Mixed Ionic–Electronic Conductors: Principles, Characterization, and Applications
Mixed ionic–electronic conductors (MIECs) are solids in which mobile ionic defects and electronic charge carriers both contribute significantly to transport. This combination makes them important in solid oxide fuel cells, oxygen-separation membranes, electrolysis cells, catalytic membrane reactors, and other electrochemical technologies.
Their defining feature is not simply high electrical conductivity. A useful MIEC must provide the appropriate ionic and electronic transport under the operating temperature and chemical environment, while maintaining chemical, structural, and mechanical stability.
1. What is a mixed ionic–electronic conductor?
In a purely ionic conductor, electrical current is carried predominantly by mobile ions or ionic defects. In an electronic conductor, current is carried by electrons and/or holes. A MIEC supports both types of transport to a meaningful extent.
For an oxide, the total conductivity can be expressed as:
\[ \sigma_{total} = \sigma_{ion} + \sigma_e + \sigma_h \]
where:
- \(\sigma_{ion}\) is the contribution from mobile ionic species, such as oxygen ions or protons.
- \(\sigma_e\) is the electronic contribution from electrons.
- \(\sigma_h\) is the electronic contribution from holes.
The relevant ionic species depend on the material and operating conditions. Oxygen-ion and proton conduction should not be assumed to occur simultaneously or with comparable magnitudes unless supported by evidence.
A material may be called a MIEC even when one contribution is larger than the others. The relative contributions are quantified through transport numbers.
2. Ionic and electronic transport numbers
The transport number of a charge carrier is its contribution to the total conductivity:
\[ t_i = \frac{\sigma_i}{\sigma_{total}} \]
For a simplified oxide containing oxygen ions, electrons, and holes:
\[ t_{O^{2-}} + t_e + t_h = 1 \]
If proton transport is also relevant, its contribution must be included:
\[ t_{O^{2-}} + t_{H^+} + t_e + t_h = 1 \]
These expressions assume that all relevant contributions have been identified and that the measured conductivity can be decomposed accordingly.
A high total conductivity does not necessarily indicate good ionic transport. For an oxygen-separation membrane, for example, electronic conductivity is needed to balance the ionic flux internally, but the oxygen-ion contribution must also be sufficiently high to sustain oxygen permeation.
Likewise, a material with high ionic conductivity but negligible electronic conductivity may require an external electronic circuit or a separate electronic phase to operate in a particular membrane configuration.
3. Defect chemistry behind mixed conduction
In many oxide MIECs, oxygen non-stoichiometry changes with oxygen chemical potential. Oxygen loss can be represented by:
\[ O_O^x \rightleftharpoons V_O^{\bullet\bullet} + \frac{1}{2}O_2(g) + 2e' \]
This reduction reaction generates oxygen vacancies and electrons. The electrons may be mobile or localized on transition-metal cations, depending on the electronic structure.
Under oxidizing conditions, oxygen incorporation can be written as:
\[ \frac{1}{2}O_2(g) + V_O^{\bullet\bullet} \rightleftharpoons O_O^x + 2h^{\bullet} \]
This is a useful formal reaction for a regime in which oxygen incorporation is compensated by hole formation. The dominant compensation mechanism is material-dependent; it should not be assumed that holes are always the only electronic response to oxidation.
The defect populations are constrained by mass-action relations and charge neutrality. For a simplified defect set:
\[ 2[V_O^{\bullet\bullet}] + [h^{\bullet}] = [e'] + [A_B'] \]
where \(A_B'\) represents a singly negatively charged acceptor defect. Other charged defects must be added when they are significant.
This is why a MIEC cannot be described by a single vacancy concentration alone. Ionic and electronic defect populations are coupled through thermodynamic equilibria.
For a deeper treatment of defect notation, oxygen loss, and charge neutrality, see Oxygen Vacancies and Defect Chemistry in Functional Oxides.
4. Why oxygen partial pressure matters
The oxygen partial pressure, \(p_{O_2}\), controls the oxygen chemical potential and can strongly influence defect concentrations. A material may show different dominant carriers in oxidizing and reducing atmospheres.
A common way to study this behavior is to measure conductivity as a function of oxygen partial pressure at fixed temperature. The data are often plotted as:
\[ \log(\sigma) \quad \text{versus} \quad \log(p_{O_2}) \]
The slope can help identify a possible defect regime. However, the interpretation depends on the assumed defect model, charge-neutrality condition, and whether the measured conductivity is dominated by ionic or electronic carriers.
