HEBM synthesis of nanocrystalline LiZn0.5Ti1.5O4 spinel and thermally induced order–disorder phase transition (P4332→Fd3¯m)

Materials Chemistry and Physics 116 (2009) 542–549

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HEBM synthesis of nanocrystalline LiZn0.5 Ti1.5 O4 spinel and thermally induced ¯ order–disorder phase transition(P43 32 → Fd3m) ˇ Jovalekic´ d , P. Vulic´ e , ´ N. Jovic´ a,∗ , M. Vuˇcinic-Vasi c´ b , A. Kremenovic´ a,c , B. Antic´ a , C. e e V. Kahlenberg , R. Kaindl a

Institute of Nuclear Sciences “Vinˇca”, Laboratory of Theoretical and Condensed Matter Physics, P.O. Box 522, 11001 Belgrade, Serbia Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovi´ca 6, 21000 Novi Sad, Serbia c Faculty of Mining and Geology, Laboratory for Crystallography, University of Belgrade, Ðuˇsina 7, 11000 Belgrade, Serbia d Institute for Multidisciplinary Studies, University of Belgrade, Kneza Viˇseslava 1, 11000 Belgrade, Serbia e Institute of Mineralogy and Petrography, University of Innsbruck, Innrain 52, A-6020 Innsbruck, Austria b

a r t i c l e

i n f o

Article history: Received 3 November 2008 Received in revised form 16 March 2009 Accepted 18 April 2009 Keywords: Nanostructures Annealing Rietveld analysis Crystal symmetry

a b s t r a c t ¯ Nanocrystalline LiZn0.5 Ti1.5 O4 disordered spinel (S.G. Fd3m) was synthesized by high energy ball milling (HEBM). TEM analysis of the sample has shown that the particle size distribution is broad ranging from 10 to 60 nm. By X-ray line broadening analysis, the average apparent size of the crystallites is found to be 19(1) nm, while the average apparent strain is 26(4) × 10−4 . The cation distribution was found to be metastable, with Zn in octahedral 16d and Ti in tetrahedral 8a position, against their known site preference. After annealing the sample at 650 ◦ C for 3 h and slow cooling down to room temperature, superstructure reflections (1 1 0), (2 1 0), (2 1 1) have been observed, indicating a cation ordering in the octahedral sublattice and a combined symmetry reduction (S.G. P43 32). The reverse symmetry change ¯ caused by increasing the temperature was studied by in situ XRPD, DSC/DTA, Landau’s P43 32 → Fd3m theory of phase transitions and Raman spectroscopy. An analysis of the topology of the order parameter vector space indicates a biquadratic or linear-quadratic coupling between the order parameters Q1 and Q2 . In LiZn0.5 Ti1.5 O4 dilatation expansion of crystal lattice as well as spontaneous strain values are rather small (order of 10−4 ), comparing to e.g. Li1.33x Co2−2x Ti1+0.67x O4 . © 2009 Elsevier B.V. All rights reserved.

1. Introduction Transition metal oxide spinels have been studied for many years for their potential in electrochemical, catalytic, magnetic and ceramic applications [1–3]. Due to novel methods of synthesis and the possibility of notably reducing crystallite sizes to a nanometric level, new electronic and chemical properties of materials have been obtained. Recently, several investigations have been devoted to find out how these properties depend on structure and microstructure parameters of the materials (e.g. cation distribution, particles size, shape and microstrain) which – to some extent – can be controlled by the synthesis procedures [4–7]. Consequently, the interest in understanding the correlation between crystal structure/microstructure, and materials properties is increased. The spinel structure represents one of the most important structure families among the double oxides with general composition AB2 O4 , where the oxygen ions form a cubic close packed array with tetrahedrally (Td ) and octahedrally (Oh ) coordinated

∗ Corresponding author. Tel.: +381 11 80 65 829; fax: +381 11 80 65 829. ´ E-mail address: [email protected] (N. Jovic). 0254-0584/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2009.04.033

interstices. In more detail, one-eighth of the tetrahedral and onehalf of octahedral sites are occupied with cations (A and B). Depending on the distribution of the cations between the Td and Oh vacancies, different principal spinel types can be distinguished: normal, (A)tet [B2 ]oct ; inverse, (B)tet [AB]oct ; or random, (A0.33 B0.67 )tet [A0.67 B1.33 ]oct . At room temperature, the cation distribution is mainly determined by the cation site preferences, but it can vary with the changes in temperature, pressure and/or due to cation substitutions. In a more general form, the cation distribution among the two cation sites can be expressed with the formula (A1−i Bi )tet [Ai B2−i ]oct , where i denotes the degree of inversion. In the case when sublattices (Td and/or Oh ) are occupied by at least two different types of cations and a particular stoichiometric ratio is achieved, there is possibility of cation ordering. Any ordering of cations into one or both sublattices is followed by lowering of the crystal symmetry. In case of a 1:3 ordering ¯ in the octahedral sublattice, the space group changes from Fd3m to P43 32 (a subgroup of index 8). The symmetry reduction is accompanied with the following splitting of the Wyckoff positions: (Td ) 8a → 8c; (Oh ) 16d → 4b + 12d; 32e (oxygen position) → 24e + 8c [8]. It has to be stressed that the preferences of a certain cation species for a particular site [9] may change significantly when bulk

