Raman measurements of temperature dependencies of phonons in LiMnPO4

Materials Chemistry and Physics 127 (2011) 391–396

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Raman measurements of temperature dependencies of phonons in LiMnPO4 a ´ Krzysztof P. Korona a,∗ , Joanna Papierska a , Maria Kaminska , Andrzej Witowski a , b ´ Monika Michalska b , Ludwika Lipinska a b

˙ 69, 00-681 Warsaw, Poland Institute of Experimental Physics, University of Warsaw, Hoza Institute of Electronic Materials Technology, Wólczy´ nska 133, 01-919 Warsaw, Poland

a r t i c l e

i n f o

Article history: Received 26 July 2010 Received in revised form 31 October 2010 Accepted 12 February 2011 Keywords: Raman spectroscopy and scattering Phonons Thermal properties LiMnPO4

a b s t r a c t We present results of Raman and infrared absorption spectroscopy research on phonons in LiMnPO4 —a new material for high capacitance rechargeable lithium-ion batteries. There is a significant interest in the structural and electrical properties of this material, because the battery performance depends strongly on the rate of lithium diffusion. Nanopowder of LiMnPO4 was obtained via a modified sol–gel method from salts of lithium and manganese. This method is cheap and effective so it is promising for the most popular applications. The material showed sharp phonon peaks in Raman and infrared spectra. In the Raman spectra, the strongest peak was Ag ␯1 mode at energy 117.77 meV (950.1 cm−1 ), at 4 K. At room temperature, its energy decreased (due to phonon–phonon interaction) to 117.5 meV (947.5 cm−1 ). The Grüneisen parameter found for this oscillation mode was relatively low, Ag ␯1 = 0.5, at about 300 K. Since the mode consisted mainly of the symmetric PO4 tetrahedra oscillations, the low Ag ␯1 value indicated that the temperature influenced rather Li–O and Mn–O bonds than the P–O bonds forming the LiMnPO4 structure. The thermal dependencies of the antisymmetric modes (Ag ␯3 and Ag ␯4 ) were stronger (Ag ␯3 = 0.7, Ag ␯4 = 1.4) what suggested that these modes experienced stronger coupling. The thermal broadening of the Ag ␯1 mode could be described in wide temperature range by exponential dependence with activation energy of 65 meV (about two times smaller than the Ag ␯1 energy), what suggested a symmetric two-phonon decay. © 2011 Elsevier B.V. All rights reserved.

1. Introduction In this paper, we present results of our research on phonons in LiMnPO4 by means of the infrared and Raman spectroscopy. LiMnPO4 with the olivine structure is considered as potential material for cathodes of rechargeable lithium-ion batteries, commonly used in laptops and other portable devices [1,2]. Phospho-olivines (lithium metal phosphates with olivine-structure) are currently being developed also for electric car batteries [2]. There is a significant interest in the structural properties of this material, because electrode capacity and battery performance depend mostly on the rate of lithium diffusion in the cathode material [2,3]. Since diffusion depends on lattice oscillations (phonons) [4] and shapes of potential in diffusion channels in the crystal structure, electric transport properties depend on the structural properties of the cathode material. LiMnPO4 can be obtained via a sol–gel method from salts of lithium and manganese. This method is relatively cheap and effi-

∗ Corresponding author. E-mail address: [email protected] (K.P. Korona). 0254-0584/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2011.02.027

cient, therefore suitable for commercial applications. The sol–gel method produces nanocrystalline material that is well suited for electrochemical applications where fast lithium diffusion out of the nanocrystals and back (during charging and discharging) is crucial. However, optical and structural measurements of such nanomaterials are difficult. Optical characterization of materials by means of photoluminescence and absorption usually gives fast and valuable information. However, in the case of lithium salts, absorption and reflectance measurements are difficult (due to powder structure of the materials), and luminescence is suppressed by fast recombination of carriers. In this situation, one of the best optical methods for characterization of these materials is Raman spectroscopy [5–9]. This method has been mainly used in the present studies. 2. Phonon modes The lithium manganese phosphate, LiMnPO4 , crystallizes in the olivine structure: the Pmnb space group of the orthorhombic crystal system. The cell is centrosymmetric and consists of 28 atoms (4 times LiMnPO4 ). The phosphorus atom of the phosphate forms with the four oxygen atoms a tetrahedron, PO4 . A frame-

