Lithium, sodium and potassium transport in fast ion conducting glasses: trends and models

Materials Science and Engineering, B I 3 (1992) 157-164

157

Lithium, sodium and potassium transport in fast ion conducting glasses: trends and models F. A. Fusco* and H. L. Tuller Crystal Physics and Optical Electronics Laboratory, Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (USA) D. P. Button Dupont Experimental Station, Wilmington, DE 19898(USA) (Received August 14, 1991 )

Abstract The ionic conductivities, glass transition temperatures (Tg) and densities were examined for an extensive number of glasses in the system R20-RCI-B203 (R=-Li, Na, K). In general, increases in RCI resulted in systematic and sharp increases in alkali ion conductivity and decreases in Tg and density. Linear decreases in the activation energy for conduction and Tg on chlorine addition are traced to major changes in the network structure. Substitution of chlorine for oxygen serves to dilate the structure, thereby lowering the strain energy associated with migration of ions between near equivalent sites. The conductivity for a given glass composition decreases as the cation radius increases in the order lithium, sodium and potassium. Although there are large differences in ion size, the 0.81 eV activation energy for potassium ion motio n in the diborate glass is only marginally different from that of sodium (0.77 eV) and lithium (0.74 eV). The larger alkali ions induce a dilation in the glass structure which compensates, at least in part, for the larger bottleneck size required for the larger ions in their motion through the structure. Chlorine additions produce more complex effects in the potassium glasses and are less efficient in enhancing the ionic conductivity. These observations are discussed with respect to the competing roles of excess volume and stiffness of the structure in controlling transport in these glasses.

I. Introduction

Fast ion conducting glasses possess properties which make them attractive materials for technological applications, e.g. as solid electrolytes in high energy density, high performance batteries. They are good ionic conductors, isotropic, lack grain boundaries (which can serve as sites for rapid chemical attack) and are easily fabricated into complex and thin-walled shapes. Perhaps most importantly, they display wide compositional flexibility which can be exploited to optimize properties of interest. One of the challenges currently facing investigators in this field is understanding the mechanisms which control ionic transport in glasses. Theories such as the weak electrolyte theory [1-3] propose that the process of carrier generation, via dissociation of complexes,

*Present address: 211 N. Robertson, 2 Leadership Sq., Laney, Dougherty, Hessin & Beavers, Oklahoma City, OK 73102, USA.

dominates the transport process, while carrier mobility remains essentially independent of composition. In this work, we regard nearly all alkali cations as intrinsically mobile and attempt to demonstrate the strong correlations which exist between glass structure and composition and the observed transport properties of these materials. We examine the role of halide additions and of varying alkali carrier cation size in modifying both transport and structure. Ionic conductivity results are interpreted in terms of the Anderson and Stuart formalism [4] which we use to assess the relative importance of the strain and electrostatic energy contributions to the migration energy. In this work, we integrate earlier results [5] with more recent unpublished data. 2. Experimental procedure

Glass samples characterized in this study were prepared by conventional glass melting and quenching techniques. Starting materials were anhydrous reagent Elsevier Sequoia

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Li, Na and K transport in.fast ion conducting glasses

