Theoretical Study On Physical Properties Of Precipitated Phases In High Nb Containing TiAl Alloy Under High Pressure

The high Nb containing TiAl alloys showing excellent strength,creep resistance and oxidation resistance compared with the traditional TiAl alloy,plays the role of solution strengthening due to the addition of Nb element to replace Ti atom occupation or A1 atom occupation.It has a wider application range than the conventional TiAl alloys,and is expected to replace the nickel base superalloy in the middle temperature and stress range.At the same time,the addition of Nb atoms changes the boundaries of ?/?+?2 and ?2/? phases in TiAl alloy,which leads to the formation of various phases on the grain boundaries and lamellaes in high Nb containing TiAl alloy.In addition,different heat treatment process and Nb content can also cause new phase precipitation,which has important influences on the physical properties such as strength,heat treatment,oxidation resistance,creep resistance and room temperature plasticity.The physical properties of high Nb containing TiAl Alloy under high pressure are different from those under normal pressure.The application of high pressure extreme conditions can change the atomic volume of high Nb containing TiAl alloy,can also change the free energy,melting point,specific heat and other physical properties of each phase in the solidification process,and may also lead to a series of important effects on the selection of primary phase,transformation thermodynamics and transformation kinetics.High pressure physics is a subject that studies the physical behavior of matter under high pressure.It has become an important means to discover new substances and reveal new phenomena and laws,and has been paid more and more attention.Based on the density functional theory and the first principle method,the high pressure physical properties of binary precipitated phases?-TiAl,DO22-Al3Ti,?2-Ti3Al;long-period precipitated phases r-Al2Ti,Al5Ti3,h-Al2Ti;ternary precipitated phases O-Ti2AlNb,?1-Ti4Nb3Al9,?"-Ti3Al2Nb are systematically studied in this thesis,which is divided into seven chapters.In the first chapter,it is pointed out that the development trend of TiAl alloys is the high Nb containing TiAl alloys,at the same time,the structure and properties of precipitate phases in high Nb containing TiAl alloys and the research status of high pressure physical properties of precipitate phases in high Nb containing TiAl alloy has been introduced.Subsequently,the purpose,significance and content of this thesis are described.In the second chapter,the first principle calculation and density functional theory are systematically described.Primanry,the basic idea of the first principle to calculate the ground state physical properties of the multi electron system is described,the formation,development and application of the density functional theory are mainly introduced based on the consideration of the single electron approximation,and the concrete forms of the widely used local density approximation and the generalized gradient density approximation are discussed.Secondly,the basic theory of elastic constant calculation,the general Hooke's laws and elastic constant calculated by stress-strain method are introduced.Once again,the thermodynamic basis of lattice vibration and the basic idea of calculating thermodynamic properties by simple harmonic approximation method are described.Finally,two calculation software VASP and phonopy are simply introduced.In the third chapter,the lattice parameters and elastic constants of the binary precipitates,?-TiAl,?2-Ti3Al,DO22-Al3Ti;long period precipitates,r-Al2Ti,Al5Ti3,h-Al2Ti,and the ternary phases,O-Ti2AlNb,?1-Ti4Nb3Al9,?"-Ti3Al2Nb are calculated systematically.All the calculated lattice parameters and elastic constants are consistent with the existing experimental and theoretical values,which shows that the calculation method is reliable.At the same time,the formation energy and the phonon spectra of nine phases are calculated.The stability of nine phases are judged by the stability criteria on energy,mechanics and dynamics.The results show that the nine phases meet the stability conditions of their respective ground states.In Chapter 4,the latticle parameters,elastic constants,formation energy and phonon dispersion spectrum of the precipitated phases in high Nb contaning TiAl Alloy under high pressure are calculated systematically,and the normalized lattice parameters are used to fit the pressure with fourth-order polynomials.Through the elastic constants under high pressure,according to the mechanical stability