High pressure behaviour of KHSO4 studied by electrical impedance spectroscopy

Article abstract of DOI:10.1016/j.ssc.2005.06.028

Measurements of the electrical conductivity were performed in KHSO ₄ at pressures between 0.5 and 2.5 GPa and in the temperature range 120-350 °C by the use of the impedance spectroscopy. The temperatures of the α-β phase transition (T_Tr) and of the melting (T _m), determined from the Arrhenius plots ln(σT) vs. 1/T, increase with pressure up to 1.5 GPa having dT/dP～+45 K/GPa. Above the pressure 1.5 GPa, the pressure dependencies of T_Tr and T_m are negative dT/dP～-45 K/GPa. At pressures above 0.5 GPa, the reversible decomposition of KHSO₄ into K₃H(SO₄) ₂+H₂SO₄ (and probably into K₅H ₃(SO₄)₄+H₂SO₄) affects the electrical conductivity of KHSO₄, with the typical values of the protonic electrical conductivity, c. 10^-1 S/cm at 2.5 GPa.

Full text of DOI:10.1016/j.ssc.2005.06.028

Solid State Communications 136 (2005) 16–21
www.elsevier.com/locate/ssc
High pressure behaviour of KHSO studied by
4
electrical impedance spectroscopy
a,
b
N. Bagdassarov
*
, G. Lentz
a
Arbeitsbereich Geophysik, Universit a¨ t Frankfurt, Felbergstrabe 47, D-60323 Frankfurt am Main, Germany
b
Mineralogisch-Petrographisches Institut und Museum, Universit a¨ t Kiel, D-24098 Kiel, Germany
Received 3 May 2005; received in revised form 22 June 2005; accepted 23 June 2005 by A.K. Sood
Available online 11 July 2005
Abstract
Measurements of the electrical conductivity were performed in KHSO at pressures between 0.5 and 2.5 GPa and in the
4
temperature range 120–350 8C by the use of the impedance spectroscopy. The temperatures of the a–b phase transition (TTr
and of the melting (T ), determined from the Arrhenius plots ln(sT) vs. 1/T, increase with pressure up to 1.5 GPa having
dT/dPwC45 K/GPa. Above the pressure 1.5 GPa, the pressure dependencies of TTr and T are negative dT/dPwK45 K/GPa.
)
m
m
At pressures above 0.5 GPa, the reversible decomposition of KHSO
K
4 3 4 2 2 4
into K H(SO ) CH SO (and probably into
5
H
3
(SO CH SO ) affects the electrical conductivity of KHSO , with the typical values of the protonic electrical
4
4
)
4
2
4
K1
conductivity, c. 10 S/cm at 2.5 GPa.
q 2005 Elsevier Ltd. All rights reserved.
PACS: 84.37; 74.25.F; 84.32.F; 82.30.N; 05.70.F; 64.60; 64.70; 61.50.K
Keywords: A. Acid potassium sulphate; D. Phase transition; D. Proton conductivity; E. Pressure
1
. Introduction
melting point. The amplitude of librational and rotational
motions of BO tetrahedra increases with heating, and the
4
KHSO
compounds with the general chemical formula AHBO
where A is a monovalent cation (Cs, Rb, NH K, Na), and B
4
belongs to the class of hydrogen bonded
AHBO framework looses its rigidity allowing protons to
4
4
,
occupy additional crystallographic sites [1]. For large
4
,
cations such as AZCs, Rb, NH the compounds exhibit
4
stands for S or Se. A typical structural feature of AHBO
compounds is the occurrence of (HBO -dimers and
4
superprotonic conductivity in high temperature phases. The
4
)
HBO -chains being separated from each other by
2
transition temperature to the superprotonic state decreases
N
4
with the increase of the cation size [2]. By doping CsHSO
with K, the superprotonic phase transition in the system
HSO vanishes for xR0.75 [3]. Note that the
crystal structures of CsHSO and KHSO are different.
