bravais_symm.f90 5.38 KB
 Daniel Wortmann committed Jun 07, 2019 1 2 3 4 5 6 7 8 9 10 11 ``````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(cell,nops,mrot) `````` Daniel Wortmann committed Jun 13, 2019 12 `````` USE m_types_cell `````` Daniel Wortmann committed Jun 07, 2019 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 `````` IMPLICIT NONE !==> Arguments TYPE(t_cell),INTENT(in) :: cell INTEGER, INTENT(OUT) :: nops, mrot(:,:,:) ! 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,PARAMETER::neig12=12! max. number of lattice vectors with same length ! (max occurs for close-packed fcc: 12) INTEGER lv1(3,neig12),lv2(3,neig12),lv3(3,neig12) `````` Daniel Wortmann committed Jun 17, 2019 28 `````` REAL, PARAMETER :: eps=1.0e-7 `````` Daniel Wortmann committed Jun 07, 2019 29 30 31 32 33 34 `````` !---> distances for the lattice vectors d1 = cell%aamat(1,1) d2 = cell%aamat(2,2) d3 = cell%aamat(3,3) `````` Daniel Wortmann committed Jun 13, 2019 35 36 37 `````` b1 = ( cell%bmat(1,1) )**2 + ( cell%bmat(1,2) )**2 + ( cell%bmat(1,3) )**2 b2 = ( cell%bmat(2,1) )**2 + ( cell%bmat(2,2) )**2 + ( cell%bmat(2,3) )**2 b3 = ( cell%bmat(3,1) )**2 + ( cell%bmat(3,2) )**2 + ( cell%bmat(3,3) )**2 `````` Daniel Wortmann committed Jun 07, 2019 38 39 40 41 42 43 44 45 `````` !---> 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 ) `````` Daniel Wortmann committed Jun 17, 2019 46 47 48 49 50 `````` !Hmm, do not really understand the code below, but IMHO these are the maximal values of entries in mrot... m1=1 m2=1 m3=1 `````` Daniel Wortmann committed Jun 07, 2019 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 `````` !---->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(cell%aamat,irot) ) - cell%aamat) > eps ) ) CYCLE nops = nops + 1 IF ( nops > SIZE(mrot,3) ) CALL juDFT_error("nop > size(mrot)", 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*cell%aamat(1,1) + 2*l2*cell%aamat(2,1)) + l2*(l2*cell%aamat(2,2) + 2*l3*cell%aamat(3,2)) + l3*(l3*cell%aamat(3,3) + 2*l1*cell%aamat(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``````