Energetics of Ion Transport in NASICON-Type Electrolytes - The

Article pubs.acs.org/JPCC

Energetics of Ion Transport in NASICON-Type Electrolytes Brian E. Francisco and Conrad R. Stoldt* Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, Colorado 80309, United States

Jean-Claude M’Peko Grupo Crescimento de Cristais e Materiais Cerâmicos, Instituto de Física de São Carlos, Universidade de São Paulo, 13566-590 São Carlos-SP, Brasil S Supporting Information *

ABSTRACT: Herein we report a study on the energetics of ion transport in NASICON-type solid electrolytes. A sol−gel procedure was used to synthesize NASICON-type lithium-ion conductors with nominal compositions Li1+XAlXGe2−X(PO4)3 where 0 ≤ X ≤ 0.6. Trends in the conductivity and activation energy, including both enthalpic and entropic contributions, were examined with electrochemical impedance spectroscopy. Physical interpretations of these results are drawn from structural characterizations performed by synchrotron powder X-ray diffraction and Raman spectroscopy. Considering X = 0 → 0.6, we conclude that initial drops in activation energy are driven by a growing Li+ population on M2 sites, while later increases in activation energy are driven by changes in average bottleneck size caused by the Al-for-Ge substitution. Values of the entropy of motion are rationalized physically by considering the changing configurational potential of the mobile Li+ population with changes in X. We conclude that entropic contributions to the free energy of activation amount to ≤22% of the enthalpic contributions at room temperature. These insights suggest that while entropic contributions are not insignificant, more attention should be paid to lowering the activation energy when designing a new NASICON-type conductor.

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phosphate is with a heterovalent doping scheme:5,6 LiGe2(PO4)3 → Li1+XAlXGe2−X(PO4)3. Since the radii of Ge4+ (0.53 Å) and Al3+ (0.535 Å) are nearly the same and there are many unfilled sites available for the additional lithium ions in the structure, the substitution is easily accomplished. This doping has been reported to increase the conductivity by up to 3 orders of magnitude. A common guideline of solid ionic conductor design is that the maximum conductivity should be achieved when exactly half of the available mobile ion sites are filled.7 By this logic, a maximum conductivity would be reached when the value of X in Li1+XAlXGe2−X(PO4)3 is unity; instead, the maximum conductivity is typically reported in the range 0.4 ≤ X ≤ 0.6.8,9 This indicates that there are more factors to consider in electrolyte design than simply the concentration of charge carriers. Structure, of course, plays an important role in defining these other factors. In NASICON crystals of general formula LiM2(PO4)3, columns of MO6 octahedra are linked by PO4 tetrahedra, as illustrated in Figure 1a.10 Lithium ions reside in two possible sites: The “M1” site, which is sixfoldcoordinated and located directly between two stacked MO6

INTRODUCTION With the demand for high-performing rechargeable lithium-ion batteries continually on the rise, much research effort over the past decade has been spent on the development of materials with enhanced electrochemical properties. As all-solid-state batteries show great promise to meet many performance needs, a targeted research effort to develop high-conducting solid-state separator materials has developed. Materials of the sodium superionic conductor (NASICON) family are promising candidates, as many have demonstrated high conductivity, electrochemical stability, and mechanical integrity.1−4 With these and other classes of ion conductor showing promise for use in next-generation energy storage technologies, it is helpful to have a clear picture of the various factors that contribute to the measured conductivities. In the case of ion-conducting solids such as the NASICONtype materials, the conductivity (σ) is governed by the relation σ = cμq, where c is the density of charge carriers, μ is the mobility of the charge carriers, and q is the charge carried by each carrier. Here we can see two obvious approaches to enhance the conductivity of such a material: increasing the concentration of charge carriers or increasing carrier mobility. Indeed, a common method of enhancing the conductivity of the established NASICON-type conductor lithium germanium © XXXX American Chemical Society

Received: April 5, 2015 Revised: June 16, 2015

A

DOI: 10.1021/acs.jpcc.5b03286 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

additional evidence for our interpretation of configurational entropy in NASICON-type solids.

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EXPERIMENTAL SECTION Synthesis of Powders. A Pechini-type sol−gel process using citric acid and ethylene glycol was used to synthesize all of the materials evaluated in this study. All of the solutions were prepared from as-received precursors in proper stoichiometric ratios. Moisture-sensitive precursors were stored in a dry argon glovebox prior to use. Aqueous solutions of precursors were prepared with the [citric acid + ethylene glycol:metal ion] ratio fixed at [4:1]. First, an appropriate amount of citric acid (Alfa, 99.5%+) was dissolved in deionized water heated to 60 °C, followed by the addition of stoichiometric amounts of LiNO3 (Alfa, 99%), Al(NO3)3·9H2O (Alfa, 98−102%), Ge(OC2H5)4 (Gelest, >95%), and NH4H2PO4 (Sigma, ≥99.99%) in that order. Ethylene glycol (Mallinckrodt Chemicals, 99%) was then added to promote polymerization of the complex upon drying, and the mixture was held at 80 °C under vigorous stirring for 6 h. Finally, the sol was transferred to an oven and dried at 120 °C overnight. The resulting dry gel was ground with a mortar and pestle and treated for 8 h at 500 °C to decompose the organics, which left a fine powder coated in carbon residue. This powder was again ground with a mortar and pestle and treated for an additional 8 h at 800−900 °C to burn off the carbon residue and complete the reaction to form fine particles of the NASICON-type materials. The final treatment temperature was chosen on the basis of previously reported phasepurity data for the LiGe2(PO4)3 system5,12,13 and on our own observations, which show that significant phase separation into GeO2 and Li9Al3(P2O7)3(PO4)2, likely driven by lithium loss, occurs above the chosen temperature. While the sol−gel synthesis procedure can yield small grain sizes, these grains often sinter into larger, irregular particles during the final heat treatment. To reduce and homogenize the particle size for subsequent analyses, each powder was wetmilled in a planetary ball miller for 30 min at 500 rpm. Agate milling jars and media were employed, and ethanol was used as the solvent. In the early stages of this work, we attempted to synthesize materials with X > 0.6. All of these attempts were unsuccessful, however, as above this X value a significant amount of Li9Al3(P2O7)3(PO4)2 (LAPP) is formed alongside the NASICON phase. While for many systems X values greater than 0.6 have been demonstrated, we conclude that the formation of LAPP is thermodynamically preferred in Al−Ge systems with high Al content. Powder X-ray Diffraction. For a detailed structural analysis, synchrotron powder XRD patterns were collected on beamline 11-BM at the Advanced Photon Source at Argonne National Laboratory. Patterns were acquired using a wavelength of λ = 0.4138 Å over the 2θ range 2−50° with a step size of 0.001° and a counting time of 1 s. Rietveld refinement and analysis of synchrotron XRD data was carried out using the General Structure Analysis System (GSAS) software with the EXPGUI user interface. Starting structural models were created from JCPDS file card no. 801922 (LiGe2(PO4)3) and results from ref 14.14 At the start of refinement, structural models assumed nominal Al substitution and full occupancy of the lithium M1 site, with the remaining lithium atoms placed on site M2. A basic refinement strategy was employed as follows. First, the lattice constants were allowed to vary until an acceptable fit to the unit cell was found.

