Fourier transform infrared studies of the N₂–O₂ binary system
Solid solutions (N₂)x(O₂)₁₋x have been investigated by infrared absorption measurements mainly in the O₂ and N₂ stretching regions, between 60–10 K, completing former similar studies by Raman scattering. We produced thermodynamically stable samples by a careful thermal treatment, followed by cool...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1208832017-06-14T03:05:52Z Fourier transform infrared studies of the N₂–O₂ binary system Minenko, M. Jodl, H.-J. Cryocrystals Solid solutions (N₂)x(O₂)₁₋x have been investigated by infrared absorption measurements mainly in the O₂ and N₂ stretching regions, between 60–10 K, completing former similar studies by Raman scattering. We produced thermodynamically stable samples by a careful thermal treatment, followed by cooling/heating cycles over weeks, during which we took spectra. From fingerprints in infrared spectra we deduce phase transition lines, solubility lines and suggest a refined, improved T–x% phase diagram with respect to inconsistencies between those in literature. Spectra of N₂–O₂ mixtures are pretty complex but referring to known spectra of pure systems N₂ or O₂ we were able to assign and interpret broad (~100 cm⁻¹) phonon side bands to fundamentals and electronic transition (O₂) depending on actual temperature and concentration. Narrow features in spectra (<10 cm⁻¹) were attributed to the vibron DOS of N₂ or O₂, whose bandwidth, band shape and intensity are different and characteristic for each phase. Differences between pure and mixed systems were pointed out. Matrix isolation technique (2 ppm of CO) was used to probe our mixture. 2006 Article Fourier transform infrared studies of the N₂–O₂ binary system / M. Minenko, H.-J. Jodl // Физика низких температур. — 2006. — Т. 32, № 11. — С. 1382–1401. — Бібліогр.: 39 назв. — англ. 0132-6414 PACS: 81.30.–t, 64.70.Kb, 64.75.+g, 78.30.–j, 63.20.Ls http://dspace.nbuv.gov.ua/handle/123456789/120883 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Cryocrystals Cryocrystals |
| spellingShingle |
Cryocrystals Cryocrystals Minenko, M. Jodl, H.-J. Fourier transform infrared studies of the N₂–O₂ binary system Физика низких температур |
| description |
Solid solutions (N₂)x(O₂)₁₋x have been investigated by infrared absorption measurements
mainly in the O₂ and N₂ stretching regions, between 60–10 K, completing former similar studies
by Raman scattering. We produced thermodynamically stable samples by a careful thermal treatment,
followed by cooling/heating cycles over weeks, during which we took spectra. From fingerprints
in infrared spectra we deduce phase transition lines, solubility lines and suggest a refined,
improved T–x% phase diagram with respect to inconsistencies between those in literature. Spectra
of N₂–O₂ mixtures are pretty complex but referring to known spectra of pure systems N₂ or O₂ we
were able to assign and interpret broad (~100 cm⁻¹) phonon side bands to fundamentals and electronic
transition (O₂) depending on actual temperature and concentration. Narrow features in
spectra (<10 cm⁻¹) were attributed to the vibron DOS of N₂ or O₂, whose bandwidth, band shape
and intensity are different and characteristic for each phase. Differences between pure and mixed
systems were pointed out. Matrix isolation technique (2 ppm of CO) was used to probe our mixture. |
| format |
Article |
| author |
Minenko, M. Jodl, H.-J. |
| author_facet |
Minenko, M. Jodl, H.-J. |
| author_sort |
Minenko, M. |
| title |
Fourier transform infrared studies of the N₂–O₂ binary system |
| title_short |
Fourier transform infrared studies of the N₂–O₂ binary system |
| title_full |
Fourier transform infrared studies of the N₂–O₂ binary system |
| title_fullStr |
Fourier transform infrared studies of the N₂–O₂ binary system |
| title_full_unstemmed |
Fourier transform infrared studies of the N₂–O₂ binary system |
| title_sort |
fourier transform infrared studies of the n₂–o₂ binary system |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2006 |
| topic_facet |
Cryocrystals |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120883 |
| citation_txt |
Fourier transform infrared studies of the N₂–O₂ binary system / M. Minenko, H.-J. Jodl // Физика низких температур. — 2006. — Т. 32, № 11. — С. 1382–1401. — Бібліогр.: 39 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT minenkom fouriertransforminfraredstudiesofthen2o2binarysystem AT jodlhj fouriertransforminfraredstudiesofthen2o2binarysystem |
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2025-07-08T18:48:44Z |
| last_indexed |
2025-07-08T18:48:44Z |
| _version_ |
1837105706600235008 |
| fulltext |
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11, p. 1382–1401
Fourier transform infrared studies of the N2–O2
binary system
M. Minenko and H.-J. Jodl
TU Kaiserslautern, Department of Physics, Erwin Schr�dinger Str., Kaiserslautern 67663, Germany
E-mail: jodl@physik.uni-kl.de
Received May 26, 2006
Solid solutions (N2)x(O2)1–x have been investigated by infrared absorption measurements
mainly in the O2 and N2 stretching regions, between 60–10 K, completing former similar studies
by Raman scattering. We produced thermodynamically stable samples by a careful thermal treat-
ment, followed by cooling/heating cycles over weeks, during which we took spectra. From finger-
prints in infrared spectra we deduce phase transition lines, solubility lines and suggest a refined,
improved T–x% phase diagram with respect to inconsistencies between those in literature. Spectra
of N2–O2 mixtures are pretty complex but referring to known spectra of pure systems N2 or O2 we
were able to assign and interpret broad (�100 cm–1) phonon side bands to fundamentals and elec-
tronic transition (O2) depending on actual temperature and concentration. Narrow features in
spectra (<10 cm–1) were attributed to the vibron DOS of N2 or O2, whose bandwidth, band shape
and intensity are different and characteristic for each phase. Differences between pure and mixed
systems were pointed out. Matrix isolation technique (2 ppm of CO) was used to probe our mixture.
PACS: 81.30.–t, 64.70.Kb, 64.75.+g, 78.30.–j, 63.20.Ls
Keywords: infrared absorbtion, Fourier-transform infrared technique, vibrational and exitonic region.
1. Introduction
Molecular crystals (rare gases, H2, N2, O2, CO,
CO2 …) have been studied extensively since 1950 by
all kinds of technique like spectroscopy, structural
studies, thermodynamic investigations, molecular dy-
namics simulation. At least two directions of research
can be identified: molecular solids as matrix material
or as simple model systems for solid state aspects.
Mixtures of these components were much less studied
on the contrary, because of several reasons: due to the
complexity in results after pure systems, due to miss-
ing theoretical modeling, due to problems in produc-
ing samples with sufficiently good crystal quality. In a
recent paper [1] we could prove that discrepancies in
published phase diagrams T–x% of N2–O2 [2,3] are
most likely due to thermodynamic instable samples.
The general aim of this paper [1] was to deduce from
fingerprints in vibron and phonon spectra lines of
phase transitions, to prove reproducibility and reli-
ability of our statements by cooling/heating cycles,
to determine quantitatively from relative Raman
vibron band intensities the solubility of N2 in O2 or
vice versa. In paper [1] we reported only about results
from Raman spectra.
With respect to Raman and infrared (IR) activity
of elementary excitations it is more than obvious to
study N2–O2 mixture spectroscopically by Raman
scattering. However, due to the admixing of elements
in the phases based on the other element some elemen-
tary excitations gain IR activity; in addition one may
expect IR active combinations of excitations. Of
course, this induced IR absorption is weak, but modern
Fourier-transform infrared (FTIR) technique is pretty
sensitive. Therefore in comparison to Raman scattering
FTIR spectra contain much more information.
The only spectroscopic paper — besides those on
excitonic transitions in O2 molecules [4] — is a far-IR
absorption analysis in solid N2–O2 solutions [5]. But
the observed transition in phonon spectra from the N2
translations (Tu
�
� 52 cm–1, Tu
�
� 73 cm–1), which are
IR active, to O2 phonons (� 55 cm–1, � 80 cm–1),
which are only Raman but not IR active, by increasing
the oxygen concentration must be considered with
many doubts. We could not find any IR active transla-
© M. Minenko and H.-J. Jodl, 2006
tions in far-IR spectra of thick solid samples of �-O2,
as it is expected from group theory. Also the second
statement in [5] about the tuning of the magnon inten-
sity in �-O2 by doping with N2 impurities (10% to
50%) is also more than questionable; because it is
agreed now [1–3] that only less or about 1% of N2 can
be solved in �*-O2. Therefore only the magnon absorp-
tion of pure O2 and the one with � 1% N2 should be
compared.
In our analysis of spectra of N2–O2 mixtures we
will base on comparison with spectra of pure O2 and
pure N2 [6–8] that were studied quite good up to now.
Publications on the binary system (N2)x(O2)1–x
with aim to determine the T-x% phase diagram are
based on structural analysis. Figure 1 shows versions
of Barrett, Meyer [3] and of Baryl’nik, Prokhvatilov
[2], which are obviously different with respect to the
existence of the X-phase, temperatures of phase transi-
tions and solubility of oxygen in nitrogen phases. By
our indirect method via optical spectroscopy we want
to clarify these differences or open questions.
