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NMR and electric impedance study of lithium mobility in fast ion conductors LiTi2 − xZrx(PO4)3 (0 ≤ x ≤ 2)
Solid State Ionics 180 (2010) 1613–1619
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Solid State Ionics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s s i
NMR and electric impedance study of lithium mobility in fast ion conductors LiTi2 − xZrx(PO4)3 (0 ≤ x ≤ 2) K. Arbi a,⁎, M. Tabellout b, J. Sanz c a b c
Universidad SanPablo-CEU, Departamento de Química, Montepríncipe, 28668 Boadilla del Monte, Madrid, Spain Laboratoire de Physique de l'Etat Condensé (LPEC), UMR CNRS 6087, Université du Maine, Av. O. Messiaen 72085 Le Mans Cedex 9, France Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciónes Científicas (CSIC), Cantoblanco, 28049 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 1 July 2009 Received in revised form 20 October 2009 Accepted 16 November 2009 Keywords: Lithium ion conductors Nasicon structure 7 Li and 31P MAS-NMR spectroscopy Electric impedance spectroscopy
a b s t r a c t Materials of the LiTi2 − xZrx(PO4)3 series (0 ≤ x ≤ 2) were prepared and characterized by powder X-ray (XRD) and neutron diffraction (ND), 7Li and 31P Nuclear Magnetic Resonance (NMR) and Electric Impedance techniques. In samples with x b 1.8, XRD patterns were indexed with the rhombohedral R3̅c space group, but in samples with x ≥ 1.8, XRD patterns display the presence of rhombohedral and triclinic phases. The Rietveld analysis of the LiTi1.4Zr0.6(PO4)3 neutron diffraction (ND) pattern provided structural information about intermediate compositions. For low Zr contents, compositions deduced from 31P MAS-NMR spectra are similar to nominal ones, indicating that Zr4+ and Ti4+ cations are randomly distributed in the NASICON structure. At increasing Zr contents, differences between nominal and deduced compositions become significant, indicating some Zr segregation in the triclinic phase. The substitution of Ti4+ by Zr4+ stabilizes the rhombohedral phase; however, electrical performances are not improved in expanded networks of Zrrich samples. Below 300 K, activation energy of all samples is near 0.36 eV; however, above 300 K, activation energy is near 0.23 eV in Ti-rich samples and close to 0.36 eV in Zr-rich samples. The analysis of electrical data suggests that the amount of charge carriers and entropic terms are higher in Zr-rich samples; however, the increment of both parameters does not compensate lower activation energy terms of these samples. As a consequence of different contributions, the bulk conductivity of Zr-rich samples, measured at room temperature, is one order of magnitude lower than that measured in Ti-rich samples. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Ion conducting solids are materials of increasing interest because of their possible use as solid electrolytes in high-energy solid-state batteries. Among ion conductors, phosphates with Nasicon structure [1] displaying a three dimensional conduction network have been extensively studied. The framework of these compounds is built up by M2(PO4)3 units in which two MO6 octahedra and three tetrahedral PO4 share oxygen atoms. The [MO6][(PO4)3][MO6] units alternate with alkali cations to make infinite chains parallel to the ternary axis (c-axis). Each PO4 tetrahedron shares oxygen with four MO6 octahedra of three M2 (PO4)3 units to form the Nasicon's framework. In this structure, alkali cations can be accommodated at different sites depending on structural distortions of the Nasicon network and the size of alkali cations: i) M1 sites surrounded by six oxygen atoms and placed at inversion centers, ii) M2 sites with an irregular ten-fold oxygen coordination and disposed symmetrically around ternary axes and iii) M12 sites located between M1 and M2 positions. ⁎ Corresponding author. E-mail address: [email protected] (K. Arbi). 0167-2738/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2009.11.010
Materials of formula LiM2(PO4)3, with M = Ge, Ti, Sn, Hf, Zr, have been extensively investigated because of their good ion conductivity [2–8]. In LiGe2(PO4)3 and LiTi2(PO4)3 compounds, a rhombohedral – symmetry (R3c space group) was deduced from X-ray (XRD) and neutron diffraction (ND) patterns [3,4]. In this phase, Li ions are octahedrally coordinated at the intersection of three conduction channels (M1 sites). When ionic radii of tetravalent cations M4+ become bigger (M = Sn, Hf, Zr), a triclinic distortion is produced to better coordinate Li ions, that disappears when samples are heated above the phase transition temperature [9–11]. In the triclinic phase, Li ions are fourfold coordinated at M12 positions, located between M1 and M2 sites. In this work, the LiTi2 − xZrx(PO4)3 series (0 ≤ x ≤ 2) has been prepared and studied by XRD, ND, NMR and Electric Impedance techniques. Structural changes produced during substitution of Ti by Zr have been followed by X-ray and neutron diffraction techniques. The distribution of Ti and Zr cations has been investigated by 31P MASNMR spectroscopy. Structural sites and local mobility of lithium have been analyzed by 7Li MAS-NMR technique. Electric impedance techniques have been used to analyze Li conductivity in LiTi2 − xZrx (PO4)3 materials.
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2. Experimental section LiTi2 − xZrx(PO4)3 samples, with 0≤x ≤ 2, were prepared by the ceramic route. Stoichiometric amounts of Li2CO3, TiO2, ZrO2 and (NH4)2HPO4 were dried at 393 K for 10 h, mixed in a platinum crucible and heated at increasing temperatures [12]. After each treatment, the mixture was ground in an agate mortar and analyzed by X-ray diffraction to assess the purity of prepared phases. Samples were stored for later use when characteristic peaks of reagents and intermediate compounds, such as pyrophosphates, were not detected. In all compositions, single phases were obtained at 1273 K. Powder XRD patterns were recorded with the Cu-Kα radiation (λ =1.5405981 Å) in the 10–70º 2θ range with a step size of 0.02º and a counting time of 0.1 s/step in a PW 1050/25 Phillips diffractometer. Unit cell parameters of formed phases were deduced by using the Fullprof program [13] (pattern matching technique). The ND pattern of the LiTi1.4Zr0.6(PO4)3 sample was collected at 300 K in the high resolution D1A diffractometer (λ = 1.913 Å) of the Institut Laüe-Langevin (ILL) at Grenoble. The ND pattern of the sample (4 g) contained in a vanadium can, was recorded between 5 and 160º 2θ with a scan step of 0.02º (4 h). In Rietveld analyses, a pseudo-Voigt function was chosen to describe the line shape of diffraction peaks. The coherent scattering lengths used for Li, Ti Zr, P and O atoms were respectively −1.90, −3.43, 7.16, 5.13 and 5.80 fm. In a first stage, scale factors, background coefficients, 2θ zero positions, width and peakshape parameters were determined. In a second stage, positional parameters, site occupations and thermal factors of atoms were deduced. In this analysis, only isotropic thermal factors were considered. 31 P and 7Li MAS NMR spectra were recorded at room temperature in a MSL-400 Bruker spectrometer (9.4 T). The frequencies used for 31P and 7Li were 161.97 and 155.50 MHz, respectively. NMR signals were obtained after π/2 pulse irradiation (3 and 4 µs respectively) with a recycling time of 10 s (single pulse experiments). During spectra recording, the sample was spun at 2 or 3 kHz (Li signal) and at 4 kHz (P signal) around an axis inclined 54º44′ with respect to the external magnetic field (MAS technique). In analyzed samples, quadrupolar interactions remain small (CQ b120 kHz), making the irradiation of central and satellite transitions of 7 Li NMR spectra non selective. The number of scans was in the range of 100–800. 7Li and 31P NMR chemical shifts were referred to 1 M LiCl and 85% H3PO4 aqueous solutions. The fitting of NMR spectra was done with the Bruker WINFIT software package [14]. This program allows the position, linewidth and intensity of components to be determined with a non-linear least-square iterative method. However, quadrupole CQ and η values have to be deduced with a trial and error procedure. Impedance measurements were performed on cylindrical pellets of 13 mm diameter and approximately 1.4 mm thickness. Pellets were first compacted by cold pressing at 3 MPa, and then sintered at 1273 K for 24 h. For electric measurements, platinum electrodes were deposited by sputtering on the two faces of the pellet. Impedance measurements were performed over the frequency range 10− 1–1.8 × 109Hz in the temperature interval 200–500 K. To cover the full frequency domain, two experimental setups were used: for the low frequency (LF) range (10− 1– 106 Hz) a Solartron SI 1260 apparatus combined with a Broadband Dielectric Converter (BDC) was used; for the high frequency (HF) range (106–1.8 × 109Hz) an HP 4291A impedance analyzer was used with a precision coaxial line for which propagation parameters were previously determined. In this study, the sample was positioned at the end of the line and the impedance was deduced from the analysis of the complex reflection factor as a function of temperature. In both ranges analyzed, the sample temperature was measured with accuracies better than 0.1 K.
