Dynamics of anions and cations in cesium hydrogensulfide (CsHS, CsDS): Neutron and x-ray diffraction, calorimetry and proton NMR investigations

Article abstract of DOI:10.1063/1.1479141

Structure and dynamics of CsHS and CsDS compounds were studied using neutron diffraction, solid state ¹-nuclear magnetic resonance, and calorimetric investigations in a wide temperature range. Large-amplitude liberations of DS^- were

Full text of DOI:10.1063/1.1479141

Dynamics of anions and cations in cesium hydrogensulfide (CsHS, CsDS): Neutron and
x-ray diffraction, calorimetry and proton NMR investigations
F. Haarmann, H. Jacobs, W. Kockelmann, J. Senker, P. Müller, C. A. Kennedy, R. A. Marriott, L. Qiu, and M. A.
White
Citation: The Journal of Chemical Physics 117, 4961 (2002); doi: 10.1063/1.1479141
View online: http://dx.doi.org/10.1063/1.1479141
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 117, NUMBER 10
8 SEPTEMBER 2002
Dynamics of anions and cations in cesium hydrogensulfide
„CsHS, CsDS…: Neutron and x-ray diffraction, calorimetry
and proton NMR investigations
F. Haarmanna) and H. Jacobsb)
¨
Fachbereich Chemie der Universitat, AC I, D-44221 Dortmund, Germany
W. Kockelmann
¨
Mineralogisch-Petrologisches Institut der Universitat, D-53115 Bonn, Germany c/o ISIS, Rutherford
Appleton Laboratory, Chilton OX11 0QX, United Kingdom
J. Senker
¨
¨
¨
Department Chemie der LMU, Lehrstuhl fur Anorganische Festkorperchemie, D-81377 Munchen, Germany
¨
P. Muller
¨
Institut fur Anorganische Chemie der RWTH, D-52056 Aachen, Germany
C. A. Kennedy, R. A. Marriott, L. Qiu, and M. A. White
Department of Chemistry, Dalhouse University, Halifax, Nova Scotia B3H 4J3, Canada
͑Received 21 February 2002; accepted 26 March 2002͒
Protonated and deuterated samples of the hydrogensulfide of cesium were studied by high-resolution
neutron powder diffraction, calorimetry and proton NMR investigations in a wide temperature
range. Primarily due to reorientational disorder of the anions, three modifications of the title
compounds are known: an ordered low-temperature modification—LTM ͑tetragonal, I4/m, Zϭ8͒, a
dynamically disordered middle-temperature modification—MTM ͑tetragonal, P4/mbm, Zϭ2͒, and
¯
a high-temperature modification—HTM ͑cubic, Pm3m, Zϭ1͒. The LTMꢀMTM phase transition
is continuous. Its order parameter, related to an order/disorder and to a displacive part of the phase
transition, coupled bilinearly, follows a critical law. The critical temperature TCϭ123.2Ϯ0.5 K
determined by neutron diffraction of CsDS is in good agreement with TCϭ121Ϯ2 K obtained by
calorimetric investigations. For the protonated title compound a shift to TCϭ129Ϯ2 K was
observed by calorimetric measurements. The entropy change of this transition is (0.24Ϯ0.04) R and
(0.27Ϯ0.04) R for CsHS and CsDS, respectively. The MTMꢀHTM phase transition is clearly of
first order. The transition temperatures of CsHS and CsDS are Tϭ207.9Ϯ0.3 K and Tϭ213.6
Ϯ0.3 K with entropy changes of (0.86Ϯ0.01) R and (0.81Ϯ0.01) R, respectively. Second moments
(M2) of the proton NMR absorption signal of MTM and HTM are in reasonable agreement with M2
calculated for the known crystal structures. A minimum in spin-lattice relaxation times (T1) in the
MTM could not be assigned by dipolar coupling to a two-site 180° reorientation of the anions, a
model of motion presumed by the knowledge of the crystal structure. The activation enthalpies
determined by fits of T1 presuming a thermal activated process are in the order of molecular
reorientations ͑Eaϭ13.5Ϯ0.5 kJ molϪ1 for the MTM and Eaϭ9.3Ϯ0.3 kJ molϪ1 for the HTM͒. In
the HTM at TϾ330 K translational motion of the cations determines T1 (Eaϭ13.8
Ϯ0.4 kJ molϪ1). © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1479141͔
I. INTRODUCTION
namics of the molecules or ions. In the case of ionic com-
pounds, the coordination potential often determines the mo-
tion of the ions.
The polymorphism of compounds is often linked to re-
orientational disorder of molecules or polyatomic ions. These
may be asymmetric charged ions (OHϪ,HSϪ,CNϪ), mol-
ecules (NH3 ,H2O) or molecules with a symmetric charge
distribution (N2 ,C22Ϫ). Many properties such as moment of
inertia, point symmetry, charge distribution, or the symmetry
and the strength of coordination potential influence the dy-
The alkali metal hydrogensulfides (MϩHSϪ/DSϪ) are
an ideal model system to study the influence of the cationic
potential on the motion of the anions. Three modifications
are known at ambient pressure for each of MHS with M
ϭNa, K, Rb, Cs.1,2 ͑The lithium compound3 is an exception
in the alkali metal hydrogensulfides and we did not include it
into our investigations.͒ The anions are antiferroelectrically
ordered in the low-temperature modifications ͑LTM͒ and
two-site 180° reorientations of the anions are observed in the
middle-temperature modifications ͑MTM͒. The cubic sym-
a͒
¨
Present address: Max-Planck Institut fur Chemische Physik fester Stoffe,
¨
Nothnitzer Str. 40, 01187 Dresden, Germany.
b͒
¨
¨
Lehrstuhl fur Anorganische Chemie I der Universitat, 44221 Dortmund,
Germany; electronic mail: Jacobs@pop.uni-dortmund.de
0021-9606/2002/117(10)/4961/12/$19.00
4961
© 2002 American Institute of Physics
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4962
J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Haarmann et al.
metry of the high-temperature modifications ͑HTM͒ is
achieved by nearly free reorientation of the anions, highly
influenced by the coordination potential. This is determined
in first approximation by the cations. The three modifications
of MHS with MϭNa, K, Rb are isostructural for the differ-
ent cations and related to the NaCl-type structure.1 In con-
trast, the structures of CsHS are related to the CsCl-type
structure.2 No significant differences between protonated and
deuterated hydrogensulfides of the alkali metals, besides a
shift of the vibrational modes and the temperatures of the
phase transitions, have been detected.
because they decompose on reaction with moisture. They
were characterized by x-ray diffraction, IR, Raman, and DSC
measurements to check for the presence of impurities. The
amount of hydrogen in the deuterated sample was deter-
mined by NMR measurements to be H/DϽ1%.
