From optical spectra to phase diagrams — the binary mixture N2–CO
We investigated the T–c% phase diagram of the binary system N2–CO. From changes in IR spectra of all kinds of mode excitations (phonons, vibrons) we were able to determine the temperature of phase transitions (solid–solid, solid–liquid). The improvements in comparison to structural investigations by...
Saved in:
| Date: | 2007 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2007
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/7773 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | From optical spectra to phase diagrams — the binary mixture N2–CO / M. Vetter, A.Brodyanski, H.-J. Jodl // Физика низких температур. — 2007. — Т. 33, № 2. — С. 1383-1392. — Бібліогр.: 18 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860255166727454720 |
|---|---|
| author | Vetter, M. Brodyanski, A. Jodl, H.-J. |
| author_facet | Vetter, M. Brodyanski, A. Jodl, H.-J. |
| citation_txt | From optical spectra to phase diagrams — the binary mixture N2–CO / M. Vetter, A.Brodyanski, H.-J. Jodl // Физика низких температур. — 2007. — Т. 33, № 2. — С. 1383-1392. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| description | We investigated the T–c% phase diagram of the binary system N2–CO. From changes in IR spectra of all kinds of mode excitations (phonons, vibrons) we were able to determine the temperature of phase transitions (solid–solid, solid–liquid). The improvements in comparison to structural investigations by x-rays or electrons are the following: sample growing and handling with perfect optical and thermodynamic quality; determination of actual concentration (N2)x(CO)y from optical spectra; reduction of thermal hysteresis by careful cooling–heating cycles of the samples.
|
| first_indexed | 2025-12-07T18:48:22Z |
| format | Article |
| fulltext |
Fizika Nizkikh Temperatur, 2007, v. 33, No. 12, p. 1383–1392
From optical spectra to phase diagrams — the binary
mixture N2–CO
M. Vetter1, A. Brodyanski1,2, and H.-J. Jodl1
1
TU Kaiserslautern, Department of Physics, Erwin-Schrödinger-Strasse, Kaiserslautern D-67663, Germany
2
IFOS, Institut für Oberflächen- und Schichtanalytik, TU Kaiserslautern
Erwin-Schrödinger-Strasse, Kaiserslautern D-67663, Germany
E-mail: jodl@physik.uni-kl.de
Received May 30, 2007, revised July 9, 2007
We investigated the T–c% phase diagram of the binary system N2–CO. From changes in IR spectra of all
kinds of mode excitations (phonons, vibrons) we were able to determine the temperature of phase transitions
(solid–solid, solid–liquid). The improvements in comparison to structural investigations by x-rays or elec-
trons are the following: sample growing and handling with perfect optical and thermodynamic quality; de-
termination of actual concentration (N2)x(CO)y from optical spectra; reduction of thermal hysteresis by
careful cooling–heating cycles of the samples.
PACS: 78.30.–j Infrared and Raman spectra;
63.20.Pw Localized modes;
63.20.Ls Phonon interactions with other quasiparticles.
Keywords: phase diagram, IR spectra, optical and thermodynamic quality.
Introduction
All kinds of phase diagrams — such as T–c%, V–c%,
p–T, p–V etc. (T — temperature, c — concentration, V —
volume, p – pressure) are routinely established on the ba-
sis of well tested techniques like x-ray and electron dif-
fraction. The book by Manzhelii [1] contains about 50
phase diagrams of binary solutions of molecular crystals
(rare gas solids, H2, N2, O2, CO etc.) found by these tech-
niques.
The aim of our work here is i) to reproduce the one or
the other phase diagram, ii) to apply a totally different
technique (optical spectroscopy including Raman scatter-
ing), iii) to use polycrystalline samples (structural tech-
niques use condensed thin films), iv) to determine di-
rectly from spectra the real concentrations.
We have chosen the binary solutions N2–CO (as an
ideal system) because of several reasons: it is perfectly
solvable; the T–c% diagram is pretty simple (Fig. 1); thin
film condensation for structural investigations as well as
growing of large polycrystals for optical spectroscopy
can be achieved; all fundamental modes (phonons,
vibrons) are Raman and IR active and their spectra are
well understood. These studies at ambient pressure will
be the basis for high pressure studies on pure CO and
N2–CO system to establish the p–T–c% phase diagram.
Our method — from spectra to phase diagrams — should
be applicable to other, more complex systems as well.
The paper is organized such that we will describe in
the experimental section the production of samples and
the determination of the real concentration. The second
section contains several optical spectra; from changes in
spectral fingerprints we will deduce a revised, improved
phase diagram T–c%. The third section — discussion —
© M. Vetter1, A. Brodyanski,1,2 and H.-J. Jodl1, 2007
Cubichcp + cubic
Solidus
Hexagonal
close packed
Liquidus
T
,
K
% CO in N2
70
60
50
40
30
0 10 20 30 40 50 60 70 80 90 100
Fig. 1. The N2–CO phase diagram (taken from [1]), according
to calorimetric data (�) from [2] and x-ray diffraction data
(�), from [3,4], arrows mark the four mixtures and the pure
systems which we studied.
will present interesting questions such as reproducibility
of phase transition temperatures, quality of (spectral) data
from cooling/heating cycles, thermal hysteresis, accuracy
of technical parameters (�T, �c), sample quality in terms
of thermodynamic equilibrium, evolution of phase transi-
tions with time.
Experimental
Sample preparation of a mixture with a desired con-
centration and cooling the sample to an intended p–T
point for optical studies is a delicate task (see details [5]).
