Henrik Bentzer

NorFERM 2008

The EMF technique

Outline

• The definition of transport numbers and why they are interesting

• The basics of the EMF method

• A typical EMF setup

• EMF measurements on proton conductors

• Pitfalls and problems

• Corrections for electrode polarisation resistance: When are they needed and how are they made

• Hydrogen isotopes, complimentary methods

Ionic conducting oxides

• Numerous oxides are known to conduct oxide ions (e.g. YSZ and CGO) or protons (e.g. acceptor doped strontium cerates and lanthanum niobate).

• All materials have some component of electronic conductivity, ranging from minor to dominating.

• Ionic conducting ceramics may find use in many different fields, such as fuel cells, membranes, sensors etc.

• Wether or not electronic conductivity is desired depends on the intended use of the material

The transport number

• The transport number for species i is defined as

• For example, the oxide-ion transport number in an oxide-ion conducting oxide is

• The sum of all transport numbers equals 1

• For use in fuel cell electrolytes, sensor applications etc., ionic conductivity should be as pure as possible, that is, the transport number should be as close to unity as possible under applicable conditions, to avoid current leaks.

ii

tot

t

OO

O e

t

Ambipolar transport

• In other applications, such as membranes and electrode materials, mixed ionic electronic conductivity (MIEC) is desireable.

• The (non-galvanic) transport of oxygen or hydrogen through a membrane material is governed by the so calledambipolar conductivity.Taking a mixed proton/electronconductor as an example, the ambipolar conductivity is

which is maximised when

H eamb

H e

0.5H e

The electromotive force technique

• The EMF technique for transport number determination is based on open cell voltage measurements on a sample equipped with two reversible electrodes and subjected to a gradient in chemical potential.

The setup

V

Sample

Electrodes

Thermocouple

Gold seals

Platinum wires

Spring-loaded alumina hood

Alumina tubing

How it works: The simple equations

• What ”creates” the voltage? The Nernst equation:

• What we measure:

• The maths part:

2

1

lnNernst

pRTE

nF p

lnII

th i iI

RTE t d p

nF

thavg

Nernst

Et

E

How it works: A more formal derivation

• The flux and partial current density of a species i in an electrochemical potential gradient are:

• The net current density is the sum of all partials:

• Assuming the sample is connected to an external circuit, the following expression for the electric potential is achieved:

2i i

i i i i i

i

dµ dj z e i z ej

dx dxz e

2k k

tot kk k

dµ di z e

dx dxz e

tot k k

ktot k

i t dµd

dx z e dx

• Since chemical potentials for charged species are not well defined, corresponding neutral species and electrons are used instead:

• We can now integrate over the sample thickness:

• Under open circuit conditions, using equal, intert electrodes, we get:

1tot n n e

ntot n

i t dµ dµd

dx z e dx e dx

1II II II IItot n

n entot nI I I I

i td dx dµ dµ

z e e

IIn

nn nI

tE dµ

z e

• For gaseous species:

• and so, for our one species i we get

• From here, we just need our assumption that ti is constant, and there we go.

0( ) ( ) lnn g n g nµ µ kT p

lnII

i ii I

kTE t d p

z e

Proton conductors – 3 conducting species

• In proton conducting oxides, the protons are usually created by water uptake in oxygen vacancies.

• Hydrogen and water will under the right circumstances react and form water:

• Using the equations derived above, the total voltage over a sample subjected to a gradient in hydrogen and/or oxygen partial pressure is

2 2 2½O H H O

2 2

2 2

2 2

1 1ln ln

4 2O H

th O HO H

p pRT RTE t t

F p F p

• The equilibrium between water, oxygen and hydrogen allows us to rewrite the EMF equation,

• Or

• which allows us to, theoretically, set up a number of experiments to determine transport numbers for oxide ions and protons under varying conditions

