Georges MARTIN - Academia.edu (original) (raw)
Papers by Georges MARTIN
Acta Materialia, 2019
The temporal evolution of ordered γ'(L12)-precipitates precipitating in a disordered γ(f.c.c.) ma... more The temporal evolution of ordered γ'(L12)-precipitates precipitating in a disordered γ(f.c.c.) matrix is studied in extensive detail for a Ni-12.5 Al at.% alloy aged at 823 K (550 o C), for times ranging from 0.08 to 4096 h. Three-dimensional atom-probe tomography (3-D APT) results are compared to monovacancy-mediated lattice-kinetic Monte Carlo (LKMC1) simulations on a rigid lattice, which include monovacancy-solute binding energies through 4 th nearest-neighbor distances, for the same mean composition and aging temperature. The temporal evolution of the measured values of the mean radius, <R(t)>, number density, aluminum supersaturations, and volume fraction of the γ'(L12)-precipitates are compared to the predictions of a modified version of the Lifshitz-Slyozov-Wagner coarsening model due to Calderon, Voorhees et al. The resulting experimental rate constants are used to calculate the Gibbs interfacial free-energy between the γ(f.c.c.)-and γ'(L12)-phases, which enter the model, using data from two thermodynamic databases, and its value is compared to all extant values dating from 1966. The diffusion coefficient for coarsening is calculated utilizing the same rate constants and compared to all archival diffusivities, not determined from coarsening experiments, and is demonstrated to be the inter-diffusivity, , of Ni and Al. The monovacancy-mediated LKMC1 simulation results are in good agreement with our 3-D APT data. It is demonstrated that the compositional interfacial width, for the {100} interface, between the γ(f.c.c.)-and γ'(L12)-phases, decreases continuously with increasing aging time and <R(t)>, both for the 3-D APT results and monovacancy-mediated LKMC1 simulations, in disagreement with an ansatz intrinsic to the so-called trans-interface diffusion-controlled coarsening model, which assumes the exact opposite trend for binary alloys.
Acta Materialia, 2005
Precipitation kinetics of Al 3 Zr and Al 3 Sc in aluminum supersaturated solid solutions is studi... more Precipitation kinetics of Al 3 Zr and Al 3 Sc in aluminum supersaturated solid solutions is studied using cluster dynamics, a mesoscopic modeling technique which describes the various stages of homogeneous precipitation by a single set of rate equations. The only parameters needed are the interface free energy and the diffusion coefficient which are deduced from an atomic model previously developed to study the same alloys. A comparison with kinetic Monte Carlo simulations based on the vacancy diffusion mechanism shows that cluster dynamics correctly predicts the precipitation kinetics provided a size dependent interface free energy is used. It also manages to reproduce reasonably well existing experimental data.
Le Journal de Physique IV, 1993
Acta Materialia, 2012
The kinetic pathways involved in the formation of c 0 (L1 2 structure)-precipitates during aging ... more The kinetic pathways involved in the formation of c 0 (L1 2 structure)-precipitates during aging of concentrated Ni-Al-Cr alloys at 873 K, for three distinct alloy compositions, are studied experimentally by atom probe tomography, and computationally with lattice kinetic Monte Carlo (LKMC) simulations using parameters deduced from first-principles calculations of cohesive energies, and from experimental diffusion data. It is found that the compositional evolution of the c 0-precipitate phase does not follow the predictions of a classical mean-field model for coarsening of precipitates in ternary alloys. LKMC simulations reveal that long-range vacancy-solute binding plays a key role during the early stages of c 0-precipitation. With the aid of Monte Carlo techniques using the parameters employed in the LKMC simulations, we compute the diffusion matrix in the terminal solid-solutions and demonstrate that key features of the observed kinetic pathways are the result of kinetic couplings among the diffusional fluxes. The latter are controlled by the longrange vacancy-solute binding energies. It is concluded that, because it neglects flux couplings, the classical mean-field approach to phase separation for a ternary alloy, despite its many qualitatively correct predictions, fails to describe quantitatively the true kinetic pathways that lead to phase separation in concentrated metallic alloys.