B. Diffraction
Neutron powder diffraction experiments were done at
the time-of-flight ͑TOF͒ diffractometer ROTAX23,24 at the
pulsed spallation source ISIS, UK. With respect to the small
scattering length of sulphur and the magnitude of the ex-
pected thermal motion of the ions, we increased the size of
the sample to get satisfactory counting statistics within an
acceptable time. About 15 g of CsDS was placed into a cy-
lindrical vanadium container (␾ϭ12 mm), which was
sealed with a gold gasket. To obtain the measurement tem-
perature, 4 KрTр400 K, we used a ‘‘cryofurnace’’ device
(␾ϭ70 mm) equipped with vanadium windows. The tem-
perature was determined by a thermocouple mounted on the
sample holder close to the sample. Vanadium has a very
small coherent neutron scattering length. Therefore it pro-
duces negligible Bragg reflections, but the background radia-
tion is increased by incoherent scattering. Two diffraction
patterns, one in forward and one in backward scattering ge-
ometry, were detected simultaneously. The diffraction pat-
terns were concurrently analyzed with the Rietveld refine-
ment package GSAS.25 We payed no attention to the small
amount of hydrogen in our refinements by reducing the scat-
tering length used for the deuterium sites to the weighted
average of both isotopes. An empirical correction for absorp-
tion, which is primarily due to the absorption of cesium and
vanadium, was used. To reduce the influence of correlation
between thermal displacement parameters and absorption,
the absorption coefficients were determined by simultaneous
refinement of patterns obtained in the various modifications.
The resultant coefficients were used for the analysis of all
datasets.
The alkali metal hydrogensulfides have been investi-
gated in the past by x-ray and neutron diffraction to study
their crystal structures.1–5 The dynamics of the anions were
analyzed by the use of IR/Raman spectroscopy,6–9 inelastic
and quasielastic neutron scattering,10–12 and NMR,13–16 but
no systematic study of MHS with MϭNa, K, Rb, Cs to
characterize the influence of symmetry and strength of the
coordination potential on the dynamics of the anions has
been presented. This paper is a part of a series17–20 focusing
on the structure and the dynamics in these compounds. We
used powder17 and single crystal19 neutron diffraction, quasi-
20
elastic neutron scattering,18 and H-NMR to study the hy-
drogensulfides of sodium, potassium, and rubidium. In this
paper we present results regarding the hydrogensulfide of
cesium, including neutron and x-ray diffraction, calorimetric
investigations, second moments (M2) of the NMR proton
absorption signal and the NMR spin-lattice relaxation times
(T1) of the protons.
1
In addition to our main interest to characterize the reori-
entational dynamics of the anions in the hydrogensulfides of
the alkali metals, we investigated the mechanism of the
LTMꢀMTM phase transition, because IR/Raman spectro-
scopic investigations8 indicated a continuous transition, but
no quantitative microscopic model could be drawn from
these data. Furthermore, we focus on understanding the
change of reorientational motion of the anions with tempera-
ture in the HTM, which was indicated by an IR/Raman spec-
troscopic study.8
The structure factors were extracted from the datasets
with the GSAS package of programs. Standard Fourier syn-
In addition, CsHS and CsDS are the only hydrogensul-
fides of the alkali metals stabilized by hydrogen bonds.8
Therefore the influence of hydrogen bonding on dynamics
and structure was also of interest.
`
thesis and Fourier synthesis using Cesaro sums to reduce
series cutoff effects were executed with the program
Anaref.26,27 The extracted structure factors obtained for the
HTM were used in series expansions into symmetry adapted
functions ͑SAF͒ to describe the nuclear probability density
functions ͑pdf͒ of the anions.28–31 Reflections with different
sets of Miller indices fulfilling the relation h21ϩk12ϩl12
ϭh22ϩk22ϩl22 were excluded.
II. EXPERIMENTAL DETAILS
A. Preparation of samples
Cesium was purified by high vacuum distillation. Pow-
der samples of colorless CsHS and CsDS were prepared by
the reaction of Cs with H2S and D2S, respectively, at
Tϭ323 K in an autoclave manufactured from steel resistant
against hydrogen sulfide as a corrosive gas ͑Alloy 556,
Haynes International Inc., Kokomo, Indiana͒.1 Hydrogen sul-
fide was produced by the reaction of Al2S3 ͑Sigma-Aldrich,
Steinheim, Germany, 98%͒ with doubly distilled H2O or
D2O ͑Center d’Etudes de Saclay, Gif-Sur-Yvette, France,
99.5%͒.21
X-ray powder diffraction of CsDS was carried out in the
temperature range 190 KрTр220 K in steps of ⌬Tϭ2 K. A
Guinier diffractometer G645 ͑Huber, Rimsting, Germany͒
was used in transmission geometry with CuK␣1 radiation.
The sample was covered by Kapton foil 200HN ͑thickness:
50 ␮m, August Krempel Soehne GmbH & Co., Enzweihin-
gen, Germany͒. CsDS was diluted with Si as the internal
standard for the lattice parameters and to prevent absorption.
The temperatures were obtained using a closed cycle cryostat
and determined by a calibrated Si diode situated close to the
sample holder.
The samples were handled under inert gas conditions22
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J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Dynamics of anions and cations in CsHS and CsDS
4963
TABLE I. Crystallographic parameters obtained by Rietveld refinement of neutron diffraction patterns of CsDS ͑LTM: I4/m, Zϭ8; MTM: P4/mbm,
¯
Zϭ2; HTM: Pm3m, Zϭ1͒. Refinements are based on split-atom models.
