A study of molecular motion and Raman processes in K3H(SO 4)2 and KHSO4 single crystals by observation of 1H and 39K spin-lattice relaxation

Article abstract of DOI:10.1016/j.ssc.2004.02.038

The spin-lattice relaxation rates for ¹H and ³⁹K nuclei in K₃H(SO₄)₂ and KHSO₄ single crystals, which are potential candidate materials for use in fuel cells, were determined as a function of temperature. The spin-lattice relaxation recovery of ¹H can be represented for both crystals with a single exponential function, but cannot be represented by the Bloembergen-Purcell-Pound (BPP) function, so is not related to HSO₄ motion. The recovery traces of ³⁹K, which predominantly undergoes quadrupole relaxation, can be represented by a linear combination of two exponential functions. The temperature dependences of the relaxation rates for ³⁹K can be described with a simple power law T₁^-1=αT ². The spin-lattice relaxation rates for the ³⁹K nucleus in K₃H(SO₄)₂ and KHSO₄ crystals are in accordance with a Raman process dominated by a phonon mechanism.

Full text of DOI:10.1016/j.ssc.2004.02.038

Solid State Communications 130 (2004) 481–485
www.elsevier.com/locate/ssc
A study of molecular motion and Raman processes in K H(SO )
3
4 2
1
and KHSO single crystals by observation of H and
4
3
9
K spin–lattice relaxation
*
Ae Ran Lim , Won Ki Jung, Tae Jong Han
Department of Physics, Jeonju University, Jeonju 560-759, South Korea
Received 10 December 2003; received in revised form 17 February 2004; accepted 21 February 2004 by A. Pinczuk
Abstract
The spin–lattice relaxation rates for H and K nuclei in K H(SO ) and KHSO single crystals, which are potential
candidate materials for use in fuel cells, were determined as a function of temperature. The spin–lattice relaxation recovery of
1
39
3
4 2
4
1
H can be represented for both crystals with a single exponential function, but cannot be represented by the Bloembergen–
3
9
Purcell–Pound (BPP) function, so is not related to HSO
quadrupole relaxation, can be represented by a linear combination of two exponential functions. The temperature dependences
4
motion. The recovery traces of K, which predominantly undergoes
3
9
21
2
of the relaxation rates for K can be described with a simple power law T1 ¼ aT : The spin–lattice relaxation rates for the
3
9
3 4 2 4
K nucleus in K H(SO ) and KHSO crystals are in accordance with a Raman process dominated by a phonon mechanism.
q 2004 Elsevier Ltd. All rights reserved.
PACS: 61.50 Cj; 76.60 k
Keywords: B. Crystal growth; D. Crystal structure; E. Nuclear magnetic resonance (NMR)
1
. Introduction
Tripotassium hydrogen disulfate, K H(SO ) , belongs to
3 4 2
the M
exhibits ferroelastic properties below 471 K [11–15]. The
phase transition behavior of K H(SO is unique among
hydrogen bond materials. The deuterium compound
3 4 2
H(AO ) crystal family with space group A2=a and
Proton-conducting solids are of interest because of their
3
4 2
)
potential use in fuel cells, steam electrolysis, and as sensors
1]. Proton conduction occurs in several types of materials,
[
K
3
D(SO
4
)
2
has a finite phase transition temperature ðT ¼
c
including many hydrogen-bonded systems [2–8]. In some
ferroelectric and ferroelastic hydrogen-bonded crystals,
8
5 KÞ; whereas the hydrogen compound does not exhibit
any phase transition [9,16]. No high temperature structural
phase transition has been found for K H(SO before
it melts at about 445 K. The unit cell has the dimensions
4
superionic conductivity has been discovered; MHAO and
3
4 2
)
M H(AO ) (M ¼ K, Rb, Cs, NH ; A ¼ S, Se) exhibit high
3
4 2
4
proton conductivity in their high temperature phases [9,10].
However, below the phase-transition temperature the
conductivity decreases with increasing temperature, and
this trend cannot be explained in terms of conventional
thermoactivation processes.