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spinel compounds are compared with their nanoscale counterparts [10]. The comparatively open character of the spinel structure is an interesting feature for those materials which require high mobility of lithium ions, as electrodes and electrolytes in Li-ion batteries. Li1.33 Ti1.67 O4 spinel, for example, has attracted considerable interest as a negative electrode material due to its remarkable electrochemical characteristics and lack of dilation during the charge/discharge process [11–15]. The effect of a partial substitution of lithium and/or titanium ions with transition metals (e.g. Fe, Co, Mn, Cr) on the electrochemistry of Li1.33 Ti1.67 O4 has also been studied [16–18]. From a crystallographic point of view, a special interest was dedicated to the compositions LiM0.5 Ti1.5 O4 , M = Co, Zn, Ni, Fe, Mg, which possess an ordered structure of M2+ and Ti4+ ions on the Oh sublattice [16,19–21]. Consequently, our motivation to study the title compound has its technological importance as well as investigation of crystal structure changes with thermal annealing and order–disorder phase transition. In the present paper we have investigated the microstructure of LiZn0.5 Ti1.5 O4 obtained by high energy ball milling, as well as the evolution of the crystal structure after thermal annealing of the sample. The mechanism of the observed order–disorder phase transition in LiZn0.5 Ti1.5 O4 has been studied by in situ X-ray powder diffraction, Raman spectroscopy and Landau’s theory of phase transition.

543

Fig. 1. XRPD patterns of LiZn0.5 Ti1.5 O4 (as-prepared and after annealing at 650 ◦ C), recorded at room temperature. TEM picture of the as-prepared sample (inset).

and accuracy, checked by measuring the thermal shift of the TO-LO phonon of a (1 0 0) polished single-crystal silicon wafer, was around ±5 ◦ C.

2. Experimental Polycrystalline samples of LiZn0.5 Ti1.5 O4 were produced by high energy ball milling using a Fritsch Pulverisette 5 planetary mill with vials and balls made of hardened steel. An appropriate mixture of commercial Li2 CO3 , ZnO and TiO2 powders (purity >99%) was used as starting material. The mass of the powder mixture was 10 g, the ball-to-powder weight ratio was 20:1. Mechanochemical treatment was carried out in air for 20 h. During the milling process the vial was opened for a few times in order to relieve the CO2 gas produced during the mechanochemical reaction. The as-prepared sample was subsequently heated at 650 ◦ C for 3 h and slowly cooled down to room temperature (cooling speed was around 2 ◦ C min−1 ). X-ray powder diffraction (XRPD) patterns of the as-prepared and the annealed samples were recorded at room temperature on a Philips PW1710 diffractometer using graphite monochromatized Cu K␣ radiation and a Xe-filled proportional counter. Data for the mechanochemically synthesized sample were collected in the angular range between 15.5◦ and 140◦ 2, with a step size of 0.02◦ and a counting time of 10 s per step. The measurement conditions for the annealed specimen were as chosen as follows—2-interval: 10–120◦ , step size: 0.02◦ , counting time: 20 s. The change of the crystal symmetry was investigated by in situ XRPD in the temperature range from 900 to 1100 ◦ C in temperature steps of 20 ◦ C. XRPD patterns for Rietveld structural refinements were collected in the 2 interval 10–110◦ , with a step size of 0.02◦ and a scanning time of 5 s per step on a SIEMENS D5005 diffractometer equipped with an Anton Paar HTK 1200 high temperature chamber (Cu K␣ radiation, – geometry, parallel beam optics, secondary Soller slits and scintillation counter) in synthetic air atmosphere. Before starting a single run of the high temperature series the sample was kept at the appropriate temperature for a sufficiently long time to insure thermodynamical equilibrium. Transmission electron microscopy (TEM) has been performed on a Philips M400 instrument allowing for a magnification of up to 310,000×. Differential thermal (DTA) and calorimetric (DSC) analyses were carried out up to 1180 ◦ C in air with a TA SDT 2060 device using heating and cooling rates of 15 ◦ C min−1 . To investigate the presence of impurities as well as to check the homogeneity of the distribution of elements a JEOL 8100 microprobe analyzer was employed. Raman spectra were recorded by a HORIBA JOBIN YVON LabRam-HR800 spectrometer. Samples were excited by the 514.5 nm emission line of a Ar+ -laser through a 50× long-working distance objective (numerical aperture 0.5). Size and power of the laser spot on the sample surface were approximately 3 ␮m and ranged around 5 mW. The spectral resolution, experimentally determined by measuring the full width at half maximum of the Rayleigh line, was about 1.8 cm−1 . The dispersed light was collected by a 1024 × 256 open electrode CCD detector. Confocal pinhole was set to 1000 ␮m. Spectra were recorded unpolarized. All spectra were corrected assuming linear or second order polynomial function background and deconvoluted by Gauss–Lorentz functions using the built-in spectrometer software Labspec 4. Raman shifts were calibrated by regular adjusting the zero-order position of the grating and the Rayleigh line of a (1 0 0) polished single-crystal silicon wafer. Accuracy of the determined band positions should be better than 0.5 cm−1 . In situ high temperature Raman experiments were performed in a Linkam THMS 1500 heating-stage with a quartz window and a ceramic crucible. Measurements were performed between 500 and 1200 ◦ C in steps of 100 ◦ C. Temperature precision

