106
3 – Transport in ionic solids
a. What phenomenon is responsible for this variation? Give a simple explanation for what happens.
b. Give the expression for the derivative d ΔE/dt as a function of the molar
fraction of silver, x
( )
Ag
2
, in compartment 2 and its derivative dx
( )
Ag
2
/dt.
Assume that the coefficient for the activity of silver in compartment 2
is constant.
3. Derive the expression for the electronic conductivity σ e of the glass as a
function of ΔE, d ΔE/dt, x
( )
Ag
2
, ℓ, S, and n T , where ℓ and S represent respectively the thickness and the area of the sample and n T is the total number of
moles of metallic atoms in compartment 2.
4. Compartment 2 contains a 10 mm
3
drop of mercury. The electromotive force
is 850 mV. We observe a drift of 10 mV per month. The atomic fraction of
silver is less than 6 # 10
−4
, which is its saturation value.
a. What is the upper limit of the electrical resistance?
b. What is the upper limit of the electronic transport number of the glass given
that the total conductivity is 2.2 # 10
−3
S cm
−1
? Assume ℓ/S = 0.1 cm
−1
.
Data
density of mercury: ρ Hg = 13 600 kg m
−3
molar mass of mercury: M Hg = 200 g mol
−1
Exercise 3.5 – Electrical properties of potassium chloride KCl
1. a. Give the reaction for doping KCl by BaCl 2 given that
2 the dominant disorder in KCl is Schottky pair,
2 barium substitutes for potassium.
b. Show that the doping leads to an increase in the cationic transport number t + . Neglect the mobility of Ba
2+
ions.
c. The solid solution obtained after doping has a NaCl-type structure. Denoting
its formula by (KCl) 1−x (BaCl 2 ) x , calculate the concentration in mol cm
−3
and in mol L
−1
of the potassium vacancies [V ′
K ] for x = 1.4 # 10
−4
. Given
the low value of x, we neglect the influence of BaCl 2 on the density and
on the molar mass.
Data
density of KCl: 1.984 g cm
−3
molar mass of KCl: 74.56 g mol
−1
3 – Transport in ionic solids
a. What phenomenon is responsible for this variation? Give a simple explanation for what happens.
b. Give the expression for the derivative d ΔE/dt as a function of the molar
fraction of silver, x
( )
Ag
2
, in compartment 2 and its derivative dx
( )
Ag
2
/dt.
Assume that the coefficient for the activity of silver in compartment 2
is constant.
3. Derive the expression for the electronic conductivity σ e of the glass as a
function of ΔE, d ΔE/dt, x
( )
Ag
2
, ℓ, S, and n T , where ℓ and S represent respectively the thickness and the area of the sample and n T is the total number of
moles of metallic atoms in compartment 2.
4. Compartment 2 contains a 10 mm
3
drop of mercury. The electromotive force
is 850 mV. We observe a drift of 10 mV per month. The atomic fraction of
silver is less than 6 # 10
−4
, which is its saturation value.
a. What is the upper limit of the electrical resistance?
b. What is the upper limit of the electronic transport number of the glass given
that the total conductivity is 2.2 # 10
−3
S cm
−1
? Assume ℓ/S = 0.1 cm
−1
.
Data
density of mercury: ρ Hg = 13 600 kg m
−3
molar mass of mercury: M Hg = 200 g mol
−1
Exercise 3.5 – Electrical properties of potassium chloride KCl
1. a. Give the reaction for doping KCl by BaCl 2 given that
2 the dominant disorder in KCl is Schottky pair,
2 barium substitutes for potassium.
b. Show that the doping leads to an increase in the cationic transport number t + . Neglect the mobility of Ba
2+
ions.
c. The solid solution obtained after doping has a NaCl-type structure. Denoting
its formula by (KCl) 1−x (BaCl 2 ) x , calculate the concentration in mol cm
−3
and in mol L
−1
of the potassium vacancies [V ′
K ] for x = 1.4 # 10
−4
. Given
the low value of x, we neglect the influence of BaCl 2 on the density and
on the molar mass.
Data
density of KCl: 1.984 g cm
−3
molar mass of KCl: 74.56 g mol
−1