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work of the crystal is formed by LiO6 (Ci symmetry) and MnO6 octahedra (Cs symmetry), sharing common-O corners with PO4 anions (Cs symmetry). During charge/discharge of the LiMnPO4 secondary batteries, the lithium ions are extracted from/inserted into LiMnPO4 while the central Mn ions are oxidized/reduced. Crystals with the olivine structure have 84 normal modes of vibration: 3 acoustic and 81 optical. Since the crystal cell has inversion symmetry, the modes are either infrared (IR) or Raman active. There are 38 IR active modes: 14 B1u , 10 B2u , 14 B3u (including 3 acoustic) and 36 Raman active modes: 11 Ag , 7 B1g , 11 B2g , 7 B3g . The B modes should be Raman active only in the perpendicular measurement configuration, therefore in parallel conditions (what is the case in our experiment) we expect to observe mainly the Ag modes. Since bonds between P and O atoms are expected to be much stronger (about 10 times) than between O and metal atoms, the LiMnPO4 phonon modes can be visualized as vibrations of the PO4 tetrahedrons surrounded by the metal atoms. The PO4 oscillation modes are called “internal modes”. According to Herzberg’s notation [10], oscillation modes of a single tetrahedron are a singlet A1 , ␯1 , a doublet E, ␯2 , and two triply degenerated F2 modes, ␯3 and ␯4 . In the olivine lattice the PO4 molecule symmetry is lower (Cs ), but internal modes can be related to the single tetrahedron modes. For example the ␯1 -related Raman line is usually the strongest one in LiMePO4 (Me = Ni, Co, Mn) compounds [11]. On the other hand, Li atoms are in the Ci symmetry sites, so no Li-related Raman activity is expected. As calculated theoretically [11,5] and shown by experiments [6,5,12] the strongest Raman mode in olivine is Ag ␯1 . It consists of symmetric stretching oscillations of the PO4 tetrahedron (␯1 mode), having the same phase for every tetrahedron in the unit cell (Ag -symmetry) [11]. This mode is observed in our samples at 950.1 cm−1 at 4 K, and at 947.5 cm−1 at room temperature, what is similar to data reported by other authors: 948.5 cm−1 [11]. Due to its symmetry, this mode does not include movements of the metal ions, so it has similar frequencies in other phosphates, 946–950 cm−1 in LiNiPO4 [6] and 944 cm−1 in LiCdPO4 [11]. The two antisymmetric oscillation modes ␯3 and ␯4 (stretching and bending of P–O bonds, respectively) in the olivine structure produce phonon modes of weaker oscillation strength. The ␯4 modes can be observed in the frequency region 500–700 cm−1 , the ␯3 modes are in 1000–1200 cm−1 region. The anti-symmetric oscillations of the PO4 anion induce moves of neighboring metal ions, so they are not pure PO4 modes. It was reported that the ␯3 modes are sensitive to ionization potential of the metal ions [7]. The symmetric bending PO4 mode ␯2 gives weak features at about 400 cm−1 [11]. In our measurements, crystal quality was good enough to observe a lot of sharp phonon lines including all groups of the internal modes in Raman dispersion and infrared absorption, as shown in Fig. 1. At room temperature the fully symmetric ␯1 mode (breathing mode) was not active in infrared, but it was the strongest one in the Raman spectra, so it could be easily identified at about 948 cm−1 (117.4 meV). In the best samples it had a width of 14 cm−1 (full width at half maximum). Two Ag ␯3 modes were observed in Raman at 1005 and 1064 cm−1 . In infrared absorption (IR) four B1u ␯3 modes were observed at 986 cm−1 , 1058 cm−1 , 1093 cm−1 and 1140 cm−1 in agreement with previously reported data [11]. The ␯4 modes were present in the range 540–600 cm−1 . The ␯2 were expected at about 500 cm−1 . However they were mixed with other modes and difficult to identify. The anharmonicity of phonon Hamiltonian leads to the phonon–phonon interaction, line broadening and the thermal expansion of the lattice [13,14]. The phonon frequencies change with temperature, due to changes of the lattice constant and direct interaction with other phonons. In general, the lattice parameters as well as the oscillation frequency, ˝, have nonlinear temperature

