1. Calculate the theoretical density for the BCC metal barium. 2. Calculate the
ID: 2993698 • Letter: 1
Question
1. Calculate the theoretical density for the BCC metal barium.
2. Calculate the theoretical densities and packing factors of barium zirconate (BaZrO3), and barium cerate (BaCeO3), both of which form the perovskite structure.
Use 0.132 nm for the ionic radius of O2-, 0.217 nm for the atomic radius of Ba and the ionic radii for the cations given in the table. (the Roman numeral indicates the coordination number).
Ion
Ionic Radius (nm)
IV
VI
VIII
XII
Ba2+
0.135
0.142
0.161
Ce4+
0.087
0.097
0.114
Zr4+
0.059
0.072
0.084
Ion
Ionic Radius (nm)
IV
VI
VIII
XII
Ba2+
0.135
0.142
0.161
Ce4+
0.087
0.097
0.114
Zr4+
0.059
0.072
0.084
Explanation / Answer
Solution 1)
Density of Barium:
Atomic weight of Barium: A = 137.33 atomic mass unit
Since it is a BCC structure having two effective atoms per unit cell and from the relation of lattice parameter and the radius of the Barium atom it is found that the volume of the unit call of BCC Barium: V = (lattice parameter)3 = 1.25826*10-22 cm3
Density of Barium = 3.62 grams per cm3 (lighter than commercial steel)
Solution 2)
Barium zirconate and Barium cerate forms perovskite structure, this structure is basically a ceramic structure consisting of bivalent and tetravalent ions.
Generally single unit cell of perovskite structure is composed of one bivalent ion occupying the edges of the unit cell, another bivalent occupies the face centres and tetravalent occupies the body centre of the unit call which is an octahedral void
Thus to calculate the density of given advanced ceramics, we need to use the following expression
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