Modification
LTM
4
LTM
100
MTM
170
HTM
220
HTM
280
HTM
340
HTM
400
T/K
a/Å
c/Å
x(Cs)
8.2020͑1͒
9.0245͑3͒
0a
0a
8.2268͑2͒
9.0393͑3͒
0a
0a
5.8465͑1͒
4.5259͑2͒
0
4.2880͑1͒
4.3052͑1͒
4.3271͑1͒
4.3449͑1͒
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
y(Cs)
0
a
a
z(Cs)
0.2679͑3͒
0.0053͑3͒
0.2545͑6͒
0.2425͑6͒
0.2647͑4͒
0.0131͑4͒
0.2540͑9͒
0.2424͑8͒
0
u2 (Cs) /Å2
0.0212͑5͒
0.0445͑9͒
0
0
0.056͑1͒
0
0
0.065͑1͒
0
0
0.073͑1͒
0
0
͗
͘
iso
x(S)
y(S)
0
1
2
1
2
z(S)
0
0
0
0
0
0
u2 (S) /Å2
0.0110͑6͒
0.0896͑2͒
0.2443͑3͒
0.0176͑7͒
0.0912͑4͒
0.2486͑8͒
0.0262͑7͒
0.1584͑1͒
12ϩx
0.0493͑9͒
0.2952͑7͒
0
0.0578͑1͒
0.2847͑7͒
0
0.070͑1͒
0.2763͑8͒
0
0.083͑2͒
0.2695͑9͒
0
͗
͘
iso
x(D1)
y(D1)
1
2
1
z(D1)
occ͑D1͒
0
0
0
1
0
1
0
1
0
1
b
0.974͑2͒
0.0295c
0.019͑1͒
0.031͑2͒
0.039͑1͒
1.353͑5͒
0.418d
0.224d
0
0.873͑3͒
0.0368c
0.025͑4͒
0.035͑4͒
0.051͑2͒
1.340͑7͒
0.418͑3͒
0.224͑4͒
0
u2 (D1) /Å2
0.0453c
0.035͑1͒
0.043͑2͒
0.058͑2͒
1.309͑2͒
0.0821c
0.053͑2͒
0.097͑2͒
0.1004c
0.072͑2͒
0.115͑2͒
u2 (D1)
0.1210c
0.093͑3͒
0.135͑2͒
u2 (D1)
0.1349c
0.110͑4͒
0.147͑3͒
u2 (D1)
͗
͗
͗
͗
͘
͘
͘
͘
iso
u2 (D1) /Å2
xx
u2 (D1) /Å2
yy
u2 (D1) /Å2
u2 (D1)
͗
͘
͗
͘
͗
͘
͗
͘
zz
yy
yy
yy
yy
1.266͑3͒
1.224͑3͒
1.194͑4͒
1.171͑4͒
d(D1-S)/Å
x(D2)
y(D2)
z(D2)
u2 (D2) /Å2
͗
͘
u2 (S)
u2 (S)
͗
͘
͗
͘
iso
iso
iso
d(D2-S)/Å
1.351͑5͒
174.3͑5͒
4.8/5.7
1.0–9.1
2.4–12.6
1.359͑2͒
176͑1͒
6.2/6.0
1.0–9.1
2.4–11.3
␣͑D1-S-D2͒/°
e
2
RF /%
8.7/7.4
1.4–9.1
2.4–10.3
9.7/10.0
1.5–6.6
2.5–7.6
15.8/13.5
1.5–6.6
2.5–7.4
10.2/14.2
1.5–6.7
2.5–7.4
10.1/17.7
1.5–6.3
2.5–7.4
0
Qf /ÅϪ1f
Qb /ÅϪ1f
1
2
1
4
aValues for Cs2; the position of Cs1 is ͑0
͒.
bOccupation of the deuterium positions is fixed to occ(D1)ϩocc(D2)ϭ1.
cCalculated from results of anisotropic refinement.
dNot refined.
eDetector in forward/backward scattering geometry.
fQminрQXрQmax , with X as the number of the detector.
C. Calorimetric investigations
mometer fixed in a distance of 1 cm from the sample coil.
The experiments were done at a proton resonance frequency
␯0ϭ400 MHz.
The heat capacities of CsHS and CsDS ͑sample masses
4.570 and 4.552 g, respectively͒ were determined from about
Tϭ30 K to Tϭ300 K by adiabatic heat pulse calorimetry, as
described in detail elsewhere.32 Briefly, the sample, in a
sealed calorimeter, was increased in temperature by quanti-
fied Joule heating, while adiabatic conditions were main-
tained. The temperature was monitored with a platinum re-
sistance thermometer, and the temperatures before and after
application of the heat pulse were determined. The heat ca-
pacities of the calorimeter and its addenda were determined
in separate experiments, and subtracted from the total heat
capacity to give the heat capacity of the sample. The uncer-
tainty of the heat capacity determined in this way has been
found to be within Ϯ0.5% ͑Ref. 32͒.
The spectra for an analysis of M2 were detected by a
solid-echo pulse sequence to reduce the influence of dead
time of the sample coil. To ensure that the decay of the echo
represents the FID of the signal we optimized the separation
of pulses ͑␶͒ by a variation of ␶ϭ10, 20, 30, 40, and 50 ␮s.
For the final measurement, ␶ϭ20 ␮s was used. To reduce the
influence of noise in the signal, we fitted the spectra using a
sum of Gaussian and Lorentzian lines to determine M2 . A
saturation recovery technique with a single 90° pulse for
detection was applied to measure T1 . A random variation of
the waiting periods between saturation and detection pulses
prevents systematic errors caused by slight shifts of tempera-
ture.
D. NMR
III. RESULTS AND DISCUSSION
A. Diffraction
Powder samples of CsHS were sealed into standard
NMR tubes ͑ø5 mm͒. The temperatures 150 KрTр540 K
were obtained by the use of a N2 gas flow system on an MSL
400 NMR spectrometer ͑Fa. Bruker Physik, Karlsruhe, Ger-
many͒. They were measured with a platinum resistance ther-
Neutron powder diffraction experiments on CsDS were
carried out in order to get information about the pdf of the
atoms, especially deuterium. In addition, x-ray powder dif-
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4964
J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Haarmann et al.
fraction was used to study the lattice parameters of CsDS
close to the MTMꢀHTM phase transition as a function of
temperature.
1. HTM
The crystal structure of the cubic HTM of cesium hydro-
gensulfide is related to the CsCl-type structure ͑space group:
¯
Pm3m, Zϭ1͒. Sulphur and cesium atoms occupy the posi-
tions of the ions in CsCl. The anions are reorientationally
disordered. Averaged over time, the anions are preferen-
tially aligned parallel to the cubic axes. IR/Raman
investigations8,33 indicate a change in the anion motion with
temperature within the HTM. This was concluded from the
temperature-dependent development of the line shape of the
stretching mode ␯͑HS͒. Therefore a partial occupation of
Wyckoff positions 6e, 8g, and 12i by hydrogen has been
discussed.1,8 To study this in some detail we did neutron
powder diffraction on fully deuterated samples at several
temperatures in the HTM.
We analyzed the diffraction patterns using standard split-
atom models, Fourier synthesis, and SAF. The following
split-atom models were used to take the pdf of deuterium
into consideration, keeping the total number of D atoms
fixed to the composition of the compound.
͑I͒ Exclusive occupation of Wyckoff positions 6e, 8g, or
12i, assuming anisotropic displacement of deuterium.
͑II͒ Partial occupation of the sites 6e, 8g, and 12i within
one model assuming isotropic displacement of D. The pa-
rameters of the deuterium positions were constrained to en-
sure the same interatomic distance between D and S for the
different sites. Displacement parameters of the three sites
were constrained to have the same value. The deuterium oc-
cupation numbers of the different sites were refined.
The data analysis shows that for TՇ300 K model ͑I͒
with an exclusive occupation of Wyckoff position 6e is
clearly favored. For temperatures above 300 K, results of
model ͑I͒ cannot be distinguished on the basis of goodness of
fit criteria from results of model ͑II͒, considering partial oc-
cupation of sites 6e, 8g, and 12i. The refinements yield for
model ͑II͒ occupancies of the sites 12i(5%)Ͻ8g(15%)
Ͻ6e(80%) that are not temperature dependent. Model ͑II͒
involves a higher population of electrostatic unfavored posi-
tions, where the anions point with the positive end ͑deute-
rium͒ toward the cations. Therefore, the occupation of only
one site, 6e, is more likely for the whole HTM temperature
range. Refinement results are given in Table I for four tem-
peratures in the HTM. These results of refinement are con-
firmed by Fourier analysis using observed structure factors
that were obtained from the neutron diffraction patterns on
the basis of the different 6e-, 8g-, and 12i-site models. No
significant maxima corresponding to sites 8g and 12i were
observed. Only maxima for an alignment of the anions par-
allel to the cubic axis pointing toward the faces of the anion
coordination polyhedra ͑Fig. 1͒ were found in agreement
with a sole deuterium occupation of site 6e.
