This paper was first published in Solid State Chemistry – Proceedings of the 5^th Materials Research Symposium sponsored by the Institute for Materials Research, National Bureau of Standards, October 18-21, 1971 held at Gaithersburg, Maryland, edited by Robert S. Roth and Samuel J. Schneider, Jr., Washington, D.C.: U.S. Department of Commerce and National Bureau of Standards, 1972, 139-154

           BETA ALUMINA - PRELUDE TO A REVOLUTION IN SOLID STATE ELECTROCHEMISTRY

                             M. S. Whittingham and R. A. Huggins

                       Department of Materials Science and Engineering

                                     Stanford University

                                 Stanford, California 94305

     For almost two decades solid state electrochemical techniques have been used to study the thermodynamic and transport properties of a number of materials. However, these studies have been restricted essentially to systems utilizing electrolytes containing mobile silver or copper ions at low temperatures, and oxygen ions at high temperatures.

     Transport measurements have been made on single crystals of β alumina, which has the nominal formula MAl₁₁0₁₇ where M is usually a monovalent cation, to test its suitability as a solid electrolyte. In this and related structures, the monovalent cation can be extremely mobile. By use of a group of novel non-polarizing solid electrodes, which are fully reversible to the monovalent cation, it has been possible to study the ionic conductivity of a series of β aluminas containing alkali metals as well as thallium over a wide temperature range. The electronic conductivity of silver β alumina has also been determined by use of the Wagner asymmetric polarization technique over wide ranges of temperature and oxygen partial pressure.

     The results of these studies clearly indicate that the β alumina family shows excellent promise for use as solid electrolytes, exhibiting high values of ionic conductivity and a very low electronic transference number. These properties were exhibited over extremely wide ranges of temperature, -150 °C to +820 °C, and oxygen partial pressure, 10^-24 to 1 atm. The use of β alumina opens up many new opportunities in solid state electrochemistry, particularly in the study of materials containing monovalent cations.

     Key words: Beta alumina; diffusion; electrochemical cell; electrochemical transducer; ionic conductivity; mass transport; solid electrolyte.

1. INTRODUCTION

     There has recently been a great deal of interest in a material called " β alumina", whose nominal formula is MAl₁₁0₁₇, in which M represents a cation, normally monovalent. This interest has arisen primarily because of the possibility of using materials of this phase, or more probably a related phase called " β" alumina", whose nominal formula is MAl₅0₈, as solid electrolytes in new types of batteries. This interest arose as a result of the important pioneering work at the Ford Motor Company [1,2] which not only focused attention upon the unusual physical properties of this type of material, but also [3] showed that it was possible to take a rather revolutionary approach to the battery problem, using liquid electrodes and a solid electrolyte; this is, of course, just the inverse of traditional battery designs, and leads to some very distinct advantages.

     Interest in the practical application of these materials and concepts has spread rather widely, and research is under way in a number of laboratories at the present time. In addition, serious battery development efforts have been undertaken by several companies in the United States, as well as others in England and Japan. At the present time the commercial interest seems to be focused upon the use of configurations involving a liquid sodium anode, a solid β or β" alumina electrolyte and a liquid sulfide cathode. Although there are surely various alternative approaches, it now appears that such a cell is expected to be a serious contender for widespread application as high energy density and power density secondary cells.

    One can find reviews of various new battery possibilities in a number of places [4-14], and it is not our intent to discuss this matter here other than to point out that the theoretically limiting value of energy density for a sodium-sulfur cell operating at 300 °C is about 1030 watt hours per kilogram [3], whereas the familiar lead-lead oxide cell typically gives 5 to 30 watt hours per kilogram at room temperature.

     This paper will not discuss the possibility of the use of the β aluminas as battery or fuel cell components. Instead, attention will be focused upon the potential use of these and related materials for a wide range of other purposes, primarily as experimental tools for the measurement of thermodynamic and kinetic data. We shall see that their unusual properties open up a very wide vista for the use of solid electrolytes as electrochemical transducers in a great variety of scientific as well as engineering applications.