Whereas the same procedure for structural studies is less
complicated. To achieve a powder for x-ray or electron
diffraction the sample is generally quickly condensated as
a thin film. Most of the publications on that matter are not
describing experimental details such as cooling rate, if
data were found at cooling or heating cycles, amount of
time interval to pass a phase transition or to wait till
a phase transition is completed etc.
To be successful in growing big polycrystalline sam-
ples for optical investigations we followed the general
principles of the single crystal growth (see, e.g., Ref. 6)
and adapted these for our demands. The sample cell was
evacuated up to ~ 10–6 mbar at room temperature and
purged several times by the investigated gas. After that,
the empty cell was cooled down to a temperature that was
a bit less than the boiling point of the substance investi-
gated. The sample gas was liquefied at an overpressure of
about 0.5 bar. To ensure a complete filling of the sample
cell as well as a good thermal contact of our solid sample
with walls of the sample cell during crystallization pro-
cess this gas overpressure was maintained up to finish the
crystal growth procedure. In addition this overpressure
prevented impurities from outside the system. Changes in
our samples during the whole growth procedure were con-
tinuously monitored spectroscopically. After condensa-
tion, the liquid sample was cooled down (3 K/h) towards
the melting point to grow slowly (0.1 K/h) the crystal. At
a temperature slightly lower than the crystallization point
(�T = 0.1–0.5 K), the grown crystal was annealed during
10–20 h. The annealed samples were completely transpar-
ent to visible light controlled by eye (microscope) and
their continuum transmission was almost equal to that in
liquid samples. The averaged cooling rate within the tem-
perature region of high-temperature phases was about
0.5–1 K/h depending on the number of spectra measured
in these phases. No significant changes in the continuum
transmission of the samples were observed during this
time consuming (1–3 days) cooling procedure. In the tem-
perature range of a solid—solid phase transition, the sam-
ples were cooled substantially slowly (0.05 K/h). The
phase transformation lasted about 2–3 h. Further on, we
annealed the crystal of a low-temperature phase during
10–12 h either by keeping the sample at a constant tem-
perature or by very slow (0.02 K/h) cooling. As a result,
we obtained big polycrystalline samples of the low-tem-
perature phases of an excellent optical quality.
We measured sample temperature, in the range of
10–80 K, by a calibrated silicon diode, which was directly
attached to the sample cell, absolute accuracy of tempera-
ture registration was about 0.1 K. This cell with sample
chamber (� 10 mm; three different thicknesses like 1,
5, and 20 mm) equipped with sapphire windows, was
mounted on a cold finger of a closed-cycle He cryostat
(see for details [7]). Spectra were recorded in this mid
IR region by a Fourier spectrometer (Bruker IFS120 HR)
both on cooling and warming cycles. A tungsten lamp was
used as the light source, Si on CaF2 as a beam splitter,
and liquid N2 cooled InSb as the detector (accessible
range 1900–11000 cm–1). Our spectral resolution was
0.1–0.5 cm–1, depending on the bandwidth of interest.
There are different ways to determine the real concen-
tration of the actual sample; but we will also briefly de-
scribe which errors or awkwardnesses can be made. The
wanted concentration c% is produced according to partial
pressure of initial gases (N2 and CO). It takes several days
for a uniform gas mixing, depending on the size and form
of the gas vessel. During loading the optical cell with the
gas mixture and producing the solid sample it depends se-
verely on the p–T conditions during cooling, which real
concentration will remain in this sample. Demixing may
occur especially in those cases where the gas-liquid tran-
sition for both gases is different. In literature about struc-
tural studies of binary molecular mixtures we found only
statements about concentrations, which were determined
from partial pressure. In Raman studies the real concen-
tration is easily found from relative intensities in Raman
spectra and known Raman cross sections for vibrations
(see Fig. 2 in [8]). In FTIR studies about N2–O2 mixtures
[9], which are IR inactive, we determined the actual con-
centration by means of chromatography and mass-spec-
trometry; after measurements the sample was evaporated
into a test volume and was then analyzed. Here we deter-
mined the actual concentration via relative intensities
Ipure and Imix of IR spectra of the (0–2) and (0–3) CO vi-
bration of pure CO in comparison to a mixture of N2–CO
(Fig. 2). The intensity of the vibrations in IR spectra is
proportional to the thickness d of the sample, the molar
concentration c, and the square of the change in dipole
moment. Assuming no significant change of the dipole
moment in pure CO and N2–CO mixtures, the concentra-
tion cmix of the mixture is given by
c
d
d
I
I
mix
pure
mix
mix
pure
� .
The uncertainty in concentration by this method is
�c � 5%. The impurity concentration of both initial gases
1384 Fizika Nizkikh Temperatur, 2007, v. 33, No. 12
M. Vetter, A. Brodyanski, and H.-J. Jodl
(N2, CO) were about < 5 ppm due to information by gas
companies.
Results and spectra
In this section we show in detail, how we are able to
deduce from characteristics in spectra the position of
phase transitions and how we can construct the T–c%
phase diagram. We have chosen several spectral ranges
i.e. molecular excitations to demonstrate the power of this
method. In detail we will describe only the next one, all
the rest will be briefly presented.