ꢀ
ꢀ
ꢀ
a ¼ 9:777 A; b ¼ 5:674 A; c ¼ 14:667 A; and b ¼ 102:978;
and is monoclinic for K H(SO ) at room temperature
3 4 2
[
17]. There are two crystallographically distinct potassium
species, K(1) and K(2), in each cell. Potassium hydrogen
sulfate, KHSO , is a member of the alkali acid sulfate
4
family, and is interesting because of its ferroelectric
behavior. The structure of a KHSO4 single crystal is
*
Corresponding author. Tel.: þ82-63-220-2914; fax: þ82-63-
20-2054.
E-mail address: aeranlim@hanmail.net (A.R. Lim), arl29@
cornell.edu (A.R. Lim).
2
1
5
orthorhombic with space group Pbca ðD Þ and has sixteen
2h
molecules per unit cell. The unit cell parameters are
0038-1098/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ssc.2004.02.038

482
A.R. Lim et al. / Solid State Communications 130 (2004) 481–485
ꢀ
ꢀ
ꢀ
a ¼ 8:4030 A; b ¼ 9:799 A; and c ¼ 18:945 A [18]. There
magnetization of the crystal were measured at several
different temperatures. We found that the spin–lattice
relaxation recovery patterns can be described with a single
exponential form at all the temperatures we investigated.
Thus, the spin–lattice relaxation time can be determined
from a fit of the recovery pattern with the following equation
[19]:
þ
are two crystallographically different K species in the
K
3
H(SO
4
) crystal.
The spin–lattice relaxation rate of a nucleus is a measure
of how easily the nuclear system releases its excited state
energy into the lattice, and thus provides insight into crystal
dynamics such as the nucleus–phonon interaction. In order
to obtain detailed information about such dynamics, it is
Sð1Þ 2 SðtÞ ¼ 2Sð1Þexpð2WtÞ;
ð1Þ
2
1
necessary to measure the spin–lattice relaxation rates, T
;
1
1
39
where SðtÞ is the nuclear magnetization at time t: The
of the H and K nuclei in these single crystals. However,
although the physical properties of these materials have
been reported, sufficient research into their nuclear magnetic
resonance (NMR) characteristics has not yet been con-
ducted. In this article, the temperature dependence of the
relaxation time, T ¼ 1=W; is then the slope of the
1
log{½Sð1Þ 2 Sðtފ=2Sð1Þ} vs. time ðtÞ plot. The traces
were fitted with the single exponential function in Eq. (1).
The slopes of the traces increase with increasing tempera-
ture. The temperature dependence of the spin–lattice
21
1
39
spin–lattice relaxation rates, T1 ; of the H and K nuclei
in K H(SO and KHSO single crystals grown by the slow
relaxation rate, T 12 ; for H in this single crystal is shown
1
1
3
4
)
2
4
in Fig. 1. The spin–lattice relaxation time is T ¼ 1:23 s at
evaporation method were investigated using a pulse NMR
spectrometer. These observations of the NMR behavior of
1
1
room temperature. As the temperature is increased, the H
relaxation rate drastically decreases. The T 12 data for H in
this temperature range cannot be captured by the Bloember-
gen–Purcell–Pound (BPP) function [20].
1
1
1
39
the H and K nuclei are new, and enable the comparison
of the phonon mechanisms and molecular motions of
3 4 2 4
K H(SO ) and KHSO single crystals.
For a nuclear spin system of I ¼ 3=2; the recovery laws
for quadrupole relaxation have been developed by Igarashi
et al. [21]. The transition probabilities for Dm ¼ ^1 and
Dm ¼ ^2 are defined as W and W respectively. The rate
2
. Experimental section
4 2
Single crystals of K H(SO ) were grown using the slow
1
2
equations are then as follows:
3
evaporation method at room temperature from a mixed
aqueous solution containing 3:1 mole fraction of K SO and
dn23=2=dt ¼ 2ðW þ W Þn
þ W1n21=2 þ W2n1=2
;
1
2
23=2
2
4
dn21=2=dt ¼ 2W1n
23=2
2 ðW þ W ÞWn
1
2
21=2
þ W2n3=2;
H
2
SO
a hexagonal shape, and took the form of transparent plates
with a (001) plane as the dominant face. KHSO single
4
. Most of the resulting crystals were transparent with
ð2Þ
dn1=2=dt ¼ W2n23=2 2 ðW þ W ÞWn þ W1n3=2
;
1
2
1=2
4
crystals were grown at room temperature using the slow
evaporation of an aqueous solution containing a stoichio-
metric proportion of K SO and H SO . The resulting
dn3=2=dt ¼ W2n21=2 þ W1n1=2 2 ðW þ W Þn
1
2
3=2
where n23=2; n21=2; n1=2; and n3=2 are the differences in
population between the equilibrium value and that at time t
for each energy level. The eigenvalues of these equations
are W ; W ; W þ W :
2
4
2
4
crystals had hexagonal shapes and were colorless and
transparent with good optical quality.