Fig. 1. Dielectric function from infrared measurements (up) and Raman scattering (down) spectra of a LiMnPO4 sample.

dependencies. However, at about room temperature the lattice dilatation may be assumed as linear, ax (T + T) = ax (T) + ˛x T where ˛x is the linear thermal expansion coefficient along x axis. The change of the oscillation frequency is related to the change of volume by Grüneisen parameter,  n [13]. Therefore one can expect that a linear thermal frequency coefficient of a mode n, n , should be equal: n =

1 ∂˝n = −n (˛x + ˛y + ˛z ). ˝n ∂T

(1)

Since  n at room temperature is of the order of 1, and ˛x , ˛y , and ˛z are of the order 10−5 K−1 , it is expected that the n will be of the order of 10−5 K−1 . In broader range the temperature behavior of Raman spectra is more complicated, and depends mainly on phonon–phonon anharmonic interactions. Interaction with both acoustic and optical modes must be taken into account [14]. The number of phonons, ns , changes with temperature: nS (˝, T ) =

1 . exp(¯h˝/kB T ) − 1

(2)

This dependence means that the number of optical phonons is small at a low temperature, and increases rapidly at the temperature comparable with ˝/kB . On the other hand, acoustic phonons (˝ ≈ 0) are present also at the low temperature, and for them the dependence given by (2) is nearly linear. Natural shape of the Raman line [14,15] is given by the equation: IS (˝) =

A 2

(˝n (T ) − ˝) + (n (T )/2)

2

(1 + nS (˝, T )),

(3)

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where ˝n (T),  n (T) are frequency and width of the nth phonon mode, respectively. In an ionic crystal we can expect a strong coupling between phonons. It is possible that during photon scattering two phonons can be emitted. Processes with two optical phonons lead to a shorter phonon lifetime, what causes homogeneous broadening of the phonon line [14,15]. A process including optical and acoustic phonons with opposite wavevectors k would decrease slightly the energy of the scattered photon, resulting in the shape modification: ISA (˝) = IS (˝) +



IS (˝ − kcpj )Aj (1 + nS (kcpj , T ))d3 k,

(4)