FIG. 1. CsDS at Tϭ220 K and Tϭ400 K: The probability density function
͑pdf͒ of deuterium from the refinement of neutron diffraction data using
SAF. Sulphur is omitted and the probability density of the cations deliber-
ately reduced for clarity.
But the results for c81 did not differ significantly from their
estimated standard deviation. Therefore we neglected this pa-
rameter (c81ϭ0). Due to large correlations between thermal
parameters of the anions and the bond length, we fixed the
distance to values determined by the Rietveld refinement
͑Table I͒. The results of these SAF refinements are summa-
rized in Table II. The coefficient c41 is almost constant
whereas c61 increases with temperature. While the thermal
displacement parameters of Cs obtained from Rietveld re-
finement and SAF analysis are in agreement within the esti-
mated error; those of sulphur and of the whole anion are not.
The overall thermal displacement parameter of the anion us-
ing SAF should correspond to the parameter of sulphur de-
termined by Rietveld refinement. The overall displacement
of the anion must be similar to that of the center of mass. The
discrepancies in the thermal displacement parameters as well
as the correlation between the displacement parameter and
the bond length of the anion imply coupling of its transla-
tional and rotational motion of the anion in the HTM. In Fig.
1, a three-dimensional representation of the pdf of deuterium
is given for two temperatures with respect to the coordina-
tion polyhedron.
The quality of the refinements is slightly better for the
SAF than for the split-atom model. The SAF model seems to
be more appropriate to describe the pdf of D in the HTM of
CsDS. Compared to the split-atom models, the pdf of D de-
termined by SAF is much more smeared out ͑Fig. 1͒. The
SAF analysis allows an orientation of the anion along ͗110͘.
The probability for this orientation rises with increasing tem-
perature.
TABLE II. Crystallographic parameters obtained by least-squares refine-
ment of structure factors of neutron diffraction patterns of CsDS ͑HTM͒.
Refinement based on symmetry-adapted functions ͑SAF͒.
CsDS
220 K
280 K
340 K
400 K
u2 (Cs) /Å2
0.049͑3͒
0.058͑4͒
1.9͑1͒
0.062͑6͒
0.081͑9͒
1.6͑2͒
0.066͑5͒
0.089͑9͒
1.5͑2͒
0.075͑6͒
0.11͑1͒
1.7͑2͒
͗
͗
͘
iso
u2 (DS) /Å2
͘
iso
a
c41
c61
a
In addition, we developed the extracted structure factors
into SAF. We described this procedure in detail in Ref. 17.
The momentum transfer of our measurements allows refine-
ment of the coefficients c41 , c61 , and c81 of the related SAF.
0.52͑9͒
0.6͑2͒
0.6͑2͒
1.0͑4͒
2
RF /%
9.2
13.3
12.9
12.0
0
aCoefficients of cubic harmonics ͑Ref. 28͒.
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J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Dynamics of anions and cations in CsHS and CsDS
4965
must be taken into account in order to reach satisfactory
results. As a representative for the whole MTM regime, the
results of Rietveld refinements for Tϭ170 K are summarized
in Table I.
For TϽ170 K diffuse scattering arises at dϷ3.41 Å,
which is close to the d spacing of the ͑1 2 1͒ reflection of the
LTM. This reflection is sensitive to the order of the anions
and indicates short-range order at the lower-temperature end
of the MTM.
3. LTM
As for the MTM, the LTM of CsHS is tetragonal ͑space
group: I4/m, Zϭ8͒, but with a larger unit cell. To a first
approximation, the anions are antiferroelectrically ordered at
Tϭ4 K forming cyclic S4H44Ϫ groups with S–H¯S–H hy-
drogen bonds ͓Fig. 2͑c͔͒. Two inequivalent positions of Cs
exist. While the position of Cs1 has no positional parameter
to be refined, the position of Cs2 has a free z parameter. The
inequality of the Cs sites arises from the arrangement of the
anions: Both cations are coordinated by eight anions, which
are grouped into two planar cyclic S4H44Ϫ units orientated
parallel to the a,b plane of the unit cell. Cs1 at zϭ 14 is coor-
dinated by two equivalent S4H44Ϫ groups that are character-
ized by anions with hydrogen atoms pointing onto sulphur
atoms inside the group. On the other hand, Cs2 is coordi-
nated by two inequivalent S4H44Ϫ units with anions that ei-
ther all point with the hydrogen atoms onto sulphur atoms
within the unit, or that all points with the hydrogen atoms
onto sulphur atoms outside the group ͓Fig. 2͑c͔͒. Therefore
Cs2 shifts away from the zϭ 41 position, driven by different
electrostatic interactions of the closed and the open S4H44Ϫ
rings.
To avoid correlations of the thermal displacement pa-
rameters of both Cs sites, we constrained these parameters in
our Rietveld refinements of neutron powder diffraction data.
Patterns obtained at Tϭ4 K and Tϭ100 K differ signifi-
cantly and a weakening of superlattice reflections of the LTM
with increasing temperature can be seen ͓Fig. 3͑a͔͒. The tem-
peratures of the LTMꢀMTM phase transition were esti-
mated by Raman scattering8 as TCϭ118 K and TCϭ103 K
for CsHS and CsDS, respectively. From the calorimetric re-
sults ͑vide infra͒, we see that at Tϭ100 K, the LTMꢀMTM
has already begun.
The differences in the diffraction patterns indicate a
change of the crystal structure with temperature. A model of
the crystal structure that accounts for the change near the
phase transition temperature has been derived from Fourier
analysis ͓Fig. 3͑b͔͒. A second, partially occupied D2 position
is introduced to approximate the crystal structure of the
MTM. Results of Rietveld refinements are summarized in
Table I. Even for Tϭ4 K, a small occupation of position D2
is determined. This might be due to correlations of param-
eters in the Rietveld refinements or due to the presence of a
residual static disorder. We did a series of short neutron dif-
fraction measurements in order to record the temperature de-
pendence of the D2 occupation and the Cs2 positional shift.
To refine these patterns we constrained the thermal displace-
ment parameters of D2 to that of sulphur and constrained the
parameters of the position of D2 to values determined for
FIG. 2. ͑a͒ Unit cell of the MTM ͑a,b,c͒ of CsHS with respect to the cubic
1
2
1
2
cell of the HTM (a ,b ,c ) that is shifted by ͑0,
,
͒. ͑b͒ and ͑c͒ a,b plane
Ј
Ј Ј
of CsHS in the MTM and LTM, respectively. Unit cells are marked.
