chemical properties is com-
plicated by the fact that in many cases their structure is
unknown. The attempts to make the problem easier by
arranging the samples studied in series of pseudo-binary
solid solutions often have not met with success. The rea-
son for this lies in the fact that there are some restrictions
on compatibility, heterogeneity and multicomponent char-
acter of isomorphic mixtures.
Many authors have dealt with investigation of IR ab-
sorption spectra of natural and synthetic chemical com-
pounds of spinel-like structure (see the review [1]). In [1]
these spectra were studied in spinelides belonging to the
set of (Mg, Fe)(Fe3+, Al, Cr)2O4 solid solutions. The au-
thors of [1] have obtained both structural and
spectroscopic characteristics of synthetic spinelides and
proved, on the empirical level, that the model for inde-
pendent vibrations of tetrahedral and octahedral �mol-
ecules� of spinel structure is inadequate. A comparison
between the crystal-chemical and optical parameters of
spinelides belonging to nine continuous sets of solid so-
lutions enabled the authors of [1] to treat the spectra as
resulting from vibrations of the spinelide lattice as a
whole. The predominant role of the effect of octahedral
isomorphic substitutions on the absorption spectral line
positions also has been stressed in [1].
The MgAl2O4 spinel structure is typical for the
X2+Y2
3+O4
2--type compounds where X and Y are cations
(at least one of which belongs to the transition element
group) and O is oxygen [2]. For the so-called normal
spinels the cation X is bivalent (Mg2+, Mn2+, Fe2+, Ni2+,
Zn2+), while cation Y is trivalent (Al3+, V3+, Cr3+, Fe3+,
Mn3+). The crystal has a face-centered cubic (FCC) lat-
tice. The anions (located at vertexes) form the closest
cubic three-layer package. One may recognize the fol-
lowing two cation sublattices in the spinel structure: tet-
rahedral (A-sublattice) and octahedral (B-sublattice).
Chemical bonding in the spinel structure is of mixed ion-
covalent type. In normal spinels the cations X2+ occupy
the tetrahedral (A) interstitials, while the cations Y3+
96 SQO, 5(1), 2002
N.N. Boguslavska et al.: Reststrahlen spectroscopy of MgAl
2
O
4
spinel
occupy the octahedral (B) ones. In this case the chemical
formula X2+Y2
3+O4
2- is valid. The MgAl2O4 spinel be-
longs to normal, while MgFe2O4, Fe3O4 belong to in-
verse spinels. The spinel structure is like to that of the
Fe3O4 magnetite: the Mg2+ ions occupy the tetrahedral
interstitials and the Al3+ ions are located at the octahe-
dral sites.
Highly symmetric (Fd3m) structure of cubic spinelides
results in a rather simple form of IR absorption spectrum
in the 200-1000 cm-1 region. Depending on the compound
studied and sample origin, this spectrum usually involves
from two to four intense bands and a variable number of
weaker bands that manifest themselves as �shoulders� at
the intense band slopes.
After 1955, interpretation of the IR spectra in com-
pounds of spinel structure is based on a theory that has
been initially advanced by Waldron [3]. In his model the
crystal structure considered has a rhombohedral primi-
tive cell. In the case of normal spinel this cell contains
two AO4 tetrahedrons (each having four oxygen ions and
a tetrahedral cation A at its center) and a tetrahedron B
(that involves four octahedral cations). The vibrations of
each of the above groups of ions have been classified ac-
cording to the features of the point group Td (which is
believed to correspond to vibrations of the crystal as a
whole). As a result, Waldron has concluded that only
four crystal vibrational modes are IR-active. Two of them
(having the highest frequencies ν1 and ν2) stem from oxy-
gen ion motion, while the other two modes are related to
motion of metal cations.
Comprehensive experimental studies of spinel IR spec-
tra have been performed after the paper [3] by Waldron
has appeared. Their results have been evidence in favor
of existence of four fundamental absorption bands in the
cubic spinel-type compounds. Indeed, four bands were
observed. They were accompanied by weaker bands and
inflections (�shoulders�) [3]. In two or three cases it was
possible to relate some of these weaker bands and �shoul-
ders� to presence of structural imperfections in the crys-
tals studied, but generally their nature remained unclear.
