Physical properties and lattice dynamics of bixbyite-type V2O3 [original]

ARTICLE
Physical properties and lattice dynamics of bixbyite-type V
2
O
3
Dominik A. Weber
a)
Institut für Chemie, Tecnische Universität Berlin, 10623 Berlin, Germany; and Physikalisch-Chemisches Institut,
Justus-Liebig-Universität Gießen, 35392 Gießen, Germany
Christian Schwi ckert
Institut für Anorganische und Analytische Chemie, Universität Münster, 84149 Münster, Germany
Anatoliy Se nyshyn
Heinz Maier-Leibnitz Zentrum, Technische Universität München, 85748 Garching, Germany
Martin Lerch
Institut für Chemie, Tecnische Universität Berlin, 10623 Berlin, Germany
Rainer Pöttgen
Institut für Anorganische und Analytische Chemie, Universität Münster, 84149 Münster, Germany
(Received 8 December 2016; accepted 30 March 2017)
So me ti me ag o , we re p ort e d th e syn th es is o f bix by it e- ty pe V
2
O
3
, a new met as ta bl e po ly mo rph of
van ad iu m ses qu io xid e. Si nc e, a nu mbe r of inv es tig at io ns fol lo w ed , d eali n g with d iff er en t asp ec ts
li ke el e ctro n ic an d m ag ne ti c pro per ti es of th e m at er ial, th e de vi ati o n fro m id ea l sto ic h io me try o r the
prepa ration of na nocrystal s as oxygen storage ma terial . However, most of t he physica l propert ies
wer e only eva luated on a theo reti cal basis. He re, we repor t the l attice dyna mics and physi cal
prope rties of b ixbyite-t ype V
2
O
3
bu lk mat er ia l, wh ic h w e a cq uir ed fr om ph ys ical p ro per ty
mea s ure m en ts and n eu tr on dif fr ac ti on exp e ri men ts o ver a wi de te mp er at ure ra ng e. B esid es
at tr ibu ti ng dif f er en t p os sib le ori e nta ti on s of the mag n et ic mom ent s fo r V1 an d V2 to the id ent i ﬁ ed
an ti fe rro mag n et ic (A FM ) g rou nd st a te wi th a N ée l te mp era tu re of 38 . 1(5 ) K, w e us e a ﬁ r st ord er
Gr ün eis e n ap pro xim at io n to det e rm in e la tt ice -d ep en den t p ar am eter s f o r the re la ti v el y sti ff cu bic
la tt ice , an d, a mo ng st o th ers id en ti fy th e Deb ye te mp er at ure to b e as lo w as 3 50 6 65 K.
I. INTRODUCTIO N
Because of their structural diversity, abundant physical
and chemical properties, and numerous potential appli-
cations, vanadium-based materials hold an exceptional
position amongst transition metal-based compounds.
Besides their use in electronic and optical devices,
1
chemical sensors,
2
as catalysts,
3,4
and as cathode materi-
als for high energy density lithium ion batteries,
5 – 7
even
binary vanadium oxides, due to their unique behavior,
have been subject to various investigations. In particular,
a large number of experimental and theoretical studies
have already been conducted on the thermodynamically
stable vanadium sesquioxide, as it presents a model
system for a Mott – Hubbard transition.
8 – 10
At low tem-
peratures, this polymorph of V
2
O
3
is an antiferromag-
netic (AFM) insulator, crystallizing in a monoclinic
structure (M1). At around 170 K it transforms into
a paramagnetic conductor, undergoing a structural phase
transition to the well-known rhombohedral corundum-
type structure with a notably large c / a ratio of 2.823.
9 – 14
Reg ar din g th e in im it a ble ch a ra cte ri sti cs o f the rm ody -
nam ic a ll y sta b le V
2
O
3
, th e inv es ti gat io n of th e ph y sic a l
pro p er ti es of ad dit io na l poly m orp h s of V
2
O
3
is of funda -
men ta l in te r est. A few yea rs ag o , we s yn th es iz ed a n ew
met a sta b le po ly mo rph of v anad iu m s esq ui ox id e that cr y s-
ta ll iz es in the b ix by ite -t ype str uct u re (s p ac e gro u p Ia 
3).
15
This po lymor ph of V
2
O
3
has s in ce be en the sub je ct o f
nu me ro us in ve sti ga ti on s, in cl ud in g the syn th es is o f par-
ti cl es with ur ch in -l ik e mor ph olo gy by th e rm al de co mpo -
sit io n o f vana dy l et h yle n e gly co la te
16
or of phase pur e
nan o cr ys tals b y a co ll oid a l ro ute .
