MATERIAL DESIGN – PHY 570
SOPHIE TRASTOUR – PAUL BOYER CHAMMARD
VANADIUM DIOXIDE VO2 – REPORT
Introduction
As transition metal oxides, oxides based on vanadium are receiving a tremendous
attention because of their diverse chemical structures, which result in novel properties
that can be used in a great deal of applications. Among all the oxides, we choose to work
on VO2 with oxidation state (+IV).
As far as VO2 is concerned, several kinds of crystalline phases have been reported
including VO2 rutile (R), VO2 monoclinic (M1), VO2 monoclinic (M2), VO2 tetragonal (A),
monoclinic VO2 (B), VO2 (D), BCC VO2, paramontroseite VO2, orthorhombic VO2-H20 etc.
Among all these phases, VO2 M1 has been the more attractive one to study stem
from its unique near room temperature insulator-to-metal phase transition and
technological applicability.
Electronic Structure:
VO2 M1 is particularly interesting to study because of its metal-insulator transition
that occurred at 340K and ambient pressurei. At these conditions, stoichiometric VO2
undergoes a structural first-order transition from a high-temperature rutile phase to a
low-temperature monoclinic phase. This transition is accompanied by an abrupt
change in the resistivity over several orders of magnitude.
To better understand this transition, several models have been proposed ranging
from Peierls to Mott-Hubbard-type scenarios. All these models point out the role of
lattice instabilitiesii, electron-phonon interaction and electron-electron correlations. Yet,
all these approaches are not enough to explain all the phenomena occurring in
vanadium dioxide. Today, a comprehensive and complete understanding of the rutilerelated transition-metal dioxides is not available.
The distortions of the rutile structure of VO2 is characterized by two distinct modes:
• A pairing of the metal atoms along characteristic chains parallel to the tetragonal
c axis
• A lateral zigzag-like displacement (VO2 M1 showing a monoclinic lattice: the unit
cell is twice as large as that of the rutile structure)
It is possible to study the transition-metal dioxides thanks to density functional theory
based electronic calculationsiii.
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The lattice degrees of freedom play an important role in the stabilization of the
different phases of VO2 as there are many differences between the metallic and the
insulating states. At the transition, there is change into the symmetry, a strong electronphonon coupling and a lattice softening. The lattice constants are also changed at the
phase transition: the rutile c axis increases by 1%, the a axis decreases by 0.6%. There
are also volume changes by -0.044% and the thermal expansion coefficient drops by a
factor of three.
It can be revealed that there is a strong elastic anisotropy in the metallic phase,
which disappears in the insulating state. Terauchi and Cohen also evidenced a lattice
instability at the tetragonal R-point with a wave vector parallel to gamma-R and a
polarization vector parallel to the c axis. This confirmed the symmetry analysis, which
supposed a rutile-to-monoclinic transition to be the result of a phonon instability at the
R-pointiv. By using a shell model to calculate the phonon dispersion, Gervais and Kress
(reference) found a phonon softening at the tetragonal R-point. By analyzing the
eigenvectors of the R-point soft mode, we can prove that it results in a displacement
pattern of the metal atoms equivalent to that of the monoclinic phase.
Rutile Structure of VO2:
The rutile structure of metallic VO2 is based on a simple tetragonal lattice with
space group P42/mnm. The metal atoms are located at the Wyckoff positions (2a) : (0, 0,
0), (½, ½, ½) and the oxygen atoms are located at the positions (4f): +- (u, u, 0), +-( ½ +
u, ½ - u, ½ ).
The lattice constant used in the calculations are:
4.5546 ,
2.8514 ,
0.3001.
Figure 1: The rutile structure
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For discussing the electronic structure of rutile structure we will use local
coordinate systems centered at each metal site (as the one we can see on figure 2). In
contrast to the usual adjustment of the x and y axes parallel to the metal-ligand bonds
we have rotated these axes by 45° about the local z axes such that they are parallel and
perpendicular, respectively, to the rutile c axis.
