3) Xray Scattering and Bragg Diffraction

Its not a spectrum its a …

diffraction pattern

How are Miller indices determined

identify plane opposite origin; find intercepts in xyz axes; take the reciprocal

Give the equation for Braggs Law

nλ = 2dsin(θ)

What is the Bragg angle

θ

What is the scattering angle

2θ

Why doesn’t glass produce Bragg reflections

its amorphous structure lacks long range periodicity to get constructive interference; only get a broad diffuse hump

What are the three steps of phase analysis

convert 2D data to peak positions; search for relevant materials; match observed peaks to database

Hanawalt

8 strongest peaks in decreasing height; most common as strong peaks most reliable

Fink

8 strongest peaks with largest d spacings; useful when strong peaks overlap

Long8

8 peaks with largest d spacing; useful when strong peaks overlap

How many matching peaks are need to confirm a phase

3

What weight % is needed to see a phase

>0.5%; light elements may need up to 10%

What is a unit cell

repeatable building block that represents symmetry of the structure

cubic equation

1/d² = (h² + k² + l²)/a²; only need one peak

tetragonal equation

1/d² = (h² + k²)/a² + l²/c²; need two peaksor

orthorhombic equation

1/d² = h²/a² + k²/b² + l²/c²

hexagonal equation

1/d² = 4/3(h² + hk + k²)/a² + l²/c²

How does the sin(θ)² manual indexing method work

m = h² + k² + l²; rearrange braggs law and cubic eq; take ratio of sin² for each peak with the first to get values of m; multiply by integers until all values of m are allowed

List the three peak shapes

Gaussian, Lorentzian, Pseudo-voigt

What is the integral breadth

width of rectangle with same height and area as the peak

What two factors affect peak shape

instrumental (gaussian); sample related (lorentzian)

How to correct for instrumental affects

use a standard reference material

What is the issue with sample transparency

xrays penetrate and diffract below surface; effective surface below physical surface causing low angle broadening

How does crystallite size affect peak shape

small crystallites don’t have enough layers for Braggs condition to be fully met; get constructive interference for small range of λ; peak broadens

How does the crystallite dimension ‘tau’ affect broadening

tau = Kλ/(beta cos(θ)); K = scherrer constant (spheres0.94, cubes0.89), beta = broadening in radians

Below what crystallite size do peaks start to broaden

0.5um

What crystallite sizes can we measure up to using FWHM and why

100nm; beyond this the instrument broadening affects are dominant

What is microstrain broadening caused by

dislocations; distortions; grain surface relaxation, faults; ss inhomogeneity, antiphase domain boundaries

Give the equation for microstrain broadening

B(2θ) = 4 epsilon tanθ; B is the broadening in 2θ, epsilon is the microstrain coefficient

How can we deconvolute two effects of peak broadening

Williamson-Hall plot