Phase Transformations and Non-Elliptic Free Energy Functions

1986 ◽  
pp. 223-239 ◽  
Author(s):  
R. D. James
Keyword(s):  
Free Energy ◽  
Phase Transformations ◽  
Energy Functions

Inspection of free energy functions in gradient crystal plasticity

2013 ◽  
Vol 29 (6) ◽  
pp. 763-772 ◽  
Author(s):  
Samuel Forest ◽  
Nicolas Guéninchault
Keyword(s):  
Free Energy ◽  
Crystal Plasticity ◽  
Energy Functions

Finite elasticity of elastomeric materials

2020 ◽  
pp. 637-654
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Free Energy ◽  
Constitutive Relations ◽  
Finite Elasticity ◽  
Energy Functions ◽  
Slightly Compressible ◽  
Elastomeric Materials ◽  
Volumetric Response

This chapter presents several technologically important constitutive relations for elastomeric materials. In particular, the Neo-Hookean, Mooney-Rivlin, Ogden, Arruda-Boyce, and Gent free energy functions are discussed in the context of incompressible response. Extensions to the slightly compressible case are also detailed, this includes a presentation of a number of possible volumetric response relations and their properties.

Phase-Dield Simulation of Rhombohedral and Tetragonal Phases in Ferroelectric Single Crystals

Aerospace ◽  
2006 ◽  
Author(s):  
T. Liu ◽  
C. S. Lynch
Keyword(s):  
Free Energy ◽  
Phase Transformations ◽  
Single Crystals ◽  
Electric Fields ◽  
Tetragonal Phase ◽  
Ferroelectric Materials ◽  
Integration Scheme ◽  
Ferroelectric Crystal ◽  
Domain Structures ◽  
Tdgl Equation

Ferroelectric materials exhibit spontaneous polarization and domain structures below the Curie temperature. In this work the phase field approach has been used to simulate phase transformations and the formation of ferroelectric domain structures. The evolution of phases and domain structures was simulated in ferroelectric single crystals by solving the time dependent Ginzburg-Landau (TDGL) equation with polarization as the order parameter. In the TDGL equation the free energy of a ferroelectric crystal is written as a function of polarization and applied fields. Change of temperature as well as application of stress and electric fields leads to change of the free energy and evolution of phase states and domain structures. In this work the finite difference method was implemented for the spatial description of the polarization and the temporal evolution of polarization field was computed by solving the TDGL equation with an explicit time integration scheme. Cubic to tetragonal, cubic to rhombohedral and rhombohedral to tetragonal phase transformations were modeled, and the formation of domain structures was simulated. Field induced polarization switching and rhombohedral to tetragonal phase transition were simulated.

Free energy functions of disordered dipole systems

1997 ◽  
Vol 192 (1) ◽  
pp. 29-44 ◽  
Author(s):  
V. A. Stephanovich
Keyword(s):  
Free Energy ◽  
Energy Functions

scholarly journals Measurements of to Temperatures of Supersaturated Si-As Alloys

1990 ◽  
Vol 205 ◽  
Author(s):  
Kwang-Ryeol Lee ◽  
Jeffrey A. West ◽  
Patrick M. Smith ◽  
M. J. Aziz ◽  
J. A. Knapp
Keyword(s):  
Free Energy ◽  
Pulsed Laser ◽  
Congruent Melting ◽  
Laser Melting ◽  
Concentration Region ◽  
Energy Functions ◽  
Congruent Melting Point ◽  
Liquid Phases ◽  
Chemical Free Energy ◽  
Beam Technique

AbstractThe congruent melting point, or To curve, of crystalline Si-As alloys has been measured in the range of 1.6 to 18.1 at. % arsenic by line source electron beam annealing. Alloys were created by ion implantation of As into 0.1mm Si-on-sapphire and crystallized by pulsed laser melting. To temperatures decrease from 1673±10K at 2.0 at.% As to 1516±30K at 18.1 at.% As. The results of these measurements are significantly higher than the previous results of studies using pulsed laser melting techniques. Advantages of the e-beam technique over previous techniques are discussed. Chemical free energy functions of the solid and liquid phases were calculated from existing thermodynamic data. The calculated To curve agrees with the measured values only in low concentration region (less than 8 at.%).

Sign in / Sign up

Export Citation Format

Share Document