3. Results and discussion 3.1. Structural characterization The powder X-ray diffraction pattern of LiZn0.5 Ti1.5 O4 obtained by direct mechanochemical reaction (i.e. as-prepared) confirms the ¯ presence of a disordered spinel structure (S.G. Fd3m). After annealing at 650 ◦ C for 3 h and slow cooling down to room temperature, the superstructure reflections (1 1 0), (2 1 0), (2 1 1) were observed (Fig. 1), indicating a cation ordering in the Oh sublattice and a symmetry reduction to S.G. P43 32. Broadening of XRPD reflections of the as-prepared LiZn0.5 Ti1.5 O4 sample point out to a pronounced influence of microstructural effects (size and strain) on the line profiles. The absence of cation ordering in this sample is probably a consequence of the preparation method, since high energy ball impacts can produce a lot of defects and lead to peculiar cation distributions. On the contrary, it was recently shown that a LiZn0.5 Ti1.5 O4 material synthesized by a modified polymeric precursor method [22], crystallized in an ordered spinel structure (S.G. P43 32), with particles size about 90 nm. X-ray powder diffraction data have been used to refine the crystal structure of the as-prepared as well as the annealed samples. Microprobe analysis of the sample has shown the presence of impurities that were due to the sample preparation method (source of iron) and unreacted rests of the reactant: two small peaks at 21.4◦ and 23.5◦ 2 in the XRPD pattern of as-prepared sample indicate the presence of a small amount of Li2 CO3 , which was added in excess (about 5 wt.%) during the synthesis procedure. Any trials to take into account presence of the second phase during the crystal structure refinement has not improved refinement, so asprepared sample was considered as a single phase and the crystal ¯ space group structure refinement has been performed in the Fd3m using the Rietveld profile method and Fullprof program [23]. The lattice constant for the as-prepared LiZn0.5 Ti1.5 O4 material has been determined to be 8.3759(1) Å at room temperature, which is consistent with already reported values for the same composition [22]. It is interesting to notice that analyzing lithium, zinc and titanium cation distributions over the tetrahedral 8a and the octahedral 16d positions revealed presence of all cations in both crystallographic

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Fig. 2. The projections of (a) the “average apparent size” and (b) the “average apparent strain” on the (0 0 1) plane.

sites. Some of the recent papers on spinels point out to a difference between cation distributions of nanosized materials and their bulk counterparts [24]. As we can see, the cations in sample do not follow their energy-favorable preferences for particular sites. It is known that in bulk materials zinc ions have a strong preference for the tetrahedral, while titanium ions prefer octahedral coordination. Therefore, the distribution in our sample can be classified as metastable. After annealing at 650 ◦ C and a subsequent slow cool¯ to P43 32 (Fig. 1). ing, the crystal symmetry changed from Fd3m The lattice parameter of the annealed material was determined to be 8.3711(1) Å. Furthermore, a complete 1:3 ordering of Li+ and Ti4+ ions inside the Oh sublattice was obtained. The same cation ordering exists in bulk LiZn0.5 Ti1.5 O4 [20]. TEM analysis of the as-prepared sample (inset of Fig. 1) has shown that the particle size distribution is broadened and lies in the range 10–60 nm, while the morphology of the particles can be described as pseudo-polyhedral (the edges and faces seem to be not well defined).

3.2. Microstructure characterization by X-ray powder diffraction ¯ Microstructural analysis of the as-prepared sample (S.G. Fd3m), has been carried out by refining the XRPD data using the Fullprof program suite and the incorporated integral breadth method to obtain volume averages of crystallite sizes and microstrains [25]. The TCH pseudo-Voigt profile function was employed to describe peak profiles. Generally, this function delineates the isotropic microstructural parameters (X, Y, U, IG ), while consideration of anisotropic size and strain effects can be done with several models given in Fullprof program. In our case, the anisotropic size broadening was considered as a linear combination of spherical harmonics, while strain broadening was modeled using a quartic ¯ form in reciprocal space. For the Laue class m3m, the anisotropic size broadening is described by four cubic spherical harmonics: K00 , K41 , K61 and K81 . The anisotropic strain broadening is modeled with two parameters [26], S4 0 0 and S2 2 0 , as well as the mixing Lorentzian parameter  that represents the Lorentzian weight of the strain broadened profile. The profile parameters of the TCH pseudo-Voigt function are interpreted as incorporating isotropic strain (X and U) and size (Y and IG ) contributions. However, the parameters X, U and Y may duplicate the action of the anisotropic strain (Sh k l ) and size (Kij ) contributions. For this reason it is advisable to assign zero values to the isotropic contributions during anisotropic microstructure refinement. All four combinations of isotropic/anisotropic size/strain contributions have been tested. In

