Determination of Crystal Structure (Chapt. 10) C rystalStru ctu re D iffraction Pattern U nit C ell Line Positions A tom Positions Line Intensities Guess Guess Correct? Done Yes No 1. Use the angular positions of the diffraction lines to determine the shape and size of the unit cell. Assume either cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic, or triclinic. Assign Miller indices to each reflection (“index the pattern”). If a match is not obtained, the assumption of should be changed and the pattern indexed again. Calculate the size of the unit cell based on the positions and Miller indices of the diffraction lines. 2. With the measured density of the material, the chemical composition, and the size of the unit cell, calculate the number of atoms per unit cell. 3. Find the positions of the atoms in the unit cell
Determination of Crystal Structure (Chapt. 10). 1.Use the angular positions of the diffraction lines to determine the shape and size of the unit cell. Assume either cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic, or triclinic. - PowerPoint PPT Presentation
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Determination of Crystal Structure (Chapt. 10)
Crystal Structure Diffraction PatternUnit Cell Line PositionsAtom Positions Line Intensities
Guess
GuessCorrect?
Done
Yes
No
1. Use the angular positions of the diffraction lines to determine the shape and size of the unit cell. Assume either cubic, tetragonal, orthorhombic,
rhombohedral, hexagonal, monoclinic, or triclinic. Assign Miller indices to each reflection (“index the
pattern”). If a match is not obtained, the assumption of should be
changed and the pattern indexed again. Calculate the size of the unit cell based on the positions
and Miller indices of the diffraction lines.2. With the measured density of the material, the chemical
composition, and the size of the unit cell, calculate the number of atoms per unit cell.
3. Find the positions of the atoms in the unit cell by using the relative intensities of the diffraction lines.
Preliminary Treatment of Data
We want the values of sin2 for each diffraction line (in order to find the cell size and shape), however, there can be errors to what we measure, including extraneous lines in the diffraction pattern, and systematic errors (misalignment, film shrinkage, absorption, etc.)
Extraneous Lines1. X-ray beam with multiple wavelengths:
2. Contaminants or impurities in the sample, or the specimen mount!
Systematic Errors1. Film shrinkage (see Fig. 6-5 Cullity)2. Specimen is off-centered in Debye-Scherrer camera (see Fig. 11-3 Cullity)3. Absorption in the sample
Answer mix in a reference material and calibrate. (see Fig. 10-1 Cullity)