Fig. 1. (a) X-ray diffraction patterns of LiTi2 − xZrx(PO4)3 samples. (b) Unit cell a and c parameters of rhombohedral phases (hexagonal setting) as a function of the Zr content x. Parameters reported by Casciola and Subramanaian groups are included.
space group); however that of LiZr2(PO4)3 (x = 2) exhibits peaks of the triclinic (Tr) phase (C1̅space group). The XRD pattern of the LiZr2(PO4)3 sample heated above the triclinic-rhombohedral transition, T = 333 K, shows only peaks of the rhombohedral phase. In LiTi2 − xZrx(PO4)3 series, 0 ≤x ≤ 1.8, XRD patterns recorded at room temperature only display the peaks of the rhombohedral phase. As the Zr content increases, XRD reflections shift toward lower 2θ positions as a consequence of the increment of unit cell parameters (Fig. 1b). In this study, rhombohedral unit cells were described with the hexagonal setting (a and c parameters) of the R3̅c space group. In order to analyze structural features of intermediate compositions, the ND pattern of the LiTi1.4Zr0.6(PO4)3 sample was recorded at room temperature (Fig. 2a). Taken into account relative values of Zr and Ti scattering factors (opposite signs), the contribution of octahedral cations to the ND pattern was strongly attenuated. The Rietveld analysis was carried out with the R-3c model. In this model, Ti, Zr, P and O and Li atoms were located at (12c), (18e), (36f) and (6b) Wyckoff positions. In a second stage, Li atoms were assumed to be located at general (36f) positions around M1 sites. Positional parameters, site occupations and thermal factors of atoms are depicted in Table 2. Structural features deduced in this analysis are given in Table 3 and Fig. 2b.
3. Results
3.2. NMR spectroscopy
3.1. X-ray and neutron powder diffraction
31 P MAS-NMR signal P (I = 1/2) MAS NMR spectra of analyzed samples are shown in Fig. 3a. The 31P spectrum of LiTi2(PO4)3 displays a single narrow line at −27.5 ppm that corresponds to structural sites of the rhombohedral
3.2.1.
31
The XRD pattern of LiTi2(PO4)3 (x = 0), recorded at room temperature (Fig. 1a), displays peaks of the rhombohedral (Rh) phase (R3̅c
K. Arbi et al. / Solid State Ionics 180 (2010) 1613–1619
Fig. 2. (a) Rietveld refinement of the LiTi1.4Zr0.6(PO4)3 ND pattern recorded at 300 K. Peak positions and differences between observed and calculated profiles are also given. (b) Schematic view of the Nasicon structure deduced by Rietveld analysis. Equivalent positions occupied by Li around M1 sites are indicated (blue circles).
phase. When Ti4+ is substituted by Zr4+ cations, the NMR line shifts towards more positive values and becomes asymmetrically broadened, indicating the presence of additional components. For x = 2, the 31 P NMR spectrum recorded at room temperature is formed by three lines at −22.2, − 23.6 and −24.1 ppm, that were ascribed to structural sites of the triclinic phase. The single line observed at −23.9 ppm in the spectrum of the sample LiZr2(PO4)3 heated above the phase transition, 333 K, corresponds to structural sites occupied by phosphorous in the rhombohedral R3̅c phase (not shown). In 31P MAS NMR spectra, the shift produced by the substitution of Ti by Zr was assumed to be additive, allowing the position of components P(OTi)4, P(OTi)3(OZr)1, P(OTi)2(OZr)2, P(OTi)1(OZr)3 and P(OZr)4 to be deduced (lines labeled 0, 1, 2, 3 and 4 in Fig. 3b) [15]. The quantitative analysis of 31P MAS-NMR spectra allowed the estimation of Zr/Ti ratios of samples with the expression [16,17] Zr4+ 4I + 3I3 + 2I2 + I1 x = 4 = 2−x I3 + 2I2 + 3I1 + 4I0 Ti4+
ð1Þ
where In (n = 0, 1, 2, 3, 4) stands for the intensity of bands associated with (4 − n)Ti (n)Zr environments. From Zr/Ti values, the relative amounts of Zr (x) and Ti(1 − x) were deduced (see Table 1).
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Fig. 3. (a) 31P MAS-NMR spectra of the LiTi2 − xZrx(PO4)3 series. (b) Deconvolution of the 31P NMR spectrum of x = 1.2, where NMR components associated with P(OTi)4, P(OTi)3(OZr)1, P(OTi)2(OZr)2, P(OTi)1(OZr)3 and P(OZr)4 environments are indicated (lines labeled 0, 1, 2, 3 and 4).
3.2.2. 7Li MAS-NMR signal 7 Li NMR (I = 3/2) spectra of LiTi2 − xZrx(PO4)3 samples are formed by a central component (−1/2,1/2 transition) and two satellite lines (−3/ 2,−1/2 and 1/2,3/2 transitions). In 7Li MAS-NMR spectra, satellite transitions were modulated by the sample rotation, producing equally spaced bands separated by the spinning rate (Fig. 4a). Spectra were fitted with the Bruker WINFIT program, which takes into account firstorder quadrupole interactions. From this analysis, quadrupole CQ constants and asymmetry η parameters were determined (see Table 1). The analysis of NMR spectra of Ti and Zr end members showed that Li ions occupy preferentially M1 sites (CQ ∼ 45 kHz, η = 0) in the rhombohedral Ti phase and M12 sites (CQ ∼ 180 kHz, η = 0.6) in the triclinic Zr
Table 1 Chemical composition, x, quadrupole CQ and asymmetry η parameters, and hexagonal unit cell parameters of the LiTi2 − xZrx(PO4)3 series. x (C.A.)
x (RMN)a
CQ (KHz)b
η (dimensionless)b
a (Å)c
c (Å)c
0 0.4 0.8 1 1.5 1.8 2
0 0.38 0.81 0.96 1.37 1.58 2
44 ± 2 50 ± 2 65 ± 2 88 ± 2 108 ± 2 116 ± 2 120 ± 2
0 0 0 0 0 0 0
8.511(1) 8.566(1) 8.638(1) 8.672(1) 8.764(1) 8.827(1) 8.847(1)
20.843(2) 21.071(2) 21.341(2) 21.462(2) 21.779(2) 21.968(2) 22.241(2)
a b c
Deduced from 31P MAS-NMR spectra. Deduced from 7Li MAS-NMR spectra. Deduced from XRD patterns.