In the figure below are shown the angular parts of the metal d orbitals relative to
the local reference frame of the central metal atom. According to the choice of local
coordinate system, the eg states resulting from the cubic part of the crystal field splitting
of the metal d orbitals comprise the d3z2- r2 and dxy orbitals. The t2g states are built from
the dx2- y2, dxz and dyz orbitals. Because of the geometry of the orbitals, there are several
overlapping between metal sites within the vertical chains formed by the octahedra, but
also between metals sites translated by (1, 0, 0) vectors, between atoms separated by
lattice vectors of the simple tetragonal lattice and between metal atoms which are
located at the corner and in the center of the cell.
Figure 2: d orbitals
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The M1 structure of VO2:
The monoclinic M1 structure is characterized by a simple monoclinic lattice with
space group P21/c. Its lattice constants are
4.743 ,
4.517 ,
5.375 and
4.743 . The unit cell comprises four formula units. The metal atoms, as well as the
two different types of oxygen atoms occupy the general Wyckoff position (4e): +-(x, y, z),
+-(x, ½ - y, ½ + z).
The close relationship of the monoclinic M1 structure to the high-temperature
rutile structure is visible from a comparison of the two figures.
Figure 3: The monoclinic structure M1
By observing the lattice constants of both structures, we can see that the
monoclinic cell look like a rutile cell doubled along the rutile c axis. Nevertheless, the
characteristic metal-metal pairing along the rutile c axis in the monoclinic structure
gives rise to two metal-metal distances that are different from the one observed in the
rutile structure.
Figure 4: Comparison of the two structures
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Band structure
The calculation of the electronic structure of both components can be performed
thanks to density functional theory.
Figure 5: Band structure of Rutile VO2
In Figure 6, we identify only 2 groups of bands but there are two others groups
that can be identified in the higher energies. We observe 12 bands in the energy range
from -7 eV to -2 eV. They correspond to O 2p states but have a non-negligible
contribution to the V 3d states. The next two groups, which range from -0.6 eV to 2 eV
(t2g states) and from 2 eV to 5.5 eV (eg states) contain six and four bands respectively.
They are mainly due to V 3d states. Yet, because of p-d hybridization, there are
additional O 2p contributions in this energy range. Finally the last band can be
attributed to V 4s states, starting at 7.0 eV.
The Fermi Energy is at 0 eV in the figure.
The weak hybridization of the different types of bands will have a strong impact
on our further understanding because it will allow us to establish a relation between
particular atomic displacements and the response of the electronic states.
Let’s study the electronic bands structure of monoclinic M1 VO2: we identify the
same groups of bands as for rutile structure. They contain 24 oxygen 2p dominated
bands well below the Fermi level at 0eV, and two groups of 12 and 8 bands, respectively
at and above the Fermi level. These latter two groups are mainly due to V 3d states. P-d
hybridization leads to V 3d and O 2p contributions of the order of 10% in the energy
regions where the respective other partner dominates. The separation in energy of the O
2p and V 3d dominated bands is slightly smaller than in the rutile phase. When we study
in details the density of states at the Fermi energy, we notice that the latter is lowered as
compared to the rutile value, dominated by V 3d t2g states. The changes observed in the
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density of states and in the contribution of different orbitals (dx2-y2 , dxz, dyz) can be
attributed to the pairing of the vanadium atoms along the rutile c axis and the resulting
bonding-antibonding splitting.
If we study the two bands in the rutile lattice above the Fermi energy, we see that
they give rise to the lowest states within the t2g-derived group of bands at the gammapoint, bend upwards along the line gamma-A and cross the higher lying bands. In
monoclinic structure, these two bands are separated from the other states and form a
split-off doublet, which, however, is still touching the higher lying bands at the A-point.
As a result, the Fermi energy has a finite density of states, which is the reason why we
end up with an insulating ground state with a band gap.
Figure 6: Band structure of Monoclinic M1 VO2
The upshift of the two bands as well as the bonding-antibonding splitting of the
dx2-y2 band can be interpreted as the result of the Peierls-type instability of the structure.
