Mechanism of proton conductivity of zeotypes

1. On the mechanism of proton conductivity in H3OSbTeO6
Hans Boysen a
, Martin Lerch b,n
, Felix Fernandez-Alonso c,d
, Matthew Krzystyniak e
,
Zdzislaw T. Lalowicz f
, C. Aris Chatzidimitriou-Dreismann b
, Michael Tovar g
a
Department f¨ur Geo- und Umweltwissenschaften, Sektion Kristallographie, LMU M¨unchen, Am Coulombwall 1, 85748 Garching, Germany
b
Institut f¨ur Chemie, Technische Universit¨at Berlin, Straße des 17, Juni 135, 10623 Berlin, Germany
c
ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom
d
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
e
School of Science and Technology, Nottingham Trent University, NG11 8NS Nottingham, United Kingdom
f
Institute of Nuclear Physics PAS, Radzikowskiego 152, 31-342 Krakow, Poland
g
Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz 1, 14109 Berlin, Germany
a r t i c l e i n f o
Article history:
Received 2 November 2011
Received in revised form
16 January 2012
Accepted 6 February 2012
Available online 17 February 2012
Keywords:
A. Inorganic compounds
A. Oxides
C. Neutron scattering
D. Crystal structure
D. Electrical conductivity
a b s t r a c t
Pyrochlore-type H3OSbTeO6 is a remarkable proton conductor exhibiting an outstanding electrical
conductivity even at ambient temperature. It consists of a three-dimensional interconnected (Sb,Te)O6
framework, built from randomly distributed corner-shared SbO6 and TeO6 octahedra, forming large
cages in which the H3Oþ
ions are located. The dynamics of the caged species has been investigated by
temperature-dependent neutron diffraction, quasielastic neutron scattering, and NMR experiments.
Three types of motion may be discerned, namely, stochastic rotations of the H3O group around its
3-fold axis, jumps between four equivalent positions within the cage, and long-range inter-cage
translational diffusion. The onset of ionic conductivity is clearly reflected by structural changes. Details
of the complex diffusion mechanism are given.
& 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Solids with high proton mobility are of great technical interest
as electrolyte materials in fuel cells working in the temperature
range below 600 K. Today, the commonly used so-called PEM
cells, working below 373 K, are equipped with Nafion-based
polymers. Taking into consideration the problems of such type
of cells, for example their intolerance to impurities, water and
heat management, and their high cost, the search for alternative
fast proton conductors based on inorganic solids is of importance.
It is remarkable that more than 20 years ago, in 1985, Turrillas
et al. [1] reported an antimonic acid-based compound with an
outstanding proton conductivity of $10À2
OÀ1
cmÀ1
under a
saturated water atmosphere. The most promising composition,
H3OSbTeO6, was recently tested in comparison with Nafion as a
potential candidate for fuel cells [2], resulting in a higher proton
conductivity at temperatures above 400 K. The high proton
conductivity of this material can be understood from its crystal
structure. H3OSbTeO6 crystallizes in a cubic defect pyrochlore
type consisting of a three-dimensional interconnected (Sb,Te)O6
framework, built from randomly distributed corner-shared SbO6
and TeO6 octahedra, forming large cages in which the H3Oþ
ions
are located. Structural details are given by Alonso and Turrillas
who carried out a neutron diffraction study at ambient tempera-
ture [3]. As it has been demonstrated for other fast-ion conduc-
tors, e.g. oxides and oxide nitrides [4–8], information about ion
mobility, activation energies, and diffusion pathways can be
obtained from a careful analysis of Debye–Waller factors includ-
ing anharmonic terms, and the corresponding probability density
functions (PDF’s). In this contribution, we present temperature-
dependent neutron diffraction as well as quasielastic neutron
scattering (QENS) spectroscopy on H3OSbTeO6, and deuteron
NMR measurements on D3OSbTeO6. The results concerning the
diffusion mechanism will be also discussed in relation to the
findings of our recent neutron-spectroscopy experiments and
heat capacity measurements reported in Ref. [9].
2. Experimental
Sample preparation: following Alonso and Turrillas [3], H3OSb-
TeO6 was prepared by ion exchange from KSbTeO6 (synthesized
via a solid-state reaction involving K2C2O4, Sb2O3, and TeO2) using
concentrated sulphuric acid (453 K, 12 h). Thereafter, the product
was washed with distilled water. No potassium could be detected
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Journal of Physics and Chemistry of Solids
0022-3697/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jpcs.2012.02.004
n
Correspondence to: Institut f ¨ur Chemie der TU Berlin, Sekr. C2, Straße des 17,
Juni 135, 10623 Berlin, Germany. Tel.: þ49 30 31422603; fax: þ49 30 31479656.
