crystallography and diffraction techniques
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Crystallography and Diffraction Techniques. Myoglobin. Types of diffraction. X-ray diffraction Electron diffraction Neutron diffraction. Myoglobin diffraction pattern 1962 Nobel Prize by Max Perutz and Sir John Cowdery Kendrew. - PowerPoint PPT PresentationTRANSCRIPT
Crystallography and Crystallography and Diffraction TechniquesDiffraction Techniques
Myoglobin
Types of diffractionTypes of diffraction
- X-ray diffraction
- Electron diffraction
- Neutron diffraction
Enhanced visibility of hydrogen atoms by neutron crystallography on fully deuterated myoglobin
Myoglobin diffraction pattern1962 Nobel Prize by Max Perutz and Sir John Cowdery Kendrew
X-ray DiffractionX-ray Diffraction
Water
Light
Electron
Constructive
Destructive
Diffraction from atoms
Continue
1 A
About 1 Å
Wave of mater
Wave of electrons
The electrons are accelerated in an electric potential U to the desired velocity:
Crystal diffraction
Gas, liquid, powder diffraction
Surface diffraction
Diffraction by diffractometer
Example of spots by diffractometer
X-ray Crystallography
Electron density
Deformation Electron Density
Macromolecule X-ray Crystallography
Generation of X-rays
What is K and K (for Cu) ?K : 2p 1sK : 3p 1s
X-ray tube
An optical grating and diffraction of light
Lattice planes
Lattice planes => reflection
Lattice planes review
Bragg’s Law
Bragg’s Law
Bragg’s Law
2dsin(theta)=n lumda
Bragg’s Law
Atomic scattering factor
Atomic scattering factor
intensity
Phase and intensity
Electron density
Diffraction of one hole
Diffraction of two holes
Diffraction of 5 holes
2D four holes
From real lattice to reciprocal lattice
Real holes Reflection pattern
Crystal lattice is a real lattice, while its reflection pattern is its corresponding reciprocal lattice.
TEM image of Si? or Diamond?
Real lattice viewed from (110) direction.
Si
Diamond
Electron Diffraction
Conversion of Real Lattice to Reciprocal Lattice
P P P
P P P
P P P
P P P
P P P
P P P
P P P
P P P
P P P
P P P
Ewald Sphere and Diffraction Pattern
The Ewald sphere is a geometric construct used in X-ray crystallography which neatly demonstrates the relationship between:•the wavelength of the incident and diffracted x-ray beams, •the diffraction angle for a given reflection, •the reciprocal lattice of the crystal
Paul Peter Ewald (1888~1985)
Ewald Sphere
A vector of reciprocal lattice represents a set of parallel planes
in a crystal lattice
2d sin = n
(1/dhkl)/(2/) = sin
(hkl)
Reciprocal Lattice and Ewald Sphere
Detector, Reciprocal Lattice and Ewald Sphere
3D View of Ewald Sphere and Reciprocal Sphere
Techniques of X-ray diffractionTechniques of X-ray diffraction
Single Crystal and Powder X-ray Diffractions
many many many very small single crystals
Diffractometers for Single Crystal and Powder X-ray Diffractions
Single Crystal and Powder X-ray Diffraction Patterns
The powder XRD methodThe powder XRD method
Formation of a cone of diffracted radiation
XRPD on film
electron diffractionof powder sample
Finger Print Identification Finger Print Identification for Known Compounds
by comparing experimental XRPD to those in PDF database
Some peaks may not be observed due to preferred orientation
For example, layered structure such as graphite.For example, layered structure such as graphite.
X-ray powder diffraction patternsX-ray powder diffraction patternsof crystalline and amorphous of crystalline and amorphous
samplesample
Scherrer Formulat = thickness of crystal in ÅB = width in radians, at an
intensity equal to half the maximum intensity
However, this type of peak broadening is negligible when the crystallite size is larger than 200 nm.
B is often calculated relative to a reference solid (with crystallite size >500 nm) added to the sample: B2=Bs2-Br2.
