ADVANCED MATERIALS Ferroelectric Ceramics Electroceramics : Grain Boundary Capacitances Ceramic Electrolytes Characterization by Surface Layers on Glasses Impedance Spectroscopy Ferromagnetic Ceramics By John T. S. Irvine,* Derek C. Sinclair,* and Anthony R. West * Electroceramics are advanced materials whose properties In order to characterize the microstructures and properties and applicationsdepend on the close control of structure, com- of electroceramics, techniques are required that can probe or position, ceramic texture, dopants and dopant (or defect) dis- distinguish between the different regions of a ceramic. Elec- tribution. Impedance spectroscopy is a powerful technique for tron microscopy with an analytical facility is, of course, the unravelling the complexities of such materials, which functions most direct method fo r both microstructural characteriza- by utilizing the different frequency dependences of the constit- tion and for determining compositional variations within a uent components for their separation. Thus, electrical inhomo- solid. Corresponding measurements of microscopic electri- geneities in ceramic electrolytes, electrode/electrolyte inter- cal properties are possible in principle, as shown by the ele- faces, surface layers on glasses, ferroelectricity, positive gant work of Dimos et al. on the effect of grain orientation temperature coefficient of resistance behavior and even ferri- mismatch on critical current densities in ceramic supercon- magnetism can all be probed, successfully, using this tech- ductor~.[~]Such measurements with miniature electrodes are nique. not easy, however. Decoration techniques such as cathodo- luminescence have been developed for direct observation of grain boundary potential barriers‘’]; these permit electrically 1. Introduction active grain boundaries to be seen although their properties are not actually measured. Electroceramics are high technology materials whose An alternative technique for measuring electrical proper- properties and hence, applications depend on a complex in- ties is impedance spectroscopy.t61 In this, AC impedance terplay of structural, processing and compositional vari- measurements are made over a wide range of frequencies and ables. The particular property of interest may be a bulk the different regions of the material are characterized ac- property of the crystals, in which case, fully dense ceramics cording to their electrical relaxation times or time constants. free from grain boundary phases are desired. Good examples Impedance spectroscopy is relatively easy to use and is appli- of this are ceramic electrolytes such as Na 8-alumina, Na,O. cable to a wide variety of materials and problems. It has - 8A1,03, used as an Na@ ion conducting membrane in undergone major developments recently with the availability Na/S batteries“] and yttria-stabilized zirconia, 0.9 ZrO,. of automatic equipment capable of spanning many decades 0.1Y,03, used as an oxide ion conducting membrane in of frequency in a single sweep. Long gone are the days of solid oxide fuel cells and oxygen sensors.[21 balancing R and C (or L) circuits using null methods, where Alternatively, the property of interest may relate specifi- it could take several minutes to obtain a single reading. cally to the grain boundaries in polycrystalline materials and The main purpose of this review is to show the usefulness perhaps, to differences in behavior between bulk and grain of impedance spectroscopy for the characterization of elec- boundary regions. Good examples are varistors, ceramic troceramics. It is fast becoming an essential technique in the materials that do not obey Ohm’s law.[31These are usually development of new and improved materials. This is primar- zinc oxide ceramics in which dopants such as Bi segregate to ily because it enables the overall electrical properties of a the grain boundaries. Instead of a linear, Z/V, Ohm’s law material to be separated into their component parts, which response, the current is given by I CL V”where “a” is typically can then be systematically studied or modified. in the range 5-50. Because of the dramatic increase in cur- rent with voltage, varistors are used in voltage surge protec- tion devices. Varistor action is far from completely under- 2. Impedance Spectroscopy stood but is, undoubtedly, associated with the grain boundary regions of the ceramic. 2.1. Theory [*I Prof. A. R. West, Dr. J. T. S. Irvine, Dr. D. C. Sinclair Department of Chemistry, University of Aberdeen In impedance spectroscopy, the impedance of a sample is Meston Building, Meston Walk, Old Aberdeen AB9 2UE (Scotland) measured over a wide range of frequency, typically lo-’ to 132 0 VCH Verlagsgesellschaft mbH, 0-6940 Weinheim. 1990 093S-9648~90/0303-0132$02.SOjO Adv. Mater. 