Glossary
Every term and acronym the unit uses, in one alphabetical list.
250 of 250 terms
- Absolute zero
The temperature at which every molecule is in the ground state. There is no lower energy, so no lower temperature.
- Accessible volume
The space available to the centre of a particle. The more room it has, the more arrangements it can take, and the more entropy.
- Activation energyE_a
The energy an ion or molecule needs to get over a barrier, such as an ion hopping to the next lattice site.
- Amorphous
Without the long-range regular order of a crystal.
- Amphiphile
A molecule with one end that likes the solvent and one end that avoids it, such as a charged head and a fatty tail. At high concentration these molecules clump so the tails hide.
- Anisotropy
Properties that depend on the direction you measure. The opposite of isotropic, where every direction looks the same.
- Antiferromagnetism
Neighbouring spins point opposite ways and cancel, so there is no net magnetisation at zero field.
- Antifluorite
Li2O type. ccp anions with all tetrahedral holes filled by cations. Coordination 4:8.
- Arrhenius equation
A rate or conductivity that grows as exp(-E_a/kT): rising temperature makes it climb fast, a bigger barrier makes it small.
- Band
A strip of allowed electron energies. In a crystal the orbitals of many atoms sit so close together that they blur into one continuous band.
- Band gap
The energy difference between the highest occupied state in the valence band and the lowest unoccupied state in the conduction band. Semiconductors are about 0.5 to 3 eV.
- BCS theoryBardeen-Cooper-Schrieffer theory
The quantum theory of superconductivity as electron pairing. It gives k_B T_c = hbar omega exp(-1/(V N(E_f))).
- Betaβ = 1/kT
The one number that sets all the populations. The lecture defines temperature so that beta is 1 over kT.
- Birefringence
When light shaking in two directions travels at two different speeds through an aligned material, so the two parts drift out of step.
- Bohr magnetonmu_B
The unit of an electron magnetic moment, 9.27 x 10^-24 A m^2.
- Boltzmann constantk
The constant that links energy to temperature, exactly 1.380649 x 10^-23 J per kelvin.
- Boltzmann distribution
The share of molecules in each energy level at equilibrium. Higher levels hold exponentially fewer molecules.
- Bomb calorimeter
A sealed steel container sitting in water, used to measure heat at constant volume.
- Born–Mayer equation
Gives lattice enthalpy from the ion charges, the ion separation d, a repulsion constant d* and the Madelung constant.
- Bragg equationn lambda = 2 d sin theta
Links the X-ray wavelength, the spacing between planes and the angle at which reflections appear.
- Bravais lattice
One of 14 distinct lattices, made from the seven crystal systems with primitive (P), base-centred (C), body-centred (I) or face-centred (F) centring.
- Caesium chloride structure
Two interpenetrating simple cubic cells, not close-packed. Coordination 8:8.
- Calorimetry
Measuring heat, by watching how much a known amount of material warms or cools.
- Canonical ensemble
An imaginary pile of many copies of the whole system, all with the same number of particles, volume and temperature.
- Canonical partition functionQ
The sum of exp(-E/kT) over every state of the whole system. It replaces the molecular partition function when particles interact.
- Carrier concentrationn
The number of charge carriers per volume that can be excited to move. Only electrons within a few kT of the Fermi level count.
- Carrier mobilitymu
How easily carriers move, mu = e tau / m*. Impurities and lattice vibrations lower it.
- Catalyst
Something that speeds up a reaction by lowering the Gibbs free energy of activation. It does not change where the reaction ends up.
- Characteristic temperatureΘ = ΔE/k
The temperature set by a system energy spacing. Well above it the system is hot and many states are used. Well below it only the ground state is used.
- Chemical potentialμ
What becomes equal between a system and its surroundings when particles can swap across the boundary.
- Chiral
A molecule that cannot be put on top of its mirror image, like a left and right hand. It has no improper symmetry element.
- Cholesteric phasechiral nematic
A nematic made of twisted-handed molecules, where the pointing direction turns slowly along an axis. The distance for one full turn is the pitch.
- Classical mechanics
Describes the world with positions and velocities (trajectories). Fine when the de Broglie wavelength is much smaller than the system.