grade alkali carbonates, anhydrous B203 and alkali halide salts. Charges of these well-mixed powders were melted in air in an electric furnace in covered platinum crucibles. Melt times of approximately 20 or 25 min at temperatures between 950 and 1050 °C were adequate to produce completely fused homogeneous melts. Short melt times and covered crucibles were used to minimize alkali and halide losses due to volatilization. Nevertheless, some shifts in composition occasionally occurred which were detected by wet chemical analyses (performed by Owens-Illinois Analytical Services, Toledo, OH). The accuracies (all relative) claimed are as follows: Li, _+0.2%-0.5°/,,; Na, less than +0.5%; K, _+0.2%-0.5%; B, _+0.2%-0.5%; CI, _+ 1%-2%; I, + 0.2%-0.5%. The physical and transport properties of the potassium glasses doped with iodine or high levels of chlorine (greater than 15% (KCI)2/K2Z; Z---CI2, O) display unexpected behavior. While the possibility of phase separation in these materials cannot be unequivocally ruled out, we found the melts to be homogeneous and the glasses to be clear to visual inspection with no evidence of multiple 7g values. Glass systems studied included: alkali dichloroborate glasses in the system (0.33 - y)RzO-y(RCI)z-0.67B203 where R -= Li, Na or K, a lithium metachloroborate glass (0.50-y)R20-y(RC1)2-0.50B203 and a potassium diiodoborate glass ( 0 . 3 3 - y ) K 2 0 - y ( K I ) 2 0.67B203 where y ranged from 0.00 to 0.017 because of the low solubility limit of KI in these glasses. Also studied were series of potassium and lithium chloroborate glasses in which the ratio R20/B203, as parametrized by the ratio of oxygen to boron species or so-called O/B ratio, was held fixed at 1.7. Thus the effects of alkali modifier and halide anion content on the network structure are isolated [6, 7]. Glasses were quenched in air between preheated steel plates (150 °C) for the lithium and sodium specimens and between room temperature graphite blocks for the potassium glasses (potassium glasses quenched between steel plates devitrified during the quenching process). Lithium and sodium conductivity samples were annealed at 50 °C below Tg for 24 h and then furnace cooled. Potassium glasses were annealed for 1.5 h at ~ - 75 °C in air and then allowed to furnace cool. Since alkali borate glasses are hygroscopic, glass samples were handled with tweezers or gloves and stored in dry environments. Ionic conductivity measurements were made on regular parallelepipeds with shape factors between 10 and 20 cm J with sputtered platinum electrodes arranged in a two or four probe configuration. A.c. multifrequency electrical measurements were made using a ratio arm impedance bridge (Gen Rad 1616) and a laboratory built cross-correlator [7] (frequency

range, 10 Hz to 100 kHz) for the lithium and sodium glasses and a computer controlled impedance spectrometer, including a Solartron frequency response analyzer (frequency range, 10-5 Hz to 65 kHz), for the higher impedance potassium glasses. The conductivity was measured over the temperature range 100-350 °C in an electrically shielded chamber flushed with dry nitrogen. All the lithium and potassium glasses and the sodium chloroborates displayed very nearly ideal responses readily interpretable using complex impedance analysis for obtaining bulk conductivity values. However, the pure sodium diborate exhibited a convoluted frequency response and was analyzed using complex modulus formalism. Glass density was measured according to the American Society for Testing and Materials (ASTM) standard test method [8]. Measurements were made at room temperature using toluene as the immersion fluid. Density values were accurate to + 0.01 g cm - ~. Glass transition temperatures Tg for the lithium and sodium glasses were determined using a Perkin-Elmer DSC 2 differential scanning calorimeter operating at a scan rate of 10 K min J between 500 and 800 K. Two to five samples were run for each glass composition analyzed, with a reproducibility of between 2 and 4 K. 7~ values for the potassium glasses were measured with a Perkin-Elmer DSC 4 instrument. Identical scanning conditions were used as described above. 7~ values for the potassium glasses are the average of three sample trials and an excellent agreement of less than _+3 K was obtained between samples. The Tg values reported here are defined as the temperature at which the heat capacity is one-half of its maximum value.

3. Results

Conductivity values for three alkali diborate glasses are compared in the Arrhenius plot in Fig. 1. Since these three glasses have an analogous diborate chemical composition (R20-2BEO3), they each have the same alkali modifier (R:O) to network former (B203) ratio and hence identical alkali cation carrier concentrations. Only the nature of the modifier cation, which also serves as the charge carrier, varies. Despite the fact that the K ÷ cation is considerably larger than the Li + or Na + cations (rK+= 1.38 A, rNa+= 1.02 A and ru+=0.74 A), the potassium diborate glass is not dramatically less conductive than its counterparts containing smaller, presumably more mobile, carrier species. Its conductivity is within half an order of magnitude of that of the sodium diborate glass and its activation energy is greater by only 0.04 eV. Previous workers have demonstrated that halide additions result in conductivity enhancement in lithium