What are the aims of this paper? First of all we
have to produce thermodynamically equilibrated sam-
ples checking their quality by means of optical spec-
troscopy. That means to find proper cooling and
warming rates and to check hysteresis effects and
reproducibility of spectra. Second, we plan to deduce
from FTIR spectra in the vibrational and excitonic re-
gion indirectly the T–x% diagram. In pure systems
clear changes in spectra are seen on the way through
phase transitions and we do believe to recognize the
same in mixtures. As the third aim we consider the de-
termination of solubility of O2 in �*-N2 phase being
one of the most obvious discrepancies between the two
existing variants of the T–x% diagram. And finally,
we want to detect all changes in spectra of mixtures in
comparison with spectra of pure systems.
2. Experimental
Nitrogen (99.999%) and oxygen (99.998%) were
premixed in a relatively large vessel in the desired
composition (via partial pressures) at room tempera-
ture. The mixture remained there for 2–3 days for ho-
mogenous mixing before loading the optical cell. This
cell with sample chamber (� 10 mm, thickness
1.2 mm), equipped with sapphire windows, was
mounted on a cold finger of a closed-cycle He
cryostat. To avoid partial demixing in the gas-liquid
region (see Fig. 2 [1]) and via contact between vapors
over the sample and the gas mixing system we fol-
lowed here another strategy. The cell temperature was
set at T = 11 K, and the cell was filled with the imme-
diately freezing gaseous mixture (couple of seconds),
so that there was no chance for a concentration
change. Then the cell was disconnected from the gas
mixing system. Samples were warmed up to the liquid
phase and were annealed for a couple of hours. Then
we cooled the samples through the liquid-solid phase
transition simultaneously measuring spectra. About
1 K below the transition temperature samples were an-
nealed again for few hours. During the very slow cool-
ing (0.5–0.1 K/h) of samples, we controlled their
optical quality by measuring their total light trans-
mission. We achieved to cool down the samples to
11 K with good optical quality.
Temperature was determined by a calibrated Si-di-
ode attached directly to the optical cell with an abso-
lute accuracy of the sample temperature determination
of about 0.1 K in the whole temperature range studied
here (11–60 K).
Spectra in the vicinity of the O2 fundamental
(� 1600 cm–1), N2 fundamental (� 2300 cm–1), their
combination and the electronic transition in oxygen
(� � � at 8000 cm–1) were recorded by a Fourier spec-
trometer (Bruker IFS 120 HR). The following light
Fourier transform infrared studies of the N2–O2 binary system
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11 1383
T
,K
*
* *
*
* *
*
Fig. 1. T–concentration (x%) phase diagram for N2–O2
from structural analysis reported by two different groups
(solid lines by [3], broken lines by [2]; liquid region –
dots – is taken from [2], the authors: M. Ruheman, H.
Lichter, and P. Komarov, Phys. Z. Sovjetunion 8, 326
(1935)). We studied several concentrations by Raman scat-
tering (R [1]) and by FTIR absorption (ir).
sources and beam splitters were used: a glowbar
source and a KBr beam splitter (spectral range
800–5000 cm–1) as well as a tungsten lamp and a CaF2
beam splitter (spectral range 1900–11000 cm–1). Liq-
uid-N2-cooled InSb and MCT detectors were used.
Frequency resolution was varied from 0.015 cm–1 to
1 cm–1 depending on the band width of investigated
spectral lines; frequency accuracy was 0.01 cm–1 due
to used interference pattern of the He gas laser. The
empty optical cell delivered the reference spectrum.
The actual concentration (N2)x(O2)1–x was con-
trolled after measurements by evaporating the sample
into a test volume. This sample gas was then analyzed
by means of chromatography and mass-spectrometry.
This actual concentration and the concentration of the
initial mixture, determined by partial pressures, al-
most coincided and the error in concentration is
� 1 mol %.
In Fig. 1, showing the existing variants of the
phase diagram T–x% we marked the 5 different mix-
tures studied by means of FTIR spectroscopy as well
as 6 mixtures studied by means of Raman spectroscopy
[1]. Our variant of the phase diagram is based there-
fore on data from all 11 measured mixtures.
3. Results and spectra
In the following we will present IR spectra of exci-
tations in our samples from lower to higher frequen-
cies. Although these spectra at first glance look pretty
complex and manifold they can be unambiguously as-
signed primarily by comparing them with similar spec-
tra of the pure systems (O2 and N2). The evolution of
spectra with temperature during warming cycles will
be described in detail and changes in spectra document
phase transitions. Topics of more common interest like
solubility, metastability/hysteresis or vibron density
of states will be discussed later.
3.1. Oxygen fundamental region (� 1550 cm–1)
Figure 2 shows for one selected concentration
(N2)0.55(O2)0.45 the changes in spectra in the region
of the O2 stretching band and its phonon combination
band (side band, SB) during warming. Lines on the
right hand side of this figure separate phase regions.
Since the overview of spectra is pretty overcharged,
we use in the next figures enlargements to show de-
tails along with the text.
Liquid phase and �*-N2*
The only spectral features, which can be identified
between 60 and 43 K, are a relatively narrow band
(band width 1–2 cm–1) at 1552 cm–1 on top of a broad
band, which is very similar to the SB in liquid or �-O2
(see Fig. 3). We assign these features to the IR ab-
sorption of the O2 fundamental (stretching band or vi-
bration) in liquid mixture and in �*-N2 plus side band
to it. The symmetric stretching of O2 molecules (the
narrow band) becomes IR active due to a symmetry
breaking in the molecule’s environment in mixture.
The difference between spectra in liquid and in the
�*-N2 phase can be seen in Fig. 3. The broad wings on
both sides of the fundamental are typical for liquids
[9] and are generally assigned to the rotational diffu-
sion excited via vibration/rotation coupling. In �*-N2
the narrow band seems to be not connected with the
1384 Fizika Nizkikh Temperatur, 2006, v. 32, No. 11
M. Minenko and H.-J. Jodl
* A star is commonly used to characterize the phase in mixture; without it one deals with a pure system.
A
ar
b
. u
n
its
F –
L
*
* *
**
**
**
Fig. 2. Absorption spectra in the region of oxygen funda-
mental (� 1550 cm–1) as a function of temperature, col-
lected during the warming cycle of (N2)0.55(O2)0.45 mix-
ture. Different phases are indicated on the right side.
(Details of this overview are presented in the following
Figs. 3–5).
broad band (SB). An unambiguous deconvolution of
SB in plastic phases is hindered by a variety of differ-
ent types of motion, each possessing a broad band of
energies, and their specific interactions. In both oxy-
gen and nitrogen the biggest role are playing rota-
tional (±30 cm–1 around the fundamental) and
translational (centered at +65 cm–1) motions. From
the similarity with the SB in �-O2 we can deduce that
O2 molecules imbedded in �*-O2 or in �*-N2 structure
participate in similar types of motion.
Due to our measurements at different concentra-
tions (liquid + �-N2) two-phase region is a bit more
narrow (in temperatures) than in the phase diagram
by Barrett–Meyer. We confirm that the maximal solu-
bility of O2 in �*-N2 is around 55% (see Fig. 1).
�*-O2
Starting from T = 42 K the narrow band (< 1 cm–1)
at 1552 cm–1 (band 1 in Fig. 4) is getting weaker and
on the low-frequency side appears a broader band
(� 3–4 cm–1) which includes a narrow (< 1 cm–1) fea-
ture at 1551 cm–1 (band 2 in Fig. 4). The broad fea-
ture (SB) gains some intensity at about 60–70 cm–1 on
the Stokes side of the zero-phonon band increasing the
similarity of this band with the side band in pure �-O2.
We assign band 2 to the defect-induced IR absorption
of the O2 vibration or, in other words, to a smeared
out vibron DOS in �*-O2 (see section 4.2). The inten-
sity of that band is quite substantial due to the rela-
tively high solubility (� 10%) of nitrogen in �*-O2
that means that practically each O2 molecule has at
least one N2 molecule as a neighbor. At lower tempera-
tures band 2 is more pronounced, whereas the band at
1552 cm–1 (band 1) almost vanishes (assigned to the
vibration of O2 molecules in �*-N2).
So from Fig. 4 one can derive that at the concentra-
tion (N2)0.55 (O2)0.45 �*-O2 phase surely exists in the
temperature interval (38–42 K). From the decrease of
the band 1 intensity we conclude that solubility of O2
in �*-N2 strongly depends on temperature; namely, it
is decreasing lowering temperature. The exact range of
the �*-N2 phase existence should be cleared out with
Fourier transform infrared studies of the N2–O2 binary system
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11 1385
A
b
so
rb
an
ce
,a
rb
. u
n
its
Frequency, cm–1
Liquid
*
Fig. 3. Absorption spectra in the region of oxygen vibra-
tion of the liquid mixture and of �*-N2. Subtle changes of
the fundamental mode (bandwidth, band shape) are
stressed by arrows. Spectrum from pure �-O2 (T = 44 K)
is added for comparison.
A
b
so
rb
an
ce
, a
rb
. u
n
its
Frequency, cm–1
2
1
**
**
*
Fig. 4. The same spectra, as in Fig. 2, but in a more nar-
row frequency range, demonstrate changes of the funda-
mental only: band 1 is the IR absorption of O2 solved in
�*-N2, band 2 (shaded area) represents the vibron DOS of
�*-O2.
the help of the analysis of spectra in the N2 stretching
band vicinity (see later).
In this range our variant of the phase diagram
(Fig. 21) differs strongly from both previous (Fig. 1).