Overtone region CO
Figures 3,a–f are showing IR spectra of the (0–2) CO
vibrational mode in pure N2 (Fig. 3,a), in four mixtures
(Fig. 3,b–e) and in pure CO (Fig. 3,f); a spectral region
around 4250 cm–1 (�0 = 2139 cm–1). From changes
in bandshape we determine the (�–� -phase transition
temperature T��. Our pure N2 gas contains a few ppm CO
molecules. In �-N2 (crystal structure Pa3) the (0–2) CO
vibrational absorption (around 4253 cm–1) produces
a narrow (< 0.1 cm–1) band, whereas in �-N2 (P63/mmc
— crystal structure with orientational disorder) this band
is very broad (> 5 cm–1). For comparison: the band-
From optical spectra to phase diagrams — the binary mixture N2–CO
Fizika Nizkikh Temperatur, 2007, v. 33, No. 12 1385
4150 4160
0
0.1
0.2
0.3
4150 4160
0
0.1
0.2
0.3 (N )2 0.59 0.41(CO)CO
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
Frequency, cm–1
Frequency, cm–1Frequency, cm–1
Frequency, cm–1
6335 6340 6345
0
0.05
0.10
6335 6340 6345
0
0.05
0.10
(0–2)12 18C O (0–2)13 16C O (0–2)12 18C O (0–2)13 16C O
CO
(0–3)12 16C O
(N )2 0.59 0.41(CO)
(0–3)12 16C O
a
b
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
Fig. 2. Method to determine the real concentration c%: (0–2) CO
mode in pure CO and in a mixture (N2)0.59(CO)0.41 (a); (0–3) CO
mode in pure CO and in a mixture (N2)0.59(CO)0.41 (b).
4252 4254
0.32
0.34
0.36
0.38
N2
20 K
30 K
35.5 K
35.7 K
4250 4300
0.1
0.2
0.3
(N )2 0.91 0.09(CO) (N )2 0.59 0.41(CO)
(N )2 0.19 0.81(CO)
(N )2 0.76 0.24(CO)
30 K
38 K
38.5 K
50 K
(0–2)
4230 4260 4290 4320
0
0.5
1.0
30 K
44 K
45 K
55 K
(0–2)
4250 4300 4350
0
0.2 40 K
47 K
48.5 K
49.5 K
52 K
60 K(0–2)
4250 4300 4350
0
2
4
50 K
57 K
58 K
67 K(0–2)
(0
–
2
)
4250 4300 4350
1.0
1.5
50 K
60.9 K
61.1 K
66 K
CO
(0–2)
Frequency, cm
–1
Frequency, cm
–1
Frequency, cm
–1
Frequency, cm
–1
Frequency, cm
–1
Frequency, cm
–1
a b c d
e f
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
40
50
60
70
T
,
K
0 20 40 60 80 100
% CO in N2
g
Fig. 3. IR spectra of the overtone region of the CO molecule (around 4250 cm
–1
) as a function of concentration and temperature,
during warming up (a–f); T–c% diagram (solid line from Fig. 1) (g).
width of the fundamental mode of ppm CO in �-N2 is
0.01 cm–1 [10]. We find for T�� = 35.6 K. The spectrum
in pure �–CO (Fig. 3,f) contains the very intense (0–2)
CO vibron (around 4250 cm–1), the (0–1)(0–1) two
vibron band (~ 4280 cm–1) of neighboring CO molecules
and a broad phonon sideband to the zero phonon line
(ZPL as (0–2) mode). Details and justification for assign-
ment are given in [11]. The (0–1)(0–1) two vibron band,
marked by a broken rectangle in Fig. 3,b–f, is only IR ac-
tive in �–CO (crystal structure P213 with four molecules
in unit cell), but IR inactive in �–CO (D h6
4 with two mole-
cules in unit cell). We find for T�� = 61 K. Similar consid-
erations in IR spectra for the four mixtures are presented
in Fig. 3,b–e. As a result we are able to construct the
T–c% diagram (Fig. 3,g), which confirms the one from
structural analysis (Fig. 1). The main difference is a more
narrow region of phase coexistence (hcp + cubic) during
cooling/warming cycles, see later.
Second overtone region of CO
Figures 4,a–e show IR spectra of the (0–3) CO vib-
rational model in pure CO and four mixtures (around
6340 cm–1). From distinct changes in bandwidth �(c,T)
(Fig. 4,g) we determine the (�–� -phase transition tempe-
rature T��. The bandwidth is small (~ 1–3 cm–1) in the
ordered �-phase and much broader (> 10 cm–1) in the
orientational disordered �-phase. Fig. 4,f presents the
T–c% diagram.
Fundamental mode of N2:
Figures 5,a–c show the region of the IR nonactive
(0–1) vibration of N2 molecules (~ 2329 cm–1) in three
different mixtures N2–CO. The IR-activity is induced by
the presence of neighbouring CO molecules; either by
breaking the local translational symmetry and/or by the
permanent dipole-moment of CO, which induces a di-
1386 Fizika Nizkikh Temperatur, 2007, v. 33, No. 12
M. Vetter, A. Brodyanski, and H.-J. Jodl
6300 6350
0.2
0.3
30 K
38 K
38.5 K
50 K
6300 6400
0.2
0.4 30 K
43 K
45 K
55 K
6330 6360
0.05
0.10
0.15
40 K
47 K
48.5 K
49.5 K
52 K
6325 6350 6375
0.5
1.0
50 K
57 K
58 K
64 K
6320 6340 6360
0.8
1.0
CO
50 K
60.9 K
61.1 K
66 K
(N )2 0.91 0.09(CO) (N )2 0.59 0.41(CO) (N )2 0.19 0.81(CO)(N )2 0.76 0.24(CO)
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
Frequency, cm
–1
Frequency, cm
–1
Frequency, cm
–1
Frequency, cm
–1
Frequency, cm
–1
a b c d
e
0 20 40 60 80 100
0
20 40 60
% CO in N2 T , K
F
W
H
M
,
cm
–
1
10
(N )2 0.59 0.41(CO) gf
T
,
K
70
60
50
40
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
Fig. 4. IR spectra of the second overtone region of the CO molecule (around 6340 cm
–1
) as a function of concentration and tem-
perature during warming up (the spectrum of concentration (N2)0.76(CO)0.24 (Fig. 4,b) at T = 30 K shows a «strange» basis at the
(0–3) absorption; this is due to the fact that we used only here a thick sample (5 mm); in IR spectra the refractive index must
contain real (scattering) and imaginary (absorption) components) (a–e); T–c% diagram (solid line from Fig. 1) (f); Bandwidth �
as a function of temperature T at concentration (N2)0.59(CO)0.4 (g).
