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Ferroelastic-assisted phase transition to fast ionic conduction in LiKSO4. A correlative ac conductivity-specific heat study
Materials Letters 15 (1992) 162-166 North-Holland
Ferroelastic-assisted phase transition to fast ionic conduction in LiKS04. A correlative ac conductivity-specific
heat study
M.E. Kassem ’ PhysicsDepartment, Universityof Qatar,P.0. Box t713, Doha, Qatar Received 14 April 1992; in final form 20 August 1992
The ac conductivity (u) of LiKS04 crystals was measured along the ferroelastic b axis in the temperature range 300-800 K and frequency range 5-5 x 10’ Hz, using a Tesla impedance meter. Specific heat measurements demonstrate the presence of several phase transitions: the prominent ferroelastic transition being at T,=?OS K. A correlative study, of both techniques, reveals that the superionic conductivity features are the results of the ferroelastic phase transition. This is evident as conductivity decreases by more than three orders of magnitude from 9.5 x 10e9 to 1.4~ 10-5R-’ cm-‘, with the activation energy being slightly increased.
I. Introduction In the last few years, increasing interest has been directed to the applications of superionic conductors. The double salts LiMX04 (M=Na, K, Rb or Cs and X=S or Se) constituted one family distinguished by fast ionic conduction features [ 11, A sudden conductivity rise by 2-4 orders of magnitude with increasing temperature has been reported [ 2,3 1. Transition to superionic conduction has been assigned [4] to enhanced ion mobility of Li around the central, tetrahedral X0,. The transition to superionic conduction has recently been reported [ 51 to constitute a first-order structural phase transition. The conductivity in the latter case was modified abruptly at T,.Since the activation energy did not significantly alter upon shifting to fast ionic conduction, the modified conductivity has therefore been attributed to the ferroelastic structural displacement. LiKSO, exhibits a hexagonal symmetry with polar point group 6 and space group P63 at room temperature. It undergoes several structural phase transitions below [ 6,7 ] and above [ 8-101 room temperature. Until recently, the reported data for electric ’ Permanent address: Physics Department, Alexandria University, Egypt.
162
conductivity have been from dc measurements. It could be of interest to compare the dc data with data derived from ac measurements, which should shed more light on the nature and mechanism of conduction. The aim of this work is to report on the nature of conduction in the vicinity of the structural ferroelastic phase transition taking place at 708 K.
2. Experimental Crystals of LiKS04 were isothermally grown at 3 15 K from an aqueous solution containing the initial simple salts at the stoichiometric ratio, following the method of dynamical and slow evaporation [ 111. The crystals were untwinned and of good optical quality. Samples were cut perpendicular to the b axis into thin slab plates of 0.1 cm thickness and 1x 1 cm2 area. The plates were silver-coated, using the evaporation technique. The electric impedance was measured in the temperature range 300-800 K and frequency range 5-5 x lo5 Hz, using a Tesla impedance meter operating at 5 mV. The sample was placed inside a specially evacuated holder [ 121, where the temperature was stabilized within + 0.1 K. The specific heat at constant pressure, C,, was
0167-577x/92/% 05.00 Q 1992 Eisevier Science Publishers B.V. All rights reserved.
Volume 15, number 3
MATERIALS LETTERS
measured using a DSC technique, where a Heraeus DSC cell was connected to a Heraeus DTA 500 thermal analyser. The measurements were performed by applying the base-line method [ 13 1. Lidded pans, made of aluminium, were used to eliminate sloping of the base line. A Pt 100 thermocouple was used as the temperature sensor, while a heating rate of 2 K/ min was applied.