17
In te res ti ng ly , th es e
nan o cr ys tals w er e only re c en tl y sho wn to rev er s ibly in -
co rpo r at e up to two ad dit io nal o xy gen at o ms per uni t cell
on to vac a nt an io n sit es in th e cry sta l str u ct ure ,
18
ﬁ tt in g
wel l w it h the p re dic ti on s o n in trin s ic d ef ect s th at we
stu d ie d on de ns it y- fu nct io na l th eo ry ( DF T) le v el .
19
Th es e
vacant site s are l ocate d at the 16 c Wy ck off p os it io n in the
bix by it e st ru ct ure , w hic h ca n be tr ea te d a s an an io n-
de ﬁ cient 2  2  2 s upe rc e ll of th e ﬂ uorit e st ructure wi th
a qu ar te r of th e an io n s rem o ved ( Fi g. 1) . Whi le th e cat io n s
ar e dis tr ib ute d o ver two s ym met ry - ine q uiv al ent pos it io ns ,
8 b and 2 4 d , res p ecti v ely , th e an io n s po pu late the 48 e
po sit io n s, giv in g a tota l of 80 at om s per un it ce ll ( Z 5 16 ) .
Shortly after our ﬁ rst contribution on the new poly-
morph of V
2
O
3
, we theoretically studied the structural,
Contributing Editor: Michael E. McHenry
a)
Address all correspondence to this author.
e-mail: [email protected]
DOI: 10.1557/jmr.2017.144
J. Mater. Res., Vol. 32, No. 12, Jun 28, 2017 Ó Materials Research Society 2017 2397
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thermodynamic, and electronic properties of the new
phase amongst other possible polymorphs and found
strong indications for the formation of a band gap in an
AFM ground state.
20
Up to that point, we were not able to isolate the phase-
pure material and physical property measurements were
therefore carried out on samples that contained at least
18 wt% of the corundum-type polymorph as a side phase.
Hence, we were not able to ascribe the observed
phenomena for these samples solely to the bixbyite-
type phase. Here, we present results of in-depth studies of
the physical properties of phase-pure bixbyite-type V
2
O
3
bulk material, which we recently were able to synthe-
size,
21
and link them to results from temperature-
dependent neutron and X-ray diffraction. For the ﬁ rst
time, we determine the lattice dynamics of bixbyite-type
V
2
O
3
, and con ﬁ rm the AFM order of the material
predicted by quantum-chemical calculations.
II. EXPERIMENTAL SECTION
A. Sample preparation
All reactions were carried out in a conventional tube
furnace equipped with a corundum tube with an inner
diameter of 50 mm. The reaction gas was led directly onto
the sample by a second corund um tube with an in ner
diameter of 5 mm. The ﬂ ow rate of the reactio n gas
[40 vol% H
2
in Ar (both Air Liquide, Dusseldorf,
Germany), gas stream piped through a water- ﬁ lled washing
ﬂ ask] was regulated with a parallel arrangement of two
digital volumetric mass ﬂ ow controllers (Brooks Instrument
LLC, Hat ﬁ eld, Pennsylvania) and set to 10 L/h. For each
batch, 500 mg of V
2
F
6
 4H
2
Oo rV
2
F
6
 6H
2
O (synt hesiz ed
from vanadium powder and aqueous H
2
SiF
6 22
)w e r ep l a c e d
in a small alumina boat inside the tube and heated under
ﬂ owing reaction gas for 2 h at 753 K, applying a heating
ramp of 300 K/h. After the dwell was comp lete, the furnace
was swung open to allow for fast heat dissipation.
Simultaneously, the atmosp here was changed to 10 L/h of
dry argon (5.0, Air Liquide). A fter cooling, the grayish-
black product was obtained witho ut further treatment.
B. Basic characterization
The obtained products were characterized by X-ray
powder diffraction (PANalytical X ’ Pert PRO MPD with
Cu K
a
radiation, PIXcel detector, PANalytical B.V.,
Almelo, The Netherlands) at ambient temperature. Struc-
tural re ﬁ nements were performed in the same manner as
described in the neutron diffraction section. Quantitative
analysis of the oxygen content was performed by the
well-established hot gas extraction method (LECO
TC300/EF300, LECO Corp., St. Joseph, Michigan),
using zirconia and corundum-type V
2
O
3
as standards.