Peierls transitionv:
It is a metal insulator transition underwent by a quasi-one dimensional metal when
it reaches the Peirls temperature Tp. By quasi-one dimensional one must understand
that there is a three dimensional metal where the atoms form chains in one direction
that are responsible for the electric conductivity.
• Above Tp, the atoms are equally spaced with the lattice constant a
• Below Tp, there is a distortion and as a result, the periodicity of the lattice
doubles to 2a because of electron-phonon interactions in the conduction band
This process is called dimerization and happens spontaneously when the metal is cooled
down.
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Figure 7 Dimerization
In the case of a metal, the bands are only half filled. When the periodicity of the
lattice doubles, the brillouin zone boundary also doubles, moving in to the point where
the last filled state is . The filled states go to a lower energy and the empty ones to a
higher. That process causes a gap in the dispersion relation at the Fermi energy using
the perturbation theory. By undergoing that transition, the system gains electronic
energy when atoms pair, but it has also a cost of elastic energy to perform the transition.
Thus, it only takes place when there is more energy gained that it costs.
When we go from rutile to monoclinic we observe a strong splitting of the dx2-y2
band into two narrow subbands at the lower and upper edge of the t2g group of bands.
This is a consequence of the metal-metal dimerization.
In addition to that, the V 3dxz and dyz band are upshift because of the zigzag-like
antiferroelectric displacement of the vanadium atoms.
So, in the low-temperature M1 structure of VO2 metal-metal dimerization slit the
dx2-y2 band into bonding and antibonding branches, whereas other states shift to higher
energy due to reduced V-O distances. As a result, insulating state is interpreted as due to
a Peierls-like instability of the dx2-y2 band in an embedding reservoir of electrons. This
Peierls instability allows us to explain both the destabilization of the rutile structure in
terms of increased metal-metal bonding and the metal-insulator transition.
Even if the strong dimerization, as well as the non-magnetism suggest that VO2
might be a typical case of Peierls insulator, several experimental work showed that
minute amounts of Cr-substitutions, as well as, uniaxial stress applied to pure VO2 lead
to a new phase M2 in which only half of the V-atoms dimerize, while the others are
contained in chains of equally spaced atoms that behave like spin ½ Heisenberg chains.
The fact that this phase is also an insulating one suggests that VO2 can be described also
as a Mott-Hubbard insulator.
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Mott-Hubbard transition:
In this theory, the metal-insulator transition is caused by the strong electronelectron correlation effects. At low temperatures the majority of electrons are in their
proper places in the ions of the crystal because of the strong electrostatic interaction
between them that prevents them from moving. In the Mott insulators, delocalized
electrons, which leads to band formation, is not energetically favored compared to a
state where electrons are localized in their own atomic sites. Thus a localized state is
favored over an itinerant state: the system undergoes a metal-insulator transition. The
competition between the two states determines a critical value above which the crystal
is insulator and metallic below.
Hubbard introduced a model which gives a meaningful description to the two
competing forces presented by Mott. The electron hopping process (which is the kinetic
energy term) likes to delocalize the electrons into Bloch states and thus giving a metallic
behavior to the crystal. By contrast, the correlated electron-electron interaction tends to
delocalize the electrons into their own atomic states thus making the crystal an
insulator.
Optical properties
The optical properties depend on the temperature. At room temperature, the
band gap of the monoclinic structure is approximately 0.6 eV between the a1g filled
states and the empty egπ states. Thus, a bulk vanadium dioxide crystal has a high
transmittance in infrared and visible wavelengths.
Figure 8: Energy level diagrams of
Monoclinic (M1) and Rutile (R) phases.
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After the phase transition, the gap between the highest unoccupied band and the
lowest fully occupied band collapses and leads to these two bands being both partially
filled. Since the Fermi level is now in the middle of a partially occupied state, the rutile
structure is considered as a metallic phase. The resistivity of the phase varies by several
orders of magnitude. The resulting optical properties are a close to 0% infrared
transmission.