j

where cpj is the velocity of acoustic phonon mode j, Aj is coupling strength between optical and acoustic phonons. 3. Experiment Nanopowders of pure and Ti-doped LiMnPO4 were obtained via a modified sol–gel method [16]. Lithium phosphate (Li3 PO4 , Aldrich), manganese(II) acetate tetrahydrate ((C2 H3 O2 )2 ·4H2 O, 99%, CHEMPUR), phosphoric(V) acid (H3 PO4 , 85%, CHEMPUR) and titanium(IV) isopropoxide (C12 H28 O4 Ti, 97%, Aldrich) were used as reactants. The stoichiometric amounts of reactants were dissolved in deionized water. Citric acid was used as a chelating agent for the formation of the gel. The gels were dried at 423 K for several hours in air and then ground in an agate mortar to obtain fine powder. The powder was further calcined from 623 to 773 K for few hours in the air. The material was nanocrystalline (about 100 nm) what is important for the electrochemical performance of the LiMnPO4 cathodes [17]. We were able to obtain Schottky type diodes on LiMnPO4 pellet. The material showed high electric resistivity  = 106 –108  cm, due to a low carrier concentration and their low mobility. The LiMnPO4 is a wide gap (3.8–4.0 eV) [18] and ionic material, therefore strong electric polarization of the lattice is expected. Interaction of electrons with phonons leading to formation of polarons reduces carrier mobility. Therefore, the undertaken investigations of phonons seem to be important also for explanation of the electrical properties of LiMnPO4 . The Raman spectroscopy was measured in backscattering geometry with use of a TRIAX 550 spectrometer with a LN2 -cooled charge-coupled device (CCD) detector. For an exact calibration of the wavelength, mercury spectral lines were recorded. A 532 nm light of a frequency doubled Nd:YAG laser, which lies in the transparent spectral range of the samples, was used. Measurements were made in a continuous-flow helium cryostat (Konti Mikro) in 4–325 K temperature range. Infrared reflection and absorption measurements were performed at room temperature, using a Fourier transform spectrometer Bruker IFS 113 V. The light was striking the sample under oblique incidence. The results of the infrared spectroscopy are presented in Fig. 1. The Kramers–Krönig transform of the reflection spectra gave the dielectric function ε(ω) = εR (ω) + iεI (ω). The fully symmetric ␯1 mode (not active in infrared) was hardly visible. It had very weak peaks at 944.7 cm−1 in the εI (ω) spectrum, and at 945.6 cm−1 in the loss function (−Im(1/ε)) spectrum. The four B1u ␯3 modes were observed at 986 cm−1 , 1058 cm−1 , 1093 cm−1 and 1140 cm−1 in the εI (ω) spectrum and at 1017 cm−1 , 1080 cm−1 , 1118 cm−1 and 1152 cm−1 in the loss function spectrum. The ␯4 modes were present at 548.5 cm−1 , 576.5 cm−1 , 633 cm−1 in the εI (ω) spectrum and at 559.5 cm−1 , 584 cm−1 , 645 cm−1 in the loss function spectrum. The peaks in the εI (ω) and −Im(1/ε(ω)) spectra can be interpreted as the eigenfrequencies of the transverse and longitudinal phonon modes [19].

Fig. 2. Raman spectra of Ag ␯1 and Ag ␯3 a measured at various temperatures. Consecutive spectra are shifted upward in order to improve visibility. Inset: temperature dependence of the Ag ␯1 height.

The results of the Raman scattering measured at different temperatures are plotted at Fig. 2. During heating, we observed red-shifts of the phonon peaks, increase of widths and changes of heights of the phonon peaks (see Figs. 2 and 3). At 4 K, the strongest peak was Ag ␯1 mode at energy 950.1 cm−1 (117.77 meV). At room temperature, its energy decreased (due to phonon–phonon interaction) to 947.5 cm−1 (117.5 meV). The difference was 2.6 cm−1 . The Ag ␯3 peaks shift faster than the Ag ␯1 one. Peak Ag ␯3 a from 1078.6 cm−1 at 4 K to 1017.0 cm−1 at 295 K what made a difference of 14.2 cm−1 . So the frequency of the antisymmetric Ag ␯3 was 5 times more sensitive to the temperature than in the case of symmetric Ag ␯1 mode. The average shift for the two Ag ␯3 peaks was 14.8 cm−1 . Also two Ag ␯4 peaks were observed. Their average shift was 6.3 cm−1 . At the low temperature the peaks were narrower, the Ag ␯1 peak had a width,  , of 8 cm−1 . Heating caused broadening up to 14 cm−1 , at 295 K (in the case of the Ag ␯1 peak). The heights of the peaks generally decreased during heating. For example, the Ag ␯1 peak was about 1.5 times smaller at the room temperature than at 4 K (see inset in Fig. 2). However, since the

Fig. 3. Raman spectra measured at various temperatures. The vertical scale is enlarged in order to show weak peaks. Consecutive spectra are shifted upward in order to improve visibility.