- Clausius-Clapeyron equation
The slope of a phase boundary on a pT diagram: dp/dT equals the entropy change divided by the volume change of the transition.
- Coercive fieldE_c (electric), H_c (magnetic)
The reverse field needed to bring the net polarisation (or magnetisation) back to zero.
- Coexistence
Two phases, such as liquid and gas, present together at equilibrium, with the same chemical potential.
- Colloid
A mixture where tiny particles stay spread through a liquid. The particles are between the size of a solution and a suspension.
- Conduction band
The band made of unoccupied orbitals. Electrons promoted into it can carry current.
- Conductivitysigma
How well a material carries current, in S per cm. It is the inverse of resistivity, sigma = 1/rho.
- Configuration (macrostate)
A group of microstates that give the same bulk property, like "two heads out of four coins". In chemistry it is the list of occupation numbers.
- Cooper pair
Two electrons paired up at low temperature (BCS theory). The pairs move through the lattice without scattering, which gives zero resistance.
- Coordination number
How many nearest neighbours an atom or ion has. For ionic crystals it is written cation first, then anion.
- Critical point
The end of the liquid-gas line on a phase diagram. Beyond it liquid and gas cannot be told apart.
- Critical radiusr*
The size a nucleus must reach to survive. Smaller ones shrink, bigger ones grow. r* = 2 gamma / DeltaG_V.
- Critical temperatureT_c
The temperature below which a material becomes superconducting.
- Crystal system
One of seven cell shapes: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, cubic.
- Cubic close-packed (ccp, fcc)
Spheres stacked in layers ABCABC. The same as face-centred cubic. 12 nearest neighbours and 74 percent of space filled.
- Curie law
The paramagnetic susceptibility falls with temperature as chi = C_Curie / T.
- Curie temperatureT_C
The temperature at which a ferroelectric becomes paraelectric, or a ferromagnet becomes paramagnetic. For BaTiO3 it is 120 C.
- Curie-Weiss law
The susceptibility above the ordering temperature of a ferromagnet or antiferromagnet, chi = C/(T - theta).
- de Broglie wavelengthlambda = h / p
The size of the wave that goes with a moving particle. If it is much smaller than the thing you study, you can treat the particle classically.
- Debye temperaturehbar omega / k_B
A temperature standing for the collective (acoustic) vibration of the lattice. It appears in the BCS equation.
- Defect
A flaw in an otherwise perfect crystal, like a missing egg in an egg tray. Defects change strength, conductivity and colour.
- Degeneracyg
The number of states that share one energy level.
- Delocalised electronic conduction
Conduction by electrons spread over the whole crystal through a band, as in metals, silicon and graphite. The opposite is localised conduction.
- Dendrite
A branching, tree-like crystal that grows when diffusion limits growth and the tips get the most supply, as in a snowflake.
- Density of statesDOS
The number of permitted electronic states in an energy interval. In plain words, how many seats there are at each energy.
- Diamagnetism
A weak repulsion from a magnetic field that all materials show, from paired electrons. chi is negative and temperature-independent.
- Dielectric
An electrical insulator that can be polarised by an applied electric field. Its charges shift slightly when a field is applied.
- Differential rate law
An equation for how fast a concentration is changing right now, in terms of the concentrations.
- Diffusion
Net movement of matter from high to low concentration, caused by random motion of the particles.
- Diffusion-controlled reaction
A reaction that happens every time the partners touch. Its speed is set only by how fast and how far the partners diffuse.
- Dimensional analysis
A quick estimate that uses how quantities scale with size, for example mass with length cubed and area with length squared, to test an idea.
- Director
The average direction that the rods point in a liquid crystal. Written as n-bar.
- Dislocation
A line defect. Edge dislocations are an extra half-row of atoms. Screw dislocations spiral like a staircase.
- Double exchange
An unpaired electron hopping between magnetic ions of different oxidation states, easy only if spins stay aligned. It favours ferromagnetic order.
- Drude model
The conductivity formula sigma = n e^2 tau / m*, built from carrier number, charge, relaxation time and effective mass.
- DSCdifferential scanning calorimetry
A technique that heats a sample and an empty reference pan at the same rate and records the extra heater power the sample needs. Works on milligram samples.