4
A-cations. It is believed that the hydrogen bonding pattern
between HSOK tetrahedral ions in the dimers and chains is
4
Cs1KxK
x
4
responsible for the ferroelectric phase transitions in this
class of compounds. Members of this type of compounds are
known to undergo few reversible and irreversible phase
transitions above the room temperature and below the
4
4
The mechanism of proton transport in the high
temperature phases consists essentially in a motion of H
within a double-well potential and the associated migration
of H between two adjacent crystallographic sites. The
conductivity in the low temperature phases was suggested to
be related to the dynamics of H-bonds inside chains [4].
That is called the Grotthuss mechanism of proton
conductivity [5]. At higher temperatures an additional
*
Corresponding author. Tel.: C49 69 79823376; fax: C49 69
9823280.
E-mail address: nickbagd@geophysik.uni-frankfurt.de
N. Bagdassarov).
7
(
0038-1098/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ssc.2005.06.028

N. Bagdassarov, G. Lentz / Solid State Communications 136 (2005) 16–21
17
contribution to proton conductivity arises from the
synchronous reorientation of H-bonds between dimers and
the reversible chemical dehydration (178, 212 8C) on the
surface of KHSO crystals.
4
chains in the crystal structure. The role of BOK tetrahedra
A suitable doped potassium hydrogen sulphate crystal is
known to be a pure proton conductor [4,20]. Previous
4
rotation (or libration) is in the assisting of a break of a
double-well H-bond. The activation energy of proton
transfer in superprotonic conductor is defined by the
energetic barrier within the double-well hydrogen bond
and is of the order of w0.1–0.6 eV [1]. The phase transition
in a superprotonic conductor is affected by moisture,
pressure and concentration of impurities. During the phase
transition, the electrical conductivity jumps to values of
conductivity measurements on KHSO
ambient pressure and are summarised in Fig. 1. The non-
doped crystals of KHSO do not show the signature of a
were performed at
4
4
superprotonic phase transition. Instead, the differing
conductivity values were found at lower temperatures,
together with variations in phase transition and melting
temperatures.
K3
K2 K1
Contrary to KHSO
phases of RbHSO and NH
4
, the high temperature tetragonal
HSO are known to possess a
1
0
–10
U
/cm, and materials become plastic [6,7].
The typical activation energy of the electrical conductivity
in high temperature phases of hydrogen bonded sulphates is
4
4
4
superprotonic state at high pressures, i.e. a decrease in radius
of A in AHSO4 compound is equivalent to a pressure
increase (see Ref. [7,23] and references therein). Under the
0
.3–0.45 eV [7]. The proton conductivity in these com-
pounds does not need a humid atmosphere making these
materials attractive for fuel-cell applications. The low
temperature non-conductive phase often does not appear
upon cooling of the high temperature conductive phase.
hydrostatic pressure 0.6 and 0.28 GPa RbHSO
NH HSO become superprotonic conductors, respectively
4
and
4
4
[
7]. The question still remains whether K-cation, which is
even smaller than Rb or ammonium, also allows the
transformation to a high-pressure superprotonic state.
KHSO
4
, also known as the mineral mercallite, crystal-
1
5
lizes in the orthorhombic space group PbcaZD [8,9],
2h
Consequently, the temperature dependence of the KHSO
conductivity at high pressures were studied.
4
with two inequivalent H-sites, and a total of 16 formula units
per unit cell. The dimensions of the unit cell are 8!9!
3
Structural properties of KHSO
unknown. The only high pressure study published so far
concerns the investigation of phase transitions in KHSO by
at high pressure are
˚
4
1
8 A . As mentioned above, the two different types of
HSO K4 tetrahedra in the asymmetric unit are differently
linked by hydrogen bridges: one type forms dimers across a
centre of symmetry with O/O distances varying from 2.67
4
Raman-spectroscopy [24]. In the present paper the electrical
impedance of polycrystalline KHSO has been measured in
4
˚
to 2.619 A; the other type is linked into infinite chains along
the temperature interval from 100 to 330 8C at pressures of
0
the a-axis with O/O distances varying from 2.67 to
.2, 0.5, 1.5, 2.0 and 2.5 GPa.
