VANADIUM-VANADIUM BONDS IN THE
Ti1-xVxO2 SYSTEM
T. Hörlin, T. Niklewski, M. Nygren
To cite this version:
T. Hörlin, T. Niklewski, M. Nygren.
VANADIUM-VANADIUM BONDS IN THE
Ti1-xVxO2 SYSTEM. Journal de Physique Colloques, 1976, 37 (C4), pp.C4-69-C4-73.
<10.1051/jphyscol:1976411>. <jpa-00216525>
HAL Id: jpa-00216525
https://hal.archives-ouvertes.fr/jpa-00216525
Submitted on 1 Jan 1976
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
JOURNAL DE PHYSIQUE
Colloque C4, supplkment au no 10, Tome 37, Octobre 1976, page C4-69
VANADIUM-VANADIUM BONDS IN THE Ti, - ,Vx02 SYSTEM
T. HORLIN, T. NIKLEWSKI and M. NYGREN
Department of Inorganic Chemistry, Arrhenius Laboratory,
University of Stockholm, S-104 05 Stockholm, Sweden
Resume. - Une ktude sur poudre du syst6me TiOpV02 a et6 conduite par ATD, diffraction X
et mesure de susceptibilite magnetique. Le diagramme de phase prQente indique la prksence de
plusieurs phases de'structure rutile ou derivant de celle-ci. Les mesures magnetiques montrent que
des liaisons vanadium-vanadium non magnetiques se forment a basse tempkrature sur l'ensemble du
domaine de composition. La rupture de ces liaisons se produit dans un intervalle de temperature
trop etroit pour 6tre explique uniquement par la presence &interactions antiferromagnetiques
d'Heisenberg. L'interaction entre paires metal-mktal non magnktiques doit &treenvisagke pour
expliquer 1'6volution de la susceptibilite magnetique avec la temperature.
Abstract. - Powder samples of the TiO2-V02 system have been studied by DTA, X-ray powder
diffraction and magnetic susceptibility measurements. A phase diagram displaying several phases
with rutile or rutile related structures is presented. The magnetic susceptibility measurements
showed that nonmagnetic vanadium-vanadium bonds form at low temperatures over the entire
range of composition. These bonds rupture in a temperature interval too narrow to be explained only
by antiferromagnetic Heisenberg interaction. Interaction between the nonmagnetic metal-metal
pairs must be considered in order to expiain the temperature dependence of the magnetic susceptibility.
1. Introduction. - The system Ti0,-VO, has been
studied since the mid-fifties by several investigators
with respect to : (i) the metal-nonmetal transition of
V 0 2 and how it is affected by substitution of vanadium
ions by titanium ions, (ii) the magnetic properties and
(iii) the relation between the c/a ratio and the number
of valence electrons available for metal-metal bonds.
In a previous paper [ l ] we treated only a narrow
0.94)
range of composition (Til-xV,O, with 1 x
and the experimental data were discussed in terms
which are related to the first point of interest mentioned
above. The results of DTA, X-ray powder diffraction
and magnetic susceptibility measurements for the
entire range of compositions are reported in this article
with a particular emphasis paid to the second and third
aspects.
2. Experimental. - The starting materials were
V205 (Fisher, Sc. Co., p. a.) and TiO, (Baker, Sc. Co.,
p. a.).VO, was prepared and characterized as described
in ref. [l].Powder samples of Ti,-,V,O, were obtained
from thoroughly mixed powders of VO, and TiO,
heated at 1 175 K for one week in evacuated silica
tubes. The heat-treatment was terminated and the
samples were allowed to cool inside the furnace with an
approximate initial cooling rate of 10 K per minute.
In order to control the stoichiometry and to promote
the rate of reaction a small amount of V205 (< 0.5
weight percent) was added to the dioxide mixtures
before the heat treatment. The excess of V,O, and a
not too high cooling rate appear to be very important
in order to achieve reproducible results. After the
firing the dioxide phase was easily separated from the
excess V205 as the latter strongly adhered to the walls
of the silica tubes.
The procedure described above assures the stoichiometry to be at the oxygen rich extreme of the dioxide
phase area which is believed to be very close to the true
dioxide.
2 . 1 DTA. - The measurements were performed
in an apparatus which enables simultaneous analysis of
five samples in the temperature range 100-600 K [2].
2.2 X-RAY POWDER DIFFRACTION ANALYSIS. - At
ambient temperature the X-ray powder patterns were
recorded in a Guinier-Hagg focusing camera, with
CuKa, radiation. Above room temperature a powder
diffractorneter with CuKa radiation was used. In both
cases KC1 was used as internal standard. The thermal
expansion of KC1 was taken account of using data from
Glover [3]. The cell parameters were calculated with the
least squares program Tetlin [4].