The experimental error for this method amounts to  2%
of the presented values (i.e., V
2
O
3 6 0.06
).
C. Physical property mea surements
Magnetic measurements were performed in the t emper-
ature range of 2. 5 – 305 K, using a Quantum Design
Physical-Property-Measurement-System (Quantum Design,
San Diego, Cali fornia) with magnetic ﬂ ux densities o f up to
80 kOe. All measurements were carried out using the VSM
option by p acking the powde red sample (15. 642 mg) in
a polypropylene capsule an d a ttaching it to a brass sample
holder. A heat capacity measurement was performed in the
temperature range of 2.1 – 305 K, using the sam e Quantu m
Design Physical-Property-Measurement System. For the
measurement, a compact sample was prepared and embed-
ded into Apiezon N grease ( Apiezon Products, M&I
Materials Ltd., Manchester, United Kingdom) to ensure
thermal couplin g with the sample holder platfor m.
D. Neutron diffraction
Elastic coherent neutron scattering experiments were
performed at the Heinz Maier-Leibnitz Zentrum
FIG. 1. S t r u c t u r a l r e l a t i o n s h i p b e t w ee n ﬂ uorite fcc and bixbyite bcc structure. Besides 16 ordered anion vacancies (16 c position, pink), the bixbyi te structure
comprises two symmetry-inequivalent cation positions (8 a , r ed and 24 d , orange, respectively) as well as 48 equivalent anion positions (48 e ,b l u e ) .F o rV
2
O
3
in this structure type, reversible incorporation of up to two a dditional oxygen atoms per unit cell is pos sible, utilizing the 16 c position.
D.A. Weber et al.: Physical properties and lattice dynamics of bixbyite- type V
2
O
3
J. Mater. Res., Vol. 32, No. 12, Jun 28, 2017 2398
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(Garching near Munich, Germany) on the high-resolution
diffractometer SPODI.
23
Monochromatic neutrons ( k 5
1.5482 Å) were obtained at a 155° take-off angle, using
the 551 re ﬂ ection of a vertically-focused composite Ge
monochromator. A vertical position-sensitive multidetec-
tor (300 mm effective height) consisting of 80
3
He tubes
and covering an angular range of 160 deg. 2 h was used
for the data collection. Measurements were performed in
Debye – Scherrer geometry. The powder sample (approx-
imately 1 cm
3
in volume) was ﬁ lled into a thin-walled
(0.15 mm) vanadium can of 10 mm in diameter, which
wa s then m oun ted in th e top -loa din g clos ed-c ycl e re-
frig erat or. Hel ium 4. 6 was us ed as a heat tr ans mitt er. Th e
te mper atu re was me asure d ins tant aneo usly , usin g two th in
ﬁ lm res is tanc e cryo geni c tem pe rat ure sen sors (Cer nox ™ ,
La ke Sh ore Cyr otro nic s Inc ., We ste rvil le , OH) an d con -
tr olle d by a tem per atur e cont roll er fro m Lak eSho re Cyro -
tr onic s Inc. Tw o-d imen sio nal pow der dif frac tio n dat aset s
we re coll ect ed at ﬁ x ed te mpe ratu res in th e ra ng e of
4 – 320 K . Dep endi ng on th e temp erat ure , dif fere nt ex po-
su re tim es were ap pli ed, i . e . , to rev ea l the weak ef fec t of
ma gn etis m in V
2
O
3
, the da ta at 4 K wer e coll ecte d fo r
21 h, wh il st sho rter dat a coll ecti on time s wer e app lied at
60 K (1 0 h) an d 300 K (5 h ). Add itio nally , a nu mber o f
di ffra ctio n pat te rns wi th sho rt exp osu re tim es (3 0 min) wa s
coll ecte d at ﬁ xed te mpe rat ures in th e tem per atur e rang e 4,
10 , 20, 30, .. . 320 K. T he co llec ted 2D d iffr ac tio n pat ter ns
we re then co rrec ted for g eom etri ca l a ber rati on s and
cur vatu re of the Deb ye – Sc herr er ring s.
24
Rietveld re ﬁ nements were carried out using the
software package FullProf Suite.
