1. 1 Radius Determination GLY 4200 Fall, 2014

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

3. 3 Comparison of Radii

4. 4 Squashed versus Unsquashed Left, metallic or covalent radius Right, Van der Waals radius

5. 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

6. 6 Coulomb’s Law F ≃ (Z 1 Z 2 )/r 2  where Z i = charge on each ion  r = distance between ions

7. 7 Spin State High-spin versus low-spin

8. 8 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

9. 9 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

10. 10 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

11. 11 Ionic Radii versus CN

12. 12 Ionic Character Example: CaF  Ca = 1.1 F = 4.1 Difference = 3.0 Close to 90% ionic Example: SiN  Si = 1.8 N = 3.1 Difference = 1.3 28% ionic