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Fig. 4. (a) 7Li MAS-NMR spectra of rhombohedral LiTi2(PO4)3 and LiZr2(PO4)3 phases recorded at 295 and 333 K. For sake of comparison, the 7Li NMR spectrum of the triclinic LiZr2(PO4)3 phase recorded at 295 K is included. (b) Dependence of quadrupole CQ constants on the Zr content of rhombohedral LiTi2 − xZrx(PO4)3 samples.
phase [18]. The triclinic-rhombohedral transition reduced CQ from 180 to 120 kHz in LiZr2(PO4)3 (Fig. 4a). In rhombohedral LiTi2 − xZrx (PO4)3 samples, quadrupole CQ constants measured at room temperature, increase progressively from 40 to 120 kHz as the Zr content increases (Fig. 4b [15] and Table 1), suggesting the existence of exchange processes between M1 and M12 sites. 3.3. Impedance measurements The frequency dependence of the real conductivity (σ′), measured at different temperatures, is illustrated in Fig. 5a and b for x = 0.4 and x = 1.5 samples. The plateau detected in the frequency range 100– 103 Hz and the dispersive regime observed at 105 Hz, were ascribed to the grain boundary response. Another plateau was observed in the high frequency range 107–109 Hz that corresponds to grain interior (or bulk) response. As the temperature increases, a new dispersive regime was detected below 100 Hz that was ascribed to the Li blocking at the pellet electrodes. Experimental σ′(ω) data were fitted taking in account grain interior and grain boundary responses. For the grain interior (bulk) contribution, it was assumed that the complex conductivity takes the form " ˆ b = σb;dc 1 + σ
iω ωbp
!n # + iωε∞
ð2Þ
Fig. 5. Real conductivity vs. angular frequency at indicated temperatures for (a) x = 0.4 and (b) x = 1.5 samples. In all analyzed samples similar variations were detected with temperature.
where σb,dc accounts for the conductivity measured at the plateau, ωbp is the cross-over frequency from the plateau (dc conductivity) to the dispersive regime, n is the correlation parameter and ε∞ is the permittivity for ω → ∞. For the grain boundary, it hwas assumed i that ˆ g = σg;dc 1 + iω where the complex conductivity takes the form σ ωgp
the parameters σg,dc and ωgp have similar meanings tothose ofthe −1 , former equation. The fitting equation used was σˆ = σˆ1 + σˆ1 g b where σ̂ accounts for the overall conductivity. The fitting of experimental results permitted to estimate separately dc-conductivity of grain interior and grain boundary responses. In all analyzed samples, it was observed that grain boundary conductivity is considerably lower than bulk conductivity. The variation of the grain interior and grain boundary dc conductivity vs. reciprocal temperature (1000/T) is shown in Fig. 6a and b, respectively. The values of conductivity depicted in two figures are similar to those reported by Casciola and Subramaniam groups [19,20]. The experimental values of conductivity were fitted to the Arrhenius expression σdc ⋅T = A⋅ expð−EM = kTÞ
ð3Þ
where A is the pre-exponential factor, EM is the activation energy, k is the Boltzmann constant, and T is the absolute temperature. Values of A and EM deduced from this analysis are outlined in Table 4. The analysis of dc-conductivity values showed the existence of two regimes for Ti-rich samples but only one for Zr-rich samples. Activation
K. Arbi et al. / Solid State Ionics 180 (2010) 1613–1619
Fig. 6. (a) Grain interior and (b) grain boundary dc-conductivities vs. reciprocal temperature in LiTi2 − xZrx (PO4)3 samples. Open symbols correspond to conductivity values measured at 295 and 573 K by the Subramanian's group [20].
energy of all samples are similar (0.36 eV) in the temperature 200– 300 K range; however, they decrease considerably above 300 K in Tirich samples (0.23 eV) (Fig. 6a). From the fitting of conductivity data measured between 300–500 K, the pre-exponential factor A of all samples was estimated. The plot of A as a function of the zirconium content (x) is given in Fig. 7a. It is observed that Zr-rich samples display higher pre-exponential factors than Ti-rich samples. 4. Discussion The combined XRD, ND and 31P MAS-NMR analysis of LiTi2 − xZrx (PO4)3 series has shown that samples with x b 1.8 display rhombohedral symmetry (R3̅c space group). However, the indexation of XRD patterns of x ≥ 1.8 samples with the rhombohedral model becomes difficult because the presence of the triclinic phase. The triclinic phase transform into the rhombohedral one at 333 K. The plot of unit cell parameters of rhombohedral (hexagonal setting) phases versus the Zr content, x, showed a linear behavior (Fig. 1b), indicating according to the Vegard's law [21], that Ti and Zr cations are randomly distributed in the Nasicon structure. Lattice parameters deduced in this work are similar to those previously reported by Casciola and Subramanian groups in more reduced compositional ranges [19,20]. From the quantitative analysis of 31P MAS-NMR spectra (Fig. 3a), the chemical composition of samples was estimated. In Ti-rich samples deduced compositions agree with nominal ones, indicating that miscibility of Ti and Zr is very high (see Table 1). However, estimated
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Fig. 7. Dependence of pre-exponential factors on (a) Zr content and (b) activation energy of LiTi2 − xZrx (PO4)3 samples.
and nominal compositions differ in Zr-rich samples, suggesting that some segregation is produced in triclinic phases. This behavior has been attributed to structural modifications induced by cations with different ionic radii, Zr4+ (0.72 Å) and Ti4+ (0.60 Å). In order to analyze structural features of the LiTi2 − xZrx(PO4)3 series, the Rietveld analysis of the LiTi1.4Zr0.6(PO4)3 ND pattern, collected at 300 K, was undertaken (Fig. 2a). In this refinement, the rhombohedral R3̅c model was used (Table 2). The octahedral compositions deduced in this analysis agree with the nominal ones. On the other hand, positional parameters are similar to those reported previously [22]. Li ions were first placed at M1 sites, but the resulting thermal factor (7.1 Å2) and Li–O distances (2.32 Å) were too high. In order to reduce Li–O distances, the structural position (0.120, 0.025, 0.184) deduced for lithium by Catti [22] in α-LiZr2(PO4)3 was tested. In structural refinements, the agreement factor RB decreased slightly from 5.1 to 4.9%, but Li–O distances (2.26 Å) and lithium thermal factor (1.3 Å2) decreased considerably. In the final model, deduced lithium coordinates (0.036, 0.055, 0.015) are slightly different from those deduced in α-LiZr2(PO4)3. The information deduced in structural refinement is given in Tables 2 and 3. In Fig. 2b, it is shown that Li ions occupy six equivalent positions (M′1) around M1 sites. In order to investigate local mobility of lithium, quadrupole CQ constants were investigated (Fig. 4b). The analysis of 7Li MAS-NMR spectra showed that CQ ∼ 50 kHz in Ti-rich samples, but it increases up to 120 kHz in Zr-rich samples. In all cases η = 0, indicating that structural sites occupied by Li display axial symmetry.
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Table 2 Structural parameters deduced from the Rietveld analysis of LiTi1.4 Zr0.6(PO4)3. In this analysis, the rhombohedral model (hexagonal setting) was used to fit Neutron Diffraction (ND) pattern.
σdc ⋅T = Kn ⋅ωbp = Kn ⋅ωe ⋅ expð−EM = kTÞ
Atom
x
y
z
B
Occ
Li(M1′) Ti Zr P O1 O2
0.036(2) 0 0 0.291(1) 0.187(1) 0.190(1)
0.055(2) 0 0 0 − 0.004(1) 0.167(1)
0.015(2) 0.860(3) 0.860(3) 0.250 0.191(1) 0.082(1)
1.40(10) 0.73(5) 0.73(5) 0.66(2) 1.23(5) 0.90(5)
1.08(6) 1.40(2) 0.60(2) 3 6 6
a = 8.6057(5) Å, c = 21.2143(8) Å. Vol = 1360.6 (2) Å3. RB = 4.96, RF = 3.27, Rp = 8.16, Rwp = 10.2 %, Chi2 = 1.35.