2d sin =
Some equations to calculate cell parameters (d-spacings)
X-ray powder diffraction patterns for potassium halides
Structure Factor, Intensity and Electron
Density
R1 = ||Fo| - |Fc||/ |Fo|
Fcalc
Fobs
Electron density maps by X-ray Electron density maps by X-ray diffractiondiffraction
Scattering of X-rays by a crystal-systematic Scattering of X-rays by a crystal-systematic absencesabsences
Systematic Absences
Systematic absence for C-center: (x,y,z) ≣ (x+1/2, y+1/2, z)
Fhkl = (1/V) fjexp[2i(hxj+kyj+lzj)]
=(1/V)fj[cos2(hxj+kyj+lzj)+isin2(hxj+kyj+lzj)]
=(1/V)fj{cos2(hxj+kyj+lzj)+cos2[h(xj+1/2)
+k(yj+1/2)+lzj)]}+i{sin2(hxj+kyj+lzj)
+sin2[h(xj+1/2)+k(yj+1/2)+lzj)]}
j=1
N
j=1
N/2
let 2(hxj+kyj+lzj)=j
cos(A+B)=cosAcosB-sinAsinBsin(A+B)=sinAcosB+cosAsinB
(1/V)fjcos2(hxj+kyj+lzj)+cos2h(xj+1/2)+k(yj+1/2)+lzj)]}
+isin2(hxj+kyj+lzj)+sin2h(xj+1/2)+k(yj+1/2)+lzj)]}
=(1/V)fjcosj+cosj+h+k))+i[sinj+sinj+h+k))]}
=(1/V)fjcosj+cosjcosh+k)]+isinj+sinjcosh+k)]}
={[cosh+k) + 1]}/V fjcosj+ isinj]
So when cosh+k) = -1 that is when h+k = 2n+1, Fhkl = 0
Condition for systematic absences caused by C-center:For all (hkl), when h+k = 2n+1, Ihkl = 0
Fhkl =(1/V)fjcos2(hxj+kyj+lzj)+isin2(hxj+kyj+lzj)]
=(1/V)fj{cos2(hxj+kyj+lzj)+cos2(-hxj+k(yj+1/2)-lzj)]
+isin2(hxj+kyj+lzj)+ sin2(-hxj+k(yj+1/2)-lzj)]}
For reflections at (0 k 0)
Fhkl = (1/V)fj{[cos(2kyj)+ cos(2kyj)cos(k)]
+ i[sin(2kyj)+ sin(2kyj)cos(k)]}
=[(cos(k)+1)/v] fj[cos(2kyj)+ i[sin(2kyj)]
Systematic absences for 21//b where (x,y,z) (-x,y+1/2,-z)≣
So the conditions for 21//b screw axis:For all reflections at (0 k 0), when k = 2n+1, Ihkl=0
Conditions of Systematic Absences
I-center: for all (hkl), h+k+l = 2n+1, Ihkl = 0F-center: for all (hkl), h+k = 2n+1, h+l = 2n+1 k+l = 2n+1, Ihkl = 0 (or h, k, l not all even or all odd)c-glide (b-axis), for all (h0l), l = 2n+1, Ihkl = 0n-glide (b-axis), for all (h0l), h+l = 2n+1, Ihkl = 0d-glide (b-axis), for all (h0l), h+l = 4n+1, 2 or 3, Ihkl = 031//b screw axis, for all (0k0), k = 3n+1, 3n+2, Ihkl = 0
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Setup of Conventional Single Crystal X-ray Diffractometer
Electron diffractionElectron diffractione- 0.04 Å
Can see crystal structure of very small area
Associated with TEM
f much larger than that of X-ray: can see superlattice
Ni–Mo alloy (18 % Mo) with fcc structure. Weak spots result fromsuperlattice of Mo arrangement.
Secondary diffraction of Secondary diffraction of electron diffractionelectron diffraction
Extra reflections may appear in the diffraction pattern
The intensities of diffracted beam are unreliable
Neutron diffractionNeutron diffraction
Antiferromagnetic superstructure in MnO, FeO and NiO
MnOMnO
FeFe33OO44
The most famous anti-ferromagnetic, manganese oxide (MnO) helped earn the Nobel prize for C. Shull, who showed how such magnetic structures could be obtained by neutron diffraction (but not with the more common X-ray diffraction).
Schematic neutron and X-ray diffraction patterns for MnO