1H Spin-Lattice Relaxation in a NH4HSO4 Single Crystal

Article abstract of DOI:10.1143/JPSJ.71.2268

The proton NMR line width and spin-lattice relaxation times for the NH ₄HSO₄ single crystal were studied over a wide temperature range. The proton spin-lattice relaxation time for NH₄HSO ₄ has a minimum value, which is attributed to the effect of molecular motion. The ¹H spin-lattice relaxation times occurring in phases I and III are attributed to the same motions of NH₄ ions. The activation energies for the reorientation motions in phases I and III are 0.98 and 4.61 kcal/mol, respectively. In phase II, the activation energy is 5.92 kcal/mol. The large change in the activation energy between phases I and II indicates that the NH₄ groups are affected during this transition; however, the motion of the NH₄⁺ ions between phases II and III does not play an important role in the phase change.

Full text of DOI:10.1143/JPSJ.71.2268

J. Phys. Soc. Jpn. 2002.71:2268-2270.
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Journal of the Physical Society of Japan
Vol. 71, No. 9, September, 2002, pp. 2268–2270
#2002 The Physical Society of Japan
1H Spin-Lattice Relaxation in a NH4HSO4 Single Crystal
ꢀ
1
1
Ae Ran LIM , Tae Jong HAN, Jae Kap JUNG and Hyun Min PARK
Department of Physics, Jeonju University, Jeonju 560-759, Korea
1Korea Research Institute of Standards and Science, Taejeon 305-600, Korea
(Received March 11, 2002)
The proton NMR line width and spin-lattice relaxation times for the NH4HSO4 single crystal were
studied over a wide temperature range. The proton spin-lattice relaxation time for NH4HSO4 has a
minimum value, which is attributed to the effect of molecular motion. The 1H spin-lattice relaxation
times occurring in phases I and III are attributed to the same motions of NH4 ions. The activation
energies for the reorientation motions in phases I and III are 0.98 and 4.61 kcal/mol, respectively. In
phase II, the activation energy is 5.92 kcal/mol. The large change in the activation energy between phases
I and II indicates that the NH4 groups are affected during this transition; however, the motion of the NH4þ
ions between phases II and III does not play an important role in the phase change.
KEYWORDS: ferroelectrics, crystal growth, nuclear magnetic resonance
DOI: 10.1143/JPSJ.71.2268
change. From this information, it was concluded that a
change in NHþ4 motion accompanied and reflected the phase
1. Introduction
The hydrogen sulphate family, MHSO4 (M=Na, K, Rb, transition.15) Thus, studies of the spin-lattice relaxation time
Cs and NH4), has received much attention owing to its were performed to determine more about the rates of motion.
interesting properties.1–3) The NH4HSO4 crystal undergoes This study examines the line width and spin-lattice
two phase transitions, one at Tc ¼ 270 K and the other at relaxation time, T1, for 1H in a NH4HSO4 single crystal
Tc ¼ 160 K, and is ferroelectric in the temperature range grown by using the slow evaporation method. Our main
4–6)
between 160K and 270K.
bonds play an important role in the dielectric behavior of this the types of motion that govern the relaxation and to relate
It is believed that N–HÁ Á ÁO intent was to obtain quantitative activation parameters for
1
crystal. The transition at Tc ¼ 270 K exhibits properties them to the phase transition. Based on H NMR data, we
typical of a phase transition of the second-order.7) The strove, in particular, to explain for the first time the role of
crystal under study undergoes a transition of the first-order at NHþ4 in the mechanism of the phase transitions.
Tc ¼ 160 K.8) Kondo et al.9,10) later reported that this crystal
2. Crystal Structure
was ferroelastic in the room-temperature phase.
The NH4HSO4 crystal has been the subject of several
X-ray examination indicates the true symmetry of the
experiments, including Raman scattering,11) infrared absorp- crystal at room temperature to be monoclinic, pseudo-
tion,12) nuclear magnetic resonance (NMR),13) and neutron orthorhombic. The symmetry of the pseudo-orthorhombic
inelastic scattering.14) General agreement exists that the cell is B21=a with a ¼ 24:90 A, b ¼ 4:54 A, c ¼ 14:90 A,
internal vibrations of the NHþ4 ions do not change when and ꢀ ¼ 90:18ꢁ, and Z ¼ 16. The conventional designation
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
passing through the upper transition, though the lower for this symmetry is P21=c with a ¼ 14:51 A, b ¼ 4:54 A,
ꢁ
ꢀ
transition may be associated with an ordering of these ions. c ¼ 14:90 A, and ꢀ ¼ 120:18 , and Z ¼ 8. The c-axis is the
Both transitions appear to be accompanied chiefly by a same for both cells.4,16,17) In the room-temperature phase,
change in the character of hydrogen bonding in the structure. the ammonium groups NH4(1) and NH4(2) and the sulfate
The internal vibrations of the SO24À ions are reported to groups SO4(1) and SO4(2) are inequivalent as shown in
showed no change at either transition.11,12) The results of Fig. 1. Nevertheless, the symmetrically inequivalent ammo-
Rush and Taylor14) suggest that the rotational freedom of the
NHþ4 ion is quite high. Miller et al.13) reported on the H
1
spin-lattice relaxation time, and based on their results, a new
phase transition was proposed at 173 K, to replace the one
previously reported at 160K; they observed a striking
change in the 1H spin-lattice relaxation time at 173 K. In this
paper, we classify NH4HSO4 single crystals into three
phases (I, II, and III) separated by two transition tempera-
tures.
Information regarding the structure and the internal
motion of solids can be obtained from nuclear magnetic
resonance techniques. From relaxation time measurements,
it was determined that in the neighborhood of the phase
transition temperature the slope of the relaxation time
plotted as a function of temperature underwent an abrupt
Fig. 1. Crystal structure of NH4HSO4 in the room temperature phase
projected onto (010).
ꢀCorresponding author. E-mail: aeranlim@hanmail.net
2268

