8) Absences, Space Groups and Stress

What is the structure factor

influences I; depends on which atoms are present (form factors), where they are in the unit cell, and how they scatter xrays relative to each other

What are systematic absences

when different atoms scatter xrays in antiphase to fully destructively interfere producing zero I; peak not present

Why are systematic absences important

fingerprints of crystal structure; tell us about Bravais lattice type; essential for identifying space groups and crystal structures

Give an example of a systematic absence

in bcc central atom (if the same atom) reflects in antiphase with 100 plane so this peak is not see; note the structure factor is the same for each as total (8 × 1/8 = ) 1 atom in corners and 1 in centre

What are the conditions for a systematic absence

equal no of diffracted beams in antiphase and of same amplitude; determined by form factors

Give the rule for a reflection to be observed in the primitive lattice type P

none

Give the rule for a reflection to be observed in the body centred lattice type I

h+k+l=2n

Give the rule for a reflection to be observed in the face centred lattice type F

h,k,l either all odd or all even

Give the rule for a reflection to be observed in the side centred lattice type C

h+k = 2n

Give the rule for a reflection to be observed in the rhombohedral lattice type R

-h+k+l = 3n (or h-k+l=3n)

Partial destructive interference

when two planes are spaced such that they could reflect in antiphase but the form factor of each atom is different then wont get full cancellation; only get partial destructive interference

What are space groups

define the symmetry and potential atomic sites of a structure; 230 of them labeled from lowest to highest symmetry

Hermann Mauguin notation

first letter = bravais lattice type; subsequent letters = essential symmetryW

What does Pba2 mean

Primitive lattice; glide plane symmetries along a and b axes; 2 fold rotation in z

What does Fm-3m mean

fcc; mirror symmetry along principle axes; 3 rotoinversion symmetry along diagonals; mirror symmetry along face diagonals

What is Wyckoff Notation and what does 4a mean

shows where atoms can be found in a crystal; 4 is multiplicity of that site; a is just a label

What is Rietveld analysis

refinement of theoretical diffraction pattern using least squares to model peaks

What can be refined in Rietveld analysis

thermal parameters; scale factors; phase fractions; specimen displacement; background

What needs to be known to do Rietveld analysis

lattice parameters; atomic positions; site occupancies; wavelength; profile parameters

What are optional in Rietveld analysis

Preferred orientation; crystallite size and microstrain; absorbtion/transparency

How does residual stress affect d spacings

tensile stress increases d spacing of planes perpendicular to the stress and decreases those parallel to it (Poisson strain); peak shifts mainly seen at large angles >120deg

What is residual stress

stress locked into structure via machining, thermal shrinkage etc

What can XRD determine about residual stress

magnitude, direction, compressive vs tensile

How does XRD determine residual strain

record xrd spectra while tilting specimen; plot d spacing vs sin²(tilt angle); -ve slope = compression (+ve tensile); steeper = greater magnitude; high angle reflections are required for measurable shifts; surface sensitive so can require electropolishing

What is shot peening

bombard surface with spherical beads to induce compressive stress at surface; applicable to anything prone to fatigue failure

Why is residual compressive stress desirable

applied tensile stress must overcome this before cracks can form; 10-100x improvement in service life; permanent until heat treated, machined or otherwise disturbed

What are non-ambient experiments

perform xrd on sample in situ or operando to see how structure changes during use

How are diamond anvil cells used

sample compressed between diamonds up to over 20 million atm; pressure medium maintains hydrostatic conditions