A schematic qualitative picture is:
- In some reducing regimes, electron concentration increases as oxygen is removed.
- In some oxidizing regimes, hole concentration increases as oxygen is incorporated.
- Ionic conductivity may vary with oxygen non-stoichiometry, but its response also depends on vacancy mobility and defect association.
- Intermediate regimes may be controlled by dopant concentration or by a balance between different defects.
There is no universal conductivity-versus-\(p_{O_2}\) curve for all MIECs. A slope should never be assigned to a particular defect species without checking whether the corresponding assumptions are physically reasonable.
5. Chemical potential gradients and ambipolar transport
The defining application of many MIECs is the simultaneous transport of ionic and electronic charge under a chemical potential gradient.
For an oxygen-permeable membrane, oxygen is adsorbed and reduced at the high-oxygen-activity surface. Oxygen ions then move through the oxide lattice, while electronic charge is transported in the opposite direction to maintain charge balance. At the low-oxygen-activity surface, oxygen ions release electrons and recombine to form molecular oxygen.
The overall process can be represented as:
\[ O_2(g, high\ p_{O_2}) \rightarrow O_2(g, low\ p_{O_2}) \]
The membrane transports oxygen selectively without requiring a gas-phase pressure-driven flow through open pores, provided it is dense and free of leaks or pinholes.
The ionic and electronic fluxes are coupled. If either transport pathway is too slow, it can limit the overall oxygen permeation rate.
6. Oxygen permeation through dense ceramic membranes
A dense MIEC membrane can transport oxygen from one side to the other when an oxygen chemical potential gradient is imposed. In a simplified bulk-diffusion-controlled regime, the ambipolar conductivity is often written as:
\[ \sigma_{amb} = \frac{\sigma_{ion}\sigma_{e}} {\sigma_{ion}+\sigma_e} \]
Here, \(\sigma_e\) may represent the total electronic conductivity, including electrons and holes where appropriate.
This expression illustrates an important principle: the coupled transport is limited by the less conductive pathway. If electronic conductivity is much larger than ionic conductivity, then \(\sigma_{amb}\) approaches \(\sigma_{ion}\). If ionic conductivity is much larger, it approaches \(\sigma_e\).
The equation is a simplified description. Real membrane performance can also be limited by surface exchange, gas-phase mass transfer, microstructure, membrane thickness, and concentration polarization.
A commonly used conceptual decomposition is:
- Gas-phase transport to the membrane surface.
- Oxygen adsorption and surface exchange.
- Charge transfer and oxygen incorporation.
- Bulk ionic and electronic transport.
- Oxygen release at the permeate surface.
- Gas-phase removal of the permeated oxygen.
Improving bulk conductivity alone may not improve the measured permeation rate if surface exchange is rate-limiting.
7. Surface exchange and bulk diffusion
Two kinetic parameters are frequently used to describe oxygen transport in oxides:
- Chemical diffusion coefficient, \(D_{chem}\): describes the rate at which oxygen non-stoichiometry relaxes through the material under a chemical potential gradient.
- Surface exchange coefficient, \(k_{chem}\): describes the rate of oxygen exchange between the gas phase and the solid surface.
Their units are commonly \(m^2\,s^{-1}\) and \(m\,s^{-1}\), respectively, although reporting conventions should always be stated.
The characteristic time for bulk diffusion scales approximately as:
\[ \tau_D \sim \frac{L^2}{D_{chem}} \]
where \(L\) is a characteristic diffusion length. A corresponding surface-exchange timescale scales as:
\[ \tau_s \sim \frac{L}{k_{chem}} \]
The ratio of these timescales is related to the dimensionless Biot number for chemical transport:
\[ Bi = \frac{k_{chem}L}{D_{chem}} \]
The exact characteristic length and boundary conditions depend on sample geometry and the experiment. A small \(Bi\) generally indicates that surface exchange is slow relative to bulk diffusion; a large \(Bi\) indicates that bulk diffusion is more likely to dominate the relaxation.
Isotope exchange depth profiling and electrical conductivity relaxation (ECR) are established methods for investigating these parameters. Reliable analysis requires suitable sample geometry, controlled gas switching, temperature stability, and an appropriate diffusion model.