˚
2
.573 A [8]. Due to the chain orientation parallel to the a-
axis, KHSO crystals possess a marked anisotropy of the
elastic stiffness (c11Z57 GPa, c22zc33Z31 GPa) and the
4
2
. Experimental
K6
thermal expansion coefficients (a11Z5.6!10 , a22
Z
) [10]. The length of
K6
K6 K1
5
9!10 , and a33Z68!10
K
4
Crystalline powder of KHSO was prepared from an
K
four S–O bonds in HSO4 in early studies has been reported
aqueous solution of K SO and H SO at the ratio 1:2 by
2
4
2
4
4
all equal [8], later it was shown that in KHSO , in the
slow evaporation. The products before and after the high
pressure runs were identified by the X-ray powder
tetrahedral ion SO4K, the S–O bonds are 1.44, 1.475 A long,
2
˚
˚
an S–OH bond is longer, cZ1.57 A [9,11,12].
4
Phase transitions in KHSO have been studied by several
techniques: TGA, DTA, DSC [13–15], dilatometry [16],
NMR [13,17], electrical conductivity measurements [13,
1
7], and in situ X-ray measurements [18]. There is a general
consensus about the phase transition at 178 8C [13,14,17],
which was earlier interpreted as a superposition of two
phase transitions at 164 and 181 8C. The melting point of
potassium hydrogen sulphate is still the matter of
discussions and has been estimated from 207 8C by
electrical conductivity [19] and 208 8C by DSC to 215 8C
from electrical conductivity measurements [13]. The phase
transition at 120 8C has been identified by DTA [14],
electrical conductivity measurements [17] and by in situ
X-ray powder diffraction [18]. In Ref. [14] the changes of
Fig. 1. The electrical conductivity measurements in KHSO
MPa [2,4,13,16,17,19–22]. The melting point T estimated by
different authors is: 207 8C [19], 215 8C [13], 205–208 8C [15],
12 8C [14]. The phase transition to the high temperature
4
at 0.
1
m
4
physical properties in KHSO at 120, 178 and 212 8C are
2
interpreted as not related to the structural phase transition,
conductive phase prior to melting has been estimated as 178 8C
from electrical conductivity measurements [13].
but rather as a result of the water desorbtion (1208) and of

18
N. Bagdassarov, G. Lentz / Solid State Communications 136 (2005) 16–21
diffraction. The crystals are slightly hydroscopic and hence,
were dried for 24 h at 110 8C prior to the conductivity
measurements.
electric conductivity prior to melting. It is difficult to
elaborate a criteria to determine the phase transition and the
melting temperatures from log(sT) vs. 1/T, K plot. The
phase transition in a conductive phase may be identified by a
temperature point corresponding to the steep increase of
log(sT) vs. 1/T, K and to the abrupt change of the activation
2
.1. Electrical conductivity measurements
The measurements of the electrical impedance were
performed at pressures up to 1 GPa and temperatures up to
00 8C. The KHSO powder was pressed in the coaxial gap
between two concentric cylindrical electrodes made from
Pt-tubes having 3.8 and 2.2 mm diameters and 0.1 mm
thickness. The length of the capacitor varied from 6.5 to 4.
energy E
s
[13]. In the low temperature phase E
is 0.37 eV,
s
above the phase transition temperature E
s
exceeds 2–3 eV.
5
4
The melt characterises by the activation energy about
0.2 eV. However, in Ref. [17], the phase transition
temperature was identified in the middle of the temperature
interval, where the steep increase of conductivity occurs, i.e.
TTr relates to a change of the activation energy from 3.3 to
3.9 eV. In the present study, the electrical impedance
measurements were realised during heating and cooling
with a rate w1 K/min.
5
mm. The inner part of the high-pressure cell and the
pressure calibration procedure are described elsewhere [25].
