Structural disorder and enhanced ion transport in amorphous conductors

Solid State Ionics 9 & 10 (1983) 585-592 North-Holland Publishing Company

585

STRUCTURAL DISORDER AND ENHANCED ION TRANSPORT IN AMORPHOUS CONDUCTORS

D. P. Button, L. S. Mason, H. L. Tuller and D, R. Uhlmann Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 USA Conductivity (o) data are reported for Li2B407 and LiBO 2 crystals. While the o behavior of boracite glass has been suggested to be comparable to its fast ion conducting (FIC) crystalline form, diborate and metaborate glasses are observed to be substantially better conductors than their crystalline counterparts. Both here and in the literature, framework disorder can be associated with enhanced o's. Data on density and lithium vibration spectra are considered in a critical analysis of the borate structures. The distribution of anionic species about the framework, and in turn, about interstices in the carrier sublattice, is shown to influence critically the transport behavior. Paradigms for FIC are reevaluated in light of a closer inspection of structure-transport relationships in polymorphic materials.

i.

INTRODUCTION

In a recent review of fast ion transport in glasses, we have observed that many glasses exhibit alkali or silver ion conductivities (o) that are either comparable to or significantly higher than those of their crystalline forms. 1 In this study we report ~ data for lithium diborate (Li2B407) and metaborate (LiBO2) crystals. We observe that the corresponding amorphous forms of these crystals are substantially better Li ion conductors. In contrast, the chloroborate glass with composition Li4B O C1 has been reported by Levasseur et al. 75 . to exhibit transport behavior similar to its fast ion conducting (FIC) crystalline form, y boracite. 2 A fast ionic conductor is a material that exhibits high o's (i.e.,?10 -2 (~CM)-! at temperatures well below its melting polnt). Upon further review of the glass literature, we have noted that FIC is a general characteristic of ionic glasses with high Li, Na or Ag modifier contents (> 30-50 mole %). One would presume that FIC materials, whether crystalline or amorphous, must have some special structural features. In this investigation we examine the validity of structural paradigms for FIC, established in the crystal literature over the past decade, by analyzing the structural characteristics of lithium borate polymorphs exhibiting dramatically different transport behaviors. Particular emphasis is placed on excess volume relationships and the nature of charged-anion distributions in the framework. 2. 2.1.

STRUCTURAL CONSIDERATIONS Fast Ion Conduction (FIC)

In the past many investigators of FIC crystalline systems have proposed that a number of

0 167-2738/83/0000-0000/$ 03.00 © 1983 North-Holland

structural features are essential for optimized o (e.g., see Refs. 3, 4). These include: (i) a highly-ordered, immobile framework complemented by ~2) a highly-disordered interstitial sublattice in which carriers are randomly distributed over an excess or multiple number of equipotential sites. These low-potential sites comprising the carrier sublattice must be sufficiently interlinked to provide continuous transport paths necessary for optimal conduction. Moreover, the rigid framework must provide windows that are sufficiently open for relatively unhindered movement of carriers between sites. The multiplicity of sites in the carrier sublattice accounts for the exceptionally high carrier concentrations common to these materials, which often approach the intrinsic maximum limit. Framework disorder appears to be associated with enhanced ionic conduction, in apparent contradiction to the FIC model. Nevertheless, the interstitial sublattice of a glass is disordered as well, at least to the extent of long-range structure. In general, glass structures are relatively open due to lower atomic parking efficiencies. Glass transport studies have clearly shown that larger windows and enhanced mobilities can be associated with volume expansion resulting from variations in composition5, 6 or thermal history. 7

*The interstitial sublattice consists of the space enclosed by the rigid framework sublattice, including the subset of sites occupied by carriers (i.e., carrier sublattice), even though from a crystallographic standpoint the mobile ions may not be strictly interstitial.