pole-moment in N2 molecules. FTIR spectra of pure opti-
cally perfect N2 crystals contain in that spectral region
only a phonon sideband to the fundamental mode of N2;
the shape of the phonon sideband is different in both
phases �,�-N2(Fig. 1 in [5]). The vibron density of states
(DOS) is modelled by standard lattice dynamics; only
vibron excitations at wave vector k = 0 are known from
Raman scattering (see Fig. 22 in [9]). Some details of the
shape of the vibron DOS can be deduced from the
two-vibron spectra in �-N2; this is a combinational exci-
tation of (0–1) in one molecule and (0–1) in a neighbour-
ing molecule (Fig. 3 in [11]). With that spectral informa-
tion and unambiguous assignment we are able now to
discuss spectra of Fig. 5. Spectra of the N2-rich mixture
((N2)0.91(CO0.09)) of �*-N2 (Fig. 5,a) are pretty similar to
the vibron DOS of the (0–1)(0–1) excitation [12]: broad
(~ 1 cm–1), asymmetric triangular band. If we increase
concentration of CO this broad asymmetric triangular
band is only smeared out. At the (�–�)-phase transition
this impurity induced vibron DOS of N2 disappears in that
form. In �-N2 the N2-vibration is slightly IR active by the
presence of CO molecules and the spectral feature is a
broad (~ 30 cm–1) very weak band (Fig. 5,a). In a static
model we explain the broad band by the absorption of vi-
brating N2 molecules, surrounded by and interacting with
CO molecules in a partially disordered crystal structure of
�*-N2 i.e. inhomogeniety. In a more dynamic model this
broad (~ 30 cm–1) band in the stretching mode region of
�-phase is dominated by a quasi-elastic Lorentzian-like
component, centered around �0 as zero phonon line (ZPL
— here �0 in N2 at 2330 cm–1) which we attribute to over-
damped orientational modes, i.e. rotational diffusion. The
residual feature (a little narrow (< 0.5 cm–1) peak at �0
(ZPL) is an IR absorption of a small fraction of N2 mole-
cules, only vibrating without vibration-rotation coupling.
(Similar spectra in Ar:O2 mixtures, Fig. 2 of Ref. 13.)
Fig. 5,d shows the found T–c% diagram.
CO isotopes
Figures 6,a–d present the region of the (0–2) vib-
ration of several CO isotopes in pure CO and in mix-
tures (~ 4150 cm–1). The respective fundamental modes
(2100–2150 cm–1) generate a very strong absorption in
this IR spectra, therefore we studied the overtone region.
Since the fundamental frequencies for the isotopes are
known and since the natural abundances as well, the spec-
tral assignment is obvious (Table 1).
Table 1. Spectral characteristics of CO isotopes.
C
O
co
m
p
o
u
n
d
s
N
at
u
ra
l
ab
u
n
d
an
ce
[1
4
]
R
el
at
iv
e
in
te
g
ra
te
d
in
te
n
si
ty
F
re
q
u
en
cy
o
f
C
O
in
N
e
[1
5
],
cm
–
1
E
st
im
at
ed
2
�
0
–
2
�
ex
e
(�
ex
e
~
1
3
cm
–
1
),
cm
–
1
O
u
r
d
at
a
at
3
0
K
,
cm
–
1
12
C
16
O
0.9866
99%
— ~ 2141 4256 4252
13
C
16
O
0.0110
1%
5
~ 100%
~ 2094 4162 4159
12
C
18
O
0.0020
0.2%
1
20%
~ 2090 4154 4152
12
C
17
O
0.0004
0.04%
0.3
6%
~ 2114 4202 4199
The frequency difference (estimated value — our va-
lue, about 2–4 cm–1) is obvious, because the matrix shift
in Ne is about 2.4 cm–1 and the solid shift is 3.5 cm–1 [15].
From optical spectra to phase diagrams — the binary mixture N2–CO
Fizika Nizkikh Temperatur, 2007, v. 33, No. 12 1387
2320 2330 2340
0
0.4
0.8
30 K
38 K
38.5 K
40 K
2325 2330
0.8
1.0
1.0
40 K
47 K
48.5 K
49.5 K
2326 2328 2330
0.6
0.8
40 K
50 K
57 K
58 K
60 K
70
60
50
40
0 20 40 60 80 100
(N )2 0.91 0.09(CO) (N )2 0.19 0.81(CO)
% CO in N2Frequency, cm
–1
Frequency, cm
–1
Frequency, cm
–1
T
,
K
a b c
d
(N )2 0.59 0.41(CO)
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
Fig. 5. IR spectra of the N2 fundamental mode around 2330 cm
–1
as a function of concentration and temperature; during cooling
down (a); during warming up (b,c); T–c% diagram (solid line from Fig. 1) (d).