For each temperature and pressure, the impedance Z over
K2
the frequency range 3!10 –3!10 Hz has been
5
measured. The bulk electrical conductivity of KHSO was
4
The results of the bulk electrical conductivity measure-
ments for K H(SO ) from Ref. [27] are shown in Fig. 2 for
estimated from Argand plots, the dependence of KIm[Z]
from Re[Z]. The intersection of the KIm[Z] arc with the
Re(Z) axes defines the bulk resistance of the sample. The
frequency scan data can be fitted to a sum of two relaxation
functions:
3
4 2
comparison. Fig. 2(a) represents three subsequent heating
cycles plotted in the Arrhenius diagram. The identification
of the melting temperature is straightforward, it corresponds
to the activation energy 0.23 eV. The T , the temperature of
Tr
the a–b phase transition, corresponds to the point of the
deviation of the bulk electrical conductivity from the
Arrhenius dependence. The cooling and heating cycles
follow different paths (Fig. 2(a)), which is due to disordering
R1
R2
Zp Z
C
(1)
p
n
1
Cðjute:p:
Þ
1 Cðjutd:l:Þ
where the first term corresponds to the low frequency
dispersion, and the second term stands for the dielectric
4
of the KHSO structure above TTr and in the phase melt.
losses in the sample [26] with Z
p
is the measured impedance,
After annealing of the high temperature phase at Tw100 8C
over c. 1–2 h, the conductivity decreases to the initial value
of the low temperature phase. During several successive
cycles of heating and cooling, the conductivity data, melting
temperature and TTr were reproducible. Up to 1 GPa TTr and
pffiffiffiffiffiffi
R
i
is the active resistance, j is K1, u is the frequency, t
i
is
the dielectric relaxation time. The temperature dependence
of td.l. determines the activation energy of the dielectric loss
peak. The parameter n in Eq. (1) characterises the broadness
of the dielectric loss peak in comparison with a Debye peak
T
m
increase with pressure. In experiment at 1 GPa
(
nZ1).
The bulk DC-conductivity sDC of the sample is
calculated from Eq. (1) according to sDCZ1/(R G), where
G is the geometric factor of the capacitor cell (5–8 cm in this
(Fig. 2(b)) the measurements have been done also after
the pressure release from 1 to 0.2 GPa. The bulk
conductivity data in a depressurised sample indicates the
reversible decrease of melting and phase transition
temperatures after decompression. The measurements
obtained at pressures 1.5, 2 and 2.5 GPa demonstrate a
decrease of melting and phase transition temperatures with
increasing pressure above 1.5 GPa.
1
study). The activation energy of the bulk conductivity, E
s
was derived from the Arrhenius equation as follows
KEs=ðkTÞ
sDCT Z s0e
(2)
where T is the temperature in Kelvin, k is the Boltzmann’s
constant, s is the pre-exponential factor.
The activation volume calculated from E
a
which was
0
measured from the data in Fig. 2(a)–(c) is c. C0.2G
3
.1 cm /mol at pressures below 1.5 GPa and is c. K0.2G
0
0
3
.1 cm /mol at PO1–5 GPa. The reported activation
3
. Results
volume of the electrical conductivity for CsHSO is 0.1–
4
3
3
1
4 4
cm /mol and for NH HSO is !2 cm /mol [23].
