VASP

Cij

§1§2§3

σ

[1,2]Voigt

(zfhou@)

2006

8

21

VASP

Cij

§1

[1,2]

Cij

xx→1,yy→2,zz→3,yz→4,xz→5

e1

2e5

=

1

12e41

2e4

.e3 σi=

1

,

i

=0

Cij=

1

,

i j

=0

1

123

xy→6

(1)

(2)

(3)

2

i,j=1

6

Cijeiej+...

→′

R

(4)

E(V0,0) →R

V0

→′ →

R=R (I+ )

(5)

I

a

=e=(e1,e2,e3,e4,e5,e6)

(△E=E(V, ) E(V,0))

C11,C12,C13,C33

C44

§2

√ →a1

2

a

1

R= 3

2a00

0c

c

a2a3

= .

e=(δ,δ,0,0,0,0)

C11+C12[3]

E

V=

1

V=

1

V=C0

44δ2

e=(δ,δ,δ,0,0,0)

C11C12C13

C33

E

(6)

(10)

AlN2

3.11553

1.0000000.0000000.000000-0.5000000.8660250.0000000.0000000.0000001.60500022Direct

0.000000000.000000000.000000000.3333333330.6666666670.500000000.000000000.000000000.3814836730.3333333330.6666666670.881483673

C%%%%%%%%%Definethestrain%%%%%%%%%%%%%%

strain(1)=deltastrain(2)=deltastrain(3)=0.0strain(4)=0.0strain(5)=0.0strain(6)=0.0

C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%C>thissimpleprogramtogettheprimitivevectorsafterC$\delta$strain,inordertocalculatetheindependentCelasticconstantsofsolids.Cusage:C!!!!!PleasefirstpreparetheundeformedPOSCARinC>defvector.xC>typedefvector.x>createnewPOSCARinfilefort.3

C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

programdefvector

real*8privect,strvect,delta,strten,strain,pos,alat

dimensionprivect(3,3),strvect(3,3),strten(3,3),strain(6)dimensionpos(50,3)

character*10bravlat,title,directintegeri,j,k,ntype,natomi,nndimensionnatomi(10)

OLDPOS

C%%%%%%%%%Readtheundeformedprimitivevectorandatomicpostion%%%%%%%

open(7,file=’OLDPOS’)

C%%InfirstlineofOLDPOS,pleaseaddthenumberC%%ofthetypeofatomsafterthetitle

read(7,*)title,ntype

read(7,*)alatdoi=1,3

read(7,*)(privect(i,j),j=1,3)write(*,*)(privect(i,j),j=1,3)enddo

read(7,*)(natomi(i),i=1,ntype)nn=0

doi=1,ntype

nn=nn+natomi(i)enddo

read(7,*)directdoi=1,nn

read(7,*)(pos(i,j),j=1,3)enddo

C%%%%%%%%%Readtheamtiofstrain%%%%%%%%%%%%%%%

read(*,*)delta

C%%%%%%%%%Definethestrain%%%%%%%%%%%%%%

strain(1)=deltastrain(2)=0.0strain(3)=0.0strain(4)=0.0strain(5)=0.0strain(6)=0.0

C%%%%%%%%%Definethestraintensor%%%%%%%%%%%%%%%%%%%%%%%%

strten(1,1)=strain(1)+1.0

4

defvector.f”10I4”

ntype

10

natomi(10)

”write(3,’(10I4)’)(natomi(i),i=1,ntype)”

defvector.f

defvector.f

g77-odefector.x

INCAR.relax

defector.f)

defvector.x

VASP

KPOINTS

POTCAR

INCAR.static

POSCAR

Etot(δ)

POSCAR

defvector.x

δ

Etot(δ) Etot(0)

#!/bin/sh

foriin

-0.018-0.015-0.012-0.09-0.060.030.060.090.0120.0150.018

-0.030.00\

do

echo$i|defvector.xcpfort.3POSCAR####

cat>INCAR<<!SYSTEM=AlNENCUT=400ISTART=0ICHARG=2

ISMEAR=0;SIGMA=0.2NSW=60;IBRION=2EDIFF=1E-5EDIFFG=-1E-2ISIF=2

6

2

3

Etot(δ) Etot(0)