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Conductivity and dielectric relaxation phenomena in lithium manganese spinel
Solid State Ionics 176 (2005) 2153 – 2161 www.elsevier.com/locate/ssi
Conductivity and dielectric relaxation phenomena in lithium manganese spinel J.R. Dygasa,*, M. Kopec´a, F. Kroka, D. Lisovytskiyb, J. Pielaszekb b
a Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warszawa, Poland Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland
Received 5 July 2004; received in revised form 10 January 2005; accepted 11 January 2005
Abstract Electrical conductivity and dielectric properties of lithium manganese spinels, Li1+d Mn2d O4, d = 0 and d = 0.005, obtained by sol – gel method, were studied by impedance spectroscopy. Parameters of relaxation function were obtained by fitting model response to the measured impedance. As evidenced by the X-ray powder diffraction, samples heat-treated at 800 -C undergo upon cooling a phase transition from cubic to an orthorhombic structure at about 16 -C. Appearance of the orthorhombic distortion is accompanied by a decrease of conductivity by a factor about 10. In the orthorhombic phase, two distinct relaxation processes were observed: (i) at high frequencies, a dielectric like process exhibiting relaxation strength De D ffi 5 and an activation energy about 0.25 eV; (ii) at frequencies near the onset of the conductivity dispersion, a charge carrier relaxation. Samples obtained by sol – gel synthesis and heat-treated up to 580 -C do not undergo a phase transition and exhibit only charge carrier relaxation in their dielectric function. The activation energy of the charge carrier relaxation has nearly the same value as that of the dc conductivity, i.e. about 0.33 eV. The charge carrier relaxation strength is between De C ffi 11 for samples sintered at 800 -C and De C ffi 80 for samples calcined at 300 -C. D 2005 Elsevier B.V. All rights reserved. PACS: 72.80.Ga; 77.22.Ch; 77.22.Gm; 71.38.Ht; 81.30.Hd; 64.70.Kb Keywords: Lithium manganese spinel; Dielectric relaxation; Charge carrier relaxation; Phase transition; Polaron hopping
1. Introduction Lithium manganese spinels are promising cathode materials for advanced rechargeable lithium-ion batteries because of their high cell voltage, acceptable large reversible capacity and wide operating temperature range. Also important is the fact of their low toxicity and lower cost compared to LiCoO2 or LiNiO2 [1– 3]. The structure of the spinel LiMn2O4 (space group Fd3m) consists of cubic close-packed oxide ions with manganese ions in half of the octahedral sites and lithium ions in one eighth of the tetrahedral sites formed by the oxide lattice [1,2]. In stoichiometric spinel, the manganese ions coexist in two valence states Mn3+ and Mn4+ in equal proportions, thus the
* Corresponding author. Tel.: +48 22 6608213; fax: +48 22 6282171. E-mail address: [email protected] (J.R. Dygas). 0167-2738/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2005.01.012
chemical formula can be written as Li(Mn3+Mn4+)O4. The electrons of the partially occupied e-orbital of manganese ions remain localised, trapped in local lattice vibrations [4]. The conductivity is due to thermally activated hopping of small polarons between mixed valence manganese ions in neighbour sites [4 –6]. Close to room temperature LiMn2O4 spinel undergoes a reversible phase transition upon cooling and heating. Above the transition temperature the crystal structure is cubic. It was first reported that below the transition temperature a mixture of tetragonal and cubic phases existed [7,8]. The phase transition was attributed to a long range ordering of the local Jahn –Teller distortion of Mn3+O6 octahedra [9]. Later it was concluded that below the phase transition there is a single phase of orthorhombic symmetry (space group Fddd). The orthorhombic superstructure of the cubic spinel structure was attributed to a partial charge ordering on manganese sites [10 – 12]. The superstructure is composed
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of columns of Mn3+ type ions running along the [001] direction, which are surrounded by Mn4+ ions [11]. In the present work, electrical properties of spinels Li1+d Mn2d O4 obtained by a sol –gel method are presented. We have studied samples of two compositions of d = 0 (stoichiometric) and d = 0.005 (delta), which underwent heat treatment at various temperatures (up to 800 -C). Electrical conductivity and dielectric relaxation were studied by the impedance spectroscopy. Crystal structure was examined by the X-ray powder diffraction.
2. Experimental The lithium manganese spinels were obtained by the sol – gel method [13,14]. The colloid was dried and then calcined at 300 -C. The synthesised powder was pressed into pellets (10 mm in diameter and about 1 mm thickness). This way the low temperature spinel samples: stoichiometric LiMn2O4 (symbol SL) and delta Li1.005Mn1.995O4 (symbol DL) were obtained. Two pellets were sintered in air at 800 -C for 24 h and cooled rapidly down to room temperature. These were the high temperature spinel samples: stoichiometric (SH) and delta (DH). For electrical measurements gold or platinum electrodes were sputtered on the polished surfaces of the pellets. Samples were placed between spring loaded contact plates in a closed chamber preserving argon atmosphere. Measurements were carried out using the Solartron 1260 impedance analyser equipped with Keithley 428 current amplifier [15]. Impedance spectra were measured with an ac signal of 30 mV rms in the frequency range from 10 MHz to 0.1 Hz (some spectra to 0.01 Hz). Constant temperature in the range between 60 -C and 100 -C was maintained by a thermostat heated and cooled by Peltier elements. A bipolar dc power supply of a cascade thermoelectric stack was controlled by Eurotherm 2008 temperature controller. Heating and cooling ramps were performed with varied temperature step (between 10 -C and 1 -C). A narrow temperature step was programmed near room temperature, where the phase transition was expected. Measurements of impedance spectrum at a constant temperature were automatically repeated when a drift of impedance was detected by the data acquisition algorithm [16]. The limiting value for the root-mean-square relative drift of impedance was 1%. After completion of impedance studies in the temperature range between 60 -C and 100 -C, impedance measurements of the samples SL and DL were made at higher temperatures. Using another sample holder and an electric oven, heating and cooling runs with a temperature step of 20 -C or 10 -C were performed between the room temperature and progressively higher upper temperatures: 300 -C, 400 -C, 500 -C, 580 -C. This way the pellets SL and DL with gold electrodes were annealed in air and the effect of heat treatment on the conductivity was recorded in situ. After
heating to each consecutively higher temperature above 300 -C, the dc conductivity measured above the room temperature assumed higher values. The conductivity values measured during consecutive cooling runs for the sample DL are presented in Fig. 1, the results for the sample SL were similar. After completion of the in-situ impedance studies at elevated temperatures, the impedance measurements on pellets heat-treated up to 580 -C were repeated at low temperatures without applying new electrodes. The obtained data sets are denoted as SL-580 and DL-580. Later the same two pellets, placed on a gold foil, were annealed in air at 800 -C for 24 h and rapidly cooled. After annealing at 800 -C the resistance of the sputtered electrodes, measured between two points on the surface, increased from about 2 V to over 20 MV, which indicated that the gold films lost continuity as a result of diffusion of gold in the sample. Surfaces of pellets were polished and new gold electrodes were sputtered. Impedance measurements at low temperatures, between 60 -C and 100 -C, were made again— data sets SL-800 and DL-800. Impedance spectra were analysed by non-linear least squares fitting of an equivalent circuit. The shape of the equivalent circuit presented in Fig. 2 was determined by examination of complex plane diagrams and spectral plots of data with fitted response. Simultaneously with fitting the equivalent circuit, the program FIRDARVN [17,18] was used so as to correct for non-ideal gain-phase characteristics of current to voltage converters at high frequencies. According to the procedure described previously [15], the measured impedance was fitted by an impedance function computed as a product of the impedance of an equivalent circuit and a correction factor expressed as a linear or a
Fig. 1. Temperature dependence of the dc conductivity of the low temperature delta spinel DL measured during cooling after heating in air to subsequently higher temperatures: 300 -C, 400 -C, 500 -C and 580 -C.