The bulk resistance was determined from the Arrhenius
plots of the electrical measurements covering the tempera-
ture range both below and above the solid phase transitions
and the melting of KHSO . Fig. 2(a)–(c) shows the
4. Discussion
4
measurements at 0.5, 1, 1.5, 2, and 2.5 GPa, the first heating
and the subsequent cooling and heating cycles. The data are
presented in a form of the Arrhenius plot. The change of the
slope on the curve evidences the drastic increase of the
The pressure dependence of a–b phase transition and
melting in KHSO may be estimated from Klasius–
Clayperon relationship
4

N. Bagdassarov, G. Lentz / Solid State Communications 136 (2005) 16–21
19
dT
dP
DV
DS
TDV
DH
Z
Z
(3)
where DV and DH are the changes of specific volume and
enthalpy at normal pressure. There are only few measure-
ments of the volume and enthalpy changes of the a–b
phase transition in KHSO . In Ref. [16] the reported DV/V is
4
wC0.12%. The measured endothermic DH is 2.11 kJ/mol
at 178 8C [13,15]. Using the specific volume at 22 8C,
3
8.83 cm /mol, and the volume thermal expansion coeffi-
K4 K1
5
cient, 1.33!10
K
at 178 8C is K0.0725 cm /mol and the calculated dT/dP is
, from Ref. [10], the extrapolated DV
3
3
wC15.5 K/GPa. For melting, DVZC2.65 cm /mol or 4%
[
19], DHZ16.6–16.2 kJ/mol [13,15], and the estimated dT/
dP is from 77 to 79 K/GPa. The recent determinations of
enthalpies for melting (crystallisation) are 14.6 (14.8) kJ/
mol at 205 (188 8C) and for the a–b phase transition is
1
.63 kJ/mol at 182 8C during heating [28]. These values
provide a slope C87 and C20 K/GPa for melting and the
a–b phase transition, respectively. This difference in slopes
of the pressure dependence of melting and the a–b phase
transition means that with the pressure increase the
temperature interval of the b-phase stability should be
larger before melting occurs. In Ref. [23] the reported
pressure dependence of the superprotonic phase transition
temperature in CsHSO is c. 5 K/GPa, and about 0 K/GPa in
4
NH HSO . In comparison, melting temperatures of CsHSO
4
4
4
depends much stronger on temperature dT
m
/dPwC100 K/
GPa [23], and, thus, the pressure increases the temperature
range of the superprotonic phase stability. In contrast, for
3 4 2
A H(SO ) crystals dTTr/dP is negative from K40 to
K60 K/GPa [7].
Fig. 3 represents the measured temperatures of the a–b
phase transition and melting temperatures estimated from
electrical conductivity measurements by using log(sT) vs.
1
/T plots in Fig. 2(a)–(c). The estimated dT/dP slopes for
melting differ significantly from the predicted values.
Moreover, above 1.5 GPa the dT/dP slopes become
negative. This could be caused by an unknown phase
transition or a pressure induced amorphization in potassium
hydrogen sulphate. However, the most plausible explanation
Fig. 2. (a) The electrical conductivity measurements at 0.5 GPa in
KHSO . (1) The first heating to 225 8C characterised by E Z1.
1 eV prior to a–b transition in KHSO ; the phase transition and
melting points are 219 and 234 8C, respectively. (2) The second
heating to 240 8C characterised by E Z0.77 eV prior to a–b and
4
s
6
4
is the instability of KHSO
scattering experiments in diamond anvils [24] demonstrated
that at PO0.4 GPa the Raman spectrum of KHSO evolves
4
under pressure. The Raman
s
higher temperatures of transformation 224 8C and melting 245 8C.
The electrical impedance results are affected by the decomposition
4
in spectrum similar to K
sition reaction is as follows:
3
H(SO
4
)
2
. The suggested decompo-
(4)
4
process of KHSO
H(SO melting is characterised by E
s
4
. In a decomposed mixture of KHSO
4
and
K
3
4
)
2
Z0.23 eV above 289 8C.
The low temperature phase has an activation energy 0.42 eV. These
values are in good agreement with the data of [17], where the low
3KHSO 4K HðSO Þ CH SO
4
3
4 2
2
temperature phase possesses E
transition E changes from 3.2 to 3.9 eV and in the melt E
8 eV. The difference in conductivity during cooling and heating
cycles reflects the disordering of K H(SO –KHSO structure near
the a–b phase transition at 236 8C. The data of the electrical
conductivity in K H(SO from Ref. [27] are shown for
comparison. (b) The electrical conductivity measurements in
KHSO at 1 GPa and after pressure release to c. 0.2 GPa. Prior to
s
Z0.39 eV, and prior to the a–b
is 0.
the temperature of the phase transition E
respectively. The data of electrical conductivity in K
Ref. [27] are shown for comparison. (c) The electrical conductivity
of KHSO at 1.5, 2.0 and 2.5 GPa. The arrows indicate the phase
transition and melting temperatures. E of the electrical conduc-
s
is 0.42 and 0.53 eV,
s
s
1
3
H(SO from
4 2
)
3
4
)
2
4
4
3
4
)
2
a
tivity in the high temperature phase is 0.56, 0.42 and 0.23 eV,
respectively.
