Powder Diffraction BIERINGER

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10th Canadian Neutron Summer School slide 7 June 16th, 2009
Mario Bieringer__________________________________________________________________________
* also described as rhombohedral: a=b=c α = β = γ ≠ 90˚ __________________________________________________________
10th Canadian Neutron Summer School slide 8 June 16th, 2009
Applications of Powder Diffraction
diffraction = elastic scattering momentum transfer at constant energy, i.e. incident λ = diffracted λ
600 Intensity (counts)
Why do we care about diffraction experiments: • identification of materials/phases • determination of structural details, i.e. local environments within an extended structure • evaluation of order and disorder in structures • phase transitions (structural distortions or reconstruction) • chemical reactions • relate structure and properties
System cubic hexagonal trigonal* tetragonal orthorhombic monoclinic triclinic u.c. symmetry m-3m 6/mmm 3/mmm 4/mmm mmm 2/m -1 unit cell parameters a=b=c a=b≠c a=b≠c a=b≠c a≠b≠c a≠b≠c a≠b≠c α = β = γ = 90˚ α = β = 90˚ γ = 120˚ α = β = 90˚ γ = 120˚ α = β = γ = 90˚ α = β = γ = 90˚ α = γ = 90˚ β ≠ 90˚ α ≠ β ≠ γ ≠ 90˚
slide 9 June 16th, 2009
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10th CanaMario Bieringer__________________________________________________________________________
In-situ Powder X-ray Diffraction:
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10th Canadian Neutron Summer School slide 6 June 16th, 2009
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10th Canadian Neutron Summer School slide 5 June 16th, 2009
Mario Bieringer__________________________________________________________________________
Body centered I Base centered
A total of 14 Bravais Lattices exist (see next page for illustration) cubic: hexagonal: trigonal: tetragonal: P, I, F P P P, I orthorhombic: P, I, F, (A,B,C) monoclinic: P, C triclinic: P
Mario Bieringer__________________________________________________________________________
Applications of Powder Diffraction
chemistry physics engineering life sciences biochemistry materials science geological sciences archeology
10th Canadian Neutron Summer School slide 3 June 16th, 2009
Mario Bieringer__________________________________________________________________________
Routine Powder X-ray Diffraction:
500 400 300 200 100 0 40
Si powder neutron diffraction pattern C2 Chalk River λ = 1.329
60
2θ ( )
0
80
100
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presented at the
10th Canadian Neutron Summer School
June 15 – 18, 2009 Chalk River, Ontario
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10th Canadian Neutron Summer School slide 1 June 16th, 2009
Mario Bieringer__________________________________________________________________________
Routine Powder X-ray Diffraction:
M D
A
S
XRA Y
c b a
BE A
M
Preferred Orientation of flat sample mounts:
Mario Bieringer__________________________________________________________________________
Neutron Powder Diffraction
Mario Bieringer Department of Chemistry University of Manitoba
Mario Bieringer__________________________________________________________________________
Description of Crystallographic Structures
Bravais Lattices: Centering conditions can be described with translation vectors:
Intensity (a.u.)
Mario Bieringer__________________________________________________________________________
What is a Powder?
powder = polycrystalline solid large number of crystallites of µm length scale ideal powders (for diffraction) show random orientation of crystallites ⇒ orientational average of single crystals • large number of preparative methods available. • powders can be prepared in large quantities (g, kg, etc.) • fast synthesis • real world materials are often polycrystalline • in reality powders are often multiphasic
Description of Crystallographic Structures
Unit Cell: Smallest repeating unit capable of describing the entire crystal by means of three non-parallel translation vectors. paralleliped The 7 Crystal Systems
Lattice Primitive Symbol P A B C Face centered F translations +(0, 0, 0) +(½, ½, ½) +(0, ½, ½) +(½,0, ½) +(½, ½, 0) +(0, ½, ½), +(½, ½, 0), +(½,0, ½) lattice points 1 2 2 2 2 4