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2.0
fC
a)
SL SL-580 SL-800 SH
fC
log(ε ')
1.5
fD
fC fC
1.0
fD 0.5 2
3
4
5
6
7
log(f / Hz) 1.5
fC
b)
SL SL-580 SL-800 SH
fC 1.0
fC
log(ε ")
quadratic complex function of frequency. Coefficients of the correction polynomials, independent for each amplification range of the current to voltage converters, were adjusted during fitting. For presentation of the spectra in Fig. 3, the distortions were removed by applying the estimated apparatus corrections to the data, i.e. the measured impedance was divided by the appropriate correction factor. Capacitance of the empty sample holder (including capacitance of that part of capacitor formed by the contact plates, which extended beyond the sample) was subtracted from the data presented as the real part of dielectric function. Powders from the same batches as used for making pellets were examined by the X-ray powder diffraction using Siemens D5000 diffractometer with standard Bragg – Brentano geometry and Ni filtered Cu Ka radiation. Data collected at room temperature in the range 2h from 10- to 90- with a narrow step (0.02-) and long counting time (10 s) were analysed by Rietveld procedure using Fullprof program [19]. Structure refinements were made in the space group Fd3m taking the initial model of the cubic spinel structure with atomic coordinates from the ICSD card #068174. Additional minor crystalline phases were also included in the refinement when identified. In order to test for occurrence of the cubic to orthorhombic structural phase transition, the X-ray diffractograms were additionally collected at 25 -C (or 4 -C) and at 50 -C over 2h range near the 400 reflection of the cubic structure, which undergoes splitting into 400, 040 and 004 reflections upon orthorhombic distortion. The XRD patterns were also collected from the pellets used for impedance measurements after heat treatment at 800 -C (SH, DH, SL-800, DL-800). Structure of samples after heat treatment at 580 -C was deduced from parallel experiments of an in-situ X-ray diffraction study in the temperature range up to 600 -C performed on powders from the same batches as used for making pellets [13,20]. The average crystallite size was calculated using the Scherrer formula. Calculations were made from the integral width of the 400 reflection of the
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fD
0.5
fC 0.0 2
3
4
5
6
7
log(f / Hz) Fig. 3. Frequency dependence of the real part (a) and the imaginary part (b) of the dielectric function measured at 59 -C for the stoichiometric spinel samples after various heat treatments. The dc conductivity has been subtracted. Relaxation frequencies of charge carriers, f C, and dipoles, f D, are marked by arrows. The continuous curves represent the fitted response of the equivalent circuit of Fig. 2.
cubic spinel. Correction of the integral width for the instrumental broadening was applied based on calibration measurement of the standard quartz sample.
3. Results and discussion 3.1. X-ray diffraction
Fig. 2. Equivalent circuit used to model the ac response of lithium manganese spinel.
The powders synthesised by the sol – gel method and calcined at 300 -C exhibited broad diffraction peaks corresponding to the Fd3m structure and weak diffraction
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lines not accounted for to the cubic spinel structure. The Rietveld refinement allowed identification of three crystalline phases (1) the major lithium manganese spinel with lattice constant a = 816.2 pm, (2) lithium manganese spinel with lattice constant a = 824.8 pm, (3) manganese oxide Mn3O4 on the basis of ICSD data base card #068174. The simultaneous refinement of the three phases was improving significantly the goodness of fit factors with respect to the refinement of only a single spinel phase [21]. In the SL and DL samples, the relative weight fractions of the three phases, as estimated by the Rietveld refinement, were about 94%, 4% and 2% respectively, with deviations about 1%. Based on the value of lattice constant, the dominant phase (1) can be identified as a lithium manganese spinel exhibiting high Mn oxidation state—average valence of manganese ions close to 4. Literature values of the lattice constant for the spinel Li1.33Mn1.67O4 with Li substitution on octahedral manganese site: a = 813.7 pm [22] or between a = 814.05 pm and a = 816.1 pm, depending on the temperature of synthesis [23]; as well as those for the spinel Li0.89Mn1.78O4 with partial occupation of both Li and Mn sites: a = 817.4 pm [24] or a = 817.9 pm [25] are close to the value of a = 816.2 pm refined for the phase (1). The phase (2) has lattice constant typical for the stoichiometric spinel LiMn2O4 with average valence of manganese ions equal to 3.5. After heating up to 580 -C the powders SL and DL exhibited XRD pattern of a nearly single phase lithium manganese spinel with the lattice constant a = 823.7 pm sample SL-580 and a = 823.0 sample DL-580. Trace amounts (below 1%) of manganese oxides: Mn2 T xO3 T x (ICDD card #09090) or Mn3 T xO4 T x (ICDD card #68174) were detected for the SL-580 and DL-580 powders, respectively. The increase of lattice constant with respect to samples calcined at 300 -C reflects the decrease of the average valence of the manganese ions. According to Gao and Dahn [26] the actual composition of lithium manganese spinel depends on the upper temperature at which the sample was equilibrated with oxygen. Samples prepared with excess lithium, Li1+d Mn2d O4, can be converted to the spinel with a lower value of d when heated above 600 -C. The transformation is accompanied by a release of oxygen [26]. Oxygen release was also observed by thermogravimetric measurements above 400 -C for the sol – gel synthesised spinel samples similar to those used in the present study [13,14,27]. Although in the present case, the nominal composition was with d equal or close to 0, the sol – gel synthesised material after calcination at 300 -C was a spinel with lattice constant characteristic for the average valence of manganese ions close to 4 rather than equal 3.5 as assumed. Values of the lattice constant after annealing at 580 -C correspond to composition with d between 0.06 and 0.09 according to Fig. 4 in Ref. [26], that is with average valence of manganese ions equal to about 3.6. The spinel samples heat-treated at 800 -C showed at room temperature a well resolved XRD pattern of single phase LiMn2O4 with following values of lattice constant:
a = 824.7 for SH, a = 824.5 for DH, a = 825.0 for both SL800 and DL-800. These values of lattice constant indicate that a nearly stoichiometric spinel LiMn2O4 was obtained with average valence of manganese ions close to 3.5. The four samples that had been heat-treated at 800 -C exhibited splitting of the 400 reflection at temperatures below 0 -C, thus were undergoing a phase transition from cubic to orthorhombic symmetry upon cooling below the room temperature. A detailed in-situ X-ray diffraction and impedance study of this phase transition in the samples sintered at 800 -C (SH and DH) is reported separately [28]. There was no indication of the phase transition in the low temperature samples (SL and DL) and also in samples heattreated at 580 -C. A comparison of the X-ray patterns near the 400 reflection of the stoichiometric samples heat-treated at 580 -C and at 800 -C is presented in Fig. 4. Heat treatment had also effect on the average size of crystallites as estimated by the width of the 400 reflection measured above room temperature. The average crystallite
Fig. 4. The X-ray diffraction pattern near the 400 reflection of cubic spinel measured at 50 -C and at temperature below 0 -C for: a) the stoichiometric spinel heat-treated at temperatures up to 580 -C; b) annealed for 24 h at 800 -C and rapidly cooled.