An alternative approach to the problem of spectra in-
terpretation has been advanced in [3]. The experimen-
tally observed spectral features have been explained in
terms of vibrations of crystal as a whole. It was shown
that IR absorption in MgAl2O4 could be rather ad-
equately described with a spectrum whose peaks were re-
lated to the critical points in the Brillouin zone.
Three intense bands (at frequencies of 692, 526 and
307 cm-1) are observed in the IR absorption spectrum of
synthetic MgAl2O4 spinel, along with a weaker peak or
�shoulder� at a frequency of 720 cm-1 (see Table 1). The
experiments for a set of spinels where MgAl2O4 is a prin-
cipal component showed that two other important fre-
quencies also lie near 570 and 455 cm-1. The observed
spectrum features might depend on the preparation tech-
nique and material stoichiometry.
The absorption spectrum of the natural spinel is known
to slightly differ from that of the synthetic material [3]. A
comparison between the data for synthetic and natural
spinels published by different authors is given in Table 1.
The features of reflection spectrum for the natural
MgAl2O4 single crystal published in 1964 by Slack [4]
are also of interest; they are given in Table 2.
Table 1. IR absorption spectra of MgAl2O4 spinel [3].
For spinel whose primitive unit cell contains 14 ions 42
branches are to exist for the phonon dispersion. Thus, the
problem of adequate interpretation of IR spectra is rather
complicated due to the lack of additional information con-
cerning the phonon dispersion curves. Since the ordinary
unit cell of spinel belongs to the cubic (FCC) lattice, the
Brillouin zone for spinel is similar to that of sphalerite (zinc
blende) [4]. Therefore the phonon wave vectors at critical
points are known.
The author of [4] has measured optical reflection from
MgAl2O4 and FeAl2O4 in the 0.03 up to 2.0 eV range to deter-
mine the strong lattice absorption region and obtain reflection
coefficient R. The measurements have been performed at a tem-
perature of 300 K and almost normal incidence of light beam.
Intense peaks of lattice absorption have been found in the pho-
ton energy range from 0.03 to 0.11 eV. The MgAl2O4 sample
used was a natural spinel crystal from Burma; it was pale-rose
colored. The synthetic FeAl2O4 crystal has been grown without
additional annealing. The crystal surfaces were polished in
such a way as to be optically flat for reflection measurements.
The results of MgAl2O4 reflection spectrum recording
are shown in Fig. 1. The principal lattice absorption peaks
lie at 0.066 and 0.091 eV (533 and 735 cm-1).
Spectral Frequency Frequency Frequency
feature ν, cm-1 (a) ν, cm-1 (b) ν, cm-1 (c)
Synthetic Synthetic Natural Natural
spinel spinel spinel spinel
�Shoulder� 720 750 752 760
Peak 692 690 685 688
�Shoulder� 570 - 578 580
Peak 526 538 521 522
�Shoulder� 455
Peak 307 309
Spectral features Energy, eV Frequency, cm-1
Weak �shoulder� 0.104 840
Sharp peak 0.091 735
�Shoulder� 0.072 582
Broad peak 0.066 533
�Shoulder� 0.059 477
Sharp peak 0.0375 304
Table 2. Reflection spectrum of MgAl2O4 spinel natural single
crystal [4].
[a] - X.W. Grimes, A.J. Collett // phys. status solidi (b) 43, p. 591
(1971).
[b] - S. Hafner, F. Laves // Z. Krist. 115, p. 321 (1961).
[c] J. Preudhomme, P. Tarte // Spectrochim. Acta 27A, p. 1817
(1971).
N.N. Boguslavska et al.: Reststrahlen spectroscopy of MgAl
2
O
4
spinel
97SQO, 5(1), 2002
100
60
20
0
0.03 0.1 0.3 1.0 3.0
R
,
R
ef
le
ct
iv
it
y
,
%
h , photon energy, eVν
Fig. 1. Reflection spectrum of MgAl2O4 spinel natural single
crystal [4].
The data on other (less intense) peaks obtained are
given in Table 3. The values of MgAl2O4 reflection coef-
ficient R at normal incidence of light beam onto the sam-
ple (Table 3) are believed to be rather accurate [4]. The
values of R for FeAl2O4 recorded at angle of incidence
equal to 30° are approximate, but they still give relative
intensities of different peaks.
