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3 – Transport in ionic solids
1. Write the equation for cerium substituted by gadolinia in ceria. What is the
point of this substitution?
2. a. Graph the product DT as a function of temperature in Arrhenius coordinates.
b. Determine the activation energy for ionic diffusion in gadolinia-doped
ceria in kJ mol
−1
and in eV.
3. What are the units of electric mobility of a charge carrier?
4. Assuming that 50% of the vacancies are mobile, calculate the diffusion
coefficient, the electric mobility, and the conductivity at 800 °C.
Data
Lattice parameter for ceria in the temperature range considered
a = 5.426 A c .
Exercise 3.12 – Electrical conductivity of solid vitreous solution
(SiO 2 ) 1−x (Na 2 O) x
Consider the following electrochemical chain:
O 2 (P),Pt / (1 − x 1 ) SiO 2−x 1 M 2 O / (1 − x 2 ) SiO 2−x 2 M 2 O / Pt,O 2 (P)
GαH
G1H
G2H
Gα ′ H
in which the phases G1H and G2H are fused silica glass SiO 2 with different fractions x 1 and x 2 of an alkali metal oxide M 2 O. P denotes the oxygen partial
pressure, which is the same at both terminals of the chain. The phases GαH
and Gα ′ H consist of platinum Pt in contact with oxygen.
1. Given that the glasses are conducting due to the M
+
cations, express the
voltage between G1H and G2H as a function of the chemical potential of the M
+
ions in G1H and G2H.
2. Assuming that the temperature is sufficiently high to establish the equilibrium
2
1
O 2(g) + 2e GPtH m O
2−
(glass)
which we may also write in the form
2
1
O 2(g) + 2M
+ + 2e GPtH m M 2 O
give the expression for the emf ΔE at the chain terminals as a function of
the thermodynamic activity a M 2 O of the alkali-metal oxide in G1H and G2H.
3 – Transport in ionic solids
1. Write the equation for cerium substituted by gadolinia in ceria. What is the
point of this substitution?
2. a. Graph the product DT as a function of temperature in Arrhenius coordinates.
b. Determine the activation energy for ionic diffusion in gadolinia-doped
ceria in kJ mol
−1
and in eV.
3. What are the units of electric mobility of a charge carrier?
4. Assuming that 50% of the vacancies are mobile, calculate the diffusion
coefficient, the electric mobility, and the conductivity at 800 °C.
Data
Lattice parameter for ceria in the temperature range considered
a = 5.426 A c .
Exercise 3.12 – Electrical conductivity of solid vitreous solution
(SiO 2 ) 1−x (Na 2 O) x
Consider the following electrochemical chain:
O 2 (P),Pt / (1 − x 1 ) SiO 2−x 1 M 2 O / (1 − x 2 ) SiO 2−x 2 M 2 O / Pt,O 2 (P)
GαH
G1H
G2H
Gα ′ H
in which the phases G1H and G2H are fused silica glass SiO 2 with different fractions x 1 and x 2 of an alkali metal oxide M 2 O. P denotes the oxygen partial
pressure, which is the same at both terminals of the chain. The phases GαH
and Gα ′ H consist of platinum Pt in contact with oxygen.
1. Given that the glasses are conducting due to the M
+
cations, express the
voltage between G1H and G2H as a function of the chemical potential of the M
+
ions in G1H and G2H.
2. Assuming that the temperature is sufficiently high to establish the equilibrium
2
1
O 2(g) + 2e GPtH m O
2−
(glass)
which we may also write in the form
2
1
O 2(g) + 2M
+ + 2e GPtH m M 2 O
give the expression for the emf ΔE at the chain terminals as a function of
the thermodynamic activity a M 2 O of the alkali-metal oxide in G1H and G2H.