In presence of Li exchange processes, CQ values are given by the expression CQ =
CQ1 P1 + CQ12 3P12 P1 + 3P12
ð4Þ
where C1Q and C12 Q are quadrupolar constants and P1 and P12 are occupations of M1 and M12 sites. According to measured CQ values, Li ions reside most part of time at M1 sites in Ti-rich samples; but exchange between M1 and M12 sites in Zr-rich samples [23,24]. At intermediate compositions Li ions exchange positions between M1 and M12 sites, but residence times at two sites change, decreasing residence times at M1 sites when unit cell become progressively expanded. On the other hand, it has been observed that dc-conductivity in Zrrich samples is lower than in Ti-rich samples, suggesting that long range Li motions are less favored in Zr-rich samples. In order to explain the apparent contradiction between NMR and conductivity results, residence times at structural sites were estimated. From the analysis of NMR spectra, it was concluded that residence times at structural sites in two phases are larger than 10− 5 s at 300 K. This analysis indicates that exchange processes must be considered local motions and do not affect necessarily dc-conductivity of LiTi2 − xZrx (PO4)3 samples. At increasing temperatures, residence times should decrease, reducing quadrupole interactions and increasing dc-conductivity of samples. When conductivity of the LiTi2 − xZrx(PO4)3 series is analyzed in a large domain of temperature, it is observed that dc-conductivity of Tirich samples display two regimes, but that of Zr-rich samples only display one regime. In this series, dc-conductivity of samples extrapolated at infinite temperatures tend towards the same value. Described results agree with the trend reported by Robertson et al. in a larger amount of ion conductors [25]. Activation energy of all samples is similar (∼0.36 eV) in the temperature range 200–300 K; however, it decreases considerably about 300 K in Ti-rich samples (0.23 eV). In LiTi2(PO4)3 sample, conductivity values are near those reported by Subramanian and Casciola groups, but considerably higher than those reported by Martinez et al. [8] and discussed in ref
Table 3 Interatomic distances (Å), and O–Ti–O, O–P–O angles (°) deduced from the Rietveld analysis of LiTi1.4 Zr0.6(PO4)3. P–O1 = 1.523 (5) x2 P–O2 = 1.524 (5) x2
Ti,Zr–O1 = 1.952 (7) x3 Ti,Zr–O2 = 1.985.(7) x3
Li(M1)–O2 = 2.32 (4) x6 Li(M′)–O2 = 1.85 (4), 2.15 (4), 2.37 (4), 2.38 (4) 1
O1–P–O1 = 109.9 (9) O1–P–O2 = 107.1 (9) O1–P–O2 = 111.7 (9) O2–P–O2 = 109.5 (9) O1–Ti–O1 = 92.2 (9) O1–Ti–O2 = 88.4 (9) O1–Ti–O2 = 94.4 (9) O1–Ti–O2 = 173.2 (9) O2–Ti–O2 = 84.8 (9) b Li–ON = 2.19
[15]. In the series investigated in this work, the conductivity of Ti-rich samples is higher than that of Zr-rich samples. In general, dc-conductivity can be expressed as: ð5Þ
= Kn ⋅ω0 ⋅ expð−EM = kTÞ⋅expðΔSM = kÞ: where Kn · ωe is the pre-exponential factor (A), and EM and SM are the activation energy and entropy for Li migration. In this expression, ωe stands for the crossover ωbp frequency extrapolated to infinite temperature, ω0 is the attempt frequency and Kn is a factor proportional to the charge carriers concentration. In order to further analyze Li motions, pre-exponential Kn · ωe factors (A in expression (3)), deduced from the extrapolation of σdc · T values to infinite temperatures, are given in the Table 4. Kn · ωe factors increase from 6 × 102 (x = 0) to 5 × 103 Scm− 1 K (x = 1.8) when Zr increases. On the other hand, ωe parameters were deduced from the extrapolation of crossover ωbp values to infinite temperature. From both parameters, Kn values were finally deduced, suggesting that the amount of charge carriers increases slightly along the series when the amount of Zr increases (Table 4). At this point it is important to discuss the physical meaning of the term ωe of the expression (5). In general, ωe can be expressed as [26]: ωe = ω0 expðΔSM = kÞ
ð6Þ
where, ω0 is the attempt frequency and ωe can be considered as an effective frequency for Li motions [27]. In Ti and Zr-rich samples ωe values are appreciably different. Taken into account that ω0 is assumed to be almost the same in most materials, changes observed in ωe should be ascribed to changes in the migration entropy [27]. The analysis of the electrical behavior of samples showed that dcconductivity of the Ti end member (1.6 × 10− 4 S cm− 1) is higher than that of the Zr end member (4 × 10− 6 S cm− 1) at 300 K. This fact indicates that the increment of the unit cell volume in the LiTi2 − xZrx (PO4)3 series, produced by the substitution of Ti by Zr, does not improve ionic conductivity, suggesting that other parameters than unit cell volume affect the conductivity. Similar conclusions were deduced in the Li1 + xTi2 − xAlx(PO4)3 series, where substitution of Ti by smaller Al cations decreases unit cell dimensions but increased Li mobility [17]. The analysis of conductivity data showed important differences in activation energy and pre-exponential factors of samples. In Ti-rich samples activation energy is appreciably lower than in Zr-rich samples. The plot of pre-exponential factors against the samples composition, x, shows again two regimes: the first corresponding to samples with low mobility of lithium, where entropic terms are important, and the second corresponds to samples with higher mobility of lithium, where entropic terms are small (Fig. 7a). This analysis shows that changes in two parameters are better correlated with changes on Li occupation of M1 and M12 crystallographic sites, deduced by 7Li MAS-NMR spectroscopy, than with those produced on the volume cell, deduced by XRD technique. Finally, the dependence of the pre-exponential factor on activation energy is analyzed in Fig. 7b. In investigated samples, both parameters are strictly proportional indicating that activation energy and preexponential factors are strongly correlated. This behavior, often observed in semiconductors and ion conductors, is called “MeyerNeldel” or compensation rule [28]. According to this rule, motions with important activation energy improves considerably the entropic term, but motions with lower activation energy only improves slightly entropy associated with Li motion. In Zr-rich samples, the increment of pre-exponential terms does not compensate the lower contribution of activation energy terms. The stabilization of the rhombohedral phase in Zr doped samples eliminates problems derived from stresses produced at the triclinic-
K. Arbi et al. / Solid State Ionics 180 (2010) 1613–1619 Table 4 Activation energies Ea, pre-exponential factors A, cross-over frequencies extrapolated to infinite temperatures ωe, and compositional factors Kn deduced from conductivity plots (300–500 K) of LiTi2 − xZrx (PO4)3 samples. x 0 0.4 0.8 1.2 1.5 1.8
Ea (eV) 0.21 0.23 0.25 0.36 0.35 0.39
A (Scm− 1 K) 600 150 250 3500 3000 5000
ωe (rad/s) 10
9 × 10 4 × 1010 5.2 × 1010 6 × 1011 5 × 1011 6 × 1011
1619
Madrid (Project S-505/PPQ-0358) for financial support. K. Arbi thanks Spanish Ministry of Science and Innovation for the financial support under the contract “Juan de la Cierva”. Authors thank Prof. J. M. Rojo, M. A. Aranda and S. Bruque for helpful discussions.