Figure 1. (a) Representation of a typical NASICON unit cell. Blue octahedra are MO6 units, purple tetrahedra are PO4 units, green spheres are M1 sites, and yellow spheres are M2 sites. Pathways for Li+ motion between M1 and M2 sites are drawn. (b) Close-up view of the conduction bottleneck region, with oxygen atoms shown in red and Al/Ge shown in the center of the octahedra. (c) Representative section of the Li+ conduction pathways showing the relative configuration of M1 (green) and M2 (yellow) sites.

units, and/or the “M2” site, which lies in an eightfoldcoordinated location between two columns of MO6 units. During long-range motion, the ions hop between these two sites as they traverse the crystal. An illustration of a portion of this conduction pathway is presented in Figure 1c. Of the factors influencing this motion, we must consider the restrictive “bottleneck” points that form a window between mobile-ion sites (shown in Figure 1b), the relative energies of each ion site, and the total lithium population in these sites. In previous work, we found evidence that the configuration of lithium ions within the crystal plays a role in determining the overall conductivity of the material.11 At rest, in the absence of an electric field, a certain distribution of Li+ across M1 and M2 sites exists. Under the influence of a field that causes “activation” of the charge carrier population and long-range Li+ motion, a different distribution may exist. We now hypothesize that it is the difference between these two distributions, which represent two different configurations of the Li+ population, that gives rise to the measurable entropy of ion motion in these solids. To provide clarity about the many factors that influence the conductivity in NASICON-type conductors, with a specific focus on the effects of composition on ion transport, we designed a study around the Li1+XAlXGe2−X(PO4)3 system. In this system, the similar sizes of Al3+ and Ge4+ allow good mixing, where the lattice parameters of such solid solutions exist in a tight range and structural distortion should be minimized. By employing a sol−gel synthesis, we can exert careful control over the chemistry and crystal homogeneity. This process also produces smaller grains with a tighter size distribution, which is beneficial for the accuracy of subsequent analyses. Here we synthesized Li1+XAlXGe2−X(PO4)3 with 0 ≤ X ≤ 0.6. We used electrochemical impedance spectroscopy (EIS) to measure various thermodynamic parameters that define the conductivity, synchrotron powder X-ray diffraction (XRD) to accurately study the crystal structure of each material, and Raman spectroscopy to investigate the local bonding environment of the structure. We leverage the observed structural features to propose physical explanations for the trends in the thermodynamic parameters of conductivity and also to provide B


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response can be slowed into the experimental frequency window with cooling. An example spectrum is shown in Figure 2. As shown in the inset of Figure 2, each spectrum was fit with an equivalent circuit involving resistances (R) and constantphase elements (CPEs) using the software ZView.

Next, parameters affecting the line shape were allowed to vary until an acceptable fit to the peak profiles was obtained. Following background refinement, the atomic positions were allowed to vary freely, followed by the isotropic displacement parameters (Uiso). Once this model had converged, the Al/Ge ratio and, finally, the occupancy of the lithium M1 site were refined. Every few refinement cycles, the occupancy of the M2 site was manually updated on the basis of the Al/Ge ratio and M1 occupancy. Constraints were applied such that all of the oxygen Uiso values were equal, the Al and Ge Uiso values were equal, and the Al−Ge site occupancy was unity. As it is very difficult to analyze lithium content in a material with X-rays because of poor scattering, Uiso for Li was fixed at a reasonable value of 0.025 Å2. It should be noted that for each composition besides X = 0, the refined value of X is slightly different than the nominal value. In the Discussion we reference nominal X values, but all of the calculations and estimations were performed with X values determined from synchrotron X-ray data. Raman Spectroscopy. Raman spectra were recorded over the range 200−1300 cm−1 using a JASCO NRS-3100 system equipped with a 532 nm laser at a power level of 22 mW. The Raman shift was calibrated using a silicon standard, and the accuracy was estimated to be ±2.5 cm−1 Electrochemical Impedance Spectroscopy. Samples for EIS measurements and subsequent analysis were prepared by uniaxially pressing powders into cylindrical pellets in a stainless steel die at 330 MPa. Pellets approximately 6 mm in diameter and 1 mm in thickness resulted. Each pellet was sintered for 8 h at the chosen final calcination temperature on platinum foil in air. The final density was calculated from the pellet geometry and weight. From the theoretical densities estimated from refined X-ray diffraction patterns, the final relative density of each sample was ≥90%. We note an unexpected disintegration of sintered pellets of LiGe2(PO4)3 in deionized water, which prevented Archimedes density measurements in this medium. Analysis of dried material collected from measurement beakers suggested that no chemical or structural changes occurred as a result of disintegration. To enable electrical measurements, a Technics Hummer V sputter coater was used to deposit a 500 nm layer of pure gold onto each face of the pelletized samples. Pellets were dried for several hours in a vacuum oven and then sealed in a custom apparatus that allowed tests to be conducted in flowing dry argon, thereby excluding the effects of moisture. Impedance (Z* = Z′ − iZ″) spectra were recorded over the range 1 Hz to 1 MHz using a Solartron 1250B FRA + 1287 electrochemical interface. The amplitude of perturbation was fixed at 100 mV. To best resolve bulk impedance contributions, it was necessary to cool the samples, thereby bringing the natural high-frequency bulk spectral features into the experimental frequency window. Cooling to −70 °C was accomplished by submerging the airtight test apparatus in a bath of ethanol and dry ice.

