User:Benjah-bmm27/degree/2/SRH

Solid state, SRH
Solid State Chemistry Oxford VR Chemistry: Solid State Oxford first year inorganic: Structures of Simple Inorganic Solids Cambridge introduction to structures of some solids

Crystal structures

 * Close-packing of spheres, HCP, CCP
 * Unit cell, Miller indices


 * Common structure types: Cubic diamond, NaCl, CsCl, NiAs, β-ZnS, α-ZnS, CdCl2, CdI2, TiO2, CaF2, CaTiO3, ReO3


 * {| class="wikitable" style="text-align:center;"

! !!A!!AB!!AB2 ! cubic close packed ! hexagonal close packed ! body-centred cubic ! primitive cubic
 * ccp || NaCl, β-ZnS || CaF2, Na2O, CdCl2
 * hcp || NiAs, α-ZnS || hcp-CaF2, CdI2, TiO2
 * bcc || ||
 * cubic P || CsCl ||
 * }


 * Molybdenum disulfide: layer sulfide - weak interactions between layers, so they slip past each other easily - makes MoS2 a useful lubricant
 * Lattice energy: Born-Landé equation, Madelung constant, Kapustinskii equation

Lattice energy
Lattice energy, E, is the energy required to destroy a crystal structure, so for NaCl, E is ΔH for the process NaCl(s) → Na+(g) + Cl−(g)

For an idealised ionic solid, the lattice energy can be considered to arise from four effects, each with its own energy term:
 * 1) Electrostatic interactions (Coulomb energy), EC, based on Coulomb's law
 * 2) Repulsive interactions, EA
 * 3) van der Waals (dispersion) interactions, ED
 * 4) Zero-point energy (vibrational energy), E0


 * The lattice energy is a sum of these terms: $$\ E = E_C + E_A + E_D + E_0$$


 * Coulomb's law (force between two ions, + and &minus;, separated by a distance d): $$F_{+-} = \frac{1}{4\pi\varepsilon_0} \frac{z^+ z^-}{d^2}$$


 * Energy due to electrostatic interaction between two charged ions (+ and &minus;): $$E_{+-}={1 \over 4\pi\varepsilon_0}{z^+ z^- \over d} \ $$


 * The Coulomb energy of the ionic solid is therefore the sum of the energies of all the electrostatic interactions between all possible pairs of ions: $$E_C =  - \frac\sum {\frac{d}}$$


 * Combine the geometrical part (distance of each ion from a reference point) into one term called the Madelung constant, A, which is different for each structure type.


 * For example, NaCl. Using one Na+ as a reference point, coordinates (0,0,0), there are 6 Cl− at a distance $$\ d$$, 12 Na+ at a distance $${\frac{d}}$$, 8 Cl− at a distance $${\frac{d}}$$, and many more ions at greater distances.


 * $$E_C =  - \frac\frac{d}\left[ { - 6\left( 1 \right) + 12\left( {\frac{1}} \right) - 8\left( {\frac{1}} \right) +  \ldots } \right]$$


 * $$A = \left[ { - 6\left( 1 \right) + 12\left( {\frac{1}} \right) - 8\left( {\frac{1}} \right) + \ldots } \right]  \to 1.748$$

For NaCl, the electrostatic energy term in the lattice energy is $$E_C =  - \frac\left( {\frac{2}} \right)$$

An approximate expression for the lattice energy, independent of crystal structure, is $$L_0 = \frac$$

Radius ratio

 * Cation-anion radius ratio, radius ratio = r2 / r1, where r1 is the radius of the larger ion (usually the anion) and r2 is the radius of the smaller ion (usually the cation)
 * {| class="wikitable" style="text-align:center;"

!Radius Ratio!!Coordination number!!Type of hole!!Example
 * 0.225-0.414||4||Tetrahedral||ZnS, CuCl
 * 0.414-0.732||6||Octahedral||NaCl, MgO
 * 0.732-1.000||8||Cubic||CsCl, NH4Br
 * }
 * 0.732-1.000||8||Cubic||CsCl, NH4Br
 * }
 * }

Pauling's rules

 * Pauling's rules:


 * 1. Coordination polyhedra: "The coordination number of the cation will be maximized subject to the criterion of maintaining cation-anion contact"


 * 2. Electrostatic valence principle: "In a stable ionic structure, the charge on an ion is balanced by the sum of electrostatic bond strengths to the ions in its coordination polyhedron"


 * 3. Polyhedral linking: "The stability of structures with different types of polyhedral linking is vertex sharing > edge-sharing > face-sharing"


