Based on the radii for cations and anions in respect to their ionic charge: a. p

Question

Based on the radii for cations and anions in respect to their ionic charge: a. please predict the coordination of the cations for the following structure types (will the cations occupy tetrahedral sites (CN=4) or octahedral sites (CN=6 ?): i. Fe_2O_3 (hematite) ii. FeO (wuestite) iii. ZrO_2 (zirconia) iv. Al_2O_3 (alumina, corundum) v. Fe_2SiO_4 (fayarlite, olivine) b. What is the fraction of tetrahedral and octahedral positions occupied? c. Calculate the theoretical density of orthorhombic fayalite (a; 4.82 A, b = 10.48 A, and c = 6.09 A) for Z (or n) = 4

Explanation / Answer

1. a) i) r+/r-=0.069/0.140=0.49( as it's between 0.414-0.732) So Fe2O3 will occupy octahedral sites.

ii)r+/r-=0.077/0.140=0.55 It will occupy octahedral sites.

iii) r+/r-=0.073/peroxide ion it will be between 0.224-0.414 So ZrO2 will occupy tetrahedral site

iv) r+/r-=0.053/0.140=0.378 It is in between 0.224 -0.414 So Al2O3 will occcupy tetrahedral site

v) r+/r-=0.040/0.140 =0.28 So Fe2SiO4 will occupy tetrahedral sites.

b) In Fe2O3 50 % of the octahedra void is occupied. Total octahedral void is 4. Occupied 2

In FeO 25 % octahedral void is occupied

In ZrO2 25 % octahedral void is occupied

In Al2O3 25 % tetrahedral void is occupied, total tetrahedral void is 8 and occupied 2

c) Theoretical density d=z*A/(NA*V)

z=4, A=2*56+28+64=204, Volume V=a*b*c=4.82*10.48*6.09*10^-24 cc NA=avogadro number=6.023*10^23

Now putting all these values we get d=4*204/(6.023*10^23*3.07*10^-22) g/cc=4.41 g/cc

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