1. Radius Determination
GLY 4200
Fall, 2012

2. X-ray Diffraction Image
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Images like these can be used to determine crystal structures

3. Comparison of Radii
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4. Squashed versus Unsquashed
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Left, metallic or covalent radius
Right, Van der Waals radius

5. 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
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6. Coulomb’s Law F ≃ (Z1Z2)/r2 where Zi = charge on each ion
r = distance between ions

7. Covalent Radius 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 = 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 lines
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9. 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 Goldshmidt and Pauling ionic radii
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10. Ionic Radii versus CN
From Shannon and Prewitt, Acta Cryt. B25, 725 (1969) and B26, 1046 (1970).

11. Ionic Character Example: CaF Difference = 3.0 Close to 90% ionic
Example: SiN
Si = N = 3.1
Difference = % ionic