E-mail address: martin.lerch@tu-berlin.de (M. Lerch).
Journal of Physics and Chemistry of Solids 73 (2012) 808–817

2. by X-ray fluorescence spectroscopy after two cycles. The hydro-
gen content was determined by chemical analysis (combustion
method). It was measured to be 0.83(1) wt%, which is exactly the
theoretical value calculated from the chemical formula. Rietveld
refinement of the X-ray powder pattern shows single-phase
(H3O)SbTeO6. For the synthesis of small amounts of D3OSbTeO6,
fully deuterated sulphuric acid and D2O were used.
Neutron diffraction: neutron scattering experiments were
performed at the neutron powder diffractometer E9 (BER II
facility, HZB) using an incident wavelength of 130.782 pm. The
measurements at 50, 300, and 500 K were carried out in a
standard orange cryostat in vacuum. The exposure time for all
three measurements was 2 days. The programme package Full-
Prof [10] was used for initial structural refinements. In the final
ones, JANA2006 [11] was used to include anharmonic terms in the
Debye–Waller factor and to produce PDF maps. Peak profiles were
fitted with a Pseudo-Voigt function, and the background approxi-
mated by Legendre polynomials. The considerable line asymme-
try at low angles was modelled by refining detector and sample
divergences according to Ref. [12]. During the initial refinements,
also the occupancies of O2 and H constituting the hydronium
moiety were varied. While a 1:3 ratio was well kept within error
margins, the overall occupancy was somewhat reduced, in contra-
diction to the stoichiometric ratios obtained from chemical
analysis. However, fixing these occupancies at their nominal
values did not deteriorate the fit quality significantly (the good-
ness of fit was unchanged while Rwp increased by 0.01, see
Table 1). This effect is caused by the (usual) strong correlation
between occupancies and atomic displacement parameters (here-
after ADP’s). It is also seen that the test refinements including
anharmonic terms in the Debye–Waller factor did not improve
the fits significantly, i.e., only anisotropic harmonic terms were
varied in the final refinements. From these ADP’s, or the corre-
sponding Debye–Waller factors, respectively, PDF’s illustrating
time- and space-averaged atomic distributions were calculated
with JANA2006. Assuming independent single-particle motion
governed by Boltzmann statistics, one-particle potentials (OPP’s)
were calculated from these PDF’s by in-house programs (for more
details see e.g. [13]).
Quasielastic neutron scattering (QENS) measurements were
carried out on the OSIRIS spectrometer, ISIS Facility, Rutherford
Appleton Laboratory, United Kingdom. OSIRIS is a high-resolution
low-energy neutron spectrometer operating as a time-of-flight
(TOF) inverted-geometry instrument. Final-energy analysis is
achieved via Bragg diffraction from highly oriented pyrolytic
graphite crystals. The use of pyrolytic graphite affords the
possibility of two analyser reflections, 002 and 004, with analys-
ing energies of 1.845 and 7.375 meV, providing energy resolutions
of 24.5 and 99 meV at full width half maximum (fwhm), respec-
tively. The regions of energy and momentum transfer correspond-
ing to the 002 and 004 reflections are, DE¼ À3–4 meV, q¼0.4–
3.6 ˚AÀ1
, and DE¼ À0.2–1 meV, q¼0.2–1.8 ˚AÀ1
, respectively. For
these experiments, an aluminium cylindrical cell was used to
keep instrumental backgrounds as low as possible. An annulus of
thickness 0.50 mm was chosen in order to minimize excessive
beam attenuation as well as absorption and multiple-scattering
effects. Several temperature scans were performed over the
temperature range T¼4–500 K. For a more detailed description
of the experimental set-up see Ref. [9].
NMR: the NMR experiments were performed with an APOLLO
spectrometer (Techmag, USA), operating with a 7.04 T, 89 mm
superconducting magnet (deuteron resonance frequency
46 MHz). At low temperatures, the NMR probe was placed in
the Oxford CF1200 continuous-flow cryostat, and the temperature
was stabilized by an Oxford CT503 temperature controller. The
temperature accuracy and stability were within 70.1 K over the
whole temperature range.
Spin–lattice relaxation times were measured through the
saturation-recovery method. An aperiodic ten-pulse saturating
sequence was followed by a 2 ms read pulse after a variable time
delay. The amplitude of the magnetization recovered during the
delay was determined by recording the free induction decay (FID).