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glasses, the magnitude of which increases with increasing halide anion radius in the order I > Br > C1 > F [9]. In contrast with these general observations, recent results indicate that fluorine doping decreases lithium conduction in these glasses [10]. As started earlier, the compositions of the glasses in our study are controlled such that the alkali metal concentration is fixed even as the halide replaces the oxide. The effects of replacing alkali oxide with chloride on the ionic conduction parameters are illustrated in Fig. 2 for the lithium, sodium and potassium diborate glass systems. Chloride substitutions result in dramatic and near-linear increases in logarithmic conductivity for the lithium and sodium glasses outside of a small anomaly at low sodium content. In contrast, the potassium dichloroborate conductivity is independent of chloride doping level and hovers around the conductivity observed for the pure potassium diborate glass (Fig. 2(a)). The increased conductivity with chloride substitution observed for the lithium and sodium glasses is associated with distinct, monotonic decreases in Ea, the activation energy for conduction. The E a value for the potassium glasses instead displays a weak dependence on chloride content except for fluctuations around the 10% and 15 % (KCI)2/K2Z compositions. For the most part, Ea remains close to the 0.81 eV value measured for the pure potassium diborate glass. Linear leastsquares fits of the chloride dependence of E a result in slopes of - 0.0048, - 0.0042 and - 0.0004 for the lithium, sodium and potassium glasses respectively, as shown in Fig. 2(b). The overall magnitude of the effect of chlorine on E~ diminishes as the size of the alkali modifier cation is increased. The excess volume provides an estimate of the "interstitial volume" available through which a carrier cation can migrate. The quantity defined here as Vr~E represents the difference between the total glass volume per mole of boron and the volume of the

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network anionic species (02-, or C1- and I-). Referring to Fig. 3, we observe that the boron excess volumes in the halide-free alkali diborates vary as V~E (Na)>V~E (K)>Vr~ E (Li). Chloride substitution results in monotonic and near-linear increases in V~E for all the lithium and sodium glasses, as well as for the lightly doped KCIB and KIB glasses (less than 10% (KCI)2/K2Z). Unlike its sodium and lithium diborate counterparts, V~E for the potassium diborate series exhibits a second behavioral regime beginning at the 15% (KCI)2/K2Z level. When we examine the correlation between E a and excess volume shown in Fig. 4, we find that, in the lithium and sodium chloroborate glasses, without exception, decreasing Ea is associated with increasing molar volume. It is interesting to note that the larger cations require larger excess volumes to achieve an equivalent activation energy, as might be expected if E a is largely a consequence of the increased

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The glass transition temperature Tg for halide-free diborates varies at Tg (Li)> Tg (Na)> Tg (K) (Fig. 5). Multiple regimes of Tg behavior can be distinguished in these data. Two are observed for the lithium and sodium chloroborates and three for the potassium chloroborates. The transition from the first to the second regime occurs at 10% (RCI)z/R2Z for all three glass systems. For the lithium and sodium glasses, the second regime is a region of steeper decline in Tg, whereas for the potassium glasses it represents a region of steep rise in Tg followed by a plateau between 20% and 30% (RCI)2/R2Z. As done previously for the lithium chloroborate glasses [6], a series of potassium chloroborate glasses, in which the O/B ratio was held constant, was studied in order to examine the effects of chloride additions while keeping the framework oxide structural groups fixed [6]. Chloride substitutions to these potassium glasses with fixed O/B ratios have a much more distinct effect on ionic conductivity than those presented in Fig. 2. In Fig. 6(a), we see a strong initial increase in conductivity with chloride substitution, followed by a decrease at high chloride content. These changes in conductivity are mirrored in the chloride dependence of the activation energy which exhibits a minimum at 10% (KCI)z/K2 Z in Fig. 6(b). If we examine the chloride dependence of molar volume and Tg for these glasses (see Figs, 7(a) and 7(b), we find that the initial increases in molar volume and decreases in Tg tend to saturate at high chloride levels. The change in the transport parameters appears to be coupled with these structural changes. Iodine additions to the potassium diborate glass surprisingly result in a drop in conductivity (Fig. 8). An increase in Ea from 0.81 to 0.87 eV is responsible for this reduction in conductivity. Tg is also found to increase from 433 to 445 °C.

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The conductivity results, combined with those obtained for the excess volume per mole of boron and Tg in the alkali diborate glasses support a model where mobility, rather than carrier generation, plays the dominant role in determining ionic transport. On the basis of purely electrostatic considerations, we would expect oK> O'Na > OLi since this would reflect the relative bond strength between alkali cations and the non-bridging oxygens and the BO4 units of the glass network. Instead, we find OLi> ONa> OK which follows an inverse trend in ionic radii among these cations. Since noble gases such as helium, neon and argon exhibit measurable diffusivities in glasses, they may serve as probes of the interstitial volume of glasses. Furthermore, since they are uncharged, they may be used to probe the "doorways" or "bottlenecks" between mobile ion sites and thereby isolate the strain contribution to the migration energy, E m. Button and coworkers [11, 12] have combined the results of diffusion [13] and conductivity studies to estimate the size of the strain energy contribution to E a