25,26
The peak pro ﬁ le
shape was mo deled by a pseudo- Voigt function. The
background of the di ffraction pattern was ﬁ tted using
a linear interpolation between selected data points in
nonoverlappin g regions. To deduce the evolution of the
lattice parameters, the Rietveld method was applied for
the analysis of the neutron data with no vanadium
contribution, taking into account the anomalously low
coherent neutron scattering length of the
51
V isotope,
which dominates in natura l v anadium (99.75 %). For
the coherent nuc lear part of the s cattering process, this
low scattering length ca uses “ blindness ” of neutrons
against vanadium. The magnetic form factor, on the
other hand, depends on the magnetization distribution
of the atoms, and therefore the detection of magnetic
moments on natural vanadium atoms usin g nonpolar-
ized neutron diffraction, is possible. The scale factor,
the lattice parameter, the fracti onal coordinates of the
atomic sites, and their isotropic displacement parame-
ters, the zero angula r shift, the pro ﬁ le shape parameters
and the half width (Caglioti) parameters were varied
during the ﬁ tting. Selected exemplary results for the
data acquired at T 5 4 K are p resented in Table I
together with the data from X-ray diffraction at room
temperature.
III. RESULTS AND DISCUS SION
A. Syntheses and crystal chemist ry
Phase-pure bixbyite-type vanadium sesquioxide
was successfully obtained as described in the exper-
imental section. Quantitative oxygen analysis of the
here-presented samples resu lted in 31.8 wt% ox ygen,
leading to a composition of V
2
O
2.98
. This res ult is in
fair agreement with the ideal bixbyite stoichiometry.
The grayish-black product was struc turally charac-
terized using X-ray powder diffraction. The results of
the Rietveld re ﬁ nement ar e given in Fig. 2 and
Table II.
The lattice parameter of a 5 939.64(2) pm shows no
signi ﬁ cant deviation (  0.02%) from the one we reported
in our ﬁ rst contribution [939.47(2) pm].
15
Furthermore,
the determined atomic parameters are in good agreement
with the formerly reported ones.
B. Magnetic properties
Th e tem per atur e depe nde nt in ver se su sce pti bil ity
[ v
 1
( T )d a t a ]o fV
2
O
3
, m eas ure d wit h mag net ic ﬂ ux
den sit ies o f 1 and 1 0 kO e (a lmos t iden ti cal te mp er atu re
dep end ence ) is dep icte d in Fi g. 3(a ). Th e ins et of F ig. 3 (a)
sh ows th e low te mper atu re re gim e of a te mp eratu re d e-
pen den t susc epti bil ity m ea su re men t in zero- ﬁ el d-c oole d
(Z FC )/ ﬁ eld-c ooled (FC ) mo de acqu ired wi th a lo w mag -
neti c ﬂ u x den sit y of 100 Oe .
A least-squares ﬁ t of the inverse magnetic susceptibil-
ity data of the 10 kOe measurement in the temperature
range of 100 – 300 K with a modi ﬁ ed Curie – Weiss law
TABLE I. Experimental structural parameters of bixbyite-type V
2
O
3
(obtained from neutron diffraction data at T 5 4 K and X-ray
diffraction data at T 5 298 K). The space group is Ia 
3 (No. 206).
The structural data were modeled for the V1, V2, and O1 ions
occupying the Wyckoff positions 8 a [0, 0, 0], 24 d [ x , 0, 1/4] and
48 e [ x , y , z ]. Numbers in parentheses give estimated standard
deviations in the last signi ﬁ cant digit.
Neutron diffraction @ 4 K a 5 9.3824(2) Å, V 5 825.93(3) Å
3
Atom site x / ay / bz / cB
iso
,Å
2
V1 0 0 0 0.6(4)
V2 0.289(2) 0 1/4 0.6(4)
O1 0.1394(1) 0.1290(2)  0.0963(1) 0.82(2)
l 5 0.4(1) l
B
; R
p
: 1.59%, R
wp
: 2.15%, R
exp
: 0.59%, v
2
: 13.3
X-
ray diffraction @ 298 K a 5 9.3936(2) Å, V 5 828.90(3) Å
3
Atom site x / ay / bz / c
B
iso
,
Å
2
V1 0 0 0 0.80(5)
V2 0.28173(6) 0 1/4 0.95(4)
O1 0.1426(2) 0.1286(3)  0.0952(4) 0.45(4)
R
p
: 1.60%, R
wp
: 2.13%, R
exp
: 1.91%, v
2
: 1.24
D.A. Weber et al.: Physical properties and lattice dynamics of bixbyite- type V
2
O
3
J. Mater. Res., Vol. 32, No. 12, Jun 28, 2017 2399
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v  1 ¼ v 0  1 þ T  h
C
yielded an experimental magnetic moment of l
exp
5
1.72(1) l
B
/vanadium-atom, a Weiss constant of
h
P
5  71.4(5) K and a temperature independent contri-
bution v
0
5 6.49(1)  10
 4
emu/mol, where v
0
takes
into account Van-Vleck and core corrections, as well as
paramagnetic contributions of conduction band electrons.
