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Unformatted text preview: 36 Atomic Size Factors Because the distortions in imperfect crystal lattices depend on the relative sizes of the atoms we must have a way to determine the atomic sizes in crystals. Hard sphere radius It is common to treat atoms in a crystal as spheres and to calculate the atomic sizes from the measured lattice parameters (measured using x-ray diffraction). We call this the hard sphere approach. Consider the face of an FCC lattice where the atoms are most closely spaced and make touching contact along a face diagonal. Face of an FCC unit cell showing atomic touching along a face diagonal The face diagonal can be expressed as 4 r H = a 2 so that the hard sphere radius would be r H = a 2 4 for an FCC lattice. This is clear and unambiguous for pure components (metals) but is not very useful for solid solutions where atoms of different sizes are present. Also, the hard sphere radius is not very useful if we wish to keep track of the volume occupied by atoms of different kinds, because the volume of the hard spheres do not include the volume in the interstices between the atoms. For atomic sizes in solid solutions and for keeping track of volume it is more common to use the Seitz radius, which is defined as the radius of the hypothetical sphere that would account for all of the volume in the crystal. Start with the average atomic volume (again using the FCC lattice for illustration). 37 ¡ = volume of unit cell atoms per unit cell = a 3 4 (for an FCC crystal) We then imagine a sphere of radius r s such that 4 3 ¡ r s 3 = ¢ so that the Seitz radius is then r s = 3 ¡ 4 ¢ £ ¤ ¥ ¦ § ¨ 1/3 = a 3 16 ¢ £ ¤ ¥ ¦ § ¨ 1/3 ....
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- Spring '08
- Coefficient of thermal expansion, atomic volume, Seitz radius, average atomic volume