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in sodium borate glasses. From 0 to 10 mol.% Na20 , the helium diffusion energy Eu(He ) increases from 0.22 to 0.39 eV, while VM decreases by over 10% (38 to 34 cm 3 mol-l). Beyond 10 mol.%, data on Eo(He ) are unavailable (due to inadequate sensitivity of instrumentation); yet VM continues to decrease markedly up to the diborate composition (by another 17%). Thus a

F. A. Fusco et aL / Li, Na and K transport in fast ion conducting glasses

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conservative extrapolation of Ed(He), and hence of the strain energy component Es(Na) of the migration energy (rNa = 1.02 A and rile = 1.00 A) for the diborate composition, should yield at least 0.5 eV. This estimate for E~(Na) at the diborate composition indicates that the primary energy component of E m (0.77 eV) is a strain factor. This suggests that compositional changes in the diborate glasses influence mobility rather than effective carrier concentration. We now consider more explicitly those parameters which influence the strain energy. In the theoretical model for ionic conduction developed by Anderson and Stuart [4] and modified by McElfresh and Howitt [14] the total measured activation energy represents the sum of two terms: a coulombic term E b and a strain energy term E~. These terms take the following form

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where r is the carrier cation radius, rj is the radius of a non-bridging oxygen, e~ is the high frequency dielectric constant, 2 is the jump distance between equivalent sites near non-bridging oxygens and r D is the radius of a network doorway or interstice opening. We focus our attention on the E S term which also depends on the shear modulus G, a measure of network coherency or stiffness. In this study, we have monitored Tg to indicate glass network rigidity and the excess volume to obtain information about the glass interstitial structure such as r D. As expected, G and Tg follow the same trend with composition in the alkali borate binary glass systems, which demonstrates that Tg data may be reliably used to assess the role played by glass network rigidity in the E S term. The conductivities of the sodium, potassium and lithium borate glasses remain within an order of magnitude of each other. Increasing excess volume and network compliance (as reflected in lower values of Tg and thus G) should partly compensate for the larger size of the sodium and potassium cations with respect to strain energy barriers to transport. Data for G obtained by Shaw [15] indicate that shear moduli for the lithium, sodium and potassium diborate glasses decrease in the order 2.84 x 10 ~1 dynes cm -2, 2.32 x 1011 dynes cm -2 and 1.44 x 1011 dynes cm-2 respectively. From the strain energy standpoint, both increasing excess volume and decreasing Tg (and correspondingly decreasing G) should result in decreased migration

energies and increased ionic conductivities. Of the two factors (see eqn. (3)), variations in excess volume are expected to play the dominant role in determining migration energies. We examine these expectations below. For both the lithium and sodium dichloroborates, the decrease in E, with chloride content is accompanied by increases in excess volume and decreases in Tg (see Figs. 2, 3 and 5). Here, both the volume and Tg variations work towards a lowering of E,. For the potassium dichloroborate, in the range 10%-20% (KCI)2/K2Z, the excess volume and 7"8 values play competing roles, resulting in a rise in E,, followed by a decrease once Tg saturates. Similar observations can be made when examining our data for lithium metachloroborate (LCB 50) glasses (see Fig. 9) where two regimes of E a behavior are observed. The decline in E a at lower chlorine doping levels is more gentle than that observed at higher chlorine contents because the effect of increasing free volume is moderated by competition with that of increasing network coherency. In the iodoborate glasses, both E. and Tg rise with iodide additions, confirming the important influence of the network coherency on migration.

Lithium ChloroBorate Property-Composition Relationships Schematic

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Li, Na and K transport in fast ion conducting glasses