Kn 6.7 × 10− 9 3.7 × 10− 9 4.8 × 10− 9 5.8 × 10− 9 6 × 10− 9 8.3 × 10− 9
rhombohedral transition, and enlarges the electrochemical window as a consequence of the lower reducibility of Zr cations. However, dcconductivity of Zr-rich samples is not improved with respect to that of Ti-rich samples. 5. Conclusions Samples of the LiTi2 − xZrx(PO4)3 series have been prepared and characterized by XRD, ND, NMR and impedance techniques. In this series, rhombohedral phases were obtained in the compositional range 0 ≤ x b 1.8, but triclinic phases accompany rhombohedral ones in samples with x ≥ 1.8. The substitution of Ti by Zr increases unit cell volume but decreases conductivity measured at room temperature from 1.6 × 10− 4 S cm− 1 to 4 × 10− 6 Scm− 1. Described results prove that other parameters than the unit cell volume affect conductivity. In analyzed samples, activation energy decreases from 0.33 to 0.21 eV in Ti-rich samples, but remains near 0.36 eV in Zr-rich samples in the temperature range 200–500 K. Along the analyzed LiTi2 − xZrx(PO4)3 series, activation energy measured between 300 and 500 K increases with the composition in a non-linear way from ∼ 0.23 to 0.36 eV. Finally, the amount of charge carriers and entropic terms are higher in Zr-rich samples; however, the increment of these two parameters does not compensate the decrement produced on activation energy terms. Acknowledgements Authors gratefully acknowledge the Spanish Agency CICYT (MAT2007-64486-C07 projects) and the Regional Government of
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Solid State Ionics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s s i
NMR and electric impedance study of lithium mobility in fast ion conductors LiTi2 − xZrx(PO4)3 (0 ≤ x ≤ 2) K. Arbi a,⁎, M. Tabellout b, J. Sanz c a b c
Universidad SanPablo-CEU, Departamento de Química, Montepríncipe, 28668 Boadilla del Monte, Madrid, Spain Laboratoire de Physique de l'Etat Condensé (LPEC), UMR CNRS 6087, Université du Maine, Av. O. Messiaen 72085 Le Mans Cedex 9, France Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciónes Científicas (CSIC), Cantoblanco, 28049 Madrid, Spain
a r t i c l e
i n f o
Article history: Received 1 July 2009 Received in revised form 20 October 2009 Accepted 16 November 2009 Keywords: Lithium ion conductors Nasicon structure 7 Li and 31P MAS-NMR spectroscopy Electric impedance spectroscopy
a b s t r a c t Materials of the LiTi2 − xZrx(PO4)3 series (0 ≤ x ≤ 2) were prepared and characterized by powder X-ray (XRD) and neutron diffraction (ND), 7Li and 31P Nuclear Magnetic Resonance (NMR) and Electric Impedance techniques. In samples with x b 1.8, XRD patterns were indexed with the rhombohedral R3̅c space group, but in samples with x ≥ 1.8, XRD patterns display the presence of rhombohedral and triclinic phases. The Rietveld analysis of the LiTi1.4Zr0.6(PO4)3 neutron diffraction (ND) pattern provided structural information about intermediate compositions. For low Zr contents, compositions deduced from 31P MAS-NMR spectra are similar to nominal ones, indicating that Zr4+ and Ti4+ cations are randomly distributed in the NASICON structure. At increasing Zr contents, differences between nominal and deduced compositions become significant, indicating some Zr segregation in the triclinic phase. The substitution of Ti4+ by Zr4+ stabilizes the rhombohedral phase; however, electrical performances are not improved in expanded networks of Zrrich samples. Below 300 K, activation energy of all samples is near 0.36 eV; however, above 300 K, activation energy is near 0.23 eV in Ti-rich samples and close to 0.36 eV in Zr-rich samples. The analysis of electrical data suggests that the amount of charge carriers and entropic terms are higher in Zr-rich samples; however, the increment of both parameters does not compensate lower activation energy terms of these samples. As a consequence of different contributions, the bulk conductivity of Zr-rich samples, measured at room temperature, is one order of magnitude lower than that measured in Ti-rich samples. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Ion conducting solids are materials of increasing interest because of their possible use as solid electrolytes in high-energy solid-state batteries. Among ion conductors, phosphates with Nasicon structure [1] displaying a three dimensional conduction network have been extensively studied. The framework of these compounds is built up by M2(PO4)3 units in which two MO6 octahedra and three tetrahedral PO4 share oxygen atoms. The [MO6][(PO4)3][MO6] units alternate with alkali cations to make infinite chains parallel to the ternary axis (c-axis). Each PO4 tetrahedron shares oxygen with four MO6 octahedra of three M2 (PO4)3 units to form the Nasicon's framework. In this structure, alkali cations can be accommodated at different sites depending on structural distortions of the Nasicon network and the size of alkali cations: i) M1 sites surrounded by six oxygen atoms and placed at inversion centers, ii) M2 sites with an irregular ten-fold oxygen coordination and disposed symmetrically around ternary axes and iii) M12 sites located between M1 and M2 positions. ⁎ Corresponding author. E-mail address: [email protected] (K. Arbi). 0167-2738/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2009.11.010
Materials of formula LiM2(PO4)3, with M = Ge, Ti, Sn, Hf, Zr, have been extensively investigated because of their good ion conductivity [2–8]. In LiGe2(PO4)3 and LiTi2(PO4)3 compounds, a rhombohedral – symmetry (R3c space group) was deduced from X-ray (XRD) and neutron diffraction (ND) patterns [3,4]. In this phase, Li ions are octahedrally coordinated at the intersection of three conduction channels (M1 sites). When ionic radii of tetravalent cations M4+ become bigger (M = Sn, Hf, Zr), a triclinic distortion is produced to better coordinate Li ions, that disappears when samples are heated above the phase transition temperature [9–11]. In the triclinic phase, Li ions are fourfold coordinated at M12 positions, located between M1 and M2 sites. In this work, the LiTi2 − xZrx(PO4)3 series (0 ≤ x ≤ 2) has been prepared and studied by XRD, ND, NMR and Electric Impedance techniques. Structural changes produced during substitution of Ti by Zr have been followed by X-ray and neutron diffraction techniques. The distribution of Ti and Zr cations has been investigated by 31P MASNMR spectroscopy. Structural sites and local mobility of lithium have been analyzed by 7Li MAS-NMR technique. Electric impedance techniques have been used to analyze Li conductivity in LiTi2 − xZrx (PO4)3 materials.
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2. Experimental section LiTi2 − xZrx(PO4)3 samples, with 0≤x ≤ 2, were prepared by the ceramic route. Stoichiometric amounts of Li2CO3, TiO2, ZrO2 and (NH4)2HPO4 were dried at 393 K for 10 h, mixed in a platinum crucible and heated at increasing temperatures [12]. After each treatment, the mixture was ground in an agate mortar and analyzed by X-ray diffraction to assess the purity of prepared phases. Samples were stored for later use when characteristic peaks of reagents and intermediate compounds, such as pyrophosphates, were not detected. In all compositions, single phases were obtained at 1273 K. Powder XRD patterns were recorded with the Cu-Kα radiation (λ =1.5405981 Å) in the 10–70º 2θ range with a step size of 0.02º and a counting time of 0.1 s/step in a PW 1050/25 Phillips diffractometer. Unit cell parameters of formed phases were deduced by using the Fullprof program [13] (pattern matching technique). The ND pattern of the LiTi1.4Zr0.6(PO4)3 sample was collected at 300 K in the high resolution D1A diffractometer (λ = 1.913 Å) of the Institut Laüe-Langevin (ILL) at Grenoble. The ND pattern of the sample (4 g) contained in a vanadium can, was recorded between 5 and 160º 2θ with a scan step of 0.02º (4 h). In Rietveld analyses, a pseudo-Voigt function was chosen to describe the line shape of diffraction peaks. The coherent scattering lengths used for Li, Ti Zr, P and O atoms were respectively −1.90, −3.43, 7.16, 5.13 and 5.80 fm. In a first stage, scale factors, background coefficients, 2θ zero positions, width and peakshape parameters were determined. In a second stage, positional parameters, site occupations and thermal factors of atoms were deduced. In this analysis, only isotropic thermal factors were considered. 31 P and 7Li MAS NMR spectra were recorded at room temperature in a MSL-400 Bruker spectrometer (9.4 T). The frequencies used for 31P and 7Li were 161.97 and 155.50 MHz, respectively. NMR signals were obtained after π/2 pulse irradiation (3 and 4 µs respectively) with a recycling time of 10 s (single pulse experiments). During spectra recording, the sample was spun at 2 or 3 kHz (Li signal) and at 4 kHz (P signal) around an axis inclined 54º44′ with respect to the external magnetic field (MAS technique). In analyzed samples, quadrupolar interactions remain small (CQ b120 kHz), making the irradiation of central and satellite transitions of 7 Li NMR spectra non selective. The number of scans was in the range of 100–800. 7Li and 31P NMR chemical shifts were referred to 1 M LiCl and 85% H3PO4 aqueous solutions. The fitting of NMR spectra was done with the Bruker WINFIT software package [14]. This program allows the position, linewidth and intensity of components to be determined with a non-linear least-square iterative method. However, quadrupole CQ and η values have to be deduced with a trial and error procedure. Impedance measurements were performed on cylindrical pellets of 13 mm diameter and approximately 1.4 mm thickness. Pellets were first compacted by cold pressing at 3 MPa, and then sintered at 1273 K for 24 h. For electric measurements, platinum electrodes were deposited by sputtering on the two faces of the pellet. Impedance measurements were performed over the frequency range 10− 1–1.8 × 109Hz in the temperature interval 200–500 K. To cover the full frequency domain, two experimental setups were used: for the low frequency (LF) range (10− 1– 106 Hz) a Solartron SI 1260 apparatus combined with a Broadband Dielectric Converter (BDC) was used; for the high frequency (HF) range (106–1.8 × 109Hz) an HP 4291A impedance analyzer was used with a precision coaxial line for which propagation parameters were previously determined. In this study, the sample was positioned at the end of the line and the impedance was deduced from the analysis of the complex reflection factor as a function of temperature. In both ranges analyzed, the sample temperature was measured with accuracies better than 0.1 K.