The isotopes in solid CO or in mixtures represent
the matrix-isolated case; therefore we expect a narrow
(~ 1 cm–1) band in �-phase and a broad (> 10 cm–1) band
in �-phase due to static disorder and/or dynamic interac-
tions. This change in bandwidth at the
�–�)-phase transi-
tion is clearly visible in our spectra. Figure 6,e shows the
found T–c% diagram. Change in bandwidth �(c,T) and
obvious constant integrated intensity I(c,T) are displayed
in Fig. 6,f.
In general it is difficult to measure integrated intensity
with sufficient accuracy (�I ~ %) and to use this spectral
quality for physical arguments. But in our case either op-
tical quality of samples or FTIR-technique were elabo-
rated enough to perform this kind of studies (see Fig. 6,f
or Fig. 11).
ppm CO2 in samples
Figure 7 shows the region of (0,0,1) fundamental
vibration of CO2 molecules (~ 2348 cm–1) in pure N2
(Fig. 7,a), three mixtures (Fig. 7,b–d) and in pure CO
(Fig. 7,e). Similar spectra were also taken of the (0,2,1)
mode (~ 3600 cm–1) and (1,0,1) mode (~ 3710 cm–1).
From a clear jump in vibrational frequencies at these
phase transition we are able to determine the phase transi-
tion temperature T��. The amount of CO2 molecules in
the initial gas (N2, CO, or mixtures) is about ppm, due to
these gas delivering companies. In a series of papers
[7,10] we described in detail this probing technique (M/A
ratio 10–6, M — matrix, A — impurity; typical M/A ~ 10–3
for standard matrix-isolation technique). In there we ex-
plain how we determined the residual amount of CO2
molecules via optical spectroscopy in combination with
other techniques.
The situation of ppm CO2 in pure N2 is the easiest
case: CO2 is replaced on one substitutional site in �-N2
and on two substitutional sites in �-N2, surrounded
by N2-molecules; this fact gives rise to one or two
IR-bands (see for details [10]). The transition tempera-
ture is T�,� ~ 35.5 K. In pure CO we register in spectra
one band due to CO2 molecules in �-CO and one band in
�-CO with a clear frequency jump of this mode
(1–2 cm–1) at T = 61.0 K (Fig. 7,g,h). In cooling the �-CO
phase this spectrum gets complex and more pronounced.
In the three mixtures we find one band of CO2 molecules
1388 Fizika Nizkikh Temperatur, 2007, v. 33, No. 12
M. Vetter, A. Brodyanski, and H.-J. Jodl
10 20 30 40 50 60
2
4
6
8
10
12
0
0.1
0.2
0.3
0.4
0.5
4150 4175 4200
0.2
0.4
0.6
30 K
38 K
38.5 K
50 K
(0
–
2
)
C
O
1
2
1
8
(0
–
2
)
C
O
1
2
1
7
(0
–
2
)
C
O
1
3
1
6
(0–2) C O
13 16
(N )2 0.91 0.09(CO)
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
Frequency, cm
–1
a
4150 4175 4200
0
0.1
0.2
40 K
47 K
48.5 K
49.5 K
60 K
(0
–
2
)
C
O
1
2
1
8
(0
–
2
)
C
O
1
2
1
7
(0
–
2
)
C
O
1
3
1
6
(N )2 0.59 0.41(CO)
Frequency, cm
–1
b
4150 4175 4200
2.5
3.0
50 K
60.9 K
61.1 K
66 K
(0
–
2
)
C
O
1
2
1
8
(0
–
2
)
C
O
1
2
1
7
(0
–
2
)
C
O
1
3
1
6
Frequency, cm
–1
d
f
4150 4175 4200
50 K
57 K
58 K
64 K
(0
–
2
)
C
O
1
2
1
8
(0
–
2
)
C
O
1
2
1
7
(0
–
2
)
C
O
1
3
1
6
(N )2 0.19 0.81(CO)
Frequency, cm
–1
c
2.0
% CO in N2
e
T
,
K
70
60
50
40
0 20 40 60 80 100
F
W
H
M
,
cm
–
1
Integrated intensity
In
t.
in
te
n
si
ty
,
cm
–
1
FWHM
T , K
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
Fig. 6. IR spectra of the overtone region of CO isotopes in pure CO and in mixtures as function of temperature during warming
up (a–d); T–c% diagram (solid line from Fig. 1) (e); evolution of integrated intensity and bandwidth with temperature near phase
transition for (N2)0.59(CO)0.41 (f).
in �-CO, one band in �-CO at higher temperatures, with a
clear frequency jump of this band at T��. In cooling the
�-phase of these mixtures we observe a complex and pro-
nounced spectrum (Fig. 7,b–d); this spectrum looks dis-
tinctly different for the N2 rich case (an asymmetric broad
band towards lower frequencies with up to 8 maxima) and
for the CO rich case (a broad symmetric band and on top
several narrow bands). We interpret these structures in the
following way: CO2 molecule, which is spectroscopi-
cally investigated, is surrounded by 12 nearest neigh-
bours, which can be either N2 or CO molecules due to
concentration. In addition the CO molecule has two posi-
tions (dipol moment CO, OC; head-tail disorder) [16].
Fig. 7,f shows the found T–c% diagram.