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J. Phys. Soc. Jpn., Vol. 71, No. 9, September, 2002
A. R. LIM et al.
2269
nium ions are in very similar asymmetric environments. The
symmetry of the intermediate, ferroelectric phase is Pc with
the twofold screw axis disappearing at the phase transition
ꢀ
temperature. Lattice constants then become a ¼ 14:26 A,
ꢁ
ꢀ
ꢀ
b ¼ 4:62 A, c ¼ 14:80 A, and ꢀ ¼ 121:18 at 243 K. Below
154 K, the symmetry is triclinic. Observations at 133 K show
ꢀ
ꢀ
ꢀ
space group P1 with a ¼ 14:24 A, b ¼ 4:56 A, c ¼ 15:15 A,
and ꢀ ¼ 123:24ꢁ, ꢁ ꢂ 90ꢁ, ꢂ ꢂ 90ꢁ.4)
3. Experimental Procedure
NH4HSO4 is ordinarily obtained by slow evaporation of
an aqueous solution of a stoichiometric mixture of
(NH4)2SO4 and H2SO4 at room temperature. The prepared
crystals are transparent and colorless, and their dimensions
are usually 5 Â 4 Â 4 mm3.
Fig. 3. Temperature dependence of the spin-lattice relaxation time, T1, for
1H in a NH4HSO4 single crystal.
1
The nuclear magnetic resonance signals from the H in
NH4HSO4 were measured using a pulsed 200 MHz NMR
spectrometer at the Korea Basic Science Institute. The static
magnetic field was 4.7 T, and the central rf frequency was set
at !o=2ꢃ ¼ 200 MHz for the 1H nucleus. The 1H NMR
spectra were taken using a solid echo pulse sequence,
(ꢃ=2x À ꢄ À ꢃ=2y), to eliminate artifacts due to probe
ringing. The width of the ꢃ=2 pulse used was 5 ꢅs, and
the pulse separation ꢄ was 40 ꢅs. The sample temperature
was maintained at a constant value by controlling the helium
gas flow and the heater current, giving an accuracy of
Æ0:1 K.
200 MHz. The spin-lattice relaxation recovery patterns can
be quite well described with a single exponential at all
temperatures. The values of T1 measured below 300 K are
given as a function of 1000=T in Fig. 3. The change in the
curve of T1 near 160K corresponds to the phase transition,
although the line width is unchanged. However, the other
phase transition (¼ 270 K) cannot be distinguished from the
NMR results. The variation of T1 with temperature exhibits a
minimum of 289 ms at 202 K. This result is consistent with
the trend of T1 for the 1H nucleus in NH4H2PO4 and
NH4SCN single crystals.19–21) This feature of T1 indicates
that distinct molecular motion is present. The T1 in phase I
below 160K corresponds to slow motion. In phase III above
270K, the relaxation time increases with increasing
temperature, corresponding to fast motion. In phase II, the
form of the proton T1 vs. inverse temperature curve leads us
to believe that the relaxation process is caused by the NH4þ
motion. However, the calculated T1 (minimum) value of
38.8 ms is much lower than the observed value of 289 ms,
the depth of the minimum being determined by the
magnitude of the second moment modulated by the variation
of the N–H dipolar interaction.
In studies of molecular motion in relation to the
experimental relaxation time, it is important to know
whether the relaxation time is located on the slow side of
the minimum or on the fast side of the minimum as a
function of the inverse temperature. Also, the T1 values can
be related to corresponding values of the rotational
correlation time, ꢄc, the rotational correlation time being
the length of time that a molecule remains in a given state
before the molecule reorients. As such, ꢄc is a direct measure
of the rate of motion. For spin-lattice relaxation times, the
experimental value of T1 can be expressed in terms of an
isotropic correlation time ꢄc for molecular motions by using
the Bloembergen–Purcell–Pound (BPP) function:18,22)
4. Experimental Results and Analysis
Figure 2 shows the variation of the FWHM (full width at
1
half maximum) of the H line as a function of temperature.
As the temperature is lowered, the line width increases in a
step-like shape, reaching a rigid lattice value at lower
temperatures. This stepwise narrowing is generally consid-
ered to be caused by internal motions which have a
temperature-dependence connected with that observed for
the line width.18) In the transition region between 160K and
270K, the shape of the line changes, going progressively
from the Gaussian-like shape of a rigid lattice to a
Lorentzian shape. For temperatures above 270K, a very
considerable narrowing of the line occurs, and it has nearly a
Lorentzian shape.
The proton spin-lattice relaxation time was measured in
the temperature range of 120K to 300K at a frequency of
T1À1 ¼ 9=10ðꢂ2h=r3Þ2½ꢄ =ð1 þ !2ꢄ2Þ þ 4ꢄ =ð1 þ 4!2ꢄ2Þꢃ
ꢁ
c
c
o
c
o c
ð1Þ
Here, ꢂ represents the gyromagnetic ratios for the 1H
ꢀ
nucleus, r is the proton–proton separation, 1.68 A for the
NH ion, h ¼ h=2ꢃ where h is the Planck’s constant, and !
ꢁ
represents the proton Larmor frequencies. The minima occur
4
o
Fig. 2. 1H NMR line width as a function of temperature.
when the NH4 ions have !oꢄc ¼ 0:616. The BPP relation