Fig. 1. (a) X-ray diffraction patterns of LiTi2 − xZrx(PO4)3 samples. (b) Unit cell a and c parameters of rhombohedral phases (hexagonal setting) as a function of the Zr content x. Parameters reported by Casciola and Subramanaian groups are included.
space group); however that of LiZr2(PO4)3 (x = 2) exhibits peaks of the triclinic (Tr) phase (C1̅space group). The XRD pattern of the LiZr2(PO4)3 sample heated above the triclinic-rhombohedral transition, T = 333 K, shows only peaks of the rhombohedral phase. In LiTi2 − xZrx(PO4)3 series, 0 ≤x ≤ 1.8, XRD patterns recorded at room temperature only display the peaks of the rhombohedral phase. As the Zr content increases, XRD reflections shift toward lower 2θ positions as a consequence of the increment of unit cell parameters (Fig. 1b). In this study, rhombohedral unit cells were described with the hexagonal setting (a and c parameters) of the R3̅c space group. In order to analyze structural features of intermediate compositions, the ND pattern of the LiTi1.4Zr0.6(PO4)3 sample was recorded at room temperature (Fig. 2a). Taken into account relative values of Zr and Ti scattering factors (opposite signs), the contribution of octahedral cations to the ND pattern was strongly attenuated. The Rietveld analysis was carried out with the R-3c model. In this model, Ti, Zr, P and O and Li atoms were located at (12c), (18e), (36f) and (6b) Wyckoff positions. In a second stage, Li atoms were assumed to be located at general (36f) positions around M1 sites. Positional parameters, site occupations and thermal factors of atoms are depicted in Table 2. Structural features deduced in this analysis are given in Table 3 and Fig. 2b.
3. Results
3.2. NMR spectroscopy
3.1. X-ray and neutron powder diffraction
31 P MAS-NMR signal P (I = 1/2) MAS NMR spectra of analyzed samples are shown in Fig. 3a. The 31P spectrum of LiTi2(PO4)3 displays a single narrow line at −27.5 ppm that corresponds to structural sites of the rhombohedral
3.2.1.
31
The XRD pattern of LiTi2(PO4)3 (x = 0), recorded at room temperature (Fig. 1a), displays peaks of the rhombohedral (Rh) phase (R3̅c
K. Arbi et al. / Solid State Ionics 180 (2010) 1613–1619
Fig. 2. (a) Rietveld refinement of the LiTi1.4Zr0.6(PO4)3 ND pattern recorded at 300 K. Peak positions and differences between observed and calculated profiles are also given. (b) Schematic view of the Nasicon structure deduced by Rietveld analysis. Equivalent positions occupied by Li around M1 sites are indicated (blue circles).
phase. When Ti4+ is substituted by Zr4+ cations, the NMR line shifts towards more positive values and becomes asymmetrically broadened, indicating the presence of additional components. For x = 2, the 31 P NMR spectrum recorded at room temperature is formed by three lines at −22.2, − 23.6 and −24.1 ppm, that were ascribed to structural sites of the triclinic phase. The single line observed at −23.9 ppm in the spectrum of the sample LiZr2(PO4)3 heated above the phase transition, 333 K, corresponds to structural sites occupied by phosphorous in the rhombohedral R3̅c phase (not shown). In 31P MAS NMR spectra, the shift produced by the substitution of Ti by Zr was assumed to be additive, allowing the position of components P(OTi)4, P(OTi)3(OZr)1, P(OTi)2(OZr)2, P(OTi)1(OZr)3 and P(OZr)4 to be deduced (lines labeled 0, 1, 2, 3 and 4 in Fig. 3b) [15]. The quantitative analysis of 31P MAS-NMR spectra allowed the estimation of Zr/Ti ratios of samples with the expression [16,17] Zr4+ 4I + 3I3 + 2I2 + I1 x = 4 = 2−x I3 + 2I2 + 3I1 + 4I0 Ti4+
ð1Þ
where In (n = 0, 1, 2, 3, 4) stands for the intensity of bands associated with (4 − n)Ti (n)Zr environments. From Zr/Ti values, the relative amounts of Zr (x) and Ti(1 − x) were deduced (see Table 1).
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Fig. 3. (a) 31P MAS-NMR spectra of the LiTi2 − xZrx(PO4)3 series. (b) Deconvolution of the 31P NMR spectrum of x = 1.2, where NMR components associated with P(OTi)4, P(OTi)3(OZr)1, P(OTi)2(OZr)2, P(OTi)1(OZr)3 and P(OZr)4 environments are indicated (lines labeled 0, 1, 2, 3 and 4).
3.2.2. 7Li MAS-NMR signal 7 Li NMR (I = 3/2) spectra of LiTi2 − xZrx(PO4)3 samples are formed by a central component (−1/2,1/2 transition) and two satellite lines (−3/ 2,−1/2 and 1/2,3/2 transitions). In 7Li MAS-NMR spectra, satellite transitions were modulated by the sample rotation, producing equally spaced bands separated by the spinning rate (Fig. 4a). Spectra were fitted with the Bruker WINFIT program, which takes into account firstorder quadrupole interactions. From this analysis, quadrupole CQ constants and asymmetry η parameters were determined (see Table 1). The analysis of NMR spectra of Ti and Zr end members showed that Li ions occupy preferentially M1 sites (CQ ∼ 45 kHz, η = 0) in the rhombohedral Ti phase and M12 sites (CQ ∼ 180 kHz, η = 0.6) in the triclinic Zr
Table 1 Chemical composition, x, quadrupole CQ and asymmetry η parameters, and hexagonal unit cell parameters of the LiTi2 − xZrx(PO4)3 series. x (C.A.)
x (RMN)a
CQ (KHz)b
η (dimensionless)b
a (Å)c
c (Å)c
0 0.4 0.8 1 1.5 1.8 2
0 0.38 0.81 0.96 1.37 1.58 2
44 ± 2 50 ± 2 65 ± 2 88 ± 2 108 ± 2 116 ± 2 120 ± 2
0 0 0 0 0 0 0
8.511(1) 8.566(1) 8.638(1) 8.672(1) 8.764(1) 8.827(1) 8.847(1)
20.843(2) 21.071(2) 21.341(2) 21.462(2) 21.779(2) 21.968(2) 22.241(2)
a b c
Deduced from 31P MAS-NMR spectra. Deduced from 7Li MAS-NMR spectra. Deduced from XRD patterns.