586

D.P Button et al. / Structural disorder and enhanced ion transport

One important aspect of glass structure relevant to cationic transport is the nature of the anion distribution over the framework. Since the carrier gs a charged species, site potentials will largely be a function of local electrostatic interactions between the carrier and its nearestneighbors. The distribution of anionic species or charge in the framework structure directly determines, therefore, the distribution of sites with low-electrostatic potentials in the carrier sublattice. In highly-ordered anionic frameworks, for example, a multiple number of interstitial positions are equivalent by virtue of symmetry relations, which also implies that an abundance of sites have common anion environments. In crystals with low-order symmetry, on the other hand, few atomic positions, whether anionic or interstitial, are related by symmetry; and thus carrier species tend to fully occupy special sites. While highly-ordered FIC crystals are characterized by intrinsic carrier populations, ionic conduction in crystals with loworder symmetry would typically be contingent upon motion of either vacancy or interstitial defects. When comparing transport behaviors of amorphous and crystalline polymorphs, glasses appear to be superior conductors relative to crystalline forms with low-order symmetry relations, such as the lithium silicates, phosphates or niobates. Conversely, glasses exhibit comparable o's relative to crystalline forms with higher-order symmetry relations such as boracite and Beucryptite. 1 Far infrared spectroscopy can provide information about the electrostatic characteristics of sites occupied by alkali ions. The vibration of alkali cations in anionic cages is a direct consequence of bond stretching, and will be dominated by electrostatic forces. 8,9 In a first approximation, the IR resonance frequency for two unlike species in a spatially disordered material is related to the local atomic force constants as: n <~.

>

2

=

l

Z.k.. (~_!__~l)

where the effective mass of vibration ~ is roughly that of Li. I0 One would expect a direct correlation between <~Li >2 and the aveage number of charged O species in a Li coordination shell. Using far IR spectroscopy, one can explore the carrier sublattice in glasses and monitor the average electrostatic interaction o f Li ions with their nearest-neighbor O anions as a function of composition. 2.2.

Lithium Borate Crystal Structure

Similar to binary lithium silicates, diborate and ~ metaborate crystals structures are highly anisotropic, where Li ions fully occupy special sites. The ~ metaborate crystal structure consists of long polymeric chains of BOy triangles, each with a nonbridging oxygen. II° These chains are all aligned in the b axis

direction, and are interlinked by electrostatic forces. The diborate framework is two-dimensional in nature in which layers of two independent diborate networks are again interconnected by Li ions. 12 3. 3.1.

EXPERIMENTAL PROCEDURE Sample Preparation and Physical Characterization

Glasses were prepared by melting reagent grade powders which included Li2C03, anhydrous-BoO 3 and LiCI mixed in appropriate portions. 13,~4 All glass samples were chemically analyzed for Li, B and CI. Polycrystalline diborate and metaborate samples were made from pure (99.999% metals basis) and reagent grade (98% di-, 99% meta-) powders (Alfa products). Pellets were hydrostatically pressed followed by sintering at approximately 0.84 T M (750°C) for 48.5 and 70 hours respectively. Mierostructural analysis and X-ray powder diffraction indicated that a single phase was produced. 15 Sample densities were measured at room temperature according to ASTM standards for "density of glass by buoyancy" and for "porous whitewares" using toluene as the immersion fluid. Differential scanning calorimetry (10°K/min) was used to determine glass transformation temperatures (Tg).13,14 Far IR spectroscopy measurements (Perkin-Elmer B580) were made in the range 700 to 180 cm -I with a resolution of 5 cm -±. Glasses and polyerystals were ground to micron size powder using an agate mortar and pestal. The boracite powder was obtained from a solid state reaction of LiCI, Li2CO~ and anh-B2Oo 16 The ground powders were dlspersed in Nujol and smeared on polyethylene film to produce IR samples. Typically two to three samples of each material were run two to three times with unaltered and delayed grating-change conditions. Each run consisted of an average of three to five scans. Variations in spectral positions generally remained within the + 5 cm -I resolution range. Further details of this and the other procedures used in this study may be found in a forthcoming publication on our IR investigations, 17 and in Refs. 14 and 15 along with others specified above. 3.2.

Electrical Characterization

Glass conductivity (a) samples were annealed at roughly Tg-75°C and then furnace-cooled. The heat treatment conditions were: metaborate 350°C/I0 min; boracite 400°C/60 min; diborate 420°C/24 hrs. All a samples, cut into small parallelpipeds (e.g., ~l.5x0.2x0.2 cm), were electroded with Pt, sputtered onto the sample ends in a 2-probe configuration. The shielded a chamber was flushed by either dry 02 or N 2. Atmosphere did not appear to influence the polycrystalline o's. The glasses were never exposed to temperatures above

D.P. Button et al.

