The Free Energy Simulation Approach to Grain Boundary Segregation In Cu-Ni

1990 ◽  
Vol 209 ◽  
Author(s):  
H. Y. Wang ◽  
R. Najafabadi ◽  
D. J. Srolovitz ◽  
R. Lesar
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Grain Boundary ◽  
Chemical Potential ◽  
Boundary Segregation ◽  
Configurational Entropy ◽  
Accurate Method ◽  
Increasing Temperature ◽  
Atomic Coordinates ◽  
Good Agreement

ABSTRACTA new, accurate method for determining equilibrium segregation to defects in solids is employed to examine the segregation of Cu to grain boundaries in Cu-Ni alloys. The results are in very good agreement with the ones given by Monte Carlo. This method is based upon a point approximation for the configurational entropy, an Einstein model for vibrational contributions to the free energy. To achieve the equilibrium state of a defect in an alloy the free energy is minimized with respect to atomic coordinates and composition of each site at constant chemical potential. One of the main advantages this new method enjoys over other methods such as Monte Carlo, is the efficiency with which the atomic structure of a defect, segregation and thermodynamic properties can be determined. The grain boundary free energy can either increase or decrease with increasing temperature due to the competition between energetic and configurational entropy terms. In general, the grain boundary free energy increases with temperature when the segregation is strongest.

Free Energy Simulation of Grain Boundary Segregation and Thermodynamics In Ni3−xAl1+x

1990 ◽  
Vol 213 ◽  
Author(s):  
R. Najafabadi ◽  
H. Y. Wang ◽  
D. J. Srolovitzt ◽  
R. LeSar
Keyword(s):  
Free Energy ◽  
Low Temperature ◽  
Grain Boundary ◽  
Bulk Composition ◽  
Boundary Segregation ◽  
Simulation Method ◽  
Energy Simulation ◽  
Grain Boundary Segregation ◽  
Free Energies ◽  
Increasing Temperature

ABSTRACTThe free energy simulation method is employed to study segregation to Σ5 and Σ13 (001) twist grain boundaries and their free energies in ordered Ni3−xAl1+x. In the temperature range studied (300–900K), it is shown that there is almost no segregation, strong Al segregation, and weak Ni segregation to the grain boundary for the stoichiometric, Al-rich, and Ni-rich bulk compositions respectively. It is also shown that the segregation is limited to a few (002) planes around the grain boundary and its magnitude decreases with increasing temperature. For Al-rich bulk composition, it is demonstrated that segregation at low temperature substantially lowers the grain boundary free energy.

A Monte Carlo Simulation on the PFZ Microstructures in Al-Based Alloys during Multistep Annealing

2005 ◽  
Vol 475-479 ◽  
pp. 937-940 ◽  
Author(s):  
Hiroshi Okuda ◽  
Shojiro Ochiai
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Grain Boundary ◽  
Chemical Potential ◽  
Volume Fraction ◽  
Boundary Segregation ◽  
Free Zone ◽  
Fcc Lattice ◽  
Grand Canonical ◽  
Present Simulation

A Monte Carlo simulation using semi grand canonical ensemble method was applied to examine the condition that precipitation free zone (PFZ) appears in an Al-based composite materials under two step aging. The present simulation uses a fcc lattice with a periodic boundary condition for y and z directions, and a grain boundary existing at the end for x direction. A simple grain boundary segregation case gave a nealy parabolic growth law in PFZ width and the volume fraction of precipitates. Different origin of PFZ, namely, mobility or chemical potential, lead to the opposite effect upon secondary heat treatment.

Modelling of Grain Boundary Stability of Materials under Severe Plastic Deformation and Experimental Verification

2010 ◽  
Vol 638-642 ◽  
pp. 2724-2729
Author(s):  
Yoshiyuki Saito ◽  
Chitoshi Masuda
Keyword(s):  
Monte Carlo ◽  
Grain Boundary ◽  
Computer Simulations ◽  
Phase Field ◽  
Field Methods ◽  
Simulation Results ◽  
Boundary Stability ◽  
Textured Materials ◽  
Phase Field Methods ◽  
Good Agreement

Thermodynamic stability of Grain boundary in materials under severe plastic deformation was simulated by the Monte Carlo and the phase field methods. Computer simulations were performed on 3-dimensional textured materials. The Monte Carlo simulation results were qualitatively in good agreement with those by the phase field model. The classification of the solution of differential equations based on the mean-field Hillert model describing temporal evolution of the scaled grain size distribution function was in good agreement with those given by the Computer simulations. The ARB experiments were performed for pure Al and Al alloys-sheets in order to validate the computer simulation results concerning the grain boundary stability of textured materials. With use of the Monte Carlo and the phase field methods. Effect of grain boundary mobilises and interface energy given by the computer simulations.

Thermodynamic Properties of Wurtzite and Zinc-Blende AlN

2013 ◽  
Vol 455 ◽  
pp. 127-130
Author(s):  
Xue Mei Cai ◽  
Jing Mei Wang ◽  
Qian Neng Zhou
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Room Temperature ◽  
Potential Method ◽  
Zinc Blende ◽  
Phonon Spectra ◽  
The Difference ◽  
Increasing Temperature ◽  
Pseudo Potential ◽  
Good Agreement

In this paper, we carry out linear response calculation to determine the phonon density of states and the thermodynamic properties of the wurtzite and zinc-blende AlN by using the norm-conserving pseudo-potential method. The optimized lattice constant is in good agreement with the available experimental data. The internal energies increase almost linearly with temperature and the phonon free energy curves move down with increasing temperature in both structures. The zero value of the lattice vibration free energy appears at temperature 707K in wurtzite and 728K in zinc-blende AlN respectively. The specific heat capacity of the wurtzite AlN is higher than that of the zinc-blende AlN at room temperature owing to the difference of the phonon spectra.

Alloy thermodynamics in nanostructures

1994 ◽  
Vol 9 (1) ◽  
pp. 4-7 ◽  
Author(s):  
Jörg Weissmüller
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Grain Boundary ◽  
Boundary Segregation ◽  
Topological Defects ◽  
Grain Boundary Segregation ◽  
Conceptual Basis ◽  
Boundary Area ◽  
Nanostructured Alloys ◽  
Qualitative Discussion

The importance of the interactions between alloy atoms and topological defects for the thermodynamic properties of nanostructured alloys is pointed out. The McLean model for grain boundary segregation is extended to yield an expression for the total Gibbs free energy of an alloy polycrystal. This provides a simple conceptual basis for a qualitative discussion of the thermodynamic properties of nanocrystalline alloys. It is demonstrated that certain alloy poly- or nanocrystals may reach a metastable state, where the alloy is stable with respect to variation of its total grain boundary area.

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