4

20
N. Bagdassarov, G. Lentz / Solid State Communications 136 (2005) 16–21
reversible character of the decomposition reaction. The
XRD of samples quenched at 0.5 and 2.5 GPa and 100 8C
are identical to the XRD of a starting sample and a standard
XRD of mercallite. Only in the quenched sample at 2.5 GPa
and 320 8C there are small features (!1%) of XRD of
K
5
H
3
(SO
), small peaks at 2qZ24.5, 31.8 and 42.58 were observed.
This may also suggest a possible decomposition reaction
KHSO 4K (SO CH SO , but there are no reliable
4 4
) (PDF 17-0597 from the ICDD data bank PDF-
2
5
4
5
H
3
4
)
4
2
4
PDF data to confirm this. In any case, the decomposition
reaction of mercallite at high pressure seems to be almost
reversible.
Fig. 3. The results of the melting and TTr temperature measurements
obtained by the electrical impedance measurements. The melting
point and TTr at 0.1 MPa are from Ref. [13] black filled symbols,
measured by the differential enthalpic analysis. The grey filled
5. Conclusions
symbols are phase transition temperatures in K
27]. Above the turnover point 1.5 GPa, the negative slopes of
dT/dP indicate probably a decomposition of KHSO . The arrows
indicate the calculated slope dT/dP for melting and a–b phase
transition in KHSO . The vertical trend of points at 0.5 GPa is
probably a result of the progressive decomposition of KHSO into
H(SO
3
H(SO
4
)
2
from Ref.
1. KHSO
starts to decompose into K
3 4 2
H(SO ) (and
4
[
possibly in K
5
H
3 4 4
(SO ) ) at pressure above 0.5 GPa.
4
The turnover point of the decomposition reaction on P–T
diagram is 1.5 GPa. According to XRD of quenched
samples this decomposition reaction is reversible.
4
4
2
3
. With the pressure increase up to 1.5 GPa the pressure
dependencies of TTr and T
K
3
4 2
) .
m
are positive, having
dT/dPwC45 K/GPa. Above the pressure 1.5 GPa the
pressure dependencies of TTr and T
having dT/dPwK45 K/GPa.
The results of the electrical conductivity measurements
m
are negative,
obtained at 0.5 GPa (Fig. 2(a)) clearly demonstrate the
change of physical properties of the starting composition
after few successive heating–cooling cycles. The decrease
of the activation energy and the increase of the characteristic
points on the curves log(sT) vs. 1/T, K evidence the
progressive increase of the K H(SO ) content in the
. The high temperature phase measured in experiments
under pressure, presumably a mixture of KHSO with
K H(SO ) and, probably, K H (SO ) , possesses a
4
3
4 2
5
3
4 4
typical values of the protonic electrical conductivity c.
K1
3
4 2
1
0
S/cm up to 2.5 GPa.
starting KHSO
the measured log(sT) vs. 1/T, K curves at pressures and the
results for K H(SO in Ref. [27] suggests a certain
similarity of the electrical conductivity behavior vs. T
Fig. 2(a)–(c)). Clearly, this similarity is noticeable at
.0 GPa. At atmosphere pressure, K H(SO undergoes
4
composition. The comparison of
3
4 2
)
Acknowledgements
(
1
3
4 2
)
This research was funded by the German Science
Foundation DFG under contract Kn 507/3-1.
several phase transitions prior to melting point. During
subsequent heating–cooling cycles the transition tempera-
tures may decrease from 227 and 190 to 223 and 185 8C,
respectively [27]. DSC study of K
dehydration reaction at 206 8C and melting at 269 8C [29].
In a mixture of the K H(SO and KHSO compo-
sitions, the characteristic temperatures on the Arrhenius
plots may be located between those for K H(SO and
KHSO . The reason for the negative slope of phase
3 4 2
H(SO ) indicates a
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3
4
)
2
4
[
[
[
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[
[
[
[
[
[
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