/ Structural

Tg-IO0°C. Their o behavior was reproduced i n both heating and cooling cycles. Conductivity measurements were made on the polycrystalline samples over a temperature range of 460 to 660°C. The polycrystalline samples exhibited some temperature instability. Initial a measurements revealed a second regime of behavior below roughly 10 -4 (~CM) -I. Upon further exposure to temperatures above 600°C, these lower-temperature conductivities stabilized at values consistent with the higher temperature transport behavior. Previous investigators have attributed anomalous transport behavior of lithiabased mixed oxides to the effects of moisture and LiOH. 18 A diffraction peak at 1.44 A apparent both prior to and after sinteriug suggested, however, that LiH may be a contaminant in our samples. This initial anomalous behavior at low temperatures may have been due to an hydration effect as well. Multifrequency electrical impedance measurements of the pol~rystals were made using a CrossCorrelator (100-50K Hz), and Wayne-Kerr Universal Autobalance Bridge (B642; 200-20K Hz). A Gen-Rad, High Capacitance Bridge (1616; I0-I00K Hz) was used to measure the glass sample o's. Frequency-independent, bulk values were determined from complex plane analysis techniques, primarily complex impedance. The electrical responses of the polycrystalline samples exhibited both bulk and grain boundary contributions with a (bulk) being extracted by following the iteratlve method developed by Kleitz and Kennedy 20. Details of these measurements are to be published elsewhere 21. 4. 4.1.

disorder and enhanced ion transport

587

Transport parameters obtained from a classical log aT vs. I/T analysis are compiled in Table i. The diborate and metaborate crystals exhibit o's that are significantly lower than the others in spite of preexponential factors (ao) that are 1 1/2 to 2 orders of magnitude larger. The activation energies (EAT) of all six conductors are seen, however, to correlate inversely with o levels. Moreover, the diborate and metaborate glasses exhibit EaT, s that are about half those of their crystalline forms. In contrast, the boracite polymorphs are characterized by similar o o and EaT values. 4.2.

Physical Properties

A compilation of physical properties for the polymorphs is also presented in Table i. No obvious trends are observed regarding the relative density and Li vibration values for the polymorphs. The diborate and boracite glasses are less dense than their crystalline forms, whereas the metaborate glass is slightly denser than the ~ metaborate crystal. All three crystals and the diborate glass exhibit a

Temp~C) go0

700

~

300

'

~

'

metabora '~.

100

' '

1

-2

RESULTS Transport Properties

Transport results for three sets of lithium borate polymorphs are presented in Fig. i. All data plotted in this curve were obtained in our laboratory, except that for the single crystal ¥ boracite, which was taken from Jeitschko et al. 16. The a data for the polycrystalline samples represent an averaging of the real anisotropic characteristics of the crystals. The polycrystalline transport behavior did not appear to be sensitive to extrinsic factors. There was no significant variation in results between the reagent grade and pure compositions in spite of significant variations in impurity level, porosity, or grain size. 21 The lithium diborate and metaborate crystals, with similar o's, are poorer conductors by several orders of magnitude than either their glassy counterparts or the boracite polymorphs The boracite polymorphs exhibit similar o's, although the FIC crystal is a better conductor by roughly one order of magnitude. While the metaborate glass exhibits comparable a's, those of the diborate glass lie one to two orders of magnitude below.

E

-3

,90 >,

.> "d

-4

\\

c"

,.t

\

-5

0 J

Metaborate

\ \\\\

' V j,\\

. \

\

Li2B407

\\ . . . . . . . ys~,

\ \

'\ \ • \

g"~

\

\ i

1.0

i

i

1.5

,

\ \ I

2.0 10~'T (°K3

,

I

2~

Figure i. Arrhenius plot of bulk conductivities. Data for crystalline y boracite taken from Ref. 16.

D.P. Button et al. / Structural disorder and enhanced ion transport

588

vibration mode of roughly 420 cm-l; a peak frequency is observed in the metaborate glass that is larger by 38 cm -I. The peaks at %420 cm -I in the diborate and metaborate crystals have previously been assigned to Li. 22 Lithium containing glasses exhibit very broad peaks in the 300-500 cm -I range that have also been interpreted as Li vibration modes. I0 Extensive IR studies of Licontaining compounds indicate that peaks in the range of 300-500 cm-1 are characteristic of Li coordinated by four O nearest-neighbors (e.g., see Tarte references in Ref. 23). In the IR spectrum of the boracite crystal, a second peak at 370 cm-I, which is relatively broad and slightly larger than the broad peak at 415 cm-l, also falls in the range that appears to be characteristic of Li modes, particularly in borate crystals and glasses. This is presumably associated with the second Li site in boracite, an oxychloride tetrahedron. 16 One would anticipate a lower electrostatic force from the larger C1 ion than from a singlycharged 0 ion. Therefore, a Li ion residing in a tetrahedron consisting of one C1 and three O's should have a smaller vibration frequency than one with four 0 nearest-neighbors, which is likely the source of the 415 cm -I peak. As estimated from the spectra of a similar glass, the boracite glass exhibits a vibration mode that occurs in a regime between the two apparent Li peaks in the crystal; this peak is, however, situated much closer to the lower frequency, oxychloride peak. 5.