A satisfactory signal-to-noise (SNR) ratio was achieved by accu-
mulating a number of signals. Typically 25 delays, covering the
Table 1
Refined structural parameters and standard agreement factors for H3OSbTeO6 at 50 K, 300 K, and 500 K.
50 K 300 K 500 K
a/pm 1014.26(3) 1014.71(3) 1015.52(4)
x Sb/Te 1/2 1/2 1/2
y Sb/Te 1/2 1/2 1/2
z Sb/Te 1/2 1/2 1/2
x O1 0.42861(12) 0.42844(13) 0.42885(15)
y O1 1/8 1/8 1/8
z O1 1/8 1/8 1/8
x O2 0.0724(4) 0.0734(8) 0.076(2)
y O2 0.0724(4) 0.0734(8) 0.076(2)
z O2 0.0724(4) 0.0734(8) 0.076(2)
x H 0.0927(5) 0.0947(7) 0.0973(15)
y H 0.0927(5) 0.0947(7) 0.0973(15)
z H À0.0241(7) À0.0215(10) À0.016(2)
Sb/Te U11/U22 0.0003(3)n
0.0022(4)/0.0022(4) 0.0048(4)/0.0048(4)
Sb/Te U22/U12
n
Uiso 0.0022(4)/À0.0002(4) 0.0048(4)/À0.0004(4)
Sb/Te U13/U23 À0.0002(4)/À0.0002(4) À0.0004(4)/À0.0004(4)
O1 U11/U22 0.0039(5)/0.0029(3) 0.0072(6)/0.0065(4) 0.0121(7)/0.0122(5)
O1 U33/U12 0.0029(3)/0 0.0065(4)/0 0.0122(5)/0
O1 U13/U23 0/À0.0019(4) 0/À0.0042(5) 0/À0.0062(6)
O2 U11/U22 0.0143(12)/0.0143(12) 0.033(2)/0.033(2) 0.077(8)/0.077(8)
O2 U33/U12 0.0143(12)/0.0006(14) 0.033(2)/0.012(3) 0.077(8)/0.031(8)
O2 U13/U23 0.0006(14)/0.0006(14) 0.012(3)/0.012(3) 0.031(8)/0.031(8)
H U11/U22 0.031(3)/0.031(3) 0.031(3)/0.031(3) 0.061(9)/0.061(9)
H U33/U12 0.024(5)/0.004(3) 0.071(9)/0.001(3) 0.32(3)/0.005(9)
H U13/U23 0.007(2)/0.007(2) 0.004(3)/0.004(3) À0.035(12)/À0.035(12)
Rwp 2.39 2.32 2.64
RBragg 2.56 2.81 3.27
GOF 1.28 1.30 1.20
H. Boysen et al. / Journal of Physics and Chemistry of Solids 73 (2012) 808–817 809

3. range from 0 to about 3T1, were used to determine the magne-
tization recovery. An additional data point was measured at times
longer than 5T1, in order to determine precisely the equilibrium
magnetization. This approach was found to improve the accuracy
of the three-parameter single exponential fit to the data.
3. Results
3.1. Crystal structure
Temperature-dependent neutron diffraction experiments were
carried out at 50 K, 300 K, and 500 K using $6 g of H3OSbTeO6
powder exhibiting good crystallinity. In spite of the large
incoherent scattering caused by the presence of H atoms, the
obtained diffraction patterns are of sufficient quality. Fig. 1
depicts the powder patterns for all investigated temperatures
together with the fits of the Rietveld refinements; in Table 1, the
final refined structural parameters are presented together with
the main agreement factors reflecting the quality of the fits. First
of all, it can be stated that the structural model given by Alonso
and Turrillas [3] was confirmed and not that of Pontonnier et al.
[14], in particular the existence of an almost regular hydronium
ion. At 50, 300, and 500 K H3OSbTeO6 crystallizes in a defect-
pyrochlore structure (space group Fd3¯m). The main basic building
unit can be described as a large cage surrounded by 16 corner-
shared (Sb,Te)(O1)6 octahedra (Fig. 2). It is centred at the 8a
position possessing local tetrahedral symmetry. Inside this cage
(diameter larger than 6 ˚A), one hydronium ion is located, statis-
tically occupying one of four possible positions. In Fig. 2, all of
these positions are depicted. However, for reasons of clarity, in all
the following figures only a single position for the hydronium
(H3(O2)þ
) ion will be shown. The hydronium ions are located
near the large windows ($5 ˚A in diameter), which is suggestive of
long-range inter-cage translational diffusion. These windows are
formed by a puckered ring of 6 octahedra centred at the
centrosymmetric 16c position (see Fig. 2). Hydronium ions above
and below this ring are rotated by 601 with O2 directed opposite
to each other towards the 8a cage centres. The H atoms point to
the nearest O1 atoms forming hydrogen bonds. From these
structural features, it is evident that two types of ion mobility
must be distinguished: mobility within one particular cage and
long-range diffusion between the cages. The latter diffusion
process is an indispensable prerequisite for significant macro-
scopic ionic conductivity, either through motions of Hþ
ions
alone, Hþ
and O2À
separately, or complete H3Oþ
ions.