2. ELECTROCHEMICAL TRANSDUCERS

  2.1. INTRODUCTION

     Although there had previously been a few papers in which solid electrolytes had been used for thermodynamic studies [15], attention was drawn to the broad possibility of using such ionically conducting solids as electrochemical transducers for a number of purposes in an important paper by Carl Wagner in 1953 [16], in which he used silver iodide in a simple solid state cell configuration to measure a number of properties of silver sulfide. A few years later, a pair of papers by Kiukkola and Wagner [17,18] expanded this horizon considerably by pointing out a variety of possible applications, as well as indicating several other ionically conducting solids which could be used as solid electrolytes. In addition to discussing the extension of this type of work by the use of other simple binary salts, they pointed out that cubic oxides with the fluorite structure, such as calcium-doped zirconium dioxide, could be used in a similar manner at temperatures in the range 750 to 1150 °C. Since that time, there have been a number of laboratories who have pursued these ideas, as well as extending them, and one can find reviews of much of this work in several places [15, 19-21].

     Before mentioning some of these areas of application and pointing out the implications of β alumina and related materials to them, we shall very briefly review a few elementary concepts for those who are not familiar with this particular field.

     If two neighboring regions within a solid are in thermodynamic equilibrium with each other under isothermal conditions, the concentrations of all species (including all defects) in both regions will be time-independent. This means that there must be no net forces present in such a system which tend to cause the transport of either mass or charge from one microscopic region to the other.

     Let us focus our attention upon this question of forces acting upon species. We know that in general one can express the force F_i acting on any species i as

                                       F_i = - grad U_i                                     (1)

where U_i is the total potential energy or thermodynamic potential of species i at a given location. The requirement for equilibrium, then, is that the gradient in U_i must be equal to zero for all species.

     There are several different kinds of potential that can contribute toward the total thermodynamic potential of a particular species in a solid. Here we will restrict ourselves to the discussion of only two, the chemical potential, (or partial molar free energy) μ_i, and the electrostatic potential, z_iFΦ (Φ is the local value of the electrostatic macropotential, whereas z_iF is the electrostatic charge carried per mole of i). The sum of these two is known as the electrochemical potential, η_i, so we can write

                                       η_i = μ_i + Z_iFΦ                               (2)

    For simple one-dimensional transport, the flux density of a species i can be written as

                           J_i = c_i v_i       (J_i = no./cm²sec)                          (3)

where c_i is the concentration (no./cm³) and v_i is the average velocity of the species i (cm/sec) relative to a stationary observer. The absolute mobility B is defined as the velocity per unit force,

                                       B_i  =  v_i/F_i                                      (4)

Note that this is a different quantity from the electrical mobility u, which is defined as the velocity per unit electrostatic field, or

                                           u_i =  v_i/(dΦ/dx)                                (5)

We find that although these two different "mobilities" have different dimensions, they are related by

                                      u_i= z_i q B_i,                                     (6)

where q is the electronic charge. If there are two gradients present, a chemical gradient and an electrostatic gradient, we can write the force acting upon a particle of species i as

                            F_i = -dη_i/Ndx = - [dμ_i/Ndx +  z_i q dΦ/dx]                  (7)

where N is Avogadro's number. These equations can be combined to get a general expression for the flux density,

                           J_i = c_i B_i [dμ_i/Ndx +  z_i q dΦ/dx]            (8)

     It is obvious from this expression that under equilibrium conditions, when the particle and charge flux are both zero, one could have a chemical gradient that is just balanced by an electrostatic gradient.

                                          dμ_i/Ndx = -  z_i q dΦ/dx                       (9)

If one deals with a material in which the transference number for ionic species is close to unity, essentially all the charge transport is by means of ions, and such an equilibrium situation can exist and, in fact, be used to transduce between chemical and electrical quantities. This simple case is illustrated schematically in figure 1. In that figure, a difference in the chemical potential of species i is assumed to exist upon the two sides of a solid that is an ionic conductor for species i. Integrating eq. (9) between the two interfaces, we find that

                               μ_i^I  - μ_i^II =  - z_i F E                                  (10)

where E is the electric potential difference between the electrodes placed at the two interfaces. By substitution of the general relation between chemical potential and activity

                            μ_i = μ_i⁰  + R T ln a_i                  (11)

it can be rewritten as

                              E = -RT/z_iF  ln(a_i^I/a_i^II               (12)

which is the familiar Nernst equation.

     It is obvious from these simple considerations that if one has a situation in which no current passes through the ionic conductor, that is, if the forces causing transport of the ions are exactly balanced, a measurement of the open circuit electric potential difference between the two interfaces is a direct measure of the difference in chemical potential or activity in the pertinent species at those locations. If some care is taken, one can play this game both ways and use a chemical potential difference to generate an electrical voltage, or an electric potential difference to generate a difference in chemical activity.