Neither in infrared, nor in Raman studies we found
any evidence for the X-phase. �*-O2 phase was found
at temperatures as low as 37.5 K (warming cycle
value).
�*-O2
At T = 35 K both narrow band(s) in the vicinity of
the O2 stretching band (Fig. 4) and broad phonon
band on its Stokes side (Fig. 2) differ substantially
from all the spectra at higher temperatures. The
phonon side band is now very similar to the one in
�-O2 [6,7]. The band at the O2 vibration is much less
intensive and consists actually out of three features
(this could be seen better in Fig. 5 at lower tempera-
tures): a plateau (1547–1553 cm–1) with maximum at
about 1552 cm–1 and a very narrow peak (< 0.2 cm–1)
at 1552.5 cm–1 (both are tentatively assigned to the im-
purity-induced vibron DOS of �*-O2); at 1552.7 cm–1
(T = 35 K) the already known band 1 (vibration of O2
molecules in �*-N2 , band width < 1 cm–1). The evolu-
tion of the band 1 with temperature is better seen in a
more N2-rich sample (N2)0.92(O2)0.08 (Fig. 6). The
(�*– �*)-N2 phase transition at T � 34 K can be identi-
fied due to a jump in the band frequency, band width
and changes in band shape. One can recognize only a
very weak response from the �*-O2 phase since the O2
concentration is low and the amount of the O2 phase is
even smaller. Between 34.6 and 36 K �*-O2 phase dis-
appears and only �*-N2 remains.
The jump in frequency (��tr) of the O2 stretching
band in nitrogen at the (�*–�*)-N2 phase transition
phase can be estimated comparing the values of the en-
vironmental shifts in nitrogen phases (at the transi-
tion temperature) from [7]:
��tr � ��env(�
*-N2) – ��env (�*-N2) =
= – 1.8 – (– 2.4) = 0.6 cm–1,
��tr (exp) = 1.2 cm–1.
It should be noticed that the used values for the en-
vironmental shifts correspond to undistorted struc-
tures. The larger experimental jump value can be ex-
1386 Fizika Nizkikh Temperatur, 2006, v. 32, No. 11
M. Minenko and H.-J. Jodl
A
b
so
rb
an
ce
, a
rb
. u
n
its
Frequency, cm–1
1
* *
* *
* *
Fig. 5. The same part of spectra like in Fig. 4 at lower
temperatures. Dotted lines are baselines for vibron DOS
in �*-O2 and �*-O2. Broken line follows the evolution of
the band 1 (O2 in �*- and �*-N2).
A
b
so
rb
an
ce
, a
rb
. u
n
its
Frequency, cm–1
1
* *
* *
*
*
*
*
Fig. 6. Spectra of (N2)0.92(O2)0.08 in a narrow frequency
range around O2 fundamental. Broken line as in Fig. 5
follows band 1. Dotted line follows a weak absorption of
O2 in �*-O2.
plained by an influence of dissolved molecules (e.g.,
by a variation in their amount), and would hint on a
jump in solubility of oxygen during the (�*–�*)-N2
phase transition.
From spectra of O2 vibration and its phonon side
band we were able to detect not only (�*–�*)-O2 phase
transition but also (�*–�*)-N2. Spectral fingerprints
confirm the phase mixture of �*-O2 and �*-N2 in the
temperature range 34–36.5 K that is closer to the vari-
ant of Barrett—Meyer but is not as narrow as theirs
(Figs. 1, 21).
�*-O2
At T = 22.5 K the phonon SB starts getting more
pronounced and maxima, known from the SB of pure
�-O2 [6,7], can be recognized, although these features
are impurity-broadened (Fig. 2). The band at the fun-
damental contains additional features in comparison
to spectra of �*-O2. The broad band between 1546 and
1553 cm–1 is gaining intensity and becomes pla-
teau-like at 11 K (Fig. 5); intensity of the narrow fea-
ture at 1552.5 cm–1 is decreasing lowering tempera-
ture, whereas a new narrow (< 0.2 cm–1) feature at
1552 cm–1 is showing up in �*-O2 . It looks as if both
decrease/increase evolutions in intensities of these
bands are linked together. We assign � 7 cm–1 broad
band together with these narrow features to the
vibron DOS of �*-O2 ; for discussion see later. Band 1
at 1554.7 cm–1 (T = 11 K) is still present (assigned to
O2 molecules in �*-N2).
Temperature of the (�*–�*)-O2 phase transition
(T � 23 K) according to us is lying somewhere be-
tween the values from two previous phase diagram
variants (Fig. 1).
3.2. Nitrogen fundamental region (� 2330 cm–1)
An overview of spectra in the region of the N2
stretching band as a function of temperature (52–12 K)
during cooling for one concentration (N2)0.92(O2)0.08
is shown in Fig. 7. Since the phonon side band of N2 is
much less intensive than the one of O2 we are forced to
choose a nitrogen-rich mixture in order to demonstrate
changes in this side band.
Changes in the closest vicinity of the N2 stretching
band with temperature are demonstrated by spectra of
the (N2)0.55(O2)0.45 mixture (Fig. 8), which undergoes
more phase transitions than the N2-rich sample does.
�*-N2
Spectra of the side band in �*-N2 phase (Fig. 7) can
be deconvoluted in a narrow (< 1 cm–1) peak-like
band at � 2327 cm–1, broad (� 30–40 cm–1) bands
centered at about 2345 cm–1, 2390 cm–1 and in
low-temperature �*-N2 another one around the stretch-
ing band frequency 2327 cm–1. We assign the narrow
spectral component to the impurity-induced vibron
density of states in �*-N2 (for details see Sec. 4.2).
A smeared out peak of matrix-isolated CO2 at
� 2347 cm–1 ( 3 mode) is also present in our spectra (a
star in Fig. 7) together with its very weak side band.
These 3 broad bands in this mixture are similar to
excitations in pure �-N2 [7] and in N2–Ar [10]. There-
fore we were able to achieve a consistent decon-
volution of spectra into the induced fundamental and
the phonon side bands. The band at � 60 cm–1 with re-
spect to the zero-phonon line (ZPL; 0 � 2327 cm–1) is
due to translational contributions to the phonon side-
band. The band at � 15–20 cm–1 we associate, due to
literature, with the nutational motion of molecules
Fourier transform infrared studies of the N2–O2 binary system
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11 1387
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Frequency, cm–1
*
*
*
Fig. 7. Absorption spectra in the region of nitrogen funda-
mental (� 2330 cm–1) as a function of temperature col-
lected during the cooling cycle of (N2)0.92(O2)0.08 mix-
ture. Different phases are indicated on the right side. The
broad bands (phonon side band) are distinctly changing
lowering temperature. Dotted lines serves as baseline of
side bands. Changes of the band shape near the N2 funda-
mental inside of �*-N2 are stressed by a broken line (spec-
trum at 33 K), which repeats the shape in high-tempera-
ture �*-N2. Peak assigned by a star (*) is due to
absorption of CO2 (� ppm; �3 mode).
(correlated orientational oscillation of molecular axes
relative to the c axes of hcp structure [11]) or to
librational jumps [12]. The remaining broad band,
centered at ZPL, present only in low-temperature
�-N2, arises probably due to a partial freezing of the
nutational motion (glassy �-N2).
�*-N2 is the only phase between 53 and 43 K in
(N2)0.55(O2)0.45 mixture and between 60 and � 35 K
in (N2)0.92(O2)0.08 mixture.
�*-O2 and �*-N2
An additional structured band at 2326–2327 cm–1
with 3 maxima separated by less than 0.2 cm–1 is present
between 42 and 38 K in spectra of (N2)0.55(O2)0.45 mix-
ture (Fig. 8). They exist at cooling and at warming in
the temperature interval of phase coexistence of �*-O2
and �*-N2. The signal/noise ratio unambiguously em-
phasizes the existence of several peaks. The fact that
frequencies of these peaks are slightly changing with
temperature also confirms the physical origin of these
peaks.
One expects in this temperature interval in O2-rich
mixtures either �*-O2 or an X-phase in coexistence
with �*-N2 (Fig. 1). But we did not find any spectral
evidence for the X-phase. Since this structured band
represents vibrations of nitrogen molecules and since
the solubility of N2 in �*-O2 is expected to be quite
high (10–12% [2,3]), we assign the new band to vi-
brations of N2 molecules in �*-O2. The nature of the
infrared activity is usual for mixtures; it is a broken
symmetry of the molecules’ environment in the host
crystal. But what is the origin of 3 peaks?
The �-O2 is a phase with 8 molecules per cell: two
molecules on site a (sphere-like) and 6 molecules on
site c (disk-like) [13]. The splitting of the Raman-ac-
tive O2 vibron is about 1.2 cm–1 [14]. One may imag-
ine that N2 molecules may occupy these two different
sites. But an energy splitting due to sites is too large
in comparison to separation of 3 maxima (
0.2 cm–1).
On the other hand it is known from experiments on
N2–Ar, that the monomer/dimer splitting is about
0.15 cm–1 [15]. Since the solubility of N2 in �*-O2 is
10–12% (Fig. 1), the probability to find a dimer or a
trimer of N2 molecules in �*-O2 (Pm3n) is substantial
(30%). Then a possible explanation of the triplet
would be the different number of nitrogen molecules
among nearest neighbors of the oscillating N2 mole-
cule: none, one or two. But we should also take in ac-
count that due to the existence of different sites there
is a number of combinations for the pair of N2 mole-
cules: sphere—sphere, sphere—disk or disk—disk.