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3.2. Impedance spectroscopy There was no indication of electrode polarisation seen in the impedance spectra of the studied spinel samples. The phase angle of impedance was equal to zero at frequencies below the frequency range in which relaxation phenomena were observed. In spectral plots of the real part of the admittance a plateau representing the dc conductivity extended over several decades down to the lowest measured frequencies. Absence of the electrode polarisation indicates that ionic contribution to the electrical conductivity is negligible. The impedance spectra also did not indicate blocking of charge carriers at grain boundaries, which would be manifested by a second semicircle in the complex impedance diagrams at low frequencies. The impedance spectra were analysed by fitting parameters of an equivalent circuit shown in Fig. 2. The circuit comprises four parallel branches: a resistor R representing the dc conductivity r 0, a capacitor C V representing the high frequency limiting value of the dielectric constant e V and two branches composed of a constant phase element and a capacitor connected in series. A series connection of a capacitor and a constant phase element represents the Cole – Cole relaxation function [29]. Impedance of the equivalent circuit of Fig. 2 can be expressed as: 1 d r0 þ je0 eTðxÞ S
ð1Þ
where S is an area of each electrode, d is a distance between electrodes, e 0- permittivity of vacuum, j—imaginary unit. The complex dielectric function e*(x) in this case is given by: eTðxÞ ¼ eVðxÞ je VðxÞ ¼ eV þ þ
DeC 1 þ ð jx=xC Þ1nC DeD
1 þ ð jx=xD Þ
1nD
:
ð2Þ
Here De C and De D denote relaxation strength, x C = 2kf C and x D = 2kf D are relaxation frequencies, n C and n D are exponents, which characterise departure of the relaxation function from the ideal Debye-like relaxation. The indices C and D denote a charge carrier relaxation and a dipolar relaxation, respectively. Representative spectral plots of the real and imaginary parts of the dielectric function obtained from the impedance
log(σ0 / Sm-1)
Z ðxÞ ¼
spectra measured at temperature 59 -C are compared in Fig. 3. The dc conductivity has been subtracted from the real part of admittance after fitting the equivalent circuit of Fig. 2. In the case of samples heat-treated at 800 -C (SH, DH, SL-800, DL-800), two well-separated relaxation processes can be identified in the spectra measured at temperature range below 35 -C. Only one relaxation process was identified in the spectra of the low temperature spinels (samples SL and DL), also after heat treatment up to 580 -C (SL-580 and DL-580). In the latter case, the relaxation branch denoted as dipolar was excluded from the equivalent circuit (De D = 0). The limiting high frequency values of the dielectric constant e V were estimated between 5.5 and 7.4 for different samples. A large scatter of values reflected the experimental uncertainty. Nevertheless, values of e V for samples heat-treated at 800 -C appeared to be lower than for the low temperature samples. Temperature dependence of the electrical conductivity and of the relaxation frequencies for the studied samples of lithium manganese spinel are presented in Figs. 5 – 8. Values of the dc conductivity at temperatures 50 -C and 0 -C, average values of the relaxation strength, values of the activation energy of the dc conductivity and of the frequencies of relaxation, are collected in Table 1. Samples calcined at 300 -C (SL and DL), also after heat treatment at temperatures up to 580 -C (SL-580 and DL580), exhibit Arrhenius type temperature dependence of both the dc conductivity and the frequency of charge carriers relaxation with well defined activation energy in the entire temperature range from 60 -C to 100 -C (Figs. 5 and 6). Values of the activation energy of the dc conductivity and of the charge carrier relaxation frequency 2
8
1
7
0
6
-1
5
-2
4
-3
3 conductivity SL conductivity SL-580 conductivity SL-800 cooling conductivity SL-800 heating f carriers SL f carriers SL-580 f carriers SL-800 cooling f carriers SL-800 heating f dipoles SL-800
-4 -5
log(f / Hz)
size in SL and DL samples, calculated from the width of the 400 reflection of the dominating phase (1), was 11 nm. The average crystallite size increased during heat treatment above 300 -C. It was 27 nm for SL-580, 30 nm for DL-580 and somewhat bigger for samples annealed or sintered at 800 -C—between 38 nm for DL-800 and 42 nm for SH. Thus the sol – gel synthesised spinel had nanometric crystallites, whose average size remained lower than 100 nm even after heat treatment at 800 -C.
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2 1
-6
0 2.4
2.8
3.2
3.6
4.0
4.4
4.8
1000/T / K-1 Fig. 5. Temperature dependence of the dc conductivity and of the frequencies of relaxation for the low temperature stoichiometric spinel as received (SL) and after heat treatments at 580 -C (SL-580) and at 800 -C (SL-800).
2
8
1
7
1
7
0
6
0
6
-1
5
-1
5
-2
4
-2
4
-3
3
-3
3
conductivity DL conductivity DL-580 conductivity DL-800 cooling conductivity DL-800 heating f carriers DL f carriers DL-580 f carriers DL-800 cooling f carriers DL-800 heating f dipoles DL-800
-4 -5 -6 2.4
2.8
3.2
3.6
4.0
4.4
log(σ 0 / Sm-1)
8
log(f / Hz)
2
2
-4
1
-5
0
-6
4.8
conductivity cooling conductivity heating f carriers cooling f carriers heating f dipoles
log(f / Hz)
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log(σ0 / Sm-1)
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2 1 0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
-1
Fig. 6. Temperature dependence of the dc conductivity and of the frequencies of relaxation for the low temperature delta spinel as received (DL) and after heat treatments at 580 -C (DL-580) and at 800 -C (DL-800).
Fig. 8. Temperature dependence of the dc conductivity and of the frequencies of relaxation for the high temperature delta spinel sample (DH) with platinum electrodes.
are close to each other for all low temperature spinels, e.g. for the sample SL E j = 0.32 eV and E f C = 0.31 eV. Values of the dc conductivity are similar for the samples SL and DL. After heat treatment up to 580 -C, the samples SL-580 and DL-580 exhibit the dc conductivity values higher by a factor equal about 4 than prior to the heat treatment. The increase of conductivity progressing in course of consecutive heat treatments at temperatures up to 580 -C is presented in Fig. 1. It can be rationalised by the decrease of
the average valence of the manganese ions in the major spinel phase from about 4 for samples calcined at 300 -C to about 3.6 for samples after heating to 580 -C, as deduced from the increase of the lattice constant. Since the mechanism of charge transport in lithium manganese spinel is hopping of polarons between manganese sites of different valence, the presence of nearly equal numbers of Mn3+ and Mn4+ is favourable for high conductivity. There are no traces of phase transition visible in the temperature dependence of the dc conductivity of samples SL, DL, SL-580 and DL-580, in agreement with results of the X-ray powder diffraction (Fig. 4). After heat treatment at 800 -C, the samples SL-800 and DL-800 exhibit a phase transition near the room temperature. In the plots of temperature dependence of the dc conductivity, the phase transition occurring upon cooling is recognised as a decrease of conductivity at a constant temperature. Such decrease of conductivity with time, which progressed slowly for several hours after lowering of the sample temperature, occurred in the temperature range between 16 -C and 14 -C. The time dependence of conductivity was automatically recorded with the aid of the impedance drift detection algorithm. An increase of conductivity during heating occurred between 25 -C and 34 -C. In the temperature range above the phase transition, the values of the dc conductivity for SL-800 and DL-800 samples are higher than for the same pellets prior to heat treatment at 800 -C. The appearance of the phase transition and the increase of conductivity in the cubic phase as results of the heat treatment at 800 -C are well correlated with the values of lattice constant, which indicate attainment of the average valence of manganese ions close to 3.5.
2
8
1
7
0
6
-1
5
-2
4
-3
3 conductivity cooling conductivity heating f carriers cooling f carriers heating f dipoles
-4 -5
log(f / Hz)
1000/T / K
log(σ 0 / Sm-1)
1000/T / K-1
2 1
-6
0 2.6
3.0
3.4
3.8
4.2
4.6
5.0
-1
1000/T / K
Fig. 7. Temperature dependence of the dc conductivity and of the frequencies of relaxation for the high temperature stoichiometric spinel sample (SH) with gold electrodes.
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Table 1 Values of the dc conductivity at temperatures 50 -C and 0 -C, average values of the relaxation strength (De C and De D), values of activation energy of the dc conductivity (E j) and of the frequencies of relaxation (E f C and E f D) for stoichiometric and delta spinel samples Sample
Temperature range 20 -C / 90 -C r 50
SL SL-580 SL-800 SH DL DL-580 DL-800 DH
-C
1
/Sm
1.6 10 2 5.4 10 2 8.3 10 2 15 10 2 1.4 10 2 6.0 10 2 8.5 10 2 13 10 2
60 -C / 0 -C 1
E j / eV
r0
0.342(1) 0.326(1) 0.323(3) 0.324(3) 0.342(1) 0.335(1) 0.337(2) 0.268(6)
1.7 10 3 6.0 10 3 0.9 10 3 1.3 10 3 1.5 10 3 6.3 10 3 1.0 10 3 2.0 10 3
-C
/ Sm
60 -C / 35 -C E r / eV
De C
E f C / eV
De D
E f D / eV
0.321(1) 0.342(1) 0.374(3) 0.366(4) 0.321(1) 0.331(1) 0.364(3) 0.378(5)
80 30 33 11 85 56 51 11
0.311(3) 0.334(6) 0.37(1) 0.344(4) 0.318(2) 0.31(1) 0.34(2) 0.39(1)
– – 4.7 5.3 – – 3.8 6.0
– – 0.27(1) 0.25(1) – – 0.23(1) 0.25(2)
Data for cooling runs. Values of the activation energy are followed by standard deviation of the least significant figure (in parentheses).