2 (1990) No. 3 A. R. West et al./Impedance Spectroscopy ADVANCED MATERIALS lo7 Hz. Impedances usually have both resistive and reactive intragrain, or bulk and intergrain, or grain boundary re- (capacitive/inductive) components, both of which must be gions. A typical case is shown in Figure 1a for the oxide ion determined. This can be achieved in various ways; one is to conductor Ca,,A1,,0,, .[’I Impedance data are presented in apply an alternating voltage across a sample and a standard the form of imaginary, Z” (capacitive) against real, 2’ (resis- resistor which are in series. The in- and out-of-phase compo- tive) impedances. Each parallel RC element (two in Fig. 1) nents of the voltage across the sample are then measured. gives rise to a semicircle (ideally) from which the component Dividing these components by the magnitude of the current R and C values may be extracted. R values are obtained from gives the resistive and reactive components of the the intercepts on the Z’ axis, as shown; Cvalues are obtained impedance. The measurements are repeated as a step-wise by applying Equation 2 to the frequency at the maximum of function of frequency. each semicircle. In this particular case, the two capacitance Different regions of a ceramic sample are characterized by values are determined to be - 1 x F and 4 x lo-’ F a resistance and a capacitance, usually placed in parallel. The and the corresponding resistances 0.45 Mohm and 1.15 characteristic relaxation time or time constant, 2, of each Mohm. ‘parallel RC element’ is given by the product of R and C Having obtained values for these R and C components, (Equation 1). the next stage is to assign them to regions of the sample. The assignment is based on the magnitudes of the capacitances (Table 1). For a parallel plate capacitor with area A, separa- tion 1 between the plates and a medium of permittivity E‘ between the plates, the capacitance is given by Equation 3. In the frequency domain, RC elements are separable due to the relation shown in Equation 2 which holds at the fre- A quency of maximum loss, om,,, in the impedance spectrum. C=c‘e-01 (3) From the impedance spectrum, it is therefore usually possi- ble to identify different RC elements and assign them to where e, is the permittivity of free space, 8.854~ appropriate regions of the sample. The values of the individ- F cm-’. For a material with unit cell constant (i.e. ual R and C components may then be quantified. Let us now 1/A = 1 cm-’) and a typical permittivity of - 10, a capaci- see some practical examples of data and their interpretation. tance value of - 1 x lo-” F is expected. Thus, this is a A common type of impedance spectrum for electroceram- typical value for the bulk capacitance of a sample. The high ics shows the presence of two distinct features attributable to frequency semicircle in Figure 1 has a capacitance of this John 7: S. Irvine (left) has B.Sc. Chemical Physics (Edinburgh 1981) and Ph.D. (Ulster 1986) degrees. He came to Aberdeen in 1985 where he has been researchfellow, Royal Society of Edinburgh Research Fellow and now, Lecturer in chemistry. His Ph.D. topic was on photoelectrochemistry and his research interests have expanded to include high- ceramic superconductors, solid electrolytes and solid state electrochemistry. Derek C. Sinclair (center) obtained his B.Sc. (1986) and Ph.D. (1989) from Aberdeen University and is currently a Research Fellow in the Chemistry Department. His Ph.D. topic was on the characterization of electroceramics and he is currently researching into high- T, superconductors. Anthony R. West (right) has B.Sc. (Wales 1968), Ph.D. (Aberdeen 1971) and D.Sc. (Aberdeen 1984) degrees. He has been, successively, Lecturer, Senior Lecturer and Reader in chemistry and in f 989 was appointed to a personal professorship in Aberdeen. His research covers many aspects of solid state chemistry and ceramics, and he is author of about 180 research publications and the books ‘Solid State Chemistry and its Applications’ and ‘Basic Solid State Chemistry’. Adv. Mafer.2 (1990)No. 3 0 VCH Verlagsgesellschaf1 mbH. 0-6940 Weinheim,1990 093S-9648/90/0303-0133$02.50/0 133 ADVANCED A. R. West et al./Impedance Spectroscopy MATERIALS 0 8- GRAIN BOUNDARY, C-~X~O-~F 2':Mohm 4-C~1x10-12FBULK . - .J... *......i .. ** .&I ;t //LU ,04y100 I I , Fig. 2. Brickwork model of grain and grain boundary regions in a ceramic placed between metal electrodes. Rb Z', Mohm Rb*Rgb from the inverse relation between thickness and capacitance given by Equation 3. A wide variety of ceramic microstruc- tures occur in practice and it is found that the grain boundary capacitance usually lies in the range lo-" to lo-' F; the higher capacitances occur in materials that are well-sintered, with narrow intergranular regions. The lower capacitances are often found with poorly sintered samples that contain constriction resistances or narrow contacting 'necks', between grains.['] For the case in Figure 1, the grain boundary capacitance is quite large, indicating a well-sin- 1000 IT ( K-'l tered sample. Nevertheless, the overall resistance of these Fig.