热力学性质第一原理计算VASP+PHONOPY(重庆大学)

Firstprinciplescalculationsonthethermodynamics王锐InstituteforStructureandFunctionChongqingUniversity2011.09.23Contents1.Theoreticalbackground2.PhononsfromForceconstantsmethod3.CalculationsofthephononbyVASPandPHONOPY4.Calculationsofthermalexpansionandrelatedproperties5.Calculationsofthethermalelectronicspecificheatandfreeenergy.1.TheoreticalbackgroundTheHelmholtzfreeenergyattemperatureTandconstantvolumeVisgivenbyE0(V)——TheenergyofgroundstateatT=0K(VASPdirectly);Fel(V,T)——Thermalelectroniccontributiontofreeenergy;Fvib(V,T)——Phononfreeenergyfromlatticevibration.ThermalelectronicfreeenergyIntroducethecalculationsofelectronicDOSfinally.Thevibrationalfreeenergy(,)vibharmanhFVTFFWeonlyconsiderthequasiharmonicapproximation(QHA)ToobtaintheFvibintheQHAexactly,itisnecessarytocalculatethephononfrequencyinthefirstBZ.IntroducetwoearliermodelIn1906，EinsteinmodelTheallfreedomdegreeofvibrationsareindependentlyandhavethesamefrequency.DebyemodelThekeywordofDebyemodel:ContinuumapproximationSoundvelocityforanisotropiccrystalas2233()2DVgv0()3DgdN/DDBkDebyetemperatureThelimitationofDebyemodelTheDebyemodeliscorrectatlowtemperature!2.PhononsfromForceconstantsmethodThecrystalneartheequilibriumconfiguration:denotesthedisplacementofatomsinunitcelllPotentialenergyofphononsystemTherelationbetweentheforceandrelation3.CalculationsofthephononbyVASPandPHONOPYThefirststep:constructthesuper-cellPreparetwofilesincurrentdirection:INPHONPOSCARATOM_NAME=AlLSUPER=.TRUE.NDIM=444INPHONSYSTEMAl4.0470.50.50.00.00.50.50.50.00.51Direct0.00.00.0POSCARThesecondstep:Usesuper-celltocalculateforcebyVASPcode1.CopyPOSCAR-001toPOSCAR2.PrepareINCARPOTCARKPOINTSSYSTEM=AlENCUT=470ISTART=0;ICHARG=2ISMEAR=2SIGMA=0.05NSW=0;IBRION=-1NGX=83;NGY=83;NGZ=83ISIF=0POTIM=0.2EDIFF=1.0E-6;PREC=AccurateLREAL=.FALSE.INCARauto0Monk5550.00.00.0KPOINTSAl1.00000000000000008.09399999999999948.09399999999999940.00000000000000000.00000000000000008.09399999999999948.09399999999999948.09399999999999940.00000000000000008.093999999999999464Direct0.00087361845958310.00000000000000000.00000000000000000.25000000000000000.00000000000000000.0000000000000000…………………………………………………………………………………………POSCARRunVasp1.SetPOSCARwithinitialprimitivecell2.Usetheoutputfilevasprun.xmlgenerateForcephonopy–fvasprun.xmlThethirdstep:CalculatetheForce110.00087361850.00000000000.0000000000-0.0319975300-0.03199753000.00000000000.00908978000.00908978000.00000000000.00064651000.00064651000.00000000000.00868766000.00868766000.0000000000-0.00083296000.00422163000.0047318200-0.0001033700-0.0002407600-0.0002385500-0.0002434500-0.00010571000.00023784000.0041680800-0.0008130500-0.0046518800-0.00016339000.00021437000.00043155000.00013445000.0001334800-0.00000067000.0002143700-0.0001633900-0.00043155000.00013348000.00013445000.0000006700-0.0002407600-0.0001033700-0.0002385500-0.0002054000-0.00020540000.0001378200…………………………………………………………ForcesTheforthstep:Calculatethephononandrelatedproperties1.PhononModifiedthefileINPHONATOM_NAME=Al#LSUPER=.TRUE.NDIM=444ND=5NPOINTS=61QI=0.0000.0000.0000.5000.0000.5000.5000.2500.7500.5000.5001.0000.0000.0000.000QF=0.5000.0000.5000.5000.2500.7500.5000.5001.0000.0000.0000.0000.5000.5000.5002.PhononDOSModifiedthefileINPHONATOM_NAME=Al#LSUPER=.TRUE.NDIM=444#ND=5#NPOINTS=61#QI=0.0000.0000.0000.5000.0000.5000.5000.2500.7500.5000.5001.0000.0000.0000.000#QF=0.5000.0000.5000.5000.2500.7500.5000.5001.0000.0000.0000.0000.5000.5000.500MP=515151ThethermalpropertiesF,Cv,Sphonopy–t--tmax=900–tstep=5#T[K]F[kJ/mol]S[J/K/mol]C_v[J/K/mol]0.0003.66753610.00000000.00000005.0003.66753550.00056870.002054510.0003.66752270.00578040.018500315.0003.66746090.02119820.068761220.0003.66728020.05508180.187947825.0003.66685850.11999020.426678730.0003.66600420.23042060.825251035.0003.66445840.39821151.393901240.0003.66191530.62991902.115788545.0003.65805030.92681072.959444450.0003.65254301.28614283.889356655.0003.64509351.70262854.872095360.0003.63543242.16964435.8790488………………………………………………………………PhononfreeenergyEntropySpecialheatatconstantvolume4.CalculationsofthermalexpansionandrelatedpropertiesFirststep:Calculationsofthevolume-energyrelationofthegroundstateandsavingasthefilev-e.dat15.13985-3.71291215.48947-3.72763515.84442-3.73742116.20477-3.74264716.57062-3.74365816.94185-3.74077717.31860-3.73430817.70087-3.72452818.08872-3.71170018.48232-3.69607918.88147-3.67791919.28632-3.65759319.69692-3.635248Secondstep:Calculationsthethermalpropertiesataseriesvolumessavingasthefilesthermal_properties-i.yamlNote:1.i=1……N;2.Theorderofthecalculatedvolumesshouldbesameasabovecalculations;3.Thethermal_properties-i.yamlatvolumepointshavetobecalculatedwiththesametemperaturerangesandsametemperaturesteps.Thirdstep:PreparethefollowingfilesinthecurrentdirectionINCAR,POTCAR,KPOINTS,INPHON1,INPHON2INCARSYSTEM=AlENCUT=470ISTART=0;ICHARG=2ISMEAR=2SIGMA=0.05NSW=0;IBRION=-1NGX=83;NGY=83;NGZ=83ISIF=0POTIM=0.2EDIFF=1.0E-6;PREC=AccurateLREAL=.FALSE.IALGO=38LWAVE=.FALSE.LCHARG=.FALSE.INPHON1ATOM_NAME=AlLSUPER=.TRUE.NDIM=444#MP=515151INPHON2ATOM_NAME=A