At T = 35 K we observe only one narrow (0.5 cm–1)
band at 2327 cm–1, which we assign to the induced
vibron DOS of �*-N2 (Fig. 8).
As a consequence of these spectral findings we can
specify in the T–x% diagram the area of phase coexis-
tence of �*-O2 and �*-N2 (see Fig. 21). Since we did
not find any spectroscopic response from N2 in �*-O2
we confirm a weak (
1%) solubility of N2 in �*-O2.
�*-N2
Below 34.5 K in �*-N2 the spectral features are get-
ting more pronounced. The induced stretching band,
which is symmetric in the �*-phase and centered
at 2327 cm–1 (T > 33.5 K), is now asymmetric in
the �*-phase with a maximum at about 2328 cm–1
(T < 33.5 K) (Fig. 8) (details on vibron DOS in
Sec. 4.2). To higher frequencies with respect to the
fundamental mode (or ZPL) we register a broad band
with two maxima (+ 30 and + 65 cm–1), which we as-
sign to be the smeared out phonon side band known
from pure �-N2 [16,17]. Theoretically determined
DOS of lattice modes of �-N2 [17] associate the first
maximum at 30–35 cm–1 to lattice modes with
the librational character, the second maximum at
1388 Fizika Nizkikh Temperatur, 2006, v. 32, No. 11
M. Minenko and H.-J. Jodl
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Frequency, cm–1
* *
* *
*
* *
Fig. 8. Spectra of (N2)0.55(O2)0.45 mixture in a narrow
frequency range. Dotted lines are baselines for vibron
DOS in �*- and �*-N2. A band with 3 peaks at lower fre-
quencies is the IR absorption of N2 solved in �*-O2.
+ 60 cm–1 to lattice modes with the translational cha-
racter.
Bands centered near the fundamental and at about
+ 20 cm–1 (T = 35 K) disappear at the (�*–�*)-N2
phase transition completely (Fig. 7). In orientation-
ally ordered �*-N2 the nutations are frozen out. The
orientational motion is represented by librations.
There is no indication of the (�*–�*)-O2 phase
transition in spectra of the N2 fundamental region at
� 2320 cm–1 (estimated value: �gas – ��env). With
our very sensitive FTIR technique we do not observe
any fingerprints of N2 solved in �*- and �*-O2 in spec-
tra. Taking in account our signal/noise ratio we agree
with previous investigators that the solubility of N2 in
�*- and �*-O2 is about or less than 1% (see Fig. 1).
3.3. Overtone region (3000–5000 cm–1)
In pure systems phonon side bands to the overtones
(ZPL (0-2) + SB) are 100 times less intense than side
bands to the fundamental. We do not observe these
structures here because our samples were relatively
thin (
1 mm). But at low temperatures we observe
two relatively narrow bands in that overtone region.
At 4656–4657 cm–1 we detect a band (width
� 1 cm–1), which vanishes at the (�*–�*)-N2 phase
transition. The overview spectra as a function of
temperature during warming for the concentration
(N2)0.92(O2)0.08 is shown in Fig. 9,a. The assignment
is obvious comparing this spectrum with the one in
pure �-N2 (Fig. 9,b). Legay [18] modeled this band in
pure N2 as follows: in �-N2 with 4 molecules per unit
cell two neighboring molecules can perform a simulta-
neous out of phase vibration ((0–1)Ag symmetry and
(0–1)Tg symmetry); this combined excitation — cal-
led two-vibron — is IR active; whereas in �-N2 such
excitation is not expected because there exists only
one stretching mode (Fig. 9,a). The case in mixture is
similar in principle, but the spectrum is slightly
broader and more smeared out (Fig. 9,b) due to impu-
rities (O2 in �*-N2). Legay [18] gave a full description
of the IR absorption: band position, band shape, inte-
grated intensity and assignment with respect to
Raman active modes (Ag, Tg). The position of this
two-vibron excitation in pure �-N2 (T = 11 K) can be
estimated qualitatively as follows:
�min = �Raman (A
g
) + �Raman (T
g
) =
= 2327.6 + 2328.6 = 4656.2 cm–1,
�max = 4657.4 cm–1.
In our case �min (exp) �4656.5 cm–1 and �max (exp) =
= 4657.5 cm–1.
Therefore we confirm the model of Legay, which
can be extended to mixtures considering that a part
of the band’s integrated intensity is defect-induced.
This spectral fingerprint is a good indicator of the
(�*–�*)-N2 phase transition: from Fig. 9,a follows that
it occurs between 34 and 34.6 K at this concentration.
At 3883–3884 cm–1 we detect another band
(Fig. 10), which we assign to a simultaneous com-
bined («mixed») excitation of the N2 (0–1) and O2
(0–1) vibrations in �*-N2. Since the solubility of O2
in �*-N2 was approximated by 5–8% [1] and less than
1% of N2 is soluble in �*- and �*-O2 we believe that
this «mixed» excitation is taking place in �*-N2 only.
This conclusion is supported by the increase of the
band intensity with an increase of the N2 concentra-
tion and thus of the �*-N2 amount. In order to esti-
mate the approximate frequency of such band we just
add frequencies of corresponding vibrations:
�N2+O2
= �
R
(A
g
or T
g
N2) + � (O2 in �*-N2) =
= 2327.6 or 2328.6 + 1554.7 = 3882.3–3883.3 cm–1,
in comparison to � (exp) = 3882.5–3884.2 cm–1.
Fourier transform infrared studies of the N2–O2 binary system
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11 1389
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Frequency, cm–1
Frequency, cm–1
a
b
*
*
*
Fig. 9. Overview of absorption spectra in the region of
the two-vibron ((0–1) N2 + (0–1) N2) � 4600 cm–1 around
(�*–�*)-N2 transition temperature, collected during the
warming cycle of (N2)0.92(O2)0.08 mixture (a); comparison
of two-vibron in pure N2 (broken line) and in �*-N2 (T =
= 11 K) (b).
The intensity ratio of this N2+O2 band and the
N2–N2 two-vibron band is 1:3, whereas one would ex-
pect a much weaker intensity of the «mixed» band due
to a low amount of oxygen in �*-N2 . Obviously it is
compensated by the induced dipole moment due to a
large distortion of the symmetry of the O2 molecules’
environment caused by a presence of other O2 mole-
cules among the host (N2) ones.
The integrated intensity of two-vibron bands
(I � �2, � is an orientational order parameter) allows
us to discuss the orientational ordering between neigh-
boring molecules [19]. In Fig. 11 we plotted tempera-
ture dependences of the reduced orientational order
parameter of oxygen (�) and nitrogen (�) in �*-N2
and of nitrogen in pure N2 (solid line). While N2 mo-
lecules are almost as oriented as in the pure system till
relatively high temperatures, O2 molecules, possessing
a much smaller electric quadrupole moment, are con-
siderably less oriented in �*-N2. It is well known that
orientational order in �-N2 is predominantly caused by
the electric quadrupole—quadrupole interaction be-
tween nitrogen molecules.
3.4. Exciton region of oxygen (� 8000 cm–1)
The absorption bands of the pure electronic and
electonic-vibronic transitions (phonon side bands to
them) in solid oxygen are already well studied [4],
also as a function of temperature [8] and pressure
[20]. We concentrate here on the lowest energy transi-
tion 3 10 0� �g g
�
�
( ) ( ) . In �-O2 this band has
a fine structure: the strongest peculiarities are as-
signed to the exciton–magnon bound state [4]. The
zero phonon line (ZPL) of this band was determined
recently [8]. This made possible an assignment of
other peculiarities. The spectrum of (N2)0.92(O2)0.08
mixture at T = 11 K in comparison with the one of
pure oxygen (with reduced intensity) is shown in
Fig. 12. The band in mixture is clearly smeared out so
that some features of the above mentioned fine struc-
ture are not resolved. In general, the band shape is
comparable with spectra of pure O2 at T = 20–22 K.
There are two additional weak bands on the anti-
Stokes side that are making the difference (arrows in
Fig. 12, see also Fig. 14). Electronic absorption bands
are characteristic for a phase and thus could serve as a
good indicator of phase transitions. The existence in a
mixture of a band, which is similar to the one in �-O2 ,
gives us a right to claim the existence of the �*-O2 in
this mixture at a given temperature (11 K). This ob-
servation means that the solubility of O2 in �*-N2 is
less than O2 concentration (8%) in this mixture. Spec-
tra in earlier works [4] should be reinterpreted with
the knowledge of the new solubility value at low tem-
peratures (see Sec. 4.1).
1390 Fizika Nizkikh Temperatur, 2006, v. 32, No. 11
M. Minenko and H.-J. Jodl
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Frequency, cm–1
Fig. 10. Spectrum of a «mixed» two-vibron ((0–1) N2 +
+ (0–1) O2) in (N2)0.92(O2)0.08 mixture at T = 11 K. Ar-
rows indicate �min and �max.
T, K
�
Fig. 11. Reduced orientational order parameter (�(T)/�
(11 K)) as a function of temperature: triangles — O2 mo-
lecules and circles — N2 molecules in the mixture
(N2)0.92(O2)0.08, solid line — pure N2 [19].