8. MIECs in solid oxide fuel cells and electrolysis cells
MIECs can be used as electrode materials in solid oxide fuel cells (SOFCs) and solid oxide electrolysis cells (SOECs).
In an SOFC, fuel oxidation and oxygen reduction occur at different electrodes. A conventional composite electrode may combine an ionic conductor with an electronic conductor to extend the electrochemically active region beyond the immediate electrolyte interface.
A MIEC electrode can, in principle, transport both ions and electrons through the same phase. This can extend the reaction zone into the electrode, provided that gas access, surface reaction kinetics, and the relevant transport pathways are adequate.
In an SOEC, the direction of the electrochemical reaction is reversed by applying an external voltage. The electrode must remain active and stable under the corresponding oxygen chemical potentials and gas compositions.
Important electrode design requirements include:
- Adequate ionic and electronic conductivity.
- High surface-exchange activity.
- Chemical compatibility with the electrolyte and interconnects.
- Thermal expansion compatibility.
- Resistance to coarsening, segregation, and phase decomposition.
- Stability under both oxidizing and reducing operating conditions, where applicable.
A high initial conductivity is not sufficient evidence of long-term electrode durability.
9. Protonic and oxygen-ion mixed conduction
Some oxides can support more than one ionic carrier. In humid atmospheres, oxygen vacancies may hydrate:
\[ H_2O(g) + V_O^{\bullet\bullet} + O_O^x \rightleftharpoons 2OH_O^{\bullet} \]
The resulting protonic defects may contribute to ionic conductivity. Depending on composition, temperature, oxygen partial pressure, and water-vapour pressure, electronic carriers and oxygen-ion defects may also contribute.
A material with protonic and electronic transport is sometimes described as a protonic–electronic mixed conductor. Its behavior should be evaluated under the actual humidity and gas composition of the intended device.
The presence of hydroxyl-related defects does not prove that proton transport dominates. Carrier-specific evidence is needed, and the measured total conductivity must be interpreted with the relevant defect equilibria.
See Proton-Conducting Oxides: Defect Chemistry and Hydrogen Applications for a focused discussion of hydration and proton transport.
10. How to characterize a MIEC
A convincing MIEC study should establish both the ionic and electronic contributions rather than infer them from total conductivity alone.
10.1 Conductivity under controlled oxygen partial pressure
Measure conductivity over a suitable range of temperature and oxygen partial pressure. Ensure that the sample reaches equilibrium at each condition and that the gas composition at the sample is known.
A four-probe configuration can reduce the influence of contact resistance, but it does not separate ionic from electronic current.
10.2 Electrochemical impedance spectroscopy
EIS can help distinguish bulk, grain-boundary, and electrode-related responses when the processes are sufficiently separated in frequency and have physically justified assignments.
Equivalent-circuit fits are not unique by themselves. Report the measurement geometry, electrode material, frequency range, perturbation amplitude, temperature, atmosphere, and fitting assumptions.
For a practical measurement and interpretation workflow, see Electrochemical Impedance Spectroscopy: A Practical Guide.
10.3 Ionic transport number
The ionic transport number can be investigated using suitable concentration-cell or electromotive-force methods, depending on the electrolyte, electrode reversibility, and gas conditions.
For an idealized oxygen concentration cell with reversible oxygen electrodes, the Nernst voltage provides a reference for the oxygen chemical potential difference. The measured open-circuit voltage can be compared with the ideal value, but electrode polarization, leakage, and non-equilibrium conditions must be considered.
A transport number should be obtained using a method whose assumptions are appropriate for the material and cell configuration.
10.4 Oxygen permeation measurements
For dense membranes, measure oxygen flux under a defined oxygen partial pressure gradient. Report membrane thickness, exposed area, temperature, feed and sweep gas compositions, flow rates, sealing method, and leak checks.
A non-zero oxygen flux is not sufficient by itself to establish intrinsic MIEC transport. Gas leakage through cracks, pores, or seals can mimic permeation. Dense microstructure and leak-tight sealing are essential controls.
10.5 Electrical conductivity relaxation
ECR follows the transient conductivity response after a rapid change in oxygen partial pressure. With a suitable model, the response can provide estimates of chemical diffusion and surface exchange coefficients.
The analysis must consider whether the sample is limited by bulk diffusion or surface exchange, and whether the conductivity is sufficiently sensitive to oxygen non-stoichiometry in the investigated regime.