Solid—liquid phase transition
For all three mixtures we have studied the solid-liquid
phase transition. We analyzed spectra of three modes,
such as a combinational mode around 4460 cm–1 ((0–1)
vibration of N2 molecule plus a (0–1) vibration of a
neighbouring CO molecule), an overtone mode (0–3) of
From optical spectra to phase diagrams — the binary mixture N2–CO
Fizika Nizkikh Temperatur, 2007, v. 33, No. 12 1389
2347 2348 2349
0.1
0.2
30.3 K
35.3 K
35.9 K
40.2 K
N2
*
2345 2350
0
0.5
(N ) (CO)2 0.91 0.09
30 K
38 K
38.5 K
50 K
2340 2345 2350
0.3
0.6
40 K
47 K
48.5 K
49.5 K
60 K
2343 2346 2349
5
10
40 K
57 K
58 K
66.6 K
2345 2350
0.45
0.60
50 K
60.9 K
61.1 K
66 K
CO
0 20 40 60 80 100
40
50
60
70
% CO in N2
20 40 60 80
2344
2346
T, K
20 30 40
2347
2348
2349
Frequency, cm–1
Frequency, cm–1Frequency, cm–1
Frequency, cm–1
(N ) (CO)2 0.59 0.41 (N ) (CO)2 0.19 0.81
T
,
K
F
re
q
u
en
cy
,
cm
–
1
CO in CO2 CO in N2 2
F
re
q
u
en
cy
,
cm
–
1
T, KFrequency, cm–1
a b c d
e
f
e
g h
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
Fig. 7. IR spectra of the fundamental (�3 ~ 2348 cm
–1
) of ppm CO2 in pure N2, pure CO and in mixtures as a function of tempera-
tures (a–e); during cooling down (a), during warming up (the peak marked by a star (Fig. 7,a) is due to CO2 molecules condensed
externally on the sample cell or as rest gas in the purged sample chamber of the spectrometer) (b–e); T–c% diagram (solid line from
Fig. 1) (f); frequency of this mode as a function of temperature near phase transition in pure CO (g) and in pure N2 (h).
4450 4500
0
0.2
Frequency, cm–1
63 K
64.5 K
65.5 K
70 K
liq
A
d
so
rb
an
ce
,
ar
b
.
u
n
it
s
64 66 68 70
4466.2
4466.4
4466.6
T, K
64 66 68 70
12
14
16
T, K
F
re
cu
en
cy
,
cm
–
1
F
W
H
M
,
cm
–
1
a b c
Fig. 8. IR spectra of the combinational mode ((0–1)N2 + (0–1)CO) of the mixture (N2)0.59(CO)0.41 as a function of temperature
during cooling down (a); frequency (b) and band width (c) of this mode as a function of temperature near phase transition.
CO (around 6340 cm–1) and fundamental (0–1) impurity
induced N2 vibration (around 2330 cm–1).
This phase transition is not easy to be monitored spec-
troscopically. From structural point of view the �-phase
(plastic phase i.e. orientational disorder with structural
order) is only slightly different from the liquid phase. We
studied carefully the (�–�)-N2 phase transition [5,11]: the
volume jump at T�� is small; dominant short-range
orientational order between neighbouring molecules in �
and liquid phase play a role. As an example we show in
Fig. 8,a some spectra of the combinational mode
((0–1)N2 + (0–1)CO) of the mixture (N2)0.59 (CO)0.41 at
the (�–�)-phase transition. Looking at spectra only, this
phase transition is hardly recognizable; but the detailed
analysis, of these spectra reveals this phase transition.
Therefore Figs. 8,b,c displays the change in band fre-
quency �(T,c%) and in band width �(T,c%). As a result
we find T�� = 65.5 K; similar results for all 3 mixtures as
well as pure cases were found and incorporated, in the
T–c% diagram of Fig. 9.
As a resumee comparing now all results T–c% from
spectra of different mode excitations — such as vibrons,
overtone excitations, vibrations, impurity excitations
(Fig. 3,g, Fig. 4,e, Fig. 5,d, Fig. 6,e, Fig. 7,f) — are deli-
vering the same temperature values for the phase transi-
tion; i.e. the whole system N2–CO reacts in the same way,
which is a fundamental thermodynamic requirement at a
phase transition.
Discussion
In this section we describe a few aspects only such as
how reliable our data are, what is the quality of our sam-
ples — thermodynamically stable etc.
Phase-diagram
By Fig. 9 we confirm the T–c% phase diagram of
N2–CO found by other methods (structural and calorimet-
ric analysis) [2–4] and by indirect spectroscopic investi-
gations. The phase coexistence region (hcp and cubic) of
low temperature phases is more narrow in our case; as
well the solidus—liquid range, i.e. that our method —
from changes in optical spectra to phase diagrams — is
working and can be applied to the other phase diagrams
like pressure/concentration for N2–O2 [9] or N2–CH4 (in
progress); we already finished similar studies at high
pressure (p < 10 GPa) and low temperatures (T < 300 K)
of pure CO and N2–CO mixtures [18].
Thermal hysteresis
The reproducibility of our data is well documented in
Fig. 10, which is showing spectra of the �3-CO2 mode and
�0-N2 in mixture during cooling/heating cycle; even little
details of the IR bands are conserved. In general due to
experiences with the binary mixture N2–O2 [9] we relay
more on the second cycle — the warming cycle, because
in that case we have thermodynamically stable samples
which we proved by spectroscopy (e.g. homogeneous
bandwidth); in the first cooling down of the sample over-
cooling effects may occur which shift phase transitions.