     In addition, if no charge-generating or charge-consuming reaction takes place at the interfaces, one can obtain a direct measurement of the ionic transport through the electrolyte by evaluation of the electronic current through the electrode circuit. As will be mentioned shortly, this allows the use of this type of system for measurements of mass transport and related matters.

  2.2. RANGE OF APPLICATIONS

     Although most of the earlier applications of solid electrolytes as electrochemical transducers involved their being employed in emf cells to measure free energy changes of various reactions, recent work has extended over quite a range of different applications. Some of these are listed in table 1.

3. PRACTICAL CONSIDERATIONS

     Although this appears quite simple, there are several practical considerations that must be given attention. These include the magnitude of the ionic conductivity of the transducer phase under the conditions (e.g., temperature and chemical environment) in which it is to be used. In a static situation, this conductivity must be high enough that equilibrium can be established within a reasonable period of time. This typically means that one must have a conductance value of about 10^-10ohm^-1 or greater. Furthermore, if the transducer phase is to be used for transport measurements, or under conditions in which transport is expected to occur within it, its conductivity must be considerably greater, so that the electric potential difference across it (the IR drop) does not seriously interfere with the operation of the cell. Under these conditions, it is generally considered necessary that the conductance be equal to 10^-4ohm^-1 or greater.

                     Fig. 1. Schematic representation of simple electrochemical cell with solid electrolyte.

                                          Table 1

           Examples of the Application of Solid State Electrochemical Techniques

        Static Emf Measurements

            Free energy of formation of binary and ternary compounds

            Free energy changes accompanying various cell reactions

            Thermodynamics of binary phases

            Determination of limits of stoichiometry of compounds

            Phase diagram determination

            Thermodynamics of phase transformations

            Effective mass of electrons or holes in semiconductors

            Solubility of gases in liquids

        Time-dependent Emf Measurements

            Phase boundary migration kinetics

            Supersaturation required for nucleation within and upon solids and liquids

        Combinations of Emf and Current Measurements,

             Diffusion in liquid and solid metals and mixed conductors

             Transport of both ionic and electronic species across phase boundaries

             Kinetics of condensation and vaporization processes

             Oxidation and reduction reactions on solid surfaces

             Thermodynamics of gaseous species

             Studies of the mechanism of catalysis

             Ionic and electronic partial conductivities in mixed conductors

             Structure of electrode-electrolyte interfaces

        Technological Applications

             Batteries

             Fuel cells

             Thermoelectric devices

             Memory elements

             Solute valence control in semiconductors and ionic solids

             Purification of liquids and gases

             Measurement and control of gas compositions

     Another important consideration is the assumption made in the simple discussion of the Nernst equation that the only charge-carrying mobile species is the ionic species in question. Obviously, if the transducing phase is also an electronic conductor, electronic transport will seriously interfere with, if not completely nullify, the electric potential difference generated by the difference in chemical potentials at the two interfaces. This is obviously a matter of real concern. For, instead of needing to know just the ionic conductivity, one must also know the value of the electronic conductivity or the ratio of electronic conductivity to total conductivity (the transference number for electronic species, t_e). The influence of a small but significant electronic transference number results in a measured open circuit potential, Em, for a simple cell of the type illustrated in figure 1, given by [17,22,23]

                              E_m = E –I/zF ∫t_edμ_i  (the limits of the integral being μ_i ^I and μ_i^II)            (13)

     As a rule of thumb, it is normally considered that the electronic transference number should be less than 10^-2 throughout the usable range in order for a solid electrolyte to be useful as an electrochemical transducer under static conditions. Since the electronic transference number typically varies with the stoichiometry, the thermodynamic range over which an electrolyte is useful can thus be quite severely restricted.

    Another important matter is the thermodynamic stability of the transducer phase with respect to reactions with chemical species present at its interfaces. As a first approximation, if a solid electrolyte MX is in contact with species N, it is necessary that the displacement reaction

                                  MX +N ↔ NX + M                               (14)

not proceed in the forward direction. Another way of saying this is that it is normally necessary that the element N be more noble than the element M.

