Research On Phonon Spectrum And Vibration Property Of Metal Material By Modified Analytic Embedded Atom Method

In this paper,the embedded atomic method has been combined with the lattice dynamics theory to derive the specific analytical expressions of interplane force constants,and the vibration model of the clean surfaces,adsorption surfaces,the step surfaces and the crystal have been constructed.On the basis of the lattice statics,the program compiled by using Matlab software was used to calculate the multi-layer relaxation of the surface structure according to principle of lowest energy.On the basis of this,the phonon spectrums of the low index clean surfaces Ag(100),Ag(110)and Ag(111),step surfaces Ag(211),Ag(221),Ag(311),Ag(331),Ag(511),Ag(711)and Ag(977),and the absorption surfaces Ag(100)/Al,Ag(100)/ Au,Ag(110)/Al,Ag(110)/Au,Ag(111)/Al and Ag(111)/Au were simulated.According to the discriminant method of the surface mode,the distribution diagrams of surface mode for various surfaces were drawn.In addition,three metals of strontium,chromium,magnesium with common crystal structures and B2 type tantalum tungsten ordered alloy under atmospheric pressure were simulated,and the bulk phonon spectra of copper and molybdenum under high pressure were simulated.The main conclusions are as follows:First of all,it was found in the low index clean surface that most of the surface modes were distributed at the boundary of the body band or the band gap,and a few of the surface modes were distributed in the body mode band,in which the maximum amplitude of some surface modes was limited to the outermost layer,the other maximum amplitude of the surface mode was limited to the second or third layer and so on.The local mode in the deeper atomic layer exists in a very small range of the Brillouin zone.In some low index surfaces,the vibration branch of two surface modes with lower vibration frequency may have the phenomenon of avoiding crossing,independent real crossing and contact crossing.For same metal,different orientation surfaces had different band gap.In the body mode band,the maximum vibration frequency was related to the mass of the atom.As the atomic mass increases,the maximum vibration frequency gradually decreases.Secondly,in the step surfaces,as the crystal face index increases,the band gap area becomes smaller and smaller,while there were always two or three surface modes around the band gap.Surface modes outside the lower edge of the body mode band decreased as the facet index increases,and at the same time,more surface modes were peeled off.In addition to the Ag(221)step surface,small surface modes were distributed in the body mode bands of the other surfaces.These surface modes vibrated very weakly with accompanying modes attachedto them.For the(111)-(11(?))series of stepped surfaces,there were mode transitions in the lower surface modes in the (?) symmetrical direction,ie the platform surface modes were converted to step surface modes or the step surface modes were converted to platform surface modes.Thirdly,when the single atomic layer was adsorbed on the base film,the body mode almost did not change,and the surface mode was affected to varying degrees.The surface mode of the local adsorptive layer was always located on the upper or lower edge of the body mode belt.The surface modes localized near the surface either disappeared in the body mode band or frequency shifts occured,whereas the surface modes buried in the atomic layer were unaffected by the adsorbed layer.Light adsorption atoms increased surface mode dispersion branch,at the same time,reducing the the local of surface mode,and heavy atoms reduced the surface mode vibration frequency,but enhanced local surface mode.Finally,in bulk acoustic dispersion,the two dispersion branches with same type of vibration mode can merger into a dispersion branch.The two dispersion branches can not be distinguished from the vibrational frequency but can be distinguished from the polarization of the vibrational mode.In metallic Mg,in the optical vibration mode,both atoms in the original cell moved in the opposite direction on the same straight line,while in the acoustic branch,the movement of the two atoms was consistent.In the [?00] direction,although the two atoms moved in the opposite direction on the same straight line in the longitudinal wave optical branch,the moving distance of the two atoms was different,and the moving distance of the second atom is about twice that of the first atom.Under high pressure,the phonon frequencies increase with increase of loading pressures,and the heat capacity of copper decreases with the increase of pressure whten the temperature is constant.