October 7th, 2010
Class 9
Atomic Radii
Atomic radius cannot be defined in a unique way; the electron density of an atom does not
actually have a defined radius, in fact it is only zero at an infinite distance from the nucleus.
However, given a particular chemical environment, atoms tend to form bonds as if they have a
particular radius. The atomic radius will be different whether they form an ionic bond, or a
covalent bond, or Van der Waals bond, but every time they bind with one of the particular bond
types defined above, they seems to behave as if they do have a defined radius. Table 9, in page
71 shows the values of different radius.
Defining three different radius, 1 for a 6-coordinated ionic bond, one for the 4-coordinated
covalent bond, and one for the 12-coordinated metals, the bond length between two atoms can be
predicted by simply adding the appropriate radius. For instance
 the ionic radius of Na+ and Cl- are respectively 0.97 Å and 1.81 Å, predicting a Na+-Clbond of 2.78 Å. The actual bond is 2.82 Å, which is fairly close.
 For the NaF bond, the predicted bond length is 2.33 Å, the observed bond length in the
crystal is 2.32 Å.
 The C-C bond in diamond is 1.54 Å. The covalent radius of C is 0.77 Å.
 The covalent C-Si bond is predicted to be 1.94 Å, in good agreement with the observed
1.89 Å (see table 9).
For ionic bonds, the atomic radius is obtained considering each atom bonded to 6 neighbors, if
more or less neighbors exist, the actual bond length can be calculated with an appropriate
correction (table 10 page 72)
BaTiO3 Structure
Image from http://www.geocities.com/ctas61/IMAGEQJQ.JPG
Ba atoms are on a sc lattice position, Ti are in a body centered position, and O atoms are on the
faces. So, Ba-O distance corresponds to that of first neighbors in an fcc lattice, thus each Ba
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have 12 nearest neighbors O atoms. Ti has 6 O atoms as first neighbors as it can be seen in the
picture. In Barium Titanate, the Ba-O distance is then (using table 9)
D12=RBa +RO +Correction= 1.35+1.40+0.19=2.94 leading to a lattice constant
o
o
a= 2  2.94 A  4.16 A 4.16Å
If instead Ti-O distance is used
D6=0.68+1.40=2.08 or a=4.16 Å
The actual lattice constant for Barium Titanate is 4.004 Å the difference being due to the partial
covalent nature of the bonds.
The biggest discrepancy with these simple predictions will be observed with bonds that are not
totally ionic, or covalent or Van der Waals. Another source of discrepancy for ionic crystals is
that the ionic radius is calculated by considering six-fold coordination. Ionic crystals however
can have different coordination number.
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