Temperature dependences of the dc conductivity and of the relaxation frequencies for samples sintered at temperature 800 -C, measured with gold electrodes in the case of the stoichiometric spinel SH and with platinum electrodes in the case of the delta spinel DH, are presented in Figs. 7 and 8, respectively. For both samples the phase transition is observed as a decrease of conductivity at a constant temperature upon cooling. Upon heating, a gradual recovery of the higher conductivity takes place over a range of temperature above the temperature, at which the conductivity drop occurred during cooling, thus a thermal hysteresis is observed. The hysteresis loop is narrower for the delta spinel than for the stoichiometric spinel, which correlates well with a slightly higher lattice constant for the sample SH than for DH, indicating that the average valence of Mn ions is closer to 3.5 in the sample SH. The decrease of conductivity upon cooling through the region of phase transition was almost twice larger for the sample SH than for DH. This observation is also in agreement with a larger difference between numbers of Mn3+ and Mn4+ ions expected for the sample DH than for SH based both on the nominal composition and on the measured lattice constant. Equal numbers of Mn3+ and Mn4+ favour the charge ordering in the orthorhombic phase, which results in the decrease of conductivity [11]. In the temperature range from 20 -C to 90 -C, a lower value of the activation energy of conductivity was obtained for sample DH (0.27 eV) than for other samples (between 0.32 and 0.34 eV—Table 1). This discrepancy is an artefact of using sputtered platinum electrodes, which exhibited much higher surface resistance than the gold electrodes and introduced a systematic error into measurements of a low resistance of the sample at elevated temperature. For samples sintered at high temperature (SH and DH), and also for the low temperature samples after heat treatment at 800 -C (SL-800 and DL-800), two distinctive relaxation phenomena were observed in the dielectric function measured in the temperature range below the phase transition. The high frequency relaxation, which could be well identified within the available frequency window at
temperatures below 35 -C, exhibited the relaxation strength equal about De D ffi 5 and the activation energy of about 0.25 eV (Table 1). Since the activation energy is distinctly lower than that of the dc conductivity, the high frequency relaxation is not directly related to the dc conductivity. This relaxation has been observed only for the low temperature orthorhombic phase and it seems to be related to the partial charge ordering postulated for this phase [10 – 12]. Tentatively, it can be assigned to relaxation of dipolar configurations of Mn3+ and Mn4+ ions formed as a result of the charge ordering. Reorientation of dipolar moment may occur via local hopping of small polarons, which involves lower potential barriers than the potential barriers encountered by the charge carrying polaron on the conduction pathway. The relaxation strength De D is quite high in accordance with participation of a significant number of Mn3+ – Mn4+ pairs in forming active dipoles. Extension of measurements to lower temperatures is expected to aid in interpretation of the dipolar relaxation, which in the present study was within the experimental frequency window only at the low end of the covered temperature range. The low frequency dispersion, whose relaxation frequency, x C, followed nearly the same temperature dependence as the dc conductivity, can be identified as a relaxation of charge carriers. The relaxation strength was De C ffi 11 in the case of samples sintered at 800 -C (SH and DH). In the case of samples that underwent gradual heat treatment terminated with annealing at 800 -C, the strength of charge carrier relaxation was higher: De C ffi 33 for stoichiometric (SL-800) and De C ffi 51 for delta (DL-800) spinels. These higher values of relaxation strength were similar to those obtained for samples heat-treated at 580 -C: De C ffi 30 for SL-580 and De C ffi 56 for DL-580. However, the charge carrier relaxation frequency in the case of samples SL-580 and DL-580 assumes values higher by a factor between 20 and 30 than in the case of samples SL-800 and DL-800. The higher values of the charge carrier relaxation frequency are correlated with the higher values of the dc conductivity for samples SL-580 and DL-580 at low temperatures.
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The samples made of powders calcined at 300 -C (SL and DL) exhibited the highest values of the strength of charge carrier relaxation, De C ffi 80. The relaxation frequency assumed values lower than in the case of samples heat treated at 580 -C by a factor of about 4, which is close to the ratio of the dc conductivity after heat treatment to that of pristine samples. The strength of the low frequency relaxation was significantly lower in the case of samples sintered at 800 -C directly after synthesis than in the case of samples that underwent the stepwise heat-treatment. This difference in electrical properties occurred despite the fact that no significant differences were noticed between the X-ray diffraction patterns of various samples heat-treated at 800 -C. A plausible explanation points out to the possibility that the microstructure of the samples affects the low frequency relaxation. The connectivity of the grains might be different for samples sintered at 800 -C in one step treatment than in those, which were stepwise annealed at consecutively higher temperatures. The low frequency relaxation, observed in lithium manganese spinel, is likely to be of the same nature as the charge carrier relaxation observed in ionic conductors. The thermally activated hopping of small polaron from Mn3+ to a neighbour Mn4+ site presents charge transport mechanism similar to the thermally activated hopping of ion to a neighbour vacant site.
4. Conclusions Lithium manganese spinels obtained by the sol – gel method and calcined at 300 -C did not undergo phase transition near the room temperature. After heat treatment up to 580 -C the dc conductivity of the spinels increased about 4 times without promoting the phase transition. The low temperature spinels exhibited charge carrier relaxation, whose strength decreased after annealing at 580 -C. Samples heat-treated at 800 -C, either directly after synthesis or in the course of a stepwise annealing procedure, exhibited phase transition near the room temperature, which was visible on the X-ray diffraction patterns. The transition was observed by the impedance spectroscopy as a drop of the dc conductivity at a constant temperature of about 16 -C taking place over a period of several hours after lowering of temperature. For these samples, two relaxation phenomena were observed: (i) at high frequencies associated with reorientation of charge ordered regions via local hopping of small polarons, (ii) at low frequencies associated with relaxation of charge carriers. In general, the structural and electrical properties of Li1+d Mn1-d O4 samples were dependent on the heat-treatment, which seemed to determine the actual valence state of the manganese ions, while the slight difference of the nominal composition d = 0 or d = 0.005 had only minor influence. The orthorhombic distortion, associated with the
charge ordering, appeared below the room temperature only in those samples, which as a result of the heat treatment at 800 -C attained the average valence of the manganese ions close to 3.5, as indicated by the value of the lattice constant. In the present work we propose an explanation of the influence of heat treatment on the electrical properties of the sol –gel synthesised lithium manganese spinel in terms of changes of the average valence of manganese ions; however the conductivity and the charge carrier relaxation may also depend on the microstructure of polycrystalline samples.
Acknowledgements The authors are very grateful to Janina Molenda (University of Mining and Metallurgy, Krako´w) for supplying samples of the sol – gel synthesised lithium –manganese spinel. This project was supported by the Polish Committee for Scientific Research under grant PBZ KBN 013/T08/12.
References [1] M.M. Thackeray, W.I.F. David, P.G. Bruce, J.B. Goodenough, Mater. Res. Bull. 18 (1983) 461. [2] J.B. Goodenough, M.M. Thackeray, W.I.F. Dawid, P.G. Bruce, Rev. Chim. Miner. 21 (1984) 435. [3] J.M. Tarascon, D. Guyomard, J. Electrochem. Soc. 138 (1991) 2864. [4] J.B. Goodenough, A. Manthiram, B. Wnetrzewski, J. Power Sources 43-44 (1993) 269. [5] J. Sugiyama, T. Atsumi, A. Koiwai, T. Sasaki, T. Hioki, S. Noda, N. Kamegashira, J. Phys. Condens. Matter. 9 (1997) 1729. [6] E. Iguchi, N. Nakamura, A. Aoki, Philos. Mag., B 78 (1998) 65. [7] A. Yamada, M. Tanaka, Mater. Res. Bull. 30 (1995) 715. [8] Y. Shimakawa, T. Numata, J. Tabuchi, J. Solid State Chem. 131 (1997) 138. [9] H. Yamaguchi, A. Yamada, H. Uwe, Phys. Rev. B 58 (1998) 8. [10] J. Rodriguez-Carvajal, G. Rousse, C. Masquelier, M. Hervieu, Phys. Rev. Lett. 81 (1998) 4660. [11] G. Rousse, C. Masquelier, J. Rodriguez-Carvajal, M. Hervieu, Electrochem. Solid State Lett. 2 (1999) 6. [12] G. Rousse, C. Masquelier, J. Rodriguez-Carvajal, E. Elkaim, J.-P. Lauriat, J.L. Martinez, Chem. Mater. 11 (1999) 3629. [13] D. Lisovytskiy, Z. Kaszkur, N.V. Baumer, J. Pielaszek, M. Molenda, R. Dziembaj, J. Marzec, J. Molenda, J.R. Dygas, M. Kopec´, F. Krok, Mol. Phys. Rep. 35 (2002) 26. [14] R. Dziembaj, M. Molenda, D. Majda, S. Walas, Solid State Ionics 157 (2003) 81. [15] J.R. Dygas, M.W. Breiter, Electrochim. Acta 41 (1996) 993. [16] J.R. Dygas, P. Kurek, M.W. Breiter, Electrochim. Acta 40 (1995) 1543. [17] J.R. Dygas, Ph. D. Thesis, Northwestern University, Evanston, 1986. [18] J.R. Dygas, M.W. Breiter, Electrochim. Acta 44 (1999) 4163. [19] J. Rodriguez-Carvajal, T. Roisnel, Fullprof.98 and WinPLOTR, Int. Union for Crystallography, Newsletter No.20, http://www-llb.cea.fr/ fullweb/winplotr/winplotr.htm, 1998. [20] D. Lisovytskiy, Z. Kaszkur, V.N. Baumer, J. Pielaszek, J. Marzec, J. Molenda, J. Dygas, M. Kopec, F. Krok, Mater. Sci. Forum 443 – 444 (2004) 311.