Lattice constants show a non-linear increase with temperature
(Fig. 3a) signalling some structural anomalies, possibly connected
with the onset of ionic conduction around 300 K. While the only
free structural parameter of the framework atoms x(O1) stays
roughly constant or slightly increases with temperature within
the error bars, those of hydronium x(O2), x(H), and z(H) show a
similar behaviour as the lattice constant, i.e. a stronger increase at
the highest temperature investigated, namely, 500 K. Although
the error bars are quite large, some trends may be appreciated
from the behaviour of the various bond lengths and angles. The
Sb/Te–O1 bond length and the Sb/Te–O1–Sb/Te bond angle both
increase in such a way that the overall thermal expansion is
governed first by a volume increase and then by the rotation of
the octahedra. The latter process leads to an initially constant
Fig. 1. Neutron powder-diffraction patterns for H3OSbTeO6 at three different
temperatures together with the results of the Rietveld refinements.
Fig. 2. Left: basic building unit, consisting of 16 corner-shared (Sb,Te)O6 octahe-
dra. All four possible positions for the H3Oþ
ion are depicted (yellow: Sb/Te, red:
O1, blue: O2, green: H). Right: ring of 6 octahedra forming the ‘‘window’’ for
hydronium ion diffusion. Two adjacent hydronium ions are shown, dark/light
colours denoting locations above/below the plane of the figure. View slightly off
the [111] direction. (For interpretation of the references to colour in this figure
legend, the reader is referred to the web version of this article.)
H. Boysen et al. / Journal of Physics and Chemistry of Solids 73 (2012) 808–817810

4. opening of the window followed by a significant increase at 500 K
(Fig. 3b). The H–O2–H angle of hydronium stays roughly constant,
while the O2–H distance decreases slightly and the O1–H distance
increases considerably. The O1..H-O2 bond angle involving the
O1..H hydrogen bond is perfectly linear at 50 K but decreases by
about 31 at 500 K. In summary, these results imply that hydro-
nium ions move away from the window centred at the 16c
position (Fig. 3c), or, in other words, they go nearer to the cage
centre at 8a. This behaviour is consistent with the onset of
localized diffusion above 300 K seen in the QENS data as
explained in more detail below. The ions executing jumps across
intra-cage sites lead to an average density of H3Oþ
ions nearer to
the centre of the cage, as determined from the Bragg intensities.
First hints of static and dynamic disorder may be obtained from
the (equivalent) isotropic ADP’s Uiso (Fig. 4). All of them show an
upward bend at 300 K which is most pronounced for O2 and H.
The latter clearly indicate the high mobility of hydronium at
500 K. The contribution of static disorder may be derived in
principle via extrapolation to 0 K. Although this is difficult with
only three points, it may be clearly appreciated that only Uiso(Sb/Te)
tends to zero at 0 K, i.e. there is practically no static contribution,
while O2 and H show a strong static disorder component at least
at low temperatures. The slight positive value for O1 can be
understood as a secondary effect of hydronium disorder, since the
O1 positions may depend on whether the nearest hydrogen
position is occupied or not to form hydrogen bonds. More
information can be obtained from a detailed analysis of the
anisotropic ADP’s.
3.2. ADP analysis
As mentioned in the introduction, information on diffusion
pathways and activation energies can be obtained via a careful
analysis of the refined ADP’s. In a first step, the cage-type basic
building unit of H3OSbTeO6 is shown for all investigated tem-
peratures (Fig. 5), where ADP’s are reflected in terms of the size
and shape of the depicted atoms. At 50 K, they are mainly
governed by static disorder. At 300 K and, particularly at 500 K,
where good proton conductivity is known from impedance
spectroscopy [1,2], strong elongations are observed for both H
and O2. It is remarkable that the elongation of the H atoms points
towards the nearest O1 atoms of the window, which may be
interpreted as a clue to the diffusion pathway (see below).
