Scattering from imperfect crystals see Cowley Sect 7
- Slides: 30
Scattering from imperfect crystals (see Cowley Sect. 7. 1) Two types average lattice exists (point defects, dislocations, thermal vibrations) no average lattice (stacking faults, twinning)
Scattering from imperfect crystals (see Cowley Sect. 7. 1) Two types average lattice exists (point defects, dislocations, thermal vibrations) no average lattice (stacking faults, twinning)
Scattering from imperfect crystals (see Cowley Sect. 7. 1) Two types can't put in all atoms; consider average of atoms surrounding particular set of N atoms
Scattering from imperfect crystals Two types can't put in all atoms; consider average of atoms surrounding particular set of N atoms for a monatomic solid
Random vacancies (see Cowley Sect. 7. 3) Suppose n random vacancies in monatomic solid w/ N atom sites Consider vectors ri - rj
Random vacancies (see Cowley Sect. 7. 3) Suppose n random vacancies in monatomic solid w/ N atom sites Consider vectors ri - rj
Random vacancies Rearranging:
Random vacancies Rearranging: scattering power of ordered structure - no defects, reduced f
Random vacancies Rearranging: scattering power of ordered structure - no defects, reduced f conts distrib of scatt power - decreases w/ u - approx proportional to n
Random vacancies Rearranging: scattering power of ordered structure - no defects, reduced f conts distrib of scatt power - decreases w/ u - approx proportional to n
Random vacancies Now consider Patterson Suppose n random vacancies in monatomic solid w/ N electron density for ordered structure deviation from ordered structure
Random vacancies Now consider Patterson Suppose n random vacancies in monatomic solid w/ N electron density for ordered structure deviation from ordered structure
Random vacancies
Vacancy clusters Use Patterson approach again
Interstitials Assume n small interstitials w/ negligible scattering power Average structure is
Interstitials Assume n small interstitials w/ negligible scattering power
Interstitials Assume n small interstitials w/ negligible scattering power
Thermal vibrations Einstein: monatomic, independent, harmonic, 1 -D Spread electron density by Gaussian
Thermal vibrations Except for origin peak, all Patterson peaks spread by
Thermal vibrations Except for origin peak, all Patterson peaks spread by Intensity is
Thermal vibrations Except for origin peak, all Patterson peaks spread by Intensity is
No average lattice Except for origin peak, all Patterson peaks spread by
No average lattice Except for origin peak, all Patterson peaks spread by d(z) is a set of fcns (r) considered periodic in x, y
No average lattice Except for origin peak, all Patterson peaks spread by d(z) is a set of fcns (r) considered periodic in x, y reciprocal lattice
No average lattice Use Gaussian distrib w/ mean = c
No average lattice Use Gaussian distrib w/ mean = c
No average lattice
No average lattice
No average lattice
No average lattice