Figure 2. Typical complex impedance data recorded for the composition X = 0.10 at −39.2 °C.

The CPE represents a nonideal capacitor with an impedance response of the form ZCPE = 1/Q(iω)n,15 where Q is a capacitance-like empirical parameter, ω is the frequency of perturbation, and 0 ≤ n ≤ 1. The parameter n is typically associated with the existence of either a distribution of capacitance values or a correlation between mobile charges in the dielectric structure.16 When n = 1, the CPE reduces to a simple capacitive element (C). In the compounds studied here, the bulk value of n varied as 0.87 ≤ n ≤ 0.99. According to the accepted criterion for the order of magnitude of capacitance in electroceramics,15,17,18 the features attributed to Li+ motion in the bulk (high-frequency semicircle, C ∼ 10−11 F), at the grain boundaries (intermediate-frequency semicircle, C ∼ 10−9 F), and at the blocking electrode interfaces (low-frequency spike, C ∼ 10−6 F) were identified for each material. In this study, we focused on an analysis of the bulk response only. Using the estimated resistance values from the spectral fitting of room-temperature data, we calculated the roomtemperature conductivity by applying the relationship σB = t/ (A·RB), where σB is the bulk conductivity, t is the sample thickness, A is the geometrical area of the sample faces, and RB is the bulk resistance. These results are shown in Figure 3a. There is a clear trend of room temperature conductivity with composition. As the X increases, conductivity increases and reaches a maximum in the range studied at X = 0.5. Typically, solid-state conductors are characterized by their conductivity and activation energy as shown in eq 1. σ σ = 0 ·e−Ea / kT (1) T where σ is the conductivity, σ0 is the exponential prefactor, Ea is the activation energy for ion conduction, k is the Boltzmann constant, and T is the absolute temperature. To thoughtfully

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RESULTS Ionic Conductivity. In order to characterize the conductivity and to determine the thermodynamic parameters governing ion migration in these solid-state conductors, we evaluated each material using EIS. Spectra were recorded for each material at temperatures from room temperature down to −65 °C. This was necessary to best resolve the bulk feature of each impedance spectrum, as this natural high-frequency C


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Coloumbic attraction and local elastic strain near the site of the dopant can lead to “sticking” of the charge carrier. This phenomenon is typically observed in oxygen conductors, where heterovalent doping introduces ions with large valence and size differences, causing the trapping of the oxygen charge carriers that they created. In NASICON materials, where the dopants are similar to the constituents they replace in terms of size and electronegativity, such as the situation in this study, this type of trapping is likely to be negligible, and ΔHt ≈ 0. Therefore, the concentration of charge carriers is not thermally activated, and we can say that ΔGc ≈ 0 in NASICON materials. Thermal activation of the ion hopping rate can be represented as follows:

⎛ −ΔGm ⎞ ⎟ ν = ν0 exp⎜ ⎝ kT ⎠

ν0 =

C0 = Nnc(1 − nc)

(3)

2mLi d 2

⎛ ΔS ⎞ ⎛ ΔHm ⎞ ⎟ ν = ν0 exp⎜ m ⎟ exp⎜ − ⎝ k ⎠ ⎝ kT ⎠

design such a conductor, however, it is important to understand the various factors that contribute to Ea and σ. The value of Ea represents the enthalpy for ion conduction, that is, an energy barrier that must be overcome for long-range motion of an ion through the crystal. This value is a convolution of several other enthalpies, which have matching entropy contributions that are contained in the exponential prefactor in eq 1.19,7 These free energies determine the temperature dependence of the conductivity, and they result from thermal activation of the charge carrier concentration and the ion hopping rate. Activation of the charge carrier concentration can be described as follows: (2)

ΔHm (5)

where ν is the hopping rate of a mobile ion, also called the “relaxation frequency” of Li+, ν0 is the fundamental attempt frequency for ion hopping derived from the harmonic potential well expression,20 ΔHm is the enthalpy of charge carrier migration, mLi is the mass of a lithium cation, and ΔGm is the free energy of ion migration. Rewriting eq 4 and expanding the free energy term ΔGm, we have

Figure 3. Variation in the conductivity and conduction energetics with X in the formula Li1+XAlXGe2−X(PO4)3: (a) room-temperature conductivity (±5%); (b) activation energy (Ea) and enthalpy of ion migration (ΔHm); (c) entropy of ion migration (ΔSm).

