Thermodynamics of FGM: New Approach for Free Energy and the Equilibrium State Calculations

2009 ◽  
Vol 631-632 ◽  
pp. 59-64
Author(s):  
Michael M. Gasik ◽  
Yevgen Bilotsky ◽  
Bohdan Lev
Keyword(s):  
Free Energy ◽  
Binary System ◽  
Inhomogeneous Distribution ◽  
Interacting Particles ◽  
New Approach ◽  
Infinite Systems ◽  
Field Distributions ◽  
Spatially Inhomogeneous ◽  
Finite Space ◽  
Locally Homogeneous

FGM thermodynamics has been mostly based on adaptation of classical Gibbs-Helmholtz approach for infinite systems to locally “homogeneous” zones. A statistical sum calculation in this theory cannot predict inhomogeneous distributions. A new approach to the statistical description of solid solutions is suggested, which takes into account possible formation of spatially inhomogeneous simultaneous particle and field distributions in finite space domains. The formation of new periodical or gradated structure in binary system is described. The effective free energy of system was determined and the condition of formation of such spatially inhomogeneous distribution of interacting particles was obtained. New method may be applied to FGM to calculate ab initio free energy of these systems without usual limitations of classical theory.

λ‐dynamics: A new approach to free energy calculations

1996 ◽  
Vol 105 (6) ◽  
pp. 2414-2423 ◽  
Author(s):  
Xianjun Kong ◽  
Charles L. Brooks
Keyword(s):  
Free Energy ◽  
Free Energy Calculations ◽  
New Approach ◽  
Energy Calculations

scholarly journals Gravitational differentiation in the regimes from stokes settling to Rayleigh–Raylor flows

2019 ◽  
pp. 15-30
Author(s):  
V. P. Trubitsyn
Keyword(s):  
Viscous Fluid ◽  
Interacting Particles ◽  
Small Particles ◽  
Continuous Transition ◽  
New Approach ◽  
Earth's Core ◽  
The Core ◽  
The Earth ◽  
Large Particles ◽  
Two Component

The Earth’s core was formed under gravitational differentiation in the course of the separation of iron and silicates. Most of the iron has gone into the core as early as when the Earth was growing. However, iron continued to precipitate even during the subsequent partial solidification which developed from the bottom upwards. At the different stages and in the different layers of the mantle, iron was deposited in different regimes. In this paper, the mechanisms of the deposition of a cloud of heavy interacting particles (or drops) in a viscous fluid are considered. A new approach suitable for analytical and numerical tracing the changes in the structure of the flows in a two-component suspension under continuous transition from the Stokessettling (for the case of a cloud of large particles) to the Rayleigh–Taylor flows and heavy diapirs (for the case of a cloud of small particles) is suggested. It is numerically and analytically shown that the both regimes are the different limiting cases of the sedimentation convection in suspensions.

Modeling of Liquid-Liquid Demixing Curve in Lead-Zinc Binary System

2018 ◽  
Vol 18 ◽  
pp. 49-54
Author(s):  
Naceur Amel ◽  
Adjadj Fouzia
Keyword(s):  
Mathematical Model ◽  
Free Energy ◽  
Phase Separation ◽  
Binary System ◽  
Free Energies ◽  
Common Tangent ◽  
Different Temperatures ◽  
Lead Zinc ◽  
The Common ◽  
Zn Alloys

In this work we discussed the modeling of the demixing curve in the liquid state in the Lead – Zinc binary system. We are interested to recalculate the free energies relating on Pb-Zn alloys for several temperatures based on the thermodynamic data collected in the bibliography. This calculation allows us to trace the curve of phase separation from a program after obtaining the mole fractions corresponding to the common tangent to the curve of the free energy with two minima at different temperatures. To do this, we used the Matlab 7.1 as the programming language and the Redlich-Kister polynomial as a mathematical model of development. The results obtained are very satisfactory by comparing them with those of the bibliography.

scholarly journals Thermo-Solutal Modelling of Microstructure Formation during Multiphase Alloy Solidification - a New Approach

2014 ◽  
Vol 790-791 ◽  
pp. 103-108
Author(s):  
Peter C. Bollada ◽  
Andrew M. Mullis ◽  
Peter K. Jimack
Keyword(s):  
Free Energy ◽  
Dynamical Equations ◽  
New Approach ◽  
Phase Field Models ◽  
Diffusion Parameters ◽  
Multiphase Alloy ◽  
Standard Models ◽  
Multi Phase ◽  
First Time ◽  
Temperature Equation