2. MTM
The crystal structure of the MTM of CsHS is tetragonal
͑space group: P4/mbm, Zϭ2͒ and related to the CsCl-type
structure ͓Fig. 2͑a͔͒. A two-dimensional net of hydrogen
bonds is built in the a,b plane of the unit cell ͓Fig. 2͑b͔͒. The
anions are reorientationally disordered; both positions of hy-
1
2
drogen are equivalent and occupied with probability.
The patterns of the MTM obtained by the neutron dif-
fraction of CsDS were refined using standard split-atom
models. A considerable anisotropy of the pdf of deuterium
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4966
J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Haarmann et al.
FIG. 4. ͑a͒ Primary order parameter ͓Eq. ͑1͔͒ of CsDS as a function of
temperature ␩0(T)ϭ1Ϫ2•occ, with occ as the fractional occupation of
position D2. The full line indicates the critical law fitted to ␩0 . ͑b͒ Second-
ary vs primary order parameter ͑displacive ␩ and order/disorder ␩ ͒.
FIG. 3. ͑a͒ Neutron diffraction pattern of CsDS at Tϭ4 K and Tϭ100 K
͑LTM͒. The positions of weakened reflections are marked. The background
was subtracted to focus on the change in intensity. ͑b͒ Fourier maps of the
a,b plane with zϭ0 of CsDS obtained from the neutron diffraction pattern at
Tϭ4 K and Tϭ100 K. Dotted lines indicate pdfр0; full lines pdfϾ0.
1
0
n
TCϪT
␩ T͒ϭf•
,
͑3͒
͑
ͩ
ͪ
TC
Tϭ100 K. In addition, we fixed the sum of the fractional
with TCϭ123.2Ϯ0.5 K as the critical temperature, fϭ1.20
Ϯ0.02 as a scaling factor, and nϭ0.30Ϯ0.02 as the critical
exponent for CsDS ͓Fig. 4͑a͔͒. The diffraction patterns are
less sensitive to the shift of Cs2, but the results of a fit of
␩1(T) using a critical law agrees well within the estimated
standard deviations to those of ␩0(T) (TCϭ122Ϯ2 K, f
ϭ1.18Ϯ0.09, nϭ0.26Ϯ0.06). The bilinear coupling of the
primary order parameter ␩0(T) and the so-called pseudopri-
mary order parameter35 ␩1(T) are presented in Fig. 4͑b͒. The
coupling of the order parameters supports the hypothesis that
the shift of Cs2 is due to electrostatical interactions. These
are averaged out by the increasing disorder with rising tem-
perature.
occupations of D1 and D2 occ(D1)ϩocc(D2)ϭ1 . The
͓
͔
resultant parameters did not depend on whether the measure-
ment temperature was approached by heating or cooling of
the sample.
Two order parameters were introduced to characterize
the LTMꢀMTM phase transition. A primary order param-
eter ␩0(T) describing the order/disorder part of the phase
transition and depending on the occupation of D2 was de-
fined as
␩
T͒ϭ1Ϫ2•occ D2͒.
͑1͒
͑
͑
0
In addition, an order parameter ␩1(T) is related to the shift
of Cs2:
⌬zCs2 T͒
͑
4. Temperature dependence of lattice and thermal
displacement parameters
␩
T͒ϭ
,
͑2͒
͑
1
⌬zCs2 max T͒
͑
with ⌬zCs2(T)ϭzCs2(T)Ϫ 41. This order parameter is related
to the displacive part of the phase transition.
The temperature dependence of ␩0(T) is presented in
Fig. 4͑a͒. The order parameter of the order/disorder part fol-
lows a critical law:34
While the LTMꢀMTM transition is continuous, the
MTMꢀHTM transition is of first order. The volume in-
creases at the MTMꢀHTM transition by about 1%, as also
found for MDS with MϭNa,K,Rb.36 Hysteresis of the tran-
sition of about ⌬Tϭ6 K was detected using powder x-ray
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J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Dynamics of anions and cations in CsHS and CsDS
4967
FIG. 6. Thermal displacement parameters of CsDS as a function of tempera-
ture. ͑a͒ Isotropic displacement, ᭢: D calculated from refinement of aniso-
tropic displacement, ᭡: S, ᭹: Cs and ͑b͒ principal axis of anisotropic deu-
FIG. 5. Lattice parameters of CsDS as a function of temperature for the
LTM and MTM. ͑a͒ a and ͑b͒ c . The phase transition at Tϭ123 K and the
Ј
Ј
beginning of observed disorder at Tϭ65 K are marked by dotted lines. Full
lines represent a guide to the eye.
terium displacement parameters, ᭹: u2
, , . The
᭡: u2 ᭢: u2
͗ ͘ ͗ ͘
y z
͗
͘
x
temperatures of the phase transitions and the beginning of observed disorder
at Tϭ65 K are marked by dotted lines. Full lines represent a guide to the
eye. Points at Tϭ200 K belong to the HTM.
diffraction. For heating CsDS in the temperature range
202 KрTр210 K, both modifications were observed simul-
taneously. The amount of the HTM increases with tempera-
ture, detected by the rising intensity of the reflections of the
HTM. For cooling of the sample, a similar behavior was
observed.
A distinct precursor effect of the lattice parameters can
be seen in the c/a ratio that approximates cubic symmetry at
temperatures close to the MTM→HTM phase transition.
With the onset of orientational disorder of the anions at
the beginning of the LTM→MTM phase transition at T
Ϸ65 K, an increase of the lattice expansion was detected
͑Fig. 5͒. Whereas the a parameter above TϷ65 K grows lin-
ear up to the phase transition MTM→HTM ͓Fig. 5͑a͔͒, the
expansion along the c axis in the interval 65 KрTр110 K
has a significant higher slope ͓Fig. 5͑b͔͒, but about 10 K
below the MTM→HTM transition it decreases with increas-
ing temperature.
spect CsDS behaves distinctly at the MTMꢀHTM phase
transition, different from NaDS and KDS, both of which dis-
play a much larger rise of the cation displacement parameters
than the thermal parameters of D and S ͑Ref. 17͒.
The anisotropy of the thermal displacement of deuterium
is significant ͓Fig. 6͑b͔͒. The motion of the anions can be
separated into a reorientational jump process and reorienta-
tions of relative small amplitude and the translation of small
amplitude. The reorientations of small amplitude are due to
librational motions and in a first approximation they are rep-
resented by the thermal displacement parameters of deute-
rium. These can be distinguished in the LTM and MTM by
u2 and u2 for motion parallel to the c axis and within the
͗
͘
͗
͘
y
z
a,b plane of the unit cell, respectively. While the amplitude
of the translational motion, approximately u2 , increases
͗
͘
x
The isotropic thermal displacement parameters of the at-
oms of CsDS determined by Rietveld refinement of the neu-
tron diffraction pattern are presented in Fig. 6͑a͒. In the
temperature range 65 KрTр123 K, just below the
LTM→MTM phase transition, a sharp increase of thermal
displacement parameters with temperature was observed.
