Lattice Stability and Thermal Properties of Metals from First Principles
|School||Central South University|
|Course||Materials Physics and Chemistry|
|Keywords||First-principles calculations Phase transformation Thermal properties Density functional theory Pseudopotential method|
The dissertation is devoted to the study of phase stabilities under pressure and thermal properties of some metals from first principles within density functional theory (DFT)and density functional perturbation theory(DFPT).Materials are always used under certain circumstance which is often described by pressure and temperature,so the study of phase stabilities under pressure and thermal properties is of great theoretical and practical significance.The pressure dependencies of total energy and enthalpy of different structures for some metals(W,Pt,Be,Mg,Sc,Y,Ti,Zr)are calculated with plane wave pseudopotential methods based on density functional theory,and the phase transition pressures are determined.The equations of state(EOS)are obtained.The electronic structures such as density of state(DOS)and electronic population are calculated,and different possible transition paths are discussed.The phonon spectra and elastic constants of some structures are calculated with the density functional perturbation theory(DFPT),and the mechanical stabilities of some structures under pressure are discussed according to these calculations.The thermal properties of some metals are investigated by performing DFT and DFPT calculations within the quasiharmonic approximation.The temperature dependence of various quantities such as the anisotropic thermal expansion and the heat capacity are calculated.The electronic contribution to the thermal expansion and heat capacity are discussed.The results of this paper show that:1.Be undergoes a transition from hcp to bcc via the intermediate phase 9R at 4570 KBar and 5480 KBar respectively.It has never been considered in earlier work that 9R phase might occur under pressure.Unlike earlier work,our calculation shows zeropoint vibration can be neglected when determining transition pressure.Mg undergoes a transition from hcp to bcc at 520 KBar.The calculated and experimental results agree satisfactorily.According to the calculated elastic constants and phonon spectra,both fcc and hcp phases of Be and Mg are mechanical stable under high pressure.The bcc phase of Be is not mechanical stable under ambient pressure because of the softening of its[ξξ0]transverse phonon modes,although its elastic constants satisfies the conditions of mechanical stability.It shows that earlier work which judges phase stability only by elastic constants is not sufficient.2.The structures of Sc follow a systematic sequence,from hcp→9R→dhcp→distorted-fcc→Sc-V.The transition pressures are 170 KBar,320 KBar,730 KBar,and 2440 KBar,respectively.Sc-V phase has never been considered in earlier work.The total energy and enthalpy show that 9R phase is the ground state of Y,and discover successive transitions to dhcp,distorted-fcc,Sc-V at 70 KBar,520 KBar,and 2200 KBar, respectively.The observed hcp phase under ambient temperature might be due to the thermal effect.3.W undergoes a transition from bcc to fcc at 10840 KBar and Pt from fcc to bcc at 14950 KBar.The calculations of phonon spectra and bcc→fcc and bcc→hcp phase transform path are agreement with the results of total energy and enthalpy.The fcc and hcp phases of Pt are mechanical stable under pressure(0～16000 KBar)according to the phonon spectra.Ti undergoesω→γ→δ→bcc transition under pressure according to calculation and the experiment results are hcp→ω→γ→δ.Theωphase is found to be the ground state of Ti and it shows successive transitions toγ,δ,bcc.However,the theoreticalδ→bcc occurs at 1310 KBar,which is not in agreement with the experiment result thatδphase is stable up to 2200 KBar.We suggest that the stability ofδmay be due to nonhydrostatic conditions.Zr undergoes a transition from hcp toωand bcc.The theoretical and experimental results agree satisfactorily.4.The calculated thermal properties are in good agreement with available experimental data in a wide range of temperature.The different anisotropy of thermal expansion is due to their different anisotropy in elasticity and anharmonicity of vibrations.Be shows larger thermal expansion in a-axis because of its smaller elastic rigidness in the same direction,while the larger thermal expansion in c-axis for Y can be attributed to the larger anharmonicity of vibrations in the same direction.The anisotropic thermal expansion of Ti and Zr are due to their anisotropic Gruneisen parameters,while Mg has almost isotropic thermal expansion because of its isotropic Gruneisen parameters and elasticity. 5.The calculated specific heat at constant pressure shows that the electronic contribution is negligible for simple metals Be and Mg but not for transition metals,because the electronic constants are very small in considering range of temperature for Be and Mg but large for transition metals.We can expect that the electronic contribution to specific heat is important when the electronic constant is large or the temperature is very high.