 * 4. Cation evasion: In a crystal containing different cations, those of high valency and small coordination number tend not to share polyhedron elements with each other


 * 5. Environmental homogeneity or The principle of parsimony The number of different kinds of constituent in a crystal tends to be small


 * Rule 2 means local electroneutrality must be preserved to minimise repusive Coulombic interactions - i.e. to maximise the Madelung potential


 * $${\text{electrostatic bond strength of a cation-anion bond}} = \frac$$


 * Rule 3 explains why no hcp analogue of the fluorite structure has been observed: the hcp fluorite structure has face-sharing tetrahedra which give rise to strong electrostatic repulsion between ions of like charge at the centres of neighbouring tetrahedra


 * Rule 5 means crystals tend to have similar environments for chemically similar atoms.

Band theory

 * Free electron model, Density of states
 * Band theory
 * Fermi energy, Fermi level

Solid state reactions

 * Solid-state synthesis: ceramic method (heat and beat, shake and bake)
 * Coprecipitation, Solid-state reaction, fr:Chimie douce, Redox, Comproportionation, Electrolysis
 * Intercalation: potassium graphite
 * Ionic conductivity: fast ion conductors

Defects

 * Lattice defects:
 * Schottky defects
 * Frenkel defects
 * Dislocations:
 * Edge dislocations
 * Screw dislocations
 * Burgers vector describes orientation and magnitude (perpendicular to dislocation line for edge dislocations, but parallel to line for screw dislocations)
 * Dislocations lead to work hardening (so many dislocations present that they impede each others' movement)
 * Annealing: heating a crystal to remove dislocations

One-dimensional conductors

 * Atomic wires - cyanoplatinates - Jmol models:
 * Crystal structure of K2[Pt(CN)4].3H2O: Inorg. Chem. (1976) 15, 74–78
 * Crystal structure of K2[Pt(CN)4]Br0.3·3H2O: Mater. Res. Bull. (1975) 10, 411-415 (plus this and this)
 * Crystal structure of K2[Pt(CN)4]: Z. Anorg. Allg. Chem. (2004) 630, 1462-1468
 * Crystal structure of K2[Pt(CN)4Br2]: Z. Naturforsch. B (2004) 59b, 567-572


 * K2[Pt(CN)4].3H2O + 0.15 Br2 → K2[Pt(CN)4]Br0.3·3H2O


 * {| class="wikitable sortable"

! Formula !! xtal colour !! Pt ox. state !! Pt d e− !! Pt···Pt separation
 * K2[Pt(CN)4].3H2O || yellow || +2.0 || d8 || 3.48 Å
 * K2[Pt(CN)4]Br0.3·3H2O || bronze || +2.3 || d7.7 || 2.89 Å
 * }
 * K2[Pt(CN)4]Br0.3·3H2O || bronze || +2.3 || d7.7 || 2.89 Å
 * }
 * }


 * c.f. Pt metal, Pt···Pt 2.77 Å


 * K2[Pt(CN)4].0.3Br.3H2O good conductor along Pt···Pt axes, poor conductor perpendicular to Pt···Pt axes.


 * Conductivity disappears below 150 K


 * Form a band due to overlapping Pt 5d$2 z$ orbitals - band is full in reduced salt K2[Pt(CN)4].3H2O, but partially occupied (loss of 0-0.4 electrons per Pt) in oxidised salt K2[Pt(CN)4]Br0.3·3H2O. Top of band is antibonding, so removal of electrons from it increases Pt-Pt bonding and reduced Pt···Pt separation. Fermi level within the band leads to conductivity along chain.


 * Peierls’ Theorem: "a 1-D chain will distort to split a partially filled band at the Fermi level, thereby reducing the electronic energy and destroying conductivity".


 * Above 150 K, distortion is not apparent due to thermal vibration, but below 150 K, a band gap appears, and the oxidised salt becomes a semiconductor.

Magnetism

 * Electron magnetic dipole moment


 * Magnetic structure: magnet, diamagnetism, paramagnetism, magnetic susceptibility, Curie–Weiss law, ferromagnetism, antiferromagnetism, ferrimagnetism, antiferrimagnetism, Néel temperature


 * Other magnetism stuff: spin glass, photomagnetism, metamagnetism, superparamagnetism

Superconductivity

 * Superexchange: MnO, FeO, CoO, NiO;
 * Superconductivity: zero resistance + Meissner effect, Heike Kamerlingh Onnes, high-temperature superconductivity, yttrium barium copper oxide


 * Semiconductors