The thermal parameters of all the atoms show the same be-
havior around the MTMꢀHTM phase transition. In this re-
nonlinearly with temperature, the amplitudes of librational
motion increase linearly with temperature. At the
MTMꢀHTM phase transition, there is a continuous cross-
over of the translational amplitude curve, but with a distinct
change of gradient at the transition temperature ͓Fig. 6͑b͔͒.
However, the amplitudes of the librational motions, which
are symmetry equivalent in the HTM, undergo an instanta-
neous jump at the MTMꢀHTM transition temperature.
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4968
J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Haarmann et al.
owing to the lower LTMꢀMTM transition temperature and
a higher MTMꢀHTM phase transition temperature. ͑It is
only possible to do the calorimetric experiments in the heat-
ing mode, so they do not give information about hysteresis.͒
The similarities in transition temperature and entropy change
indicate that most likely both CsHS and CsDS have very
similar origins for the LTMꢀMTM and the MTMꢀHTM
transition, in contrast with, for example, sodium hydroxide in
which deuteration adds an additional phase transition.38 The
shapes of the calorimetric curves for CsHS and CsDS indi-
cate that the higher-temperature transition is first order, and
the lower-temperature transition is of higher order. These re-
sults are in agreement with the present diffraction data.
From the diffraction studies presented above, it is known
that the LTM has the anions antiferroelectrically ordered, al-
though reorientational disorder sets in well below the LTM
→MTM phase transition. In addition, there is displacive
shift of the Csϩ ions in LTM. In the MTM, the anions are
reorientationally disordered, with two equivalent H ͑or D͒
positions, both occupied with 50% probability. If the LTM
→MTM phase transition was simply a matter of the onset of
two-fold dynamical disorder of the HSϪ ͑or DSϪ͒ ions, the
associated entropy change would be ⌬trsSϭR ln 2ϭ0.69 R,
considerably more than observed ͓⌬trsSϭ(0.24Ϯ0.04) R for
CsHS and (0.27Ϯ0.04) R for CsDS͔. That the observed en-
tropy change is less than R ln 2 is consistent with the diffrac-
tion experiments, which show some residual anion disorder
in LTM and some short-range ordering of the anions well
above the LTM→MTM phase transition.
FIG. 7. The heat capacity of ͑a͒ CsHS and ͑b͒ CsDS as a function of
temperature. The circles denote the experimental data and the full lines show
the baseline heat capacity in the region of the phase transitions.
For each of CsHS and CsDS, the excess heat capacity at
the lower-temperature transition, ⌬Cp , determined by sub-
traction of the baseline heat capacity ͓Figs. 7͑a͒ and 7͑b͔͒
from the experimental heat capacity, was fit to the function
B. Calorimetric investigations
The heat capacities of CsHS and CsDS, shown in Figs.
7͑a͒ and 7͑b͒, respectively, both show the same main fea-
tures, namely a lower-temperature phase transition with a
significant gradual component, and a higher-temperature
phase transition that is much sharper. ͑The experimental data
have been deposited and are available through EPAPS.͒ The
enthalpy and entropy changes at the lower-temperature tran-
sition were determined by direct integration, and over the
sharper high-temperature transition these were determined
by the ‘‘long heat’’ method.37 The differences between the
heat capacities of CsHS and CsDS are rather small. In gen-
eral, and certainly above Tϭ70 K, the heat capacity of CsDS
is a little larger than that of CsHS ͑e.g., by about 5% at
Tϭ160 K͒, as one would expect based on the more massive
deuterated salt having more closely spaced vibrational en-
ergy levels. The shift in transition temperature and enthalpy
and entropy change on deuteration is also rather minor
͑Table III͒, with CsDS having the longer range for the MTM
n
TCϪT
⌬C ϭf
,
͑4͒
Ј
ͯ ͯ
p
TC
and the best fit ͑Fig. 8͒ was found with nϭ0.3 ͑TCϭ129 K
for CsHS and TCϭ121 K for CsDS͒, in good agreement with
the fit for the CsDS neutron powder diffraction experiments
͑vide supra͒. The observed transition is not as sharp as the
calculated critical heat capacity fit, but this rounding is not
unusual and could be associated with a distribution of do-
mains in such a large sample.39
From the diffraction studies and NMR second-moment
analyses, the high-temperature phase appears to have in-
creased anionic disorder, well described by a six-site jump
process. On the basis of an increase from two-site disorder in
MTM to six-site disorder in HTM, and an increase in volume
of about 1% at the MTM→HTM phase transition ͑Sec.
III A 4͒, one would expect a transition entropy change of
⌬trsSϭR ln(6/2)ϩR ln(1.01)ϭ1.1 R, where the dynamical
disorder contribution is about 100 times that of the volume
increase. This estimate of ⌬trsS is about 30% greater than
observed ͓(0.86Ϯ0.01) R for CsHS and (0.81Ϯ0.01) R for
CsDS͔, in line with the finding from the NMR spin-lattice
relaxation studies ͑Sec. III C 2͒ that there is more disorder in
the MTM than described by the two-site model.
TABLE III. Phase transition summary for CsHS and CsDS based on calo-
rimetric studies. R is the gas constant.
T
trs /K
Comments
⌬
trsH/J molϪ1
⌬trsS/R
CsHS
CsDS
129Ϯ2
207.9Ϯ0.3
260Ϯ40
1492Ϯ8
0.24Ϯ0.04 Higher order
0.86Ϯ0.01 First order
121Ϯ2
213.6Ϯ0.3
270Ϯ40
1440Ϯ20
0.27Ϯ0.04 Higher order
0.81Ϯ0.01 First order
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J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Dynamics of anions and cations in CsHS and CsDS
4969
FIG. 8. Critical exponent fit to the excess heat capacity, ⌬Cp at the lower-
temperature phase transition in ͑a͒ CsHS and ͑b͒ CsDS.
C. NMR
The structural and especially dynamical properties of
CsHS were investigated by proton NMR. We used the
method of the second moments (M2) and analyzed the spin-
lattice relaxation times (T1). Dipolar coupling of the spins
was assumed to be the dominant interaction and therefore
only Cs–H and H–H coupling were considered in our calcu-
lations. With the small natural abundance of 33S, sulphur has
no relevant contribution to the dipolar interaction of the sys-
tem.
FIG. 9. ͑a͒ Proton NMR spectra of CsHS at various temperatures. The
spectra are scaled to unity and shifted by a small offset. The temperature of
the MTMꢀHTM phase transition is marked. ͑b͒ Second moments (M2) of
CsHS calculated from the absorption signal. The error bars indicate an un-
certainty of Ϯ5%. Full lines indicate M2 calculated for the known structure
of CsDS at Tϭ220 K and Tϭ170 K ͑Secs. III A 1 and III A 2͒. The dotted
line represents a guide to the eye.