Next we want to answer — via spectroscopy — how
broad is the range of phase coexistence hcp/cubic; due to
literature about 5–10 K (see Fig. 9). During cooling we
1390 Fizika Nizkikh Temperatur, 2007, v. 33, No. 12
M. Vetter, A. Brodyanski, and H.-J. Jodl
0 20 40 60 80 100
40
50
60
70
% CO in N2
T
,
K
Liq
Fig. 9. Refined phase diagram T–c% of the binary system
N2–CO: our data (�), all the rest from literature, see Fig. 1 (�).
2325 2350
0.5
1.0
1.5
55 K
45 K
30 K
20 K
40 K
48 K
56 K
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
Frequency, cm
–1
T
im
e
Fig. 10. Reproducibility of spectra: IR spectra of the impurity
induced N2-fundamental mode (around 2328 cm
–1
) and of
the �3 mode (around 2345 cm
–1
) of ppm CO2 in mixture
(N2)0.59(CO)0.41, during cooling and subsequent warming.
determine T��, during warming T��, do they agree? What
is the uncertainty of �T for those values. Figures 7,a–e are
showing the �3-mode of ppm CO2 in pure N2 (Fig. 7,a), in
different mixtures (Fig. 7,b–d) and in pure CO (Fig. 7,e).
If we plot for all 5 cases the integrated band intensity of
the �3-mode of CO2 as a function of temperature this
value must be constant over the whole temperature range;
but the same band intensity for this �3-mode of CO2 in
one phase is decreasing near phase transition and the band
intensity in the other phase must increase accordingly.
The range of temperature, where these changes in band
intensity are occurring, we define as the range of phase
coexistence �T. Two examples only: in pure N2 we find
�T < 0.5 K (Fig. 11,a) and in the mixture (N2)0.59(CO)0.41
we find �T = 2 K (Fig. 11,b). This range �T of phase -
coexistence in mixtures should be compared with the ther-
mal hysteresis in pure systems: T��(warming) – T��(cool-
ing) is about
0.2 K for pure N2 and
0.4 K for pure O2.
This statement is based on IR spectra of ppm CO in these
pure systems [7]. Since we used a calibrated Si-diode to
measure sample temperature, the uncertainties in temper-
ature is �T
0.1 K in that range.
Vibron DOS
The two vibron density of states (DOS) of pure �-N2 is
well measured and modelled by Legay [17]. In addition
we studied the temperature evolution of this IR-band
around 4650 cm–1 (�0 ~ 2330 cm–1) (Fig. 3 in [11]).
This combined excitation (0–1)(0–1) between neigh-
bouring molecules requires a perfect crystal from theoret-
ical [17] and experimental [11] point of view. Since N2
molecules and CO molecules are very similar, especially
all their mechanical characteristics (such as mass, mo-
ment of inertia, geometrical dimensions) we would ex-
pect that the vibron DOS of pure N2 doped with CO is
hardly influenced. Fig. 12 is showing the combined exci-
tation (0–1)(0–1) of N2 as a function of concentration at
lowest temperature.
The spectral feature (width of basis is ~ 1 cm–1) of
pure N2 is like in literature [11]. With increasing amount
of CO in this mixture this spectral feature is smeared out
(due to CO-impurities), is getting weaker (due to number
of N2-molecules) and is slightly more narrow.
For our kind of studies here the message by Fig. 12 is
that all our samples have pretty good crystal quality and
From optical spectra to phase diagrams — the binary mixture N2–CO
Fizika Nizkikh Temperatur, 2007, v. 33, No. 12 1391
30 400
5
10
T
N2
50 60
0
1
2
2
1
a
T , K
T , K
In
t.
in
te
n
si
ty
,c
m
–
1
In
t.
in
te
n
si
ty
,c
m
–
1
T b(N )2 0.59 0.41(CO)
Fig. 11. Phase coexistence region: Integrated band intensity
of �3-mode of CO2 in pure N2 (a) and in the mixture
(N2)0.59(CO)0.41 (b) as a function of temperature are plotted;
respective spectra are Figs. 7,a–c. In �-phase we observe one
band, in �-phase two bands. If we sum the band intensity of
band a and b in �-phase, we get the total band intensity (*).
The range of �T�� is marked by vertical lines (a). One band
in �-phase (�) transforms to one band in �-phase (�); the
range of �T�� is marked by vertical lines (b).
4656 4658
0
1
x2
x20
x20
T = 10 K
A
b
so
rb
an
ce
,
ar
b
.
u
n
it
s
(N )2 0.59 0.41(CO)
(N )2 0.19 0.81(CO)
Frequency, cm
–1
(N )2 0.91 0.09(CO)
N2
Fig. 12. Vibron DOS: IR spectra of the combined excitation
(0–1)(0–1) of neighbouring N2-molecules at T = 10 K in pure
N2 and in mixtures. Increasing the amount of CO in these
mixtures, this spectrum of the combined excitation of N2 is
decreasing; therefore we had to multiply these bands with a
factor (see right side).
that changes in this vibron DOS of pure �-N2 by the ad-
mixing of CO molecules can be modelled in principle by a
theoretical vibron DOS of a mixture and are not simple
due to crystal imperfections.
Time dependence of phase transition
We followed the liquid-solid phase transition by visual
observation and the (�–�)-phase transition by the changes
in the continuum transmission (i.e. changes in the
interferogram). As a consequence all phase transitions
here in a case of N2–CO binary mixture used to happen in
less than a hour.