4. PROPERTIES OF SOME SOLID STATE ELECTROCHEMICAL TRANSDUCERS

  4.1. MAGNITUDE OF THE IONIC CONDUCTIVITY

     As we have mentioned, it is important that electrochemical transducers have relatively large values of ionic conductivity. Typical values for such materials are indicated in figure 2, which also shows conductivity data for several other common ionic solids as a function of temperature. It is clear that the conductivity of ionic conductors can vary over an immense range. Materials which are useful as solid electrochemical transducers must have good values of conductivity in the temperature range in which they are to be used. Thus, it is quite obvious, for example, that the fluorite structure oxides will not be very useful below about 600 °C. On the other hand, it is clear that there are several materials which have large ionic conductivities at unusually low values of temperature. These are of two general types, materials which are closely related to the body-centered cubic alpha AgI structure, in which silver is typically the mobile ion, and the β aluminas. An important aspect of the latter case is that there are several choices for the mobile cation.

     One of the difficulties encountered in the evaluation of the ionic transport in these unusually good ionic conductors (for which the term "super ionic conductors" was coined by Rice and Roth [24]) is the avoidance of polarization effects at measuring electrodes.  It is common practice to use ac conductivity techniques to evaluate ionic motion in ionic conductors. If polarization occurs at the electrodes, the conductivity appears to be frequency dependent and the normal procedure is to increase the frequency until it is in a range at which this frequency dependence disappears. This is not a great difficulty in the case of the traditional ionic conductors such as the alkali halides, but it becomes a very severe problem with solids in which the conductivity is high. Even frequencies of the order of 10⁸ Hz are often not high enough to avoid polarization effects in the β aluminas [25].

     An alternate approach to this problem is to use reversible electrodes. If this is properly done, the frequency dependence is eliminated. It has been shown [26] that with proper care it is possible to use solid elemental Ag as a reversible electrode to get reliable values of the ionic conductivity of the silver ion in β alumina from 800 °C all the way down to room temperature.

                    Fig. 2. Conductivity data for various ionic conductors.

    Another more novel approach was the demonstration [27] that a mixed conductor, in which the important ion has a high diffusion coefficient, can also be used as a nonpolarizing electrode in connection with materials such as the β aluminas. By use of this technique, it was possible to measure the conductivity of the sodium ion in sodium β alumina from 820 °C all the way down to -150 °C.

     By use of this nonpolarizing electrode technique, reliable data on the ionic conductivity of single crystals of several of the β aluminas have now been obtained over a wide temperature range. These are illustrated in figures 3-6 for silver, sodium, potassium and thallium ions. Also included in those figures are data obtained by the Ford research group by means of radiotracer [1,2,28] and the dielectric loss [2] techniques. Allowing for correlation effects, it is seen that the results obtained by the conductivity and radiotracer methods coincide very well in all cases. The dielectric loss data also give good agreement in the sodium and potassium cases, and moderate agreement in the silver case, but deviate by about a factor of ten for thallium β alumina. It appears that the absolute values of the conductivity obtained by these various techniques agree better than one might expect from just consideration of the activation energy values determined separately over relatively small

temperature spans [2].

     Conductivity measurements have also been made on a single crystal sample of β alumina containing lithium. In this case, electrodes of a cubic lithium tungsten bronze were used, rather than the tetragonal or hexagonal bronze phases used with the others. This was necessary as the small lithium ion is only found in the cubic phase. Although we were thus apparently able to avoid a frequency dependence in the conductivity, indicating reversible electrodes, more scatter was present in the data in this case. In addition, the conductivity data seem to fall along two different straight lines when plotted in the normal way to determine the temperature dependence. This is clearly evident in figure 7. Although the conductivity and tracer diffusion data lie comfortably close to one another above 180 °C, it is not obvious that the low temperature conductivity measurements and the dielectric loss experiment are evaluating the same physical process. As a further complication, it was found that annealing the sample above 800 °C caused a marked drop in the low temperature conductivity.

                     Fig. 3. Conductivity, tracer diffusion, and dielectric

                              loss data for silver β alumina.

Fig. 4. Conductivity, tracer diffusion, and dielectric

         loss data for sodium β alumina.

Fig. 5. Conductivity, tracer diffusion, and dielectric

         loss data for potassium β alumina.

Fig. 6. Conductivity, tracer diffusion, and dielectric

         loss data for thallium β alumina.

 Fig. 7. Conductivity, tracer diffusion, and dielectric

           loss data for lithium β alumina.

There is evidently more to do before we should feel that we understand what is happening in lithium β alumina. One possibility that should certainly be given consideration is that at high temperatures a direct interstitial jump mechanism is becoming important, rather than transport being dominated by the interstitialcy mechanism that seems to prevail [26] in the other β aluminas.