Journal of the Less Common Metals
Abstract A short survey is presented of recent advances in the theory of stability criteria for p... more Abstract A short survey is presented of recent advances in the theory of stability criteria for phases under irradiation. The reason why standard thermodynamical criteria do not apply is discussed. As an example we show that among the many cases of irradiation induced stabilization of metastable phases, some are simple enough to deserve a detailed quantitative theoretical interpretation. Such is the case for the Ni4Mo compound where irradiationinduced inversion of the respective stability of two ordered structures was first reported, as well as irradiation-induced bistability. The Lyapunov function formalism introduced by the authors, makes it possible to describe quantitatively the competition between the chemically driven formation of compounds with their ballistic destruction and to assess the respective stability of various compound structures under irradiation. The model has now reached a degree of sophistication such that good quantitative agreement with the reported behaviour is achieved. We argue that a similar type of approach might be useful for predicting the type of phase to be stabilized by mechanical alloying.
Scripta Metallurgica, 1976
Materials Science Forum, 1994
Materials Science Forum, 1995
Physical Review B, 2002
The relaxation rates of concentration and long-range-order fields in substitutional alloys are kn... more The relaxation rates of concentration and long-range-order fields in substitutional alloys are known to be coupled not only by the driving forces, as they derive from a single free-energy functional, but also by kinetic coefficients, since the very same atomic jumps drive both relaxations. For the simplest kinetic lattice model (the kinetic counterpart of the Bragg-Williams model), the detailed expressions of the coefficients of the appropriate mobility matrix that had been derived previously [G. Martin, Phys. Rev. B 50, 12 362 (1994)] contain two errors, which are corrected in the present paper. Then, using these expressions, we discuss the conditions for the existence of coupling of the relaxation rates of composition and long-range order. In the most general case, where relaxation takes place around an equilibrium state that is inhomogeneous and ordered, the presence of this kinetic coupling is confirmed. In the case where relaxation takes place around a disordered state (homogeneous or inhomogeneous), we show that the mobility matrix reduces to a diagonal form, i.e., that there is no kinetic coupling. In the case of an ordered homogeneous equilibrium state, however, the mobility matrix is found to be symmetrical with off-diagonal terms which do not vanish, in general, although they may vanish for some specific crystallographic structures, or along specific crystallographic directions. It is shown that, near the homogeneous equilibrium state, even in the presence of kinetic coupling, the relaxation rates are such that the free energy of the system decreases monotonically with time, as expected from the second law of thermodynamics. The model is applied to a few ordered structures with cubic or tetragonal symmetry.
Handbook of Materials Modeling, 2005
The classical theories of diffusion-controlled transformations in the solid state (precipitate-nu... more The classical theories of diffusion-controlled transformations in the solid state (precipitate-nucleation, -growth, -coarsening, order-disorder transformation, domain growth) imply several kinetic coefficients: diffusion coefficients (for the solute to cluster into nuclei, or to move from smaller to larger precipitates...), transfer coefficients (for the solute to cross the interface in the case of interface-reaction controlled kinetics) and ordering kinetic coefficients. If we restrict to coherent phase transformations, i.e., transformations, which occur keeping the underlying lattice the same, all such events (diffusion, transfer, ordering) are nothing but jumps of atoms from site to site on the lattice. Recent progresses have made it possible to model, by various techniques, diffusion controlled phase transformations, in the solid state, starting from the jumps of atoms on the lattice. The purpose of the present chapter is to introduce one of the techniques, the Kinetic Monte Carlo method (KMC).
Defect and Diffusion Forum, 1997
ABSTRACT
Physical review. B, Condensed matter, 1994
We propose a mean-field lattice rate model for describing the kinetics of equilibrium as well as ... more We propose a mean-field lattice rate model for describing the kinetics of equilibrium as well as irradiation-induced surface segregation in concentrated alloys. The kinetics and thermodynamics are treated in a mutually consistent way. The model treats the composition field of the chemical constituents and of the point defects. The latter are nonconservative and are produced and destroyed either by the
Solid State Physics, 1996
Defect and Diffusion Forum, 2001
Materials Science Forum, 1999
... experiment : anneal a dilute Л1Х (X= Zn, Cu, Ge) solid solution =10 Kelvin below the melting ... more ... experiment : anneal a dilute Л1Х (X= Zn, Cu, Ge) solid solution =10 Kelvin below the melting point for 10 minutes; then cool the specimen down to room temperature at a rate ~ 7 Kelvin per minute. ... Anthony deduced W3/W1 ratios which complemented the lew existing data. ...