DISCUSSION

The lithium borates investigated here exhibit electrical properties ranging from the insulating character of crystalline LiBO 2 to FIC glasses and crystals such as LiBO 2 and Li4B7012CI. The use of glass and crystalline polymorphs with identical compositions provides

the opportunity to isolate those characteristics of structure which lend themselves to FIC, be they in ordered, crystalline or disordered, glassy materials. All of the systems considered here have an extremely high density of Li ions bound into their structure (see Table i). The critical issue relative to FIC is to what extent are they free to move upon application of an electric field. The poor conductivities that are characteristic of the Li diborate and metaborate crystals could be anticipated on the basis of their crystal structures. The Li positions in both structures are fully occupied, I1,12 and appear to be strategically placed so as to bind the oxyanionic framework together. Under these circumstances, Li conductivity must be contingent upon a defect formation process which typically results in carrier densities many orders of magnitude lower than those found in FIC's. A Frenkel defect process appears more likely in these borates than Schottky disorder given the relative stability of the boron-oxygen network. Disorder does not radically alter the transport behavior of boracite, yet it results in nearly a 15% increase in molar volume (24.7 to 28.1 cm3/mole). The key features of the carrier sublattice in the cubic boracite cristal are apparently maintained in the glass in spite of its total lack of symmetry. When the crystalline diborate and metaborate structures become disordered, a significant change in the carrier sublattice must take place, as exemplified by the large observed increases in conductivity in going from the crystalline to the respective glassy phase. Since the glasses are generally less dense than the corresponding crystals, one might presume that this could result in less restricted ion movement in glasses as a consequence of lower strain contributions to the migration energies. This is clearly not the source of enhanced

Table i. Transport and Physical Characteristics of Lithium Borate Polymorphs [data from following Refs. included: p(crystal) - ii, 12, 16; transport (beracite ~) - 16.] Li~Z m/o (Z~0,C121

Oo (~cm)-%

EoT (eV)

1.3

9x10 -8

917

3x10 -2

2.43

1.73

421

0.74

ixl0 -4

500

5x10 -3

2.27

1.62

412

1.4

ixl0 -8

845

ixl0 -2

2.22

2.69

416

0.58

4x10 -3

417

2x10 -2

2.28

2.74

454

0.5

8x10 -3

850

!xl0 -I

2.44

1.78

415/ 370

0.59

2x10 -3

463

2x10 -2

2.15

1.75

(375)

Diborate Li2B407 crystal

33.3

7x106

glass

33.3

2.4xi05

Metaborate LiBO 2 crystal ~

50

glass

48.6

2.8xi05

Boracite Li.B~O~2CI ~y(2~%ILi2Cl2 ) 36.4

ixl05

glass (27.6% Li2CI2)

37.9

4x107

1.6x105

o(300°C) (~cm) -I

Tm or T °max PR n i (°C) g (~cm) -I (g~cm 3) (102~cm -3)

~Li 1

(cm-)