     These conductivity data are compiled in table 2, assuming an Arrhenius relation of the form

                                 σ₀ = (σ₀/T)exp(-H/RT).                         (15)

Also included are values of the apparent correlation factor, f, the ratio of the radiotracer diffusion coefficient to the diffusion coefficient obtained from the ionic conductivity data, calculated for temperatures at the center of the tracer data. It is seen that the correspondence to the theoretical value [26] for the interstitially diffusion mechanism in this structure, 0.599, is quite good.

     Some measurements have also been made upon samples of the phase β" alumina. It has been reported [29] that both sodium and potassium ions have greater conductivities in this phase than in the β alumina structure. This appears to be true for both single crystals and dense sintered polycrystalline bodies.

     Using the reversible solid electrode technique, we have done a few experiments on hot pressed polycrystalline samples of the β" phase. The results are indicated in figure 8, along with data from the Ford laboratory [29]. Also shown (dotted line) is the conductivity of single crystal sodium β alumina [27]. Above 315 °C the polycrystalline data are essentially frequency-independent and evidently lie upon a straight line parallel to the single crystal β alumina data. At lower temperatures, a frequency dependence appears and there is a deviation from linearity. Preliminary measurements [30] using the complex admittance method [31] gave essentially the same value of conductivity at room temperature, as also indicated on figure 8. A plot of these data on the complex admittance plane is shown in figure 9.

  4.2. ELECTRONIC CONDUCTIVITY

     It was pointed out earlier that a desirable electrochemical transducer should have an electronic transference number less than 10-2. Measurements have been made of the electronic component of the total conductivity of silver β alumina [26] by use of the Wagner asymmetric polarization technique [23,32-34] from 555 to 790 °C over a wide range of oxygen partial pressure. Below about 750 °C changes in oxygen partial pressure did not appear to influence the electronic conductivity beyond normal experimental scatter. It was not possible to extend these, measurements to lower temperatures because of prohibitively long times required for

                                           Table 2

            Summary of Data on Ionic Conductivity in Single Crystal Β Aluminas

     Ion      Temp. Range          σ₀         Activation   Conductivity    Correlation

                  degreesC           (ohm-cm)^-1 K     Energy       at 25 °C        Factor, f

                                               kJ/mole      (ohm-cm)-l

     Ag        25 - 800           1.6 x 103      16.5         6.7 x 10^-3      0.61

     Na      -150 - 820           2.4 x 103      15.8         1.4 x 10^-2      0.61

     K        -70 - 820           1.5 x 103      28.4         6.5 x 10^-5       -

     Tl       -20 - 800           6.8 x 102      34.3         2.2 x 10^-6      0.58

     Li       180 - 800           9.7 x 103      35.8             -

     Li      -100 - 180           5.4 x 101      18.0         1.3 x 10^-4

                  Fig. 8. Conductivity data for single crystal and poly-

                           crystalline sodium β" alumina. Also shown

                           (dotted line) are values for single crystal

                           sodium β alumina, and measurement made by

                           complex admittance method.

equilibration (presumably due to very slow electron diffusion). From these results and total conductivity values one can compute the electronic transference number t_e over this temperature range. Figure 10 shows the variation of the electronic transference number for single crystalline silver β alumina with temperature. It is obvious that an extrapolation of these data to lower temperatures indicates that the β alumina phase should have an extremely low electronic conductivity at temperatures at which its high ionic conductivity makes it a very interesting electrochemical transducer.

                      Fig. 10. Temperature dependence of the electronic

                                transference number, silver β alumina.

  4.3. RANGE OF APPLICABILITY

     It was pointed out earlier that the range of thermodynamic conditions over which a solid electrolyte can be beneficially used can be limited by two general types of problems, the appearance of an appreciable component of electronic conduction, or what might be referred to as chemical instability with respect to interaction with adjacent phases or structural changes such as phase transformations.

     Information concerning the thermodynamic conditions under which solid electrolytes are usable and have sufficiently low values of electronic transference numbers has been compiled by Patterson [35,36], as an extension of an approach initiated by Schmalzried [37,38]. Such information is included in figure 11 for β alumina and several of the common solid electrolytes. As pointed out by Patterson, reliable information of this type is only available for a relatively few materials. These fall into two general groups, the fluorite structure oxides, which are good conductors for oxygen ions and are generally useful only above about 700 °C, and a group of halides, primarily the silver and copper families. These halides have low melting points and tend to be relatively unstable, reactive and hard to handle. They are only useful under limited conditions between about 150 and 450 °C. Thus the roster of available solid electrolytes that can be used as electrochemical transducers has been quite limited until recently. Essentially only three ions could be considered, silver, copper and oxygen, and each of these over only limited temperature and thermodynamic ranges.