The data presented in Fig. 4 reveal several interesting insights into the correlation between glass structure and ionic transport. The amount of "excess" or "interstitial" volume available to a migrating cation does not exclusively determine the migration energy barrier. If we draw an "iso- Vr~E line" at 9.5 cm 3 (mol B)- t we find two different E, values associated with this V~E point: for the 5% (KCI)2/K2Z and 5% (KI)2/K2Z potassium borate glasses. This suggests that other factors influence the transport process. As discussed above, in addition to the number and size of windows, their connectivity and the network rigidity (i.e. its resistance to dilation by carriers) control the transport process. Although the nuclear magnetic resonance (NMR) results of Bray et aL [16] indicate that the number of boron atoms in tetrahedral coordination (N4) displays a nearly identical dependence on the total alkali modifier content, regardless of the identity of the cation, the dependence of excess volume on the alkali cation identity in the diborate glasses suggests that the identity of the modifier cation does influence the glass structure. A study of the densities of potassium borate glasses by Lim et al. [17] corroborates our findings and concludes that the structural units present in the potassium borate glasses are larger than those in corresponding lithium and sodium glasses. Thus it is not surprising that chlorine additions will have a different impact on glass structure depending on the identity of the alkali modifier cation. Krogh-Moe's well-known structural model for glasses proposes that a glass is composed of a random arrangement of the same short-range structural units found in crystals of similar chemical composition. Krogh-Moe's structural determinations for the lithium, sodium and potassium diborate crystals [18-22] reveal that the boron-anion framework in these crystals is composed of different structural groupings. The lithium diborate is composed of diborate groups exclusively, the sodium diborate of triborate and dipentaborate groups, and the potassium diborate of planar triangles, diborate groups and triborate groups. The results of Raman spectroscopy studies of alkali borate glasses corroborate this hypothesis. Raman spectra obtained by Konijnendijk and Stevels [23] and Lor6sch et al. [24] suggest that slight intermediaterange structural dissimilarities may exist among borate glasses having the same total alkali modifier content, but different modifier cation identities. Recent wellresolved Raman data support the existence of intermediate-range structural ordering which depends on the modifier cation identity [25]. In the light of Tg and molar volume evidence available for the alkali borate glasses, the existence of such structural differences is expected. An assessment of the relative importance of strain

163

and electrostatic barriers to cation migration is fundamental to the development of a complete understanding of ionic conduction in glasses. Papers by Wang et al. [10] and Miiller et aL [26] represent two recent efforts to address this important issue. Both conclude that the strain energy contribution to the total cation migration energy is negligible or non-existent, a view clearly contradicted by the evidence advanced in this paper. According to calculations made by Wang et al. [10] for a series of lithium haloborate glasses, E~ represents only 15%-20% of the total measured activation energy. However, they obtained the doorway radius rD (see eqn. (3)) from the fairly crude approximation (rD - r,,) _ 1 ( V - Vo) r,, 3 V,,

(4)

where r0 is the known doorway radius of pure B203, V0 is the molar volume of B203 and V is the molar volume of the glass composition of interest. We recall that it is not the molar volume, but the "excess" or "interstitial volume", which is relevant to the carrier migration process. Furthermore, they calculated their E~ values using the Anderson and Stuart [4] formalism which provides a less physically accurate description of the transport event than that advanced by McElfresh and Howitt [14] (see eqn. (3)). Miiller et al. [26] have attempted to obtain a more accurate measure of this "interstitial volume" by combining the results of density and optical refractivity data. They calculate the glass anion molar volume from density and anion formula weights and consider this to be the overall volume of a glass containing such a mole fraction of anionic species. The gauge the actual volume occupied by all particles by measuring the molar refractivity. They claim that the difference between these two quantities represents a first approximation of the free space within the structure which we have described as the "interstitial volume". Based on these studies and subsequent calculations, they reject a strain energy interpretation of the ionic transport process in glasses. However, we should note that they overlook the fact that the magnitude of this "interstitial volume" and its connectivity influence cation transport in glasses. They explain the conductivity behavior observed in lithium chloroborate glasses in terms of variations in bond strength, with the bond strength of available lithium sites varying with their neighbors in the order CI < NBO < BO4, where NBO are non-bridging oxygens. However, their analysis is restricted exclusively to lithium glasses and this "bond strength" hypothesis is inadequate to explain the trends in ionic transport with alkali cation size reported in this paper. Careful examination of this work reveals that it does

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Li, Na and K transport in fast ion conducting glasses

not p r o v i d e a convincing a r g u m e n t against a strain energy interpretation of the ionic transport process.

5. Conclusions O n the basis of the significant effect of alkali ion size on glass structure and transport properties, we conclude that migration rather than carrier c o n c e n t r a t i o n dominates the transport process. T h e role of halides in modifying o differs d e p e n d i n g on the nature of the binary alkali b o r a t e glass n e t w o r k as d e t e r m i n e d by the identity of the alkali modifier cation. Increases in excess v o l u m e are s h o w n to clearly contribute to o enhancement. In already highly dilated glasses, n e t w o r k stiffness and c o h e r e n c y as reflected in T~ d o m i n a t e the transport process.

Acknowledgment This w o r k was s u p p o r t e d by the D e p a r t m e n t of E n e r g y t h r o u g h a s u b c o n t r a c t f r o m L a w r e n c e Berkeley L a b o r a t o r i e s u n d e r c o n t r a c t 45 4 8 0 1 0 .

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