Exercises
21
Exercise 1.8 – Departure from stoichiometry of barium fluoride BaF 2
At high temperature, solid barium fluoride BaF 2 exhibits an atomic disorder
of the anionic Frenkel type. Consider a BaF 2 crystal placed in a container in
which we can vary the partial pressure of fluorine gas F 2(g) . Assume that the
entire system is at thermodynamic equilibrium.
1. Using Kröger-Vink notation, enumerate the various structure elements in
the crystal. For each case, give the real charge of the corresponding center.
2. Draw the Brouwer diagram log[i] = f(log P F 2 ) where [i] and P F 2 denote the
concentration of species i and the partial pressure of fluorine, respectively.
We shall consider successively the P F 2 domains corresponding to:
a. high P F 2 ,
b. low P F 2 ,
c. Intermediate P F 2 . For this domain, draw the diagram for the two following
cases:
2 ionic defects are dominant
Data
K AF = 10
−8
  K e = 10
−17
  K g = 10
−23
2 electronic defects are dominant
Data
K AF = 10
−17
  K e = 10
−8
  K g = 10
−23
Note – Assume that the fluoride ions occupy normal and interstitial positions.
3. The departure from stoichiometry of BaF 2(1+ε) can be expressed by the
quantity δ, which is defined by δ = |F ′ i | – |V
•
F |, where |F ′ i | and |V
•
F | are site
fractions.
a. Establish the expression relating δ to ε and |F ′
i | or |V
•
F |. Assume that each
crystal cell can accept only one interstitial anion.
b. Establish the law describing how δ varies with fluorine partial pressure
for the various domains of approximation given in question 2.