The intense reflection peaks are related to strong ab-
sorption. There is close similarity between these lattice
vibrational peaks for MgAl2O4 and FeAl2O4 because both
crystals belong to the spinel structure and their lattice
parameters are almost the same. A Fe atom is heavier
than a Mg one; the FeAl2O4 reflection peaks lie at ener-
gies that are below those in MgAl2O4 by about 5%. The
reflection coefficient R for MgAl2O4 is very low (from 2
to 8%) in the energy range from 0.12 to 3.0 eV (actually
up to 4 eV). The overall situation for FeAl2O4 is similar.
Optical properties of spinel that served as substrate
when growing silicon layers were studied in [5]. The
MgAl2O4 substrate was Czochralski-grown; it had the
structure of normal cubic spinel. Two principal MgAl2O4
absorption bands (lying at 688 and 522 cm-1) have been
identified. They are related to the O-Al complex in the
octahedron.
Table 3. Reflection spectrum of MgAl2O4 spinel natural single
crystal [4]. (Greek letters are used for absorption bands labeling.)
Fig. 2. Reflection spectra of MgAl2O4 spinel synthetic single
crystals: 1, 2 � experimental spectra for two samples; 3 � spec-
trum taken from [5]; 4 � calculated spectrum with parameters
R(ν) given in Table 4.
2. Results and discussion
Here we present some results of our experiments deal-
ing with the optical properties of Czochralski-grown syn-
thetic MgAl2O4 spinel. We used IR reflectance
spectroscopy and surface polariton spectroscopy in the
reststrahlen region. The IR reflection spectra in the 400-
1400 cm-1 range were taken with spectrometer IKS-29
(equipped with attachment IPO-22) using polarized ra-
diation. These spectra (Fig. 2, curves 1, 2) somewhat dif-
fer from those given in [5]. The reflection peaks taken in
[5] (see Fig. 2, curve 3) lie at frequencies of 745 and 545 cm-1.
They refer to the same lattice vibrations as the absorp-
tion peaks. The reflection peaks are shifted toward higher
frequencies as compared to the absorption peaks. This is
characteristic of strong absorption bands. The reflection
coefficient R = 0.13 in the 0.3-3 µm wavelength range
leads to the refraction index value n = 1.7. This value
agrees with those (1.7-1.72) obtained in a number of pa-
pers at a wavelength of 0.6 µm. From the interference
fringes observed in experiments with spinel transparence
it follows that the refraction index value is close to 3; at
low (near 1 kHz) frequencies the spinel permittivity is
8.4.
A comparison between the MgAl2O4 reflection spec-
tra obtained in [4] and [5] evidences that they differ sub-
stantially. In [4] it was stated that the reflection spectrum
has two peaks corresponding to total (100%) reflection.
Contrary to this, the reflection peaks at frequencies of
745 and 545 cm-1 obtained in [5] corresponded to reflec-
tion coefficient of about 80% and 65%, respectively. No
model has been advanced in either [4] or [5] that could
give a quantitative description for the spinel reststrahlen
region.
Band Energy, eV Frequency, Reflection Spectral
label cm-1 coefficient features
R, %
α 0.0375 303 36 Broad
peak
β 0.059 476 89 Sharp
peak
γ 0.066 533 100 Broad
peak
δ 0.072 581 75 �Shoulder�
ε 0.091 735 100 Sharp
peak
ζ 0.104 840 50 Slightly
pronounced
�shoulder�
θ 0.176 Low
98 SQO, 5(1), 2002
N.N. Boguslavska et al.: Reststrahlen spectroscopy of MgAl
2
O
4
spinel
A computer analysis of variance made for the spectra
obtained enabled us to advance a mathematical model
for spinel reflection spectra. In our calculations we used
the consistent data on the optical parameters of spinel
single crystals that were obtained by comparing the ex-
perimental and calculated spectra.
When calculating the reflection coefficient, we used
the following well-known expression [6]:
Table 4. Optical parameters of the reflection spectra model R(ννννν) and ATR for spinel.
400
500
600
700
800
900
1000
30
32
34
37
0
0,5
1
I/I
o
ν, cm
-1
α,
o
Fig. 3. Experimental SP ATR spectra of MgAl2O4 spinel syn-
thetic single crystal (curves 1, �, 8 have been taken at reflection
angles of 30.3, �, 39.3°).
