Theoretical Modeling On The Coherent Cu Rich Precipitation In ?-Fe

The second phase aging precipitation is one of the important methods that are used to enhance the mechanical properties of materials.With the development of science and technology,it has become one of the most attractive topics of materials science to initiatively control the second phase precipitation phenomenon through the evaluation of the relationships among composition,structure and properties.One of the keys to successfully design and control the properties of materials is to understand in depth on the thermodynamic behaviors of the interested material.The coherent Cu rich precipitation in a-Fe is one of the typical precipitation phenomenon with coherent second phase in the 3d-transition-metal alloys.It not only is one the major reasons of the embrittlement of reactor pressure vessel steels,but also is the primary source of the extraordinary mechanical strength of new high-strength low-alloyed steels.The temperature effects of the thermodynamics of steels play important roles on the coherent Cu rich precipitation phenomenon with respect to the driving force,the composition of precipitates and the precipitation kinetics.Particularly,the fundamental thermodynamic quantities,such as the solution energy of Cu,change significantly with the temperature under none-zero finite temperature conditions.However,a consensus on the influence of the finite temperature effects has not been reached by the experimental and theoretical approaches.One of the research methodology on the finite temperature effects of thermodynamics is to theoretically decouple the different contributions and then analyze each of them.This theoretical approach could ensure the universality of the discovered thermodynamic rules.Currently,it has been recognized that the finite temperature effects should be attributed to the non-configurational free energies,including the vibrational free energy,the electron excitation free energy and the magnetic free energy.The magnetic free energy is a special feature of steels,on which there is a lack of mature theoretical models.The present work is dedicated to the modelling of the thermodynamic properties of steels under finite temperatures with a focus on the Fe-Cu-Ni alloys,and is aimed at the study of the coherent Cu rich precipitation in a-Fe.In this work,we explore the modelling on the magnetic free energy of the Fe-Cu alloys to analyze the finite temperature effects of the thermodynamics of precipitation,and extend the studies on thermodynamics and kinetics into multi-component alloys with Ni selected as the representative alloying element.In the thesis,in the first part,the influence of driving force on Cu precipitation kinetics is analyzed;then a non-configurational free energy model of Fe-Cu built upon the first principles calculations and magnetic energy model is discussed;finally,the role of non-configurational free energy on the thermodynamics of the ternary Fe-Cu-Ni alloys is investigated.The major achievements of the present work are summarized as follows:(1)Using first principles calculation data parameterized kinetic Monte Carlo simulations,the Cu precipitation kinetics is investigated.The precipitation driving force is found to have insignificant effect on the time to reach the peak of number density of precipitates.While the number densities of precipitates significantly increase with a larger driving force.The driving force controls the growth mechanism of precipitates.With smaller driving force,the Cu atoms can be more easily pulled out from the precipitates by vacancies,so that the conventional evaporation-condensation mechanism is favored.Otherwise,the cluster migration and coagulation mechanism is favored.It is found that through segregation Ni atoms induce two-fold effects on the Cu precipitation.On one hand,the segregated Ni atoms enhances the nucleation of Cu precipitates;on another hand,the segregated Ni atoms inhibit the mobility of Cu precipitates,which temporally delays the precipitation process.(2)Based on the first principles calculations,the magnetic cluster expansion is used to develop a magnetic energy functional of Fe-Cu alloy,which is a representative of the alloys consist of magnetic and non-magnetic elements.The magnetic ordering/disordering behaviors of Fe-Cu is systematically investigated.In Fe-Cu,due to the screen effects of Cu upon the interactions among Fe atoms,there are significant alloying effects on the magnitude of magnetic moments and magnetic short range ordering under finite temperature conditions.Nonlinear enhancement of atomic magnetic moments of Fe with increasing Cu concentration is discovered,whose nonlinearity is strongest under the ordered ferromagnetic state and decreases with the magnetically disordering.The enhancement of magnetism of Fe upon Cu alloying induces a Cu concentration dependence of magnetic energy.The concentration dependence of magnetic energy is strongest under ferromagnetic state and reduces with respect to the magnetically disordering.The influence of magnetically disordering upon the concentration dependence of magnetic energy is stronger in the dilute concentration region than that in the concentrated region.Cu alloying also influences the short range ordering factors of Fe-Cu solid solutions under finite temperature conditions,which are larger with higher Cu concentration under the homologous temperatures.The above Cu alloying effects lead to linearly decreasing Curie temperature with respect to Cu concentration.(3)Using the developed magnetic energy functional,the analysis of the relationship between magnetic behaviors and the precipitation thermodynamics indicates that the magnetic states strongly influence the driving force of Cu precipitation.Under fully ordered magnetic states,the magnetism of Fe insignificantly changes the substitutional energy of Cu,so the driving force is not significantly affected;however,the binding energies between Cu-Cu pairs increase,thus the clustering of Cu could be enhanced.Under disordered states,the substitutional energy and binding energies are reduced simultaneously,which lower the driving force and the clustering possibilities.The magnetic free energy and vibrational free energy are combined to obtain an accurate model on the solution energy and solubility of Cu for a wide range of temperatures,which provide a theoretical reference for experiments.(4)The finite temperature thermodynamics of Fe-Cu-Ni alloy is constructed within an ab initio approach using the cluster expansion method and calculations of non-configurational free energies.It is found that,the mixing free energy is negative in the dilute region of Cu-Ni,thus the segregation of Ni at the interface of Cu precipitates could lower the system energy with a segregation amount in proportion to the Ni level of the alloy.The relative energy of introducing a single Cu impurity atom in the Fe-Ni alloys decreases with Ni level.As the result,the Cu solubility increases with Ni level.The segregation amount of Ni decreases with rising temperature because the minimum of the free energy of the Cu-Ni solid solution moves toward the dilute limit with rising temperature.