Interestingly, also the O atoms of the hydronium ions (O2) show
strong elongations in the direction of the window which may also
be considered as a first indication of long-range inter-cage
diffusion or hopping of whole hydronium ions as opposed to
individual protons.
As long as the ADP’s or the corresponding PDF’s are mainly
governed by individual diffusing particles, OPP’s governing the
diffusion behaviour can be deduced. In these potential landscapes,
the valleys represent the diffusion pathways and the saddle
points the barriers to migration, which can be compared with
otherwise determined activation energies. Figs. 6–8 show these
OPP’s for H and O2 for all temperatures. In addition, Fig. 8b shows
the corresponding PDF’s in order to illustrate the sections chosen.
In both cases, the centre of the picture coincides with that of the
‘window’ alluded to earlier in our discussion. For H, the section
includes 4 H atoms on both sides of the ring (which is vertical
here), cf. Fig. 2. Note that the densities from adjacent hydronium
ions within the cages are visible. These, however, lie not exactly
on this plane. Two types of saddle points can be discerned: those
between hydrogen above and below the window and those
between hydrogens within the cage. The former (Eal) is related
to long-range diffusion, the latter (Eas) to rattling motions within
the cage. The analysis gives Eal ¼60, 350, and 400 meV, and
Eas¼10, 60, and 40 meV for 50, 300, and 500 K, respectively. It
should be emphasized that these values are very rough estimates,
since at low temperatures the densities at the migration barriers
are still rather low. In fact, the associated error bars can only
provide an order of magnitude for activation energies and
associated diffusion pathways. The much lower values at 50 K
are typical artefacts and can be taken as yet another indication of
the dominance of static disorder [13]. The O2 PDF’s and OPP’s are
shown in sections perpendicular to the xxz-plane containing two
atoms above and below the ring (which is inclined here) and two
further ones within each cage. Note that the local diffusion
pathway along [111] is also imposed by symmetry, which allows
Fig. 3. Temperature variation of lattice constant (a), window opening (b), and
distances of O2 (squares) and H (circles) from the window centre at 16c (c).
H. Boysen et al. / Journal of Physics and Chemistry of Solids 73 (2012) 808–817 811

5. elongation of the ellipsoids only along the 3-fold axis. Here the
activation energies may be estimated as Eal¼200, 350, and
250 meV and Eas¼60, 120, and 50 meV for 50, 300, and 500 K,
respectively.
3.3. Quasielastic neutron scattering
In order to identify the different types of motion responsible
for the onset of proton conduction, previous studies have exam-
ined the dependence of QENS spectra on sample temperature up
to T¼500 K [9]. As reported in Ref. [9], two distinct motional
regimes characterised by momentum-transfer-independent spec-
tral widths (i.e. localised diffusion) were discernable, namely: a
high-temperature regime characterized by an attempt frequency
of 0.49 psÀ1
and activation energy EA ¼7977 meV, and a low-
temperature regime with an attempt frequency of 0.07 psÀ1
and
activation energy EA ¼21714 meV. Contrary to naı¨ve expecta-
tion, these QENS experiments found no evidence for inter- or
intra-cage translational diffusion of the H3O ion in the pyrochlore
lattice over timescales in the range 0.5–50 ps.
In order to provide additional insight into the nature of
diffusive motions above room temperature, further analysis of
the QENS data in the high-temperature regime has been per-
formed. Fig. 9 shows QENS data measured at T¼458 K as a
function of momentum transfer. These data are adequately
described by the presence of a strong resolution-limited elastic
mode and a single (Lorentzian) QENS mode. Following the same
procedure as in Refs. [15–17] integrated elastic and quasielastic
intensities (hereafter ‘‘form factors’’) have been fitted to a model
for stochastic proton jumps across three distinct sites [18], as
reported in Fig. 10. The characteristic 3-fold-symmetric jump
diffusion length scale obtained from the fits of the elastic and
quasielastic form factors is 0.8670.02 ˚A and 0.8770.02 ˚A,
respectively. These values are in excellent agreement with the
trigonal geometry of the hydronium ion, characterised by a H–H
bond length of 1.67 ˚A, and a distance between hydrogens and the
3-fold rotation axis equal to 0.96 ˚A (see the inset in Fig. 10). These
findings confirm that H3Oþ
ions are allowed to execute random
rotational jumps about a fixed point, leading to no net translation
of the hydronium ion as a whole within the cage. Inter-cage
proton diffusion must therefore involve a small fraction of the
total H3O-ion population, as well as cooperativity between pro-
ton-accepting and donating species across neighbouring cages.