J.R. Dygas et al. / Solid State Ionics 176 (2005) 2153 – 2161 [21] D. Lisovytskiy, J. Pielaszek, V.N. Baumer, in: H. Morawiec, D. Stro´z˙ (Eds.), Proc. XIX Conf. Applied Crystallography, World Scientific, Singapore, 2004, p. 77. [22] R.J. Gummow, A. de Kock, M.M. Thackeray, Solid State Ionics 69 (1994) 59. [23] T. Takada, E. Akiba, F. Izumi, B.C. Chaukamakos, J. Solid State Chem. 130 (1997) 74. [24] A. de Kock, M.H. Rossouw, L.A. de Picciotto, M.M. Thackeray, Mater. Res. Bull. 25 (1990) 657.
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[25] P. Strobel, A. Ibarra Palos, M. Anne, J. Power Sources 97-98 (2001) 381. [26] Y. Gao, J.R. Dahn, J. Electrochem. Soc 143 (1996) 1783. [27] R. Dziembaj, M. Molenda, J. Power Sources 119-121 (2003) 121. [28] D. Lisovytskiy, Z. Kaszkur, J. Pielaszek, M. Marzantowicz, J.R. Dygas, Solid State Ionics 176 (2005) 2057 (this issue). doi:10.1016/j.ssi.2004.08.043. [29] K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1941) 341.
Conductivity and dielectric relaxation phenomena in lithium manganese spinel J.R. Dygasa,*, M. Kopec´a, F. Kroka, D. Lisovytskiyb, J. Pielaszekb b
a Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warszawa, Poland Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland
Received 5 July 2004; received in revised form 10 January 2005; accepted 11 January 2005
Abstract Electrical conductivity and dielectric properties of lithium manganese spinels, Li1+d Mn2d O4, d = 0 and d = 0.005, obtained by sol – gel method, were studied by impedance spectroscopy. Parameters of relaxation function were obtained by fitting model response to the measured impedance. As evidenced by the X-ray powder diffraction, samples heat-treated at 800 -C undergo upon cooling a phase transition from cubic to an orthorhombic structure at about 16 -C. Appearance of the orthorhombic distortion is accompanied by a decrease of conductivity by a factor about 10. In the orthorhombic phase, two distinct relaxation processes were observed: (i) at high frequencies, a dielectric like process exhibiting relaxation strength De D ffi 5 and an activation energy about 0.25 eV; (ii) at frequencies near the onset of the conductivity dispersion, a charge carrier relaxation. Samples obtained by sol – gel synthesis and heat-treated up to 580 -C do not undergo a phase transition and exhibit only charge carrier relaxation in their dielectric function. The activation energy of the charge carrier relaxation has nearly the same value as that of the dc conductivity, i.e. about 0.33 eV. The charge carrier relaxation strength is between De C ffi 11 for samples sintered at 800 -C and De C ffi 80 for samples calcined at 300 -C. D 2005 Elsevier B.V. All rights reserved. PACS: 72.80.Ga; 77.22.Ch; 77.22.Gm; 71.38.Ht; 81.30.Hd; 64.70.Kb Keywords: Lithium manganese spinel; Dielectric relaxation; Charge carrier relaxation; Phase transition; Polaron hopping
1. Introduction Lithium manganese spinels are promising cathode materials for advanced rechargeable lithium-ion batteries because of their high cell voltage, acceptable large reversible capacity and wide operating temperature range. Also important is the fact of their low toxicity and lower cost compared to LiCoO2 or LiNiO2 [1– 3]. The structure of the spinel LiMn2O4 (space group Fd3m) consists of cubic close-packed oxide ions with manganese ions in half of the octahedral sites and lithium ions in one eighth of the tetrahedral sites formed by the oxide lattice [1,2]. In stoichiometric spinel, the manganese ions coexist in two valence states Mn3+ and Mn4+ in equal proportions, thus the
* Corresponding author. Tel.: +48 22 6608213; fax: +48 22 6282171. E-mail address: [email protected] (J.R. Dygas). 0167-2738/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2005.01.012
chemical formula can be written as Li(Mn3+Mn4+)O4. The electrons of the partially occupied e-orbital of manganese ions remain localised, trapped in local lattice vibrations [4]. The conductivity is due to thermally activated hopping of small polarons between mixed valence manganese ions in neighbour sites [4 –6]. Close to room temperature LiMn2O4 spinel undergoes a reversible phase transition upon cooling and heating. Above the transition temperature the crystal structure is cubic. It was first reported that below the transition temperature a mixture of tetragonal and cubic phases existed [7,8]. The phase transition was attributed to a long range ordering of the local Jahn –Teller distortion of Mn3+O6 octahedra [9]. Later it was concluded that below the phase transition there is a single phase of orthorhombic symmetry (space group Fddd). The orthorhombic superstructure of the cubic spinel structure was attributed to a partial charge ordering on manganese sites [10 – 12]. The superstructure is composed
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of columns of Mn3+ type ions running along the [001] direction, which are surrounded by Mn4+ ions [11]. In the present work, electrical properties of spinels Li1+d Mn2d O4 obtained by a sol –gel method are presented. We have studied samples of two compositions of d = 0 (stoichiometric) and d = 0.005 (delta), which underwent heat treatment at various temperatures (up to 800 -C). Electrical conductivity and dielectric relaxation were studied by the impedance spectroscopy. Crystal structure was examined by the X-ray powder diffraction.
2. Experimental The lithium manganese spinels were obtained by the sol – gel method [13,14]. The colloid was dried and then calcined at 300 -C. The synthesised powder was pressed into pellets (10 mm in diameter and about 1 mm thickness). This way the low temperature spinel samples: stoichiometric LiMn2O4 (symbol SL) and delta Li1.005Mn1.995O4 (symbol DL) were obtained. Two pellets were sintered in air at 800 -C for 24 h and cooled rapidly down to room temperature. These were the high temperature spinel samples: stoichiometric (SH) and delta (DH). For electrical measurements gold or platinum electrodes were sputtered on the polished surfaces of the pellets. Samples were placed between spring loaded contact plates in a closed chamber preserving argon atmosphere. Measurements were carried out using the Solartron 1260 impedance analyser equipped with Keithley 428 current amplifier [15]. Impedance spectra were measured with an ac signal of 30 mV rms in the frequency range from 10 MHz to 0.1 Hz (some spectra to 0.01 Hz). Constant temperature in the range between 60 -C and 100 -C was maintained by a thermostat heated and cooled by Peltier elements. A bipolar dc power supply of a cascade thermoelectric stack was controlled by Eurotherm 2008 temperature controller. Heating and cooling ramps were performed with varied temperature step (between 10 -C and 1 -C). A narrow temperature step was programmed near room temperature, where the phase transition was expected. Measurements of impedance spectrum at a constant temperature were automatically repeated when a drift of impedance was detected by the data acquisition algorithm [16]. The limiting value for the root-mean-square relative drift of impedance was 1%. After completion of impedance studies in the temperature range between 60 -C and 100 -C, impedance measurements of the samples SL and DL were made at higher temperatures. Using another sample holder and an electric oven, heating and cooling runs with a temperature step of 20 -C or 10 -C were performed between the room temperature and progressively higher upper temperatures: 300 -C, 400 -C, 500 -C, 580 -C. This way the pellets SL and DL with gold electrodes were annealed in air and the effect of heat treatment on the conductivity was recorded in situ. After
heating to each consecutively higher temperature above 300 -C, the dc conductivity measured above the room temperature assumed higher values. The conductivity values measured during consecutive cooling runs for the sample DL are presented in Fig. 1, the results for the sample SL were similar. After completion of the in-situ impedance studies at elevated temperatures, the impedance measurements on pellets heat-treated up to 580 -C were repeated at low temperatures without applying new electrodes. The obtained data sets are denoted as SL-580 and DL-580. Later the same two pellets, placed on a gold foil, were annealed in air at 800 -C for 24 h and rapidly cooled. After annealing at 800 -C the resistance of the sputtered electrodes, measured between two points on the surface, increased from about 2 V to over 20 MV, which indicated that the gold films lost continuity as a result of diffusion of gold in the sample. Surfaces of pellets were polished and new gold electrodes were sputtered. Impedance measurements at low temperatures, between 60 -C and 100 -C, were made again— data sets SL-800 and DL-800. Impedance spectra were analysed by non-linear least squares fitting of an equivalent circuit. The shape of the equivalent circuit presented in Fig. 2 was determined by examination of complex plane diagrams and spectral plots of data with fitted response. Simultaneously with fitting the equivalent circuit, the program FIRDARVN [17,18] was used so as to correct for non-ideal gain-phase characteristics of current to voltage converters at high frequencies. According to the procedure described previously [15], the measured impedance was fitted by an impedance function computed as a product of the impedance of an equivalent circuit and a correction factor expressed as a linear or a
Fig. 1. Temperature dependence of the dc conductivity of the low temperature delta spinel DL measured during cooling after heating in air to subsequently higher temperatures: 300 -C, 400 -C, 500 -C and 580 -C.
