characterisation of solid state

what is do ellipsoid figures show and represent?

atoms shown as cross hatched ellipsoids

represents an area where there is 50% probability that electron density of that atom is contained within its boundary

what is the unit cell an average of? how does this vary for ordered vs disordered structures?

average structure across entire crystal lattice and across all crystallites

ordered - no significant variations across unit cells

disordered - randomly dispersed variations across unit cells

what is disorder?

what are the sites like?

when sites within unit cells may be one type of element in some, and another type in other unit cells

this gives sites of mixed elemental character

what is non-stoichiometry?

what are 2 reasons for this?

compounds have elemental composition and proportion cannot be represented by integers

• sites have mixed elemental character due to doping

• sites have low occupancy as some unit cells are missing ions

what are crystallographic rotation axes limited to?

restricted to those than product shapes that fill space

• no gaps

what are examples of shapes with 2-fold, 3-fold, 4-fold, 5-fold and 6fold?

do they all fill space?

what are unit translations?

how is a crystal lattice generated?

translations of whole unit cell lengths

unit translations in 3D generate crystal lattice

what is a screw axis?

what is n_m?

translation plus rotation

n_m - translate m/n of unit x, rotation 360/n around direction of translation

show 2₁ screw axis?

what is a glide plane?

show example

translation of half the unit x plus reflection across mirror plane parallel with translation direction

what is crystal structure defined by? 3

unit cell parameters (e.g. a, b, c, alpha etc)

space group - braves lattice type, symmetry elements

atom types and fractional coordinates of asymmetric unit

what is an asymmetric unit?

part of structure that can’t be related to another part by symmetry elements

wavelength range of X-rays?

0.1-10Å

conventional source of X-rays

where? what produces them? how?

diagram of electron movement?

in X-ray tube, electron beam hitting metal target

electron beam ionises core electron from atom in metal. upper shell electron relaxes to fill hole - X-rays emitted

diagram of X ray tube and metal target

what produces electrons? where do x rays go?

what is K, L and M shell?

K n =1

L n =2

M n=3

show M, L, K and ∞ energy levels - show electron beam causing ionisation and then electrons moving down, what the names of L→K, M→K and M→L emissions?

what is a broad hump on X ray emission spectrum?

white radiation

accelerate/decelerate charged particles and need to relax KE so white radiation is released

what are characteristic radiation spikes? (specific and show diagram)

quantised electronic transitions - K_ɑ and K_β

why is there more than two peaks when it shows K_ɑ and K_β?

coming from 2s or 2p, and 3s or 3p

what energy is wanted for diffraction experiments?

what is used to achieve this?

just one energy of X-rays

use metal filters or monochromators to remove white radiation, or any less intense emission wavelengths

what is synchrotron radiation?

speed? what type of radiation? energy?

when charged particles travel in curved paths

• speeds close to speed of light

• white/ broadband radiation

• energy ranges from microwave to X-rays

single slit experiment - what does slit do?

show diagram of X rays approaching slit and after

slit acts as secondary scattering source for light

what happens when you use 2 slits in X-ray diffraction?

how are x-rays scattered?

broad lines as waves constructively interfere

scattered in all directions from both slits

what happens when you have many slits in X-ray diffraction vs 2?

narrower lines, more detailed patterns

what is wavelength in slit experiment?

λ≈slit separation

what does a diffraction grating give and what is it caused by?

what is needed for constructive interference to occur?2

diffraction pattern from incident waves

pattern caused by constructive interference between scattered waves

sources of secondary scattering (e.g. slit) must be in ordered array, and separated by approximately the wavelength of the wave

what are x-rays scattered by? separation?

regions of high electron density e.g. atoms

0.8-4Å

why are x-rays diffracted from crystals?

atoms/ions are in regular pattern

areas of high electron density as atoms with close separation

what is equation for d_nh,nk,nl? e.g. show d₂₀₀ vs d₁₀₀

what did Bragg consider X-ray diffraction to be, instead of secondary scattering?