the case that only isotropic size and strain influence were considered, the isotropic Gaussian contribution of size and strain, IG and U, were neglected because the peak profiles matched a Lorentziantype shape pretty well and any attempt to incorporate IG and U into the refinement procedure produced unreliable results. Instrumental broadening was taken into account by convolution of the experimental TCH pseudo-Voigt function. The best refinement of the XRPD pattern was obtained by considering anisotropic contributions of size and strain to X-ray line broadening. The average apparent size of the sample is found to be ≈19 nm (187 Å) with the standard deviation of 1 nm, and the average apparent strain is 26 × 10−4 with a standard deviation of 4 × 10−4 . It is important to note that the standard deviation obtained by Fullprof represents a measure of the degree of anisotropy. The standard deviation of the calculated average apparent size are small indicating negligible anisotropy of X-ray line broadening caused by the size effect, while the anisotropy of the apparent microstrain is found to be ≈17%. According to microstructure analysis, the fact that high energy ball milling is a well-established technique to produce nanomaterials with significant anisotropic microstrain is confirmed for our material. The apparent sizes (strains) along different directions can be reconstructed from the refined cubic harmonic (quartic form) coefficients. The projections of the threedimensional body representing the “average apparent size” and “average apparent strain” on the crystallographic plane (0 0 1), plotted with the GFOURIER [27] program, are given in Fig. 2(a) and (b). If we compare particle size determined by TEM and crystallite size (size of the coherent domains) it can conclude that in average the particles are composed from few crystallites (between 1 and 5).

3.3. Order–disorder phase transition To study the order–disorder phase transition in the annealed LiZn0.5 Ti1.5 O4 sample, XRPD patterns were collected in the temperature range 900–1100 ◦ C. It was noticed that the reflections demanding the existence of a primitive Bravais lattice disappeared between 1020 and 1040 ◦ C (two selected XRPD patterns are given in Fig. 3). In good agreement with this observation an exothermic peak was found in the DSC experiment at about 1033 ◦ C (Fig. 4). It is interesting to underline that in the sample obtained by ball milling the order–disorder phase transition occurred at temperatures about 120 ◦ C lower than in the sample obtained by solid-state reactions (1150 ◦ C) [20], while in LiCo0.5 Ti1.5 O4 it occurred at 930 ◦ C [19].

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545

and Q2 =

12d 4b 1  |Ni − Ni | , 3 Nitot

(2)

i

Fig. 3. XRPD patterns of LiZn0.5 Ti1.5 O4 at 960 and 1040 ◦ C with observed and calculated intensities and their difference that appears below. The vertical bars, at the bottom, indicate reflection position.

To analyze the mechanism of the phase transformation we have used Landau’s theory of phase transition [28]. The most important parameter in Landau’s theory is the macroscopic ordering parameter, Q. In an ordered spinel phase (S.G. P43 32), two parameters of ordering exist, Q1 and Q2 , defined by the following formulas [29]: Q1 =

oct tet 1  |Ni − Ni | tot 3 Ni

(1)

i

Fig. 4. DSC (up) and DTA (at the bottom) curves recorded in the temperature range 900–1100 ◦ C.