3.4. NMR
The deuteron NMR spectra recorded for D3OSbTeO6 at
T¼240 K and T¼295 K are shown in Fig. 11. The spectra at both
temperatures adopt simple Gaussian profiles with standard
deviations of 2470750 Hz and 2135731 Hz, respectively. This
result implies that deuterons in the caged D3Oþ
ion perform very
fast stochastic motions with the effective rate given by the
inverse of their effective correlation time, 1/tc, a value much
larger than both the Larmor frequency, o, and the quadrupolar
coupling constant, w. This disparity in frequency scales leads to
the complete averaging of quadrupolar line shapes with both
spin-spin and spin–lattice relaxation lying in the so-called
‘‘extreme narrowing regime’’, o2
tc
2
51.
The Arrhenius plot of deuteron spin–lattice relaxation rates in
D3OSbTeO6 in the temperature region between 200 and 300 K is
Fig. 4. Temperature variation of (equivalent) isotropic atomic displacement parameters, those of Sb/Te and O2 enlarged on different scale for clarity.
Fig. 5. Basic building unit of H3OSbTeO6 at three different temperatures. The
refined ADP’s are reflected by the size and shape of the atoms (yellow: Sb/Te, red:
O1, blue: O2, green: H). (For interpretation of the references to colour in this figure
legend, the reader is referred to the web version of this article.)
H. Boysen et al. / Journal of Physics and Chemistry of Solids 73 (2012) 808–817812

6. shown in Fig. 12. It corresponds to the high temperature side of
the relaxation rate maximum, appearing at a temperature where
otc¼0.616, which gives another indication that the extreme
narrowing condition is fulfilled. The activation energy fitted from
the slope of these data amounts to 93712 meV. This energy scale
has to be compared with the dominant spectral features asso-
ciated with the H3Oþ
ion in the inelastic (INS) and quasielastic
(QENS) neutron scattering spectrum of H3OSbTeO6 recorded
between 200 and 300 K [9]. In the INS data, two distinct spectral
regions were clearly distinguishable: a band at 20 meV due to
longitudinal vibrational motions of the entire H3Oþ
ion, and a
librational band at 80 meV attributable to hindered rotations
owing to the crystal field imposed by the lattice. The energies of
these two modes also coincided with the activation energies
derived from the QENS measurements, suggesting that localized
diffusion of the H3Oþ
ion is first activated by longitudinal lattice
modes, to be then followed by rocking motions at higher tem-
peratures [9]. The activation energy calculated from the Arrhenius
plot of the spin–lattice relaxation, 93712 meV, agrees very well
with the vibrational mode at 80 meV in the INS spectrum,
corresponding to hindered rotations of the H3Oþ
ion. As evi-
denced by the QENS data, this motion is responsible for diffusive
motions of the hydronium ion in the temperature range between
200 and 300 K. Thus, the dominant NMR relaxation mechanism
visible in the deuteron spin–lattice relaxation of D3OSbTeO6 in
this temperature region corresponds to hindered rotations of the
hydronium ion.
Information on the shape of the effective potential, responsible
for the rotational diffusion of the H3Oþ
ion, responsible for the
NMR relaxation response between 200 and 300 K can be gained
from an analysis of the effective quadrupolar coupling constant of
deuterons in D3OSbTeO6. In the case of the dominant spin–lattice
relaxation mechanism being caused by stochastic jumps, the spin
lattice relaxation rate, 1/T1, is given by [19]:
1
T1
¼ K
tc
1þo2tc
2
þ
4tc
1þ4o2tc
2
tc ¼ t0 exp
Ea
RT
where tc is the correlation time for the motion, t0 is its value at
infinite temperature, and o is the Larmor precession frequency. In
addition, Ea is the activation energy for the motion influencing T1,
and K depends on the square of the strength of the dominant
nuclear-spin interaction (in this case the square of the quadru-
polar coupling constant, w2
, in units of sÀ2
) and the exact nature
of the reorientational motion [20,21].
Fig. 6. OPP of H (left) and O (right) at 50 K. Contour lines are in steps of 50 meV starting at 1 meV to mark the average atom position by a small circle.
Fig. 7. OPP of H (left) and O (right) at 300 K. Contour lines as in Fig. 6.
