Solid state chemistry Flashcards
2 types of solids but 1 has 2 subtypes.
1.Crystalline: Single crystals, Polycrystalline (many small crystals pack together)
2. non crystalline/amorphous (egglass)
Electrostatic bonding of ions equation. What is z and r?
F = -z1z2/4πEr^2 where z=charges of ions and r = distance between the 2 point charges
What is the internal energy (U) based on work done on ions (work = force x distance)
U = -z1z2/4πEr
Properties of ionic solids
Brittle, electronically insulating, high MP
Props of covalent solids
Rigid, electrically insulating, high MP
Props of metallic solids
Ductile, electrically conducting, high MP
Props of molecular solids
Soft, electrically insulating, low MP
Why are ionic solids brittle
If ions are displaces, all ions line up with similar charges which repel. It reduces the bonding so they separate
Why are ionic solids insulators
Extra electrons on anions are firmly attached so can’t carry electric current. Ions locked in position by electrostatic forces. Will conduct once melted tho
2 diff ways and names of enthalpies used when dissolving ionic solid
ΔHlattice = boiling into gaseous ions (very +ve) then ΔHsolvation (hydration) = water to gaseous ions (very -ve). OR ΔHsolution where solid dissolved in water. Sometimes +ve or -ve
Equation for gibbs E
ΔG = ΔH - TΔS
Why are cations smaller than anions
+ve charge pulls e- inwards
2 evidences for ionic solids
- Electron density maps: shows where e- density is. Metal + covalent have e- between atoms but ionic doesnt.
- Thermodynamic properties predicted using ionic model agree with experimentally measured props
First ionisation energy, Ie, definition
Change in internal energy for gas atom -> gas atom+. AT 0K! (0 kelvin)
What sign is ionisation energy always
Postive as E has to be put into the system to remove an e-
What does it mean to have a positive value for electron affinity Ea
Energy is released, exothermic. Different to normal
What sign is always 2nd electron affinities
Always endothermic so -ve. Energy is required
What does the Born-Lande potential equation represent
total coulombic interaction between 2 ions based on repulsion (electrons) + attraction (+ve and -ve charge). It is just the one you draw on the graph that goes below then above and plateaus
What is the unit for the Born-Lande potential equation
J per ion pair
What does the Born-Mayer equation calculate + in what unit
Lattice energies in J per mol
What is the constant A in Born-Mayer equation
Madelung’s constant
How is Madelungs constant calculated in a certain structure
Taking every distance between one ion to all other ions in a lattice and adding together. Repulsive = +ve, attractive = -ve
When is Kapustinskii’s equation used and what it works out
If structure and therefore Madelungs const is unknown, equation using number of ions etc in formula of compound works out lattice energy
What does rho in Born-Mayer equation come from
Compressibility data
What is Kapustinski’s equation based on
The fact that the Madelung constant/V (number of ions in the formula) is nearly constant for all structures
What is r0 in Born-Mayer equation + other eqa
The minimum distance between opposite ions = their equilibrium separation. Energy of system is a minimum
How is experimental value of UL found (lattice)
Bron-Haber/Thermodynamic cycle
3 approximations used in solid state thermodynamic cycles
- Enthalpy used rather than internal energy because H is at constant pressure but U is constant volume. ΔH = U + PΔV where ΔV is very small for solids so ΔH ≈ ΔU
- Ie & Ea are defined at 0K but thermodyn quants defined at 298 K. Only introduces a small error of 2-5kJ mol-1.
- ΔH are often so big that they determine if reaction is spontaneous. Don’t bother with ΔG and ΔS much. May need to for solubility when terms are closely balanced
Enthalpy equation based on internal energy
ΔH = ΔU+ PΔV
What is important to remember in Born Haber cycle about electron affinity. Thing used instead of Ea
If it is +ve then make it negative in calculation as it actually is exothermic. ΔHa (enth of electron gain) used in stead which is -Ea -5/2 RT but last bit not important bc very small
5 characterisation methods
Thermogravimetric analysis (TGA), Differential scanning calorimetry (DSC), Crystallography and X-ray diffraction, electrical+magnetic+optical properties (not covered), solid state NMR (not covered)
How does thermogravimetric analysis (TGA) work
Determines amount of volatile components in materials. Weight measured. Heated up and plot weight against temperature. Then can find x in eg Al2Si2O7 . xH2O as an integer
How does Differential Scanning Calorimetry (DSC) work
Empty crucible (ref) + sample crucible heated linearly. Power applied adjusted so both are at same temperature. Thermocouples measure temp. Graph of Difference in power (Pref - Psample) against temperature and time shows where more power needed (dip in graph) = endothermic = eg when H2O driven off. Peak = exothermic phase change eg from kaolinite -> mullite (exothermic phase change). Area in peak gives energy (power * time) -> shows enthalpy change
Lattice points definition
Positions within a crystal which all have identical environments
Motif (or Basis) definition
Atoms/molecules associated with each lattice point
Crystal structure def
Periodic arrangement of MOTIFS - has translational symmetry
Crystal lattice def
Periodic arrangement of LATTICE POINTS
What does a primitive unit cell have
Lattice point at each of the 8 corners. Vectors of any length + any angle. Only 1 lattice point per unit cell so 1 motif per unit cell.