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Frequency, cm–1
Fig. 12. Comparison of electronic absorption of O2 mole-
cules (�
) in pure �-O2 (thin line) with reduced inten-
sity and in mixture at T = 11 K. Arrows point on the con-
tribution from O2 in �*-N2 on the anti-Stokes side of the
spectrum in mixture.
An overview of spectra at different temperatures
(11–50 K) during warming of the (N2)0.92(O2)0.08
mixture is shown in Fig. 13. We have discussed al-
ready the spectrum in �*-O2. At the (�*–�*)-O2 phase
transition this band transforms in a broad featureless
asymmetric band, typical for �-O2; its maximum
jumps for about 80 cm–1 to lower frequencies. These
changes are explained by the loss of the long-range
magnetic order [8]. The spectrum at T = 23 K mirrors
the superposition of two phases, confirming the
(�*–�*)-O2 phase transition at T � 23 K. But the spec-
trum at T = 41 K differs from all others substantially:
its intensity is in the order of magnitude smaller than
those of bands in �*-O2. Whereas intensity of elec-
tronic bands in pure �-O2 is only three times smaller
than in �-O2 [8]. In addition the band maximum of
spectrum at 41 K in mixture is moved for about
50 cm–1 to lower frequencies from the value in �-O2.
So if this band cannot be linked to the �*-O2 phase it
must be formed by oxygen molecules embedded in
�*-N2 phase. Therefore we are able to claim that there
is no oxygen-based phase in (N2)0.92(O2)0.08 mixture
at T = 41 K; that is in agreement with the phase dia-
grams in Fig. 1 and is confirmed by our spectra in the
fundamental region.
Now, after identifying a spectrum of the electronic
excitation of oxygen molecules imbedded in the nitro-
gen phase, we can return to the discussion of the
anti-Stokes wing of the spectrum at T = 11 K
(Fig. 14). The spectrum of pure O2 at T = 22 K serves
as a measure of broadening of the main band from O2
in �*-O2 and can be taken as a tentative baseline for
IR absorption in this frequency range. Spectrum at
T = 41 K (assigned to absorption of O2 in �*-N2) is
shown for comparison: intensity of the whole band is
comparable with intensity of the anti-Stokes side of
the spectrum at 11 K and frequency of the band’s max-
imum lies between those two features of the low-tem-
perature spectrum. Thus we assign the big part of in-
tensity on the anti-Stokes wing of the spectrum at
11 K to the electronic excitation of O2 molecules dis-
solved in �*-N2 (7864 cm–1 – first feature) and its
combination with phonons of this phase (phonon side
band), the most prominent of which (at +32 and
Fourier transform infrared studies of the N2–O2 binary system
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11 1391
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Frequency, cm–1
*
*
*
Fig. 13. Evolution of electronic spectra with temperature
of (N2)0.92(O2)0.08 mixture. Please note the distinct
change in absorbance for O2 solved in �*-N2 (T = 41 K).
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Frequency, cm–1
*
Fig. 14. Details of spectra on the anti-Stokes side of ZPL:
solid line — mixture at T = 11 K (see Fig. 12), broken
line — pure O2 at T = 22 K, dotted line — O2 solved in
�*-N2 at 41 K (see Fig. 13). Arrows indicate band maxima
(see text).
+38 cm–1; librons [21]) are seen as the second feature
at 7900 cm–1. Therefore the whole band at T = 11 K
represents a superposition of the absorption of O2 mo-
lecules in �*-N2 and in �*-O2.
Electronic transition bands of O2 appeared to be
very useful spectral fingerprints in studies of the
N2–O2 phase diagram. The shape of the band and its
intensity tell us whether oxygen molecules form their
own (O2-rich) phase or they are dissolved in the
N2-rich phase. And as in the pure O2 we can trace
phase transitions from changes in spectroscopic char-
acteristics of the electronic bands. Moreover, one can
obtain valuable information about the solubility of O2
in N2 at a given temperature (details in 4.1).
4. Discussion
4.1. Phase diagram T–x%
Phase transitions lines. In Sec. 3 we already de-
scribed how one can deduce from changes in spectra of
different modes the phase transitions in N2–O2 mix-
tures. Here we would like to summarize the results
outlining the most suitable excitations for demonstra-
tion of the main transitions: � � � � � in O2 and
�� � in N2. We put the stress on differences with pre-
vious phase diagrams (Fig. 1), preparation and ther-
mal treatment of samples and we discuss solubility of
oxygen in nitrogen-rich phases that is one of the most
prominent deviations between two previous variants
of the diagram.
The (�*–�*)-O2 transition (T � 23 K) in N2–O2 is
seen the best from changes in spectra of electronic
transition (��� , � 8000 cm–1). The frequency jump
of the band origin (� � 90 cm–1) and drastic changes
in band shape can be explained by magnetism of �-O2
[8]. The phase transition temperature differs just mar-
ginally (< 1 K) from literature values [2,3].
The (�*– �*)-O2 transition (T � 37 K) in our mixture
is well documented by changes in spectra of the O2 fun-
damental and its phonon side band ( 0 � 1550 cm–1):
like in the pure case, changes in the SB shape are ac-
companied by a frequency shift of the band maximum.
In addition in �*-O2 we can see a very intensive in-
duced vibron band. The phase transition temperature
differs substantially (4–8 K) both from literature data
and from the one in pure O2 (T � 43.8 K). Due to dif-
ficulties to obtain thermodynamically stable samples
at cooling we took into consideration only the transi-
tion temperature recorded at warming.
The ��*–�*)-N2 transition (T � 34 K) can be fol-
lowed in several ways: changes in spectra of the side
band to the N2 fundamental, of the two-vibron band
and of the induced vibron band (� 2328 cm–1). As an
example, the phase coexistence of �*- and �*-N2 is
demonstrated in Fig. 15 between 34 and 34.6 K in a
N2-rich mixture during warming.
We claim T � 34 K to be the (�*–�*)-N2 phase tran-
sition temperature for a wide range of concentrations,
i.e., the horizontal line in the T–x% diagram, separat-
ing the two-phase regions. That is 1–2 K higher than
in previous diagrams (Figs. 1, 21).
Phase transitions lines, found by two groups on the
basis of structural studies [2,3], are shown in Fig. 1. In
these publications neither the history of samples, nor
the path in the T–x% diagram, nor the time of tempera-
ture changes are mentioned. Our studies revealed that
the temperature of a phase transition depends sensi-
tively on the fact, whether this transition was moni-
tored during cooling or warming cycle, on the rate of
temperature changes and on the annealing time.
Differences in spectra during cooling and warming
cycles are well documented in Figs. 16, 17; consider-
ing as example the most problematic phase transitions
(�*–�*)-O2 and ��*–�*)-N2. The induced O2 vibron
band (around 1550 cm–1) and its phonon side band are
1392 Fizika Nizkikh Temperatur, 2006, v. 32, No. 11
M. Minenko and H.-J. Jodl
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Frequency, cm–1
Fig. 15. Absorption spectra in the region of nitrogen fun-
damental (� 2328 cm–1) as a function of temperature, col-
lected during the warming cycle of (N2)0.92(O2)0.08 mix-
ture. In this narrow temperature interval the coexistence
of phases (�*+ �*)-N2 is demonstrated.
shown in Fig. 16. Changes in shape and intensity of
the side band during cooling between T = 32 and 31 K
and during warming between T = 35 and 38 K indicate
the (�*–�*)-O2 phase transition. We were not able
to reduce this difference in transition temperature
(� 5 K) although we changed temperature quite
slowly (hours/K) and we annealed the sample for
several hours before each measurement. This phenome-
non could be explained as follows. Solubility of N2 in
�*-O2 (� 10%) differs substantially from the one in
�*-O2 (� 1%). Therefore during the (�*–�*)-O2 phase
transition a massive demixing of nitrogen from the
oxygen phase should take place, but it is hindered by a
low rate of diffusion at these relatively low tempera-
tures. The system becomes undercooled; there is not
enough energy for the phase transition.
Spectra in Fig. 17, that were taken simultaneously
with those in Fig. 16, document similar discrepancies
for warming/cooling cycles in the vicinity of the im-
purity-induced N2 vibron band. During cooling the
(�*–�*)-N2 phase transition occurs simultaneously
with the (�*–�*)-O2 transition between 32 and 31 K.
Whereas during warming they are clearly separated:
we register the (�*–�*)-N2 transition between 33 and
35 K and the (�*–�*)-O2 transition happens between
35 and 38 K.
So the message is: the difference between transition
temperatures in our studies and the ones in literature
could be due to the difficulty to achieve thermody-
namically stable samples that was, most likely, not re-
alized in earlier investigations.
X-phase and solubility. There are two further open
questions in the published T–x% diagrams [2,3]: an
X-phase [3] and solubility of oxygen in N2-rich phases.
We have studied 5 concentrations (N2)x(O2)1–x by
means of infrared absorption and we have not detected
any sign in spectra which might be brought in relation
with an X-phase. All the spectra in these mixtures can
be traced back to phases of pure systems. Therefore we
claim that the T–x% diagram at ambient pressure con-
sists only of known phases of the pure systems.
There is a big discrepancy in literature in solubility
of oxygen in �*-N2 determined by structural studies:
one group [3] predicted a strong decrease in solubility
from � 10% at the (�*–�*)-N2 phase transition (� 34 K)
to less than 1% at about 20 K, another group [2]
claimed it to be as large as 18% and independent on
temperature.