H. Boysen et al. / Journal of Physics and Chemistry of Solids 73 (2012) 808–817 813

7. In the extreme narrowing case of fast stochastic jumps,
o2
tc
2
51, the equation above simplifies to:
1
T1
¼ 5Kt0exp
Ea
RT
log
1
T1
¼ logð5Kt0Þþ
Ea
RT
The multiaxial N-fold rotations of a trigonal ion, discussed in detail
in Refs. [20,21], provide a good model of D3Oþ
ions isotropic
reorientation at 300 K. From Eq. (17) in [21] we get K¼3/10 p2
w2
.
The above formula for K assumes no distortion of the D3Oþ
ion. The
quadrupole coupling constant also depends on the length of the X–D
bond. As an example, ND4
þ
ions exhibit w¼180 kHz [21].
The linear fit to Arrhenius plot of the spin–lattice relaxation
rates in Fig. 11 yields an y-intercept of 0.3770.05 sÀ1
. Substitut-
ing the value of the attempt frequency obtained for the librational
mode of the hydronium ion at 80 meV, obtained from the QENS
data [9], 1/t0 ¼0.49 psÀ1
in the relation 0.3770.05¼log(5Kt0)
with K¼3/10 p2
w2
yields a value of the quadrupolar coupling
constant for the hydronium ion, w¼22176 kHz.
In order to gain further insight into the nature of the motion of the
hydronium ion in H3OSbTeO6, one has to analyse different degrees of
line-shape averaging of the deuteron NMR signals which depend on
the rate of reorientation and the orientation of the principal axis of
the electric-field-gradient tensor relative to the rotation axis. To this
end, the obtained value of w can be compared with values obtained
from a deuteron NMR study of oxonium perchlorate by Ratcliffe [22].
The measurements on oxonium perchlorate were conducted down to
the temperature of 110 K where static NMR lines were observed.
A transition from isotropic to the 3-fold rotation was observed at
245 K. Above the transition into phase I close to room temperature,
line shapes consisted of a sharp feature (indicating isotropic D3Oþ
motions) riding on a second and much-broader dominant component.
This complex anisotropic behaviour is typical of samples where the
crystallite orientations are not distributed completely at random. As a
consequence of different averaging mechanisms, all of the observed
phases were characterised by different effective values of quadrupolar
coupling constants, namely: static motions below 110 K (w¼169.4
kHz), rotations about the 3-fold symmetry axis between 110 K and
254 K (w¼74.7 kHz), and a complex anisotropic motional regime
above 254 K (w¼21.77 kHz) [22]. In this context, our result (w¼
22176 kHz) seems to be indicating the presence of rotations about
the 3-fold symmetry axis between 200 and 300 K. However, our
deuteron line shapes obtained in this temperature region are purely
Gaussian, thus pointing at isotropic rotations. The only possible way
to reconcile these two seemingly contradicting motional scenarios is
to postulate an additional averaging mechanism. A clue for such
mechanism is provided by the diffraction data showing that a given
hydronium ion statistically occupies one out of four possible positions
inside the cage. In this scenario, jumps between these four possible
sites lead to an effective averaging of the 3-fold rotation-induced
NMR line shapes. Such additional motional averaging process has
been reported previously in the case of onium salts [23]. Also, a recent
NMR study by Soler et al. [2] indicated that intramolecular spin–spin
interactions present in H3Oþ
are considerably reduced as a conse-
quence of local mobility of these groups. Moreover, this proposed
motional-averaging model is consistent with our QENS data in that
we observe no net displacement of the centre of mass of the
Fig. 8. (a) OPP of H (left) and O (right) at 500 K. Contour lines as in Fig. 6 and (b) PDF of H (left) and O (right) at 500 K.
H. Boysen et al. / Journal of Physics and Chemistry of Solids 73 (2012) 808–817814

8. hydronium ion. Notwithstanding the above, and on the basis of
results for oxonium perchlorate, one cannot exclude rotations about
the 3-fold symmetry axis of the hydronium ion as the dominant
diffusive mechanism in H3OSbTeO6 at temperatures below 200 K.
4. Discussion
On the basis of our structural and spectroscopic results, three
types of motion of the hydronium ion in H3OSbTeO6 may be
discerned, namely: rotations around its 3-fold axis at a given
crystallographic site, jumps between four equivalent positions
within the cage and long-range intra-cage translational diffusion.
The former two may be discerned from the spectroscopic mea-
surements, but are not easily separated from a PDF analysis.
Remarkably, however, the order of magnitude of the correspond-
ing activation energies is in good agreement with the QENS and
NMR results, therewith confirming the analysis as well as the
physical picture that emerges from our experimental data. The
static disorder at 50 K, derived from the temperature dependence
of the Uiso’s (Fig. 4), is also apparent from the extreme smearing of
the PDF’s (Fig. 6), in particular the circular appearance of O2. This
is confirmed by the fact that QENS was not observed at 50 K.