Bcc structure
1/8 lattice point in each corner + 1 in middle. Total 2
Fcc (ccp) structure
1/8 in each corner, 1/2 on each face. Total 4 lattice points
Why are some non-primitive unit cells chosen over primitive
All crystals have primitive ones but can be harder to draw + visualise
What are 3 types of symmetry for crystals
Translational, point group and combined translation and point group symmetry
What is point group symmetry
Rotations and reflections about certain points in the crystals that leave crystal looking the same
What is combined translation + point group symmetry
Glide planes: translate crystal by 1/2 a unit cell in direction parallel to glide plane, then reflect crystal across glide plane. Screw axes also exist but not covered in this course.
What are the “only” rotation axis that exist
1 fold (no symmetry at all), 2 fold (180), 3, 4, 6. 5 is only quasi crystals. This is bc unit cells must tesselate and other rotational symmetry will create gaps. You can’t have gaps if you also have unit cells
What is tessellation
Arranging shapes closely together with no gaps - happens in crystal so only 1,2,3,4,6 fold rotations can happen
How many fundamental types of lattices are there and what is their name
14 and Bravais lattices
What are the seven crystal systems
1) Triclinic: non-equiv or perpendicular sides. No axes of symmetry. 2) Monoclinic: 2 faces at right angles to third. 3 edges different lengths. 3) Trigonal (rhombohedral): all edges are the same length. 4) Hexagonal: 2 edges same length (120° between them). 3rd at right angles to them. 5) Orthorhombic: all faces at right angles + all different lengths. 6) Tetragonal: All faces right angles. 1 square face. 7) Cubic: All faces right angles + same length edges
How many ways are there of stacking the 7 possible crystal systems (block shapes) for crystals
14 - Bravais lattices
Energy of X-ray equation
E=hv=hc/λ. = very small number. Divide by e- charge = around 6200 eV
When is diffraction the most pronounced
When wavelength is comparible to spacing
What is a thermal neutron
The speed/energy they would have if neutrons were a gas at room temperature
What is the Bragg equation + meaning + use
nλ=2dsinθ. d is distance between atom layers. n is order of diffraction. If equation is true for a θ, then it is constructive interference as beam bouncing off lower layer will continue in phase with beam off upper layer of crystal. All other θ are destructive. Use: Find length between atom layers in crystals (d) since we know λ and can find θ
Which values are known/measured in Bragg equation
nλ=2dsinθ. We know λ from what we aim at crystal. θ is measured and d is worked out.
How much of X-ray is diffracted by crystal
About 0.01%, but each layer of crystal reflects that much which results in a strong beam
Separation d(hkl) between planes given by what eqn
d(hkl) = a/sqrt(h^2+k^2+l^2)
Use of miller indices
We use the three miller indices (h k l) to refer to sets of planes with a particular spacing d(hkl). They are used in reciprocal space.
How to produce X-ray using electrons (3 ways but 2 are similar)
- e- excited then releases photon as it drops back into hole.
- e- deceleration gives Bremsstrahlung radiation = continuum of white (all freqs) radiation.
- OR e- accelerated in magnetic field gives curve with increasing radius. Diff radii gives diff rate of change of velocity = white radiation emitted
4 devices used for generating X-rays + explain first 2
- Standard X-ray generator: e- from filament go through field and hit copper target. Sudden breaking + the acceleration releases X-rays + peaks (2 or more) from e- in copper being excited then releasing photons
- Synchrotron bending magnet: accelerates e- around circle. Gives Bremsstrahlung x-rays (all)
- Synchrotron Wiggler
- Synchrotron Undulator
What devices can be used for synchrotons
- Synchrotron Wiggler. Makes e- wiggle down then back up in normal path to increase x-ray intensity since it gets accelerated (change in direction)
- Synchrotron undulator: Wiggles it loads and loads. Since e- is almost at x-rays releaseds speed but longer path length means interference - causes intermittent peaks of higher intensity than wiggler.