Conclusion
We have confirmed the T–c% phase diagram of the
mixture N2–CO, known by standard structural tech-
niques. From changes in optical spectra of all kinds of
mode excitations of these molecules we could clearly de-
termine the temperatures of phase transitions. In addition
we succeeded in refining this phase diagram; i.e. a more
narrow phase coexistence region hcp/cubic due to better
— thermodynamic more stable — crystal quality. As a
consequence this method — from optical spectra to phase
diagrams — is now applicable to more complicated sys-
tems.
This work was supported by the Deutsche Forschungs-
gemeinschaft (grant No. Jo86-11/2).
1. V.G. Manzhelii, A.I. Prokhvatilov, I.Ya. Minchina, and
L.D. Yantsevich, Handbook of Binary Solutions of
Cryocrystals, Begell House, New York (1996).
2. M. Ruheman, H. Lichter, and P. Komarov, Phys. Z. Sov.
8, 326 (1935).
3. M.J. Angwin and J. Wassermann, J. Chem. Phys. 44, 417
(1966).
4. L. Meyer, Adv. Chem. Phys. 16, 343 (1969).
5. A.P. Brodyanski, S.A. Medvedev, M. Vetter, J. Kreutz,
and H.-J. Jodl, Phys. Rev. B66, 104301 (2002).
6. A.A. Chernov, Modern Crystallography III: Crystal
Growth, Springer Series in Solid-State Sciences, Springer
Verlag, Berlin (1984), v. 336.
7. M. Minenko, M. Vetter, A.P. Brodyanski, and H.-J. Jodl,
Fiz. Nizk. Temp. 26, 947 (2000) [Low Temp. Phys. 26, 699
(2000)].
8. M. Minenko, J. Kreutz, Th. Hupprich, and H.-J. Jodl, J.
Phys. Chem. B108, 6429 (2004).
9. M. Minenko and H.-J. Jodl, Fiz. Nizk. Temp. 32, 1382
(2006) [Low Temp. Phys. 32, 1050 (2006)].
10. M. Vetter, M. Jordan, A.P. Brodyanski, and H.-J. Jodl, J.
Phys. Chem. A104, 3698 (2000).
11. M. Vetter, A.P. Brodyanski, S.A. Medvedev, and H.-J.
Jodl, Phys. Rev. B75, 014305 (2007).
12. I.I. Abram, R.M. Hochstrasser, J.E. Kohl, M.G. Semack,
and D. White, J. Chem. Phys. 71, 153 (1979).
13. J. Xie, M. Enderle, K. Knorr, and H.-J. Jodl, Phys. Rev.
B55, 8194 (1997).
14. J. Emsley, The Elements, Claredon Press, Oxford (1992).
15. H. Dubost, Chem. Phys. 12, 139 (1976).
16. M. Vetter et al., Head-Tail Disorder in �-CO by Ma-
trix-Isolation-Probing Spectroscopy (In preparation).
17. F. Legay and N. Legay-Sammaire, Chem. Phys. 206, 367
(1996).
18. M. Vetter et al., Phonon DOS of Phases of Solid CO by
Optical Studies (in print).
1392 Fizika Nizkikh Temperatur, 2007, v. 33, No. 12
M. Vetter, A. Brodyanski, and H.-J. Jodl
|
| id | nasplib_isofts_kiev_ua-123456789-7773 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T18:48:22Z |
| publishDate | 2007 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Vetter, M. Brodyanski, A. Jodl, H.-J. 2010-04-12T13:14:28Z 2010-04-12T13:14:28Z 2007 From optical spectra to phase diagrams — the binary mixture N2–CO / M. Vetter, A.Brodyanski, H.-J. Jodl // Физика низких температур. — 2007. — Т. 33, № 2. — С. 1383-1392. — Бібліогр.: 18 назв. — англ. 0132-6414 https://nasplib.isofts.kiev.ua/handle/123456789/7773 We investigated the T–c% phase diagram of the binary system N2–CO. From changes in IR spectra of all kinds of mode excitations (phonons, vibrons) we were able to determine the temperature of phase transitions (solid–solid, solid–liquid). The improvements in comparison to structural investigations by x-rays or electrons are the following: sample growing and handling with perfect optical and thermodynamic quality; determination of actual concentration (N2)x(CO)y from optical spectra; reduction of thermal hysteresis by careful cooling–heating cycles of the samples. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Динамика кристаллической решетки From optical spectra to phase diagrams — the binary mixture N2–CO Article published earlier |
| spellingShingle | From optical spectra to phase diagrams — the binary mixture N2–CO Vetter, M. Brodyanski, A. Jodl, H.-J. Динамика кристаллической решетки |
| title | From optical spectra to phase diagrams — the binary mixture N2–CO |
| title_full | From optical spectra to phase diagrams — the binary mixture N2–CO |
| title_fullStr | From optical spectra to phase diagrams — the binary mixture N2–CO |
| title_full_unstemmed | From optical spectra to phase diagrams — the binary mixture N2–CO |
| title_short | From optical spectra to phase diagrams — the binary mixture N2–CO |
| title_sort | from optical spectra to phase diagrams — the binary mixture n2–co |
| topic | Динамика кристаллической решетки |
| topic_facet | Динамика кристаллической решетки |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/7773 |
| work_keys_str_mv | AT vetterm fromopticalspectratophasediagramsthebinarymixturen2co AT brodyanskia fromopticalspectratophasediagramsthebinarymixturen2co AT jodlhj fromopticalspectratophasediagramsthebinarymixturen2co |