Alex Selimov
5 years ago
commit
c89b7d3b59
@ -0,0 +1,520 @@
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module opt_disl
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!This module contains all code associated with dislocations
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use parameters
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use elements
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use subroutines
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use box
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implicit none
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real(kind=dp), dimension(3) :: line, slip_plane, centroid!dislocation line, slip plane vectors, centroid,
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real(kind=dp) :: burgers(3) !burgers vector of loop
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real(kind=dp) :: poisson, char_angle, lattice_parameter!Poisson ratio and character angle, lattice_parameter for burgers vector
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character(len=10) :: lattice
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character(len=1) :: loop_normal
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real(kind=dp) :: loop_radius !Dislocation loop radius
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real(kind=dp) :: b !burgers vector
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public
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contains
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subroutine dislocation(option, arg_pos)
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!Main calling function for all codes related to dislocations
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character(len=100), intent(in) :: option
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integer, intent(inout) :: arg_pos
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select case(trim(adjustl(option)))
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case('-dislgen')
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call parse_dislgen(arg_pos)
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call dislgen
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case('-disloop')
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call parse_disloop(arg_pos)
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call disloop
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end select
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end subroutine dislocation
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subroutine parse_dislgen(arg_pos)
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!Parse dislgen command
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integer, intent(inout) :: arg_pos
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integer :: i,arglen
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character(len=8) :: ori_string
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character(len=100) :: textholder
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!Parse all of the commands
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arg_pos = arg_pos + 1
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line(:) = 0.0_dp
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call get_command_argument(arg_pos, ori_string, arglen)
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if (arglen==0) STOP "Missing line vector in dislgen command"
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call parse_ori_vec(ori_string, line)
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arg_pos=arg_pos + 1
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slip_plane(:) = 0.0_dp
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call get_command_argument(arg_pos, ori_string, arglen)
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if (arglen==0) STOP "Missing plane vector in dislgen command"
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call parse_ori_vec(ori_string, slip_plane)
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do i = 1, 3
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arg_pos = arg_pos + 1
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call get_command_argument(arg_pos, textholder, arglen)
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if (arglen==0) STOP "Missing centroid in dislgen command"
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call parse_pos(i, textholder, centroid(i))
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end do
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print *, centroid
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arg_pos = arg_pos + 1
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call get_command_argument(arg_pos, textholder, arglen)
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if (arglen==0) STOP "Missing character angle in dislgen command"
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read(textholder, *) char_angle
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arg_pos = arg_pos + 1
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call get_command_argument(arg_pos, textholder, arglen)
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if (arglen==0) STOP "Missing poisson in dislgen command"
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read(textholder, *) poisson
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arg_pos = arg_pos + 1
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call get_command_argument(arg_pos, lattice, arglen)
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if (arglen==0) STOP "Missing lattice in dislgen command"
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arg_pos = arg_pos + 1
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call get_command_argument(arg_pos, textholder, arglen)
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if (arglen==0) STOP "Missing lattice parameter in dislgen command"
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read(textholder, *) lattice_parameter
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arg_pos = arg_pos + 1
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!Now set the vurgers vector based on the lattice paarameter and lattice type
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select case(lattice)
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case('fcc')
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b = lattice_parameter / sqrt(2.0_dp)
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! case('bcc')
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! b = lattice_parameter * sqrt(3.0_dp) / 2.0_dp
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case default
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print *, 'Error: Lattice structure', lattice, ' is not accepted for dislgen option'
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STOP
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end select
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end subroutine parse_dislgen
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subroutine dislgen
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!This subroutine creates the actual dislocation
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integer :: i, sub_box, inod, ibasis
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real(kind=dp) :: ss_ori(3,3), ss_inv(3,3), be, bs, slipx(3), disp_transform(3,3), inv_transform(3,3), &
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actan, r(3), disp(3)
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!Calculate screw and edge burgers vectors
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be = sin(char_angle*pi/180.0_dp)*b
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bs = cos(char_angle*pi/180.0_dp)*b
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!Figure out which sub box you are in so you can access it's orientation, this code will not work
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!with overlapping sub_boxes
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do i = 1, sub_box_num
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if(in_block_bd(centroid, sub_box_bd(:,i))) then
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sub_box = i
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exit
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end if
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end do
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!Construct the slip system orientation matrix in an unrotated system