D.P. Button et al. / Structural d&order and enhanced ion transport

conductivity in the metaborate glass given its lower molar volume as compared to the crystal: 22.1 vs. 22.4 (cm3/mole) respectively. Similarly, many crystalline FIC's are significantly better conductors than their lower-temperature polymorphs in spite of negligible differences in molar volume (e.g., see 24, 16). Moreover, the high-temperature ~ ~hase of Agl, a classic FIC is 18% more dense than the B phase, a much poorer conductor. 25 These observations suggest that molar volume (Vm), by itself, is often not the critical factor in transport. While an increase in free volume does not necessarily accompany phase transitions to FIC modifications, an increase in framework symmetry often does. The e metaborate and diborate crystals have lower-order symmetries, and are reasonably poor Li conductors, while their amorphous polymorphs are significantly better conductors. Meanwhile, the highlyordered crystal, cubic y boracite, is a reasonably good conductor whose amorphous form exhibits similar transport behavior. Enhanced conductivity thus seems to be associated with either of the two extremes of framework symmetry. In examining the source of FIC in crystalline systems such as boracite, it is clear that the influence of the higher order symmetries on enhanced conduction is based on the fact that large numbers of sites are brought into equivalency whereas in less symmetric structures many of them are not occupied. This results in the high density of carriers and sites necessary for FIC. The question remains in what manner does the generation of disorder in glasses lead to a similar end result? First taking a more general view, spatial disorder of the framework can be expected to yield a near continuum of interstitial Li in the diborate, metaborate, and boracite glasses. The differences in potential energy between these sites are likely to be small given the relatively uniform distribution of anion charge over the carrier sublattice. In contrast, lower-order symmetry relations in crystals yield specific low-energy sites. In the glass, Li ions are likely to occupy a significantly larger fraction of interstitial sites given their more general nature. This aspect of interstitial site multiplicity in the glasses resembles that obtained in crystalline FIC's but by an entirely different route. We now attempt to draw a more detailed picture of the site geometries and distributions likely to exist in the borate glasses considered here. Positively charged Li ions are viewed as being distributed about interstices in the boronoxygen network that are coordinated by anions of compensating negative charge. Two common kinds of negatively-charged anionic species are known to occur in borate frameworks. These include a nonbridging oxygen which is solely associated with borate triangles (i.e., B threefold coordinated by oxygens) and BO 4 tetrahedra

589

consisting of an sp 3 boron hybrid covalently bonded to four oxygen atoms. BO 4 tetrahedra form almost exclusively in borate materials with less than 33.3 mole percent alkali modifier.26, 27 Nonbridging oxygens, on the other hand, arise and become increasingly more prevalent with larger alkali oxide contents. It should be noted that in Li20-B20 $ glasses, (a) over relatively extensive composltlon ranges both types of anionic species co-exist and (b) the total number as well as the ratio of such charged borate species can be varied in a nearly continuous fashion by control of the Li20/B203 ratio in binary borate glasses and by % Li2CI2/Li2Z in chloroborate glasses.2B, 29 By contrast the diborate and metaborate crystals represent two extremes of anionic borate behaviour. Half the boron atoms in the diborate crystal are in four-fold coordination and all oxygens are bonded to tetrahedra. ~2 Conversely, only non-bridging oxygen anions occur in the metaborate structure, and these comprise half of the oxygen population. Far IR results on Li borate crystals 17'22 indicate that an oxygen on a tetrahedron can behave in a manner electrostatically similar to a non-bridging oxygen. This is a remarkable implication. Lithium borate crystals ranging from a pentaborate (16.7 m/o Li20)22 , to boracite (26.4 m/o Li2Z , Z=O, C12) to ~ metaborate (50 m/o Li20) all exhibit a vibration mode at ~420 cm -I that is characteristic of Li cage rattling. Structural information for the triborate (25 m/o Li20)30 ; boracite 16, diborate 12 and metaborate II crystals indicates that all these Li sites are coordinated by four oxygens that are either non-bridging or tetrahedral. Meanwhile, bondlengths may vary and the total number of coordinating oxygens may range from 4 to 6 without markedly influencing the vibration frequency. It would thus appear that the crucial factor tying the four types of crystal sites together, with the same electrostatic force sum, is the similar anionic behavior of nonbridging and tetrahedron corner oxygens. 17 The diborate glass has essentially the same number and type of charged species distributed over its framework as its crystalline form. 27 Furthermore, Li sites in these polymorphs appear to be electrostatically similar, as one would expect should the coordinating behavior of the tetrahedra oxygens in these frameworks be comparable as well. Recent EXAFS investigations of oxide glasses indicate that amorphous and crystalline polymorphs, including Na diborate, do exhibit similar nearest-neighbor oxygen configurations about sodium ions. 31 The lithium vibration modes of the metaborate polymorphs are significantly different as are their eharged-o~ygen populations. Unlike the crystal, a significant fraction of the boron atoms in the metaborate ~lass network are in four-fold coordination. 27 Statistically one can determine that every oxygen in the metaborate glass is either non-bridging or bonded to a tetrahedron. Therefore, every oxygen

