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^VASPX O ‹N 5~ŒCij n ߲„(zfhou@fudan.edu.cn)E ˘ nX˘‹ 20068 21F` ' –8Æ‹ Ǒ~0 ˇLVASPO ‹N 5~ŒCij †N § 'SN ? /“ ¥ 8„§1 5~Œ Vg[1,2]1§28Æ‹N 5ACU AC’X2§3 NO ‰3§1 5~Œ Vg[1,2] 5~Œ£ª ‹NØ \ACǫ ǑA f 3ACØ „e§NX SU AC 3 g 5’X£ ‰˘⁄§ 5~ŒCij ·£ªø« g 5’X§= g 5 XŒ ^VoigtIP xx→1,yy→2,zz→3,yz→4,xz→5 xy→6AC ǫ‰´Ǒ ǫ=e112e612e512e6e212e412e512e4e3.(1)A σ‰´Ǒ σi=1V∂E(V,ǫj)∂ǫiǫ=0,(2) 9 5~ŒǑ Cij=1V∂2E(V,ǫk)∂ǫi∂ǫjǫ=0,(3)12 „e§AC NX oUE(V,ǫ)UAC ǫ? U V?Œ mǑ E(V,{ǫi})=E(V0,0)+V06Xi=1σiei+V026Xi,j=1Cijeiej+...(4) ¥E(V0,0)·ACNX oU§V0·AC N¨, §AC ˜¥−→R′ AC ˜¥−→R m ’XǑ −→R′=−→R•(I+ǫ)(5) ¥IǑ ˇd A‰ ACǫ=e=(e1,e2,e3,e4,e5,e6)§O 3 | AC NXoU Cz(△E=E(V,ǫ)−E(V,0))§2 oU Cz¤AC ØA |Œ :§?1 g…Œ[ g XŒ= ‹N , 5~Œ‰ 5~Œ | Ø ‹X ‹N§ˇǑØ¡5 ’X§§ Æ 5~Œ·(‰ ’XØ8Æ‹X ‹N§§ Æ 5~ŒǑ C11,C12,C13,C33 C44§28Æ‹N 5ACU AC’XØ8Æ‹X ‹N§ ˜¥ – Ǒ −→R=a1a2a3=√32a12a0−√32a12a000c.(6) ¥a c·‹N ‹ ~Œ – \ø ACe=(δ,δ,0,0,0,0)5O C11+C12[3] ΔEV0=(C11+C12)δ2(7) \ACe=(0,0,0,0,0,δ)5 C11−C12 ΔEV0=14(C11−C12)δ2(8)ØuC33§ \ACe=(0,0,δ,0,0,0)5 ΔEV0=12C33δ2(9)ØuC44§ \ACe=(0,0,0,δ,δ,0)5 ΔEV0=C44δ2(10) § \ACe=(δ,δ,δ,0,0,0) C11!C12!C13 C33 | ΔEV0=(C11+C12+2C13+C33/2)δ2(11)dd §ˇL \˚ A‰ AC§ X δ AC§ ΔE∼δŒ :§2'OU ¡˚ ’X“Ø A ΔE∼δ?1[ g XŒ§ ØÆ § 8Æ‹X‹N Æ 5~Œ23§3 NO ‰3O §kA: AO5¿ a)§ S f3AC·˜¶ ¶b)§k: ·˜v §ˇǑ3AC § Ø¡5‹u)Cz§= k: §3{ p « ) k:Œ8· ˇd§k: v §– y 5~ŒO (5¶c)§AC δ •¥§XJ {§ ACU£AC NX Cz⁄Ø §3O 5~Œ §‹ O e¡–O 8ÆAlN£n¶( ⁄Ǒ~§3O L§ ˜ AC f I ¶ § N ‰Xe •kØ8ÆAlNNÆÆ ‹ ºŒ£‹ ~Œ f ⁄‘z §ø AC POSCAR§¿r§ ⁄e¡defvector.fI ^ \' OLDPOS§¿ØOLDPOS ?nˇǑOLDPOS3 “ kAˇ a!3OLDPOS 1 1§3title i˛G § 2\ OLDPOS¥ f «aŒ8§’XAlN¥k a f§title ǑAlN§o OLDPOS 1 1 ·”AlN2”b!OLDPOS “ POSCAR aq§ ·§ ·'Œ I5 f –8ÆAlNǑ~§ø OLDPOS SNXe AlN23.115531.0000000.0000000.000000-0.5000000.8660250.0000000.0000000.0000001.60500022Direct0.000000000.000000000.000000000.3333333330.6666666670.500000000.000000000.000000000.3814836730.3333333330.6666666670.881483673•ØA‰ AC§3e¡ defvector.f¥”Definethestrain” '§rA‰ ACˇL strain(i) D ’XØ ¡J e=(δ,δ,0,0,0,0)^5O C11+C12§o Ødefvect.f¥ ”Definethestrain”U ⁄Xe /“ C%%%%%%%%%Definethestrain%%%%%%%%%%%%%%strain(1)=deltastrain(2)=deltastrain(3)=0.0strain(4)=0.0strain(5)=0.0strain(6)=0.0 ¥ defvector.f·^5 , AC §# POSCARAC a.U”Definethe33” '5‰´§ AC I3§S?¨ §$1?