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slipx = cross_product(slip_plane, line)
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ss_ori(1,:) = unitvec(3,slipx)
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ss_ori(2,:) = unitvec(3,slip_plane)
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ss_ori(3,:) = unitvec(3,line)
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call matrix_inverse(ss_ori, 3, ss_inv)
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!Apply the rotation
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disp_transform = matmul(sub_box_ori(:,:,i), ss_inv)
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call matrix_inverse(disp_transform,3,inv_transform)
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if(atom_num > 0) then
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do i = 1, atom_num
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r=r_atom(:,i) - centroid
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r=matmul(inv_transform, r)
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if (r(1) == 0) then
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actan=pi/2
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else
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actan = datan2(r(2),r(1))
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end if
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if ((r(1)**2 + r(2)**2) == 0) cycle
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!This is the elastic displacement field for dislocation according to Hirth and Lowe
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disp(1) = be/(2.0_dp*pi) * (actan + (r(1)*r(2))/(2.0_dp*(1.0_dp-poisson)*(r(1)**2.0_dp + r(2)**2.0_dp)))
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disp(2) = -be/(2.0_dp*pi)*((1.0_dp-2.0_dp*poisson)/(4.0_dp-4.0_dp*poisson) * &
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log(r(1)**2.0_dp + r(2)**2.0_dp) &
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+ (r(1)**2.0_dp - r(2)**2.0_dp)/(4.0_dp*(1.0_dp-poisson)&
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*(r(1)**2.0_dp+r(2)**2.0_dp)))
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disp(3) = bs/(2.0_dp*pi) * actan
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!This transforms the displacement to the correct orientation
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disp = matmul(disp_transform, disp)
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r_atom(:,i) = r_atom(:,i) + disp
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end do
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end if
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if(ele_num > 0) then
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do i = 1, ele_num
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do inod=1, ng_node(lat_ele(i))
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do ibasis = 1, basisnum(lat_ele(i))
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r = r_node(:,ibasis,inod,i)
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r = matmul(inv_transform, r)
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if (r(1) == 0) then
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actan = pi/2
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else
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actan = datan2(r(2),r(1))
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end if
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if ((r(1)**2 + r(2)**2) == 0) cycle
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!This is the elastic displacement field for dislocation according to Hirth and Lowe
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disp(1) = be/(2.0_dp*pi) * (actan + (r(1)*r(2))/(2.0_dp*(1.0_dp-poisson)*(r(1)**2.0_dp + r(2)**2.0_dp)))
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disp(2) = -be/(2.0_dp*pi)*((1.0_dp-2.0_dp*poisson)/(4.0_dp-4.0_dp*poisson) * &
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log(r(1)**2.0_dp + r(2)**2.0_dp) &
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+ (r(1)**2.0_dp - r(2)**2.0_dp)/(4.0_dp*(1.0_dp-poisson)&
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*(r(1)**2.0_dp+r(2)**2.0_dp)))
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disp(3) = bs/(2.0_dp*pi) * actan
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disp = matmul(disp_transform, disp)
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r_node(:,ibasis,inod,i) = r_node(:,ibasis,inod,i) + disp
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end do
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end do
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end do
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end if
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end subroutine dislgen
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subroutine parse_disloop(arg_pos)
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!This subroutine parses the disloop command
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integer, intent(inout) :: arg_pos
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integer :: i,arglen, sbox
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character(len=8) :: ori_string
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character(len=100) :: textholder
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!Parse all of the commands
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arg_pos = arg_pos + 1
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loop_normal = ' '
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call get_command_argument(arg_pos, loop_normal, arglen)
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if (arglen==0) STOP "Missing loop_normal in disloop command"
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!Convert the loop_normal to the dimension
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select case(loop_normal)
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case('x','X', 'y', 'Y', 'z', 'Z')
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continue
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case default
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print *, "Dimension argument must either be x, y, or z not", loop_normal
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stop 3
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end select
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arg_pos = arg_pos + 1
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loop_radius = 0
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call get_command_argument(arg_pos, textholder, arglen)
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if (arglen==0) STOP "Missing loop_size in disloop command"
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read(textholder, *) loop_radius
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do i = 1, 3
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arg_pos = arg_pos + 1
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call get_command_argument(arg_pos, textholder, arglen)
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if (arglen==0) STOP "Missing centroid in disloop command"
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call parse_pos(i, textholder, centroid(i))
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end do
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burgers(:) = 0.0_dp
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do i = 1, 3
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arg_pos = arg_pos + 1
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call get_command_argument(arg_pos, textholder, arglen)
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if (arglen==0) STOP "Missing burgers vector in disloop command"
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read(textholder, *) burgers(i)
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end do
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arg_pos = arg_pos + 1
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call get_command_argument(arg_pos, textholder, arglen)
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if (arglen==0) STOP "Missing poisson ratio in disloop command"
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read(textholder, *) poisson
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arg_pos = arg_pos + 1
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!Now check to make sure that the dimension selected is actually a 1 1 1 direction.