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width of the peak increased 1.5 times, the oscillator strength was nearly constant. The strength of the Ag ␯3 a and Ag ␯4 a were also nearly constant. The strength of the A␯3 b peak increased significantly with the increase of temperature. The A␯4 b peak seemed to decrease its strength with the increase of temperature, however due to its weakness, its parameters were difficult to determine precisely. The frequencies of the phonon lines had nonlinear temperature dependencies. As visible in Figs. 2 and 3, the peaks had nearly constant positions at temperatures below 150 K, but shifted significantly above 150 K. In narrow temperature range around the room temperature, the dependencies could be approximated as linear. The linear thermal frequency coefficients, n , were determined at about room temperature as 2 × 10−5 , 3 × 10−5 , 3 × 10−5 , 3 × 10−5 , and 9 × 10−5 K−1 , for the modes n: Ag ␯1 , Ag ␯3 a, Ag ␯3 b, Ag ␯4 a, and Ag ␯4 b, respectively. It can be noticed that the Ag ␯1 peak had the lowest thermal coefficients, ␯1 . The n , values are small but in the expected range, comparable to thermal expansion coefficients. The thermal coefficients at room temperature are 1.4 × 10−5 K−1 for the a and b directions and 1.7 × 10−5 K−1 for the c direction [20]. According to the dependence (1), the Grüneisen parameters,  n , for the modes: Ag ␯1 , Ag ␯3 a, Ag ␯3 b, Ag ␯4 a, and Ag ␯4 b were equal: 0.5, 0.7, 0.8, 0.8, and about 2, respectively. The average value for the antisymmetric stretching modes was Ag ␯3 = 0.7, and for the antisymmetric bending modes was Ag ␯4 = 1.4. For a chain of atoms interacting by Coulomb potential the  is 3/2 [13], also for real crystals, for example alkali metal halides, the  values at room temperature are about 3/2 [21]. Comparing to that, the Grüneisen parameters Ag ␯1 , and Ag ␯3 modes are relatively low, indicating that the thermal dilatation of the LiMnPO4 crystal takes place mainly within the weakly bound lithium and manganese octahedra, so the phosphate-tetrahedra vibration are less affected by temperature. The similar observations have been reported also for other phosphates [22]. For Li(Mny Fe1−y )PO4 , it was observed also that the PO4 stretching modes generally contain less metal (Li and Mn) motion than the bending modes, thus, ␯1 and ␯3 are more localized than ␯4 modes [23].

Fig. 4. Raman spectra at 290 K—thick solid curve, plus Gaussian curve (dashed line) and curve given by Eq. (4)—dotted line. Data measured at 4 K—thin solid line.

4. Analysis of thermal dependence and discussion In order to analyze precisely the thermal dependencies of the phonon peaks, the spectra were fitted with theoretically expected curves. Shape of the phonon line can be influenced by inhomogeneities of the crystal, so frequently the Gaussian curve gives the best fit to the experimental data [14]. However, some of the peaks in our spectra were asymmetric. We interpreted this feature as interaction with acoustic phonons that can be described by Eq. (4). Therefore we made two types of fitting: symmetric with use of the Gaussian curves and asymmetric using Eq. (4). The resulting curves were compared with experimental data in Fig. 4. In fact, the difference between experimental data and two calculated curves (symmetric and asymmetric) was important only for red wings of the peaks. The symmetric curve underestimated these wings, while the asymmetric curve fitted well. It was found that at a low temperature both procedures gave very similar oscillator frequencies ˝n , and the differences were revealed only at higher temperature when the procedure with asymmetric curve gave higher ˝n . The obtained fitting parameters are presented in Fig. 5. It can be observed that the energy of all peaks decreased monotonically with temperature, and their widths increased monotonically. The temperature dependencies of the phonon frequency and linewidth come from anharmonic terms in the vibrational Hamiltonian of the crystal lattice [14,15]. Taking into account anharmonic terms in the Hamiltonian, we considered two phonon (third order)

Fig. 5. Upper: temperature dependencies of energy of the Ag ␯1 peak (left) and the Ag ␯3 peak (right). Lower: temperature dependencies of the width  . Circles and squares show parameters obtained by fitting of Gaussian curve (symmetric). Parameters obtained by fitting of Eq. (4) are plotted by crosses. The solid lines present curves fitted according to Eq. (5).

