Slater - Solid State Chemistry Flashcards
What 5 pieces of information can be determined by theXRD experiment?
Size, shape and electron density distribution within the unit cell
Type of atoms and position of atoms within the unit cell
What were the 7 types of crystal systems?
Triclinic Monoclinic Orthorhombic Tetragonal Trigonal Hexagonal Cubic
What are the four types of centring of a unit cell
Primative
Body centred
Face centred
Base centred
What is Braggs law
Lambda = 2dhkl sin ø
What is the indexing pattern for a cubic unit cell
1/dhkl = (h^2 + k^2 + l^2) / a^2
Indexing pattern for tetragonal
1/dhkl = (h^2 + k^2) / a^2 + l^2/ b^2
Indexing pattern for orthorhombic
1/dhkl = (h^2) / a^2 + k^2/ b^2 + l^2/ c^2
What equation do you use that incorporates braggs law to find a ( bond length )
4a^2 = lambda^2 (h^2 + k^2 + l^2) / sin ^2 ø
Explain thermogravemetric analysis
A precise microbalance used to monitor the mass whilst it is heated under a variety of atmospheres
Information about component ratios can be calculated but not their defects
What is the general formula for the perovskites crystal
ABO3 where a is the large cation and b is the small cation
Close packing spheres
Small cation occupies 1/4 of octahedral holes
Primative structure
What are the two groups of defects
Intrinsic - stoichiometric and therefore not changing overall ratio
Extrinsic - non-stoichiometric used to improve properties such as conductance
What are the two intrinsic defects?
Schottky and frenkel
What is the driving force for intrinsic defects?
Toss off between favoured entropy changes (increased disorder) and unflavoured enthalpy changes
What is the third law of thermodynamics
Crystals can have complete atomic order only at zero kelvin - at all other temperatures disorder will reduce the free energy
Explain schotty defects
Introduction of vacancies in an anion and cation site following the stoichiometry of the crystal. I.e. 1:1 removed if formula is NaCl but if MgCl2 then 1:2 removed
Explain frankel defects
Displacement of the cation or anion into an interstitial site within the lattice
Normally cation because they tend to be smaller
When is it not possible for schotty and frankel defects to occur
In non stoichiometric solids
Explain schotty defects in terms of entropy and enthalpy
Increased defects, increases entropy and increases enthalpy
Enthalpy is related to but not equal to the size of the lattice energy in schotty defects
Explain the frankel defects in terms of enthalpy, instability and repulsion
Moving a cation towards the interstitial site will move the ion closer to a neighbouring cation which will increase repulsion between the two positively charged species leading to a more unstable material
Enthalpy Change is related to energy required to move the io into a less favourable site
In a large crystal, how many ions do we have in a one mole lattice ?
Avogadros constant 6.02x10^23
What is the equation used to calculate the entropy change per mole of crystal changed?
S=k lnΩ
Where k = Boltzmann constant
S = number of statistical arrangements (typically avagadros number)
What eventually happens with the enthalpy entropy balance with schotty defects
Eventually delta g and delta h will balance out and the formation of a schotty defect will no longer be favourable
As you decrease the temperature, the number of defects…
…decreases
What are the most favourable intrinsic defects?
Schotty defects
Because a frankel defect usually involves an octahedral cation moving into a tetrahedral site which is highly endothermic and unfavourable. Partly due to size of ion
Which 3 examples prefer frenkel defects and why
AgCl, AgBr and AgI
Displacement of the Ag+ into a tetrahedral interstitial site is preferred because Ag prefers tetrahedral coordination as opposed to octahedral coordination
Why would frenkel defects be favoured?
Any vacant sites that are unoccupied by cation mean that the anions can displace from their original site and and displace to the vacant square - good for conductance
At 800 degrees C, how many defects are there in a cube of crystal approximately 20 unit cells long (100 angstroms)
1
Why is it hard to predict the number of defects at low temperatures?
Thermodynamic vs kinetic effects
At low temperatures the cations motion is typically frozen so defects cannot be moved
How can you prepare a solid with high defects
Prepare at high temperatures and rapidly cool so the ions don’t have time to move back, leading to more defects in the solid than expected
Why are some lattices such as TiO seen as metallic?
Overlap of the cations T2g orbitals forms a partially filled band of electrons therefore leaving the solid with metallic properties. The band is filling the whole structure, not truely ionic
What are the two types of extrinsic defects
Aliovalent - doping vacancies with ions of different charge
Isovalent - doping with ions of the same charge
When doping, what is the most important factor to consider?
Ionic size - needs to be similar to the ionic site
When doping a crystalline solid, how is the excess charge of the positive charge balanced?