⎛ −ΔGc ⎞ ⎟ C = C0 exp⎜ ⎝ kT ⎠

(4)

(6)

There are several possible contributions to the enthalpy term in eq 6: ΔHm = ΔHh + ΔHr + ΔHgap

(7)

where ΔHh is the energy required to hop through the constrictive bottleneck point, ΔHr is the energy required to “relax” the surrounding lattice when an ion hops into a previously vacant site, and ΔHgap represents the potential energy difference between the M1 and M2 sites. The term ΔHh exists in all ion conductors to varying degrees, depending primarily on the configuration of the conduction pathways and the bottleneck points, and represents the energy required to push through these steric plus electrostatic restrictions. As the Li+ coordination environments at the M1 and M2 sites are different, ΔHr will also be different for each site. However, considering the comfortable fit of Li+ into the available lattice sites, the lattice strain induced by Li+ hopping into a previously empty site, and in turn this relaxation energy, is likely to be small. In simple conductors, ΔHgap is the energy difference between normal and interstitial lattice sites. In framework conductors like these NASICON materials, we consider ΔHgap to represent the difference in the depths of the energy wells at the M1 and M2 sites. The entropy term, ΔSm, to this point has not been well studied and is not well understood. This term will be discussed later within the context of the configuration of the lithium population. Building these derivations into a detailed relationship for conductivity, we see that

where C is the concentration of mobile ions participating in conduction, C0 is the concentration of potentially mobile ions, N is the concentration of energetically equivalent mobile-ion sites, nc is the fraction of mobile-ion sites that are occupied, and ΔGc is the free energy of the charge carrier concentration. The energy ΔGc is a convolution of energies related to charge carrier formation and trapping: ΔGc = ΔGf + ΔGt. In this context, charge carrier formation represents a process similar to defect pair generation, whereby charge carriers are created where they did not exist previously. In fast ion conductors such as those in the NASICON family, all of the charge carriers (mobile alkali ions) are already “formed”, and ΔGf = 0. Charge carrier trapping can result in doped structures, where the D


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The Journal of Physical Chemistry C ⎡ 2 2 ⎢ fxαz d Nnc(1 − nc)ν0 exp σ=⎢ kT ⎢⎣

( )⎤⎥ exp⎛⎜− ΔH ΔSm k

⎥ ⎥⎦

⎝

m⎞

⎟ kT ⎠ (8)

where f, x, and α are factors related to the hopping mechanism (often called the “Haven ratio”), the mobile site coordination number, and the dimensionality of the conduction pathways, respectively, z is the charge on a carrier, and d is the jump distance from one mobile ion site to the next. Since f, x, α, z, and N are composition-independent (depending only on the general framework structure), they do not change in this analysis. All of the other values in eq 8 vary with composition. On the basis of eq 1, measurement of the temperature dependence of the conductivity allows the determination of the parameter Ea. These results are presented in Figure 3b. With an understanding that ΔHm comes from the temperature dependence of the ion hopping rate (eq 6) and the ion hopping rate is the physical manifestation of the relaxation frequency, it is possible to probe this value analytically using the following equations: ν = ω0 =

1 RBC

(9)

and C = Qω0 n − 1 = (QRB1 − n)1/ n

(10)

where RB is the bulk resistance from the sample, C is the ideal capacitance of the sample, and Q and n have been previously defined. Using the fitted values of RB, Q, and n from the bulk impedance response, as shown in Figure 2, we calculated the ion hopping rate at each temperature. The temperature dependences of the conductivity and hopping rate are presented in Figure 4. The slopes of the data sets in Figure 4a,b provide Ea and ΔHm, respectively, while their intercepts at T = ∞ are related to σ0 and ΔSm, respectively. It is in this way that we obtained the results for Ea, ΔHm, and ΔSm shown in Figure 3b,c. We found that ΔHm systematically registers slightly smaller than Ea, but within the experimental error (±5%) these values are equivalent. It may be that there exists some small trapping enthalpy related to the Al substitution, but we cannot confirm that with the present analysis. Analysis of the hopping rate activation permits easy access to the parameter ΔSm, which has not been well studied and is not well understood. Later we will discuss the results in Figure 3c with regard to the distribution of Li+ within the structure. Crystal Structure. In order to perform an accurate analysis of the structure of each material, synchrotron powder X-ray diffraction was carried out at beamline 11-BM at the Advanced Photon Source. This instrument possesses the resolution and sensitivity necessary to resolve the structural details of each composition. Figure 5 shows each diffraction pattern in the 2θ range 2−15° (λ = 0.4138 Å). Worthy of note are the flat baselines and sharp peaks, which indicate good crystallinity and the lack of obvious impurity phases. A Rietveld refinement was carried out on each pattern with the ultimate goal of reaching an estimate of the occupancy of the M1 lithium site. During refinement, the X value of each material, as defined by the relative amounts of Al and Ge in the structure, was allowed to vary while full site occupancy was maintained. The lithium occupancy of site M1 was assumed to

Figure 4. Arrhenius plots of (a) the bulk conductivity and (b) the hopping rate for all of the NASICON compositions evaluated in this study.

be 1.0 at the start of refinements, with the remaining Li, as required by the composition, placed on site M2. These values were fixed until the background, profile, lattice, and structural models had converged, at which point the M1 occupancy was freely varied. Figure S1 in the Supporting Information provides a visual of a refined pattern, and a summary of results is presented in Table 1. The nominal X values listed in the table are those targeted during synthesis, and the refined X values are those determined from refinement of the Al/Ge ratio. It is not unexpected that these values are slightly different. In the Discussion, we will make reference to the nominal X values for simplicity, but all analyses were carried out in reference to the refined X values. It is worth noting that for the composition X = 0.25, the diffraction pattern was best fit with two NASICON phases with slightly different Al/Ge ratios and lattice constants. Figure S2 in the Supporting Information shows that this two-phase model fits the data well. At present, an explanation for this unexpected result cannot be given. In Table 1, weighted averages of values from the two phases are presented. Despite the apparent phase separation, the weighted-average values fall within the established trend in the data, and the overall analysis remains valid. Without immediate access to neutron diffraction, synchrotron powder XRD measurements are the next-best approach for the structural analysis of lithium-containing compounds. However, measurements of a parameter as delicate as the occupancy factor of a lithium site may contain inaccuracies of up to 10%.21 In order to add confidence to the values of the M1 E


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Figure 5. Synchrotron powder XRD patterns. The nominal composition is labeled on the baseline of each pattern, and the refined composition is given in parentheses. The inset shows a close-up view of the boxed region of the patterns, highlighting the slight lattice changes with composition. Bragg peak positions are noted along the bottom of the figure.