2 2

2 2

2 2

1 1ln ln

4 2O H O

th O H HO H O

p pRT RTE t t t

F p F p

2 2

2 2

2 2

1 1ln ln

2 2H O H

th O O HH O H

p pRT RTE t t t

F p F p

Different setups

Experimental setup

Gas, outer compartment

Gas, inner compartment,

constant

Gas, innercompartment,

variedConditions

Transport number

determined

A O2/N2 - O2

Dry, High pO2

tO

B H2/N2 - H2

Dry, Low pO2

tH

C O2/N2/H2O O2/H2O ratio (H2) O2, H2OWet, High

pO2

tO

D H2/N2/H2O H2/H2O ratio (O2) H2, H2OWet, Low

pO2

tH

E O2/N2/H2O O2 H2OWet, High

pO2

tH

F H2/N2/H2O H2 H2OWet, Low

pO2

tO

G N2/H2O - H2O Wet tO-tH

Gas setup

Air orH2/N2

Air orH2/N2

N2, Airor

H2/N2

Furnace

Inner tube

Sample

Exhaust

Oxide ion transport number measurements on SrCe0.95Y0.05O3

600°C

Oxide ion transport number measurements on SrCe0.95Y0.05O3

800°C

Difficulties with the method

• Samples need to be dense, and seals need to be gas-tight

• Impurities in gas mixtures must be avoided

• The gas mixture in each chamber should be uniform, that is, partial pressures at the sample surface should be the same as the known gas bulk partial pressures

• Thermo-emf’s must be either avoided or corrected for by reversing and averaging

• The electrodes should be reversible

The problem of electrode polarisation

• The assumption that the electrodes are completely reversible does not hold

• The figure shows the relative error made by ignoring the electrode polarisation resistance as calculated by Kharton and Marques.

1

1obsO

Nernst O e

REt

E R R

• Gorelov suggested using a variable resistor in parallel to the sample

• By making a series of voltage measurements while varying the resistance, a plot can be constructed and the electronic resistance found.

• An EIS measurement allows a determination of the polarisation resistance.

Approach I: The Gorelov method

1

1obsO

Nernst O e

REt

E R R

1 ONernst

obs e

R RE

E R

1 11Nernst

Oobs e b

ER R

E R R

Approach II: The Liu-Hu method

• Liu and Hu instead suggested using only impedance measurements, using both the high and low frequency limit measurements.

• The high frequency measurement gives the bulk resistance, Rb , while the low frequency measurement gives the total resistance of the cell, RT.

• Individual resistances can then be found as

1 1 1

t be O

meas b meas

Nernst T Nernst

R RR R

E R EE R E

( )

( )O eO e

b TO e O e

R R RR RR R

R R R R R

1 1

T b

meas b meas

Nernst T Nernst

R RR

E R E

E R E

Polarisation corrections for protonic conductors

1 1 1

O H

O O H Hmeas

O O H H e

E ER R R R

E

R R R R R

1 1 1

O H

O Hth

O H e

E ER R

E

R R R

The hydrogen isotope cell

• If a cell is set up with H2/H2O in one compartment and the same partial pressures of D2/D2O in the other, a voltage might develop over the cell.

• If the sample is a pure proton conductor, the voltage can be calculated as

• If the sample is an oxide ion conductor, a negative EMF will develop, due to the different equilibrium constants of the H2/H2O/O2 and D2/D2O/O2 reactions.

2 2 2

2

0 0 0 0 2 2

2 2

2 2ln

2 2

D D H H H D Dth

D H H

µ µ µ µ p uRTE

F F p u

Hydrogen isotope cell measurements

Alternative methods: Faradaic efficiency measurements

• Faradaic efficiency measurments are based on the same theory as the EMF technique, however, the measurements are performed on a closed circuit.

• A current is applied over the sample, and the flux of species i is measured

• The partial current density of species i is calculated from the flux, and divided by the total current to yield the transport number.

• Many of the problems from the EMF technique also apply to faradaic efficiency measurements.

Alternative methods: Hebb-Wagner technique

• The Hebb-Wagner technique utilizes conductivity measurements with and without blocking electrodes to find the transport number.

• For example, YSZ is a very pure oxide ion conductor, and can be used to block electrons in measurements of oxide-ion transport numbers.

• Obstacles include making a setup where complete blocking is actually achieved.

Alternative methods: Conductivity measurements

• Conductivity measurements, especially if a series of measurements where partial pressures of oxygen and water as well as temperature is varied will give you a lot of information.

• While conductivity measurements do not allow for very precise determination of the transport number, the extra information gained might be worth it.

Recommended reading (references)

• Basic equations:

C. Wagner, Z. Phys. Chem. (1933)T. Norby’s Defect Chemistry CourseD. P. Sutija, T. Norby and P. Björnbom, SSI 77 (1995)

• Electrode polarisation resistance

V. P. Gorelov, Elektrokhimiya, 24 (1988)M. Liu, H. Hu, J. Elchem. Soc. 143 (1996)V. V. Kharton, F. M. B. Marques, SSI 140 (2001)

• Hydrogen isotope cells

H. Matsumoto, K. Takeuchi, H. Iwahara, J. Elchem. Soc. 146 (1999)H. Matsumoto, K. Takeuchi, H. Iwahara, SSI 125 (1999)V. I. Tsidilkovski, SSI 162-163, (2003)