10.6 Structural and chemical characterization
XRD can identify phase changes and structural evolution. TGA can quantify mass changes associated with oxygen non-stoichiometry under controlled conditions. Microscopy and elemental analysis can reveal microstructural degradation or segregation.
No single technique proves mixed conduction. The strongest case combines transport measurements with independent chemical and structural evidence.
11. Practical experimental workflow
A useful sequence for evaluating a candidate MIEC is:
- Confirm phase identity. Use XRD and complementary methods to check phase purity before transport measurements.
- Establish chemical stability. Expose the material to the intended atmospheres and temperatures; check for decomposition or irreversible reactions.
- Measure total conductivity. Use a suitable geometry and verify ohmic behavior and contact stability.
- Map oxygen-pressure dependence. Identify changes in conductivity and possible defect regimes at fixed temperature.
- Determine ionic contribution. Use an appropriate transport-number or electrochemical method.
- Evaluate oxygen exchange. Use permeation, isotope exchange, or conductivity relaxation as appropriate.
- Separate bulk and surface limitations. Vary sample thickness or geometry where possible and analyze the relevant characteristic times.
- Test cycling and durability. Repeat atmosphere and temperature cycles and examine phase and microstructure after testing.
- Report operating conditions completely. Include gas composition, flow, humidity, temperature, geometry, electrode details, and uncertainty.
12. Common mistakes in MIEC research
- Equating high total conductivity with high ionic conductivity.
- Assuming that oxygen vacancies automatically produce fast oxygen-ion transport.
- Ignoring electronic compensation when interpreting oxygen non-stoichiometry.
- Assigning a conductivity-versus-\(p_{O_2}\) slope without validating the defect model.
- Treating a dense membrane as leak-free without performing leak checks.
- Assuming bulk diffusion controls oxygen permeation when surface exchange may be limiting.
- Comparing permeation rates without accounting for membrane thickness and oxygen chemical potential gradient.
- Reporting fitted EIS components as uniquely identified physical processes without independent validation.
- Ignoring chemical expansion, thermal expansion mismatch, and long-term phase stability.
13. Key design principles
The design of a practical MIEC requires balancing several properties:
| Property | Why it matters |
|---|---|
| Ionic conductivity | Supports oxygen-ion or proton transport |
| Electronic conductivity | Maintains charge balance and enables coupled transport |
| Surface exchange activity | Controls gas–solid oxygen exchange |
| Chemical stability | Prevents decomposition under operating conditions |
| Thermal and chemical expansion | Limits mechanical stress and cracking |
| Microstructural stability | Maintains transport pathways over time |
| Compatibility | Reduces reactions with adjacent cell components |
The optimal material is application-specific. Oxygen-separation membranes, SOFC electrodes, and SOEC electrodes do not necessarily require the same balance of ionic conductivity, electronic conductivity, surface exchange, and chemical stability.
14. Key takeaways
Mixed ionic–electronic conductors enable coupled transport of ionic and electronic charge. Their performance is governed by defect equilibria, carrier mobility, oxygen chemical potential, surface exchange, and microstructure.
A meaningful MIEC assessment must distinguish total conductivity from ionic and electronic contributions. For membranes, both transport pathways are needed, and the slower pathway can limit oxygen flux. For electrodes, surface reaction kinetics and chemical compatibility can be as important as bulk conductivity.
The most reliable materials evaluation combines controlled-atmosphere electrical measurements, transport-number determination, oxygen exchange or permeation tests, and structural and chemical characterization.
Further reading
- J. A. Kilner and M. Burriel, “Materials for intermediate-temperature solid-oxide fuel cells,” Annual Review of Materials Research 44 (2014), 365–393.
- H. J. M. Bouwmeester and A. J. Burggraaf, “Dense ceramic membranes for oxygen separation,” in The CRC Handbook of Solid State Electrochemistry, CRC Press, 1997.
- S. J. Skinner and J. A. Kilner, “Oxygen ion conductors,” Materials Today 6 (2003), 30–37.
- J. A. Kilner, “Fast oxygen transport in acceptor doped oxides,” Solid State Ionics 129 (2000), 13–23.
- H. Tuller, “Ionic conduction in nanocrystalline materials,” Solid State Ionics 131 (2000), 143–157.
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