where Nioct (Nitet ) denotes the site occupancy factor—(S.O.F.) for the i type of cation in all octahedral (tetrahedral) positions and, analogously, Ni12d (Ni4b ), denotes the S.O.F. for the 12d (4b) site. Nitot represents the sum of S.O.F. for i type cation in all sites. The parameter Q1 describes the degree of ordering/disordering between the Td and Oh sites, while the parameter Q2 delineates ordering/disordering between two distinct Oh sites in space group ¯ symmetry. These two parameters P43 32 and is equal to zero in Fd3m of ordering completely describe the thermodynamic state during the phase transformation. In order to apply Landau’s theory we needed to find values of site occupancy factors (N) at different temperatures. In situ collected high temperature X-ray data were used to refine crystal structures parameters. Since the cation distribution of annealed LiZn0.5 Ti1.5 O4 at room temperature was found to be fully ordered, the starting cation occupancies in the refinement procedure for the ordered phase (S.G. P43 32), were set up as follows: the 8c site was shared by Li+ and Zn2+ , the 4b site was fully occupied by Li+ and the 12d site fully occupied by Ti4+ (i.e. (Li0.5 Zn0.5 )8c [(Li0.5 )4c (Ti1.5 )12d ]). During the refinement process, two models were used to describe the cation re-arrangement caused by heating the specimen. In the first model, we allowed migration of Zn2+ and Li+ ions between the tetrahedral 8c and the octahedral 4b sites, as well as cations mixing inside Oh sublattice. In the second model, we assumed that only an exchange of Li+ and Ti4+ ions between the two distinct octahedral sites, 4b and 12d, occurred. At temperatures higher than 1033 ◦ C, crystal structure refinements of LiZn0.5 Ti1.5 O4 were done in space ¯ group Fd3m. It was shown that the first model fits better experimental results (residuals and goodness of fit for this model were significantly lower). The same result was obtained analyzing the phase transition by Landau theory (details are not given). Therefore, our further analysis is based on this model. During the data refinement process pseudo-Voigt profile function was used and soft distance constraints were applied to three (two) cation–anion distances in the ordered (disordered) spinel phase. Regarding the results reported previously [20], where a volatilization of LiO2 had been observed only at temperatures higher than 1250 ◦ C the refinements in the temperature range between 900 and 1100 ◦ C were done without changing the stoichiometry. A summary of the results of refinement is given in Table 1. Fig. 5 shows the temperature changes of site occupancy factors, N, for the set of cations which participate in disordering process. It can be noticed that temperature increasing caused the movement of Zn2+ ions from tetrahedral, 8c to octahedral, 4b site, and vice versa for Li+ ions, stressed near the phase transition temperature, ¯ Tc (P43 32 → Fd3m), even it has been contradictory with the cation site preference for zinc ions. On the contrary, it was perceived that at 1080 ◦ C Li+ ions again gravitated to the 4b sites. At temperatures higher than Tc , the tetrahedral 8a site is occupied by Li+ (in excess) and Zn2+ ions, and the octahedral 16d site was occupied by Li+ , Ti4+ and a portion of Zn2+ ions (occupancy of Zn2+ deviate around value 0.085), randomly distributed. Obtained cation distribution at each temperature was further checked using a common approach based on comparing the metal–oxygen bond lengths calculated from: (i) the refined crystal data (i.e. the unit cell and atomic position parameters), dFP and (ii) the obtained cation distribution and corresponding ionic radii, dcalc . We used Shannon effective ionic radii for fourfold and sixfold coordination [30]: rIV (Li+ ) = 0.59 Å; rVI (Li+ ) = 0.76 Å; rIV (Zn2+ ) = 0.60 Å; rVI (Zn2+ ) = 0.74 Å; rIV (Ti4+ ) = 0.42 Å; rVI (Ti4+ ) = 0.605 Å and rIV (O2− ) = 1.38 Å. Distance constraints were applied (in so-called

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Table 1 Summary of the results of crystal structure refinement. Atom

Site

x/a

y/b

z/c

Occupancy, N

0.9988(5)

0.9988(5)

0.9988(5)

0.625

0.625

0.625

0.125 0.3878(11) 0.1000(9)

0.3685(3) 0.3878(11) 0.1297(7)

0.8814(3) 0.3878(11) 0.3879(7)

0.539(3) 0.461(3) 0.922(3) 0.078(3) 1 1 1

0.9997(3)

0.9997(3)

0.9997(3)

0.625

0.625

0.625

0.125 0.3946(4) 0.1132(8)

0.3718(4) 0.3946(4) 0.1262(5)

0.8781(4) 0.3946(4) 0.3870(6)

0.125

0.125

0.125

0.5

0.5

0.5

0.2609(2)

0.2609(2)

0.2609(2)

◦

T = 900 C; S.G. P43 32; a = 8.4731(3) Å Li+ 8c Zn2+ 8c 4b Li+ 4b Zn2+ 12d Ti4+ 8c O2− (1) 2− O (2) 24e RB = 3.95; Rwp = 8.14; GOF = 1.25 T = 1000 ◦ C; S.G. P43 32; a = 8.4905(3) Å Li+ 8c Zn2+ 8c Li+ 4b Zn2+ 4b Ti4+ 12d O2− (1) 8c 2− O (2) 24e

0.566(3) 0.434(3) 0.868(3) 0.132(3) 1 1 1

RB = 4.61; Rwp = 8.32; GOF = 1.28 ¯ T = 1100 ◦ C; S.G. Fd3m; a = 8.5086(3) Å 8a Li+ 8a Zn2+ Li+ 16d 16d Zn2+ Ti4+ 16d 2− O (1) 32e

