scattering from imperfect crystals (see cowley sect. 7.1) two types average lattice exists (point...
TRANSCRIPT
Scattering from imperfect crystals (see Cowley Sect. 7.1)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)
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)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)
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)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
Two types
can't put in all atoms; consider average of atoms surrounding particular set of N atoms
Scattering from imperfect crystalsScattering 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
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)Random vacancies (see Cowley Sect. 7.3)
Suppose n random vacancies in monatomic solid w/ N atom sites
Consider vectors ri - rj
Suppose n random vacancies in monatomic solid w/ N atom sites
Consider vectors ri - rj
Random vacancies (see Cowley Sect. 7.3)Random vacancies (see Cowley Sect. 7.3)
Suppose n random vacancies in monatomic solid w/ N atom sites
Consider vectors ri - rj
Suppose n random vacancies in monatomic solid w/ N atom sites
Consider vectors ri - rj
Random vacanciesRandom vacancies
Rearranging:
scattering power of ordered structure - no defects, reduced f
Rearranging:
scattering power of ordered structure - no defects, reduced f
Random vacanciesRandom vacancies
Rearranging:
scattering power of ordered structure - no defects, reduced f conts distrib of scatt power
- decreases w/ u- approx proportional to n
Rearranging:
scattering power of ordered structure - no defects, reduced f conts distrib of scatt power
- decreases w/ u- approx proportional to n
Random vacanciesRandom vacancies
Rearranging:
scattering power of ordered structure - no defects, reduced f conts distrib of scatt power
- decreases w/ u- approx proportional to n
Rearranging:
scattering power of ordered structure - no defects, reduced f conts distrib of scatt power
- decreases w/ u- approx proportional to n
Random vacanciesRandom vacancies
Now consider PattersonSuppose n random vacancies in monatomic solid w/ N
electron density for deviation from ordered structure ordered structure
Now consider PattersonSuppose n random vacancies in monatomic solid w/ N
electron density for deviation from ordered structure ordered structure
Random vacanciesRandom vacancies
Now consider PattersonSuppose n random vacancies in monatomic solid w/ N
electron density for deviation from ordered structure ordered structure
Now consider PattersonSuppose n random vacancies in monatomic solid w/ N
electron density for deviation from ordered structure ordered structure
InterstitialsInterstitials
Assume n small interstitials w/ negligible scattering power
Average structure is
Assume n small interstitials w/ negligible scattering power
Average structure is
InterstitialsInterstitials
Assume n small interstitials w/ negligible scattering powerAssume n small interstitials w/ negligible scattering power
InterstitialsInterstitials
Assume n small interstitials w/ negligible scattering powerAssume n small interstitials w/ negligible scattering power
Thermal vibrationsThermal vibrations
Einstein: monatomic, independent, harmonic, 1-D
Spread electron density by Gaussian
Einstein: monatomic, independent, harmonic, 1-D
Spread electron density by Gaussian
Thermal vibrationsThermal vibrations
Except for origin peak, all Patterson peaks spread by
Except for origin peak, all Patterson peaks spread by
Thermal vibrationsThermal vibrations
Except for origin peak, all Patterson peaks spread by
Intensity is
Except for origin peak, all Patterson peaks spread by
Intensity is
Thermal vibrationsThermal vibrations
Except for origin peak, all Patterson peaks spread by
Intensity is
Except for origin peak, all Patterson peaks spread by
Intensity is
No average latticeNo average lattice
Except for origin peak, all Patterson peaks spread by
Except for origin peak, all Patterson peaks spread by
No average latticeNo average lattice
Except for origin peak, all Patterson peaks spread by
d(z) is a set of fcns
(r) considered periodic in x,y
Except for origin peak, all Patterson peaks spread by
d(z) is a set of fcns
(r) considered periodic in x,y
No average latticeNo 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
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 latticeNo average lattice
Use Gaussian distrib w/ mean = c
Use Gaussian distrib w/ mean = c
No average latticeNo average lattice
Use Gaussian distrib w/ mean = c
Use Gaussian distrib w/ mean = c