- Dulong-Petit law3R = 24.9 J/K/mol
At high temperature the molar heat capacity of a simple solid approaches 3R.
- Effective ionic radius
The size given to an ion, based on the minimum in electron density between ions. It depends on coordination number.
- Effective massm*
How heavy a carrier acts in a crystal. It depends on band width, which depends on orbital overlap.
- Ehrenfest classification
Sorting phase transitions by which derivative of the Gibbs energy is discontinuous.
- Einstein solid
A model where each atom of a crystal is an independent 3D harmonic oscillator, and all share one frequency.
- Electric susceptibilitychi_e
The size of the polarisation response, chi_e = epsilon_r - 1, with P = epsilon_0 chi_e E.
- Electron density map
A 3D map of where the electrons are, built from the diffraction pattern. It shows geometry and bonding.
- Elementary process
A single real step in a reaction, either one molecule changing or two molecules meeting. Its rate law follows from its molecularity.
- EnthalpyH = U + pV
Internal energy plus pV. At constant pressure, its change equals the heat flowing in. Exothermic and endothermic usually refer to its change.
- EntropyS = k ln W
A measure of how many microstates a configuration has. More ways to arrange things means higher entropy.
- Excluded volumeNb
The room the molecules themselves take up, which is not free for them to move in.
- Expectation value
An average over states, with each state weighted by how likely it is.
- Extrinsic defect
A defect that thermodynamics does not require, such as an impurity atom.
- Extrinsic semiconductor
A semiconductor with a deliberate impurity added (doped). Most semiconductors used in electronics are this kind.
- Fermi levelE_F
A hypothetical electron energy at which the probability of occupation is 50%. In a metal it sits inside a partly filled band.
- Ferrimagnetism
Opposing moments that do not cancel, so there is a spontaneous net magnetisation. Magnetite is an example.
- Ferroelectric
A dielectric with spontaneous polarisation that is kept when the field is removed.
- Ferromagnetism
All spins aligned, giving spontaneous magnetisation below the Curie temperature.
- Fick's first law
The flux across a surface is proportional to the area and to the concentration gradient. J = -D A dc/dx.
- Fick's second law
How the concentration at a point changes with time. dc/dt = D d2c/dx2. Bumps flatten and dips fill.
- First law of thermodynamics
Energy is conserved. In this unit, the change in internal energy equals heat entering plus work done on the system: delta U = Q + W.
- First-order transition
A transition with latent heat, where the first derivatives of G (entropy and volume) jump. Boiling and freezing are examples.
- Fractional coordinates
Where an atom sits in the cell as fractions (0 to 1) of each cell edge.
- Frenkel defect
An atom that has hopped out of its site into a nearby gap, leaving a vacancy behind. Found where ion sizes differ a lot, like AgCl.
- Fundamental postulate
Every microstate is equally likely. So the most likely configuration is the one with the most microstates.
- Gibbs free energyG = H - TS
The test for spontaneous change at constant temperature and pressure. A spontaneous change has delta G of zero or less.
- Glass
An amorphous solid that shows a glass transition. Think of a liquid frozen in place before it could crystallise.
- Glass transitionT_g
The gradual, reversible change between the brittle glass and the liquid on heating. It happens over a range that depends on cooling rate.
- Glide plane
A reflection followed by a slide, usually half a cell edge or diagonal. It changes handedness.
- Grain boundary
The surface between two crystal grains that point in different directions in a polycrystalline solid.
- Half-life
The time for a concentration to fall to half. For first order it is ln(2)/k and does not depend on the starting concentration.
- Hard-particle model
A model where particles cannot overlap and have no other forces. With no interaction energy, only entropy decides the stable phase.
- HeatQ
Energy that crosses the boundary because of a temperature difference. It is energy in motion, not energy stored.
- Heat capacityC = dQ/dT
How much heat you must add to raise the temperature by one unit.
- Helmholtz free energyA = U - TS
The most work you can get out of a system at constant temperature. At constant T and V a spontaneous change lowers A.
- Heterogeneous nucleation
Seeds of the new phase starting on a wall or an impurity particle.
- Hexagonal close-packed (hcp)
Spheres stacked in layers ABAB. Each sphere has 12 nearest neighbours.
- Homogeneous nucleation
Seeds of the new phase appearing spontaneously inside the liquid itself.