Table 1. Structural Data Derived from Rietveld Refinement of Powder X-Ray Diffraction Data fitting results

X nominal

refined

a (Å)

c (Å)

call volume (Å3)

density (g/cm3)

hopping distance (Å)

M1 occupancy

c/a ratio

wRp (%)

RF2 (%)

χ2

0 0.05 0.10 0.25 0.50 0.60

0 0.07 0.14 0.27 0.48 0.57

8.273989(7) 8.272968(6) 8.27895(1) 8.27236(3) 8.26590(2) 8.26510(3)

20.45422(2) 20.45439(2) 20.45914(4) 20.5269(1) 20.61554(9) 20.6374(1)

1212.672(2) 1213.560(2) 1214.420(4) 1216.502(7) 1219.849(7) 1220.90(1)

3.590 3.565 3.541 3.497 3.411 3.388

3.1828 3.1836 3.1844 3.1856 3.1878 3.1886

1.000 1.000 0.979 0.940 0.714 0.668

2.472 2.472 2.471 2.481 2.494 2.497

9.27 8.10 10.84 6.98 9.96 12.66

5.92 6.20 7.56 5.78 7.08 12.84

4.28 3.29 5.96 2.56 5.44 8.81

site occupancy obtained directly from Rietveld refinements, we can also infer this parameter from the crystal dimensions. Shown in Figure 6 is the variation of the M1 occupancy and c/a axis ratio with composition. Earlier work has demonstrated that as the Li+ occupancy shifts from M1 sites to M2 sites, the structure expands in the c direction and contracts in the a direction.22,23 This is driven by electrostatic Li−O attractions at each lattice site. As Li+ leaves M1 sites, the attractive force of the Li+ on surrounding oxygen atoms of MO6 groups vanishes, and the resulting repulsive force between these groups works to expand the c axis. 8 Simultaneously, new Li−O interactions are formed in M2 sites, and because the closest oxygen atoms lie in the ab plane, the M2 site occupancy acts to shrink the a axis. Therefore, the M1/M2 occupancy ratio can be correlated to the c/a ratio for a given material. As both the accuracy and precision of lattice constant estimations from synchrotron data analysis are very high, values of the c/a ratio can be considered accurate and the relationship with the M1 occupancy is meaningful. In Figure 6 we observe the expected trend of increasing c/a ratio as the M1 occupancy decreases. This indicates that as the X increases, the occupancy of the M1 site decreases.23,8 An important point to make here is that this measurement reflects site occupancies of

Figure 6. Relationship between the M1 site occupancy, c/a axis ratio, and crystal composition.

the material while in a state of “rest”, i.e., while there is no applied electric field. The importance of this point will become clear in the discussion of the results for ΔSm. F


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Figure 7. Raman spectra recorded over the range 200−1300 cm−1. Two groupings of vibrations are observed and are attributed to bending modes at lower energy and stretching modes at higher energy.

It can be seen in Figure 6 that the M1 occupancy and c/a ratio remain basically unchanged up to X = 0.10. This would indicate that the additional Li+ brought into the structure with increasing X is placed in M2 sites, while the M1 sites remain near full occupancy. As recent reports have suggested that any X > 0 has an effect on the M1 occupancy,24 this result may simply reflect the error in X-ray-based estimations of Li occupancy. Our data suggest that for X > 0.10, the addition of Li+ creates sufficient Li−Li repulsive force to reconfigure the population over M1 and M2 in such a way that vacancies are introduced at site M1. This trend is observed to continue up to X = 0.60. Local Structure and Bonding. To support the discussion of crystal structure and the energetics of ion migration, a study of the local structural order and bonding was carried out using Raman spectroscopy. In phosphate compounds like those in the NASICON family, the Raman response results primarily from excitation of vibrations of the PO4 structural group.25 In the NASICON structure, the PO4 group provides a link between MO6 octahedra, sharing oxygen atoms with the Al3+/ Ge4+ and Li+ ions in the structure. Factor group analysis of these compounds with space group R3̅c dictates 14 Ramanactive vibrational modes (six stretching modes and eight bending modes) for the PO4 structural unit.26 Figure 7 displays Raman spectra recorded over the range 200−1300 cm−1 for each material, with the groupings of bending and stretching modes labeled. In general, we observe that the peak broadness increases with X. There are two likely explanations for this observed broadening trend. The first source of broadening may come from Al3+ replacing Ge4+ in the structure. As X increases, there is a monotonic change in the Ge/Al ratio. This means a monotonic change in the number of Ge−O bonds versus the number of Al−O bonds. The polarization strength of an ion is roughly proportional to the ratio of the ion charge to the ionic radius,27 making Ge−O bonds slightly different than Al−O bonds. This change in average M−O bonding would be observed in the Raman data because, more specifically, the

bonding is Ge−O−P or Al−O−P, and Raman spectra of NASICONs primarily show P−O vibrations. Prior work11,28 has shown that broadening in Raman peaks can be related to the size of the bottleneck regions. By this logic, we conclude from the Raman data that the average bottleneck region becomes harder to pass as X increases, and the relationship is linear. The second source of broadening is related to the distribution of lithium ions in the crystal. At X = 0, all of the Li+ are in M1 sites, which are positioned directly between pairs of MO6 units stacked along the c axis.29 However, above this X value, it is necessary that some amount of Li+ is in M2 sites. When a Li+ ion occupies an M2 site, new Li−O bonds are created. These new bonds will necessarily affect the P−O bonding and will have a similar broadening effect on the peaks due to PO4 vibrations.28 It is likely that both of these effects are observed in Figure 7 with varying composition.

