PXRD
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applications of X-ray diffraction
• fingerprinting of solid-state materials -> different materials have different x-ray diffraction patterns -> unknown samples can be checked against database • forensic analysis -> small sample size which can be recovered (non-destructive technique) • geology -> evaluating purity of limestone -> determining extractability of metals from ore-bearing deposits • biology -> analysis of oligopeptides, co-factor, steroid hormones
requirements for PXRD experiment
• monochromatic (single wavelength) x-ray beam • crystalline material
why is Be used?
z = 4 (light metal) not a lot of e- (transparent to x-rays) BUT v. toxic -> careful when handling
effect of using metals further down group
absorb more of x-rays x-rays interact with e- cloud heavier metals have denser e- cloud
crystals
= periodic arrangement of matter (repeats at regular intervals) classified according to unit cells
unit cells
smallest repeating volume unit which shows full symmetry of structure
how many types of geometric shapes of unit cells are there?
7 known as CRYSTAL SYSTEMS
how many Bravais lattices are there?
14
how many LP in a P lattice type per unit cell?
1
how many LP in a I lattice type per unit cell?
2
how many LP in a F lattice type per unit cell?
4
how many LP in a C lattice type per unit cell?
2
crystal structure vs Bravais lattice
CRYSTAL STRUCTURE - gives information of the exact location of atoms or ions within the unit cell BRAVAIS LATTICE - only gives information on where environments are identical (i.e. lattice points) -> many compounds have same Bravais lattice type
what are the 2 naming systems for planes?
• WEISS INDICES - intercepts axes (a,b,c) • MILLER INDICES - reciprocals of the Weiss indices with the fractions cleared
Weiss index = ∞ meaning?
parallel with axis
what happens to the d-spacing as the Miller indices increase?
increases
x-ray diffraction
x-rays “see” e- cloud each LP acts as a secondary source of radiation x-rays send each e- on an atom into vibration each vibrating charge emits x-rays with the same frequency as x-ray beam = diffraction pattern
what does Bragg’s law indicate?
determines the set of conditions needed to observe reflection of x-rays from a given (h,k,l) no indication of amplitude
2 methods of recording diffraction patterns
• Debye-Scherrer camera (detector = film) • Automatic powder diffractometer (detector = digital)
diffraction pattern composition
millions of microcrystallites randomly oriented -> plane of reflected beam also random gives rise to cone of reflection for each Miller index (h,k,l)
what do the positions of the lines relate to?
hkl (d) of unit cell/lattice parameters
selection rule for I-type lattice
Miller indices = even (2n) number
selection rule for F-type lattice
either (even, even, even) or (odd, odd, odd)
when is a reflection not observed for given h,k,l values?
when set of planes doesn’t contain all LPs in structure