- Identity (E)
The operation that does nothing. Every molecule has it.
- Importance sampling
Generating configurations with the probability they have at equilibrium, so each can be counted equally, instead of weighting random ones afterwards.
- Improper operation
Any operation with a reflection or inversion in it. It flips handedness. A molecule with one cannot be chiral.
- Improper rotation (Sn)
A rotation by 360/n followed by a reflection in the plane across the axis. S1 is the same as sigma and S2 is the same as i.
- Inert pair effect
Heavy cations such as Sn2+, Pb2+ and Bi3+ keep a lone pair of s electrons that is not spherical, which distorts the structure.
- Integrated rate law
An equation for the concentration at any time. It is what you get by integrating the differential rate law.
- Intercalation
Sliding atoms or molecules between the layers or cages of a host, such as K into graphite to give KC8, or alkali metals into C60.
- Interfacial energygamma
The energy cost of creating a surface between the new and old phase. Always positive.
- Internal energyU
The total energy of all the molecules in their occupied states.
- Interstitial impurity
A foreign atom squeezed into a hole between the regular atoms. Hydrogen in palladium is an example.
- Intrinsic defect
A defect that thermodynamics makes, such as a Schottky or Frenkel pair. All solids have some above absolute zero.
- Intrinsic semiconductor
A pure, undoped semiconductor. Heating promotes electrons from the valence band to the conduction band across a small gap.
- Inversion axis (n-bar)
A rotation by 360/n followed by inversion through a centre point. Used mostly for crystals.
- Inversion centre (i)
A point through which every atom can be sent straight across to an identical atom at the same distance on the other side.
- Ionic conductivity
Electric current carried by ions hopping through a solid, which needs defects to move through.
- Ising model
A lattice of spins that can only point up or down, interacting with nearest neighbours. The simplest model of a magnet.
- Isochoric and isobaric
Isochoric means constant volume. Isobaric means constant pressure.
- Isoelectronic
Having the same number of valence electrons. In the lecture, elements in the same group.
- Ketelaar's triangle
A triangle showing a smooth range between ionic, covalent and metallic bonding.
- Krogmann salt
Partly oxidised K2[Pt(CN)4], the first molecular metal. It conducts along chains of platinum units (1D).
- kTBoltzmann constant times temperature
The size of a typical thermal push. About 2.5 kJ/mol at 25 degrees C. An energy gap much bigger than kT is almost never crossed by heat alone.
- Latent heat
Heat absorbed or released during a change of state without the temperature changing, like ice melting in a drink.
- Lattice enthalpyDelta H_L
The energy to pull one mole of an ionic crystal apart into separate gaseous ions.
- Lyotropic phase
An ordered phase that forms when molecules such as amphiphiles are dissolved. The phase depends on concentration and temperature, and can shift with pH or salt.
- Madelung constantA
A number that depends on the crystal structure. It adds up the attraction and repulsion from every shell of neighbours around an ion.
- Magnetic domain
A patch of a magnet where all the spins line up. If the domains point randomly, the piece has no net magnetisation.
- Magnetic susceptibilitychi
How strongly a material becomes magnetised in a field, from M = chi H. Negative for diamagnets, positive for the others.
- MagnetisationM
Magnetic moment per unit volume of a material.
- MagnetiteFe3O4, lodestone
A ferrite with an inverse spinel structure. It is ferrimagnetic and conducts through Fe2+ <-> Fe3+ + e-.
- Martensite
A very hard metastable form of steel made by quenching, which is why quench hardening works.
- Mean-field theory
An approximation that replaces all the separate pushes and pulls a particle feels with one average push. It is crude but shows transitions clearly.
- Meissner effect
A superconductor pushing magnetic fields out of itself as it cools through its critical temperature. It is perfect diamagnetism.
- Mesogen
A molecule that can form a mesophase.
- Mesophase
An equilibrium phase between liquid and crystal. It has some liquid properties, such as flowing, and some crystal properties, such as long-range alignment.
- Metastable
Not at equilibrium but stuck in a shallow dip behind an energy barrier, like a book standing on its edge. Glass, diamond and martensite are examples.
- Metropolis rule
Accept a move that lowers the energy. Accept one that raises it with probability exp(-beta dE).