1
39
The NMR signals of H and K nuclei in the K
H(SO
4
)
2
1
2
1
2
3
and KHSO single crystals were measured using the Bruker
4
MSL 200 FT NMR, Bruker DSX 400 FT NMR and Varian
INOVA 600 FT NMR spectrometers at the Korea Basic
Science Institute. The static magnetic fields were 4.7, 9.4,
and 14.1 T respectively. The temperature-dependent NMR
measurements were obtained in the temperature range 140–
400 K. The sample temperatures were maintained at a
constant value by controlling the helium gas flow and the
heater current with an accuracy of ^0.1 K.
3
. Experimental results and analysis
3
.1. K H(SO ) single crystal
3 4 2
1
3 4 2
The H spin–lattice relaxation times for K H(SO )
were obtained in the temperature range 180–400 K at a
frequency of 400 MHz. The inversion recovery traces of the
Fig. 1. Temperature dependence of the spin–lattice relaxation rate,
1
21
3 4 2
T1 ; for H in a K H(SO ) single crystal.

A.R. Lim et al. / Solid State Communications 130 (2004) 481–485
483
2
1
39
T1 data for the K nucleus can be described with the
When the central line is saturation, a recovery function
for the center line is calculated to be [22]
21
26
2
equation T1 ¼ ð2:51 £ 10 ÞT :
Sð1Þ 2 SðtÞ ¼ 2Sð1Þ½0:5 expð22W tÞ þ 0:5 expð22W tފ
1
2
3
.2. KHSO single crystal
4
ð3Þ
1
The H spin–lattice relaxation times for the KHSO
where SðtÞ is the nuclear magnetization corresponding to the
central transition at time t after saturation. The relaxation
times are given by
4
single crystal were obtained from measurements at a
frequency of 200 MHz. Each spin–lattice relaxation time,
T ; was obtained by applying a pulse sequence of p–t–p/2.
1
1
=T ¼ ½2ðW þ 4W ފ=5
ð4Þ
The carrier frequency was fixed at 27.99 MHz, which is the
1
1
1
2
The nuclear magnetization SðtÞ of H at time t after the p
pulse was determined from the inversion recovery sequence
following the pulse. The recovery traces of the magnetiza-
tion of the crystals were measured at several different
temperatures. The spin–lattice relaxation times were then
determined from a fit of the recovery patterns with Eq. (1).
3
Larmor frequency of the K nucleus in a magnetic field of
9
3
9
1
abundance 93.1%) in K H(SO was measured at several
4.1 T. The NMR spectrum of K (I ¼ 3=2; natural
3
4 2
)
temperatures. When the crystal is rotated about the crystal-
lographic axis, crystallographically equivalent nuclei give
rise to three lines: one central line and two satellite lines.
However, six resonance lines are obtained instead of one
The temperature dependence of T 12 for H in this single
1
crystal is shown in Fig. 3. In the case of the H nucleus, the
1
1
spin–lattice relaxation time is long: T ¼ 382 s at room
1
3
9
21
central resonance line for K nuclei in the case of the
H(SO crystal. This result points to the existence of
temperature. The variation of the relaxation rate, T1 ; with
temperature exhibits a minimum. As the temperature is
K
3
4
)
2
1
increased, the H relaxation rate at first slowly decreases,
three types of crystallographicallyinequivalent K(1) and K(2).