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Fig. 4. (a) 7Li MAS-NMR spectra of rhombohedral LiTi2(PO4)3 and LiZr2(PO4)3 phases recorded at 295 and 333 K. For sake of comparison, the 7Li NMR spectrum of the triclinic LiZr2(PO4)3 phase recorded at 295 K is included. (b) Dependence of quadrupole CQ constants on the Zr content of rhombohedral LiTi2 − xZrx(PO4)3 samples.
phase [18]. The triclinic-rhombohedral transition reduced CQ from 180 to 120 kHz in LiZr2(PO4)3 (Fig. 4a). In rhombohedral LiTi2 − xZrx (PO4)3 samples, quadrupole CQ constants measured at room temperature, increase progressively from 40 to 120 kHz as the Zr content increases (Fig. 4b [15] and Table 1), suggesting the existence of exchange processes between M1 and M12 sites. 3.3. Impedance measurements The frequency dependence of the real conductivity (σ′), measured at different temperatures, is illustrated in Fig. 5a and b for x = 0.4 and x = 1.5 samples. The plateau detected in the frequency range 100– 103 Hz and the dispersive regime observed at 105 Hz, were ascribed to the grain boundary response. Another plateau was observed in the high frequency range 107–109 Hz that corresponds to grain interior (or bulk) response. As the temperature increases, a new dispersive regime was detected below 100 Hz that was ascribed to the Li blocking at the pellet electrodes. Experimental σ′(ω) data were fitted taking in account grain interior and grain boundary responses. For the grain interior (bulk) contribution, it was assumed that the complex conductivity takes the form " ˆ b = σb;dc 1 + σ
iω ωbp
!n # + iωε∞
ð2Þ
Fig. 5. Real conductivity vs. angular frequency at indicated temperatures for (a) x = 0.4 and (b) x = 1.5 samples. In all analyzed samples similar variations were detected with temperature.
where σb,dc accounts for the conductivity measured at the plateau, ωbp is the cross-over frequency from the plateau (dc conductivity) to the dispersive regime, n is the correlation parameter and ε∞ is the permittivity for ω → ∞. For the grain boundary, it hwas assumed i that ˆ g = σg;dc 1 + iω where the complex conductivity takes the form σ ωgp
the parameters σg,dc and ωgp have similar meanings tothose ofthe −1 , former equation. The fitting equation used was σˆ = σˆ1 + σˆ1 g b where σ̂ accounts for the overall conductivity. The fitting of experimental results permitted to estimate separately dc-conductivity of grain interior and grain boundary responses. In all analyzed samples, it was observed that grain boundary conductivity is considerably lower than bulk conductivity. The variation of the grain interior and grain boundary dc conductivity vs. reciprocal temperature (1000/T) is shown in Fig. 6a and b, respectively. The values of conductivity depicted in two figures are similar to those reported by Casciola and Subramaniam groups [19,20]. The experimental values of conductivity were fitted to the Arrhenius expression σdc ⋅T = A⋅ expð−EM = kTÞ
ð3Þ
where A is the pre-exponential factor, EM is the activation energy, k is the Boltzmann constant, and T is the absolute temperature. Values of A and EM deduced from this analysis are outlined in Table 4. The analysis of dc-conductivity values showed the existence of two regimes for Ti-rich samples but only one for Zr-rich samples. Activation
K. Arbi et al. / Solid State Ionics 180 (2010) 1613–1619
Fig. 6. (a) Grain interior and (b) grain boundary dc-conductivities vs. reciprocal temperature in LiTi2 − xZrx (PO4)3 samples. Open symbols correspond to conductivity values measured at 295 and 573 K by the Subramanian's group [20].
energy of all samples are similar (0.36 eV) in the temperature 200– 300 K range; however, they decrease considerably above 300 K in Tirich samples (0.23 eV) (Fig. 6a). From the fitting of conductivity data measured between 300–500 K, the pre-exponential factor A of all samples was estimated. The plot of A as a function of the zirconium content (x) is given in Fig. 7a. It is observed that Zr-rich samples display higher pre-exponential factors than Ti-rich samples. 4. Discussion The combined XRD, ND and 31P MAS-NMR analysis of LiTi2 − xZrx (PO4)3 series has shown that samples with x b 1.8 display rhombohedral symmetry (R3̅c space group). However, the indexation of XRD patterns of x ≥ 1.8 samples with the rhombohedral model becomes difficult because the presence of the triclinic phase. The triclinic phase transform into the rhombohedral one at 333 K. The plot of unit cell parameters of rhombohedral (hexagonal setting) phases versus the Zr content, x, showed a linear behavior (Fig. 1b), indicating according to the Vegard's law [21], that Ti and Zr cations are randomly distributed in the Nasicon structure. Lattice parameters deduced in this work are similar to those previously reported by Casciola and Subramanian groups in more reduced compositional ranges [19,20]. From the quantitative analysis of 31P MAS-NMR spectra (Fig. 3a), the chemical composition of samples was estimated. In Ti-rich samples deduced compositions agree with nominal ones, indicating that miscibility of Ti and Zr is very high (see Table 1). However, estimated
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Fig. 7. Dependence of pre-exponential factors on (a) Zr content and (b) activation energy of LiTi2 − xZrx (PO4)3 samples.
and nominal compositions differ in Zr-rich samples, suggesting that some segregation is produced in triclinic phases. This behavior has been attributed to structural modifications induced by cations with different ionic radii, Zr4+ (0.72 Å) and Ti4+ (0.60 Å). In order to analyze structural features of the LiTi2 − xZrx(PO4)3 series, the Rietveld analysis of the LiTi1.4Zr0.6(PO4)3 ND pattern, collected at 300 K, was undertaken (Fig. 2a). In this refinement, the rhombohedral R3̅c model was used (Table 2). The octahedral compositions deduced in this analysis agree with the nominal ones. On the other hand, positional parameters are similar to those reported previously [22]. Li ions were first placed at M1 sites, but the resulting thermal factor (7.1 Å2) and Li–O distances (2.32 Å) were too high. In order to reduce Li–O distances, the structural position (0.120, 0.025, 0.184) deduced for lithium by Catti [22] in α-LiZr2(PO4)3 was tested. In structural refinements, the agreement factor RB decreased slightly from 5.1 to 4.9%, but Li–O distances (2.26 Å) and lithium thermal factor (1.3 Å2) decreased considerably. In the final model, deduced lithium coordinates (0.036, 0.055, 0.015) are slightly different from those deduced in α-LiZr2(PO4)3. The information deduced in structural refinement is given in Tables 2 and 3. In Fig. 2b, it is shown that Li ions occupy six equivalent positions (M′1) around M1 sites. In order to investigate local mobility of lithium, quadrupole CQ constants were investigated (Fig. 4b). The analysis of 7Li MAS-NMR spectra showed that CQ ∼ 50 kHz in Ti-rich samples, but it increases up to 120 kHz in Zr-rich samples. In all cases η = 0, indicating that structural sites occupied by Li display axial symmetry.
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Table 2 Structural parameters deduced from the Rietveld analysis of LiTi1.4 Zr0.6(PO4)3. In this analysis, the rhombohedral model (hexagonal setting) was used to fit Neutron Diffraction (ND) pattern.
σdc ⋅T = Kn ⋅ωbp = Kn ⋅ωe ⋅ expð−EM = kTÞ
Atom
x
y
z
B
Occ
Li(M1′) Ti Zr P O1 O2
0.036(2) 0 0 0.291(1) 0.187(1) 0.190(1)
0.055(2) 0 0 0 − 0.004(1) 0.167(1)
0.015(2) 0.860(3) 0.860(3) 0.250 0.191(1) 0.082(1)
1.40(10) 0.73(5) 0.73(5) 0.66(2) 1.23(5) 0.90(5)
1.08(6) 1.40(2) 0.60(2) 3 6 6
a = 8.6057(5) Å, c = 21.2143(8) Å. Vol = 1360.6 (2) Å3. RB = 4.96, RF = 3.27, Rp = 8.16, Rwp = 10.2 %, Chi2 = 1.35.