     Two important changes have occurred in the solid electrolyte business in the last few years. A group of ternary silver salts, generally related to the a AgI structure, have been discovered, and the β aluminas have appeared. This first group includes materials such as Ag₃SI and RbAg₄I₅ that have very high values of ionic conductivity to remarkably low temperatures. They have attracted a lot of attention as possible battery components, and a good review of much of this work has recently been presented by Owens [9].

     Although these materials have impressive values of ionic conductivity at low temperatures, one should not have too much enthusiasm concerning their potential use as electrochemical transducers because all present members of this group are only good conductors for

                     Fig. 11. Electrolytic conduction domains for several

                               common solid electrolytes and β alumina.

one ion, silver. Also, they tend to have relatively poor thermodynamic stability.  As an example of this latter point, the material Ag₃SI is apparently not sufficiently ionic (t_e > 0.01) in contact with iodine at 25 °C to be very usable as a solid electrolyte. Also, their general structural instability is indicated by the fact that a number of them undergo phase transformations at quite low temperatures. Some examples of this are shown in table 3.

     In contrast to these limitations, the stability and scope of apparent applicability of the β aluminas is very impressive. This phase is essentially an oxide ceramic with a rigid structural skeleton. It is mechanically very stable, melting incongruently at about 2000 °C [39]. We shall not discuss the available information concerning either its structure or its various other properties here, however, as such information, as well as discussions of possible transport mechanisms, can be found in a number of other places [24-27, 29, 39-43].

     The chemical stability of the β alumina phase is also very impressive. This phase is apparently stable at temperatures in the vicinity of 300 °C and lower in contact with the alkali metals. This is equivalent to being in equilibrium with extremely low oxygen partial pressures.

     We should hasten to point out, of course, that we are not talking about true equilibrium in this respect but practical noninteraction, or if you will, "selective equilibrium". In materials like β alumina, the oxide structural skeleton is apparently stable enough that one can treat it as an inert matrix or framework within which the M cations can readily move about in response to various forces and achieve their own version of equilibrium.

     Experiments upon silver β alumina [26] between 600 and 800 °C showed that there was no apparent influence of oxygen partial pressure in the range from 0.2 to 10^-24 atm. upon the ionic conductivity of this phase. The indications [26] that the β alumina phase has unusually low electronic conductivity and its apparent lack of oxygen pressure dependence below about 750 °C also show the broad range of its applicability.

     Perhaps the most important feature of the β aluminas is the fact that this phase can act as a transducer for a whole new set of ions for which no satisfactory transducer was previously available. Instead of being able to work with just silver, copper, and oxygen, the

                                          Table 3

                       Examples of Solid Ionic Conductors that have

               Phase Transformations at Relatively Low Temperatures [9,44]

               Material                            Transition Temperature

               CuBr                                   470, 420 °C

               CuI                                         400 °C

               Ag3SI                                        235 °C

               AgI                                          144 °C

               Cu2HgI4                                      67 °C

               Ag2HgI4                                      50 °C

               [C5H5NH]Ag5I6                                50 °C

               KAg4I5                                      -136 °C

               RbAg4I5                                    -155 °C

solid state electrochemistry community now has a much wider range of available species with which to deal. Although well defined transport measurements have only been made on β aluminas containing silver, sodium, potassium, and thallium, it has been demonstrated that this phase can also contain Rb+, Cu+, Li+, NH4+, In+, NO+, Ga+, and H30+ ions [29], and it is reasonable to expect it to be usable as a transducer for some, if not all of those as well. The ability to exchange one type of cation for another by equilibration techniques [1] or in some cases by electrochemical pumping [25], adds a new degree of freedom to the materials synthesis problem.

5. SOME APPLICATIONS

     Although, as mentioned already, most of the work that has been done by the use of solid electrolytes as electrochemical transducers has involved either oxide, copper- or silver-containing systems, one begins to see the use of the β alumina family for such purposes. For example, Belton and Morzenti [45] reported the use of sodium β alumina for thermodynamic studies of liquid sodium-lead alloys, and Gupta and Tischer [46] employed this phase for measurements of the sodium-sulfur system. Likewise, Hsueh and Bennion [47] have used this material to make emf measurements of the sodium activity in liquid sodium-mercury alloys at 30 °C.