590

D.P. Button et al. / Structural disorder and enhanced ion transport

in the glass, including those coordinating an occupied lithium site, can assume a negative charge. Conversely, only half the oxygens in the ~-metaborate crystal are non-bridging or charged, as well as only ~ four of the five oxygens that coordinate Li sites. II The larger ~Li exhibited by the metaborate glass clearly indicates that (i) oxygen anions are distributed differently in the glass framework than in the crystal structure and moreover,(2) its carrier sublattice is significantly different as well. 17 In contrast to crystals, there is evidence to suggest that a specific low energy site configuration does not arise in glasses. Whereas ~Li remains essentially constant when comparing lithium borate crystals with markedly different Li20/B203 ratios, the lithium peak frequency is observed to increase markedly and continuously in glasses above 18 mol % Li20 as the modifier content is increased. 17 That is, the average force of electrostatic interactions in lithium occupied sites increases monotonically with increases in the amount of anionic charge distributed over the framework. This implies a distribution of near equivalent sites in the glass which nevertheless shifts with composition. The increase in ~Li with lithia is more pronounced in glasses with less than 33 m/o Li20. In glasses with higher alkali contents, the statistics of borate structure units 27 indicate that all oxygens are either nonbridging or tetrahedral, and thus charged. Meanwhile, below 33 m/o Li20, only a fraction of oxygens are charged: a fraction that increases with increasing modifier content. Increasing the fraction of charged oxygens in low-alkali glasses appears, therefore, to have a greater influence on site distributions than increasing the amount of charge that is uniformly distributed over the oxyanionic framework in high-alkali glasses. Implications for transport in low and high alkali glasses are considered below. In low-alkali glasses, only a small fraction of network oxygens are charged. Consequently it is to be expected that the potential of lithium interstitial sites could vary substantially depending on their position relative to the charged oxygens. Consequently a broad and bifurcated distribution of site potentials would result. A minimum number of charged oxygens would thus be necessary to assure the existence of continuous paths of low-potential sites associated with such nearest-neighbor oxygens. A percolation threshold can be envisioned to occur when roughly 20-30% of all oxygens are charged.32,14 Atsuch a composition, a dramatic decrease in potential differences would occur in at least the subset Of low potential sites that are interconnected, thereby distinguishing a glass with enhanced o's from the more typical insulating glass. A rapid rise in ~ with increasing alkali content is charaeteristic of glasses in the range of 15 to 25 m/o R20 (e.g., see 33, 34,

35). This may therefore be associated with the onset of percolation, especially given the charged-oxygen statistics of this composition range. 14 Several authors have suggested such a percolation model including Kro~h-Moe 36, Blair & Milberg 35, and Greaves et al. 37. At higher alkali levels, for example beyond 33 m/o Li20 in borate glasses, variations in transport characteristics are not as sensitive to alkali oxide increases. Meanwhile,significant increases in free volume induced by chlorine substitutions in such glasses, correlate with significant increases in conductivity.13,38, 6 At 150°C, for example, increases by over an order of magnitude in a series of lithium chloroborate glasses with diborate (33 m/o Li2Z), 6 boracite (36.4 m/o

Li2Z)13 and metaborate (50 m/o Li2Z) 38 compositions. Once large numbers of near equipotential sites become available in either glasses or crystals, mobility differences seem to play a more important role in establishing the final magnitude of ionic conductivity, to be expected in FIC materials with intrinsic carrier populations. As noted above in borate glasses with greater than 33 m/o Li20 , all oxygens are charged, being either non-bridging or bonded to tetrahedral boron. Thus, charge is distributed in a somewhat uniform manner over the sublattice, and in general, only small differences in site potentials arise. In this hi~halkali regime, both V~ a n d free volumes are observed to increase markedly with increasing alkali content. 14 The metaborate glass may thus be a better conductor than the diborate glass largely on the basis of larger interstitial windows and lower migration barriers. 6.

SUMMARY AND CONCLUSION

Electrostatic interactions primarily determine the relative potentials of interstitial sites in ionic materials. The distributions of anions over the ionic framework determine the nature of both the carrier sublattice and the carrier population. An abundance of nearequivalent sites can often be achieved when a multitude of interstitial positions are related by high-order symmetry or when chargedanions are uniformly distributed over a disordered framework. In borate glasses, the charged-anionic species in the framework are nonbridging and tetrahedral oxygens. Far IR results indicate that these anionic species behave in a manner electrostatically similar. How these anionic oxygens are distributed about the frameworks of the diborate and metaborate polymorphs has a significant impact on their relative conductivity behaviors. The glasses appear to be much better conductors, with much smaller preexponential factors and activation energies, largely because of an intrinsic carrier population. Excess volume and mobility factors are significant in this high-alkali regime of borate glasses