In presence of Li exchange processes, CQ values are given by the expression CQ =
CQ1 P1 + CQ12 3P12 P1 + 3P12
ð4Þ
where C1Q and C12 Q are quadrupolar constants and P1 and P12 are occupations of M1 and M12 sites. According to measured CQ values, Li ions reside most part of time at M1 sites in Ti-rich samples; but exchange between M1 and M12 sites in Zr-rich samples [23,24]. At intermediate compositions Li ions exchange positions between M1 and M12 sites, but residence times at two sites change, decreasing residence times at M1 sites when unit cell become progressively expanded. On the other hand, it has been observed that dc-conductivity in Zrrich samples is lower than in Ti-rich samples, suggesting that long range Li motions are less favored in Zr-rich samples. In order to explain the apparent contradiction between NMR and conductivity results, residence times at structural sites were estimated. From the analysis of NMR spectra, it was concluded that residence times at structural sites in two phases are larger than 10− 5 s at 300 K. This analysis indicates that exchange processes must be considered local motions and do not affect necessarily dc-conductivity of LiTi2 − xZrx (PO4)3 samples. At increasing temperatures, residence times should decrease, reducing quadrupole interactions and increasing dc-conductivity of samples. When conductivity of the LiTi2 − xZrx(PO4)3 series is analyzed in a large domain of temperature, it is observed that dc-conductivity of Tirich samples display two regimes, but that of Zr-rich samples only display one regime. In this series, dc-conductivity of samples extrapolated at infinite temperatures tend towards the same value. Described results agree with the trend reported by Robertson et al. in a larger amount of ion conductors [25]. Activation energy of all samples is similar (∼0.36 eV) in the temperature range 200–300 K; however, it decreases considerably about 300 K in Ti-rich samples (0.23 eV). In LiTi2(PO4)3 sample, conductivity values are near those reported by Subramanian and Casciola groups, but considerably higher than those reported by Martinez et al. [8] and discussed in ref
Table 3 Interatomic distances (Å), and O–Ti–O, O–P–O angles (°) deduced from the Rietveld analysis of LiTi1.4 Zr0.6(PO4)3. P–O1 = 1.523 (5) x2 P–O2 = 1.524 (5) x2
Ti,Zr–O1 = 1.952 (7) x3 Ti,Zr–O2 = 1.985.(7) x3
Li(M1)–O2 = 2.32 (4) x6 Li(M′)–O2 = 1.85 (4), 2.15 (4), 2.37 (4), 2.38 (4) 1
O1–P–O1 = 109.9 (9) O1–P–O2 = 107.1 (9) O1–P–O2 = 111.7 (9) O2–P–O2 = 109.5 (9) O1–Ti–O1 = 92.2 (9) O1–Ti–O2 = 88.4 (9) O1–Ti–O2 = 94.4 (9) O1–Ti–O2 = 173.2 (9) O2–Ti–O2 = 84.8 (9) b Li–ON = 2.19
[15]. In the series investigated in this work, the conductivity of Ti-rich samples is higher than that of Zr-rich samples. In general, dc-conductivity can be expressed as: ð5Þ
= Kn ⋅ω0 ⋅ expð−EM = kTÞ⋅expðΔSM = kÞ: where Kn · ωe is the pre-exponential factor (A), and EM and SM are the activation energy and entropy for Li migration. In this expression, ωe stands for the crossover ωbp frequency extrapolated to infinite temperature, ω0 is the attempt frequency and Kn is a factor proportional to the charge carriers concentration. In order to further analyze Li motions, pre-exponential Kn · ωe factors (A in expression (3)), deduced from the extrapolation of σdc · T values to infinite temperatures, are given in the Table 4. Kn · ωe factors increase from 6 × 102 (x = 0) to 5 × 103 Scm− 1 K (x = 1.8) when Zr increases. On the other hand, ωe parameters were deduced from the extrapolation of crossover ωbp values to infinite temperature. From both parameters, Kn values were finally deduced, suggesting that the amount of charge carriers increases slightly along the series when the amount of Zr increases (Table 4). At this point it is important to discuss the physical meaning of the term ωe of the expression (5). In general, ωe can be expressed as [26]: ωe = ω0 expðΔSM = kÞ
ð6Þ
where, ω0 is the attempt frequency and ωe can be considered as an effective frequency for Li motions [27]. In Ti and Zr-rich samples ωe values are appreciably different. Taken into account that ω0 is assumed to be almost the same in most materials, changes observed in ωe should be ascribed to changes in the migration entropy [27]. The analysis of the electrical behavior of samples showed that dcconductivity of the Ti end member (1.6 × 10− 4 S cm− 1) is higher than that of the Zr end member (4 × 10− 6 S cm− 1) at 300 K. This fact indicates that the increment of the unit cell volume in the LiTi2 − xZrx (PO4)3 series, produced by the substitution of Ti by Zr, does not improve ionic conductivity, suggesting that other parameters than unit cell volume affect the conductivity. Similar conclusions were deduced in the Li1 + xTi2 − xAlx(PO4)3 series, where substitution of Ti by smaller Al cations decreases unit cell dimensions but increased Li mobility [17]. The analysis of conductivity data showed important differences in activation energy and pre-exponential factors of samples. In Ti-rich samples activation energy is appreciably lower than in Zr-rich samples. The plot of pre-exponential factors against the samples composition, x, shows again two regimes: the first corresponding to samples with low mobility of lithium, where entropic terms are important, and the second corresponds to samples with higher mobility of lithium, where entropic terms are small (Fig. 7a). This analysis shows that changes in two parameters are better correlated with changes on Li occupation of M1 and M12 crystallographic sites, deduced by 7Li MAS-NMR spectroscopy, than with those produced on the volume cell, deduced by XRD technique. Finally, the dependence of the pre-exponential factor on activation energy is analyzed in Fig. 7b. In investigated samples, both parameters are strictly proportional indicating that activation energy and preexponential factors are strongly correlated. This behavior, often observed in semiconductors and ion conductors, is called “MeyerNeldel” or compensation rule [28]. According to this rule, motions with important activation energy improves considerably the entropic term, but motions with lower activation energy only improves slightly entropy associated with Li motion. In Zr-rich samples, the increment of pre-exponential terms does not compensate the lower contribution of activation energy terms. The stabilization of the rhombohedral phase in Zr doped samples eliminates problems derived from stresses produced at the triclinic-
K. Arbi et al. / Solid State Ionics 180 (2010) 1613–1619 Table 4 Activation energies Ea, pre-exponential factors A, cross-over frequencies extrapolated to infinite temperatures ωe, and compositional factors Kn deduced from conductivity plots (300–500 K) of LiTi2 − xZrx (PO4)3 samples. x 0 0.4 0.8 1.2 1.5 1.8
Ea (eV) 0.21 0.23 0.25 0.36 0.35 0.39
A (Scm− 1 K) 600 150 250 3500 3000 5000
ωe (rad/s) 10
9 × 10 4 × 1010 5.2 × 1010 6 × 1011 5 × 1011 6 × 1011
1619
Madrid (Project S-505/PPQ-0358) for financial support. K. Arbi thanks Spanish Ministry of Science and Innovation for the financial support under the contract “Juan de la Cierva”. Authors thank Prof. J. M. Rojo, M. A. Aranda and S. Bruque for helpful discussions.
Kn 6.7 × 10− 9 3.7 × 10− 9 4.8 × 10− 9 5.8 × 10− 9 6 × 10− 9 8.3 × 10− 9
rhombohedral transition, and enlarges the electrochemical window as a consequence of the lower reducibility of Zr cations. However, dcconductivity of Zr-rich samples is not improved with respect to that of Ti-rich samples. 5. Conclusions Samples of the LiTi2 − xZrx(PO4)3 series have been prepared and characterized by XRD, ND, NMR and impedance techniques. In this series, rhombohedral phases were obtained in the compositional range 0 ≤ x b 1.8, but triclinic phases accompany rhombohedral ones in samples with x ≥ 1.8. The substitution of Ti by Zr increases unit cell volume but decreases conductivity measured at room temperature from 1.6 × 10− 4 S cm− 1 to 4 × 10− 6 Scm− 1. Described results prove that other parameters than the unit cell volume affect conductivity. In analyzed samples, activation energy decreases from 0.33 to 0.21 eV in Ti-rich samples, but remains near 0.36 eV in Zr-rich samples in the temperature range 200–500 K. Along the analyzed LiTi2 − xZrx(PO4)3 series, activation energy measured between 300 and 500 K increases with the composition in a non-linear way from ∼ 0.23 to 0.36 eV. Finally, the amount of charge carriers and entropic terms are higher in Zr-rich samples; however, the increment of these two parameters does not compensate the decrement produced on activation energy terms. Acknowledgements Authors gratefully acknowledge the Spanish Agency CICYT (MAT2007-64486-C07 projects) and the Regional Government of
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