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Table 1 Thermal parameters of the phonon modes (see Eq. (5)): peak energy E0 and frequency 1/0 (the values are extrapolations to T = 0 K), linear coefficient a, and the optical phonon related thermal change and activation parameters: b and . Numbers in parenthesis were taken from fit of the Ag ␯1 peak and made constant for the other peaks. Peak

Curve

E0 [meV] ±0.02

1/0 [cm−1 ] ±0.2 cm−1

a [␮eV K−1 ] ±0.05

b [meV] ±0.1

Ag ␯4 a Ag ␯4 b Ag ␯1 Ag ␯3 a Ag ␯3 b Ag ␯1 Ag ␯3 a

Sym Sym Sym Sym Sym Asym Asym

77.40 82.36 117.77 124.82 132.46 117.77 124.86

624.4 664.4 950.1 1006.9 1068.6 950.08 1007.25

0.25 1.7 0.37 0.62 0.99 0.35 0.81

3.1 7.4 2.9 3.9 4.3 2.2 1.55

process involving the photon, the optical phonon and acoustic or optical phonon as the second phonon. These processes could explain both energy and width dependencies of the Raman lines. The thermal dependencies should be proportional to the numbers of phonons. As given by Eq. (2), the number of acoustic phonons is nearly linear with temperature. Therefore we add linear term to the temperature dependence. The influence of optical photons can be described by (2) parameterized by effective phonon energy E˝ = kB . So, the following function was fitted to the data:



E(T ) = E0 − aT −





b



exp /T − 1

(5)

where energy E0 , linear coefficient a, thermal change b and phonon activation temperature were the fitting parameters. The linear coefficient a, describes influence of acoustic phonons. The thermal change b is a parameter describing interaction with optical phonons. The obtained parameters are listed in Table 1. Since the Ag ␯3 and Ag ␯4 peaks were weak, the analysis of their temperature dependencies was less precise. The obtained values were scattered, so it was impossible to use the four free fitting parameters (E0 , a, b and ) present in Eq. (5). In this situation, the Ag ␯3 and Ag ␯4 data were fitted with curve (5), but the activation temperature was fixed to value of 750 K, found for the Ag ␯1 peak. Similar analysis was made for data obtained by asymmetric shape fitting, but only for peaks Ag ␯3 and Ag ␯3 a. It was found that the thermal change b was the lowest in the case of the Ag ␯1 peak. Also the value of the Grüneisen parameter (␯1 = 0.52) was the lowest for this peak. It can be explained by weak coupling of the fully symmetric PO4 internal mode ␯1 to the other phonon modes of the LiMnPO4 crystal. The activation energy 65 meV is about two times smaller than the Ag ␯1 mode energy. It is in agreement with assumption [24] that the anharmonic interaction leads to symmetric decay of the Raman phonon into two phonons. This assumption is not true for the Ag ␯4 modes. For these modes, curves with kB = E0 /2 give poor fits. The thermal dependence of the width was plotted in Fig 5. The Ag ␯1 data were also fitted with curve given by Eq. (5) but with widths  (T) and  0 replacing the energies E(T) and E0 , respectively. The Ag ␯1 width parameters had values a = 0.87 ± 0.04 ␮eV K−1 , b = 4.5 meV, and kB = 62 ± 6 meV. It is worth to notice that the thermal activation energy, kB , is similar in the case of energy and width. Broadening of the line is caused mainly by decay of the Raman phonon mode to two or three phonons. The activation energy that is about two times smaller than the Ag ␯1 mode energy suggests that the two-phonon decay dominates. In the Raman spectra, the antisymmetric modes ␯3 and ␯4 are split into two lines. Both Ag ␯3 modes had similar thermal parameters. The distance between the Ag ␯3 modes decreased 2% (62 ± 1 cm−1 at the low temperature and 60.5 ± 0.4 cm−1 at the room temperature). In contrast to that, the two Ag ␯4 modes differ significantly. The Ag ␯4 a mode presented relatively small changes,