0.585(3) 0.415(3) 0.2075(30) 0.0425(30) 0.75 1

RB = 8.54; Rwp = 9.82; GOF = 1.46

“iteration way”). Constraint on cation–anion bond lengths were calculated from refined cation distribution and given value for ionic radii and the refinement process was done. If the cation distribution was changed, the new values for constraint cation–anion bond length were used, and refinement was repeated. The summary of cation–anion distances dFP and dcalc at different temperatures are given in Table 2. The agreement between dFP and dcalc inside maximum three estimated standard deviation was obtained. Although the ionic radii of Li+ and Zn2+ ions for tetrahedral and octahedral coordinations are very close, we suppose that the cations displacement have dominant influence on change of the average metal–oxygen bond lengths relative to increasing the temperature. We have noticed that in the vicinity of the ¯ phase transition (P43 32 → Fd3m), regarding the P43 32 region,

the 4b–O2− bond length decreased significantly with increasing temperature, while the average 12d–O2− and 8c–O2− bond lengths vary slightly with temperature: 12d–O2− bond length increased and 8c–O2− decreased with increase of temperature. Decreasing of the octahedral 4b–O2− and tetrahedral 8c–O2− bond lengths is in compliance with observed cations migration, thereby confirm the model of cation disordering. Namely, in the 4b site a part of lithium ions were displaced with zinc ions which have lower effective ionic radii than lithium for this coordination. On the contrary, in the 8c site, ionic radius of lithium is slightly lower than the zinc one, and this site is filled with more lithium ions as the temperature rises. The average 12d–O2− bond length increased due to increase ¯ region, slight increase of of temperature. In the disordered Fd3m the tetrahedral 8a–O2− and octahedral 16d–O2− bond lengths was observed with temperature rise. The phase transition has been followed by the dependence of the lattice parameter, a vs. temperature (Fig. 6). An increase of the lattice parameter with the rise of temperature is observed. The presence of two regions that belong to the ordered and disordered spinel phase is observed. It can be seen that the phase transition ¯ takes place at Tc = (1030 ± 10) ◦ C and the process of P43 32 → Fd3m disordering is not accompanied with a significant changes in the Table 2 Overview of the average cation–anion bond lengths obtained by refinement of the crystal structure, dFP , and calculated from ionic radii and refined cation distribution, dcalc , at selected temperature. Temperature (◦ C)

dFP calc d8c –O

Fig. 5. Temperature variation of the refined site occupancy factors, N, for the set of cations which participate in the disordering process. Standard uncertainties of N are of the order 10−3 and are not shown in the figure.

dFP calc d4b –O

8c–O

4b–O

dFP 12d–O calc d12d –O

Temperature (◦ C)

900

1000

1020

1100

1.997(6) 1.975

1.995(6) 1.974

1.981(7) 1.974

dFP calc d8a –O

2.159(7) 2.138

2.138(7) 2.137

2.112(8) 2.136

dFP 16d–O calc d16d –O

1.993(7) 1.985

2.007(7) 1.985

2.026(8) 1.985

8a–O

2.003(2) 1.974 2.039(2) 2.023

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547

Fig. 6. Temperature dependence of the lattice parameter a.

Fig. 8. Temperature dependence of the order parameters Q1 and Q2 , concerning the first model (Li/Zn migration between 8c/4b sites).

crystal lattice parameters. Linear fits were applied in both regions. The variation of the lattice parameters at the phase transition can be expressed in terms of a spontaneous strain, es . Spontaneous strain for a cubic structure is defined by the formula [31]: es = (a − a0 )/a0 , where a0 denotes the lattice parameter that the disordered phase would have at the temperature of the ordered phase, and a is the lattice parameter of the ordered phase. The a0 is derived by extrapolation of the linear line a(T) = 8.343 + 0.00015T (Å), obtained ¯ structure at temperatures by fitting the data points for the Fd3m where the ordered spinel phase exists. The nonlinear temperature dependence of spontaneous strain, es (T), is shown in Fig. 7. At the temperature 1020 ◦ C, very close to the temperature of phase transition, Tc , strong increment of spontaneous strain is observed. One explanation is that the sample at this temperature could be con¯ that increase es . On sidered as a two phases system, P43 32 + Fd3m, the contrary, if the observed phase transition can be deemed mostly as a first-order phase transition (referred from DSC/DTA measurements), sharply changes of physical properties in the vicinity of Tc are expected. Further, we have considered the temperature dependence of Q1 and Q2 parameters, as well as the topology of the order parameter vector space, i.e. Q1 vs. Q2 . It is known that the relationship between a phase transformation of a crystal structure and the order parameters is severely restricted by symmetry. From the temperature dependence of Q1 and Q2 (Fig. 8) we conclude that the main process triggering the phase transition is cation

disordering process of Li+ and Ti4+ ions within the Oh sublattice, followed by Li+ and Zn2+ mixing between 8c (Td ) and 4b (Oh ) sites. Reeves et al. [19] suggested that in LiCo0.5 Ti1.5 O4 a similar transformation commences with a second-order phase transition (caused by Li/Co mixing), and terminates with a first-order discontinuity (revealed from DTA measurements). The same mechanism can be assumed in our case. On the other side, it is known that cation migrations occur easier along dislocation directions and it can be reason while we obtained lower temperature of phase transition in this sample synthesized by high energy ball milling relative to solid-state reaction. By analysis of the topology of the order parameter vector space it has been studied the phase transition in LiZn0.5 Ti1.5 O4 in more detail. Likewise, exploring the relationship between spontaneous strain, es and the order parameters, Qi , is useful in describing the nature of phase transition. A general Landau expansion for the excess free energy of the transition can be written as [31]:

Fig. 7. Temperature dependence of the spontaneous strain, es , as derived from the lattice parameters. Line is a guide for eyes.