Hi
What process causes electrons to emit the x-rays used in a diffraction experiment
(Although Bremsstrahlung takes place in a sealed x-ray tube it produces polychromatic radiation.) In an x-ray diffraction we require monochromatic x-rays (a single wavelength) so we tune the instrument to use a characteristic peak (transition of electrons between energy levels) of the anode emission spectrum. Bending and wiggling electrons in a magnetic field to generate x-rays are methods only used in large synchrotron facilities.
Conditions for diffracted beams to show up in Simple cubic, bcc and fcc
Simple: All allowed
bcc: sum of no. must be even so 110 yes but 100 no.
fcc: all must be even or all odd so 200 yes but 300 no.
Care must be taken when using X-ray diffraction experiments to determine the location of hydrogen atoms in organic molecules. Why is this the case?
The electron density associated with hydrogen atoms will be pulled towards the adjacent carbon atom. The peak in the electron density map will not be centred on hydrogen atom itself.
2 types of powder x-ray diffraction and their difference.
Single crystal and crystalline powder diffraction. Hard to grow single crystal so powder has many random orientations. Produces Debye-Scherrer rings instead of dots.
What are Debye-Scherrer rings
Result of crystalline powder diffractions
How are Debye-Scherrer rings analysed
Plotted on graph of intensity vs 2theta to find crystal structure using missing diffraction beams
Why are beam stops used
99% of x-rays go through so used to stop them so machine doesn’t catch fire
What causes the intensities of diffraction beams
The motif
What causes the shape of diffraction pattern
The lattice shape
Rules for close packing
- All atoms are hard spheres - no distorion.
- Spheres packed as tightly as possible.
- Big spheres leave spaces where little spheres can fit into
What structure of layers is hcp. Coord number?
ABAB, coord: 12
What structure of layers is ccp/fcc. Coord number?
ABCABC.., 12
How much of available volume does fcc, hcp, bcc, simple cubic and fcc diamon structure occupy
fcc, hcp: 74%
bcc: 68%
Simple cubic: 52%
Fcc diamond: 34%
What is polymorphism and example of what material does that
This is where a material has different crystal structures under different experimental
conditions (e.g. temperature or pressure). Iron.
Structure of tetrahedral hole. Coord number?
Between 3 A-layer atoms and 1 B-layer atom. Coord of 4
Structure of octahedral holes. Coord number?
Between 3 A-layer atoms and 3 B-layer atoms. Coord of 6
Amount of octahedral and tetrahedral holes for FCC (ccp)
Octa: 1 on each edge (12) ans 1 in middle = total 4. Tetra: 8
Sodium chloride structure NaCl
Cl- in FCC (ccp) structure. Na+ in octahedral holes.
Calcium fluoride structure CaF2
Ca2+ in FCC lattice (coord 8). F- ions occupy all tetrahedral holes (coord 4)
Zinc Blende (ZnS) stucture
Zn2+ in FCC lattice (coord 4). S2- occupy half of tetrahedral holes diagonal to each other. (coord 4)
Diamond structure
Not ionic, covalent. Carbons in lattice points of FCC unit cell. Carbons in half of tetrahedral holes (same as ZnS blende)
In diagram to show structure of fcc, why does it just say 0 in corners, not (1, 0)
Becasue we know there are atoms at the top corners
Rules for ionic radius ratios in crystal structures
- Cations + anions in contact to minimise energy.
- As many anions as possible surround cations (normally anions are bigger so makes sense).
