CORE-Materials most recent resources

Capacitance (parallel plate)

Wed, 04 Aug 2010 17:48:33 +0100

The most basic type of capacitor involves running a potential difference over two parallel plates separated by a dielectric, causing charge to build up on the plates. This is the defining equation of this arrangement, which underpins every type of capacitor.

TeX format: C = frac{\varepsilon_0\varepsilon_r EA}{V}

C {C}= Capacitance (F) {F}
ε₀ {\varepsilon_0} = Permittivity of free space (Fm^-1) {Fm^{-1}}
ε_r {\varepsilon_r} = Relative permittivity
E {E} = Electric field strength (Vm^-1) {Vm^{-1}}

Capacitance

Wed, 04 Aug 2010 17:45:55 +0100

The electrical capacitance of a material or, more usually, a device is defined as the amount of charge than can be stored for a given electric potential (driving force).

TeX format: C = \frac{Q}{V}

C {C} = Capacitance (F) {F}
Q {Q} = Charge (C) {C}
V {V} = Potential difference (V) {V}

Piezoresistivity

Wed, 04 Aug 2010 17:41:57 +0100

Stress over a conductor will induce a strain and therefore change the resistance of the conductor. In semiconductors, strain also causes a change in the material's resistivity, causing a much larger change in resistance. This change in material conductivity brought about by strain is known as piezoresistivity. Not related to the piezoelectric effect. Used primarily in strain gauges.

TeX format: \rho_\sigma = \frac{\left(\frac{\partial\rho}{\rho}\right)}{\left(\frac{\partial L}{L}\right)}

ρ_σ {\rho_\sigma} = Piezoresistivity
∂ρ {\partial\rho} = Change in resistivity (Ωm) {\Ohm m}
∂L {L} = Change in length (m) {m}
ρ {\rho} = Original resistivity (Ωm) {\Ohm m}
L {L} = Original length (m) {m}

Resistivity / Conductivity

Wed, 04 Aug 2010 17:34:47 +0100

Material property describing how well a material can conduct electricity. Materials with high resistivity (low conductivity) are known as insulators. Materials with low resistivity are conductors. This is generally a good indication of a material's ability to conduct heat, also. Can be effected by environmental (thermodynamic) factors.

TeX format: \rho = {1\over\sigma} = R{A\over L}

ρ {\rho} = Resistivity (&Ohm;m) {\Omega m}
σ {\sigma} = Conductivity (Sm^-1) {\Omega_{-1}}
R {R} = Resistance (Ω) {\Omega}
A {A} = Cross-sectional area (m²) {m^2}
L {L} = Length of sample (m) {m}
N_e {N_e} = Density of free electrons (m^-3) {m^{-3}}
e {e} = Electron charge (C) {C}
μ_e {/mu_e} = Electron mobility (m²V^-1s^-1) {m^2V^{-1}s^{-1}}

Tafel equation

Wed, 04 Aug 2010 17:29:59 +0100

The Tafel equation relates the electrochemical reaction rate to overpotential.

TeX format: \Delta V = A ln\left(\frac{i}{i_0}\right)

ΔV {\DeltaV} = Overpotential (V) {V}
A {A} = Tafel slope (V) {V}
i {i} = Current density (Am^-2) {Am^{-2}
i₀ {i_0} = Exchange current density (Am^-2) {Am^{-2}}

Butler-Volmer equation

Wed, 04 Aug 2010 17:22:27 +0100

The Butler-Volmer equation describes how electrical current in an electrochemical reaction depends on the electrode potential, considering both a cathodic and an anodic reaction occur on the same electrode.

TeX format: I = i_0\left( exp\left( \frac{\alpha nF\eta}{RT}\right) - exp\left(\frac{-(1-\alpha)nF\eta}{RT}\right)\right)

I {I} = Current (A) {A}
i₀ {i_0} = Exchange current density (A) {A}
α {\alpha} = Transfer coefficient
F {F} = Faraday constant (Cmol^-1) {Cmol^{-1}}
R {R} = Universal gas constant (JK^-1mol^-1) {JK^{-1}mol^{-1}}
T {T} = Temperature (K) {K}
n {n} = Number of electrons
η {\eta} = Overpotential - the difference between electrode potential and equilibrium potential. (V) {V}

Nernst equation

Wed, 04 Aug 2010 17:10:51 +0100

The Nernst equation links the equilibrium potential of an electrode to its standard potential and the concentrations or pressures of the reacting components at a given temperature. It describes the electrode potential for a given reaction as a function of the concentrations (or pressures) of all participating chemical species.

TeX format: E_e = E^0 - \frac{2.303RT}{zF}\log{ \left|\frac{[reduced]}{[oxidised]}\right |}

E_e {E_e} = Electrode potential (V) {V}
E⁰ {E^0} = Standard potential (V) {V}
R {R} = Universal gas constant (JK^-1mol^-1) {JK^{-1}mol^{-1}}
T {T} = Temperature (K) {K}
z {z} = Number of moles of electrons
F {F} = Faraday constant (Cmol^-1) {Cmol^{-1}}

The notation [reduced] represents the product of the concentrations (or pressures where gases are involved) of all the species that appear on the reduced side of the electrode reaction, raised to the power of their stoichiometric coefficients. The notation [oxidised] represents the same for the oxidised side of the electrode reaction.

Dalton's law of partial pressures

Wed, 04 Aug 2010 17:05:39 +0100

Dalton's law states that the pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of the constituent gasses. Remains valid up to high pressures.

TeX format: P_{total} = \sum_{i = 1}^{n}p_i

P_total{P_{total}} = Total pressure (Pa) {Pa}
p₁, p₂ ... = Partial pressures (Pa) {Pa}

Arrhenius equation

Wed, 04 Aug 2010 17:00:33 +0100

The Arrhenius equation quantises the effect of temperature on a chemical reaction rates.

TeX format:{k}= {Ae^{ -E_a\mathrm/RT}}

k {k} = reaction rate coefficient (s^-1) {s^{-1}}
A {A} = Prefactor (mol^-1) {mol^{-1}}
T {T} = Temperature (K) {K}
R {R} = universal gas constant (JK^-1) {JK^{-1}}
E_a {E_a} = Activation energy (J.mol^-1) {J.mol^{-1}}

Fourier's law

Wed, 04 Aug 2010 16:50:54 +0100

Fourier's Law of thermal conduction can have several forms and describes the transfer of thermal energy from a hot source to a cold one.

TeX format: J = \frac{\dot{q}}{A} = -k\frac{T_2 - T_1}{x}

J {J}= Flux (Jm^-2s^-1) {Jm^{-2}s^{-1}}
dq/dt {\dot{q}} = Heat transfer rate (Js^-1) {Js^{-1}}
A {A} = Cross-sectional area (m^-2) {m^{-2
T₂ {T_2} = Hot source (>T₁) temperature (K) {K}
T₁ {T_1} = Cold source (2) temperature (K) {K}
x {x} = Distance between sources (m) {m}
k {k} = Thermal conductivity of substance between sources (Js^-1m^-1K^-1) {Js^{-1}m{-1}K{-1}}