- Microstate
One exact arrangement of every individual molecule, like which coin is heads and which is tails.
- Miller indices (h k l)
Three whole numbers that name a plane in a crystal. The plane cuts the axes at 1/h, 1/k and 1/l. A negative index has an overbar.
- Mirror plane (sigma)
An imaginary plane where one side is the mirror image of the other. sigma_v contains the principal axis. sigma_h is perpendicular to it.
- Model
A simplified picture of part of the natural world. It is simple enough to understand and still captures something real. A map is a model.
- Molar heat capacity
Heat capacity per mole of substance.
- Molecular dynamicsMD
A simulation that follows atoms through time by solving Newton's laws step by step.
- Monte Carlo simulation
A method that makes random trial moves and accepts or rejects them by a rule, to sample equilibrium configurations. It gives no real time dynamics.
- Mott-Hubbard insulator
A material where atoms are far enough apart that the band model fails and electrons stay on individual atoms or molecules, so it does not conduct.
- n-type semiconductor
A doped semiconductor whose carriers are negative electrons. The dopant has occupied levels just below an empty conduction band, such as As in Si.
- Neel temperatureT_N
The temperature below which an antiferromagnet orders. For an antiferromagnet theta = -T_N.
- Nematic phase
A mesophase where rod-shaped molecules point the same way on average but are not arranged in layers or at fixed sites.
- Nucleation
The first appearance of tiny seeds of a new phase inside the old one.
- Nucleation barrierDeltaG*
The energy hump a nucleus has to climb to reach the critical radius. It falls with deeper undercooling.
- Occupation numbern_i
How many molecules are in quantum state i.
- Octahedral hole
The gap among six packed spheres. There is one per ccp atom, with size ratio 0.414.
- Onsager theory
A calculation that predicts, from rod shape alone, the concentrations where the isotropic and nematic phases are stable. It balances orientational entropy against translational entropy.
- Open, closed and isolated system
Open swaps matter and energy with the outside. Closed swaps energy only. Isolated swaps neither.
- Order parameterS
One number that says how well rods line up. It is 1 for perfect alignment and 0 for a random (isotropic) crowd.
- Ostwald ripening
Small particles dissolve while large ones grow, so the structure coarsens over time.
- p-n junction
An n-type and a p-type semiconductor joined together. Electrons diffuse from n to p and set up an electric field. It lets current pass one way, and a solar cell is one.
- p-type semiconductor
A doped semiconductor whose carriers are positive holes. The dopant has empty levels just above a full valence band, such as Ga in Si.
- Paraelectric
A dielectric that polarises when a field is applied and loses the polarisation when the field is removed.
- Paramagnetism
Attraction to a field from unpaired electrons that the field aligns. chi is positive and follows Curie law, chi = C/T.
- Partition functionq
The sum of e to the minus beta epsilon over all states. Roughly the number of states a molecule can reach at this temperature.
- Pauli exclusion principle
No two electrons in an atom can have all four quantum numbers the same. An orbital holds at most two electrons.
- Periodic boundary conditions
Surrounding a small simulation box with copies of itself so that a particle leaving one side comes back in the other.
- Perovskite
A structure with the formula ABX3, where A is a 12-coordinate cation, B an octahedral cation and X an anion. BaTiO3 is an example.
- Phase
A state of matter whose properties change smoothly, such as ice, liquid water or water vapour.
- Phase diagram
A map of pressure and temperature (or volume) showing which phase is stable where, with boundary lines where two phases coexist.
- Phase transition
An abrupt change in a physical property, like the jump in density when water boils. It needs interactions between particles.
- Photovoltaic diodePV diode, solar cell
A p-n junction where incoming photons keep supplying new electrons and holes, so a current flows.
- Piezoelectric effect
Stress on a material produces a voltage. The reverse effect is a voltage changing the material size.
- Pitch
In a cholesteric, the distance over which the director rotates a full turn.
- Point defect
A flaw at a single lattice site, or a few. It is zero-dimensional. Vacancies, interstitials and impurities are examples.
- Point group
The full set of symmetry operations of a molecule. Molecules with the same symmetry share a point group.
