Question

Garnet typically has the chemical formula: (Fe2+, Mg2+, Ca 2+, Mn2+)3 Al3+2Si4+3O12

The formula can be broken up into structural sites (spaces where cations of a certain size range can occupy) X3Y2Z3O12 where the X-site is coordinated with 8 oxygen anions, the Y-site is coordinated with 6 oxygen anions, and the Z-site is coordinated with 4 oxygen anions. Using the table of ionic radii, calculate the predicted coordination number (CN) relative to O2- for each cation in the garnet formula. How do the calculated CNs compare to those for real garnet? Explain why they are the same or different.

Answer 1

Element: Ionic Radius in A(r), ionic radius ratio (r+/rO2-)

O2- :    rO2- = 1.32 (r+/rO2-) = 1.00

(i)
Z=Si4+: rZ = 0.30, rZ/rO2- = 0.23
The radius ratio is in the range(0.225-0.414) giving tetrahedral shape with CN=4.
This matches the observed coordination no 4.

(ii)
Y =Al3+: rY = 0.54, rY/rO2- = 0.42
The radius ratio is in the range(0.414-0.732) giving octahedral shape with CN=6.
This matches the observed coordination no 6.

(iii)

X =(Fe2+, Mg2+, Ca 2+, Mn2+)
X1=Fe2+: rFe2+=0.78, rFe2+/rO2- = 0.59
X2=Mg2+: rMg2+=0.72, rMg2+/rO2- = 0.55
X3=Ca2+: rCa2+=1.00, rCa2+/rO2- = 0.76
X4=Mn2+: rMn2+=0.67, rMn2+/rO2- = 0.51

The average radius ratio = (0.59+0.55+0.76+0.51)/4=0.6 will indicate a coordination
no. of 6. This does not match the observed CN =8.

However if there is greater amount of Ca2+, then the coordination no will change.
If X is only Ca2+, the radius ratio X=(Ca2+) rCa2+/rO2- = 0.76
This is within the range of (0.732-0.999)
giving bcc shape with CN = 8 which matches the observed CN =8.
This indicates that there is greater amount of Ca2+ in X.