Figure 9: Conductivity plotted as a function of photon energy
Synthesis:
Several preparation techniques can be used in order to obtain VO2 (B): a
hydrothermal methodvi or reduction of vanadium oxide precursors under different
atmospheres.
Hydrothermal methods provide numerous advantages by offering preparation
parameters such as time, temperature, pH, concentration, precursor dependence,
pressure, reducing agents. Playing on these parameters is a way to obtain desired
morphologies and to explore new phases.
Because we did not have a lot of time to perform the synthesis, and from an
economical and environmental point of view, we decided to synthesize VO2 at low
temperature and duration. We chose also to use abundant, inexpensive and nontoxic
precursors.
We performed a rapid hydrothermal synthesis of VO2 (B) and then we obtained
VO2 (M1) by annealing VO2 (B) under vacuum for 1 hour.
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Experimental:
The samples were synthesized via a rapid hydrothermal process: V2O5 was dissolved in
43mL of deionized water. We stirred for 15 minutes using a magnetic stirrer. Then, we
added 3.9 mmol of citric acid monohydrate (C6H8O7, H2O) and stirred for 15 minute once
again. The resultant yellow aqueous solution was transferred into a stainless steel
autoclave and kept in an oven at 220°C for 1 hour. After the reaction process, we left the
autoclave cooling at room temperature overnight. The following day, the powder was
filtered and centrifuged, washed with first distilled water and secondly ethanol to
remove unreacted species. The products were dried in air at 60°C for a night.
We finally obtained a blue powder and a blue solution that we used for further
characterization.
+
→
∙9
+
→
∙!
∙!
+
→
(#)
The powder was first kept in an oven at 100°C for 15 minutes in order to provoke the
metal-insulator transition. At the end we obtained a greenish solution. Thanks to X-ray
powder diffraction our product was analyzed: we saw that in fact the reaction had begun
processing during the night as the powder before and after the heating showed the same
XRPD pattern: VO2 rutile. VO2 monoclinic (B) was contained in the blue solution.
It was possible to observe a transition from bariandite-type mineral V10O24, 9 H2O
to VO2 (B) by a reduction dehydration process. The reducing mechanism from V(V)
(V2O5) to V(IV) (VO2 (B)) in the presence of a reducing agent (citric acid) could be
described with a three-step process (see above) from partial reduction-hydration to
complete reduction-hydration and finally dehydration.
V10O24,9H2O was formed in the early stage of the reaction process under soft
reducing conditions or at low temperature. The compound is layered with water
intercalating. As the reaction kept on, the remaining V(V) ions were reduced to V(IV),
resulting in VO2,xH2O. In the final stage of reaction process, the dehydration of VO2,xH2O
gave rise to the fully reduced V(IV) : VO2(B).
Figure 10: Comparison between the two structures of VO2
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Applications
Smart windows
The difference in infrared transmittance between the two phases can be used to
create smart glasses. The fact that both structures of VO2 have a high transmittance in
the visible wavelengths allows industrials to coat regular glass with a thin film of
vanadium dioxide. The phase transition can be provoked by applying a potential of 3 Vvii
to the film. This will have the same effect as heating it from 30 °C to 70 °C: the vanadium
oxide will have a structure change and the transmittance of infrared is more than
halved, while transmittance in visible wavelengths remains the same.
Figure 11: Smart window principle
The power consumption of this device is very low and could have promising
applications in buildings for energy saving.
By doping Vanadium Dioxide with different metals, it is possible to change the
metal-insulator phase transitionviii. The best dopant yet is Tungsten (W), which allows
the transition temperature to go as low as just above room temperature (~30 °C). The
phase transition happening this low could be an alternative to the electrical stimulation
of vanadium dioxide.
If deposited on sapphire, the thin film has abnormal thermal eminence during the
phase transitionix. It seems cooler than it actually is, having possible applications in
infrared camouflage, tagging and identification. It can also be used as a mean of thermal
regulation.
Electronic devices
Others consider using the hysteresis in the phase transition as a memory storage
Using Vanadium in a Cu/VOx/Cu cell with multiple oxidation states (V5+, V4+ and
3+
V ) leads to a reliable cell with promising applications in nonvolatile memory.