Defect and Diffusion Forum, 1997
ABSTRACT
Acta Materialia, 2019
The temporal evolution of ordered γ'(L12)-precipitates precipitating in a disordered γ(f.c.c.) ma... more The temporal evolution of ordered γ'(L12)-precipitates precipitating in a disordered γ(f.c.c.) matrix is studied in extensive detail for a Ni-12.5 Al at.% alloy aged at 823 K (550 o C), for times ranging from 0.08 to 4096 h. Three-dimensional atom-probe tomography (3-D APT) results are compared to monovacancy-mediated lattice-kinetic Monte Carlo (LKMC1) simulations on a rigid lattice, which include monovacancy-solute binding energies through 4 th nearest-neighbor distances, for the same mean composition and aging temperature. The temporal evolution of the measured values of the mean radius, <R(t)>, number density, aluminum supersaturations, and volume fraction of the γ'(L12)-precipitates are compared to the predictions of a modified version of the Lifshitz-Slyozov-Wagner coarsening model due to Calderon, Voorhees et al. The resulting experimental rate constants are used to calculate the Gibbs interfacial free-energy between the γ(f.c.c.)-and γ'(L12)-phases, which enter the model, using data from two thermodynamic databases, and its value is compared to all extant values dating from 1966. The diffusion coefficient for coarsening is calculated utilizing the same rate constants and compared to all archival diffusivities, not determined from coarsening experiments, and is demonstrated to be the inter-diffusivity, , of Ni and Al. The monovacancy-mediated LKMC1 simulation results are in good agreement with our 3-D APT data. It is demonstrated that the compositional interfacial width, for the {100} interface, between the γ(f.c.c.)-and γ'(L12)-phases, decreases continuously with increasing aging time and <R(t)>, both for the 3-D APT results and monovacancy-mediated LKMC1 simulations, in disagreement with an ansatz intrinsic to the so-called trans-interface diffusion-controlled coarsening model, which assumes the exact opposite trend for binary alloys.
Acta Materialia, 2005
Precipitation kinetics of Al 3 Zr and Al 3 Sc in aluminum supersaturated solid solutions is studi... more Precipitation kinetics of Al 3 Zr and Al 3 Sc in aluminum supersaturated solid solutions is studied using cluster dynamics, a mesoscopic modeling technique which describes the various stages of homogeneous precipitation by a single set of rate equations. The only parameters needed are the interface free energy and the diffusion coefficient which are deduced from an atomic model previously developed to study the same alloys. A comparison with kinetic Monte Carlo simulations based on the vacancy diffusion mechanism shows that cluster dynamics correctly predicts the precipitation kinetics provided a size dependent interface free energy is used. It also manages to reproduce reasonably well existing experimental data.
Le Journal de Physique IV, 1993
Acta Materialia, 2012
The kinetic pathways involved in the formation of c 0 (L1 2 structure)-precipitates during aging ... more The kinetic pathways involved in the formation of c 0 (L1 2 structure)-precipitates during aging of concentrated Ni-Al-Cr alloys at 873 K, for three distinct alloy compositions, are studied experimentally by atom probe tomography, and computationally with lattice kinetic Monte Carlo (LKMC) simulations using parameters deduced from first-principles calculations of cohesive energies, and from experimental diffusion data. It is found that the compositional evolution of the c 0-precipitate phase does not follow the predictions of a classical mean-field model for coarsening of precipitates in ternary alloys. LKMC simulations reveal that long-range vacancy-solute binding plays a key role during the early stages of c 0-precipitation. With the aid of Monte Carlo techniques using the parameters employed in the LKMC simulations, we compute the diffusion matrix in the terminal solid-solutions and demonstrate that key features of the observed kinetic pathways are the result of kinetic couplings among the diffusional fluxes. The latter are controlled by the longrange vacancy-solute binding energies. It is concluded that, because it neglects flux couplings, the classical mean-field approach to phase separation for a ternary alloy, despite its many qualitatively correct predictions, fails to describe quantitatively the true kinetic pathways that lead to phase separation in concentrated metallic alloys.