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DISCUSSION Enthalpic Contributions to Conductivity. In evaluating the conductivity in this NASICON family, let us first focus on the activation enthalpy. As shown in Figure 3b, for all compositions, Ea and ΔHm are the same within experimental error. This indicates that any ΔHc is negligible and that the only enthalpy contribution to the activation energy comes from the energy required for ion migration. It is clear that ΔHm varies with X, but it may also vary with temperature. Figure 8 shows a representation of the changes in potential energy of M1 and M2 sites with both composition (X) and temperature. We will first discuss the effects of varying X while assuming a constant low temperature. From eq 7, we posit that the observed enthalpy of migration may be parsed into contributions related to the bottleneck barrier (ΔHh), the M1−M2 site potential energy difference (ΔHgap), and the energy cost of lattice relaxation once a Li+ ion assumes residence in a previously empty site (ΔHr). The changes in ΔHr with X are likely subtle, and the contribution of this term to the total enthalpy is negligible. Therefore, for this G


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Figure 9. Enthalpic trends with X value. The curves representing ΔHh and ΔHgap were summed to yield a simulated ΔHm curve, which is plotted with the measured ΔHm values.

with temperature across a certain temperature range.30,31 At low temperatures, the long-range mobility of Li+ is limited, and these carriers become localized in the sites of lowest energy (M1 sites). When there is more Li+ than M1 sites, as is the case when X > 0, an electrostatic force balance determines the optimum distribution across the M1 and M2 sites, given that M1 is more stable than M2 in this temperature region. Once electrostatic equilibrium is attained, the carriers remain localized for long times. In this low-temperature region, ΔHgap is constant. As the temperature increases, so does the motion of Li+, and the population begins to spread across all available sites. This spreading of Li+ across M1 and M2 sites works to lower the energy difference between the two sites. Therefore, in some intermediate temperature region, ΔHgap becomes temperature-dependent and decreases toward zero. At high temperature, when the residence time of a Li+ ion at a particular site is low, ΔHgap again stabilizes at a near-zero value. For some compositions, a “superconducting” γ phase is reported in which ΔHgap drops to zero and Li+ motion becomes itinerant in the conduction pathways. A temperaturedependent ΔHgap is observed in conductivity plots as nonArrhenius behavior. It is noted that the regions of “high” and “low” temperature in reference to ΔHgap depend strongly on the composition of the framework of the crystal. For example, a temperaturedependent ΔH g a p was observed near 137 °C for Li1.2Cr0.2Ti1.8(PO4)3,31 while for Li1.2Al0.2Ti1.8(PO4)3 it was observed near −23 °C.30 Therefore, the exact composition determines the magnitude of ΔHgap and also determines where the “low” to “high” temperature transition (i.e, where ΔHgap begins to drop toward zero) occurs. As we observed no curvature in the Arrhenius plots of hopping rate in our measurement range, we conclude that for the Li1+XAlXGe2−X(PO4)3 family, ΔHgap is constant below room temperature. Entropy of Motion. Next, we turn our attention to the entropy of migration, ΔSm. The variation of ΔSm with X is shown in Figure 3c. In general, we observe an increase in ΔSm with X. At X = 0, ΔSm is negative, and at a point around X = 0.4, ΔSm changes sign and becomes positive. Until now there have not been any substantial theories about what this term might represent physically in crystalline conductors such as those in the NASICON family studied here. In a previous report,11 we proposed that ΔSm is related to

Figure 8. Potential energy diagrams of M1−M2 neighbors. The effects of increasing X value or temperature are illustrated from (1) to (3). In general, the structural changes that occur with increasing X or T act to equalize the potential energies of the M1 and M2 sites.

material system, we can maintain our focus on ΔHh and ΔHgap. As we have shown with Raman scattering, increases in X lead to a monotonic decrease in the average bottleneck size. This implies that ΔHh should increase linearly with X. The situation with ΔHgap is slightly more complicated. At X = 0, M1 is full and M2 is empty; the energy difference between these sites is maximized, which means that ΔHgap is maximized. With even the smallest increase in X, some occupancy of M2 sites is expected. This creates new Li−Li repulsions, which are soothed by redistribution of Li+ across M1 and M2 sites; this optimization results in Li+ being knocked off M1 sites and into neighboring M2 sites. This redistribution can be seen in Figure 6, where a decreasing M1 site occupancy is observed despite an increase in total Li+ concentration with increasing X. Reconfiguration of the Li+ population in this way works to lower the energy difference between M1 and M2 sites, effectively smoothing the potential energy pathway an ion faces along the conduction channel; this is reflected in a greatly decreased ΔHgap. This effect is more pronounced during the initial increment of X values above 0 and stabilizes at higher X values, where the Li+ distribution naturally becomes more even across M1 and M2 sites. A visualization of the individual trends of these enthalpic contributions is presented in Figure 9. It was assumed that ΔH h increases monotonically and ΔH gap decreases exponentially, and these predicted curves were combined and fit to the experimental data to yield ΔHm_simulated. The predicted values presented here estimate ΔHh to be 0.28 eV at X = 0.2, which correlates well with the value of 0.21 eV measured by NMR spectroscopy for Li1.2Al0.2Ti1.8(PO4)3,30 given that titanium-based NASICONs are known to have lessrestrictive bottlenecks than germanium-based analogues. Now we consider the temperature dependence of the enthalpic terms. It may be anticipated that thermal expansion of the unit cell affects the size of the bottleneck and therefore the value of ΔHh. In NASICON materials, however, the thermal expansivity is low,22,29 so ΔHh may vary minimally with temperature. On the other hand, ΔHgap has been shown to vary H