The six resonance lines correspond to three resonances in
the K(1) nucleus and three resonances in the K(2) nucleus.
This result is consistent with the crystal structure, and is in
agreement with our previous result [23].
and then begins to increase, passing through a minimum at
210 K. The T 12 curve in this temperature range has a
positive parabolic shape with a minimum near 210 K. This
1
1
result is not consistent with previous reports for H in the
21
3
9
The spin–lattice relaxation times of K in K
3
H(SO
4
)
2
hydrogen sulphate family of crystals: the shape of T1 for
1
were measured over the temperature range 160–400 K. The
spin–lattice relaxation times were obtained with the
inversion recovery method. The recovery traces for the six
H has a positive parabolic shape in KHSO
[24] and NH HSO [25] crystals the plots of T1
for H have a negative parabolic shape. Therefore, the
4
, whereas for
2
1
RbHSO
4
4
4
1
3
9
21
1
resonance lines of K with dominant quadrupole relaxation
can be represented by a linear combination of two
exponential functions as in Eq. (3). We measured the
variation of the relaxation times for the six resonance lines
change in the slope of T1 for H in KHSO
is not believed to be related to HSO motion, as claimed by
the Bloembergen–Purcell–Pound (BPP) theory [20].
4
at about 210 K
4
3
9
4
NMR spectra of K in a KHSO crystal were obtained at
3
9
for K with increasing temperature. The temperature
dependence of the nuclear spin–lattice relaxation rate,
the resonance frequency of 18.672 MHz. Instead of one
central resonance line, four central resonance lines were
39
obtained for K nuclei in the KHSO crystal. This result
4
2
1
39
21
T1 ; for K is shown in Fig. 2. The trends in T1 for the six
resonance lines are very similar. The relaxation rate
increases with increasing temperature. The spin–lattice
points to the existence of two types of crystallographically
inequivalent K(1) and K(2). The four central resonance lines
relaxation times are T ¼ 0:35 s at room temperature. The
1
Fig. 2. Temperature dependence of the spin–lattice relaxation rate,
Fig. 3. Temperature dependence of the spin–lattice relaxation rate,
1
2
1
39
T1 ; for K in a K
21
3
H(SO
4
)
2
single crystal.
4
T1 ; for H in a KHSO single crystal.

484
A.R. Lim et al. / Solid State Communications 130 (2004) 481–485
correspond to two resonances in the K(1) nucleus and two
resonances in the K(2) nucleus, all of which arise from
magnetically inequivalent sites.
The first term, F W; represents the absorption or
1
emission of a single phonon (direct process). Consider the
probability of a transition induced by the term F W between
1
3
9
0
The recovery traces of K were obtained as a function of
time t at several temperatures. The recovery traces can be
represented by a linear combination of two exponential
functions. However, it was found that the recovery traces of
the two spin states lm) and lm ) with an energy difference
"v ; which will be equal to the energy of the phonon
emitted or absorbed. The number n of phonons can be
specified as its thermal equilibrium value, which, since the
o
3
9
K in the KHSO crystal can also be explained by a single
4
nuclear spin energies "v are much smaller than kT even for
o
exponential function: W and W have the same value. The
1
the lowest temperatures obtainable, is approximately
kT="v q 1: The relaxation time can then be written as
follows:
2
temperature dependence of the nuclear spin–lattice relax-
39
o
ation rate, T2 ; for K is shown in Fig. 4. The values of T
1
21
1
1
3
for the four resonance lines of the K nucleus are very
9
2
2
2
1
=T < 9pVðF =VÞ ðv =VÞ ðkQ=mn ÞðT=QÞ
ð7Þ
where T is the relaxation time of the direct process. In the
1
1
o
similar. The spin–lattice relaxation times are short: T ¼
1
1
:20 s at 300 K.