The onset of diffusion is suggested by the strong elongation of
the O2-PDF along the [111] direction at higher temperatures. The
roughly equal activation energies of O2 and H seem to point
towards long-range translational diffusion of the molecule
as a whole (see, however, below). Moreover, their value is in
Fig. 9. QENS data as a function of momentum transfer Q measured at a sample
temperature of T¼458 K. The red solid line corresponds to a fit using an elastic
(resolution-limited) component plus a Lorentzian mode. For reference, the
instrumental resolution is shown in blue. Further details of the procedure
followed for the analysis of QENS spectra may be found in Refs. [9,15–17].
(a) Q¼0.8 ˚AÀ1
, (b) Q¼1.4 ˚AÀ1
and (c) Q¼1.8 ˚AÀ1
.
Fig. 10. Elastic and QENS form factors obtained from the data shown in Fig. 9. The
fit (solid line) corresponds to the form factor associated with stochastic proton
jumps across three equivalent sites (see equations in the figure and discussion in
the main text). The regions around 1.0 ˚AÀ1
and 1.7 ˚AÀ1
are affected by unavoid-
able coherent (Bragg) scattering from the material and have been omitted in the
analysis of these data.
Fig. 11. 2
H NMR spectra of D3OSbTeO6 acquired at T¼240 K (bottom trace) and
T¼295 K (top trace). The motional averaging of spectral data is clearly visible at
both temperatures.
H. Boysen et al. / Journal of Physics and Chemistry of Solids 73 (2012) 808–817 815

9. reasonable agreement with that of macroscopic conductivity mea-
surements (440 meV [1]) therewith confirming also this analysis.
However, a simple translational migration is not possible on geome-
trical grounds, since adjacent molecules are related by an inversion
centre. The H atom group has to rotate by 601 and O2 has to tunnel to
the opposite side (Fig. 2). In other words, the breaking of the O2–H
bond appears to be a prerequisite for diffusion.
A simple comparison of the activation energy for proton
motion deduced from spin–lattice relaxation measurements and
the one identified from the results of the analysis of INS and QENS
data on H3OSbTeO6 reveals the character and associated
timescales with diffusive proton motions ultimately responsible
for the observed NMR relaxation phenomena. As suggested by our
previous QENS and INS study on H3OSbTeO6, localized diffusion of
the H3Oþ
ion is first activated by longitudinal lattice modes, to be
then followed by rocking motions at higher temperatures in the
presence of hopping between four equivalent positions within the
cage [9].
On the basis of the present experimental results, the following
tentative scenario for the long-range diffusion process is con-
ceivable (cf. Fig. 13). First, starting with H3O attached to the
‘window’ by hydrogen bonds to the O1’s pointing into its cage, the
short distance in the O2-H..O1 hydrogen bond is transferred to
these O1’s forming O2..H-O1, i.e. O2 donates its protons to O1.
Then O2 may jump to the adjacent cage over a distance of about
2.6 ˚A, a ‘‘normal’’ jump distance as found in other oxygen ionic
conductors. This process is followed by H transfer into the next
cage by moving to the other neighbouring O1’s on the opposite
side of the 6-fold ring. Finally, the H3Oþ
ion is recovered in the
new cage after the O1’s have donated their H’s back to O2. This
view is supported by the fact that the H ellipsoids are elongated
towards the adjacent O1 atoms (Figs. 2 and 3) and not directly
towards the next cage or the target H within it. Note that the
direction of this elongation is not imposed by symmetry as it was
the case for O2. Similarly, the distance from O1 to the barrier is
equal to that of the long O1..H bond and the whole process must
proceed in a concerted manner involving all three H and O2 ions.
The strong increase of ionic conductivity is also supported by
the large increase of the opening of the cage windows (Fig. 3b). In
summary, we have a changeover from static disorder to dynamic
disorder somewhere around 300 K, as evidenced by the QENS
data. This changeover is also accompanied by a redistribution of
the overall proton kinetic energy in the hydronium moieties as a
result of the switchover from these being solely associated with
localised bound states to becoming unbound non-local states
undergoing long-range translational diffusion/proton conduction,
as evidenced by a marked decrease in specific heat above room
temperature [9].
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Fig. 12. Arrhenius plot of the deuteron spin–lattice relaxation rate in D3OSbTeO6.
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