Journal of the Less Common Metals
Abstract A short survey is presented of recent advances in the theory of stability criteria for p... more Abstract A short survey is presented of recent advances in the theory of stability criteria for phases under irradiation. The reason why standard thermodynamical criteria do not apply is discussed. As an example we show that among the many cases of irradiation induced stabilization of metastable phases, some are simple enough to deserve a detailed quantitative theoretical interpretation. Such is the case for the Ni4Mo compound where irradiationinduced inversion of the respective stability of two ordered structures was first reported, as well as irradiation-induced bistability. The Lyapunov function formalism introduced by the authors, makes it possible to describe quantitatively the competition between the chemically driven formation of compounds with their ballistic destruction and to assess the respective stability of various compound structures under irradiation. The model has now reached a degree of sophistication such that good quantitative agreement with the reported behaviour is achieved. We argue that a similar type of approach might be useful for predicting the type of phase to be stabilized by mechanical alloying.
Scripta Metallurgica, 1976
Materials Science Forum, 1994
Materials Science Forum, 1995
Physical Review B, 2002
The relaxation rates of concentration and long-range-order fields in substitutional alloys are kn... more The relaxation rates of concentration and long-range-order fields in substitutional alloys are known to be coupled not only by the driving forces, as they derive from a single free-energy functional, but also by kinetic coefficients, since the very same atomic jumps drive both relaxations. For the simplest kinetic lattice model (the kinetic counterpart of the Bragg-Williams model), the detailed expressions of the coefficients of the appropriate mobility matrix that had been derived previously [G. Martin, Phys. Rev. B 50, 12 362 (1994)] contain two errors, which are corrected in the present paper. Then, using these expressions, we discuss the conditions for the existence of coupling of the relaxation rates of composition and long-range order. In the most general case, where relaxation takes place around an equilibrium state that is inhomogeneous and ordered, the presence of this kinetic coupling is confirmed. In the case where relaxation takes place around a disordered state (homogeneous or inhomogeneous), we show that the mobility matrix reduces to a diagonal form, i.e., that there is no kinetic coupling. In the case of an ordered homogeneous equilibrium state, however, the mobility matrix is found to be symmetrical with off-diagonal terms which do not vanish, in general, although they may vanish for some specific crystallographic structures, or along specific crystallographic directions. It is shown that, near the homogeneous equilibrium state, even in the presence of kinetic coupling, the relaxation rates are such that the free energy of the system decreases monotonically with time, as expected from the second law of thermodynamics. The model is applied to a few ordered structures with cubic or tetragonal symmetry.
Handbook of Materials Modeling, 2005
The classical theories of diffusion-controlled transformations in the solid state (precipitate-nu... more The classical theories of diffusion-controlled transformations in the solid state (precipitate-nucleation, -growth, -coarsening, order-disorder transformation, domain growth) imply several kinetic coefficients: diffusion coefficients (for the solute to cluster into nuclei, or to move from smaller to larger precipitates...), transfer coefficients (for the solute to cross the interface in the case of interface-reaction controlled kinetics) and ordering kinetic coefficients. If we restrict to coherent phase transformations, i.e., transformations, which occur keeping the underlying lattice the same, all such events (diffusion, transfer, ordering) are nothing but jumps of atoms from site to site on the lattice. Recent progresses have made it possible to model, by various techniques, diffusion controlled phase transformations, in the solid state, starting from the jumps of atoms on the lattice. The purpose of the present chapter is to introduce one of the techniques, the Kinetic Monte Carlo method (KMC).
Defect and Diffusion Forum, 1997
ABSTRACT
Physical review. B, Condensed matter, 1994
We propose a mean-field lattice rate model for describing the kinetics of equilibrium as well as ... more We propose a mean-field lattice rate model for describing the kinetics of equilibrium as well as irradiation-induced surface segregation in concentrated alloys. The kinetics and thermodynamics are treated in a mutually consistent way. The model treats the composition field of the chemical constituents and of the point defects. The latter are nonconservative and are produced and destroyed either by the
Solid State Physics, 1996
Defect and Diffusion Forum, 2001
Materials Science Forum, 1999
... experiment : anneal a dilute Л1Х (X= Zn, Cu, Ge) solid solution =10 Kelvin below the melting ... more ... experiment : anneal a dilute Л1Х (X= Zn, Cu, Ge) solid solution =10 Kelvin below the melting point for 10 minutes; then cool the specimen down to room temperature at a rate ~ 7 Kelvin per minute. ... Anthony deduced W3/W1 ratios which complemented the lew existing data. ...
Defect and Diffusion Forum, 1997
ABSTRACT