D.P. Button et aL

/ Structural

where carrier sublattices are characterized by an effective multiplicity of sites. The structural paradigms for FIC established in the crystalline literature appear to be valid in principle. Nevertheless, clarification of the key features results from a few shifts in emphasis. (i) A multiple number of low-energy, interconnected sites is necessary to establish an intrinsic carrier population. Site multiplicity may be attained through high-order symmetry relations or spatial disorder. A minimum number of low-energy sites or charged framework species are necessary to achieve percolation paths in glassy materials. (2) The framework should be sufficiently open to ensure (i) an abundance of physically accessible sites and (ii) unhindered movement of ions through large windows. The virtue of these structure-transport relationships appears to be demonstrated in crystalline as well as oxide glass systems where composition, structure and properties can continuously be varied. ACKNOWLEDGEMENT The technical contributions of T. Tatad for crystalline boracite preparation and A. Wahi for extensive IR analysis are especially appreciated. Interactions with A. Pierre, B.J. Wuensch and I.D. Brown are gratefully acknowledged, along with S. Sung for the use of her IR facility. The financial support of this work by the U.S. Department of Energy is gratefully acknowledged (Subcontract No. 450381), along with funding by the MIT Undergraduate Research Opportunities Program (UROP) for A. Wahi and T. Tatad. Many thanks to L. Sayegh and P. Kearny for their skillful assistance on manuscript preparation. REFERENCES [i]

[2]

[3]

[4]

Tuller, H.L., Button, D.P. and Uhlmann, D. R., Fast ion transport in oxide glasses, J. Non-Cryst. Solids 40 (1980) 93-118. Levasseur, A., Calgs, B., R6au, J.-M. et Hagenmuller, P. Conductivit6 ionique du lithium dans les verres du syst~me B203Li20-LiCl, Mat. Res. Bull. 13 (1978) 205-209. van Gool, W., Relationship between structure and anomalously fast ion diffusion, in van Gool, W. (ed.), Fast Ion Transport in Solids (North-Holland, Amsterdam, 1973) pp. 201-215. Huggins, R.A. and Rabenau, A., What is special about fast ionic conductors?, Mat. Res. Bull. 13 (1978) 1315-1325.

d&order and enhanced ion transport

591

[5]

Shelby, J.E., Molecular solubility and diffusion, in Tomozawa M. and Doremus, R. H. (eds.), Treatise on Materials Science and Technology 17 (Academic Press, New York, 1979) pp. 1-40.

[6]

Button, D.P., Moon, P.K., Tuller, H.L. and Uhlmann, D.R., Structure-transport relationships in oxide glasses, to be published in Glastech. Ber.

[7]

Charles,R.J. Structural state and diffusion in a silicate glass, J. Amer. Ceram. Soc. 45 (1962) 105-113.

[8]

Mott, N.F. and Littleton, M.J., Conduction in polar crystals, Trans. Faraday Soc. 34 (1938) 485-499.

[9]

Rao, K.J. and Elliott, S.R., Characteristic vibrations of cations in glasses, J. NonCryst. Solids 46 (1981) 371-378.

[10] Exarhos, G.J. and Risen, W.M. Jr., Cation vibrations in inorganic oxide glasses, Solid State Comm. ii (1972) 755-758.

[ii]

Zachariasen, W.H., Crystal structure of lithium metaborate, Acta. Cryst. 17 (1964) 749-751.

[12] Krogh-Moe, J., Crystal Structure of lithium diborate, Li20.2B203, Acta Cryst. 15 (1962) 190-193; Refinement, Acta Cryst. B24 (1968) 179.

[13] Button,

D.B., Tandon, R.P., Tuller, H.L. and Uhlmann, D.R., Fast Li + ion conduction in chloroborate glasses, J. Non-Cryst. Solids 42 (1980) 297-306.

[14] Button, D.P., Structure-transport relationships in oxide glasses, Ph.D. Thesis, M.I.T., 1983.

[15] Mason,

L.S., Ionic conduction in crystalline lithium borate compounds, B.S. Thesis, MIT, 1982.

[16] Jeitschko, W., Bither, T.A. and Bierstedt, Crystal structure and ionic conductivity of Li boracites, Acta. Cryst. B33 (1977) 2769-2775. [17] Button, D.P., Wahi, A., Tuller, H.L. and Uhlmann, D.R., Far infrared spectroscopy studies of lithium borate glasses and crystals, to be published.