The experimental magnetic moment corresponds to the
value for a free V
4 1
ion (1.73 l
B
), assuming a spin-only
high-spin state rather than a V
3+
state. The Weiss
constant is indicative of dominating AFM interactions
in the paramagnetic domain. As will be discussed later,
this behavior can be explained by frustration of the
magnetic moments, leading to short-range order.
The N éel t emperat ure T
N
5 38 .1 (5 ) K was d et er min ed
fr om th e ZFC /FC mea sur emen t. As exp ecte d for par a-
mag net ic mat eria ls , the mag ne ti zati on is oth erm s [Fi g. 3(b) ]
ab ove th e obs erv ed ord erin g te mper atu re sho w a li ne ar
in cr eas e with the ap plie d ﬁ e ld. T he 5 K is oth erm ex hib it s
no tende ncy of saturat ion, whi le showing a sma ll hyster-
es is . Fr om th e cou rse of th e FC m ea sur emen t alo ng w it h
th e min ute h ys te res is of th e 5 K mag neti zati on is oth erm
[F ig . 3(b )], a ca nte d, we akl y fer rom agn et ic gro und s tate
has to be ass umed .
The temperature dependence of the speci ﬁ c heat of the
V
2
O
3
sample is presented in Fig. 4. We observe no
anomaly in the temperature window, where magnetic
TABLE II. Numerical results of the Rietveld re ﬁ nement against X-ray
diffraction data at room temperature.
Composition V
2
O
3
Structure type Bixbyite
Space group Ia 
3
Lattice parameter a 5 939.64(2) pm
Formula units 16
Unit cell volume (normalized to
one formula unit)
51.81  10
6
pm
3
Calculated density 4.80 g/cm
3
Diffractometer PANalytical X ’ Pert PRO MPD
Wavelength Cu K
a
[ k
1
5 154.056 pm; k
2
5 154.539
pm; I ( k
2
/ k
1
5 0.5)]
Pro ﬁ le points 8839
2 h range 5 – 120°
R
Bragg
0.021
R
wp
0.021
R
exp
0.019
S (Goodness of ﬁ t) 1.11
FIG. 2. X-ray powder diffract ion diagram of phase-pure bixbyite-type
V
2
O
3
at room temperature with graphical results of the Rietveld
re ﬁ nement.
FIG. 3. (a) Temperature dependent inverse magnetic susceptibilities
of cubic V
2
O
3
measured at magnetic ﬂ ux densities of 1 and 10 kOe.
The inset depicts the low temperature regime of a temperature de-
pendent magnetic susceptibility measurement of the V
2
O
3
sample in
ZFC/FC mode with a magnetic ﬂ ux density of 100 Oe. (b) Magneti-
zation isotherms of cubic V
2
O
3
measured at 5, 50 and 200 K with
magnetic ﬂ ux densities up to 80 kOe.
D.A. Weber et al.: Physical properties and lattice dynamics of bixbyite- type V
2
O
3
J. Mater. Res., Vol. 32, No. 12, Jun 28, 2017 2400
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ordering is evident in the susceptibility data. In view of
the small value of the ordered moment, this is not
surprising (see also the neutron diffraction data below).
Thus, we only ﬁ nd a small value for the entropy change
that is associated with the magnetic ordering process.
This behavior is similar to that observed for Sr
2
IrO
4
.
27
Another important point concerns small degrees of
vacancies or inhomogeneities within the oxygen sub-
structure, which can also hamper long-range ordering due
to both randomness and frustration of magnetic moments.
