add symmetry operators and a subroutine for misorientation calculation
This commit is contained in:
Eralp Demir
parent
5fc9816ff7
commit
3625afff3b
264
trunk/math.f90
264
trunk/math.f90
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@ -65,6 +65,146 @@
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! Symmetry operators for 3 different materials
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! 24 for cubic, 12 for hexagonal, 8 for tetragonal (24+12+8)x3=132
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real(pReal), dimension(132,3), parameter :: sym = &
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reshape((/&
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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-0.5_pReal,0.866025403_pReal,0.0_pReal, &
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-0.866025403_pReal,-0.5_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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-0.5_pReal,-0.866025403_pReal,0.0_pReal, &
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0.866025403_pReal,-0.5_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.5_pReal,0.866025403_pReal,0.0_pReal, &
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-0.866025403_pReal,0.5_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.5_pReal,-0.866025403_pReal,0.0_pReal, &
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0.866025403_pReal,0.5_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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-0.5_pReal,-0.866025403_pReal,0.0_pReal, &
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-0.866025403_pReal,0.5_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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-0.5_pReal,0.866025403_pReal,0.0_pReal, &
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0.866025403_pReal,0.5_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.5_pReal,0.866025403_pReal,0.0_pReal, &
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0.866025403_pReal,-0.5_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.5_pReal,-0.866025403_pReal,0.0_pReal, &
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-0.866025403_pReal,-0.5_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,1.0_pReal, &
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0.0_pReal,1.0_pReal,0.0_pReal, &
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1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal, &
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0.0_pReal,-1.0_pReal,0.0_pReal, &
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-1.0_pReal,0.0_pReal,0.0_pReal, &
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0.0_pReal,0.0_pReal,-1.0_pReal &
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/),(/132,3/))
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CONTAINS
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!**************************************************************************
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@ -85,6 +225,130 @@
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END SUBROUTINE
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! This subroutine calculates the misorientation
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! INPUTS:
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! g1: 1st orientation
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! g2: 2nd orientation
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! typ: Type of crystal symmetry; 1:cubic, 2:hexagonal, 3:tetragonal
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! OUTPUTS:
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! uvw: Misorientation axis
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! ang: Misorientation angle (in degrees)
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! dg: net rotation
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! USES:
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! Vars: cubsym,tetsym,hcpsym
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! Consts: pi
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subroutine misorientation(g1,g2,typ,uvw,ang,dg)
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implicit none
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real(8) g1(3,3),g2(3,3),uvw(3),ang,dg(3,3)
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integer typ,nosym,s1,s2
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real(8) g11(3,3),g22(3,3),dg1(3,3),dg2(3,3),sq,x1,x2,x3
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real(8) trace,temp_ang
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real(8), allocatable :: symop(:,:,:)
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integer i,j
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if (typ==1) then
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nosym=24
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allocate(symop(nosym,3,3))
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do i=1,nosym
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do j=1,3
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symop(i,j,:)=sym(i*j,:)
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enddo
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enddo
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elseif (typ==2) then
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nosym=12
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allocate(symop(nosym,3,3))
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do i=1,nosym
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do j=1,3
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symop(i,j,:)=sym(24+i*j,:)
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enddo
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enddo
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else
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nosym=8
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allocate(symop(nosym,3,3))
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do i=1,nosym
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do j=1,3
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symop(i,j,:)=sym(36+i*j,:)
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enddo
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enddo
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endif
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! Initially set the angle to be maximum
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ang=2*pi
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! 1: Crystal Symmetry to 1st orientation
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do s1=1,nosym
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g11=matmul(symop(s1,:,:),g1)
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! 2: Crystal Symmetry to 2nd orientation
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do s2=1,nosym
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g22=matmul(symop(s2,:,:),g2)
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! 3: Net rotations (g2*inv(g1)=g2*transpose(g1))
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dg1=matmul(g2,transpose(g11))
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dg2=matmul(g1,transpose(g22))
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! 5. CHECK IF THE MISORIENTATION IS IN FUNDAMENTAL ZONE
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! 5.a. For 1st result: (dg1)
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sq=dsqrt((dg1(2,3)-dg1(3,2))**2+(dg1(1,3)-dg1(3,1))**2+&
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(dg1(2,1)-dg1(1,2))**2)
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x1=(dg1(2,3)-dg1(3,2))/sq
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x2=(dg1(3,1)-dg1(1,3))/sq
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x3=(dg1(1,2)-dg1(2,1))/sq
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if (x1>=0) then
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if (x2>=0) then
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if (x3>=0) then
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if (x1<=x2) then
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if (x2<=x3) then
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trace=dg1(1,1)+dg1(2,2)+dg1(3,3)
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temp_ang=acos((trace-1)/2)
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if (abs(temp_ang).lt.ang) then
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ang=temp_ang
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dg=dg1
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uvw(1)=x1;uvw(2)=x2;uvw(3)=x3;
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endif
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endif
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endif
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endif
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endif
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endif
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! 5.a. For the 2nd result: (dg2)
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sq=dsqrt((dg2(2,3)-dg2(3,2))**2+(dg2(1,3)-dg2(3,1))**2+&
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(dg2(2,1)-dg2(1,2))**2)
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x1=(dg2(2,3)-dg2(3,2))/sq
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x2=(dg2(3,1)-dg2(1,3))/sq
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x3=(dg2(1,2)-dg2(2,1))/sq
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if (x1>=0) then
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if (x2>=0) then
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if (x3>=0) then
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if (x1<=x2) then
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if (x2<=x3) then
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trace=dg2(1,1)+dg2(2,2)+dg2(3,3)
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temp_ang=acos((trace-1)/2)
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if (abs(temp_ang).lt.ang) then
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ang=temp_ang
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dg=dg2
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uvw(1)=x1;uvw(2)=x2;uvw(3)=x3;
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endif
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endif
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endif
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endif
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endif
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endif
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enddo
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enddo
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ang=ang*180/pi
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return
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end subroutine
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!**************************************************************************
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! Quicksort algorithm for two-dimensional integer arrays
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!
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