[K] ±50 (750) (750) 750 (750) (750) 700 (700)

kB [meV] ±4 (65) (65) 65 (65) (65) 60 (60)

while the Ag ␯4 b mode had the highest observed change. The distance between the Ag ␯4 modes shrunk 15%, from 40 ± 1 cm−1 at the low temperature to 34 ± 3 cm−1 at the room temperature. The internal modes split as a consequence of two effects: (i) coupling of the oscillation modes of four PO4 ions present in the crystal unit cell and (ii) influence of a crystal field of symmetry lower than tetrahedral acting on the PO4 tetrahedra. The simplest assumption is that in crystal lattice two potentials should be added to the ion Hamiltonian. First, the potential acting between two PO4 ions: ua Dab ub . This potential includes direct PO4 –PO4 interactions due to close spacing of the ions as well as interaction mediated by metal ions. The second potential results from direct influence of crystal field on the PO4 ions. In the Ag symmetry, the influence should be the same for all PO4 ions: Q = ua Qaa ua . The potential is then: U = U0 +



ua Qaa ua +

a



ua Dab ub ,

(6)

a= / b

U0 presents potential from the part of crystal field with tetragonal symmetry. We assume that for all four PO4 ions the coupling between them was the same, and equal D = ua Dab ub . In this approximation, we find from (6) two energies for the oscillations: E1 = E0 + Q + D

(7a)

E2 = E0 + Q − 3D

(7b)

The Q term (that is due to the crystal field) adds to both energies and changes both oscillation frequencies in similar way. The difference between the energies is due to the D term. The temperature induced lattice dilatation reduces both potentials (Q and D). The Q reduction causes decrease of both energies, while the reduction of D causes decrease of the upper mode and increase of the lower mode. The analysis of the experimentally observed shifts of the Ag ␯3 and Ag ␯4 splits suggested that the antisymmetric stretching modes of the PO4 , Ag ␯3 a and Ag ␯3 b, are influenced mainly by the crystal field term. The antisymmetric bending modes, Ag ␯4 a and Ag ␯4 b, that exhibit stronger change of splitting with increase of temperature, probably have relatively higher D value what means stronger influence of coupling between the PO4 ions in the Ag ␯4 modes (comparing to the Ag ␯3 modes). 5. Conclusions Several phonon lines in LiMnPO4 were observed by IR and Raman spectroscopy and identified. Temperature dependency analyzed for peaks Ag ␯1 , Ag ␯3 and Ag ␯4 , showed that the energy of the peaks decreased significantly with increase of temperature. The frequency of the antisymmetric Ag ␯3 and Ag ␯4 modes was more sensitive to the temperature than in the case of symmetric Ag ␯1 . The shifts were 2.6 cm−1 , 14.8 cm−1 and 6.3 cm−1 for the Ag ␯1 , Ag ␯3

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and Ag ␯4 modes, respectively. The obtained Grüneisen parameters were relatively low (for example Ag ␯1 = 0.5, Ag ␯3 = 0.7). We interpret this taking into account that the observed modes involve mainly oscillation of the PO4 tetrahedra forming the LiMnPO4 structure, and that the thermal dilatation influences rather weak Li–O and Mn–O bonds than the strong P–O bonds. The weakness of the Li–O and Mn–O bonds is important for Li diffusion. The temperature dependencies can be described by a model which takes into account phonon–phonon interaction. The obtained thermal parameters revealed interaction of investigated phonon modes with other phonons: acoustic phonons (linear coefficient a) and optical phonons (thermal change and activation parameters: b and ). The activation energy was between 60 and 65 meV. It was observed that the thermal shift (the b parameter) was the lowest for the Ag ␯1 peak. It can be explained by weak coupling of the fully symmetric mode Ag ␯1 to the other phonon modes of the LiMnPO4 crystal. The thermal parameters for the antisymmetric modes (Ag ␯3 and Ag ␯4 ) are generally higher. In the case of the ␯3 and ␯4 modes splitting to the two peaks a and b was observed. The split is a consequence of two effects: coupling of the oscillation modes of the PO4 ions, and influence of crystal field. We observed that the increase of temperature changed the Ag ␯3 split by 2%, while the split of the Ag ␯4 mode shrunk 15%. These results suggested that the antisymmetric bending mode, Ag ␯4 , experienced stronger coupling between the PO4 ions than the stretching mode, Ag ␯3 . Acknowledgement This work was partially supported by EU project no. MTKD-CT2005-029671. References [1] A.K. Padhi, K.S. Nanjundaswamy, J.B. Goodenough, Phospho-olivines as positive-electrode materials for rechargeable lithium batteries, J. Electrochem. Soc. 144 (1997) 1188.