There are two ways to study solubility by means of
spectroscopy. The obvious one is to prepare samples
with different concentrations and to search for a con-
centration, at which a certain phase (documented by
Fourier transform infrared studies of the N2–O2 binary system
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11 1393
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Frequency, cm–1Frequency, cm–1
a
b
Fig. 16. Spectra of (N2)0.55(O2)0.45 mixture in the region of oxygen fundamental recorded during warming (a) and cool-
ing cycles (b).
its fingerprints in spectra) would appear or disappear.
In the mixture (N2)0.92(O2)0.08 we discovered distinc-
tive excitations, which are specific for the �-O2: side
band to the O2 fundamental and the electronic transi-
tion band. So we can claim the solubility of oxygen in
�*-N2 to be lower than 8%. In order to get a more ac-
curate value we would have to prepare and study sam-
ples with decreasing oxygen concentration until these
bands would disappear.
But there is a more time-saving way to get a solu-
bility value. It requires an existence of the distinctive
for a phase excitation, which intensity is proportional
to the amount of this phase. The key of following cal-
culations is a proportion of the phase in the mixture
(relative amount of the phase), q.
A simple lever rule, demonstrated in the Fig. 18, es-
tablishes the correlation between solubility (100 – y)
in % and the proportion of the phase (e.g., �*-O2), q.
The fact that solubility of N2 in �*-O2 can be consid-
ered zero makes the formula simpler. Taking in ac-
count that molar volumes of O2-rich and N2-rich
phases are different we have:
q = (y – x)VO2
/[xVN2
+ (y – x)VO2
],
where y is a position of the solubility line at given
temperature, mol% of N2; x is a concentration of N2 in
the sample in mol%; VN2
and VO2
are molar volumes
of �*-N2 and �*-O2 [13*,22].
The proportion of the phase q can be derived from
intensities of the bands of a distinctive excitation at
different concentrations but at the same temperature.
This is based on a simple premise: the intensity of such
band in a mixture is proportional to the effective
thickness of the phase in a sample teff , which equals
the sample thickness t multiplied by the proportion of
that phase q. Let 100% of O2 (pure system) be one of
the concentrations then
Imix / Ipure = teff / t = q,
1394 Fizika Nizkikh Temperatur, 2006, v. 32, No. 11
M. Minenko and H.-J. Jodl
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so
rb
an
ce
, a
rb
. u
n
its
Frequency, cm–1 Frequency, cm–1
a b
Fig. 17. Spectra of (N2)0.55(O2)0.45 mixture in the region of nitrogen fundamental recorded during warming (a) and cooling
(b) cycles confirm Fig. 16 and demonstrate that (�*–�*)-N2 transition at cooling occurs simultaneously with (�*–�*)-O2.
S
*
**
Fig. 18. Lever rule for our phase diagram.
* The authors: I.N. Krupskii, A.I. Prokhvatilov, Yu.A. Freiman, and A.I. Erenburg.
where Imix and Ipure are intensities of the bands in
mixture and in the pure.
Consequently the equation for the position of the
solubility line in the phase diagram:
y x
V
V
I
I I
�
�
�
�
�
�
�
�
�
�
1 2
2
N
O
mix
pure mix
.
Thus we are able to get solubility values from the
spectroscopic fingerprints of phases in our mixtures.
In our case the phases are �*- and �*-O2 and the dis-
tinctive excitations are O2 side band to the fundamen-
tal and O2 electronic absorption band. At low temper-
ature (�*-O2) the side band (Fig. 19,a) is our choice,
whereas for the �*-O2 phase the electronic transition
band (Fig. 19,b) is advantageous. Such conclusion we
made after we analyzed some spectroscopic features:
baseline, bands’ fine structure and overlapping with a
spectral response from another phase.
For our lowest temperature T = 11 K we obtain y =
= 96.5%. This means that about 3.5 mol% of O2 can be
solved in �*-N2. At T = 32 K solubility is � 5 mol%.
An absolute error of solubility values is about
±0.5 mol%. Obtained in this way solubility line is a
part of the phase diagram of Fig. 21.
This method to determine solubility can be checked
comparing intensities of the excitations of N2 mole-
cules; these intensities must be proportional to the
amount of the N2-rich phase (�*-N2). In Figs. 20,a and
20,b we present spectra of two such excitations: an in-
duced N2 vibron band (� 2328 cm–1) and a «mixed»
N2–O2 two-vibron band (� 3883 cm–1) in different
mixtures (N2)0.55(O2)0.45 and (N2)0.92(O2)0.08 at
11 K. From the chosen sample concentration and the
known solubility value (3.5% of O2 in �*-N2) we cal-
culate the relative amounts of the �*-N2 phase in these
samples: q (�*-N2) = 1 – q (�*-O2) � x/y (without
consideration of molar volumes; see Fig. 18). The ra-
tio of these values q0.55/q0.92 = 0.57/0.95 = 0.6. The
ratio of the band intensities (0.65 for an induced
vibron band and
0.6 for a «mixed» band) must be
equal in this case to the ratio of relative amounts
q0.55/q0.92 . Both experimental values agree pretty
Fourier transform infrared studies of the N2–O2 binary system
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11 1395
A
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b
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its
Frequency, cm–1
Frequency, cm–1
a
b
*
*
Fig. 19. Comparison of (N2)0.92(O2)0.08 spectra (solid
line) with spectra of pure O2 (broken line; intensities are
reduced): side band to O2 fundamental in �*-O2 and in
�-O2 (T = 11 K), Ipure/Imix � 30 (a); O2 electronic ab-
sorption band in �*-O2 and in �-O2 (T = 26 K),
Ipure/Imix � 40 (b).
Frequency, cm–1
Frequency, cm–1
a
b
A
b
so
rb
an
ce
, a
rb
. u
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its
A
b
so
rb
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, a
rb
. u
n
its
Fig. 20. Comparison of the integrated intensity of induced
N2 vibron band (a); and «mixed» two-vibron band be-
tween spectra of (N2)0.92(O2)0.08 (broken line) and
(N2)0.55(O2)0.45 (solid line) at T = 11 K (b).
well with estimated ones, despite the induced charac-
ter of the first band and a low intensity of the second.
Furthermore we confirmed the solubility value at
T = 11 K and the solubility line in a totally different
way: from spectra of matrix isolated CO (see Sec. 4.3).
Investigating thermodynamically stable samples
we clarified 3 open questions: there is no X-phase; we
determined a solubility line on the N2-rich side and we
measured accurate temperatures of the phase transi-
tions. We were able to achieve one of our aims: to de-
velop a phase diagram from fingerprints in spectra.
We suggest a modified T–x% diagram of N2–O2 mix-
ture (Fig. 21) that is based on results of infrared ab-
sorption studies and Raman scattering investigations.
4.2. Vibron density of states
Broad bands (� 100 cm–1), which we assigned in
our spectra to phonon side bands, are similar to ones
in pure systems and are well theoretically modeled
[7,17]. In spectra of our mixtures these bands are just
smeared out. Therefore we deal here only with narrow
bands (width < 10 cm–1), assigned to vibron density
of states (DOS) of N2 and O2. In general we get infor-
mation from optical spectra of Raman and infrared
allowed transitions only at the center of the Brillouin
zone (k � 0). To scan the whole Brillouin zone one is
using classically inelastic neutron scattering, which is
not feasible here. Due to the symmetry of N2 and O2
molecules this vibration is obviously IR inactive. But
in mixtures the symmetry of the molecule’s environ-
ment is broken by a second component. This causes a
local electric field, which induces a dipole moment,
which causes an IR absorption. We profit from the
fact that vibrations with all wave vectors k, being
scattered on impurities (second component), become
IR active. Therefore an intensity of the resulting in-
duced vibron band must be proportional to the vibron
DOS. It is proportional as well to the concentration of
second component in the phase (solubility), to a pro-
duct of electric quadrupole moments of N2 and O2 and
a distance depending term. Several spectra of induced
nitrogen and oxygen vibron bands are already pub-
lished [24–26], but commonly crystal quality of those
samples was bad (condensation at low temperatures)
and a spectral resolution was quite low.
N2 stretching band (� 2330 cm–1). In Figs. 22,a,b
we repeat schematically spectra in the region of the N2
fundamental (Fig. 8) at 35 K (�*-N2) and at 11 K
(�*-N2). A nearly symmetric band (width � 0.8 cm–1)
in �*-phase, which undergoes a clear frequency jump
at the phase transition, transforms into a broader
asymmetric band (� 1.3 cm–1), which remains un-
changed in �*-phase. We assign these bands to the im-
purity induced vibron DOS of �*- and �*-N2. Next we
would like to discuss the band in the �*-N2 only.
Zumofen [27] modeled Raman spectra, especially
the frequency splitting �� (Ag – Fg) � 1.2 cm–1 and
the intensity ratio I(Ag)/I(Tg) � 3:1, like in experi-
ments [14*]. Hochstrasser [28] calculated the vibron
DOS in the framework of common lattice dynamics,
assuming interaction between neighboring molecules
of the first and second shell (see Fig. 22,c, DOS).
Legay [18] improved this model taking into account
also the interaction of molecules of the third shell.
