solid states Flashcards
what is diffraction
is the bending of waves as they pass through an opening
what does each spot represent on a diffraction pattern
the intensity of a diffracted wave
what happens when we combine the correct wave amplitude with the wrong phases in the Fourier transform
the phase information is much more dominant and thus the phase object will appear
what is the bragg construction equation
nλ = 2dsinθ
where d is the distance between the lattice plane, sin is the angle of incident and diffraction
what are the miller indices and explain what (2,0,0) shows
miller indices is a notation system for lattice planes in crystal lattice
(2,0,0) = parallel to the k and l axis and intercepts the h axis twice per unit cell
what does the structure factor show
describes the intensity and phase of the X-ray or neutron diffraction pattern from a crystal lattice
what is the structure factor equation involving sine and cosine components
F = I F x exp[iϕ] I
ϕ is the phase angle
explain what effects atomic vibration have on atomic scattering
atomic vibration exaggerates the volume of the atom, making the volume bigger therefore the scattering factor decreases much quicker compared to a static atom
what is a systematic absence
when a spot is missing in the diffraction pattern in a systematic way
name and explain some method to assess the quality of the final structure
- R-factor
typically 0.02-0.05 - residual electron density delta p
delta p observed - delta p calculated - displacement of ellipsoids
do the ellipsoids have a sensible magnitude - molecular and intermolecular geometries
what is the De Broglie relationship
λ = h/mv
how are X-rays generated
- electrons accelerated through voltage from cathode to anode
- deceleration of electron results in energy emitted as X-ray
- electron ejected from the inner shells of anode and replaced by electron from higher shells leading to X-rays
what are the solutions to the phase problem in a centrosymmetric structure.
- The Patterson method (for heavy atoms)
P(xyz) can be calculated without phase angle - Direct method (small atoms)
each reflection is summed so negative features cancel out => restrictions on the phase relationship between reflections and this can be exploited to test different phase combination to probability models
explain least-squares analysis
The adjustment of these atomic parameters so as to obtain the best fit between observed and calculated structure factor amplitudes
what is disorder
all unit cells within a crystal are not necessarily identical
- unit cells can have different compositions
- molecules can have different orientations in unit cells