show diagram with two planes, P₁ and P₂, ABCd and θ

show constructive interference

considered it to be a reflection of x-rays off a family of parallel lines

how can constructive interference occur (what is the condition?) for Bragg’s law?

path difference must be a whole number of wavelengths

AB + BC = nλ

have the X-rays travelled the same distance?

second has travelled further as it has gone through crystal before being reflected by P₂

show how rule of constructive interference leads to Bragg’s law

use d_hkl/n to give law

what does each diffraction spot in a pattern correspond to?

corresponds to set of crystal planes defined by miller indices hkl

why are many diffraction patterns superimposed on each other for crystalline powders?

many many small crystallites - each has its own diffraction pattern

how does changing the orientation of crystallites give rings?

superimposed at a different orientation

change orientation of crystal changes the orientation of the diffraction pattern

pattern is being rotated as crystal is rotated leading to rings

where is 2θ?

what is each ring/line?

2θ is arrow - take 1D trace through rings

each ring corresponds to a different set of lattice planes (hkl)

how does translational symmetry change reflections?

results in destructive interference between diffracted X-rays

causes certain sets of reflections to be missing = systematic absences

what are translational symmetry examples? 3

cell centring

screw axes

glide planes

what are the reflections absent for primate, body and face centring?

primitive = none absent

body = h+k+l = odd number

face = h,k,l not all even or all odd

what is a diffractometer?

for powder diffractometer, what its measured? how are different values accessed?

instrument that measures diffraction pattern

sample ground to fine powder, 2θ vs intensity measured

sample and or detector rotated to access different 2θ measurements

diagram of powder diffractometer and detector and graph

why do different atoms have different scattering power?

ability to scatter X-rays depends on number of electrons which changes with element

what is f_j?

scattering factor of an element type j

why do non crystalline contaminants not matter for pXRD?

only crystalline material produces powder patterns

how can different polymorphs be obtained?

how can these be detected and identified? limitation?

obtained through phase change where one phase transformed to another through heat or pressure

powder diffraction experiments can detect and identify through fingerprinting

• need a more sensitive technique if only trace amounts

what does structure factor F_hkl describe?

describe amplitude (size) and phase (directionality) of diffracted wave

what is structure factor (resultant wave)

resultant wave from linear superposition of wave vectors from all atoms in the unit cell

what is each term?

N = number of atoms in unit cell

f_j scattering factor of atom j

x_j,y_j,z_j = atomic coordinates of atom j

show diagram of F_hkl for 4 atoms - consider each scattered wave as vector (length f and phase angle ϕ)

which atoms contribute to Fhkl?

all atoms - whether or not in set of crystal planes

what is ρ(xyz) and Vc?

what is the phase problem?

what does this stop from being calculated?

inability to measure phase angles

what is solving a structure? what can be calculated?

what does solved structure give

need phases assigned to reflections to calculate Fhkl and hence ρ(xyz)

solved structure gives peaks of electron density that can be assigned as atoms

what is a beam stop?

stops x-ray beams otherwise most x-rays hit detector and damage it

why is measurement of good intensity data for pXRD hard?3

weak diffraction (smaller the crystal, the weaker the diffraction)

overlap of peaks

preferred orientation

what is preferred orientation? how can it be alleviated?

when crystallites not randomly orientated

line up or lie flat against surface of sample holder

alleviated by grinding sample into finer powder

how does preferred orientation affect diffraction rings and measurement of intensity?

powder rings are incomplete - slicing means some peaks missing

wrong intensity

why is solving not needed for inorganic solid state chemistry? how can data be used?

material is of known structural type

structure of a similar material can be used as a starting material

• can be refined against the data

how are differences between calculated and measured pattern minimised?

least squares refinement - Rietveld refinement

fits line profiles for powder pattern to account for overlap of peaks