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The Journal of Physical Chemistry C the configuration of the Li+ population across the M1 and M2 sites, and here we present further data to support that idea. Shown in Figure 10 are the variations of the c/a ratio and M1

As a starting point, consider the composition X = 0. At rest, as determined by XRD analysis, M1 sites are completely occupied and M2 sites are completely vacant. When this population is activated and long-range conduction reaches equilibrium, it is necessary that at any point in time a portion of the Li+ population will be found at M2 sites. Since some portion of the Li+ population can now be found on M2 sites and these sites have a lower configurational potential than M1 sites, it is clear that this system has a higher configurational potential in the rest state than in the activated state, and ΔSm is negative. At the other end of the composition spectrum at X = 0.60, we see that ΔSm is positive. Here the refined XRD data show that Li−Li repulsions dictate a rest-state M1 occupancy of 67%. It is reasonable to deduce that when this Li+ population is activated and long-range hopping begins, this M1 occupancy must reach a steady-state (time-averaged) value greater than 67%. This makes sense if we consider that every M1 site serves as a junction to three conduction pathways and would likely spend a greater fraction of time occupied by a passing ion. Having a higher M1 occupancy means having a higher configurational potential, so for this material we can understand why ΔSm is positive. Somewhere around X = 0.4 we observe that ΔSm crosses zero and changes sign. We postulate that at this composition there is no appreciable difference between the activated- and rest-state site occupancies. This would suggest that during steady-state long-range hopping in Li1+XAlXGe2−X(PO4)3, M1 sites remain approximately 80% full. This information can be used to further rationalize the trends observed in Figure 10. For X = 0, 0.05, and 0.10, the M1 occupancy is ∼100% at rest, and the variation in ΔSm is minimal within experimental error. For X = 0.25 it is clear that the rest-state M1 occupancy is 80% < M1occ < 100%. Thus, when this composition is activated, additional Li+ ions are displaced from M1 sites to reach ∼80% occupancy, and the configurational potential of the system as a whole drops; the result is a smaller but still negative ΔSm. For X = 0.50, the reststate M1 occupancy is estimated to be 71%. When this Li+ population is activated, the M1 occupancy increases slightly to 80%, and the configurational potential of the system as a whole increases slightly; the result is a small but positive ΔSm. It may be reasonable to say that for X < 0.4, entropy hinders conduction, and for X > 0.4, entropy favors conduction. Clearly there is a link between this thermodynamic parameter and composition, as with ΔHm, and both play a role in the observed conductivity. The role played by entropy, however, is small compared with the role played by enthalpy. At room temperature, entropy terms represent ≤22% of the energy contribution of enthalpy terms. As we have measured ΔHm and ΔSm directly, we may combine them to obtain the free energy of ion migration, ΔGm. Figure 11 shows plots of the conductivity and ΔGm versus X at room temperature. We observe a minimum in the free energy at the X value where a maximum in the conductivity is measured, as expected using thermodynamic arguments for reaction spontaneity. It is often said that the conductivity should reach a maximum when exactly half of the available mobile ion sites are filled, which in this case occurs when X = 1. However, Figure 11 shows that structurally driven trends in the energetics of ion migration dominate the number of charge carriers and ultimately determine ionic conductivity.

Figure 10. (a) Variation of the c/a axis ratio and ΔSm with the X value. (b) Variation of the M1 occupancy and ΔSm with X value.

occupancy with X alongside the variation of ΔSm with X. As shown in Figure 10a, ΔSm essentially tracks with the c/a ratio, while in Figure 10b, ΔSm is seen to vary inversely with the M1 occupancy. This implies a correlation between the observed ΔSm and the occupancy of the M1 sites. Looking closely at the structure of a NASICON conductor (shown in Figure 1), we see that each M1 site is surrounded by six M2 sites and that each M2 site is surrounded by only two M1 sites. If a Li+ ion were on an M1 site and made a single hop, there would be six nearest-neighbor sites to which it could hop. For a Li+ ion sitting on an M2 site and looking to make a single hop, there are only two nearest-neighbor options. In this way, a Li+ ion on an M1 site has a higher configurational potential than a Li+ ion on the M2 site. Consider now an entire population of Li+ spread across these sites, where the overall configurational potential is derived from a sort of weighted average of the M1 and M2 distributions. Within our framework of activated ion motion, we have considered ΔG with respect to the “activated” state and the “rest” state. Experimentally, the activated state is one in which energy is supplied by a time-varying electric field such that all of the potential barriers ΔH can be overcome and the lithium population is set in motion, reaching steady-state long-range hopping. The rest state is one in which no external perturbations are applied, and a different equilibrium condition is met. Thus, we define the entropy of migration as follows: ΔSm = [activated equilibrium] − [rest equilibrium]. In terms of configurational potential, the main focus of each equilibrium state is how the Li+ population is configured across the M1 and M2 sites. I


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1231048). Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract DE-AC02-06CH11357. The authors also acknowledge the assistance of Sandia National Laboratories for access to EIS facilities. J.-C.M. is grateful for support from FAPESP and CAPES, two Brazilian funding agencies.