C. Neutron diffraction stu dies
Th e an aly sis o f th e neu tro n po wd er d iffr act ion d at a at
diff erent t emperat ures r eve aled onl y re ﬂ ec tion s tha t are
ch ar ac ter isti c for a b ody cen ter ed cu bic la ttic e (wea k tra ces
of al umin um fr om th e wal ls of th e cl os ed -cy cl e refri ger ato r
we re pre sent in th e dif fra ctio n pat te rns at al l temp era tur es),
in di cat ing th e iso stru ctu ra li ty of V
2
O
3
wit hin th e who le
stu die d temp era tur e ran ge. D ue to th e low co her ent
sca tte ring le ng th of va na diu m in th e nat ura l is oto pe ble nd,
it s lo cal iza ti on in th e la tt ic e on th e bas is o f n eu tr on d at a is
quite challenging. An attempt to include vanadium i n t o the
re ﬁ nement of the neutron powder diffraction data at room
tempera ture resu l ted in a reduction of the R factors by
approximately 0 .1 – 0.2%. The accuracy of the vanadium
lo cal iza tio n fro m ne utr on an d X- ray d iff ra cti on da ta ca n be
il lus trat ed b y th e x / a fractional coord i nate for the V2 atom:
the neutron diffr action experi ment reveale d x / a 5 0.289(2),
whereas X-ray powder diffraction ena b l ed a d eterminati on
of the V2 position at x / a 5 0.28173(6) (see Table I ), which
demonstrat es an about two orders of magni tude bet ter
resolution for the la tter.
The temperature dependent evolution of the lattice
parameter of cubic V
2
O
3
was determined by Rietveld
analysis of the “ short ” neutron powder diffraction data
sets collected in the temperature range between 4 and
320 K. The resulting thermal dependence of the lattice
parameter was obtained by combining the obtained
results with high-temperature lattice parameters, we
obtained earlier.
15
The results are shown in Fig. 5. Both,
low- and high-temperature data sets were found to be in
good agreement, thus indicating that the structure of
cubic V
2
O
3
is quite stiff to temperature changes, i.e.,
heating from 4 to 850 K resulted in a minor increase of
the lattice parameter by approximately 0.04 Å (  0.4%).
The ﬁ rst order Grüneisen approximation was applied to
interpret the obtained temperature dependence of the
structure of cubic V
2
O
3
. It can be described as
VT ðÞ ¼ V 0 þ c
K T
UT ðÞ ; ð 1 Þ
where V
0
denotes the hypothetical cell volume at zero
temperature, c is the Grüneisen constant, K is the bulk
modulus, and U is the internal energy of the system.
Both, the Grüneisen constant and the bulk modulus are
supposed to be temperature-independent and the Debye
approximation for the internal energy U in Eq. (1) has the
form
UT ðÞ ¼ U D T ðÞ ¼ 9 Nk B T T
h D

3 Z h D = T
0
x 3
e x  1 d x
"#
;
ð 2 Þ
with the characteristic temperature h
D
(Debye tempera-
ture), the number of atoms in the unit cell N and the
Boltzmann constant k
B
, providing a reasonable descrip-
tion for the cell volume, similar to the procedure applied
to data on FeSi.
28
Least-squares nonlinear ﬁ tting of the experimental data
according to Eqs. (1) and (2) resulted in an adequate
description of the lattice parameter of cubic V
2
O
3
by the
ﬁ rst order Grüneisen approximation with V
0
5 825.8 6
0.1 Å
3
, c /K 5 4.4 6 0.1  10
 12
Pa
 1
and h
D
5 350 6
65 K (see Fig. 5). The cubic modi ﬁ cation of V
2
O
3
is
characterized by a relatively low Debye temperature; for
the rhombohedral corundum-type modi ﬁ cation of V
2
O
3
,
a Debye temperature ranging from 575 to 643 K has been
reported.
29
On the other hand, the compound shows
a weak thermal expansion: The thermal expansion co-
ef ﬁ cient calculated as a l T ðÞ ¼
@ ln lT ðÞ
@ T ¼ 1
3
@ ln VT ðÞ
@ T yielded
a
l
; 5.8 K
 1
at the proximity of the phase transition to
the corundum-type phase at approximately 823 K.
15
Besides the weak anharmonicity effects, cubic V
2
O
3
is
known to order magnetically.
15
A previously performed
evaluation of the lattice dimensions versus temperature
revealed no suf ﬁ cient magnetoelastic couplings to
the lattice in V
2
O
3
. Additionally, the inspection of the
“ short ” neutron powder diffraction data sets provided no
FIG. 4. Temperature dependence of the speci ﬁ c heat of cubic V
2
O
3
measured in zero magnetic ﬁ eld.