The relaxation rate increases with increasing tempera-
1
direct process, the spin–lattice relaxation rate T 12 is
1
ture, and the T2 data for the K nucleus can be described
1
39
1
proportional to the square of the frequency v and to the
0
2
1
1
2
with the following equation, T ¼ aT with a ¼ 4:78 £
absolute temperature T for kT="v q 1:
o
27
21 22
2
1
0
s
K
over the entire temperature range. This trend
The second term, F W ; corresponds to the emission or
2
3
9
is similar to that for the relaxation rate of K nuclei in
H(SO crystals.
absorption of two phonons, or the absorption of one phonon
and the emission of another (Raman process). Here the
K
3
4 2
)
0
frequencies v and v of the two phonons involved satisfy
0
the energy conservation relation v 2 v ¼ v (where v is
o
o
4
. Discussion and conclusion
the nuclear Larmor frequency), so all phonons inside the
phonon spectrum contribute to the relaxation process. The
Raman induced spin–lattice relaxation rate is thus inde-
pendent of the Larmor frequency. In the high temperature
limit, when kT="vo q 1; we can expand expð"vo=kTÞ into
1 þ "vo=kT and obtain
In many crystals, the interaction of the nuclear quad-
rupole moment with lattice vibrations is a vital relaxation
mechanism for nuclear spin I ^ 1: This coupling can
generally be described with a spin–lattice Hamiltonian [19]
H ¼
XFðqÞ
A
;
ð5Þ
Where F and A are the lattice and the spin operators,
1=T1 < 81p=10ðF2=VÞ ðkQ=mn Þ ðT=QÞ V
ð8Þ
where Q is the Debye temperature. The Raman process
ðqÞ
2
2 2
2
ðqÞ
ðqÞ
2
ðqÞ
mechanism results in a relaxation rate proportional to T :
1
respectively, of order q: The lattice operator, F (from this
point onwards, we omit the index q for brevity), can be
expanded as a function of the stress tensor W:
39
The spin–lattice relaxation times for H and K in
K H(SO ) and KHSO single crystals grown by the slow
evaporation method were investigated using a FT NMR
3
4 2
4
2
3
F ¼ F þ F W þ F W þ F W þ …
ð6Þ
39
0
1
2
3
3 4 2
spectrometer. For the K nuclei in the K H(SO ) and
KHSO single crystals, the relaxation rate increases as the
4
At temperatures far below the melting temperature of the
crystal, we expect the thermal stress to be small, so only the
first few terms in Eq. (6) are important.
temperature is increased. The temperature dependences in
Figs. 2 and 4 can be described with the simple power law
21
2
T1 ¼ aT : The temperature dependences of the relaxation
rate are in accord with Raman processes for nuclear spin
lattice relaxation. However, the spin–lattice relaxation rates
3
9
for the K nucleus in KHSeO4 and KAl(SO ) ·12H O
4 2
2
single crystals have been shown to have a very strong
7
21
temperature dependence, T1 aT [26]. These results are
7
consistent with the T data reported by Rakvin and Dalal
2
[
from the above results.
27]. In KHSO crystals, however, the trend of T differs
4
In simple NMR theory, the general behavior of the spin–
lattice relaxation rate for random motions of the Arrhenius
type can be described in terms of two regions, the fast and
slow motion regions. The fast motion region arises for
2
1
v t p 1; T , exp½2E =RTŠ; and the slow motion region
o
c
1
a
2
1
22
arises for v t q 1; T , vo exp½E =RTŠ; where v is the
o
c
1
a
o
Fig. 4. Temperature dependence of the spin–lattice relaxation rate,
Larmor frequency and E is the activation energy. In the
a
2
1
39
T1 ; for K in a KHSO
1
4
single crystal.
3 4 2
case of H nuclei in K H(SO ) crystals, the spin–lattice

A.R. Lim et al. / Solid State Communications 130 (2004) 481–485
485
relaxation rate for random motions of the Arrhenius type
with a correlation time t is in the fast motion region in the
temperature range 160–400 K. The spin–lattice relaxation
[5] A.I. Baranov, R.M. Fedosyuk, N.M. Schagina, L.A. Shuvalov,
Ferroelect. Lett. 2 (1984) 25.
c
[
[
[
6] R. Blinc, J. Dolinsek, G. Lahajnar, I. Zupancic, L.A. Shuvalov,
A.I. Baranov, Phys. Status Solidi B (123) (1984) k83.
7] M. Friesel, B. Baranowski, A. Lunden, Solid State Ionics 35
(1989) 85.