2.3 MAGNETICSUSCEPTIBILITY MEASUREMENT. These measurements were performed according to the
Faraday method using HgCo(SCN), as standard [5].
An equipment built at this laboratory was used [6].
The measurements covered the temperature range
78-750 K. The magnetizing field was 0.7 X 106A m-'
(- 0.9 X 104Oe).
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1976411
C4-70
T. HORLIN, T. NIKLEW!SKI AND M. NYGREN
3. Phase analysis. - TiOz and VO, form solid
solutions over the entire range of composition. The
results of DTA and X-ray powder diffraction studies
are presented as a phase diagram in figure 1. The full
Our cell parameter in the R, and M, phase
areas are in agreement with those reported by Marinder et al. [9, 101.
The temperature dependence of the cR/a, ratios of
V02 (from ref. [l l]), Tio.loV, .9002and Tio.,,Vo.7502
respectively is outlined in figure 2. The corresponding
0.645
R X I R L RRTIO C/R
VS.
TEMPERRTURE/K
FIG. 1. - Phase diagram of T~I-~VXO~.
lines represent the starting points of endothermic
reactions obtained for increasing temperatures and the
broken lines represent the starting points of exothermic
reactions when the temperature was decreased.
The M, + R, transition temperatures did not vary
among different samples of the same composition but
the M, + M, transition temperatures seemed to be
very sensitive to even small changes of the procedure
of preparation. Thus the presented data refer to six
samples prepared at the same time and under the same
conditions.
The heat exchange of the M, + R, transitions is of
comparable size to the latent heat of the metal-non
metal transition of pure VO, while the heat exchange
of the lower transition temperatures is approximately
ten times less than that of the upper ones.
The transitions discussed so far are probably of the
first order with well defined starting points and hysteresis. The hatched area in figure I illustrates the increasingly broader DTA peaks without well defined starting
points observed for decreasing vanadium content.
In the R, and R, phase areas the samples possess the
rutile structure. Metallic behaviour is observed in the
R, area whereas samples in R, area exhibit semiconducting properties. Preliminary studies of the electrical conductivity indicate that the semiconducting R,
phase continuously transform into a metallic RMphase
around X = 0.75.
In the M, phase metal-metal pairs are found along
the c axis of the pseudo rutile cell [7]. In the M, structure half of the vanadium atoms form pairs while the
other half are accommodated in zig-zag chains of
equally spaced atoms also running parallel with the c,
axis [S]. The M, phase area might be regarded as an
extension of the M, phase area where some long range
order has vanished. This interpretation is supported
by : (i) the similarity of the X-ray powder patterns of
the M, and M, phases, (ii) the magnetic susceptibility
measurements described below and (iii) preliminary
studies of the electrical conductivity.
ratios of the distorted rutile phases are calculated as
(C:/V,)'~~. As expected the curves of VO, and
Ti,, ,,Vo ,,,O, exhibit discontinuities at the various
phase transition temperatures. The sudden decrease of
the axial ratio of Tio~,,Vo~,,O, around 380 K is,
however, not associated with any appearent change in
symmetry.
The decrease of the axial ratio of rutile related structure of the M, type (e. g . VO,, MOO, and WOz) with
the number of valence electrons available per metalmetal bond has been interpreted in terms of a strengthening of the bonding force between the metal atoms
within the pairs [93, [12]. From this point of view it is
interesting to note that the axial ratios of the semiconducting (Ti, V)O, samples with M, structure are
larger than those for the metallic ones with rutile
structures. MOO, and WO, are also metallic which
suggests that the above discussed variation of the axial
ratios partly can be associated to the occurrence of
metallic bondings in these compounds.
4. Magnetic Properties. - The molar magnetic
susceptibility data, converted to squared Bohr magneton numbers per metal ion according to the expression
are represented in figure 3a and b. Here p, = Bohr
magneton and p. = l in cgs emu = 4 n X 10-' in
S. I. units.
For X > 0.90 in Ti, -,V,O, sudden jumps in the
values are observed at the M, + M, and M2 + R,
transition temperatures. A more continuous increase
of the ,U& values is observed when passing through the
M, phase area. This continuous increase persists in the
C4-71
VANADIUM-VANADIUM BONDS IN THE Til-xVx02 SYSTEM
/
3.0
<
.F,
,c<-
<,,<.
..?-
SBURREO BOHR MRGNEION NUMBER
,:
/-
VXT~I-XOZ
,.'A?
.
'
4
I
,
--
OF
2.5
-
2.0
-
TI 1
- ~ V ~ 0 2 VS:
AT 700
K
-
X
0
c-
"
.-'c..