3. Results and discussion The measured impedances of all the samples at various temperatures were analysed [ 14,15 1. Fig. 1 shows typical Cole-Cole diagrams for LiKS04 crystals at various temperatures in the region of the ferroelastic-phase transition, T, = 708 K. The dependence of Z” (Z’ ) follows semicircles originating from the region with no overlap (fig. 1). This means that the surface resistance R, is zero and the sample resistance is composed mainly of the bulk resistance Rb which is in parallel with capacitance C,. Extrapolating the high-frequency limit and the low-frequency limit of the semicircles’ intercepts with the real axis Z’ gives the values of R, and Rb respectively [ 16,171. It is also clear from fig. 1 that the arc diameter of the semicircle decreases with increasing
2”
November 1992
temperature. However, the behaviour is governed differently depending whether the phase is ordered (T-c T,) or disordered (T> T,). Ionic conductivity of the samples can be estimated using the sample geometry and the dc resistance at different temperatures. The behaviour of the conductivity with temperature follows an Arrhenius linear dependence with a clear phase transition to extend from 690 to 708 K as shown in fig. 2. This behaviour is due to the thermal history which plays a great role in T, and the domain wall motions in LiKS04. Below the transition temperature, the conductivity values are low (9.5 x lop9 Q-’ cm-‘), but with quite low activation energy values. However, an abrupt increase in the conductivity occurs above T, with slight change in the activation energy. The conductivity values above T, are 1.4x lop5 R-’ cm-‘, which is more than three orders of magnitude greater than the values below T,. To understand the observed behaviour, the classical many-body theory [ 18 1, whose validity extends beyond the area of solid electrolytes, was applied. This theory treats the diffuse transport of the mobile ions hopping among the lattice in addition to interacting with the diffusion ions, The many-body interaction affects the ordering of ions inside the lat-
8
T:668 K
6
I 1.33
Fig. 1. A complex plane dependence of the imaginary part Z” on real part Z’ of the impedance in the vicinity of phase transition T,=708 K.
4
1.41
1.49 lo'/
T,
1.57
K-'
Fig. 2. Temperature dependence of the bulk conductivity 0 in the vicinity of r,.
163
November 1992
MATERIALS LETTERS
Volume 15, number 3
lo-
103
:
i
IO-
\ \ :
S
A
r1
-0
l 2
\
\
l
\
\
I
10
I
-c-f
m
I
k
l’
//
600
700
1.
8 Fig. 3. (A) A packing of 0 and K atoms in the structure of LiKSO., (xy plane). (B) Four equilibrium positions of the SO, group in the hexagonal phase [ 22 1.
tice. The phase transition in most crystals belonging to the double-sulphate family is an order-disorder transition; such transitions are related to the ordering of the tetrahedral group. In the paraelectric phase, the tetrahedral group occupies two or more equivalent positions. The order parameter describing a superionic phase transition is the density of the mobile ions, rather than the existence of spontaneous dipoles and strain in ferroelectric and ferroelastic materials [ 19 1. 164
up
\
\
I
1(r-
X
-T a I. -I
l \
I I I
s
00
m
r
102
T Y
800
K
Fig. 4. Variation of C, and conductivity with temperature.
The crystallographic structure of LiKSO, can be considered as slight distortions of the prototype aKzS04 structure. From the structure studied of such a crystal [20], one can see that the tetrahedra GO:-, SO:-, share oxygen atoms which lie on a trigonal axes, fig. 3A. In the polar b direction, Li and S atoms are nearly equidistant from K+ and a common oxygen atom is nearly 0.3 A from the midway of Li and S [ 2 I]. Hence, the effective point change associated with LiSOh may be taken at this 0 atom. The structural transition is expected as a result of various orientational orderings of the SOa- group, accompanied by ionic displacements. Four discret
Volume
15, number
MATERIALS
3
LETTERS
November
1992
where B contains all nonsingular contributions and p is a constant. The variation of d In aT/dTwith molar C, is shown in fig. 5. The value of p was calculated to be equal to 0.16, while B is equal to 0.046. The obvious correlation between the ac conductivity (i(T) and specific heat C,( T) is clear. This behaviour is attributed to the dominating role of the nonlinearities in the temperature dependence of (T and
Acknowledgement The author is very grateful to Professor Dr. Latifa Al-Houty, Chairman of the Physics Department, University of Qatar, for her fruitful discussions and continuous assistance in his work.