[2] Sung-yoon Chung, Jason T.F Bloking, Yet-ming Chiang, Conductivity and doping of olivine, Nat. Mater. 1 (2002) 123. [3] J. Molenda, W. Ojczyk, J. Marzec, Electrical conductivity and reaction with lithium of LiFe1−y Mny PO4 olivine-type cathode materials, J. Power Sources 174 (2007) 689. [4] A. Van der Ven, J.C. Thomas, Q. Xu, B. Swoboda, D. Morgan, Nondilute diffusion from first principles: Li diffusion in Lix TiS2 , Phys. Rev. B 78 (2008) 104306. [5] W. Paraguassu, P.T.C. Freire, V. Lemos, S.M. Lala, L.A. Montoro, J.M. Rosolen, J. Raman Spectrosc. 36 (2005) 213–220. [6] C.M. Julien, P. Jozwiak, J. Garbarczyk, Proceedings of the International Workshop “Advanced Techniques for Energy Sources Investigation and Testing” Sofia, 2004. [7] A. Ait Salah, P. Jozwiak, J. Garbarczyk, K. Benkhouja, K. Zaghib, F. Gendron, C.M. Julien, J. Power Sources 140 (2005) 370–375. [8] S.B. Tang, H. Xia, M.O. Lai, L. Lu, Characterization of LiMn2 O4 thin films grown on Si substrates by pulsed laser deposition, J. Alloys Compd. 449 (2008) 322–325. [9] R. Baddour-Hadjean, Pereira-RamosF J.-P., Chem. Rev. 110 (2010) 1278–1319. [10] G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules, D. Van Nostrand Company, New York, NY, 1945. [11] M.T. Paques-Ledent, P. Tarte, Spectrochim. Acta 29A (1973) 1007. [12] S. Geller, J.L. Durand, Refinement of the structure of LiMnPO4 , Acta Cryst. 13 (1960) 325. [13] N.W. Ashcroft, N.D. Mermin, Solid State Phys., Holt, Rinehart and Winston, 1976. [14] J. Menéndez, M. Cardona, Phys. Rev. B 29 (1984) 2051. [15] M. Balkanski, R.F. Wallis, E. Haro, Phys. Rev. B 28 (1983) 1928. [16] N.-H. Kwon, T. Drezen, I. Exnar, I. Teerlinck, M. Isono, M. Graetzel, Enhanced electrochemical performance of mesoparticulate LiMnPO4 for lithium ion batteries, Electrochem. Solid-State Lett. 9 (2006) A277. [17] T. Drezen, N.-H. Kwon, P. Bowen, I. Teerlinck, M. Isonod, I. Exnara, Effect of particle size on LiMnPO4 cathodes, J. Power Sources 174 (2007) 949–953. [18] F. Zhou, K. Kang, T. Maxisch, G. Ceder, D. Morgan, Solid State Commun. 132 (2004) 181–186. [19] Claus Klingshirn, Semiconductor Optics, Springer-Verlag, Berlin Heidelberg, 2007, ISBN 978-3-540-38345-1. [20] Sung-Wook Kim, Jongsoon Kim, Hyeokjo Gwon, Kisuk Kang, J. Electrochem. Soc. 156 (2009) A635–A638. [21] G.K. White, Proc. R. Soc. London A286 (1965) 204. [22] Q. Williams, E. Knittle, J. Phys. Chem. Solids 57 (1996) 417–422. [23] C.M. Burba, R. Frech, J. Power Sources 172 (2007) 870–876. [24] P.G. Klemens, Phys. Rev. 148 (1966) 845.