bravais_symm.f 6.3 KB
 Markus Betzinger committed Apr 26, 2016 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 `````` MODULE m_bravaissymm use m_juDFT !******************************************************************** ! determines the point group of the bravais lattice given the ! lattice vectors. the idea is to determine all the lattice ! vectors that have the same length as a_{1,2,3}, and then use ! these to determine the possible rotation matrices. ! these rotation matrices are in lattice coordinates. mw 12-99 !******************************************************************** CONTAINS SUBROUTINE bravais_symm( > as,bs,scale,nop48,neig12, < nops,mrot) IMPLICIT NONE !==> Arguments INTEGER, INTENT (IN) :: nop48 ! max. number of operations (typically 48) INTEGER, INTENT (IN) :: neig12 ! max. number of lattice vectors with same length ! (max occurs for close-packed fcc: 12) REAL, INTENT (IN) :: as(3,3),bs(3,3),scale(3) ! lattice information INTEGER, INTENT(OUT) :: nops, mrot(3,3,nop48) ! point group operations !==> Locals REAL amet(3,3),b1,b2,b3,d1,d2,d3,dmax,dt INTEGER i,k,k1,k2,k3,m1,m2,m3,n1,n2,n3 INTEGER irot(3,3) INTEGER lv1(3,neig12),lv2(3,neig12),lv3(3,neig12) REAL, PARAMETER :: eps=1.0e-7 !---> set up metric for distances amet = 0.0 DO i = 1,3 amet(1,1) = amet(1,1) + (scale(i)**2)*as(i,1)*as(i,1) amet(2,2) = amet(2,2) + (scale(i)**2)*as(i,2)*as(i,2) amet(3,3) = amet(3,3) + (scale(i)**2)*as(i,3)*as(i,3) amet(2,1) = amet(2,1) + (scale(i)**2)*as(i,1)*as(i,2) amet(3,2) = amet(3,2) + (scale(i)**2)*as(i,2)*as(i,3) amet(3,1) = amet(3,1) + (scale(i)**2)*as(i,3)*as(i,1) ENDDO amet(1,2) = amet(2,1) amet(2,3) = amet(3,2) amet(1,3) = amet(3,1) !---> distances for the lattice vectors d1 = amet(1,1) d2 = amet(2,2) d3 = amet(3,3) b1 = ( bs(1,1)/scale(1) )**2 + ( bs(1,2)/scale(2) )**2 & & + ( bs(1,3)/scale(3) )**2 b2 = ( bs(2,1)/scale(1) )**2 + ( bs(2,2)/scale(2) )**2 & & + ( bs(2,3)/scale(3) )**2 b3 = ( bs(3,1)/scale(1) )**2 + ( bs(3,2)/scale(2) )**2 & & + ( bs(3,3)/scale(3) )**2 !---> determine the cutoffs along each direction a_i: dmax = max( d1,d2,d3) m1 = nint( dmax * b1 ) m2 = nint( dmax * b2 ) m3 = nint( dmax * b3 ) !---->loop over all possible lattice vectors to find those with the !---->length, i.e., ones that could be rotations n1 = 1 n2 = 1 n3 = 1 lv1(1:3,1) = (/ 1,0,0 /) lv2(1:3,1) = (/ 0,1,0 /) lv3(1:3,1) = (/ 0,0,1 /) DO k3=-m3,m3 DO k2=-m2,m2 DO k1=-m1,m1 dt = distance2(k1,k2,k3) !----> check if the same length IF ( abs( dt - d1 ) < eps ) THEN IF (.not.( k1==1 .and. k2==0 .and. k3==0 ) ) THEN n1 = n1+1 IF(n1>neig12) CALL juDFT_error("n1>neig12", + calledby ="bravais_symm") lv1(1,n1) = k1 lv1(2,n1) = k2 lv1(3,n1) = k3 ENDIF ENDIF IF ( abs( dt - d2 ) < eps ) THEN IF (.not.( k1==0 .and. k2==1 .and. k3==0 ) ) THEN n2 = n2+1 IF(n2>neig12) CALL juDFT_error("n2>neig12", + calledby="bravais_symm") lv2(1,n2) = k1 lv2(2,n2) = k2 lv2(3,n2) = k3 ENDIF ENDIF IF ( abs( dt - d3 ) < eps ) THEN IF (.not.( k1==0 .and. k2==0 .and. k3==1 ) ) THEN n3 = n3+1 IF(n3>neig12) CALL juDFT_error("n3>neig12", + calledby="bravais_symm") lv3(1,n3) = k1 lv3(2,n3) = k2 lv3(3,n3) = k3 ENDIF ENDIF ENDDO ENDDO ENDDO !---> the possible rotation matrices are given by the matrix of !---> column vectors of lv_{1,2,3} nops = 0 DO k3 = 1,n3 DO k2 = 1,n2 DO k1 = 1,n1 !---> check whether determinant is +/-1 (needs to be for rotation) IF ( abs(mdet(k1,k2,k3)) .NE. 1 ) CYCLE !---> check whether this maintains lengths correctly !---> if M is the metric, then must have R^T M R = M irot = reshape( (/ lv1(:,k1),lv2(:,k2),lv3(:,k3) /) , & (/ 3,3 /) ) IF ( any( abs( & matmul( transpose(irot), matmul(amet,irot) ) - amet & ) > eps ) ) CYCLE nops = nops + 1 IF ( nops > nop48 ) CALL juDFT_error("nop > nop48", & calledby="bravais_symm") mrot(:,:,nops) = irot ENDDO ENDDO ENDDO WRITE (6,'(//," Point group of the Bravais lattice has ",i2, & " operations")') nops RETURN CONTAINS ! INTERNAL routines REAL FUNCTION distance2(l1,l2,l3) !********************************************************************* ! calculates the magnitude square for a vector (l1,l2,l3) given in ! lattice units !********************************************************************* IMPLICIT NONE INTEGER, INTENT(IN) :: l1,l2,l3 distance2 = l1*(l1*amet(1,1) + 2*l2*amet(2,1)) & + l2*(l2*amet(2,2) + 2*l3*amet(3,2)) & + l3*(l3*amet(3,3) + 2*l1*amet(1,3)) RETURN END FUNCTION distance2 INTEGER FUNCTION mdet(k1,k2,k3) !********************************************************************* ! determines the determinant for possible rotation matrix ! ( lv1(:,k1) ; lv2(:,k2) ; lv3(:,k3) ) !********************************************************************* IMPLICIT NONE INTEGER, INTENT(IN) :: k1,k2,k3 mdet = lv1(1,k1)*( lv2(2,k2)*lv3(3,k3) - lv2(3,k2)*lv3(2,k3) ) & + lv1(2,k1)*( lv2(3,k2)*lv3(1,k3) - lv2(1,k2)*lv3(3,k3) ) & + lv1(3,k1)*( lv2(1,k2)*lv3(2,k3) - lv2(2,k2)*lv3(1,k3) ) RETURN END FUNCTION mdet END SUBROUTINE bravais_symm END MODULE m_bravaissymm``````