G = L(Q ) +

 1 Ci,k ei ek + i,m,n eim Q n , 2 i,k

(3)

i,m,n

where the first term is a Landau potential, the second one represents the elastic energy and the last term corresponds to the interaction energy between es and Q, defined by the coupling coefficients  i,m,n . In the low-temperature ferroelastic phase (S.G. P43 32), both ordering parameters differ from zero and influence on the spontaneous strain scalar values. In title compound spontaneous strain values are rather small (order of 10−4 ), comparing to e.g. Li1.33x Co2−2x Ti1+0.67x O4 [32], indicating low intensity of coupling between Q and es . The second term of the expression given above can also be neglected from the same reason, so the Gibbs free energy can be represented by a Landau potential and interaction between Q parameters. Analysis of the topology of the order parameter vector space (Fig. 9) could point out to a biquadratic coupling between Q1 and Q2 , what is always allowed by symmetry [31,33]. It is worth mentioning that in the temperature stability range of the ordered phase (S.G. P43 32), there is linear relationship between Q1 and Q2 (inset of Fig. 9). However, the nature of the order parameter Q1 is non-convergent while parameter Q2 is convergent. Therefore, linear-quadratic coupling between the two ordering parameters cannot be excluded [34]. Moreover, missing of series of transitions as well as a re-entrant phase transition indicates possible linear-quadratic coupling between Q1 and Q2 . Biquadratic coupling between two order parameters has been reported to occur, for example, in Li1.33x Co2−2x Ti1+0.67x O4 [32], Li1−0.5x Fe2.5x Mn2−2x O4 [35–37], Pb3 [AsO4 ]2 [38] or NaNO3 [39], while linear-quadratic

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Fig. 9. Thermodynamically stable states represented in the vector space of the order parameters Q1 and Q2 ; inset: in the temperature stability range of the ordered phase (P43 32).

coupling is known to exist in KAlSi3 O8 [40]. The coupling mechanism between Q1 and Q2 depends on the magnitude of coupling between the two order parameters as well as on cation site preferences. 3.4. Raman analysis Raman spectroscopy has also been used to study the phase transition in LiZn0.5 Ti1.5 O4 in situ at high temperatures. In contrast to powder XRPD techniques, Raman spectroscopy allows a view into the short-range environment of the oxygen coordination around the cations in oxides. The positions and relative intensities of the Raman modes are sensitive to coordination geometry, oxidation states, and Jahn-Teller distortions [41]. It is also important to consider the laser power when interpreting Raman data [42]. According to factor group analysis for spinel-type com¯ − O7 space group), five optic modes are Raman active pounds (Fd3m h (A1g ⊕ Eg ⊕ 3F2g ). Oxygen occupying Wyckoff position 32e mostly contribute to Raman activity (A1g ⊕ Eg ⊕ 2F2g ). Additionally, cations in tetrahedrally coordinated 8a Wyckoff site are Raman active (1F2g ) as well. Ordering processes of the cations on tetrahedral and octa¯ hedral sites lead to a lowering of the crystal symmetry from Fd3m to P43 32 and, therefore, increases the number of Raman active modes significantly (5A1 ⊕ 12E ⊕ 17F2 ). Accordingly, atoms in all Wyckoff’s position are Raman active: 24e: (3A1 ⊕ 6E ⊕ 9F2 ), 12d: (1A1 ⊕ 3E ⊕ 4F2 ), 8c: (1A1 ⊕ 2E ⊕ 3F2 ), 4b: (1E ⊕ 1F2 ). Therefore, this type of phase transition in LiZn0.5 Ti1.5 O4 should be easily recognized from Raman spectra shown in Fig. 10. Raman spectra of LiZn0.5 Ti1.5 O4 spinel were recorded between 500 and 1200 ◦ C in heating and cooling, as well as at room temperature (RT) before and after thermal treatment. Some of them are shown in Fig. 11. At the temperature of 1100 ◦ C, in accordance with the factor group analysis five very weak and broad bands around 200, 350, 470, 820 and 920 cm−1 could be observed. The Raman spectrum recorded at RT (after thermal treatment) shows more narrow and intense Raman bands at 717, 652, 522, 443, 398, 347, 262 and 237 cm−1 , which is probably the consequence of the 1:3 ordering in the octahedral sublattice. Graves et al. [43] measured unpolarized Raman spectra on poly¯ crystalline Fe3 O4 (S.G. Fd3m) and detected six Raman bands at about 706(A1g ), 570(A1g ), 666(Eg ), 336(Eg ), 490(T2g ), and 226(T2g ) cm−1 . The symmetries were assigned in analogy to a polarized Raman study on NiFe2 O4 . Degiorgi et al. [44] carried out Raman and reflectivity measurements on natural single crystals of Fe3 O4 and described and assigned bands at 672 (A1g ), 542 (T2g or Eg ), 462

Fig. 10. Raman spectra collected as a function of temperature. Each spectrum was corrected for background and scaled to an approximate equal intensity of the band around 400 cm−1 .