1
of H nuclei in KHSO crystals is in the fast motion region
4
below 210 K, while above 210 K it is in the slow motion
3
9
region. In the case of K nuclei in both crystals, the spin–
lattice relaxation rates are in the slow motion region, and are
thus explained in terms of Raman processes. The spin–
8] A.I. Baranov, B.V. Merinov, A.V. Tregubchenko, V.P.
Khiznichenko, L.A. Shuvalov, N.M. Schagina, Solid State
Ionics 36 (1989) 279.
1
lattice relaxation times for H in both crystals cannot be
[
9] K. Gesi, J. Phys. Soc. Jpn 48 (1980) 886.
explained by the BPP theory, and so are not related to HSO
4
[10] A.I. Baranov, A.V. Tregubchenko, L.A. Shuvalov, N.M.
Schagina, Fiz. Tverd. Tiela 29 (1987) 2513.
3
9
motion. The relaxation behaviors of
H(SO and KHSO
by Raman processes. The K
K nuclei in
K
3
4
)
2
4
single crystals can be explained
H(SO crystal displays a
[11] S. Suzuki, J. Phys. Soc. Jpn 47 (1979) 1205.
[
12] I.P. Makarova, I.A. Verin, N.M. Schagina, Sov. Phys.
Crystallogr. 31 (1986) 105.
3
4 2
)
similar hydrogen-bonding scheme to that in the KHSO4
crystal, and the molecular motions and phonon mechanisms
of the two crystals, which have similar hydrogen-bonded
systems, are similar.
[
[
[
13] R.H. Chen, T.M. Chen, J. Phys. Chem. Solids 58 (1997) 161.
14] R.H. Chen, T.M. Chen, Phase Transitions 60 (1997) 39.
15] R.H. Chen, R.Y. Chang, C.S. Shern, J. Phys. Chem. Solids 63
(
2002) 2069.
[
16] Y. Noda, Y. Watanabe, H. Kasatani, H. Terauchi, K. Gesi,
J. Phys. Soc. Jpn 60 (1991) 1972.
Acknowledgements
[17] Y. Noda, S. Uchiyama, K. Kafuku, H. Kasatani, H. Terauchi,
J. Phys. Soc. Jpn 59 (1990) 2804.
[
[
18] D.W.J. Cruickshank, Acta Crystallogr. 17 (1964) 682.
19] A. Abragam, The Principles of Nuclear Magnetism, Oxford
University Press, Oxford, 1961.
This work was supported by grant No. R04-2003-000-
0040-0 from the Basic Research Program of the Korea
1
Science and Engineering Foundation.
[
[
[
20] N. Bloembergen, E.M. Purcell, R.V. Pound, Phys. Rev. 73
(
1948) 679.
21] M. Igarashi, H. Kitagawa, S. Takahashi, R. Yoshizak, Y. Abe,
Z. Naturforsch 47a (1992) 313.
References
22] A. Avogadro, E. Cavelius, D. Muller, J. Petersson, Phys.
Status Solidi B 44 (1971) 639.
[
[
[
[
1] S.M. Haile, D.A. Boysen, C.R.I. Chisholm, R.B. Merle,
Nature 410 (2001) 910.
[23] A.R. Lim, T.G. Jang, J.H. Chang, S.Y. Jeong. In preparation.
[24] A.R. Lim, J.K. Jung, H.M. Park, J. Phys. Soc. Jpn 70 (2001)
3708.
2] A. Kawada, A.R. McGhie, M.M. Labes, J. Chem. Phys. 52
(
1970) 3121.
3] V.H. Schmidt, J.E. Drumeheller, F.L. Howell, Phys. Rev. B4
1971) 4582.
4] A.I. Baranov, L.A. Shuvalov, N.M. Schagina, JETP Lett. 36
1982) 459.
[25] A.R. Lim, T.J. Han, J.K. Jung, H.M. Park, J. Phys. Soc. Jpn 71
(2002) 2268.
(
[26] A.R. Lim, S.Y. Jeong. In preparation.
[27] B. Rakvin, N.S. Dalal, J. Phys. Chem. Solids 57 (1996) 1483.
(