X-ray enters material, scatters (coherently or
i h tl ) ffth l t di incoherently) off the electrons surrounding
each atom
• X X-rays leaving the material are in phase if
DA + AC = 2dsin? = n?
Ewald Sphere
• Construct a 3-D
sphere in reciprocal
space based at the
( ) origin 000) with
radius = 1/?
Wh th h • When the sphere
intersects a
reciprocal lattice
point, the Bragg
reflection is allowed
More Diffraction
• Total scattering is dependent upon the “structure factor” (F)
– F is the sum of the wave amplitudes and phase angles,
i b h t i t t f t (given by each atomic structure factor f)
– f is the ratio of the scattering given by an atom to the
scattering given by a single electron
• Some F values result in allowed and not allowed diffraction
intensities
– Dependent upon crystal structure
Bravais Lattice Diffraction Present Diffraction Absent
Simple All None
Body Centered h+k+l = 2n (even) h+k+l = 2n+1 (odd)
B C t d h k ll dd h i d Base Centered h, all odd or even h, k mixed
Face Centered h, k, l all odd or even h, k, l mixed
Hexagonal l even, h+2k?3n h+2k=3n for l odd
XRD Data
Wh t XRD d t l k lik I t it 2?
• What data looks like – Intensity vs • What information can we get from this?
X-ray Source
• Use an e- beam to impact on an anode of
known composition
• Characteristic transitions within the anode
emit a high flux of x-rays through a window g y g
and into the beam path
Cu K? = 1.5418?
Inelastic Scattering – Characteristic X-ray
Formation
• Energy levels are
dependent upon the
nuclear mass and the
number of electrons
• For XRD, we can select ?
by choosing a target
l t it ifi element or its specific
transition
XRD Hardware
• MANY different ways to configure an XRD
– common: Bragg-powder
Most Bragg Brentano (diffraction)
– Additions: monochromator, 2-D detector, variable
li b f d i id slit before detector, incidence geometry ( spot vs
parallel beam), grazing incidence, XRR, SAXS,
rotating anode, single crystal g , g y
XRD Hardware
Qualitative Phase ID
• How do we determine crystalline structure from an XRD scan?
– Index 2-theta, convert to d spacings
– Use Reitveld refinement (least squares fitting) to determine likely reflections
and therefore phases from the d spacing data
– Knowing some information about the chemistry (major atomic species), can
find likely phases using indexed files
• International Center for Diffraction Data (ICDD)
• Powder Diffraction File (pdf)
• Committee Joint on Powder Diffraction Standards (JCPDS)
– UNT owns the 2007 version of the ICDD database
• Procedure:
Locate 2 theta measurement
– first d (highest intensity) from 2-– From pdf with similar chemistry, find next closest matching d with reasonable
intensity
– Compare relative intensities
– Repeat for all d values
• Determine preferred orientation wrt surface
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