criteria of each crystal system,it is concluded that the precipitated phases meet the mechanical stability conditions within the pressure range of 0-30GPa;the formation energy of the nine precipitate phases decrease in stability with the increase of pressure,but all meet the criterion of energy stability;the phonon dispersion relationship shows that the nine precipitate phases studied have no virtual frequency under the pressure of 0-30GPa,and all meet the condition of dynamic stability.In the fifth chapter,according to the elastic constants of the precipitate phases under different pressures,the mechanical properties of the precipitate phases,such as bulk modulus,shear modulus,Young's modulus,Poisson's ratio and anisotropy are calculated.The results show that the bulk modulus,shear modulus and Young's modulus of DO22-Al3Ti are the largest and increase the fastest with the increase of pressure in the binary phases;the shear modulus and Young's modulus of r-Al2Ti phase and h-Al2Ti phase are higher than that of Al5Ti3 phase in the long period precipitation phase,and the increase value with pressure is higher than that of Al5Ti3 phase;in the ternary precipitates,the bulk modulus of O-Ti2AlNb is the largest,followed by ?"-Ti3Al2Nb,and ?1-Ti4Nb3Al9 is the smallest,the sequence of shear modulus is:?1-Ti4Nb3Al9>?"-Ti3Al2Nb>O-Ti2AlNb,while the young's modulus of?1-Ti4Nb3Al9 and ?"-Ti3Al2Nb are clese,and larger than that of O-Ti2AlNb.The ductility of the precipitates phases increased with the increase of pressure.?-TiAl was brittle under 11.25GPa,but presented as ductile when the pressure was higher than 11.25GPa;although the B/G value of DO22-Al3Ti increases with the increase of pressure,but shows brittleness under the pressure in research;the ?2-Ti3Al phase shows ductility;the r-Al2Ti,Al5Ti3 and h-Al2Ti phases are brittle materials in the study pressure range,but the ductility increases with the increase of pressure;the three ternary precipitates show ductility in the study pressure range,and the ductility increases with the increase of pressure,the ductility of O-Ti2AlNb and?"-Ti3Al2Nb is better than that of ?1-Ti4Nb3Al9 under certain pressure.The anisotropy order of shear modulus and Young's modulus present ?-TiAl is the largest,followed by DO22-Al3Ti,and ?2-Ti3Al in binary precipitated phases;the order of anisotropy degree of bulk modulus under high pressure in the long period phases is h-Al2Ti>Al5Ti3>r-Al2Ti,while that of shear modulus and Young's modulus is Al5Ti3>h-Al2Ti>r-Al2Ti;the anisotropy of bulk modulus of three kinds of ternary precipitated phases under high pressure has little difference,the shear modulus at high pressure is ?1-Ti4Nb3Al9>O-Ti2AlNb>?"-Ti3Al2Nb,while the anisotropy of Young's modulus under high pressure is ?1-Ti4Nb3Al9>?"-Ti3Al2Nb>O-Ti2AlNb.In Chapter 6,the thermodynamic properties of the precipitated phases are studied based on the calculation of the phonon spectra of the precipitated phases in high Nb contaning TiAl alloy.The results show that the bulk moduli of ?-TiAl and ?2-Ti3Al are obviously higher than those of DO22-Al3Ti in the binary precipitated phase;the long period precipitated phase r-Al2Ti,Al5Ti3 and h-Al2Ti are decrease with the increase of temperature and pressure on the bulk modulus;the bulk modulus of O-Ti2AlNb is significantly higher than that of?1-Ti4Nb3Al9 phase and ?"-Ti3Al2Nb phase in the ternary precipitation phase.The Gibbs free energy order of the binary precipitated phase is the largest for ?-TiAl,followed by DO22-Al3Ti and ?2-Ti3Al;the order of long period precipitation phase h-Al2Ti>r-Al2Ti>Al5Ti3,and the order of ternary precipitated phase is ?"-Ti3Al2Nb>?1-Ti4Nb3Al9>O-Ti2AlNb.Pressure has little effect on the thermal expansion coefficient of each precipitated phase,and the thermal expansion coefficient of each precipitated phase is greatly dependent on temperature in low temperature area,but it is less affected by temperature in high temperature area.Pressure has little effect on the isobaric heat capacity of each precipitation phase,and the change of the isobaric heat capacity of each precipitation phase with temperature meets the T3 law of Debye's low temperature thermodynamics.In the high temperature range,the isobaric heat capacity of DO22-Al3Ti and ?2-Ti3Al is always greater than that of ?-TiAl in the binary phase;and in the long period phase,the order of the isobaric heat capacity is Al5Ti3>r-Al2Ti>h-Al2Ti:in the ternary precipitation phase,the isobaric heat capacity O-Ti2AlNb and ?1-Ti4Nb3Al9 is larger than ?"-Ti3Al2Nb phase.The seventh chapter summarizes the previous contents and prospects the subcensquent work.