     Measurements in our laboratory have indicated that single crystal potassium β alumina can be used as a transducer to evaluate the difference in potassium activity between two solids. In this case, a difference in potassium activity of 300 mV was found at 500 °C between two samples (x values of 0.2 and 0.33) of potassium tungsten bronze, whose nominal formula is K_xWO3. These bronzes, which are mixed conductors, as mentioned earlier, were prepared by electrolytic growth from molten salts, as described elsewhere [48]. In addition to being the first use of β alumina for electrochemical measurements upon solids, this is the first time that successful thermochemical measurements have been made on a tungsten bronze. Previous attempts [49,50] have been unsuccessful, and it was assumed that some kind of alkali ion-deficient surface layer was an inevitable structural feature of these phases.

6. SUMMARY

     In this paper we have endeavored to indicate that the β alumina phase represents a new departure in solid electrolytes. Enough information is now available about its inherent ionic conductivity, electronic transference number, and thermodynamic stability to make it reasonable to expect that it and related materials can be used in a wide variety of scientific and perhaps engineering applications as an electrochemical transducer for a group of important species not heretofore measurable and controllable.

     β alumina and similar rigid framework materials also represent a major change in another sense. Heretofore, all useful solid electrolytes were expected to attain thermodynamic equilibrium with their environment. In these materials, however, the mobility of one constituent within the structure is so much greater than that of the others that it is quite realistic to think in terms of selective equilibrium for only certain species within an essentially inert crystalline environment. This has many potential advantages, not the least of which involves mechanical properties.

     A further unusual and particularly useful characteristic of this class of materials is the ability that they afford for the synthesis of different solid electrolytes themselves. The technique of ion exchange within solids means that one can think in terms of preparing a material, or perhaps even a device, with one composition, and by use of ion exchange methods, convert it to something else in situ.

     Because of these factors, we contend that β alumina truly represents a first step across a vast new frontier.

7. ACKNOWLEDGEMENT

     Work in this area at Stanford has been supported by the Office of Naval Research, the Environmental Protection Agency, and the Advanced Research Projects Agency (through Stanford's Center for Materials Research).

8. REFERENCES

[1] Yao, Y. F. Y..and Kummer, J. T., J. Inorg. Nucl. Chem. 29, 2453 (1967).

[2] Radzilowski, R. H., Yao, Y. F. and Kummer, J. T., J. Appl. Phys. 40, 4716 (1969).

[3] Weber, N. and Kummer, J. T., Proc. Ann. Power Sources Conf. 21, 37 (1967).

[4] Foley, R. T., J. Electrochem. Soc. 116, 161 (1969).

[5] Hull, M. N., Energy Conversion 10, 215 (1970).

[6] Mrgudich, J. N., "Solid Electrolyte Batteries," Encyclopedia of Electrochemistry,

      Reinhold, New York, p. 84 (1964).

[7]  Takahashi, T., Denki Kagaku, 36, 402 (1968).

[8] Takahashi, T., Denki Kagaku, 36, 481 (1968).

[9] Owens, B. B., Advances in Electrochemistry and Electrochemical Engineering 8, 1 (1971).

[10] Cairns, E. J. and Shimotake, H., Science 164, 1347 (1969).

[11] Jasinski, R., High Energy Batteries, Plenum Press (1967).

[12] U. S. Department of Commerce Report, "The Automobile and Air Pollution," (1967).

[13] Sudworth, J. L. and Dugdale, I., Power Sources 2, 547 (1968).

[14] Sudworth, J. L. and Hames, M. D., Power Sources 4, 1 (1970).

[15] Schmalzried, H., Thermodynamics and Atomic Transport in Solids, Int. Atomic Energy

      Agency, Vienna (1965).

[16] Wagner, C., J. Chem. Phys. 21, 1819 (1953).

[17] Kiukkola, K. and Wagner, C., J. Electrochem. Soc. 104, 308 (1957).

[18] Kiukkola, K. and Wagner, C., J. Electrochem. Soc. 104, 379 (1957).

[19] Wagner, C., Advances in Electrochemistry and Electrochemical Enginering, 4, 1 (1966).

[20] Raleigh, D. 0., Prog. in Solid State Chem. 3, 83 (1967).

[21] Alcock, C. B., ed., Electromotive Force Measurements in High-Temperature Systems, Inst.

      of Mining and Metallurgy, London (1968).

 [22] Wagner, C., Z. physik. Chem. B21, 25 (1933).