( )
12
12
1
2
2
2
1
2
2
2
1
1
2
2
2
1
2
2
2
1
+
++++
+
++−+
=
εεεεε
εεεεε
νR (1)
Here ε1 and ε2 are, respectively, the real and imagi-
nary parts of the crystal permittivity that was taken in the
following form:
( ) ∑
=
∞
−−
+=+=
3
1
22
2
21
i TiTi
Tii
i
S
i
νγνν
νεεενε (2)
∑
=
N
i 1
Here ε∞ is the high-frequency permittivity; Si is the i-
th oscillator strength; νTi (γTi) is the frequency (damping
coefficient) of the i-th oscillator, i.e., transverse optical
phonon. The summation is made for the case of a
multiphonon vibrational system of the crystal lattice. A
root-mean-square deviation d of the experimental param-
eter value from the calculated one is determined from the
formula δ =[ (Rų - RT³)2]1/2/N. Here REi (RTi) is the
experimental (theoretical) reflection coefficient value at
the i-th point of the spectrum; N is the number of points of
the spectrum.
The curves 1, 2 in Fig. 2 correspond to the experimen-
tal reflection spectra of synthetic MgAl2O4 spinel. These
spectra have been compared to the theoretical one (curve
4) using analysis of variance. This enabled us to develop
a mathematical model for the reflection spectra of
MgAl2O4 spinel. These spectra are of the form that is
characteristic of the normal spinel, namely, two peaks at
frequencies of 560 and 720 cm-1 and an inflection (�shoul-
der�) at a frequency of 820 cm-1. The reflection coeffi-
cient at frequencies over 1000 cm-1 is R(ν) ≤ 0.13. A com-
parison has shown that the calculated spectra differed
from the experimental ones by 0.6% (at parameters that
are given below).
According to the developed model, the phonon sys-
tem of the crystals studied may be described with three
resonance frequencies (510, 680 and 790 cm-1); the corre-
sponding oscillator strengths and damping coefficients
are 0.58, 0.73, 0.2 and 5, 1.3, 19 cm-1, respectively. Fig. 2
(curve 4) demonstrates a rather good agreement between
the theoretical and experimental results at ε0 = 7.4 and
ε∞ = 2.89; they also agree with the data given by other
authors (see, for instance, [5]). The data obtained as a
result of such comparison made it possible to study sur-
face phonon polaritons in MgAl2O4 spinel.
At the moment there are a number of papers dealing
with investigation of surface polaritons (SP) in such com-
pounds as silicon carbide, aluminum oxide, etc. For
spinels, however, the characteristics of SP in the IR re-
gion practically have not been studied yet [7, 8]. Here we
present, for the first time, results of our investigations of
surface phonon polaritons in MgAl2O4 spinel.
One of the experimental techniques used when study-
ing SP is attenuated total reflectance (ATR). We took the
ATR spectra of SP for Czochralski-grown synthetic
MgAl2O4 spinel in the 400-1100 cm-1 frequency range. In
our experiments we used polarized radiation and
spectrometer IKS-29 equipped with attachment NPVO-
1. Shown in Fig. 3 is the so-called SP reflection surface,
R(ν, α). It is a set of eight experimental SP ATR spectra
taken at angles from 30 up to 39°. A reflection surface
R(ν, α) is a three-dimensional presentation of the system
transmission that depends on the radiation frequency ν
and angle α (angle of incidence for an ATR unit).
If there are SP damping and dissipation of the elec-
tromagnetic wave energy, then the surface R(ν, α) =
I (ν, α)/I0(ν, α) has two �canyons� connected with a
�pass�.
νΤ1 νΤ2, νΤ3, γΤ1, γΤ2, γT3, b1 b2 b3
cm-1 cm-1 cm-1 cm-1 cm-1 cm-1
510 680 795 5 1.4 16 3.58 0.73 0.2
502 650 830 65 20 136 3.58 0.73 0.2
R(ν) 7.4 2.89
ATR 7.4 2.89
0ε ∞ε
N.N. Boguslavska et al.: Reststrahlen spectroscopy of MgAl
2
O
4
spinel
99SQO, 5(1), 2002
0.4
0.6
0.8
1
400 600 800 1000
ν, ñm-1
I/
I
o
1
2
3
4
5
4
500
600
700
800
900
0.15 0.2 0.25 0.3 0.35 0.4
Kc/ωT
ν ,
cm
-1
1
2
3
4
(Here I(ν, α) is the intensity of radiation passing
through the �ATR unit (semicylinder)-gap-sample� sys-
tem; I0(ν, α) is the intensity of radiation incident onto the
ATR unit.) The �canyon� depth depends on the system
parameters: gap d3 between the ATR semicylinder and
sample, radiation frequency ν, complex permittivity ε(ν, κ)
of the sample, permittivities of the ATR unit and gap.
