Scattering from imperfect crystals (see Cowley Sect. 7.1)

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)
2
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)
3
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
4
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
5
Random vacancies (see Cowley Sect. 7.3)
Suppose n random vacancies in monatomic solid
w/ N atom sites Consider vectors ri - rj
6
Random vacancies (see Cowley Sect. 7.3)
Suppose n random vacancies in monatomic solid
w/ N atom sites Consider vectors ri - rj
7
Random vacancies
Rearranging
8
Random vacancies
Rearranging scattering power of
ordered structure - no defects, reduced f
9
Random vacancies
Rearranging scattering power of
ordered structure - no defects, reduced f conts
distrib of scatt power - decreases w/
u - approx proportional to n
10
Random vacancies
Rearranging scattering power of
ordered structure - no defects, reduced f conts
distrib of scatt power - decreases w/
u - approx proportional to n
11
Random vacancies
Now consider Patterson Suppose n random
vacancies in monatomic solid w/ N electron
density for deviation from ordered structure
ordered structure
12
Random vacancies
Now consider Patterson Suppose n random
vacancies in monatomic solid w/ N electron
density for deviation from ordered structure
ordered structure
13
Random vacancies

14
Vacancy clusters
Use Patterson approach again
15
Interstitials
Assume n small interstitials w/ negligible
scattering power Average structure is
16
Interstitials
Assume n small interstitials w/ negligible
scattering power
17
Interstitials
Assume n small interstitials w/ negligible
scattering power
18
Thermal vibrations
Einstein monatomic, independent, harmonic,
1-D Spread electron density by
Gaussian
19
Thermal vibrations
Except for origin peak, all Patterson
peaks spread by
20
Thermal vibrations
Except for origin peak, all Patterson peaks
spread by Intensity is
21
Thermal vibrations
Except for origin peak, all Patterson peaks
spread by Intensity is
22
No average lattice
Except for origin peak, all Patterson peaks
spread by
23
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
24
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
25
No average lattice
Use Gaussian distrib w/ mean c
26
No average lattice
Use Gaussian distrib w/ mean c
27
No average lattice

28
No average lattice

29
No average lattice

30
No average lattice