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2270
J. Phys. Soc. Jpn., Vol. 71, No. 9, September, 2002
A. R. LIM et al.
the NH4 groups are affected during this transition, while the
motions of the NHþ4 ions between phases II and III not
playing an important role in the phase change. These results
are consistent with those reported for several experimental
method.11,12,14) According to Miller et al.,13) the H spin-
1
lattice relaxation time shows a large change at 173 K instead
of 160K. However, the T1 for the 1H in the NH4HSO4
crystals used here was well defined by the BPP theory, and
the proton T1 showed no sudden changes near 173 K.
Consequently, NH4HSO4 single crystals may have different
properties, depending on the crystal growth conditions.
Acknowledgment
This work was supported by grant No. R05-2001-000-
00148-0 from the Basic Research Program of the Korea
Science and Engineering Foundation.
Fig. 4. Arrhenius plot of the natural logarithm of the correlation times in
phase II for the proton as a function of the inverse temperature.
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ꢄc ¼ ꢄo expðEa=RTÞ;
ð2Þ
and, the slopes of the straight line portions of the semilog
plots determine the values for the activation energy, Ea. The
activation energies for the reorientational motions in phases
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The proton NMR line width and spin-lattice relaxation
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The changes in the proton relaxation behavior in the
neighborhood of the phase transition temperature indicate
a change in the state of the internal motion at the transition.
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lattice relaxation time for random motions of an Arrhenius
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i.e., for, !oꢄc ꢄ 1, T1À1 ꢅ exp½Ea=RTꢃ, and for the slow
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