18
1 – Description of ionic crystals
that describes electric neutrality.
2 Give the sitoneutrality relations for the formula La 1−x Sr x MnO 3−x/2 .
Denote by [i] the site fraction occupied by species i, taking as reference sub-lattice A.
Exercise 1.3 – Sitoneutrality and expression of chemical formulas
The chemical formula describing a given solid solution of yttria-stabilized
zirconia can be written in the two following manners:
(ZrO 2 ) 1−x (Y 2 O 3 ) x and (ZrO 2 ) 1−y (YO 1.5 ) y
1. Find the relationship y = f(x).
2. Write the two formulas for x = 0.08.
3. For each case, calculate the number of cationic sites for one formula unit.
4. a. Write the formula (ZrO 2 ) 1−x (Y 2 O 3 ) x in the form Zr α Y β O γ V δ , expressing
α, β, γ, and δ as functions of x. V denotes an oxygen vacancy. Evaluate
the result for x = 0.08.
b. Write the formula (ZrO 2 ) 1−y (YO 1.5 ) y in the form Zr α Y β O γ V δ , expressing
α, β, γ, and δ as functions of y. Evaluate the result for x = 0.08.
Exercise 1.4 – Calculation of defect concentrations
Calculate the concentration C v in mol L
−1
of oxygen vacancies in the solid
solution (CeO 2 ) 1−x (CaO) x with x = 0.1.
Data
The solid solution crystallizes in a fluorite-type cubic structure.
The lattice parameter is 5.415 A c .
The dominant disorder in CeO 2 is of anionic Frenkel type and the calcium
substitutes for cerium.
Exercise 1.5 – Doping strontium fluoride
Anionic Frenkel disorder is the dominant ionic disorder in strontium fluoride
SrF 2 .
1 – Description of ionic crystals
that describes electric neutrality.
2 Give the sitoneutrality relations for the formula La 1−x Sr x MnO 3−x/2 .
Denote by [i] the site fraction occupied by species i, taking as reference sub-lattice A.
Exercise 1.3 – Sitoneutrality and expression of chemical formulas
The chemical formula describing a given solid solution of yttria-stabilized
zirconia can be written in the two following manners:
(ZrO 2 ) 1−x (Y 2 O 3 ) x and (ZrO 2 ) 1−y (YO 1.5 ) y
1. Find the relationship y = f(x).
2. Write the two formulas for x = 0.08.
3. For each case, calculate the number of cationic sites for one formula unit.
4. a. Write the formula (ZrO 2 ) 1−x (Y 2 O 3 ) x in the form Zr α Y β O γ V δ , expressing
α, β, γ, and δ as functions of x. V denotes an oxygen vacancy. Evaluate
the result for x = 0.08.
b. Write the formula (ZrO 2 ) 1−y (YO 1.5 ) y in the form Zr α Y β O γ V δ , expressing
α, β, γ, and δ as functions of y. Evaluate the result for x = 0.08.
Exercise 1.4 – Calculation of defect concentrations
Calculate the concentration C v in mol L
−1
of oxygen vacancies in the solid
solution (CeO 2 ) 1−x (CaO) x with x = 0.1.
Data
The solid solution crystallizes in a fluorite-type cubic structure.
The lattice parameter is 5.415 A c .
The dominant disorder in CeO 2 is of anionic Frenkel type and the calcium
substitutes for cerium.
Exercise 1.5 – Doping strontium fluoride
Anionic Frenkel disorder is the dominant ionic disorder in strontium fluoride
SrF 2 .