.08
References
I_ .04
.lO
.16
.22
CpIRTc
Fig. 5. A correlation between activation energy of the bulk conductivity and C, in the ionic phase transition region.
orientational states of each SOi- tetrahedron in cationic environment can be labelled with the help of two Ising variables [ 22 ] (up or down the hexagonal axis and turns of tetrahedron to the right or left) as shown in fig. 3B. It is well known that there exists a proportionality between n and the interaction enthalpy, h, of mobile ions. The proportionality constant gives some microscopic information about the short-range order which modifies the energy of the diffusion jump. The conductivity in LiKSO, solids, which provides a simple measure of mobility at its transition, has been shown to be 3d Ising model [ 231. The Nemst equation [ 241 gives directly the conductivity, from which the correlation between the electrical conductivity, a, and the specific heat, C,, could be obtained. Fig. 4 shows the variation of C,, as well as d In a/dT, with temperature. The relationship between (Tand C, is given by
[ 1 ] Cz. Pawlowski, F.E. Salman, A. Pawlowski, A. Pietraszko, Phase Trans. 8 (1986) 9.
2. Czapla and
[2] A.I. Baranov, L.A. Shuvalov and N.M. Shehagina, JETP Letters 36 (1982) 459. [ 31 A.P. Kovalenko, Soviet Phys. Solid State 27 ( 1985) 570. [4] M.A. Pimenta, P. Echegut and F. Gervais, J. Phys. C 19 (1986) 5519. [ 5 ] J.B. Boyce and T.M. Hayes, in: Physics of superconductors, ed. M.B. Salamon (Springer, Berlin, 1979). [6] T. Brenczewski, T. Krajewski and B. Mroz, Ferroelectrics 33(1981)9. [ 71 T. Krajewski, T. Brenczewski, M. Kassem and B. Mroz, Ferroelectrics 55 (1984) 143. [ 8 ] A.M. Okaz, S. Mahmoud and M.E. Kassem, J. Mater. Sci. 23 (1989) 998. [ 91 T. Krajewski, T. Brenczewski, P. Piskunwicz and B. M&z, Ferroelectrics Letters 4 ( 1985) 95. [lo] M.A. Pimenta, P. Echegut, Y. Luspin, G. Hauret and F. Gervais, Phys. Rev. B 39 (1989) 3361. [ 1 I ] B.M. Bartlett, J. Sci. Instr. 88 ( 196 1) 54. [ 12 ] M.E. Kassem, E.F. El-Wahidy, S.H. Kandiel and H. Gado, Ferroelectrics Letters 5 ( 1986) 7 1. [ 13 ] T. Daniels, Thermal analysis (Kogam Page, London, 1973) p. 127. [ 141 A.K. Jonscher, Dielectric relaxation in solids (Chelea Dielectric Press, London, 1983) ch. 3. [ 151 M.E. Kassem, A.Y. Kandiel and L. Al-Houty, J. Polymer Mater., to be published. [ 161 J.L. Carpentier, A. Lebrum and F. Predu, J. Phys. Chem. Solids 90 (1989) 145.
165
Volume 15, number 3
MATERIALS LETTERS
[ 171 J. Millete and M. Gillow, J. Chem. Phys. 64 (1987) 2483. [ 181 L.J. Girifalco, Statistical physics of materials (Wiley, New York, 1973); L. Ruth, D.R. Sain, H.L. Yeh and L.A. Girifalco, J. Phys. Chem. Solid 37 (1976) 649. [ 191 V.N. Bondarev and V.M. Kostenko, Soviet Phys. Solid States 25 (1983) 1406. [20 ] H.M. Alak, A.W. Brinkman, G.J. Russel and A.W. Roberts, J.Phys.D21 (1988) 1226.
166
November 1992
[21] R. Farhi and F. Condin, J. Phys. Conden. Matter 1 ( 1989) 6951. [22] V.I. Zinenko and D.Kh. Blat, Soviet Phys. Solid States 20 (1978) 2047. [ 231 H. Schulz, M. Zuker and R. French, Acta Crystallogr. B 41 (1985) 21. [ 241 H.R. Manning, C.J. Vennte and D.P. Boden, J, Electrochem. Sot. 118 (1971) 2031.