Knorr [10] studied the mixture N2–Ar and discussed
these spectra (central peak or zero phonon line and
phonon side band) in the framework of orientational
glasses. Knorr modeled the central peak ( 0) by a
Gaussian line shape, whose position coincided with
the Raman Ag component and whose band width de-
creased from 0.5 to 0.25 cm–1 rising temperature. At
low temperature this bandwidth was interpreted as
1396 Fizika Nizkikh Temperatur, 2006, v. 32, No. 11
M. Minenko and H.-J. Jodl
T
, K
**
* *
* *
* *
* *
*
Fig. 21. Modified T–x% diagram of the N2–O2 binary sys-
tem according to our spectroscopic studies (on the basis of
Fig. 1). Closed circles — phase transitions points deter-
mined directly from changes in spectra, stars — solubility
values, calculated from intensity ratios.
* The authors: K.D. Bier and H.-J. Jodl.
inhomogeneously broadened due to chemical environ-
ment (mixture plus orientational disorder). The tem-
perature dependence was explained by motional nar-
rowing. The integrated intensity I(T) was related
to a glass order parameter. Raugei [29] performed
MD-simulations of this N2–Ar system and calculated a
theoretical IR spectra of the ZPL plus side band; the
IR intensity is impurity-induced and the bandwidth is
mainly inhomogeneously broadened.
As can be seen in Fig. 22, the shape of the band in
�*-N2 is fairly similar to the shape of the vibron DOS
by Hochstrasser [28]. The obvious difference between
experiment and theory is due to fact that we deal with
mixtures (smearing out of singularities in DOS).
Theoretical models of the vibron DOS in �*-N2 are
not known to us and are problematic due to orien-
tational disorder in that phase. The increase of band
intensity within �*-N2 during warming up (see Fig. 8)
is caused by increasing solubility in this phase (more
impurities lead to larger intensity of an induced
band).
O2 stretching band (� 1550 cm–1). In Figs. 23,a,b,c
we repeat schematically spectra in the region of the
O2 fundamental (Figs. 4, 5) at 38 K (�*-O2), at
24 K (�*-O2) and at 11 K (�*-O2). In spectra of
(N2)0.55(O2)0.45 between 42–37 K (�*-O2) we observe
a relatively broad (� 4 cm–1) band, whose shape is not
changing with temperature (Fig. 4). Its prominent
narrow (� 0.7 cm–1) peak-like feature centered at
around 1551 cm–1 is also temperature independent.
This feature is similar to the induced vibron band in
�*-N2. Whereas �-N2 is orientationally disordered,
�-O2 is only partly disordered and contains two types
of molecules (disk-like and sphere-like).
A decrease of the band’s intensity during warming
is explained by a change in phases proportion in the
sample: the amount of �*-O2 decreases, whereas the
amount of the �*-N2 increases. This is caused by an in-
crease of oxygen solubility in �*-N2, giving simulta-
neously a rise to band 1 (O2 in �*-N2, see Fig. 4).
In �*-O2 at temperatures 35–23.5 K the band shape
looks completely different. It consists out of an almost
triangle-like broad band (� 7 cm–1) with a � 0.7 cm–1
broad feature at around 1552 cm–1 and a very narrow
one (< 0.1 cm–1) at the Raman frequency 1552.5 cm–1.
In �*-O2 below 23 K this pattern changes again
(Figs. 5, 23,c). The broad profile (� 7–8 cm–1) be-
comes plateau-like now. Two new features appear:
a band at 1547 cm–1 and an asymmetric, broad
(0.2 cm–1) band, with maximum at 1551.8 cm–1.
A similar complex structure near the fundamental
0 in pure O2 was found already by Cairns and
Pimentel [24]. Later Jones [26] confirmed from stu-
dies of thin films of pure O2 condensed at 10 K. In
both cases band lost in intensity after annealing but
didn’t disappear. Knorr [30] observed a band in this
frequency region in Ar–O2 mixtures, but discussed it
very briefly without giving an explanation. IR acti-
vity in mixtures is induced by the presence of another
component. To induce the IR activity in pure O2 one
has to produce samples with a very poor optical qua-
lity, in which defects of the structure would play a
role of impurities.
Unfortunately we cannot model this spectral struc-
ture by the vibron DOS of O2 like we did before for
�*-N2 since there are neither systematic experimental
studies nor theoretical works on the vibron density of
states in the �, �, � phases of oxygen. We found in li-
terature similar looking spectra: vibron DOS of a
monolayer of CO, which is a broad asymmetric broad
band with two singularities on its top [31]; vibron
DOS of para-H2 doped by ortho-H2, which is a broad
asymmetric broad band with a weak singularity at the
high-frequency edge [32]; the DOS of a 2-dim honey-
comb and 3-dim diamond fermionic lattice [33].
Fourier transform infrared studies of the N2–O2 binary system
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11 1397
A
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A
b
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rb
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n
its
Frequency, cm–1
Frequency, cm–1
Frequency, cm–1
D
O
S
a
b
c
*
*
Fig. 22. Schematic N2 vibron DOS — taken from suited
spectra: �*-N2 at T = 35 K (a); �*-N2 at T = 11 K (b);
modeled vibron DOS by Hochstrasser [28] and positions
of Raman components (c).
The sharp asymmetric feature of the stretching
band at 1551.8 cm–1 in our spectrum, which exists
only in �*-O2 , looks like the 2-dim honeycomb DOS
[33]. We would like to recall that �-O2 both from
crystal structure and from magnetic point of view is a
quasi-2-dimensional system [34]. The structure of the
basal plane is almost a honeycomb.
IR activity of the singularity at 1552.5 cm–1, pre-
sent in both �*- and �*-O2, could be caused by a pre-
sence of lattice defects and impurities. This makes this
feature dependent on crystal quality and explains its
appearance in earlier IR studies of O2 [24–26].
However the broad band (� 4–8 cm–1) seems to be
characteristic for each phase (�, �, �) and is reprodu-
cible. Therefore it cannot be simply discussed like a
spectral feature, caused by defects or impurities, de-
pending on crystal quality. According to us it mirrors
the vibron DOS of oxygen phases. Unlike in �*-,
�*-N2 or �*-O2, DOS in �*- and �*-O2 are not necessar-
ily smeared out since solubility of nitrogen in these
phases is very low (< 1%). Thus, bands in Figs. 23,b
and c may represent the true vibron DOS of pure
�- and �-O2.
To conclude we add some findings of Brodyanski
[7] from Raman and IR studies on pure oxygen. Using
the known gas phase value (1556 cm–1) [14] they de-
termined values of the environmental (D) and reso-
nance shifts (M):
�crystal (k = 0) = �gas + D + M = �Raman ,
�single = �gas + D,
M = 6 cm–1 in �-O2 (11 K), 5 cm–1 in �-O2, and
� 2 cm–1 in �-O2. The resonance frequency shift is in
most cases more or less the width of the vibron DOS.
Widths of our vibron DOS (Fig. 23): � 7.5 cm–1,
� 7 cm–1, and � 4 cm–1, respectively, that is in a fair
agreement with values above.
We do hope that our experimental results, proving
that oxygen vibron bands are not dispersionless, will
animate theoreticians to calculate vibron DOS at least
for oriented phases of oxygen.
4.3. Matrix isolated CO fundamental (�2140 cm–1)
Since the primary gases (O2 and N2) contain
� 2 ppm CO and since our FTIR spectrometer is sensi-
tive enough to monitor spectra of the matrix-isolated
(MI) CO fundamental at such concentrations, we can
gain some information about the matrix. We have al-
ready successfully applied MI technique in solid O2
and N2 [35,36].
Figure 24,a shows spectra in the CO fundamental
region as a function of temperature; one concentration
(N2)0.92(O2)0.08 is chosen, but spectra at other exam-
ined concentrations are identical. In the interval of ex-
istence of �*-N2 we register only a broad (> 4 cm–1)
band centered at about 2139 cm–1; lowering tempera-
ture we detect in �*-N2 4–5 narrow (< 0.3 cm–1)
peaks distributed between 2138.5 and 2140.5 cm–1.
Peak of the matrix-isolated CO in �-N2 (T = 9 K) lies
at 2139.77 cm–1 [37]; in oxygen (�*- and �*-O2)
� 2136 cm–1 [35], but we detect definitely no signal
(Fig. 24,a) there. So we deal here with the spectro-
scopic response from CO molecules in N2-rich phases.
The broadening of the CO fundamental in �*-N2 is
simply explained by the orientational disorder in this
phase. But the variety of peaks in the �*-N2 will be
discussed next.
With the knowledge of spectra at other concentra-
tions and temperatures we were able to deconvolute
the spectrum in �*-N2 into 5 bands (Fig. 24,a). The
main peak (peak 3) is centered at 2139.8 cm–1 (band-
width � 0.2 cm–1) at T = 12 K, that is in agreement
with the value for MI CO in N2 in literature [37].
Therefore we assign the main peak to the IR absorp-
1398 Fizika Nizkikh Temperatur, 2006, v. 32, No. 11
M. Minenko and H.-J. Jodl
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Frequency, cm–1
a
b
c
*
*
*
Fig. 23. Schematic O2 vibron DOS — taken from suited
spectra: �*-O2 at T = 38 K (a); �*-O2 at 24 K (b); �*-O2
at 11 K (c). Raman frequency, gas value ([14]; the
authors: H. Kiefte, M.J. Clouter, N.H. Rich, and S.F.