 [23] Wagner, C., Proc. Int. Comm. Electrochem. Thermo. Kinetics (CITCE) 7, 361 (1957).

 [24] Rice, M. J. and Roth, W. L., "Ionic Transport in Super Ionic Conductors," to be published

      in J. Solid State Chem. (1972).

 [25] Whittingham, M. S., Helliwell, R. W. and Huggins, R. A., U. S. Government Res. and Devel.

      Rept. 69, 158 (1969).

 [26] Whittingham, M. S. and Huggins, R. A., J. Electrochem. Soc. 118, 1 (1971).

 [27] Whittingham, M. S. and Huggins, R. A., J. Chem. Phys. 54, 414 (1971).

 [28] Kummer, J. T., personal communication.

 [29] Kummer, J. T., "β Alumina Electrolytes," to be published in Progress in Solid State

      Chemistry, 7, (1972).

 [30] Nakagawa, Y., unpublished work at Stanford (1971).

 [31] Bauerle, J. E., J. Phys. Chem. Solids 30, 2657 (1969).

 [32] Wagner, C., Z. Elektrochem. 60, 4 (1956).

 [33] Wagner, J. B. and Wagner, C., J. Chem. Phys. 26, 1597 (1957).

 [34] Patterson, J. W., Bogren, E. C. and Rapp, R. A., J. Electrochem. Soc. 114, 752 (1967).

[35] Patterson, J. W., in The Physics of Electronic Ceramics, ed. by L. L. Hench and D. B.

     Dove, Marcel Dekker, Inc., New York (1971).

[36] Patterson, J. W., J. Electrochem. Soc. 118, 1033 (1971).

[37] Schmalzried, H., Z. Elektrochem. 66, 572 (1962).

[38] Schmalzried, H., Z. physik. Chem. N.F. 38, 87 (1963).

[39] DeVries, R. C. and Roth, W. L., J. Am. Ceram. Soc. 52, 364 (1969).

[40] Demott, D. S. and Hancock, P., Proc. British Ceramic Soc. 19, 193 (1971).

[41] Roth, W. L., "Stoichiometry and Structure of the Super Ionic Conductor Silver Β-

     Alumina," General Electric Report No. 71-C-132 (1971).

[42] Sato, H. and Kikuchi, R., J. Chem. Phys. 55, 677 (1971).

[43] Bettman, M. and Peters, C. R., J. Phys. Chem. 73, 1774 (1969).

[44] Geller, S. and Owens, B. B., "Silver Ion Site-Distribution, Structure and Conductivity

     of the Solid Electrolyte Pyridinium Hexaiodopentaargentate, [C₅H₅NH]Ag₅I₆, Between -30

     and 125 °C," to be published.

[45] Belton, G. R. and Morzenti, P. T., J. Metals 22, No. 12, 26A (1970).

[46] Gupta, N. K. and Tischer, R. P., J. Electrochem. Soc. 117, 125C (1970).-

[47] Hsueh, L. and Bennion, D. N., J. Electrochem. Soc. 118, 1128 (1971).

[48] Whittingham, M. S. and Huggins, R. A. , "Electrochemical Preparation and Characteriza-

      tion of Alkali Tungsten Bronzes, MXW03," to be published in the Proceedings of the 5th

      Materials Research Symposium, Solid State Chemistry, National Bureau of Standards, (1971).

[49] Swanson, A. B., D. Phil. Thesis, Oxford University (1968).

[50] Koch, D. F. A. and Becker, H., Personal communication quoted by G. H. Taylor, J. Solid

      State Chem. 1, 359 (1969).

DISCUSSION

     G. K. Johnson: I guess this question is for either you or Dr. W. L. Roth. Would you comment on what size crystals can be grown of this material and what techniques are used?

     R. A. Huggins: Walter, why don't you answer that?

     W. L. Roth: Most of the work was with crystals obtained from the Carborundum Corporation. The crystals were frequently 1 or more centimeters in diameter, but only one or two-tenths of a millimeter thick. They are mica-like and the quality of thick individuals is poor. We have grown crystals in the laboratory that were a bit better in perfection and thickness, but only one or two millimeters in size.

     G. K. Johnson: Well, what's the general method that is used for producing these?

     W. L. Roth: We passed current between carbon electrodes inserted in a large mass of sodium carbonate and A1203. The melting point is around 2000 °C and the materials react and crystals of β-A1203 appear to grow from the melt.