The SP dispersion curves νs(k) correspond to the �can-
yons�, i.e., to the set of ATR spectra minima. (Here νs is
the SP frequency and k is the SP wave vector.) The fre-
quencies at which the minima of the experimentally de-
termined surface R(ν, α) lie, as a rule, agree with those of
the calculated dispersion curve νs(k) at the phonon damp-
ing coefficient γT = 0.
The relation between the ATR spectrum minima and
SP dispersion curve is given by the following equation:
( ) απν sin2 nck = (3)
Here ν is the frequency of the ATR spectrum mini-
mum; c is the speed of light in a vacuum; n is the refractive
index of material of the ATR semicylinder. (We used the
material KRS-5 with n = 2.37.) If the optical phonon
damping is taken into account, then one more �canyon�
appears at the reflection surface R(ν, α), with a �pass� to
the first �canyon� in the frequency region ν > νs. This
can be detected by recording the SP ATR spectra at ν =
const and scanning over the angle α values.
Three experimental ATR spectra (curves 1-3) taken
at angles α = 29.3, 31.3 and 33.3° are shown in Fig. 4.
Curves 4 and 5 are the theoretical ATR spectra calcu-
lated at α = 31.3 and 33.3°; the oscillation frequencies
were 502, 650 and 830 cm-1, while the damping coeffi-
cients were 65, 20 and 136 cm-1.
Figure 5 presents the calculated (full curves) and ex-
perimental (dots) SP dispersion curves in spinel. The fea-
ture of dispersion curves in MgAl2O4 spinel is presence of
three branches. This fact agrees with the developed math-
ematical model for spinel that takes into account contri-
butions from three oscillators (phonons) to the permittiv-
ity. The obtained consistent data concerning the optical
parameters (zero- and high-frequency permittivities, trans-
verse optical phonon frequencies and corresponding
damping coefficients) of spinel single crystals are pre-
sented in Table 4.
The R(ν) row in Table 4 has been obtained from com-
parison between the experimental and calculated spec-
tra. The ATR row gives the parameter values used when
trying to simulate the calculated ATR spectra at α = 31.3
and 33.3°. One can see from Fig. 4 that only qualitative
agreement exists between the spectra 2, 3 and 4, 5. When
comparing the data obtained from the R(ν) and ATR spec-
tra, one can see that to get better agreement one should
take essentially different frequencies of three oscillators,
as well as the corresponding damping coefficients. In
particular, the oscillator frequencies differ by 10-30 cm-1
and the damping coefficients differ by a factor of 10-15.
This indicates at the effect of a near-surface layer on the
properties of phonon SP in spinel. We propose to obtain
the data concerning optical properties of near-surface
regions in materials from quantitative comparison be-
tween the experimental and theoretical reflection surfaces
made using PC. This will make it possible to get more
detailed information on the system studied.
3. Conclusion
Using IR reflectance spectroscopy and surface
polariton spectroscopy in the reststrahlen region, we in-
vestigated Czochralski-grown MgAl2O4 spinel. The com-
puter analysis of variance made for spectra enabled us to
get a mathematical model for reflection spectra of spinel.
In our calculations we used consistent data for optical
parameters (zero- and high-frequency permittivities, trans-
verse optical phonon frequencies and corresponding
damping coefficients) of spinel single crystals that have
been obtained from comparison between the measured
and calculated spectra. These data were used when study-
ing ATR spectra and dispersion curves for surface
polaritons in MgAl2O4 spinel.
Fig. 4. Experimental ATR spectra of MgAl2O4 spinel single crys-
tal: 1-3 � experiment, 4 and 5 - calculation; reflection angle α is
29.3° (1), 31.3° (2), 33.3° (3); 31.3° (4), 33.3° (5).
Fig. 5. SP dispersion curves for MgAl2O4 spinel single crystal: 1-
3 � experiment (dots) and calculation at ATR model parameters
given in Table 4; 4 � light curve.
100 SQO, 5(1), 2002
N.N. Boguslavska et al.: Reststrahlen spectroscopy of MgAl
2
O
4
spinel
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