- PolarisationP
The shift of charges in a dielectric under a field. The lecture lists electronic, ionic, orientation and space charge mechanisms.
- Polarised light
Light whose electric field shakes in one direction only.
- Potential energy curve
A graph of energy against the distance between two atoms. It dips to a minimum where the bond sits and rises steeply when the nuclei get too close.
- Potential energy surface
A landscape of energy against the positions of the atoms. Reactants sit in one valley, products in another.
- Pre-equilibrium
A fast reversible step that stays in equilibrium while one of its products slowly goes on to react in a later step.
- Principal axis
The rotation axis with the highest n. By convention it is the z-axis.
- Principle of detailed balance
At equilibrium, the forward and backward rates of every elementary step are equal.
- Proper operation
The identity or a pure rotation. It keeps handedness.
- Quantum mechanics
Describes the world with wave functions. Needed for light particles such as electrons and for very low temperatures.
- Radius ratior cation / r anion
The size of the cation divided by the size of the anion. A bigger ratio gives a higher coordination number.
- Random walk
A path made of steps in random directions. It models Brownian motion. One walker is unpredictable, but the average of x squared across many walkers grows linearly with time.
- Rate-determining step
The slowest step in a mechanism, which acts as the bottleneck for the overall rate.
- Reaction mechanism
The list of elementary steps that make up an overall reaction. The rate law comes from the mechanism, not from the balanced equation.
- Reciprocal lattice
The lattice whose points are the diffraction spots. A pattern is a slice through it.
- Recurrent and transient random walks
A recurrent walk keeps coming back to its start. A transient walk may never return. 2-d walks are recurrent and 3-d walks are transient.
- Relative permittivitydielectric constant, epsilon_r
How readily a material polarises in a field, compared with vacuum (which is 1). It has no units. Inserting the material multiplies a capacitor capacitance by this factor.
- Relaxation timetau
The average time a carrier travels between scattering events.
- Remnant polarisationP_r
The polarisation left when the field returns to zero after a strong field.
- Reservoir
Surroundings so big that taking or giving some heat does not change their temperature.
- Residual entropy
Entropy left over at absolute zero because the lowest-energy arrangement is not unique. CO, ice and spin ice are examples.
- Reversible process
A process that is always at equilibrium, so it runs infinitely slowly.
- Rock-salt structure
NaCl type. ccp anions with all octahedral holes filled by cations. Coordination 6:6.
- Rotation axis (Cn)Rotation by 360 degrees / n
A line you can turn the molecule about, by 360/n degrees, so it looks the same.
- Rutile
TiO2 type. Distorted hcp anions with half the octahedral holes filled. Coordination 6:3.
- Saturation polarisationP_s
The polarisation reached in a strong field when all domains are aligned.
- Schoenflies notation
The point group naming that chemists use for molecules, such as C3v and D6h.
- Schottky defect
A pair of empty sites, one where a cation should be and one where an anion should be. Found in crystals like NaCl with highly coordinated ions of similar size.
- Screw axism_n
A turn plus a slide, like a spiral staircase. m_n means slide n/m of the cell and turn 360/m degrees. It keeps handedness.
- Second harmonic generationSHG
Two photons combine into one with twice the energy, such as red light turned into green in a KTP laser. The crystal has no inversion centre.
- Second law of thermodynamics
The entropy of an isolated system always increases. Heat flows from hot to cold by itself.
- Second-order transition
A transition with no latent heat, where entropy and volume are continuous and the second derivative of G jumps. Ferromagnetic and superconducting transitions are examples.
- Selective reflection
A cholesteric bounces back some colours of white light and lets the rest through, because of its repeating twist.
- Self-consistency equation
An equation with the unknown on both sides, such as m/N = tanh(beta J d m/N), solved by finding where two curves cross.
- Semi-metal
A material like graphite where thermal energy promotes a small number of electrons into the conduction band.
- Smectic phase
A mesophase where the rods point the same way and also sit in layers.
- Soft matter
Anything that can be changed by pushes as small as the random jostling of heat. Polymers, colloids and liquid crystals are examples.
- Space group
A point group combined with translation. There are 230 of them. It lists every symmetry element of a crystal.
- Specific heat capacity
Heat capacity per unit mass (the slides say per gram). It lets you compare materials fairly.