(magnon scattering), 410, 318 and 160 cm−1 at 130 K. Similar assig¯ nation may be applied to LiZn0.5 Ti1.5 O4 in Fd3m. Julien et al. [41] observed Raman spectra of ordered ␣-LiFe5 O8 in the space group P41 32 and described two intense bands located at 709 and 492 cm−1 as the dominating features. As expected, the spectrum of a disordered ␤-LiFe5 O8 phase displayed less number of active modes at 603, 405 and 293 cm−1 with medium intensities. Macounova and co-workers [45] measured Raman active vibrations of nanocrystalline Li–Ti–O spinels and compared the measured data with DFT calculations on Lix Tiy Oz cluster. Raman shifts of both experimental (668, 607, 438, 345, 236 cm−1 ) and calculated (644, 625, 597, 437, 418, 405, 369, 353, 258, 248, 245, 227 cm−1 ) Raman active vibrations roughly agree with our room temperature data of LiZn0.5 Ti1.5 O4 spinel. However, mode assignments for the ordered structure (S.G. P43 32) were not given in their paper. Generally, in transition metal oxides, the bands observed in the wavenumber range 500–700 cm−1 can be attributed to the stretching vibrations of MO6 octahedron, while the spectral feature of MO4 tetrahedra remain confined between 400 and 550 cm−1 [15,41]. Accordingly, the Raman band observed at approximately 717 cm−1 can be viewed as the symmetric (Ti/Li)–O stretching vibration of octahedral groups. The most intense band in the spectrum recorded

Fig. 11. Evolution of the Raman spectra for LiZn0.5 Ti1.5 O4 spinel with temperature change. Each spectrum was corrected for background and scaled to approximate equal intensity of the area between 300 and 600 cm−1 .

N. Jovi´c et al. / Materials Chemistry and Physics 116 (2009) 542–549

at RT, observed at 398 cm−1 became broadened, while the bands at 237 and 262 cm−1 with medium intensities, have shown a trend of increasing intensity with rise of temperature. As expected, all Raman bands are shifted towards the low-wavenumber side with increase of the temperature due to the thermal expansion. 4. Conclusions Nanocrystalline LiZn0.5 Ti1.5 O4 spinel has been produced by high energy ball milling. The sample is disordered spinel with metastable cation distribution. Annealing and slowly cooling down to room temperature led to crystallite size increase, cation re-arrangement and ordering at octahedral sites followed with changes in crystal ¯ → P43 32. Further, the order–disorder phase transymmetry, Fd3m sition was studied on heating in temperature range of 900–1100 ◦ C. Different experimental techniques and theoretical method were used: in situ XRPD and Raman spectroscopy, DSC/DTA analysis and Landau theory of phase transitions. It was shown that disordering began with the cation migration of Li+ and Zn2+ ions between the tetrahedral, 8c and octahedral, 4b sites, but the main mechanism was cation mixing inside Oh sublattice. Raman spectra confirmed change in crystal symmetry more obviously then XRPD. Landau theory of phase transition and analysis of the topology of the order parameter vector space indicates that the mechanism of coupling between Q1 and Q2 parameters is either biquadratic or linear-quadratic. Spontaneous strain values are rather small (order of 10−4 ) pointing to a good microstructure property of material, that is important in its possible application in Li-ion batteries. Acknowledgments The Serbian Ministry of Science has financially supported this work. The authors thank to Prof. Nataˇsa Bibic´ for performing TEM studies. N.J. would like to thank Dr. Jovan Blanuˇsa for helpful suggestions concerning the refinement process. One of us (A.K.) would like to acknowledge the financial support from the CEEPUS project CII-AT-0038-01-0506-M-2329. The authors are also grateful to Bernhard Sartory for conducting HT-XRPD experiments. References [1] M.A. Arillo, M.L. Lopez, C. Pico, M.L. Veiga, J. Campo, J.L. Martinez, A. SantrichBadal, Chem. Mater. 17 (2005) 4162. [2] R.M. Rojas, J.M. Ammarilla, L. Pascual, J.M. Rojo, D. Kovacheva, K. Petrov, J. Power Sources 160 (2006) 529. [3] Y.J. Lee, S.-H. Park, Ch. Eng, J.B. Parise, C.P. Grey, Chem. Mater. 14 (2002) 194. [4] S.W. Oh, H.J. Bang, Y.C. Bae, Y.-K. Sun, J. Power Sources 173 (2007) 502.

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