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2.0
fC
a)
SL SL-580 SL-800 SH
fC
log(ε ')
1.5
fD
fC fC
1.0
fD 0.5 2
3
4
5
6
7
log(f / Hz) 1.5
fC
b)
SL SL-580 SL-800 SH
fC 1.0
fC
log(ε ")
quadratic complex function of frequency. Coefficients of the correction polynomials, independent for each amplification range of the current to voltage converters, were adjusted during fitting. For presentation of the spectra in Fig. 3, the distortions were removed by applying the estimated apparatus corrections to the data, i.e. the measured impedance was divided by the appropriate correction factor. Capacitance of the empty sample holder (including capacitance of that part of capacitor formed by the contact plates, which extended beyond the sample) was subtracted from the data presented as the real part of dielectric function. Powders from the same batches as used for making pellets were examined by the X-ray powder diffraction using Siemens D5000 diffractometer with standard Bragg – Brentano geometry and Ni filtered Cu Ka radiation. Data collected at room temperature in the range 2h from 10- to 90- with a narrow step (0.02-) and long counting time (10 s) were analysed by Rietveld procedure using Fullprof program [19]. Structure refinements were made in the space group Fd3m taking the initial model of the cubic spinel structure with atomic coordinates from the ICSD card #068174. Additional minor crystalline phases were also included in the refinement when identified. In order to test for occurrence of the cubic to orthorhombic structural phase transition, the X-ray diffractograms were additionally collected at 25 -C (or 4 -C) and at 50 -C over 2h range near the 400 reflection of the cubic structure, which undergoes splitting into 400, 040 and 004 reflections upon orthorhombic distortion. The XRD patterns were also collected from the pellets used for impedance measurements after heat treatment at 800 -C (SH, DH, SL-800, DL-800). Structure of samples after heat treatment at 580 -C was deduced from parallel experiments of an in-situ X-ray diffraction study in the temperature range up to 600 -C performed on powders from the same batches as used for making pellets [13,20]. The average crystallite size was calculated using the Scherrer formula. Calculations were made from the integral width of the 400 reflection of the
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fD
0.5
fC 0.0 2
3
4
5
6
7
log(f / Hz) Fig. 3. Frequency dependence of the real part (a) and the imaginary part (b) of the dielectric function measured at 59 -C for the stoichiometric spinel samples after various heat treatments. The dc conductivity has been subtracted. Relaxation frequencies of charge carriers, f C, and dipoles, f D, are marked by arrows. The continuous curves represent the fitted response of the equivalent circuit of Fig. 2.
cubic spinel. Correction of the integral width for the instrumental broadening was applied based on calibration measurement of the standard quartz sample.
3. Results and discussion 3.1. X-ray diffraction
Fig. 2. Equivalent circuit used to model the ac response of lithium manganese spinel.
The powders synthesised by the sol – gel method and calcined at 300 -C exhibited broad diffraction peaks corresponding to the Fd3m structure and weak diffraction
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lines not accounted for to the cubic spinel structure. The Rietveld refinement allowed identification of three crystalline phases (1) the major lithium manganese spinel with lattice constant a = 816.2 pm, (2) lithium manganese spinel with lattice constant a = 824.8 pm, (3) manganese oxide Mn3O4 on the basis of ICSD data base card #068174. The simultaneous refinement of the three phases was improving significantly the goodness of fit factors with respect to the refinement of only a single spinel phase [21]. In the SL and DL samples, the relative weight fractions of the three phases, as estimated by the Rietveld refinement, were about 94%, 4% and 2% respectively, with deviations about 1%. Based on the value of lattice constant, the dominant phase (1) can be identified as a lithium manganese spinel exhibiting high Mn oxidation state—average valence of manganese ions close to 4. Literature values of the lattice constant for the spinel Li1.33Mn1.67O4 with Li substitution on octahedral manganese site: a = 813.7 pm [22] or between a = 814.05 pm and a = 816.1 pm, depending on the temperature of synthesis [23]; as well as those for the spinel Li0.89Mn1.78O4 with partial occupation of both Li and Mn sites: a = 817.4 pm [24] or a = 817.9 pm [25] are close to the value of a = 816.2 pm refined for the phase (1). The phase (2) has lattice constant typical for the stoichiometric spinel LiMn2O4 with average valence of manganese ions equal to 3.5. After heating up to 580 -C the powders SL and DL exhibited XRD pattern of a nearly single phase lithium manganese spinel with the lattice constant a = 823.7 pm sample SL-580 and a = 823.0 sample DL-580. Trace amounts (below 1%) of manganese oxides: Mn2 T xO3 T x (ICDD card #09090) or Mn3 T xO4 T x (ICDD card #68174) were detected for the SL-580 and DL-580 powders, respectively. The increase of lattice constant with respect to samples calcined at 300 -C reflects the decrease of the average valence of the manganese ions. According to Gao and Dahn [26] the actual composition of lithium manganese spinel depends on the upper temperature at which the sample was equilibrated with oxygen. Samples prepared with excess lithium, Li1+d Mn2d O4, can be converted to the spinel with a lower value of d when heated above 600 -C. The transformation is accompanied by a release of oxygen [26]. Oxygen release was also observed by thermogravimetric measurements above 400 -C for the sol – gel synthesised spinel samples similar to those used in the present study [13,14,27]. Although in the present case, the nominal composition was with d equal or close to 0, the sol – gel synthesised material after calcination at 300 -C was a spinel with lattice constant characteristic for the average valence of manganese ions close to 4 rather than equal 3.5 as assumed. Values of the lattice constant after annealing at 580 -C correspond to composition with d between 0.06 and 0.09 according to Fig. 4 in Ref. [26], that is with average valence of manganese ions equal to about 3.6. The spinel samples heat-treated at 800 -C showed at room temperature a well resolved XRD pattern of single phase LiMn2O4 with following values of lattice constant:
a = 824.7 for SH, a = 824.5 for DH, a = 825.0 for both SL800 and DL-800. These values of lattice constant indicate that a nearly stoichiometric spinel LiMn2O4 was obtained with average valence of manganese ions close to 3.5. The four samples that had been heat-treated at 800 -C exhibited splitting of the 400 reflection at temperatures below 0 -C, thus were undergoing a phase transition from cubic to orthorhombic symmetry upon cooling below the room temperature. A detailed in-situ X-ray diffraction and impedance study of this phase transition in the samples sintered at 800 -C (SH and DH) is reported separately [28]. There was no indication of the phase transition in the low temperature samples (SL and DL) and also in samples heattreated at 580 -C. A comparison of the X-ray patterns near the 400 reflection of the stoichiometric samples heat-treated at 580 -C and at 800 -C is presented in Fig. 4. Heat treatment had also effect on the average size of crystallites as estimated by the width of the 400 reflection measured above room temperature. The average crystallite
Fig. 4. The X-ray diffraction pattern near the 400 reflection of cubic spinel measured at 50 -C and at temperature below 0 -C for: a) the stoichiometric spinel heat-treated at temperatures up to 580 -C; b) annealed for 24 h at 800 -C and rapidly cooled.
