Exercises
217
1. Propose a model that explains all the defects supported by experimental
evidence. To do this, write the reactions involved and the corresponding
equilibrium constants.
2. Establish a relationship between the electrical conductivity, the constants
of formation of mobile structure defects, the hole mobility, and the oxygen
partial pressure.
3. a. By using least squares fitting and starting from the relationship obtained
in question 2, determine the expressions for the conductivity of Cu 2 O as
a function of oxygen partial pressure at 1 000 and 1 100 °C.
b. On a logarithmic scale, represent the experimental and theoretical conductivity of Cu 2 O as a function of oxygen partial pressure at 1 000 and
1 100 °C.
4. Based on the equations obtained for question 3(a) and considering a constant
hole mobility of 1 m
2
V
−1
s
−1
, calculate the values of
a. the equilibrium constant for the formation reaction for singly ionized
copper vacancies (V ′
Cu ) at 1 000 and 1 100 °C,
b. the equilibrium constant for the formation reaction for singly ionized
oxygen interstitials (O ′
i ) at 1 000 and 1 100 °C.
Exercise 5.5 – TiS 2 : insertion material
1. Define and explain the role of an insertion material (IM) in electrochemistry.
2. Give several examples, other than TiS 2 , of insertion materials for lithium
that are used for electrodes.
3. List three conditions necessary for inserting lithium into an insertion material.
4. Consider the following lithium battery:
Li / ionic Li
+
conducting electrolyte / TiS 2
a. Write the electrochemical reactions at the electrodes and the operating
reaction of the generator corresponding to a discharge rate x, and specify
the formal charges of the cations at the cathode.
We consider in what follows that insertion in TiS 2 is limited only by ions.
The insertion rate of lithium into TiS 2 as a function of the potential at
298 K is given in table 47.
217
1. Propose a model that explains all the defects supported by experimental
evidence. To do this, write the reactions involved and the corresponding
equilibrium constants.
2. Establish a relationship between the electrical conductivity, the constants
of formation of mobile structure defects, the hole mobility, and the oxygen
partial pressure.
3. a. By using least squares fitting and starting from the relationship obtained
in question 2, determine the expressions for the conductivity of Cu 2 O as
a function of oxygen partial pressure at 1 000 and 1 100 °C.
b. On a logarithmic scale, represent the experimental and theoretical conductivity of Cu 2 O as a function of oxygen partial pressure at 1 000 and
1 100 °C.
4. Based on the equations obtained for question 3(a) and considering a constant
hole mobility of 1 m
2
V
−1
s
−1
, calculate the values of
a. the equilibrium constant for the formation reaction for singly ionized
copper vacancies (V ′
Cu ) at 1 000 and 1 100 °C,
b. the equilibrium constant for the formation reaction for singly ionized
oxygen interstitials (O ′
i ) at 1 000 and 1 100 °C.
Exercise 5.5 – TiS 2 : insertion material
1. Define and explain the role of an insertion material (IM) in electrochemistry.
2. Give several examples, other than TiS 2 , of insertion materials for lithium
that are used for electrodes.
3. List three conditions necessary for inserting lithium into an insertion material.
4. Consider the following lithium battery:
Li / ionic Li
+
conducting electrolyte / TiS 2
a. Write the electrochemical reactions at the electrodes and the operating
reaction of the generator corresponding to a discharge rate x, and specify
the formal charges of the cations at the cathode.
We consider in what follows that insertion in TiS 2 is limited only by ions.
The insertion rate of lithium into TiS 2 as a function of the potential at
298 K is given in table 47.