[18] Biefeld, R.M. and Johnson, R.T., Jr., Ionic conductivity~of Li20-based mixed oxides and the effects of moisture and LiOH, J. Electrochem. Soc. 126 (1979) 1-6.

[19] Stratton, T.G., Reed, D. and Tuller, H.L., Study of boundary effects in stabilized zirconia electrolytes, in Levinson, L.M.

592

D.P. Button et aL

/ Structural

(ed.9 Advances in Ceramics I (Amer. Ceram. Soc., Colombus, 1981) pp. 114-123. [20] Kleitz M. and Kennedy, J.H., Resolution of multicomponent impedance diagrams, in Vashishta, P., MuDdy J.N. & Shenoy, G.K. (eds.) Fast Ion Transport in Solids (North-Holland, Amsterdam, 1979).

[21]

Mason, L.S., Button, D.P., Tuller, H.L., and Uhlmann, D.P., Ionic conduction in lithium diborate and metaborate crystals, to be published.

[22]

Weir, C.E. and Schroeder, R.A., Infrared spectra of the crystalline inorganic borates, J. Res. Nat. Bur. Stand. 68A (1964) 465-487.

[23]

Rao, C.N.R., Randhawa, H.S., Reddy, N.V. R. and Chakravorty, Vibrational spectra of alkali and alkaline earth metal complexes, oxide glasses and oxyanion salts, Spectrochim. Acta 31A (1975) 1283-1291.

[24]

Phillips, J.C., Structural princples of e-AgI and related double salts, J. Electrochem. Soc. 123 (1976) 934-940.

[25]

Cava, R.J., Redinger, F. and Wuensch, B. J., Single-crystal neutron-diffraction study of AgI between 23 ° and 300°C, Solid State Comm. 24 (1977) 411-416.

[26]

Edwards, J.O. and Ross, V., J. Inorg. Nucl. Chem. 15 (1960) 329r335.

[27]

Bray, P.J., Feller, S.A., Jellison, G.E., Jr. and Yun, Y.H., B I0 NMR studies of the structure of borate glasses, J. Non-Cryst. Solids 38/39 (1980) 93-98.

[28]

Geissberger A.E., Bucholtz, F. and Bray, P.J., 7Li, liB and 19F NMR in amorphous alkali halogen borate solid ionic conductors, J. Non-Cryst. Solids 49 (1982) 117-127.

disorder and enhanced ion transport

[29]

Button, D.P., Tandon, R.P., King, C., Velez, M.H., Tuller, H.L. and Uhlmann, D. R., Insights into the structures of alkali borate glasses, J. Non-Cryst. ~olids 49 (1982) 129-142.

[3o]

von KrSnig, H. and Hoppe, R., Zur Kenntnis von LIB305, Z. anorg, allg. Chem. 439 (1978) 71-79.

[31]

Greaves, G.N., Sodium environments in glass, J. de Physique 42 (1981) C4-225228.

[32]

Pike, G.E. and Seager, C.H. Percolation and conductivity, Phys. Rev. BI0 (1974) 1421-1434, 1435-1446.

[33]

Otto, K. and Milberg, M.E., Ionic conduction in alkali and thallium silicate glasses, J. Amer. Ceramic Soc. 51 (1968) 326-329.

[34]

Mazurin, O.V., Introduction: Glasses with alkali conduction, in Mazurin O.V. (ed.) Electrical Properties and Structure of Glass (Consultants Bur., New York, 1965) pp. 5-58.

[35]

Blair, H.D. and Milberg, M.E., Structure of thallium silicate glass, J. Amer. Ceramic Soc. 57 (1974) 257-260.

[36]

Krogh-Moe, J., Relation of structure to some physical properties of vitreous and molten borates, Arkiv. Kemi 14 (1959) 553566; On the structure of boron oxide and alkali borate glasses, Phys. Chem. Glasses 1 (1960) 26-31.

[37]

Greaves, G.N., Fontaine, A., Lagarde, P., Raoux, D. and S.J. Gurman, Local structure in silicate glasses, Nature 293 (1981) 611-616.

[38]

Button, D.P., Tandon, R.P.. Tuller, H.L. and Uhlmann, D.R., Fast Li ~ conductance in chloroborate glasses II-diborates and metaborates, Solid State Ionics 5 (1981) 655-658.