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3.2. Impedance spectroscopy There was no indication of electrode polarisation seen in the impedance spectra of the studied spinel samples. The phase angle of impedance was equal to zero at frequencies below the frequency range in which relaxation phenomena were observed. In spectral plots of the real part of the admittance a plateau representing the dc conductivity extended over several decades down to the lowest measured frequencies. Absence of the electrode polarisation indicates that ionic contribution to the electrical conductivity is negligible. The impedance spectra also did not indicate blocking of charge carriers at grain boundaries, which would be manifested by a second semicircle in the complex impedance diagrams at low frequencies. The impedance spectra were analysed by fitting parameters of an equivalent circuit shown in Fig. 2. The circuit comprises four parallel branches: a resistor R representing the dc conductivity r 0, a capacitor C V representing the high frequency limiting value of the dielectric constant e V and two branches composed of a constant phase element and a capacitor connected in series. A series connection of a capacitor and a constant phase element represents the Cole – Cole relaxation function [29]. Impedance of the equivalent circuit of Fig. 2 can be expressed as: 1 d r0 þ je0 eTðxÞ S
ð1Þ
where S is an area of each electrode, d is a distance between electrodes, e 0- permittivity of vacuum, j—imaginary unit. The complex dielectric function e*(x) in this case is given by: eTðxÞ ¼ eVðxÞ je VðxÞ ¼ eV þ þ
DeC 1 þ ð jx=xC Þ1nC DeD
1 þ ð jx=xD Þ
1nD
:
ð2Þ
Here De C and De D denote relaxation strength, x C = 2kf C and x D = 2kf D are relaxation frequencies, n C and n D are exponents, which characterise departure of the relaxation function from the ideal Debye-like relaxation. The indices C and D denote a charge carrier relaxation and a dipolar relaxation, respectively. Representative spectral plots of the real and imaginary parts of the dielectric function obtained from the impedance
log(σ0 / Sm-1)
Z ðxÞ ¼
spectra measured at temperature 59 -C are compared in Fig. 3. The dc conductivity has been subtracted from the real part of admittance after fitting the equivalent circuit of Fig. 2. In the case of samples heat-treated at 800 -C (SH, DH, SL-800, DL-800), two well-separated relaxation processes can be identified in the spectra measured at temperature range below 35 -C. Only one relaxation process was identified in the spectra of the low temperature spinels (samples SL and DL), also after heat treatment up to 580 -C (SL-580 and DL-580). In the latter case, the relaxation branch denoted as dipolar was excluded from the equivalent circuit (De D = 0). The limiting high frequency values of the dielectric constant e V were estimated between 5.5 and 7.4 for different samples. A large scatter of values reflected the experimental uncertainty. Nevertheless, values of e V for samples heat-treated at 800 -C appeared to be lower than for the low temperature samples. Temperature dependence of the electrical conductivity and of the relaxation frequencies for the studied samples of lithium manganese spinel are presented in Figs. 5 – 8. Values of the dc conductivity at temperatures 50 -C and 0 -C, average values of the relaxation strength, values of the activation energy of the dc conductivity and of the frequencies of relaxation, are collected in Table 1. Samples calcined at 300 -C (SL and DL), also after heat treatment at temperatures up to 580 -C (SL-580 and DL580), exhibit Arrhenius type temperature dependence of both the dc conductivity and the frequency of charge carriers relaxation with well defined activation energy in the entire temperature range from 60 -C to 100 -C (Figs. 5 and 6). Values of the activation energy of the dc conductivity and of the charge carrier relaxation frequency 2
8
1
7
0
6
-1
5
-2
4
-3
3 conductivity SL conductivity SL-580 conductivity SL-800 cooling conductivity SL-800 heating f carriers SL f carriers SL-580 f carriers SL-800 cooling f carriers SL-800 heating f dipoles SL-800
-4 -5
log(f / Hz)
size in SL and DL samples, calculated from the width of the 400 reflection of the dominating phase (1), was 11 nm. The average crystallite size increased during heat treatment above 300 -C. It was 27 nm for SL-580, 30 nm for DL-580 and somewhat bigger for samples annealed or sintered at 800 -C—between 38 nm for DL-800 and 42 nm for SH. Thus the sol – gel synthesised spinel had nanometric crystallites, whose average size remained lower than 100 nm even after heat treatment at 800 -C.
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2 1
-6
0 2.4
2.8
3.2
3.6
4.0
4.4
4.8
1000/T / K-1 Fig. 5. Temperature dependence of the dc conductivity and of the frequencies of relaxation for the low temperature stoichiometric spinel as received (SL) and after heat treatments at 580 -C (SL-580) and at 800 -C (SL-800).
2
8
1
7
1
7
0
6
0
6
-1
5
-1
5
-2
4
-2
4
-3
3
-3
3
conductivity DL conductivity DL-580 conductivity DL-800 cooling conductivity DL-800 heating f carriers DL f carriers DL-580 f carriers DL-800 cooling f carriers DL-800 heating f dipoles DL-800
-4 -5 -6 2.4
2.8
3.2
3.6
4.0
4.4
log(σ 0 / Sm-1)
8
log(f / Hz)
2
2
-4
1
-5
0
-6
4.8
conductivity cooling conductivity heating f carriers cooling f carriers heating f dipoles
log(f / Hz)
J.R. Dygas et al. / Solid State Ionics 176 (2005) 2153 – 2161
log(σ0 / Sm-1)
2158
2 1 0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
-1
Fig. 6. Temperature dependence of the dc conductivity and of the frequencies of relaxation for the low temperature delta spinel as received (DL) and after heat treatments at 580 -C (DL-580) and at 800 -C (DL-800).
Fig. 8. Temperature dependence of the dc conductivity and of the frequencies of relaxation for the high temperature delta spinel sample (DH) with platinum electrodes.
are close to each other for all low temperature spinels, e.g. for the sample SL E j = 0.32 eV and E f C = 0.31 eV. Values of the dc conductivity are similar for the samples SL and DL. After heat treatment up to 580 -C, the samples SL-580 and DL-580 exhibit the dc conductivity values higher by a factor equal about 4 than prior to the heat treatment. The increase of conductivity progressing in course of consecutive heat treatments at temperatures up to 580 -C is presented in Fig. 1. It can be rationalised by the decrease of
the average valence of the manganese ions in the major spinel phase from about 4 for samples calcined at 300 -C to about 3.6 for samples after heating to 580 -C, as deduced from the increase of the lattice constant. Since the mechanism of charge transport in lithium manganese spinel is hopping of polarons between manganese sites of different valence, the presence of nearly equal numbers of Mn3+ and Mn4+ is favourable for high conductivity. There are no traces of phase transition visible in the temperature dependence of the dc conductivity of samples SL, DL, SL-580 and DL-580, in agreement with results of the X-ray powder diffraction (Fig. 4). After heat treatment at 800 -C, the samples SL-800 and DL-800 exhibit a phase transition near the room temperature. In the plots of temperature dependence of the dc conductivity, the phase transition occurring upon cooling is recognised as a decrease of conductivity at a constant temperature. Such decrease of conductivity with time, which progressed slowly for several hours after lowering of the sample temperature, occurred in the temperature range between 16 -C and 14 -C. The time dependence of conductivity was automatically recorded with the aid of the impedance drift detection algorithm. An increase of conductivity during heating occurred between 25 -C and 34 -C. In the temperature range above the phase transition, the values of the dc conductivity for SL-800 and DL-800 samples are higher than for the same pellets prior to heat treatment at 800 -C. The appearance of the phase transition and the increase of conductivity in the cubic phase as results of the heat treatment at 800 -C are well correlated with the values of lattice constant, which indicate attainment of the average valence of manganese ions close to 3.5.
2
8
1
7
0
6
-1
5
-2
4
-3
3 conductivity cooling conductivity heating f carriers cooling f carriers heating f dipoles
-4 -5
log(f / Hz)
1000/T / K
log(σ 0 / Sm-1)
1000/T / K-1
2 1
-6
0 2.6
3.0
3.4
3.8
4.2
4.6
5.0
-1
1000/T / K
Fig. 7. Temperature dependence of the dc conductivity and of the frequencies of relaxation for the high temperature stoichiometric spinel sample (SH) with gold electrodes.