Ferroelastic-assisted phase transition to fast ionic conduction in LiKS04. A correlative ac conductivity-specific
heat study
M.E. Kassem ’ PhysicsDepartment, Universityof Qatar,P.0. Box t713, Doha, Qatar Received 14 April 1992; in final form 20 August 1992
The ac conductivity (u) of LiKS04 crystals was measured along the ferroelastic b axis in the temperature range 300-800 K and frequency range 5-5 x 10’ Hz, using a Tesla impedance meter. Specific heat measurements demonstrate the presence of several phase transitions: the prominent ferroelastic transition being at T,=?OS K. A correlative study, of both techniques, reveals that the superionic conductivity features are the results of the ferroelastic phase transition. This is evident as conductivity decreases by more than three orders of magnitude from 9.5 x 10e9 to 1.4~ 10-5R-’ cm-‘, with the activation energy being slightly increased.
I. Introduction In the last few years, increasing interest has been directed to the applications of superionic conductors. The double salts LiMX04 (M=Na, K, Rb or Cs and X=S or Se) constituted one family distinguished by fast ionic conduction features [ 11, A sudden conductivity rise by 2-4 orders of magnitude with increasing temperature has been reported [ 2,3 1. Transition to superionic conduction has been assigned [4] to enhanced ion mobility of Li around the central, tetrahedral X0,. The transition to superionic conduction has recently been reported [ 51 to constitute a first-order structural phase transition. The conductivity in the latter case was modified abruptly at T,.Since the activation energy did not significantly alter upon shifting to fast ionic conduction, the modified conductivity has therefore been attributed to the ferroelastic structural displacement. LiKSO, exhibits a hexagonal symmetry with polar point group 6 and space group P63 at room temperature. It undergoes several structural phase transitions below [ 6,7 ] and above [ 8-101 room temperature. Until recently, the reported data for electric ’ Permanent address: Physics Department, Alexandria University, Egypt.
162
conductivity have been from dc measurements. It could be of interest to compare the dc data with data derived from ac measurements, which should shed more light on the nature and mechanism of conduction. The aim of this work is to report on the nature of conduction in the vicinity of the structural ferroelastic phase transition taking place at 708 K.
2. Experimental Crystals of LiKS04 were isothermally grown at 3 15 K from an aqueous solution containing the initial simple salts at the stoichiometric ratio, following the method of dynamical and slow evaporation [ 111. The crystals were untwinned and of good optical quality. Samples were cut perpendicular to the b axis into thin slab plates of 0.1 cm thickness and 1x 1 cm2 area. The plates were silver-coated, using the evaporation technique. The electric impedance was measured in the temperature range 300-800 K and frequency range 5-5 x lo5 Hz, using a Tesla impedance meter operating at 5 mV. The sample was placed inside a specially evacuated holder [ 121, where the temperature was stabilized within + 0.1 K. The specific heat at constant pressure, C,, was
0167-577x/92/% 05.00 Q 1992 Eisevier Science Publishers B.V. All rights reserved.
Volume 15, number 3
MATERIALS LETTERS
measured using a DSC technique, where a Heraeus DSC cell was connected to a Heraeus DTA 500 thermal analyser. The measurements were performed by applying the base-line method [ 13 1. Lidded pans, made of aluminium, were used to eliminate sloping of the base line. A Pt 100 thermocouple was used as the temperature sensor, while a heating rate of 2 K/ min was applied.