1. Second moments
Proton spectra of CsHS measured at several different
temperatures are presented in Fig. 9͑a͒. In contrast to the
proton NMR signal of MHS with MϭNa, K, Rb, where a
small anisotropy of the chemical shielding tensor was
observed,20 the comparable signals of CsHS are symmetric.
At the MTMꢀHTM phase transitions, a small drop of the
signal width was observed. At the highest temperatures in the
HTM, the signal becomes Lorentzian-like.
In the case of the MTM, the arithmetic average of the
second moments determined from the spectra is about 6%
higher than the calculated M2 ͓Fig. 9͑b͔͒. Assuming that
CsHS and CsDS are similar in their physical properties, the
influence of lattice expansion on M2 within the MTM is
about Ϯ1%. A systematic decrease of M2 with temperature
in the MTM was not observed. For the HTM the width of the
signal decreases significantly with rising temperature, much
more than expected by lattice expansion. As a consequence,
observed and calculated M2 values should be compared for
the lowest temperature point measured in the HTM. M2 cal-
culated from structure parameters of CsDS, obtained by neu-
tron powder diffraction at Tϭ220 K and Tϭ400 K, reduces
with increasing temperature by about 8%. In the same tem-
perature range M2 of the signal reduces by about 77%.
The formalism and calculations of M220 are based on the
crystal structures and parameters described in Sec. III A ͑see
Table I for LTM: Tϭ4 K, MTM: Tϭ170 K, and HTM:
Tϭ220 K͒. The motion of the anions was related to a six-
and a two-site jump process of the protons for the HTM and
MTM, respectively. The calculations for the LTM are based
on the idealized ordered modification considering only one
site for the protons. The results of the calculations and the
analysis of the absorption signal are summarized in Table IV.
The calculations and the observed signal are in reasonable
agreement.
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4970
J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Haarmann et al.
TABLE IV. Second moment (M2) calculated from the proton absorption
signal ͑O͒ and for the known crystal structures ͑C͒. The structure models
were based on the results of neutron diffraction experiments ͑LTM,
Tϭ4 K; MTM, Tϭ170 K; HTM Tϭ220 K; see Sec. III A͒.
TABLE V. Observed ͑O͒ and calculated ͑C͒ minima of spin-lattice relax-
ation times (T1). The structure models were based on results of neutron
diffraction on CsDS ͑MTM, Tϭ170 K; see Sec. III A 2͒. In addition, two-
site 180° reorientations of the anions were considered. Different models
were used to describe the correlated and uncorrelated motion of the anions.
Modification
M
2(C) /G2
M2(O) /G2
␶c/10Ϫ10
s
Model
T
1 min(C) /s
a
LTM
MTM
HTM
1.510
0.711
0.675
-
0.75Ϯ0.2b
Uncorrelated
Ferroelectrical
Antiferroelectrical
7.620
8.262
7.629
5.869
5.803
5.629
0.67c
aNot within the investigated temperature range.
bMean value of all measurements in MTM.
cMaximum of the observed values in HTM.
T
1 min(O)ϭ5.6Ϯ0.6 s
Therefore a motional process other than reorientations of the
anions must influence the linewidth of the signal.
start orientation of the anions. The differences between T1
observed and calculated for the various models is between
36% and 48%. The outcome of the calculations is not very
sensitive to the lattice parameters and the bond length d͑HS͒.
A change of lattice parameters by Ϯ1% leads to a change of
T1 min of about Ϯ8% and a reduction of the bond length of
the anions from dϭ1.34 Å to dϭ1.24 Å increases T1 min by
about 14%. Even including the uncertainties of structure de-
termination, we are not able to explain the observed T1 by
two-site 180° reorientations of the anions in the MTM.
In order to understand the reasons for the deviations we
calculated several different MTM models to describe the re-
orientations of the anions. These can be separated into two
different classes: ͑I͒ Small angle reorientations around the
equilibrium positions of hydrogen (Heq), and ͑II͒ n-site jump
processes considering different populations of the sites with
orientations of the anions pointing toward the faces of the
coordination polyhedra ͓Fig. 2͑a͔͒. The motional processes
were modeled using only one common exchange rate within
a model. The proton positions of a model mentioned below
belong to each anion; no translational motion either of the
whole anion nor of the proton was considered. To model the
large amplitude of the thermal displacement parameters of
H/D parallel to the c axis of the unit cell ͑Sec. III A 4͒, we
chose this direction in model I to calculate the influence of
small angle reorientations of the molecule on T1 . The mo-
tion was simulated by a four-site jump model ͑proton sites on
Wyckoff position 8k͒. Two positions Hx enclose each of the
two positions Heq . All positions are placed on a circle around
sulphur within the a,c or b,c plane of the unit cell. An ex-
change of the protons between these positions was presumed
to have equal probability. A four-site jump reorientation par-
allel to the a,b plane of the unit cell was used in model ͑IIa͒.
Two sets of Wyckoff position 4h describe the proton posi-
tions in this model. Model ͑IIb͒ simulates a six-site jump
reorientation of the anions. In addition to the proton posi-
tions of model ͑IIa͒, Wyckoff position 4g was introduced to
describe the motion of the anions.
2. Spin-lattice relaxation
The temperature dependence of T1 is shown by an
Arrhenius plot in Fig. 10. Exponential relaxation of the lon-
gitudinal magnetization was observed at all temperatures.
The minimum of T1 at Tϭ201 K in the MTM is at slightly
lower temperatures than for RbHS, which has the lowest
temperature of the T1 minima of the isotypic hydrogensul-
fides MHS with MϭNa, K, Rb20 (␯0ϭ400 MHz).
Calculations based on results of the neutron diffraction
experiments on CsDS at Tϭ170 K ͑Sec. III A 2͒ were car-
ried out using different jump models to describe the reorien-
tational dynamics of the anions. We chose dϭ1.34 Å ͑Ref.
40͒ as the bond length of the anion for our calculations in
order to ensure comparable results for different models. The
basics of these calculations are presented in Ref. 20 and we
omit a repetition here.
Results of our calculations considering two-site 180° re-
orientations of the anions in MTM are summarized in Table
V. The agreement of calculated and observed T1 is unsatis-
factory, whether or not correlated or uncorrelated motion of
the anions was taken into account. Correlated motion means
a collective reorientation of the ions, presuming a definite
For model ͑I͒ good agreement of calculated and mea-
sured T1 was reached for Є(Hx –S–Heq)Ϸ42°. In the case
of model ͑II͒, results of calculations and measurements are in
good agreement for an occupation of Heq by about 60% for
model ͑IIa͒ and 75% for model ͑IIb͒. The rest of proton
density is equally distributed over the other positions.