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(1) Noguchi, Y.; Kobayashi, E.; Plashnitsa, L. S.; Okada, S.; Yamaki, J.-I. Fabrication and Performances of All Solid-State Symmetric Sodium Battery Based on NASICON-Related Compounds. Electrochim. Acta 2013, 101, 59−65. (2) Sun, Y. Lithium Ion Conducting Membranes for Lithium−Air Batteries. Nano Energy 2013, 2, 801−816. (3) Delaizir, G.; Viallet, V.; Aboulaich, A.; Bouchet, R.; Tortet, L.; Seznec, V.; Morcrette, M.; Tarascon, J.-M.; Rozier, P.; Dollé, M. The Stone Age Revisited: Building a Monolithic Inorganic Lithium-Ion Battery. Adv. Funct. Mater. 2012, 22, 2140−2147. (4) Zhang, M.; Takahashi, K.; Uechi, I.; Takeda, Y.; Yamamoto, O.; Im, D.; Lee, D.-J.; Chi, B.; Pu, J.; Li, J.; et al. Water-Stable Lithium Anode with Li1.4Al0.4Ge1.6(PO4)3−TiO2 Sheet Prepared by Tape Casting Method for Lithium−Air Batteries. J. Power Sources 2013, 235, 117−121. (5) Yamamoto, H.; Tabuchi, M.; Takeuchi, T.; Kageyama, H.; Nakamura, O. Ionic Conductivity Enhancement in LiGe2(PO4)3 Solid Electrolyte. J. Power Sources 1997, 68, 397−401. (6) Li, S. Phase Relationships and Electrical Conductivity of Li1+XGe2−XAlXP3O12 and Li1+XGe2−XCrXP3O12 Systems. Solid State Ionics 1988, 28−30, 1265−1270. (7) Bruce, P. G. Solid State Electrochemistry, 1st ed.; Cambridge University Press: New York, 1997. (8) Cretin, M.; Fabry, P. Comparative Study of Lithium Ion Conductors in the System Li1+XAlXAIV2−X(PO4)3 with AIV = Ti or Ge and 0 ≤ X ≤ 0.7 for Use as Li+ Sensitive Membranes. J. Eur. Ceram. Soc. 1999, 19, 2931−2940. (9) Zhang, M.; Takahashi, K.; Imanishi, N.; Takeda, Y.; Yamamoto, O.; Chi, B.; Pu, J.; Li, J. Preparation and Electrochemical Properties of Li1+XAlXGe2−X(PO4)3 Synthesized by a Sol−Gel Method. J. Electrochem. Soc. 2012, 159, A1114−A1119. (10) Hong, H.-P. Crystal Structures and Crystal Chemistry in the System Na1+XZr2SiXP3−XO12. Mater. Res. Bull. 1976, 11, 173−182. (11) Francisco, B. E.; Stoldt, C. R.; M’Peko, J.-C. Lithium-Ion Trapping from Local Structural Distortions in Sodium Super Ionic Conductor (NASICON) Electrolytes. Chem. Mater. 2014, 26, 4741− 4749. (12) Feng, J.; Xia, H.; Lai, M. O.; Lu, L. NASICON-Structured LiGe2(PO4)3 with Improved Cyclability for High-Performance Lithium Batteries. J. Phys. Chem. C 2009, 113, 20514−20520. (13) Maldonado-Manso, P.; Losilla, E. R.; Martínez-Lara, M.; Aranda, M. A. G.; Bruque, S.; Mouahid, F. E.; Zahir, M. High Lithium Ionic Conductivity in the Li1+XAlXGeYTi2−X−Y(PO4)3 NASICON Series. Chem. Mater. 2003, 15, 1879−1885. (14) Losilla, E. R.; Aranda, M. A. G.; Bruque, S.; París, M. A.; Sanz, J.; West, A. R. Understanding Na Mobility in NASICON Materials: A Rietveld, 23Na and 31P MAS NMR, and Impedance Study. Chem. Mater. 1998, 10, 665−673. (15) Barsoukov, E.; Macdonald, J. R. Impedance Spectroscopy, 2nd ed.; John Wiley & Sons: Hoboken, NJ, 2005. (16) M’Peko, J.-C.; Francis, J.; Raj, R. Impedance Spectroscopy and Dielectric Properties of Flash versus Conventionally Sintered YttriaDoped Zirconia Electroceramics Viewed at the Microstructural Level. J. Am. Ceram. Soc. 2013, 96, 3760−3767. (17) Delgado, A.; García-Sánchez, M. F.; M’Peko, J.-C.; RuizSalvador, A. R.; Rodríguez-Gattorno, G.; Echevarría, Y.; FernándezGutierrez, F. An Elementary Picture of Dielectric Spectroscopy in Solids: Physical Basis. J. Chem. Educ. 2003, 80, 1062−1073.

Figure 11. Conductivity and free energy of ion migration as measured at room temperature.

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CONCLUSIONS In this work, we synthesized NASICON-type solid solutions having nominal compositions Li1+XAlXGe2−X(PO4)3 with 0 ≤ X ≤ 0.6 and evaluated the various energetic factors contributing to the observed values of the room-temperature conductivity. While simple conduction theory predicts a maximum conductivity when the Li+ sites are exactly half-filled, i.e., at X = 1, we observed a maximum near X = 0.5. With the help of a thorough structural analysis we conclude that initial drops in activation energy are driven by a growing Li+ population on M2 sites, while later increases in activation energy are driven by changes in the average bottleneck size caused by the Al-for-Ge substitution. Values of the entropy of migration are rationalized by considering the changing configurational potential of the mobile Li+ population with changes in X. In general, the composition determines the amount of Li+ in the structure, a complex electrostatic force balance determines the M1 and M2 site occupancies, and the site occupancies determine whether conduction is entropically favored or entropically hindered. We observed that entropy contributions begin to enhance the conductivity only above X = 0.4, and they are, for the most part, overridden by increases in enthalpy. Over all compositions, entropic contributions to the free energy of activation amount to ≤22% of the enthalpy contributions at room temperature. These insights suggest that while entropic contributions are not insignificant, more attention should be paid to lowering the activation energy when designing a new NASICON-type conductor.

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ASSOCIATED CONTENT

S Supporting Information *

Examples of Rietveld refinements, including the refinement of the composition found to contain two phases (X = 0.25). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b03286.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support for this research was provided under the NSF Sustainable Energy Pathways Program (Project DMRJ


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Energetics of Ion Transport in NASICON-Type Electrolytes - The

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