-
.
.
'
_
.A<</
.&'.
2.0-
SQURRED BOHR MRGNET
l
SOURRED BOHR tlRiNETDN NUMBER
3.0-
2.5.
-
I
.'
"
, - '
,-
1.5.
,. .
Rs phase area and an anomaly is still observed at a
vanadium content as low as x = 0.10.
The plots of CL$f versus temperature are linear at
lower temperatures. The
values extrapolated to
T = 0 K and those obtained at 700 K are plotted
versus x in figure 4. The latter numbers are proportional
to the vanadium content up to X N- 0.80. The contribution from temperature independent paramagnetism
(TIP) to the observed ,U& values at 700 K can be
estimated from the slopes of the linear parts of the
curves in figures 3a and b. The
values thus corrected
for TIP are in good agreement with the expected spin
only values except for compositions close to x = 1
where the magnetic moment per metal atom is smaller
than that for a spin independent doublet indicating the
onset of Pauli paramagnetism.
The magnetic properties of the M, and M, phases
are discussed in ref. [l]. In the M , phase area spin
pairing occurs at every second site between two adjacent vanadium ions. The results described above
suggest that spin pairing also occurs between adjacent
vanadium atoms at lower temperatures in the R,
phase area.
The 0 K curve in figure 4 may be discussed in terms
of two models of spin pairing. The first model is based
on the assumption that the metal atoms are randomly
dispersed over the metal sites of the rutile structure and
that antiferromagnetic interaction occurs only between
nearest neighbour vanadium ions in the chains of
vanadium ions running in the c, direction. The ground
state of chains with an even number of vanadium ions,
terminated at both ends by titanium ions, is a nonmagnetic spin singlet whereas the ground state of
chains with an odd number of vanadium ions is a
paramagnetic spin doublet. The probability that a
certain site is occupied by a vanadium ion, which is a
member of a chain of n vanadium ions terminated by
titanium ions, is n(l - x)2 xn where x is the concentration of vanadium ions. The factor n is included as the
vanadium ion can take any of the n positions within
the chain and random dispersion is introduced by the
multiplication of probabilities. The average number of
spin doublets per metal atom is calculated by summing
the probabilities of finding chains with odd numbers of
vanadium ions. Each term in this summation is divided
by n as there are only lln doublet states per vanadium
atom in a chain containing n vanadium ions. Thus the
average number of spin doublets per metal atom,
according to this model is
The number of spin doublets is the same even if a
dimerization of the metal atoms occurs since minimum
energy is obtained by forming maximum number of
'SKI AND M. NYGREN
pairs. The second model is based on the occurrence of a
potential, p, with a period twice that of the rutile c axis,
inducing a dimerization of the randomly dispersed
metal atoms as illustrated in figure 5. Chains with even
numbers of vanadium ions are in this case split into two
types according to figure 5A and B. The energy difference between the spin singlet ground state and the first
excited spin triplet state is larger for chains of type A
than that for type B. Furthermore it is assumed that cp
is strong enough to make the singlet and triplet states
practically degenerate for chains of type B. Thus the
latter type contains two paramagnetic spin doublets
per chain while type A is non magnetic. If type A and B
are present in equal proportions and as the number of
spin doublets per chain with odd numbers of vanadium
ions in this case is the same as in the first model one can
assodate one spin doublet to each chain of vanadium
ions. Thus the average number of spin doublets per
metal atom according to this model is
The number of spin doublets per metal atom according to these two models of spin pairing is plotted versus
the composition X in figure 6. The experimental numNUMBER OF S P I N DOUBLET GROUND S T R T E S
PER METAL I O N I N T l l _ x V X O 2
VS: X
The g factors are obtained from a linear combination
of the mean values of the g factors of TiO, and
V 0 2 [13].
The second model which represents the case when
spin pairing only can occur at every second site between
two adjacent vanadium ions as in the M, structure is
obviously appropriate for higher vanadium contents.
The first model, where spin pairing can occur between
any pairs of adjacent vanadium ions, is applicable for
low vanadium concentrations whereas in the intermediate range restrictions in the spin pairing seem to be
present.
These results clearly show that non magnetic vanadium-vanadium bonds are present at low temperatures
over the entire range of composition. Figures 3a and b
thus illustrate the rupture of these bonds with increasing temperature. If no interaction is present between
the non magnetic metal-metal pairs the temperature
dependence of the
with respect to the rupture of
these bonds is described by
where 2 J is the energy difference between the singlet
and triplet state.
