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• Package: Equations in Materials Science ( resources)
• The set of physical laws and mathematical equations commonly used in Materials Science and Engineering. All units and prefixes are given in accordance with in the SI standard (The International System of Units)....
• Creator: The University of Liverpool
• Keywords:
• Date added: 01 July 2010
• ILSS equation
• This equation is used to determine the interlaminate shear strength (ILSS) of a composite material, based upon the force at failure during a 3 point bend test. The test is typically standardised, with B = 10mm, d =2mm and the distance between the two support points = 20mm.TeX format: {ILSS = \frac{3 P_{max}}{4Bd}}ILSS {ILSS} = interlaminate shear strength (Pa) {Pa}Pmax {P_{max}} = maximum force reached during test (N) {N}B {B} = sample width (m) {m}d {d} = sample thickness (m) {m}...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Black's equation
• In integrated circuit manufacture, the Mean Time To Failure (MTTF) equation is used to predict the lifetime of nano-scale connections between components such as transistors. By running short experiments at elevated temperatures the constants in the equation can be calculated, allowing the time to failure (defined as the failure of 50% of interconnect lines) at normal operating temperatures to be predicted.TeX format {MTTF = Awj^{-n}exp^{\frac{Q}{kT}}}MTTF {MTTF} = mean time to failure (s) {s}A {...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Scheil equations
• The Scheil equations describe the concentration of a solute in the solid and liquid phases during solidification. This equation is commonly used in metallurgy, during the solidification of alloys and in semiconductor wafer manufacture for the solidification of single crystals of semiconductor materials.TeX format: {C_L=C_0(f_L)^{k-1}}TeX format: {C_S=kC_0(1-f_S)^{k-1}}CL {C_L} = concentration of solute in the liquid phase (mol.m-3) {mol.m^{-3}}CS {C_S} = concentration of solute in the solid phas...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Avrami equation
• The Avrami equation describes the change of matter from one state to another at a constant temperature. A graph of y against log(t) is characterized by an initially slow rate of change (corresponding to nucleation of the new phase) followed by a faster, steady rate (growth of the new phase), and finally a decrease in rate (as the driving force behind the phase change reduces).TeX format: {y = 1 - \exp^{- kt^{n}}}y {y} = fraction of material changedk {k} = material dependant constantn {n} = mater...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Tafel equation
• 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}}...
• Creator: The University of Liverpool
• Keywords:
• Date added: 04 August 2010
• Butler-Volmer equation
• 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} = Univ...
• Creator: The University of Liverpool
• Keywords:
• Date added: 04 August 2010
• Nernst equation
• 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 |} Ee {E_e} = Electrode potential (V) {V} E0 {E^0} = Standard potential (V) {V}...
• Creator: The University of Liverpool
• Keywords:
• Date added: 04 August 2010
• Arrhenius equation
• 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}}Ea {E_a} = Activation energy (J.mol-1) {J.mol^{-1}}...
• Creator: The University of Liverpool
• Keywords:
• Date added: 04 August 2010
• Darken equations
• The Darken regime is an adaptation of Fick's Laws for substitutional diffusion by the motion of vacancies. The Darken equation is an adaptation of Fick's laws for this purpose.TeX formats:{J_A}' = - \tilde{D}\left (\frac{\partial C_A}{\partial x}\right)\frac{\partial C_A}{\partial t} = \tilde{D} \left(\frac{\partial C_A}{\partial x}\right) JA'{{J_A}'} = Diffusion flux (mol.m-2s-1) {mol.m^{-2}s^{-1}} D {\tilde{D}} = Interdiffusion coefficient (m2s-1) {m^2s^{-1}} CA {C_A} = Concentration (mol....
• Creator: The University of Liverpool
• Keywords:
• Date added: 04 August 2010
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