¨ ‹ \defvect.f SNXe C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CthissimpleprogramtogettheprimitivevectorsafterC$\delta$strain,inordertocalculatetheindependentCelasticconstantsofsolids.Cusage:C!!!!!PleasefirstpreparetheundeformedPOSCARinOLDPOSCdefvector.xCtypedefvector.xcreatenewPOSCARinfilefort.3C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%programdefvectorreal*8privect,strvect,delta,strten,strain,pos,alatdimensionprivect(3,3),strvect(3,3),strten(3,3),strain(6)dimensionpos(50,3)character*10bravlat,title,directintegeri,j,k,ntype,natomi,nndimensionnatomi(10)C%%%%%%%%%Readtheundeformedprimitivevectorandatomicpostion%%%%%%%open(7,file=’OLDPOS’)C%%InfirstlineofOLDPOS,pleaseaddthenumberC%%ofthetypeofatomsafterthetitleread(7,*)title,ntyperead(7,*)alatdoi=1,3read(7,*)(privect(i,j),j=1,3)write(*,*)(privect(i,j),j=1,3)enddoread(7,*)(natomi(i),i=1,ntype)nn=0doi=1,ntypenn=nn+natomi(i)enddoread(7,*)directdoi=1,nnread(7,*)(pos(i,j),j=1,3)enddoC%%%%%%%%%Readtheamtiofstrain%%%%%%%%%%%%%%%read(*,*)deltaC%%%%%%%%%Definethestrain%%%%%%%%%%%%%%strain(1)=deltastrain(2)=0.0strain(3)=0.0strain(4)=0.0strain(5)=0.0strain(6)=0.0C%%%%%%%%%Definethestraintensor%%%%%%%%%%%%%%%%%%%%%%%%strten(1,1)=strain(1)+1.043(1,2)=0.5*strain(6)strten(1,3)=0.5*strain(5)strten(2,1)=0.5*strain(6)strten(2,2)=strain(2)+1.0strten(2,3)=0.5*strain(4)strten(3,1)=0.5*strain(5)strten(3,2)=0.5*strain(4)strten(3,3)=strain(3)+1.0C%%%%%%%%%Transformtheprimitivevectortothenewvectorunderstrain%%%%%Cstrvect(i,j)=privect(i,j)*(I+strten(i,j))dok=1,3doi=1,3strvect(i,k)=0.0doj=1,3strvect(i,k)=strvect(i,k)+privect(i,j)*strten(j,k)enddoenddoenddoC%%%%%%%%Writethenewvectorunderstrain%%%%%%%%%%%%doi=1,3write(*,100)(strvect(i,j),j=1,3)enddo100format(3f20.15)C%%%%%%%%%CreatethePOSCARfortotalenergycalculation%%%%%%%%%%%%%%5write(3,’(A10)’)titlewrite(3,’(f15.10)’)alatdoi=1,3write(3,100)(strvect(i,j),j=1,3)enddowrite(3,’(10I4)’)(natomi(i),i=1,ntype)write(3,’(A6)’)Directdoi=1,nnwrite(3,100)(pos(i,j),j=1,3)enddoC%%%%%%%end3defvector.f¥§ f«a Œ8dC ntype5‰´ § Ǒ10§XJ f «aŒ8 §IgC ˜N Œ|natomi(10)–9 ”write(3,’(10I4)’)(natomi(i),i=1,ntype)” “”10I4”3defvector.f¥ A‰ AC § –?¨defvector.f£^g77-odefector.xdefector.f) ‹defvector.x•O VASPO \' KPOINTS POTCAR–9?1 f ¶ O INCAR.relax§§ SNXe SYSTEM=AlNENCUT=400ISTART=0ICHARG=253=0;SIGMA=0.2NSW=60;IBRION=2EDIFF=1E-5EDIFFG=-1E-2ISIF=2POTIM=0.2PREC=AccurateLWAVE=.FALSE., 3O Ø‘z ( ?1oU?1 INCAR.static§§ SNXe SYSTEM=AlNENCUT=400ISTART=0ICHARG=2ISMEAR=-5EDIFF=1E-5PR