Vanadium oxides are also known for their applications in batteries, such as silver
vanadium oxides or vanadium redox batteries.
unitx.
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Conclusion
Vanadium dioxide is the most frequently used of the vanadium oxides for its low
transition temperature, about 340K. Below Tc, the crystalline structure is monoclinic
with a P21/c space group. Above Tc, the crystal shifts into a rutile structure of space
group P42/mnm.
The band structure of vanadium oxide (R), predicted by Density Functional
Theory, shows 10 bands around the Fermi level: the t2g and eg states, an interaction of
the V 3d states with the O 2p states. In the monoclinic structure, the t2g and eg states are
separated by a gap of 0.6 eV, leading to insulator properties.
Infrared transmittance is fairly high in the (M1) structure, but drops in the (R)
structure, whereas transmittance for visible wavelengths is high in both states.
We synthesized monoclinic (M1) VO2 blue powder with a hydrothermal method
using cheap, environmentally friendly, and abundant precursors. The method used can
be adapted to many needs, as it allows use of different temperatures for the reaction and
a variable time of reaction.
This powder can then be deposited in thin films using a vacuum thermal
evaporation method. Such thin films can have many applications, such as smart
windows that can be transparent to visible wavelengths but totally reflective to infrared
radiations, or if deposited on sapphire can lead to irregular emissions of infrared light,
having possible infrared camouflage applications.
Vanadium oxides are also studied for their potential applications in batteries, as
the multiple stable oxidation states allow electronic transfers to take place.
85% of the vanadium production is used for the mechanical properties it gives as
a steel additive, but if many other applications such as detailed previously continue to
emerge, the distribution of Vanadium between its different uses might be reevaluated in
the years to come.
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References:
i
When Mott meets Peierls: the Metal-Insulator Transition in Vanadium Dioxide
S. Biermann, A.I. Poteryaev, A. Georges, A.I. Lichtenstein, Phys. Rev. Lett. 94 026404
(2005)
ii Diffuse x-ray scattering due to the lattice instability near the metalsemiconductor transition in VO2
Phys. Rev. B 17, 2494 – Published 15 March 1978
H. Terauchi and J. B. Cohen
iii The metal-insulator transitions of VO2: A band theoretical approach
Volker Eyert
iv Lattice dynamics of oxides with rutile structure and instabilities at the metalsemiconductor phase transitions of NbO2 and VO2
Phys. Rev. B 31, 4809 – Published 15 April 1985
François Gervais and Winfried Kress
v Electrons in One Dimension: the Peierls Transition
Michael Fowler 2/28/07
vi Rapid Hydrothermal Synthesis of VO2 (B) and Its Conversion to Thermochromic
VO2 (M1)
Srinivasa Rao Popuri, Marinela Miclau, Alla Artemenko, Christine Labrugere, Antoine
Villesuzanne, and MichaelL Pollet*
vii Nakano, M., Shibuya, K., Ogawa, N., Hatano, T., Kawasaki, M., Iwasa, Y. & Tokura, Y.
Infrared-sensitive electrochromic device based on VO2. Applied Physics Letters 103,
153503 (2013)
viii Tungsten-doped vanadium dioxide thin films on borosilicate glass for
smart window application
Zhangli Huang, Changhong Chen, Chaohong Lv , Sihai Chen
ix Vanadium Dioxide as a Natural Disordered Metamaterial: Perfect Thermal
Emission and Large Broadband Negative Differential Thermal Emittance
Mikhail A. Kats, Romain Blanchard, Shuyan Zhang, Patrice Genevet,
Changhyun Ko, Shriram Ramanathan, and Federico Capasso
x Analysis of the resistive switching behaviors of vanadium oxide thin film
Wei Xiao-Ying(韦晓莹), Hu Ming(胡 明), Zhang Kai-Liang(张楷亮), Wang Fang(王 芳),
Zhao Jin-Shi(赵金石), and Miao Yin-Ping(苗银萍)
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