How are ionic and electronic conductivity measured? 2/4-terminal, EIS and temperature sweep
1 Theory
Conductivity and carriers
Electrical conductivity σ = Σ n_i·q_i·µ_i is the product of carrier concentration and mobility; its unit is S/cm. Metals (10⁴–10⁶ S/cm) conduct by electrons, electrolytes and solid ionic conductors (10⁻⁸–10⁻¹ S/cm) by ions, semiconductors and mixed conductors by both. The temperature dependence distinguishes the mechanism: in metals σ falls with temperature, in ionic and semiconductors it rises in Arrhenius (σT = A·exp(−E_a/kT)) or VTF (polymer electrolytes) form.
Two-terminal, four-terminal and van der Pauw
In a two-terminal measurement contact and cable resistances add to the sample resistance; negligible on high-resistance samples (solid electrolytes, ceramics), dominant on low-resistance samples (metals, carbon, electrode composites). In a four-terminal (Kelvin) measurement the current is driven through the outer terminals and the voltage is read at the inner terminals without drawing current; contact resistance is eliminated. The four-point probe (equally spaced, with correction factor) gives the sheet resistance (Ω/sq) of thin films and plates; the van der Pauw method yields the same result on arbitrarily shaped thin samples with four edge contacts.
Ionic conductivity by EIS
On an ionic conductor pressed between blocking electrodes (Au, Pt, stainless steel) EIS shows a bulk semicircle (R_b‖C_geo) at high frequency, then the grain-boundary semicircle and at low frequency the electrode polarisation (capacitive tail). σ = L/(R_b·A). With reversible electrodes (e.g. Li|SE|Li) the interface resistance and Li transference number are measured; the Bruce–Vincent method combines DC polarisation with EIS. Dielectric representations (ε′, tan δ, modulus M″) present relaxations and permittivity through a separate window.
Temperature sweep and sample preparation
From spectra taken in temperature-controlled holders (room temperature to 1000 °C) the Arrhenius plot gives the activation energy; bulk and grain-boundary E_a may differ. Pellet density, electrode contact (sputtering/paint), thickness measurement and humidity control determine the uncertainty of the results; the atmosphere (air, N₂, dry) must be reported for every measurement.
2 Application in measurement
On electronic conductors DC 4-terminal measurement excludes the contact resistance; on ionic conductors AC (EIS) is required because of blocking electrodes: the high-frequency arc in the Nyquist plot gives the bulk resistance, followed by grain boundary and electrode polarisation (Irvine-Sinclair-West 'brick-layer' model). The resistance is converted to conductivity with the cell constant (L/A).
A temperature sweep gives the activation energy by an Arrhenius plot; the ITS-e (-40…150 °C) and HTF-1100 (…1100 °C) allow measurement in a controlled atmosphere with the CESH-e/HTSH-1100 holders. The MTZ-35 covers 10 µHz – 35 MHz.
On thin films and coatings the sheet resistance (Ω/sq) is measured with a four-point probe (Smits correction factors); the Entek FPP 510 (temperature-controlled) and FPP 630T (touch screen, 10 mm probe) are domestic auto-ranging solutions.
Key equations
σ = L/(R·A); Rs = (π/ln2)·(V/I)·k (four-point probe)
3 Applicability
Where it applies
- Solid-electrolyte and ceramic development, polymer/gel electrolytes, conductive-filler composites and thin films, textile and coating conductivity, quality control.
Limits and caveats
- On mixed conductors (electron + ion) EIS alone cannot separate the contributions; blocking/reversible electrode combinations and DC polarisation are needed.
- On porous/rough pellets the geometric area is uncertain; absolute σ requires a density correction.
4 What did the application notes find?
- Material Science AN1 — Shows the measurement of the impedance of a YSZ ceramic against temperature with the high-temperature set-up, the bulk/grain-boundary separation and the calculation of the activation energy from the Arrhenius plot.
- Material Science AN2 — Reviews the principles of conductivity measurement — carrier types, two/four-terminal, geometry corrections, AC/DC methods — and gives a decision framework for method selection.
- Material Science AN3 — Shows the comparison with the literature of the conductivity measured on an electronically conducting sample by DC (four-terminal) and AC (EIS) methods; that the two methods agree and the error created by contact resistance in two-terminal measurement.
5 Which instruments perform this measurement?
References
- article J. T. S. Irvine, D. C. Sinclair, A. R. West. Electroceramics: Characterization by Impedance Spectroscopy. Adv. Mater. 2, 132–138, 1990. doi:10.1002/adma.19900020304
- article F. M. Smits. Measurement of Sheet Resistivities with the Four-Point Probe. Bell System Technical Journal 37, 711–718, 1958. doi:10.1002/j.1538-7305.1958.tb03883.x
- article L. B. Valdes. Resistivity Measurements on Germanium for Transistors. Proc. IRE 42, 420–427, 1954. doi:10.1109/JRPROC.1954.274680