3. Results and discussion The measured impedances of all the samples at various temperatures were analysed [ 14,15 1. Fig. 1 shows typical Cole-Cole diagrams for LiKS04 crystals at various temperatures in the region of the ferroelastic-phase transition, T, = 708 K. The dependence of Z” (Z’ ) follows semicircles originating from the region with no overlap (fig. 1). This means that the surface resistance R, is zero and the sample resistance is composed mainly of the bulk resistance Rb which is in parallel with capacitance C,. Extrapolating the high-frequency limit and the low-frequency limit of the semicircles’ intercepts with the real axis Z’ gives the values of R, and Rb respectively [ 16,171. It is also clear from fig. 1 that the arc diameter of the semicircle decreases with increasing
2”
November 1992
temperature. However, the behaviour is governed differently depending whether the phase is ordered (T-c T,) or disordered (T> T,). Ionic conductivity of the samples can be estimated using the sample geometry and the dc resistance at different temperatures. The behaviour of the conductivity with temperature follows an Arrhenius linear dependence with a clear phase transition to extend from 690 to 708 K as shown in fig. 2. This behaviour is due to the thermal history which plays a great role in T, and the domain wall motions in LiKS04. Below the transition temperature, the conductivity values are low (9.5 x lop9 Q-’ cm-‘), but with quite low activation energy values. However, an abrupt increase in the conductivity occurs above T, with slight change in the activation energy. The conductivity values above T, are 1.4x lop5 R-’ cm-‘, which is more than three orders of magnitude greater than the values below T,. To understand the observed behaviour, the classical many-body theory [ 18 1, whose validity extends beyond the area of solid electrolytes, was applied. This theory treats the diffuse transport of the mobile ions hopping among the lattice in addition to interacting with the diffusion ions, The many-body interaction affects the ordering of ions inside the lat-
8
T:668 K
6
I 1.33
Fig. 1. A complex plane dependence of the imaginary part Z” on real part Z’ of the impedance in the vicinity of phase transition T,=708 K.
4
1.41
1.49 lo'/
T,
1.57
K-'
Fig. 2. Temperature dependence of the bulk conductivity 0 in the vicinity of r,.
163
November 1992
MATERIALS LETTERS
Volume 15, number 3
lo-
103
:
i
IO-
\ \ :
S
A
r1
-0
l 2
\
\
l
\
\
I
10
I
-c-f
m
I
k
l’
//
600
700
1.
8 Fig. 3. (A) A packing of 0 and K atoms in the structure of LiKSO., (xy plane). (B) Four equilibrium positions of the SO, group in the hexagonal phase [ 22 1.
tice. The phase transition in most crystals belonging to the double-sulphate family is an order-disorder transition; such transitions are related to the ordering of the tetrahedral group. In the paraelectric phase, the tetrahedral group occupies two or more equivalent positions. The order parameter describing a superionic phase transition is the density of the mobile ions, rather than the existence of spontaneous dipoles and strain in ferroelectric and ferroelastic materials [ 19 1. 164
up
\
\
I
1(r-
X
-T a I. -I
l \
I I I
s
00
m
r
102
T Y
800
K
Fig. 4. Variation of C, and conductivity with temperature.
The crystallographic structure of LiKSO, can be considered as slight distortions of the prototype aKzS04 structure. From the structure studied of such a crystal [20], one can see that the tetrahedra GO:-, SO:-, share oxygen atoms which lie on a trigonal axes, fig. 3A. In the polar b direction, Li and S atoms are nearly equidistant from K+ and a common oxygen atom is nearly 0.3 A from the midway of Li and S [ 2 I]. Hence, the effective point change associated with LiSOh may be taken at this 0 atom. The structural transition is expected as a result of various orientational orderings of the SOa- group, accompanied by ionic displacements. Four discret
Volume
15, number
MATERIALS
3
LETTERS
November
1992
where B contains all nonsingular contributions and p is a constant. The variation of d In aT/dTwith molar C, is shown in fig. 5. The value of p was calculated to be equal to 0.16, while B is equal to 0.046. The obvious correlation between the ac conductivity (i(T) and specific heat C,( T) is clear. This behaviour is attributed to the dominating role of the nonlinearities in the temperature dependence of (T and
Acknowledgement The author is very grateful to Professor Dr. Latifa Al-Houty, Chairman of the Physics Department, University of Qatar, for her fruitful discussions and continuous assistance in his work.