Ahmad) and single molecule value deduced by Brodyanski
[7] are shown for comparison.
tion of CO molecules in �*-N2 surrounded by N2 mole-
cules only.
Taking in account that our �*-N2 differs from the
pure �-N2 only by the presence of 3–5% of oxygen
(T = 11–32 K) and that the CO concentration is very
low, what makes the discussion about CO cluster
building irrelevant, we believe that this multiple
structure of the CO band is caused by the presence of
oxygen molecules in �*-N2 . A certain part of CO mo-
lecules has among 12 nearest neighbors one or more O2
molecules. Various environments give rise to different
environmental shifts that leads to a splitting of the
CO band.
To achieve an assignment of all 5 peaks we ana-
lyzed their spectroscopic characteristics. In Fig. 24,b
we plot temperature dependences of all peaks frequen-
cies for two different concentrations (N2)0.55 (O2)0.45
and (N2)0.92(O2)0.08. One can recognize that
frequencies of all peaks are decreasing with increasing
temperature but with a different pace. The weakest
temperature dependence possess peak 1 and every next
one (2, 3, 5) is steeper than the previous one, whereas
peak 4 behaves like peak 3. It is worth mentioning
that at the lowest temperature (11 K) the interval be-
tween peaks (��12, ��23, ��35) is the same and
equals 0.54 cm–1 (excluding peak 4). Thus we can
conclude that peaks 1, 2, 3 and 5 build a certain pat-
tern.
The following assignment is inspired by Loubeyre’s
article [38], in which the multiple band of H2 embed-
ded in Ne (also with equally spaced peaks) was con-
vincingly modeled by taking in account different
amount of the nearest neighbors of the H2 molecule
(H2 singles, pairs, triplets, etc.). We have a slightly
different situation since we have a third element (CO)
probing the matrix: �*-N2 — a mixture of the N2 and
O2 molecules. But the assumption of a random distri-
bution of CO and O2 molecules in �*-N2 is valid here
also. So the main idea of our assignment is as follows:
the CO molecules in �*-N2 have different number of
O2 molecules as nearest neighbors: none, one or two;
the remaining neighbors are N2 molecules.
The most intensive peak in our spectra (peak 3,
Fig. 25) we already assigned to be generated by the vi-
bration of the CO molecules surrounded by 12 N2 mo-
lecules as nearest neighbors in �*-N2; peak 2 we assign
to CO surrounded by 11 N2 and 1 oxygen molecule in
the first shell, peak 1 to CO surrounded by 10 N2 and
2 O2. This assignment is supported by the following
estimation of the frequency shifts. Frequencies of the
CO absorption: in its own solid [39] at 2138.46 cm–1,
in �-N2 [37] at 2139.77 cm–1 (shift +1.31 cm–1), in
�-O2 [35] at 2135,82 cm–1 (shift –2.64 cm–1). Num-
ber of the nearest neighbors in �*-N2 (Pa3 structure)
is 12 and in �*-O2 (C2/m) is 6. So replacing one
N2 molecule by one O2 we loose 1/12 of the N2 fre-
quency shift (–0.11 cm–1) and gain 1/6 of the O2 fre-
quency shift (–0.44 cm–1); the resulting shift equals
–0.55 cm–1. The frequency interval between peaks 1,
2, 3 and 5 at 11 K equals 0.54 cm–1.
Returning to our assignment, peak 4, which is
shifted only by +0.2 cm–1 with respect to the main
peak 3 and which possesses a temperature dependence
identical to the one of peak 3, is tentatively assigned
by us to a splitting of the peak 3 due to broken crystal
symmetry. Thus it is also a response from CO mole-
cules surrounded by 12 N2 molecules as the nearest
neighbors.
An assignment of the remaining peak 5, which is
shifted by +0.54 cm–1 with respect to peak 3, is very
challenging. Following our applied model, a positive
Fourier transform infrared studies of the N2–O2 binary system
Fizika Nizkikh Temperatur, 2006, v. 32, No. 11 1399
A
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Frequency, cm–1
Fr
e
q
u
e
n
cy
,c
m
–
1
a
b
T, K
1
1
2
2
3
3
4
4
5
5
*
Fig. 24. Spectra in the region of the CO fundamental
(� 2140 cm–1) as a function of temperature collected dur-
ing warming cycle of (N2)0.92(O2)0.08 mixture (a); tem-
perature dependence of peak maxima: peak 1 (triangles
up), peak 2 (circles), peak 3 (squares), peak 4 (rhombi),
peak 5 (triangles down) of two different mixtures
(N2)0.92(O2)0.08 (full symbols) and (N2)0.55(O2)0.45 (open
symbols) (b).
shift has the meaning of a «missing O2 molecule» as one
of the nearest neighbors. Therefore we assign peak 5 ten-
tatively to the situation like for peak 2 (CO sur-
rounded by 11 N2 and 1 O2), but in this case this O2
molecule is very close to the O atom of the CO mole-
cule, thus producing a positive shift due to the
O-atom—O-atom repulsion.
The relative integrated intensities of the peaks do
not depend on concentration and vary only weakly
with temperature. Different concentrations of the
samples (the lowest amount of O2 was 8%) play no
role since the ratio of the O2 and N2 in �*-N2 is given
by the solubility value (3–5%), which dependence on
temperature is also rather weak. At the lowest tem-
perature (11 K) the ratio of integrated intensities
is Ip1:Ip2:Ip3:Ip4:Ip5 = 2:20:60:10:10. Increasing tem-
perature the weaker peaks 1, 2 and 5 gain a bit in rela-
tive intensity, while solubility of O2 in N2 grows too.
Although there are 5 CO peaks, they correspond
only to 3 cases (Fig. 25). Between 12 nearest neigh-
bors CO molecule can have:
1) no O2 molecule (peaks 3 and 4; I3 + I4 = 70);
2) one O2 molecule (peaks 2 and 5; I2 + I5 = 30) or
3) two O2 molecules (peak 1; I1 = 2).
In case of a random distribution of O2 molecules in
�*-N2 the probability for one specific CO molecule to
have no, one or two O2 molecules as nearest neighbors
depends only on the solubility of O2 in �*-N2. Thus we
have a good occasion to check the solubility value
(3.5% at T = 11 K), obtained in Sec. 4.1. We just have
to compare intensities of CO peaks corresponding to
each of 3 cases (above) with mathematical probability
for CO to find as neighbors of CO other molecules
than N2:
1) no O2 � 64%;
2) one O2 � 31%;
3) two O2 � 5%.
In this respect it is a very good agreement!
Matrix isolation technique, applied in N2–O2 mix-
tures, turned out to be not only a good tool for tracing
phase transitions (here (�*–�*)-N2), but also a good
indicator of solubility.
Conclusion
These FTIR studies on N2–O2 complete and confirm
our Raman studies [1]. Spectra of all kinds of excita-
tions, such as bands at O2 (1550 cm–1) and N2
(2330 cm–1) fundamentals and side bands to them,
two-vibron bands (3880 cm–1, 4650 cm–1) and elec-
tronic transitions (8000 cm–1) delivered a rich body of
information. Since some of them have equivalent spec-
tra in pure systems and are well-studied, we achieved
an unambiguous assignment of spectra of our mixtures.
From fingerprints in spectra between 11 and 60 K
we were able to suggest a refined T–x% diagram,
which clears the inconsistencies in previous two vari-
ants: contains no mysterious X-phase, clarifies the sol-
ubility lines and possesses slightly different phase
transition lines. We were able to grow thermodynami-
cally stable samples, whose quality we have proven by
optical spectra. In order to exclude the undercooling
problem phase transition lines were determined during
warming samples. Owing to good crystal quality and
highly sensitive FTIR technique we were able (for the
first time) to detect the «mixed» combined excitation
(N2 vibration + O2 vibration); good resolved struc-
tured bands at frequencies of the fundamentals were
assigned to the induced vibron DOS of N2 or O2; the
electronic transition bands of O2 in N2 phases were de-
tected as well. We have demonstrated that our method
— from fingerprints in optical spectra of binary sys-
tems to T–x% phase diagram – works successfully and
that we could refine the N2–O2 phase diagram found
by structural studies. With the help of spectra of ma-
trix isolated (� ppm) CO molecules we probed the be-
havior of the matrix (e.g., phase transition) and deter-
mined independently the solubility of oxygen in �*-N2.
Theoretical modeling of our spectra, especially of the
vibron DOS in �-, �-, �-O2 phases would be interesting.
1400 Fizika Nizkikh Temperatur, 2006, v. 32, No. 11
M. Minenko and H.-J. Jodl
12 N2
11 N2
1 O2
10 N2
2 O2
peak 3 peak 4
12 1
2
3
4
5
6
7
8
9
10
11
peak 2 peak 5
peak 1
Fig. 25. Model illustrating the assignment of peaks 1–5 in
the absorption spectra of CO molecules MI in �*-N2.
Acknowledgement
We appreciate the help of A. Brodyanski during the
initial stages of experiments. We thank to A. Heydt
for the verification of samples concentration.
This work was supported by Deutsche Forschungs-
gemeinschaft (grant No. Jo 86/11).
1. M. Minenko, J. Kreutz, T. Hupprich, and H.-J. Jodl,
J. Phys. Chem. B108, 6429 (2004).
2. A.S. Baryl’nik, A.I. Prokhvatilov, and L.D. Yantse-
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