This paper shows how to move from a specification of free energy for the solidification of a binary alloy to the dynamical equations using the elegance of a dissipative bracket analogous to the Poisson bracket of Hamiltonian mechanics. A key new result is the derivation of the temperature equation for single-phase thermal-solutal models, which contains generalisations and extra terms which challenge standard models. We also present, for the first time, the temperature equation for thermal multi-phase field models. There are two main ingredients: one, the specification of the free energy in terms of the time and space dependent field variables: $n$-phases $\phi_i$, a concentration variable $c$, and temperature $T$; two, the specification of the dissipative bracket in terms of these variables, their gradients and a set of diffusion parameters, which may themselves depend on the field variables. The paper explains the method within this context and demonstrates its thermodynamic admissibility.

scholarly journals Ablative Acceleration of Foils, Their Pulsations, and Interchange Instability

1997 ◽  
Vol 15 (4) ◽  
pp. 495-506
Author(s):  
N.A. Inogamov
Keyword(s):  
Inertial Confinement Fusion ◽  
Inertial Confinement ◽  
Inhomogeneous Distribution ◽  
New Approach ◽  
Promising Tool ◽  
Current State ◽  
Confinement Fusion ◽  
Interchange Instability ◽  
Definition Of ◽  
Derivatives Of

The problem of hydrodynamic stability is important for inertial confinement fusion (ICF) systems based upon high compression of fuel before its ignition. This problem for the case of complicated multilayer foils has been studied here by a new approach describing the development of Rayleigh-Taylor or interchange instability in compressible media with inhomogeneous distribution of “entropy”s = ρ/ρk, ∂ where K = (∂ In ρ/∂ In ρ)s is an adiabatic derivative taken in the local hydrostatic values of ρ and ρ. Inhomogeneous distribution of s simulates the dynamics of development of perturbations of multilayer flyer foils and shells. Besides instability, the same approach has been used for analysis of ID pulsations of a levitated foil. The problem of pulsations is real in the case of foils. Indeed, (1) an ablative acceleration is equivalent to an effective gravity field, which causes the appearance of an atmospheric-type distribution of thermodynamic functions, (2) the duration of ablative flight of foil is at least several times larger than the time that is necessary for an acoustic wave to travel from one side of the foil to another side, and (3) there is a strong initial impulse that initiates the motion of foil. This impulse together with (1, 2) is a reason for the powerful pulsations of foils. The period of pulsations is defined by the velocity of sound in the foil material, which is dependent on the derivatives of an equation of state (EOS). The check of the derivatives gives us finer information concerning the current state of matter and the EOS than the usual measurements of material velocity and pressure that are rougher measures. Therefore, an analysis of pulsations seems to be a promising tool for tracking the dynamics of flyer foil and for the definition of thermodynamic properties of matter.

Exploring the role of ions and amino acids in directing the growth of minerals from solution

2008 ◽  
Vol 72 (1) ◽  
pp. 273-276 ◽  
Author(s):  
S. Piana ◽  
F. Jones ◽  
Z. Taylor ◽  
P. Raiteri ◽  
J. D. Gale
Keyword(s):  
Amino Acids ◽  
Computer Simulation ◽  
Free Energy ◽  
Aspartic Acid ◽  
Morphology Control ◽  
New Approach ◽  
Activation Free Energy

AbstractThe influence of both sulphate ions and aspartic acid on directing the growth of baryte has been explored using computer simulation. Both species are found to significantly reduce the activation free-energy to growth under appropriate conditions, with the influence of sulphate being surface specific. This offers the potential for a new approach to morphology control without inhibition that may have implications for biomineralization.

scholarly journals CLASSICAL DIAMAGNETISM REVISITED

2010 ◽  
Vol 24 (30) ◽  
pp. 2899-2910 ◽  
Author(s):  
ARNAB SAHA ◽  
SOURABH LAHIRI ◽  
A. M. JAYANNAVAR
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Friction Coefficient ◽  
Langevin Equation ◽  
Charged Particles ◽  
Real Space ◽  
Fluctuation Theorems ◽  
Infinite Systems ◽  
Langevin Approach ◽  
Jarzynski Equality

The well-known Bohr–van Leeuwen Theorem states that the orbital diamagnetism of classical charged particles is identically zero in equilibrium. However, results based on real space–time approach using the classical Langevin equation predicts non-zero diamagnetism for classical unbounded (finite or infinite) systems. Here we show that the recently discovered Fluctuation Theorems, namely, the Jarzynski Equality or the Crooks Fluctuation Theorem surprisingly predicts a free energy that depends on magnetic field as well as on the friction coefficient, in outright contradiction to the canonical equilibrium results. However, in the cases where the Langevin approach is consistent with the equilibrium results, the Fluctuation Theorems lead to results in conformity with equilibrium statistical mechanics. The latter is demonstrated analytically through a simple example that has been discussed recently.

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