- Spinodal decomposition
Phase separation of a mixture with no nucleation barrier, driven only by diffusion. The whole mixture clumps into two phases.
- Stacking fault
A planar defect where the usual sequence of close-packed layers (ABC for fcc, ABA for hcp) breaks.
- State function
A quantity that depends only on the current state of the system, not on how it got there.
- Steady state approximation
The assumption that a short-lived intermediate quickly reaches a constant concentration, so its rate of change is zero.
- Stirling approximation
A shortcut for the log of a huge factorial: ln n! is about n ln n minus n.
- Substitutional impurity
A foreign atom sitting on a normal lattice site, taking the place of a regular atom. Chromium in ruby is an example.
- Superconductor
A material that below its critical temperature has zero resistivity and completely expels magnetic fields.
- Supercooled liquid
A liquid cooled below its melting point that has not crystallised. A glass is a deeply supercooled liquid.
- Supercritical fluid
The single fluid phase above the critical point. Supercritical CO2 is used as a solvent, for example to decaffeinate coffee.
- Superexchange
Indirect magnetic exchange between non-neighbouring magnetic atoms through a non-magnetic atom between them. It favours antiferromagnetic order.
- Symmetry element
The axis, plane or point that a symmetry operation is carried out about.
- Symmetry operation
A move that takes a molecule onto itself, so atoms land on equivalent atoms.
- Tetrahedral hole
The gap among four packed spheres. There are two per ccp atom. Lecture 7 gives size ratio 0.225 and Lecture 5 gives 0.255.
- Thermal wavelengthΛ
A length built from h, m and beta. The translational partition function is the volume divided by Lambda cubed.
- Thermodynamic limit
What you get when the number of molecules grows without end. Only the most likely configuration is ever seen.
- Third law of thermodynamics
The entropy of a system approaches a constant value as the temperature goes to zero. For a perfect crystal that value is zero.
- Tight-binding approximation
The picture where atomic orbitals overlap with their neighbours. More atoms means more molecular orbitals, and in a crystal they merge into bands.
- Transition state
The configuration at the top of the pass between reactant and product valleys. It is the saddle point of the potential energy surface.
- Transition state theoryTST
A way to get a rate coefficient by treating the reactants and transition state as in equilibrium and multiplying by the rate of leaving the transition state.
- Translational symmetry
Shift the whole crystal by a unit cell edge and it looks the same.
- Triple point
The one temperature and pressure where solid, liquid and gas coexist. For water it is 0.01 degrees C and 612 Pa.
- TTF-TCNQ
The first organic metal. Donor TTF gives charge to acceptor TCNQ and the stacks conduct along one direction.
- Tungsten bronze
Na-doped WO3, NaxWO3, where the sodium donates x electrons per tungsten into the conduction band and makes the oxide metallic.
- Undercoolingsupercooling, DeltaT
Cooling a liquid below its melting point without it freezing. The amount is DeltaT = T_m minus the actual temperature.
- Unit cell
The smallest box that, copied along the cell vectors, builds the whole crystal.
- Valence band
The band made of occupied orbitals. In plain words, the full car park.
- Valence electrons
The outer electrons that take part in bonding.
- van der Waals equation
The ideal gas law with two fixes: take away the volume of the molecules, and lower the pressure for their mutual attraction.
- Viscosity
How thick a fluid is, its resistance to flow. Water is about 10^-4 Pa s, ketchup 10 Pa s, pitch about 10^8 Pa s.
- VSEPRValence shell electron pair repulsion
Electron groups around an atom push each other as far apart as they can. That fixes the molecule shape.
- Weight of a configurationW
How many microstates make up one configuration. W = N! divided by n0! n1! n2! and so on.
- WorkW
Energy moved by a force pushing something through a distance. In a gas, work is the push on a piston.
- YSZyttria-stabilised zirconia
A zirconia ceramic doped with yttrium so it carries oxide ions. It is the electrolyte in the solid-oxide fuel cell.
- Zeroth law of thermodynamics
If two things are each in thermal equilibrium with a third, they are in equilibrium with each other. This is why a thermometer works.
- Zinc blende (sphalerite)
ZnS type. ccp anions with half the tetrahedral holes filled. Coordination 4:4.
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