Radius Determination
GLY 4200
Fall, 2014
1
X-ray
Diffraction
Image
• Images like these can be used to determine
crystal structures
2
Comparison of Radii
3
Squashed versus Unsquashed
• Left, metallic or covalent radius
• Right, Van der Waals radius
4
Radii Across a Row
• Diagram uses metallic radii for metallic elements,
covalent radii for elements that form covalent bonds,
and van der Waals radii for those (like the noble
gases) which don't form bonds
5
Coulomb’s Law
• F ≃ (Z1Z2)/r2
 where Zi = charge on each ion
 r = distance between ions
6
Spin State
• High-spin versus low-spin
7
Covalent Radius Example
• Example:






C-C spacing in diamond is 0.154nm
Metallic Si-Si spacing is 0.234nm
C radius = 0.077nm
Si radius = 0.117nm
Si – C = 0.194 nm predicted
0.193 nm observed
8
Electron Density Contour Map of LiF
• Electron density
(electrons/volume) is the
preferred method of
determining ionic radius
• Electron density contour
map of LiF: a section
through part of the unit
cell face
• The electron density
(electrons A-3) is constant
along each of the contour
9
lines
Electron Density Variation
• Electron density
variation between Li+
and F• Note the variation has
a very flat bottom.
• M, G and P indicate
the true minimum, and
the Goldschmidt and
Pauling ionic radii
10
Ionic Radii
versus CN
11
Ionic Character
• Example: CaF
 Ca = 1.1
• Difference = 3.0
• Example: SiN
 Si = 1.8
• Difference = 1.3
F = 4.1
Close to 90% ionic
N = 3.1
28% ionic
12