D.A. Weber et al.: Physical properties and lattice dynamics of bixbyite- type V
2
O
3
J. Mater. Res., Vol. 32, No. 12, Jun 28, 2017 2401
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visible indication for a long range magnetic order below
T
C
. Only a detailed evaluation of the “ long ” diffraction
data sets collected at 4 and 60 K yielded weak additional
neutron intensities on top of the nuclear re ﬂ ections at low
angles (see Fig. 6), which can be an evidence for long
range magnetic ordering, with a magnetic lattice that has
identical metrics as the nuclear one (propagation vector
k 5 [0, 0, 0]).
Bixbyite-t ype V
2
O
3
co mp ris es tw o cry sta llo gra phic al ly
inequi valent vanadium posi tions. A n analysis of the
mag ne ti c rep res en tat io ns wa s per for med by th e Ber taut
method
30
im pl eme nte d in t he B as Irep s s oft war e,
31
re vea l-
in g 8 ir red uci bl e re pre sen ta tio ns th at fo rm a lit tle g rou p G
k
( coi nc id in g w it h t he Ia 
3s y m m e t r ya n dl e a v i n gt h e
pro pa gat ion v ecto r k inv ari an t) . Du e to th e wea k th er mal
expan sion and the weak magnitude of t he observed
mag ne ti c ef fe ct s, th e eva luat ion o f th e mag neti c str uct ur es
wa s pe rfo rmed o n th e d if fer en ti al dif frac tio n patt ern in th e
2 h angular range of 10 – 3 5° . Mag ne tic st ruc ture m odel s
bas ed o n 1D ir red uci ble re pre sen ta tio ns we re c on st ru cte d
i n di ff er ent con ﬁ gur ations, but thei r re ﬁ nement di d not
yield a n adequate description of t he magnetic intensi ties.
3D irre ducible representati ons, on the other hand, apply
fe we r co ns tr aint s to th e or ie ntati on an d mag ni tu de o f th e
magnetic mome nts in bixbyite-type V
2
O
3
.H o w e v e r ,n o
co ns is ten t co ncl us io n abo ut th e mag ne ti c str uct ur e can b e
made fro m the least-squares minimi zation due to conver-
gen ce an d cor re la tio n iss ues , wh ic h can b e rela ted to the
re str icti on s ap pl ied to th e hig hly sy mmet ric la tt ic e re -
gar din g dete rm in at io n of th e mag neti c mom ent o ri enta -
tions f rom powde r di ffraction da ta.
32
To describe the obtained residual intensities, the
iterative approach (assuming a 2D collinear AFM
structure for V
2
O
3
) has been applied. The magnetic
moments for the V
3 1
sites were aligned in 2 states:
either alongside or opposite to the c axis. With 16
formula units in bixbyite-type V
2
O
3
, the number of
possible con ﬁ gurations is limited to 2.
16
An assumption
about the AFM ground state at 4 K (supported by the
magnetization measurements) further reduces the number
of con ﬁ gurations to 12,870. Each con ﬁ guration with
a prede ﬁ ned orientation of the magnetic moments was
evaluated by Rietveld re ﬁ nement, where the amplitude of
the magnetic moments was constrained to be the same for
both V1 and V2, and was allowed to vary.
Due to the low magnitude of the observed effects and,
correspondingly, large ﬁ t residuals, the sum of the
magnetic R factor and v
2
were used as a ﬁ gure of merit
(the use of R
p
and R
wp
does not change the results). Four
con ﬁ gurations (shown in Fig. 7) possessing equal values
for R
m
1 v
2
have been identi ﬁ ed and their accuracy
cannot further be judged on the basis of the present
neutron powder diffraction data (similar models can also
be drawn, assuming an FM direction opposite to the c
axis; indistinguishable by powder diffraction). The mag-
netic moments of the V1 sites have been found to be
oriented ferromagnetically along the c axis, whilst the
moments of the V2 sites are located either alongside or
opposite to the c axis to maintain zero net magnetization.
The amplitude of the magnetic moments was re ﬁ ned to
FIG. 6. Gr a p hi ca l r e s ul t s of t h e R ie t ve l d r e ﬁ nement against neutron
powder diffraction data of bixbyite-type V
2
O
3
at 4 K; cal culated
positions of Bragg re ﬂ ections for th e nuclear and the magnetic
contribution are shown by the top and bottom row of vertical tick
marks. The inset illustrates the low temperature section of the
normalized differential diffr action patterns collected at 4 and
60 K. The red line corresponds to the model for the magnetic
contribution.