The structure will contain pockets of electrons in anion vacancies.
The structure will have an Imbalance in numbers of cations and anions therefore resultant charge requirements are met. The defects provide colour.
Also transition metals can adopt different oxidation states giving a mechanism for maintaining charge balance when defects are created
Give three examples of non stoichiometric salts
FeO
KCl
FeO
What happens to non-stoichiometry when temperature increases
The entropy term T delta S increases with increasing temperature therefore an increase in temperature increases the value of x.
How is a solid classified as non-stoichiometric?
1) chemically significant composition range (measured under chemical analysis)
2) unit cell size varies linearly (vegards law - deviations occur at high defect concentrations)
What does the composition of a non-stoichiometric solid depend on?
Partial pressure of O2 in equilibrium with solid
The chemical potential of O2 must be equal to chemical potential of the solid
When enthalpy change is small, there’s a significant composition range
How does the size of the unit cell allow determination of non-stoichiometric solids?
As composition of the cation decreases, the size of the unit cell increases - interaction between defects results in non-linear behaviour
In a non-stoichiometric solid, how does the interplay of enthalpy and entropy change dictate the structure?
Entropy favours high concentration of defects and random distribution of defects
Enthalpy favours small concentration of defects and an ordered distribution of defects
What are point defects?
Non-interacting defects, usually metallic compounds that have d orbital overlaps
Explain the structure of SrFeO2.5 and explain the change in structure upon hearing
Vacancies order to form brownmillerite with vacancies located in alternative layers leaving layers of tetrahedrally and octahedrally coordinated Fe.
Upon heating, a transition occurs at approximately 850 degrees Celsius where:
- Oxygen vacancies become randomly distributed
- a deficient oxygen perovskite is formed
- Increase influence of entropy as temp increases
Give two methods that allow variations of oxidation states of transition metals
1) formation of very high concentrations of oxide ion vacancies (reduction with hydrides) e.g. CaH2
2) reduction of Fe oxidation stage while maintaining low vacancy content e.g. PVDF and -CH2CF2- 400 degrees c
Within perovskites the cations occupying A can be….
Different oxidation states of the same cation
How are structures ordered?
Ions with different sizes and/or charges will tend to prefer order to minimise strain and electrostatic repulsion
Explain the large perovskites structure
A unit twice as large as the conventional perovskites that is face centre with systematic absences such as Sr2FeMoO6
Explain the Ruddlesden-Popper structure
Perovskites type units separated by rock salt type layers
A(n+1) B O(3n+1)
E.g. Sr Ln 0.5 Sb 0.5 O4
On an electronic spectroscopy spectra, what gives rise to unsymmetrical peaks
eg–> t2g
When analysing spectra, what should be commented on?
Number of bands
Energies of bands
Intensities of bands
Width of bands
Why does crystal field stabilisation energy fail?
It ignore electron electron repulsion
How does the repulsion energy of xz and z^2 compare to xz and z^2?
Yz and z^2 have less repulsion than xz and z^2
When labelling orbitals in CFSE what does T and E stand for
T = 3 triplet E = 2 doublet
What does the orgel diagram show
The relationship between the d1, d4, d6 and d9 showing the ground state. This is identified where all of the lines cross over.
For these four configurations you will observe a single band with energy equivalent to delta.
When you see a g subscript, what does this relate to?
Octahedral complexes
Eg to eg transition has which symmetry and which state?
3A2g
Single find symmetry
Eg to t2g transition has which symmetry and which state?
3 fold symmetry therefore 3T2g
T2g to t2g transition has which symmetry and which state?
3 fold degenerate low energy
3T1g
When does la Porte selection rule apply?
Only to octrahedral
What three factors determine the Band widths
Vibrations
Spin orbit coupling
Reduced symmetry
If vibrations are the same and the two vibrationsl lines run
(A) parallel
(B) antiparralel
What would you expect
(A) essentially the same energy and therefore a sharp peak
(B) large energy differences therefore big energy variation and broad peak
How does spin orbit coupling affect the broadness of s peak
Typically a small effect but causes splitting of T terms
How does Jahn Teller affect the peak broadness
Removes the degeneracy of the eg level resulting in splitting of the 2Eg term which causes the peak to become more broad and asymmetric
On a tanabe sugano diagram, what is the difference between the left and the right of the diagram
Left is high spin
Right is low spin
What is MLCT favoured by
Metals with low oxidation state and ligand with empty low energy orbitals (usually pi*)
What is LMCT favoured by
Usually m in high oxidation states and ligand with low ionisation energy