- Geometry must minimise anion-anion contact
CsCl structure
Bcc structure and every other atom is Cs or Cl
List of r+/r- rations compared to coordination number (structure)
1-0.732: 8 (CsCl)
0.732-0.414: 6 (NaCl)
0.414-0.225: 4 (ZnS)
0.225-0.155: 3
0.155-0: 2
Difference between conductivity and conductance
Conductance depends on dimensions but conductivity is a property of the material
How does conductivity depend on temp for conductors
Decreases as temp increases. Cations vibrate more -> obstructs e-, slows them down - stops free path of e-
How does conductivity depend on temp for semi-conductoros
Increases with temp increase
Numbers of conductivity for conductors, semiconductors and insulators
Conducts: 10^6-10^8 Ω-1m-1
Semi: 10^-4 - 10^5
Insulators: <10^-4
2 theories of behaviours of conductors, semi and insulators
Free e- theory, Linear Combination of Atomic Orbitals theory
What does density of states mean
DOS: number of orbitals (states) there are per eV, per atom in band structure
What is the Aufbau principle
Electrons fill lower-energy atomic orbitals before filling higher-energy ones
Why can metals conduct electricityin terms of e- and orbitals
Small increase in KE -> e- jumps up from filled to empty orbitals. Can conduct elec because of proximity of empty to filled orbitals.
Why are metals opaque
All wavelengths of radiation can be absorbed because a filled level always has an empty level above it so e- can jump up
Why are metals colourless
No wavelength is absorbed more strongly than another
2 types of semiconductors
Intrinsic and extrinsic
What is an intrinsic semiconductor
Ultra-pure materials
What is an extrinsic semiconductor
Deliberately made impute by embedding foreign atoms in the crystal to change electrical properties
What is valence band, band gap and conduction band
Valence: Full lower level, Band gap where no orbitals exist at all, Conduction band is empty band of orbitals
Where is fermi level in band gap
Half way up the gap
What are p type charge carrier
An apparent positive hole left in valence band as e- moves to conduction band. Can also carry current. Positive hole = p type charge carriers
What are n type charge carriers
e- that moves up into conduction band. Lots of closely spaced empty levels available to carry current- Negative e- = n type charge carriers
How does migration of a p type work
e- hops into hole left by movement of previous e-.
Why are semiconductors opaque
Light absorbed if photon energy is higher than band gap (eV). e- from valence band and excite to conduction. For a lower photon energy eg IR, material is transparent.
Reason for optical transparency
Band gap higher than 3ev so optical photons can’t be absorbed
Explain the reason for photoconductivity of semiconductors
Absorption of a photon promotes an electron from the valence band to the conduction band, leaving a hole in the valence band. There is an n-type in conduction band (e-) and p-type charge carrier in valence band (+ve hole). Both e- and hole can carry current so conductivity is proportional to amount of light absorbed
Why conductivity increases with temperature
No. of e-excited from valence to conduction band goes up exponentially. Conoductivitydepends on charge carriers so more e- and holes makes conductivity increas exponentially too
Why do insulators not conduct electricity and why are they transparent
Band gap too large to excite e- across so no charge carriers. Transparent bc no light absorbed
What is an n type semiconductor (Si)
Si doped with P. P has one more e- than Si. P energy level lies just below bottom of conduction band. P donates e- to become P+. Ion is fixed but e- can move so is an n type semiconductor.
What is a p type semiconductor (Si)
Si doped with Al. Al one less e- than Si. Al energy level just above valence bond. So Al = acceptor -> Al- ion immobile in silicon lattice but +ve hole left = charge carrier = p type semiconductor
What can be done by linking together p and n type semiconds.
Circuits and computer chips
Why are H hard to see in electron density maps
Often lost in noise of map if quality isn’t high.
Also, electron density is pulled towards carbon so more difficult to measure correctly.
Why does electron affinity of F->I have descending eV. Outlier?
Electrostat attraction between e- and nucleus gets smaller as atom size increases. Less E given out. F is unusually small because of high e- density which gives higher repulsion of e-
Enthalpy of solution vs enthalpy of hydration (solvation)
Solution = NaCl (s) -> Na+ (aq) + Cl-(aq) but hydration is them in gas phase into aq
What is lattice constant
a = the length of side of the unit cell cube, called the cubic lattice constant
What is Kapustinskis equation based on? What makes it work?
The fact that madelungs constant divided by V (number of ions in formula) is very nearly constant
What is de Broglies equation (used when calc electron wavelength and kinetic energy)
p = h/𝜆
where p = momentum = mv
Use of thermogravimetric analysis (TGA)
To determine composition - amounts of volatile components
Use of Differential Scanning Calorimetry (DSC)
Determine phase changes in solid
Use of Crystallography and X-ray Diffraction
Most important technique for structure determination
Photons of visible light have energies spanning range…?
1.5-3 eV
What does Kapustinski’s equation assume?
Purely ionic bonding comprising only
electrostatic (or Coulombic) interactions as a result of complete transfer of electrons from the cations to the anions.