.08
References
I_ .04
.lO
.16
.22
CpIRTc
Fig. 5. A correlation between activation energy of the bulk conductivity and C, in the ionic phase transition region.
orientational states of each SOi- tetrahedron in cationic environment can be labelled with the help of two Ising variables [ 22 ] (up or down the hexagonal axis and turns of tetrahedron to the right or left) as shown in fig. 3B. It is well known that there exists a proportionality between n and the interaction enthalpy, h, of mobile ions. The proportionality constant gives some microscopic information about the short-range order which modifies the energy of the diffusion jump. The conductivity in LiKSO, solids, which provides a simple measure of mobility at its transition, has been shown to be 3d Ising model [ 231. The Nemst equation [ 241 gives directly the conductivity, from which the correlation between the electrical conductivity, a, and the specific heat, C,, could be obtained. Fig. 4 shows the variation of C,, as well as d In a/dT, with temperature. The relationship between (Tand C, is given by
[ 1 ] Cz. Pawlowski, F.E. Salman, A. Pawlowski, A. Pietraszko, Phase Trans. 8 (1986) 9.
2. Czapla and
[2] A.I. Baranov, L.A. Shuvalov and N.M. Shehagina, JETP Letters 36 (1982) 459. [ 31 A.P. Kovalenko, Soviet Phys. Solid State 27 ( 1985) 570. [4] M.A. Pimenta, P. Echegut and F. Gervais, J. Phys. C 19 (1986) 5519. [ 5 ] J.B. Boyce and T.M. Hayes, in: Physics of superconductors, ed. M.B. Salamon (Springer, Berlin, 1979). [6] T. Brenczewski, T. Krajewski and B. Mroz, Ferroelectrics 33(1981)9. [ 71 T. Krajewski, T. Brenczewski, M. Kassem and B. Mroz, Ferroelectrics 55 (1984) 143. [ 8 ] A.M. Okaz, S. Mahmoud and M.E. Kassem, J. Mater. Sci. 23 (1989) 998. [ 91 T. Krajewski, T. Brenczewski, P. Piskunwicz and B. M&z, Ferroelectrics Letters 4 ( 1985) 95. [lo] M.A. Pimenta, P. Echegut, Y. Luspin, G. Hauret and F. Gervais, Phys. Rev. B 39 (1989) 3361. [ 1 I ] B.M. Bartlett, J. Sci. Instr. 88 ( 196 1) 54. [ 12 ] M.E. Kassem, E.F. El-Wahidy, S.H. Kandiel and H. Gado, Ferroelectrics Letters 5 ( 1986) 7 1. [ 13 ] T. Daniels, Thermal analysis (Kogam Page, London, 1973) p. 127. [ 141 A.K. Jonscher, Dielectric relaxation in solids (Chelea Dielectric Press, London, 1983) ch. 3. [ 151 M.E. Kassem, A.Y. Kandiel and L. Al-Houty, J. Polymer Mater., to be published. [ 161 J.L. Carpentier, A. Lebrum and F. Predu, J. Phys. Chem. Solids 90 (1989) 145.
165
Volume 15, number 3
MATERIALS LETTERS
[ 171 J. Millete and M. Gillow, J. Chem. Phys. 64 (1987) 2483. [ 181 L.J. Girifalco, Statistical physics of materials (Wiley, New York, 1973); L. Ruth, D.R. Sain, H.L. Yeh and L.A. Girifalco, J. Phys. Chem. Solid 37 (1976) 649. [ 191 V.N. Bondarev and V.M. Kostenko, Soviet Phys. Solid States 25 (1983) 1406. [20 ] H.M. Alak, A.W. Brinkman, G.J. Russel and A.W. Roberts, J.Phys.D21 (1988) 1226.
166
November 1992
[21] R. Farhi and F. Condin, J. Phys. Conden. Matter 1 ( 1989) 6951. [22] V.I. Zinenko and D.Kh. Blat, Soviet Phys. Solid States 20 (1978) 2047. [ 231 H. Schulz, M. Zuker and R. French, Acta Crystallogr. B 41 (1985) 21. [ 241 H.R. Manning, C.J. Vennte and D.P. Boden, J, Electrochem. Sot. 118 (1971) 2031.