J.R. Dygas et al. / Solid State Ionics 176 (2005) 2153 – 2161
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Table 1 Values of the dc conductivity at temperatures 50 -C and 0 -C, average values of the relaxation strength (De C and De D), values of activation energy of the dc conductivity (E j) and of the frequencies of relaxation (E f C and E f D) for stoichiometric and delta spinel samples Sample
Temperature range 20 -C / 90 -C r 50
SL SL-580 SL-800 SH DL DL-580 DL-800 DH
-C
1
/Sm
1.6 10 2 5.4 10 2 8.3 10 2 15 10 2 1.4 10 2 6.0 10 2 8.5 10 2 13 10 2
60 -C / 0 -C 1
E j / eV
r0
0.342(1) 0.326(1) 0.323(3) 0.324(3) 0.342(1) 0.335(1) 0.337(2) 0.268(6)
1.7 10 3 6.0 10 3 0.9 10 3 1.3 10 3 1.5 10 3 6.3 10 3 1.0 10 3 2.0 10 3
-C
/ Sm
60 -C / 35 -C E r / eV
De C
E f C / eV
De D
E f D / eV
0.321(1) 0.342(1) 0.374(3) 0.366(4) 0.321(1) 0.331(1) 0.364(3) 0.378(5)
80 30 33 11 85 56 51 11
0.311(3) 0.334(6) 0.37(1) 0.344(4) 0.318(2) 0.31(1) 0.34(2) 0.39(1)
– – 4.7 5.3 – – 3.8 6.0
– – 0.27(1) 0.25(1) – – 0.23(1) 0.25(2)
Data for cooling runs. Values of the activation energy are followed by standard deviation of the least significant figure (in parentheses).
Temperature dependences of the dc conductivity and of the relaxation frequencies for samples sintered at temperature 800 -C, measured with gold electrodes in the case of the stoichiometric spinel SH and with platinum electrodes in the case of the delta spinel DH, are presented in Figs. 7 and 8, respectively. For both samples the phase transition is observed as a decrease of conductivity at a constant temperature upon cooling. Upon heating, a gradual recovery of the higher conductivity takes place over a range of temperature above the temperature, at which the conductivity drop occurred during cooling, thus a thermal hysteresis is observed. The hysteresis loop is narrower for the delta spinel than for the stoichiometric spinel, which correlates well with a slightly higher lattice constant for the sample SH than for DH, indicating that the average valence of Mn ions is closer to 3.5 in the sample SH. The decrease of conductivity upon cooling through the region of phase transition was almost twice larger for the sample SH than for DH. This observation is also in agreement with a larger difference between numbers of Mn3+ and Mn4+ ions expected for the sample DH than for SH based both on the nominal composition and on the measured lattice constant. Equal numbers of Mn3+ and Mn4+ favour the charge ordering in the orthorhombic phase, which results in the decrease of conductivity [11]. In the temperature range from 20 -C to 90 -C, a lower value of the activation energy of conductivity was obtained for sample DH (0.27 eV) than for other samples (between 0.32 and 0.34 eV—Table 1). This discrepancy is an artefact of using sputtered platinum electrodes, which exhibited much higher surface resistance than the gold electrodes and introduced a systematic error into measurements of a low resistance of the sample at elevated temperature. For samples sintered at high temperature (SH and DH), and also for the low temperature samples after heat treatment at 800 -C (SL-800 and DL-800), two distinctive relaxation phenomena were observed in the dielectric function measured in the temperature range below the phase transition. The high frequency relaxation, which could be well identified within the available frequency window at
temperatures below 35 -C, exhibited the relaxation strength equal about De D ffi 5 and the activation energy of about 0.25 eV (Table 1). Since the activation energy is distinctly lower than that of the dc conductivity, the high frequency relaxation is not directly related to the dc conductivity. This relaxation has been observed only for the low temperature orthorhombic phase and it seems to be related to the partial charge ordering postulated for this phase [10 – 12]. Tentatively, it can be assigned to relaxation of dipolar configurations of Mn3+ and Mn4+ ions formed as a result of the charge ordering. Reorientation of dipolar moment may occur via local hopping of small polarons, which involves lower potential barriers than the potential barriers encountered by the charge carrying polaron on the conduction pathway. The relaxation strength De D is quite high in accordance with participation of a significant number of Mn3+ – Mn4+ pairs in forming active dipoles. Extension of measurements to lower temperatures is expected to aid in interpretation of the dipolar relaxation, which in the present study was within the experimental frequency window only at the low end of the covered temperature range. The low frequency dispersion, whose relaxation frequency, x C, followed nearly the same temperature dependence as the dc conductivity, can be identified as a relaxation of charge carriers. The relaxation strength was De C ffi 11 in the case of samples sintered at 800 -C (SH and DH). In the case of samples that underwent gradual heat treatment terminated with annealing at 800 -C, the strength of charge carrier relaxation was higher: De C ffi 33 for stoichiometric (SL-800) and De C ffi 51 for delta (DL-800) spinels. These higher values of relaxation strength were similar to those obtained for samples heat-treated at 580 -C: De C ffi 30 for SL-580 and De C ffi 56 for DL-580. However, the charge carrier relaxation frequency in the case of samples SL-580 and DL-580 assumes values higher by a factor between 20 and 30 than in the case of samples SL-800 and DL-800. The higher values of the charge carrier relaxation frequency are correlated with the higher values of the dc conductivity for samples SL-580 and DL-580 at low temperatures.
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The samples made of powders calcined at 300 -C (SL and DL) exhibited the highest values of the strength of charge carrier relaxation, De C ffi 80. The relaxation frequency assumed values lower than in the case of samples heat treated at 580 -C by a factor of about 4, which is close to the ratio of the dc conductivity after heat treatment to that of pristine samples. The strength of the low frequency relaxation was significantly lower in the case of samples sintered at 800 -C directly after synthesis than in the case of samples that underwent the stepwise heat-treatment. This difference in electrical properties occurred despite the fact that no significant differences were noticed between the X-ray diffraction patterns of various samples heat-treated at 800 -C. A plausible explanation points out to the possibility that the microstructure of the samples affects the low frequency relaxation. The connectivity of the grains might be different for samples sintered at 800 -C in one step treatment than in those, which were stepwise annealed at consecutively higher temperatures. The low frequency relaxation, observed in lithium manganese spinel, is likely to be of the same nature as the charge carrier relaxation observed in ionic conductors. The thermally activated hopping of small polaron from Mn3+ to a neighbour Mn4+ site presents charge transport mechanism similar to the thermally activated hopping of ion to a neighbour vacant site.
4. Conclusions Lithium manganese spinels obtained by the sol – gel method and calcined at 300 -C did not undergo phase transition near the room temperature. After heat treatment up to 580 -C the dc conductivity of the spinels increased about 4 times without promoting the phase transition. The low temperature spinels exhibited charge carrier relaxation, whose strength decreased after annealing at 580 -C. Samples heat-treated at 800 -C, either directly after synthesis or in the course of a stepwise annealing procedure, exhibited phase transition near the room temperature, which was visible on the X-ray diffraction patterns. The transition was observed by the impedance spectroscopy as a drop of the dc conductivity at a constant temperature of about 16 -C taking place over a period of several hours after lowering of temperature. For these samples, two relaxation phenomena were observed: (i) at high frequencies associated with reorientation of charge ordered regions via local hopping of small polarons, (ii) at low frequencies associated with relaxation of charge carriers. In general, the structural and electrical properties of Li1+d Mn1-d O4 samples were dependent on the heat-treatment, which seemed to determine the actual valence state of the manganese ions, while the slight difference of the nominal composition d = 0 or d = 0.005 had only minor influence. The orthorhombic distortion, associated with the
charge ordering, appeared below the room temperature only in those samples, which as a result of the heat treatment at 800 -C attained the average valence of the manganese ions close to 3.5, as indicated by the value of the lattice constant. In the present work we propose an explanation of the influence of heat treatment on the electrical properties of the sol –gel synthesised lithium manganese spinel in terms of changes of the average valence of manganese ions; however the conductivity and the charge carrier relaxation may also depend on the microstructure of polycrystalline samples.
Acknowledgements The authors are very grateful to Janina Molenda (University of Mining and Metallurgy, Krako´w) for supplying samples of the sol – gel synthesised lithium –manganese spinel. This project was supported by the Polish Committee for Scientific Research under grant PBZ KBN 013/T08/12.
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