The presence of an interaction between the pairs of
the type described in connection with the second model
of spin pairing can be accounted for by allowing J to
vary with the temperature as
The temperature dependence of J must be non linear
in order to prevent the occurence of ferromagnetic
interaction at higher temperatures. In equation (6)
J increases linearly with the temperature in the low
temperature limit while at higher temperatures J
approaches a constant value. The temperature dependence of p$f now becomss
3xN
N -1
+ exp I - 2 J o / k T I '
(7)
The experimental data are least squares fitted to the
following equation
X M = C1 + C 2 .
T
bers of spin doublets per metal atom represented as
rings in the figure are obtained from the ,u:ff values
at 0 K by
T
N
N - 1 + exp I
- 2 J,/kT
I + Xo
(8)
where the first term is associated to the spin doublets,
the second term as above and the third term accounts
for TIP.
The fit of the experimental data to equation (8) is
good for X < 0.30. At X = 0.30 and in the intermediary
temperature region systematic deviations start to
appear. These deviations increase with increasing x
and clearly approach the behaviour of the
versus T
curves in figure 3b where the rupture of the bonds takes
place in two steps via the M, or M, phase area.
J,, are plotted versus x in figures 7
Log N and
and 8. The N value approaches 4 when x -, 0 and the
-,
VANADIUM-VANADIUM BONDS I N THE Til-,VsOz SYSTEM
3.0
C4-73
1400
0
0
2.5
-
LOG [ N I VS.
-
X
-J K - ~ / K VS.
X
0
l000
2.0
0
0
BOO
-
600
.-
1100
-
0
0
1.5
-
'
0.5
4
D
0.1
I
0.2
I
I
0.4
0.3
I
0.5
0.6
200
I
0
l
I
,
I
I
I
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.7
FIG. S.
FIG. 7.
corresponding J, value is -- 300 k, K. The latter
number is of the same order of magnitude as found in
the M, phase [l]. This thus corresponds to the case
when antiferromagnetic Heisenberg interaction is present within the pairs but no interaction between the
pairs occurs. As N increases with x interactions between
the pairs have to be present over the entire range of
composition. The nature of this interaction has been
discussed above in connection with second model of
spin pairing.
Riidorf et al. [l41 and Ariya and Grossmann 1151
have also studied the Ti0,-VO, system by means of
X-ray and magnetic susceptibility measurements. They
have not observed the M, and M4 phase areas and
report the M, -+ RMtransition temperature to decrease
slightly with increasing titanium content. This is not in
agreement with our findings. This discrepancy is most
probably due to the different preparation techniques.
Thus we have observed that samples, deliberately made
substoichiometric, exhibit similar properties as those
reported in ref. [l41 and [15].
Acknowledgements. - The authors wish to express
their gratitude to Professor A. MagnCli and Dr. L. Kihlborg for their interest in this work.
This investigation has been sponsored by the
Swedish Natural Science Research Council.
References
[l] HORLIN,T., NIKLEWSKI,
T. and NYGREN,
M., Acta Chem.
Scand., in press.
[2] HORLIN,T., NIKLEWSKI,
T. and NYGREN,M., Chem.
Commun. Univ. Stockholm No. 9 (1975).
[3] GLOVER,
R. E., 2. Phys. 138 (1954) 222.
[4] HORLIN,
T., to be published.
S. A., USACHEV,
P. V. and YUDIN,V. M., Fiz.
[5] KIZHAEV,
Tverd. Tela 13 (1971) 2829.
[6] BLOM,B. and HORLIN,T., to be published.
[7] ANDERSSON,
G., Acta Chem. Scand. 10 (1956) 623.
181 MAREZIO,
M., MCWHAN,
D. B., REMEIKA,
J. P. and DERNIER, P. D., Phys. Rev. B 5 (1972) 2541.
%
[91 MARINDER,
B. 0. and MAGNBLI,A., Acta Chem. Scand. 11
(1957) 1635.
L101 MARINDER,
B. 0. and FRIBERG,
M., Final ~echnicalReport 1
(DA-91-591-EUC-1319)Univ. Stockholm 1960.
[l11 RAO,K. V. K., NAIDA,S. V. N. and IYENGAR,
L., J. Phys.
Soc. Japan 23 (1967) 1380.
[l21 ROGERS,D. B., SHANNON,
R. D., SLEIGH^, A. W. and
GILLSON,
J. L., Inorg. Chem. 8 (1969) 841.
1131 SHIMIZU,T., J. Phys. Soc. Japan 23 (1967) 848.
[l41 R ~ O R F
W.,
, WALTER,
G. and STADLER,
S., Z. Anorg. Allg.
Chem. 297 (1958) 1.
[l51 ARIYA,S. M. and GROSSMANN,
G., SOV.P&. Solid State 2
(1960) 1166.