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Gibbs free energy

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Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006223
EISBN: 978-1-62708-163-4
... Thermodynamics, and the Third Law of Thermodynamics. It informs that for transformations that occur at a constant temperature and pressure, the relative stability of the system is determined by its Gibbs free energy. The article describes the Gibbs free energy of a single-component unary system and the Gibbs...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005189
EISBN: 978-1-62708-187-0
... Abstract This article introduces the fundamental concepts of chemical thermodynamics and chemical kinetics in describing presolidification phenomena. For metallurgical systems, the most important thermodynamic variables are enthalpy and Gibbs free energy. A qualitative demonstration of the...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003588
EISBN: 978-1-62708-182-5
... of gas mixtures and partial pressures of volatile oxidation products. oxygen gaseous corrosion crystal structure molar volume thermal properties pure metals oxides free energy oxidation process pure divalent metal Richardson-Jeffes diagram Gibbs energy stability range METALS can...
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006277
EISBN: 978-1-62708-169-6
... Gibbs free energies and atomic mobilities are established as functions of temperature, pressure, and composition and serve directly as key inputs of any microstructure modeling. The article presents examples of the integrated computation tool set in simulating microstructural evolution. Burgers...
Series: ASM Handbook
Volume: 13C
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v13c.a0004135
EISBN: 978-1-62708-184-9
... →LiMn(IV)O 2 Lithium-carbon monofluoride nLi+(CF) n →nLiF+nC The tendency of metals to oxidize during battery discharge is reflected in their negative Gibbs free energy change. Metals that oxidize more readily have more negative Gibbs free energy change and are considered better anodes for...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005507
EISBN: 978-1-62708-197-9
... Inclination of grain boundary σ Surface tension D Diameter g Gibbs free energy per unit volume H Enthalpy, magnetic field strength k Boltzmann constant, 1.38066 × 10 −23 J/K R Radius of curvature Φ Interatomic potential r ij Atomic distance γ Grain-boundary...
Series: ASM Handbook
Volume: 24
Publisher: ASM International
Published: 15 June 2020
DOI: 10.31399/asm.hb.v24.a0006559
EISBN: 978-1-62708-290-7
... the action of the ultrasonic, the change of free energy (Δ G ) increases: (Eq 5) Δ G = G S − G L = Δ H S + T Δ S S + Δ V S Δ P The eutectic growth rate ( v ) is expressed as: (Eq 6) v = a S I 0 e x p ( π σ 2 / k B T Δ G...
Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006222
EISBN: 978-1-62708-163-4
... small in comparison to E ; therefore the enthalpy, H , can be considered as being equal to the internal energy, E ( H ∼ E ). Therefore, this allows the Gibbs energy to be expressed as: (Eq 4) G = E − T S which is the same as the Helmholtz free energy, F : (Eq 5) F = E − T S...
Series: ASM Handbook
Volume: 3
Publisher: ASM International
Published: 27 April 2016
DOI: 10.31399/asm.hb.v03.a0006221
EISBN: 978-1-62708-163-4
..., liquid, and/or solid phases with different crystal structures). When two or more phases are in mutual equilibrium, each phase must be in the lowest free-energy state possible under the restrictions imposed by its environment. This equilibrium condition means that each phase is in an internally...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005415
EISBN: 978-1-62708-196-2
... dependence on multiple field variables. For instance, a commercial alloy may have more than ten chemical elements, and the corresponding Gibbs free energy and mobility matrix are both functions of the concentration of these elements, in addition to temperature and pressure. To present them in tractable forms...
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006257
EISBN: 978-1-62708-169-6
... partly created by the stirring action of the magnetic field of the induction coil, but it is also related to the reduction in Gibbs free energy due to the contribution of the large negative entropy term, − T Δ S . Thus, as temperature increases, the entropy term contributes to making the Gibbs energy...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003582
EISBN: 978-1-62708-182-5
... − , HCO 3 − , CO 3 + , or Cl − . Equilibrium is calculated by determining that state (at fixed temperature and pressure) at which the phases, surfaces, and species within the system have reached the minimum value for the Gibb's free energy function. The minimum is determined by...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005434
EISBN: 978-1-62708-196-2
.... , Vol 20 , 1952 , p 359 – 364 48. Dean A.M , J. Phys. Chem. , Vol 89 ( No. 21 ), 1985 , p 4600 – 4608 49. Burgess D.R. , Zachariah M. , Tsang W. , and Westmoreland P.R. , Prog. Energy. Combust. Sci. , Vol 21 , 1996 , p 453 – 529 50...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001753
EISBN: 978-1-62708-178-8
... x   d x e x − 1 ] where T is temperature, and E R is the recoil energy of the free nucleus: (Eq 3) E R = E γ 2 2 M c 2 where E γ is the energy of the γ-ray, M is the mass of the nucleus, and c is the velocity of light. Useful low- and...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006646
EISBN: 978-1-62708-213-6
... − 1 where T is the temperature, and E R is the recoil energy of the free nucleus: (Eq 3) E R = E γ 2 2 Mc 2 where E γ is the energy of the γ-ray, M is the mass of the nucleus, and c is the velocity of light. Useful low- and high-temperature approximations...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005208
EISBN: 978-1-62708-187-0
... free surface, but less so for liquids and solids. Equation 7 provides the well-known relation that the surface tension is balanced by a pressure difference across the curved interface. The energy balance is one of the most important balances for solidification problems. The most convenient...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005437
EISBN: 978-1-62708-196-2
... Abstract This article presents the governing equations for moving a solidification front, based on the balance of mass, momentum, energy, and solute. It reviews how material properties and geometry can be analyzed in the context of the governing equations. The article provides several example...
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005639
EISBN: 978-1-62708-174-0
... than grow because of surface energy, Γ is the Gibbs-Thomson coefficient (= σ/Δ s f = surface tension/entropy of fusion per unit volume), and the other terms are as defined previously. While the value for λ i is quite small (∼0.025 μm), it has been calculated that the limit will occur at...
Series: ASM Handbook
Volume: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006456
EISBN: 978-1-62708-190-0
... also provides information on digital radiography, image processing and analysis, dual-energy imaging, and partial angle imaging, of a CT system. computed tomography digital radiography dual-energy imaging film radiography partial angle imaging real-time radiography X-ray computed tomography...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003579
EISBN: 978-1-62708-182-5
... driving force for chemical reactions at constant pressure is the Gibbs free energy change, which has been expressed in thermodynamic treatments as the balance between the effects of energy (enthalpy) change and entropy change. The entropy of a system is related to the number of ways in which microscopic...