The different models of motion in the MTM in CsHS,
based on the NMR studies, are not immediately reconcilable
FIG. 10. Arrhenius plots of spin-lattice relaxation times (T1) of CsHS. The
error bars indicate an estimated uncertainty of Ϯ10% in T1 . The tempera-
ture of the MTMꢀHTM phase transition is marked by a dotted line. Full
lines indicate Arrhenius fits of T1 . The calculated minimum of T1 for the
structure model of CsDS ͑MTM, Sec. III A 2͒ considering two-site 180°
reorientations of the anions is also indicated.
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J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Dynamics of anions and cations in CsHS and CsDS
4971
TABLE VI. Activation energies (Ea) and attempt frequencies (␶Ϫ1) deter-
mined by Arrhenius fits of the proton spin-lattice relaxation times of CsHS
͑see Fig. 10͒.
supports their reorientations, and the Cs compound follows
this tendency, although the crystal structure changes from the
NaCl- to the CsCl-type structure.
0
MTM
HTMa
HTMb
IV. CONCLUSIONS
Ea /kJ molϪ1
1/␶0 /sϪ1
9.3Ϯ0.3
7.1ϫ1012
13.8Ϯ0.4
13.5Ϯ0.5
(2.5Ϯ0.8)ϫ1013
1
¯
Neutron diffraction, solid state H-NMR, and calorimet-
ric investigations were carried out in a wide temperature
range on CsHS and CsDS in order to study structure and
dynamics of these compounds.
aReorientations of HSϪ.
bDiffusion of cations.
Large-amplitude liberations of DSϪ are indicated in a
distinct anisotropy of the thermal displacement parameters of
deuterium within the whole investigated temperature range.
Contrary to the NaCl-typelike compounds NaDS and KDS,
which have considerable anharmonicity of the coordination
potential of deuterium,17,19 a harmonic model fits well with
the neutron diffraction data of CsDS. This is caused by the
two-fold symmetry of the coordination potential of D in
CsDS, which is more closely related to an ellipsoid describ-
ing the pdf within the harmonic approximation than the
three-fold symmetry of the coordination potential of NaDS,
KDS, and RbDS. Nevertheless, data from neutron diffraction
show a significant influence of the coordination potential of
D highlighted by the different amplitudes of librational mo-
tion in the LTM and MTM, as seen by the length of the
principal axis of the thermal displacement parameters.
In the HTM an SAF model is more appropriate than a
split-atom model to describe the pdf of D. The shape of the
very smeared-out pdf still accounts for the influence of the
potential of the particle involved in fast reorientational dy-
namics by avoiding orientations of the anions leading to high
repulsive forces between Csϩ and Dϩ.
with the neutron diffraction studies of CsDS ͑Sec. III A͒.
However, the calorimetric investigations indicate that this is
not due to an intrinsic difference between CsHS and CsDS.
On the one hand, the difference could be related to the dif-
ference in sensitivity of different techniques to different as-
pects of dynamics.41,42 On the other hand, there might be an
influence of an amorphous phase, as mentioned in Ref. 8.
This amorphous content can be removed by heating the
samples to Tϭ473 K for two weeks and subsequent slow
cooling to room temperature.8 Further investigations taking
an improvement of the sample preparation into account
will follow to determine the reasons for the observed
discrepancies.
T1 rises drastically with the MTM→HTM phase transi-
tion and increases following an Arrhenius law with tempera-
ture up to TϷ250 K. Probably reorientational motion of the
anions dominates the spin-lattice relaxation up to this tem-
perature. At higher temperatures a change in the mechanism
of relaxation can be seen ͑Fig. 10͒. Above TϾ330 K the
relaxation becomes more efficient and T1 decreases with
temperature also following an Arrhenius form. As for the
temperature dependence of M2 in the HTM, the onset of
translational motion seems to be reasonable to explain the
observed T1 since the reorientations of the molecular ions
are faster than at T1 min and a slowing of reorientations is
unrealistic. A high mobility of the ions in the HTM can also
be expected from the enhancement of crystal quality at high
temperatures.8 A similar behavior of T1 was observed for
MHS with MϭNa, K, Rb18,20 and an increase of activation
energies with an increasing radius of M favor a diffusion of
the cations. Nevertheless, the activation energies are quite
low for long-range translational motion in solids. A combi-
nation of low- and high-resolution quasielastic neutron scat-
tering experiments should give information about transla-
tional motion of protons or the whole anions, respectively.
High-resolution experiments are necessary to analyze the ro-
tational part, which must be separated from the translational
part.
An analysis of thermal displacement and lattice param-
eters shows precursor effects for both LTMꢀMTM and
MTMꢀHTM phase transitions by a change in the tempera-
ture dependence of these parameters. The transition at high
temperature is clearly of first order, as determined by calori-
metric and diffraction investigations. The transition tempera-
tures are Tϭ207.9Ϯ0.3 K and Tϭ213.6Ϯ0.3 K for CsHS
and CsDS respectively.
The LTMꢀMTM phase transition is continuous. Order
parameters, related to the displacive and the order/disorder
part of this phase transition, couple bilinearly, and follow a
critical law. The critical exponent is close to nϭ1/4, possibly
indicating a tricritical phase transition. The transition tem-
perature in CsDS of TCϭ123.2Ϯ0.5 K determined by neu-
tron diffraction is in good agreement with results of calori-
metric investigations TCϭ121Ϯ2 K. The transition of CsHS
shows only a shift of the critical temperature to TCϭ129
Ϯ2 K and no significant change of the critical exponent was
observed.
The activation energies were determined by Arrhenius
fits of T1 for the HTM. For the MTM we used an expression
following Blombergen, Purcell, and Pound43 also, presuming
a thermal activated process. The results are summarized in
Table VI. The activation energy of the reorientational process
in the HTM is in good agreement with results from QENS
experiments.10 The activation energies of the reorientational
motion of the anions in the MTM of CsHS compared with
results for the MTM of MHS with MϭNa,K,Rb20 show a
decrease with increasing radius of the cations. This means
that the softening of the coordination potential of the anions
1
The observed second moments of the H-NMR absorp-
tion signals of CsHS are in reasonable agreement with results
of calculations based on the structure models of MTM and
HTM, assuming a model of reorientational disorder of the
anions provided by the crystal structure of CsDS. No NMR
spectra of the LTM were measured, because of the available
temperature range.
However, an analysis of spin-lattice relaxation shows a
difference of measured and calculated T1 for the crystal
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4972
J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Haarmann et al.
structure of the MTM of CsDS, assuming two-site 180° re-
orientations of the anions.
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MϭNa, K, Rb, Cs correspond to the influence of the coordi-
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of the anions. A weakening of the potential results from an
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It seems to be reasonable that in the HTM of CsHS at
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1994 ͑unpublished͒.
The experimental heat capacities of CsHS and CsDS
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44 See EPAPS Document No. E-JCPSA6-117-508224 for experimental heat
capacities for CsHs and CsDs. This document may be retrieved via the
EPAPS homepage ͑http://www.aip.org/pubservs/epaps.html͒ or from
ftp.aip.org in the directory /epaps/. See the EPAPS homepage for more
information.
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