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)

thn ionic radius ratio (r+/rO2-)

O2- :    rO2- = 1.32 (r+/rO2-) = 1.00

For: Si+4

Z=Si+4: rZ = 0.30,

the ratio = rZ/rO2- = 0.23

Find the radius ratio (from the range) --> (0.225-0.414)

this is a tetrahedral shape with CN=4.

The observation is --> coordination no 4.

(ii)

For the case of "Y" which should be Al

Y =Al+3: rY = 0.54,

the ratio --> rY/rO-2 = 0.42

the range = (0.414-0.732)

which is octahedral shape with CN=6.

This matches the observed coordination no 6.

For Fe+2

Possible valus of "X"

X =(Fe2+, Mg2+, Ca 2+, Mn2+)

Choose Fe+2

X1=Fe2+: rFe2+=0.78, rFe2+/rO2- = 0.59

Choose Mg+2

X2=Mg2+: rMg2+=0.72, rMg2+/rO2- = 0.55

Choose Ca+2

X3=Ca2+: rCa2+=1.00, rCa2+/rO2- = 0.76

Finally, choose Mn+2

X4=Mn2+: rMn2+=0.67, rMn2+/rO2- = 0.51

then..

for radius ratios:

The average radius ratio = (0.59+0.55+0.76+0.51)/4=0.6 will indicate a coordination

no. of 6.

note that this does not match the observed CN =8

therefore

If X is only Ca2+, the radius ratio X=(Ca2+) rCa2+/rO2- = 0.76

which is near the range (inside)

The range of (0.732-0.999)

Finally. deduce shape:

giving bcc shape with CN = 8 which matches the observed CN =8

Ca+2 is in greater amount in X