FIG. 5. Te m pe ra t ur e ev ol u ti on o f th e l at ti c e pa ra m et e r in cu b ic
V
2
O
3
; neutron data are shown in red, X-ray data
15
in blue color. Th e
scattered lines correspond to the results of data ﬁ tting by Eqs. (1) and
(2); the calculated thermal expansion coef ﬁ cient is sho wn in the
inset.
D.A. Weber et al.: Physical properties and lattice dynamics of bixbyite- type V
2
O
3
J. Mater. Res., Vol. 32, No. 12, Jun 28, 2017 2402
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0.71(3) l
B
, using differential data and 0.4(1) l
B
, using
a completed data set at 4 K. Anyways, these values are
considerably lower than the expected moment for V
3 1
(approximately 2.8 l
B 33
). We already reported some
discrepancies, earlier
15
and associated them with devia-
tions from the V
3 1
state of the vanadium ions, which we
also rendered possible by theoretical calculations.
19
On
the other hand, magnetic interactions may undergo a geo-
metrical frustration in bixbyite-type V
2
O
3
, with the V1
and V2 ions located on the vertices of trigonal and
hexagonal frameworks. One also has to mention that
a constraint of the magnetic moments on V1 and V2 leads
to an AFM lattice with zero net magnetization, whereas
a small discrepancy in the moment amplitudes between
the V1 and V2 magnetic sites (initially permitted by
symmetry) may result in the appearance of a weak
ferromagnetic moment. This is in excellent agreement
with the absence of a lambda type anomaly in the speci ﬁ c
heat data (Fig. 4).
IV. CONCLUSIONS
The magnetic properties of bixbyite-type V
2
O
3
have
been studied and revealed an experimental magnetic
moment of l
exp
5 1.72(1) l
B
/vanadium-atom, which
interestingly corresponds to a free V
4 1
ion (1.73 l
B
),
rather than V
3 1
. The observed Weiss constant of
h
P
5  71.4(5) K is indicative for AFM interactions in
the paramagnetic domain and a canted, weakly AFM
ground state seems to be present. A Néel temperature of
T
N
5 38.1(5) K was determined. Furthermore, only
a very small value for the entropy change during
magnetic ordering is present, most probably because of
randomness and frustration of the magnetic moments,
hampering long-range ordering in the material.
Using high-resolution neutron powder diffraction at
low and intermediate temperatures, isostructurality of
V
2
O
3
has been con ﬁ rmed in the whole temperature range
from 4 to 320 K. The cubic V
2
O
3
is characterized by
a rather low thermal expansion in the whole range of
existence (below 823 K), which can be fairly well
described by a ﬁ rst order Grüneisen approximation. For
the ﬁ rst time, the hypothetical zero Kelvin value for the
cell volume V
0
as well as the temperature independent
c / K ratio and Debye temperature h
D
have been de-
termined to be as large as 825.8 6 0.1 Å
3
, 4.4 6
0.1  10
 12
Pa
 1
, and 350 6 65 K.
Based on the iterative approach, 12,870 different
AFM con ﬁ gurations of the V
3 1
magnetic moment
arrangements adopting z ero net magnetization have
been evaluated u sing Rietveld re ﬁ nements. Based on
the ﬁ t residuals, four possible con ﬁ gurations have been
chosen, where all adopt FM arrangement of the V1
magnetic moments and ferrimagnetic o rder of V2 (with
a weak FM component op posite to that of V1). A weak
ferrimagnetic component in bixbyite-type V
2
O
3
can be
tuned by the discrepancy of the V1 and V2 magnetic
moments and the weak ferromagnetism can be attributed
to the different order temperatures (and, correspond-
ingly, saturation behavior) for t he V1 and V2 mag netic
ions.
Due to the weak magnitude of the ordered moments,
an accurate determination of their arrangement between
different vanadium sites would require neutron diffrac-
tion experiments on single crystals.
ACKNOWLED GMENT
Financial support from the German Research Founda-
tion (DFG) within the priority program SPP 1415
(LE 781/11-2) is gratefully acknowledged. The authors
further gratefully acknowledge the ﬁ nancial support pro-
vided by FRM II to perform the neutron scattering
measurements at the Heinz Maier-Leibnitz Zentrum
(MLZ), Garching, Germany.
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J. Mater. Res., Vol. 32, No. 12, Jun 28, 2017 2404
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