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! call in_sub_box(centroid, sbox)
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! if(.not.((abs(sub_box_ori(loop_normal,1,sbox)) == abs(sub_box_ori(loop_normal,2,sbox))).and. &
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! (abs(sub_box_ori(loop_normal,2,sbox)) == abs(sub_box_ori(loop_normal,3,sbox))).and. &
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! (abs(sub_box_ori(loop_normal,3,sbox)) == abs(sub_box_ori(loop_normal,1,sbox))))) then
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! print *, "The selected dimension ", loop_normal, " for sub_box ", sbox, " is ", &
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! sub_box_ori(loop_normal,:,sbox), " which is not in the (111) family of planes"
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! STOP 3
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! end if
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end subroutine
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!Code for the creation of dislocation loops is based on functions from atomsk
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!which is available from https://atomsk.univ-lille.fr/. They have been adapted to fit cacmb.
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subroutine disloop
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!This subroutine applies the displacement field for a dislocation loop to all atoms and elements.
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integer :: a1, a2, a3 !New directions
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integer :: i, j, inod, ibasis, Npoints
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real(kind = dp) :: perimeter, angle, theta, omega, xA(3), xB(3), xC(3), u(3)
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real(kind=dp), dimension(:,:), allocatable :: xloop !coordinate of points forming loop
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if(allocated(xLoop)) deallocate(xLoop)
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!Define new directions
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select case(loop_normal)
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case('x','X')
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!Loop in (y,z) plane
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a1 = 2
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a2 = 3
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a3 = 1
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case('y','Y')
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!Loop in (x,z) plane
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a1 = 3
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a2 = 1
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a3 = 2
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case default
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!Loop in (x,y) plane
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a1 = 1
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a2 = 2
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a3 = 3
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end select
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!Calculate loop perimeter
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perimeter = 2.0_dp*pi*loop_radius
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!Define the number of points forming the loop
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! The following criteria are used as a trade-off between
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! good accuracy and computational efficiency:
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! - each dislocation segment should have a length of 5 angströms;
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! - the loop should contain at least 3 points
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! (for very small loops, this will result in segments shorter than 5 A);
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! - there should not be more than 100 points
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! (for very large loops, this will result in segments longer than 5 A).
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Npoints = MAX( 3 , MIN( NINT(perimeter/5.d0) , 100 ) )
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!angle between two consecutive points
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theta = 2.0_dp*pi / dble(Npoints)
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!allocate xLoop
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allocate(xLoop(Npoints,3))
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xLoop(:,:) = 0.0_dp
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!Calculate the position of each point in the loop
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angle = 0.0_dp
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do i = 1, size(xLoop,1)
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xLoop(i,a1) = centroid(a1) + loop_radius*dcos(angle)
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xLoop(i,a2) = centroid(a2) + loop_radius*dsin(angle)
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xLoop(i,a3) = centroid(a3)
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! Increment angle for next point
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angle = angle + theta
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end do
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!Now actually calculate the displacement created by a loop for every atom
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do i = 1, atom_num
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u = 0.0_dp
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omega = 0.0_dp
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xC(:) = centroid - r_atom(:,i)
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!Loop over all dislocation segments
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do j = 1, size(xLoop,1)
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!Coordinates of point A
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if (j ==1) then
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xA(:) = xLoop(size(xLoop,1),:) - r_atom(:,i)
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else
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xA(:) = xLoop(j-1, :) - r_atom(:,i)
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end if
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!Coordinates of point B
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xB(:) = xLoop(j,:) - r_atom(:,i)
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!Displacement due to solid angle
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omega = omega + SolidAngle(xA, xB, xC)
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!Displacement due to elasticity
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u(:) = u(:) + DisloSeg_displacement_iso(xA, xB, burgers(:), poisson)
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end do
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!Total displacement
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u=u(:) + burgers(:) * omega
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!Apply displacement to atom
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r_atom(:,i) = r_atom(:,i) + u(:)
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end do
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!Repeat for element nodes
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do i = 1, ele_num
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do inod =1, ng_node(lat_ele(i))
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do ibasis = 1, basisnum(lat_ele(i))
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u = 0.0_dp
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omega = 0.0_dp
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xC(:) = centroid - r_node(:,ibasis,inod,i)
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!Loop over all dislocation segments
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do j = 1, size(xLoop,1)
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!Coordinates of point A
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if (j ==1) then
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xA(:) = xLoop(size(xLoop,1),:) - r_node(:,ibasis,inod,i)
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else
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xA(:) = xLoop(j-1, :) - r_node(:,ibasis,inod,i)
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end if
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!Coordinates of point B
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xB(:) = xLoop(j,:) - r_node(:,ibasis,inod,i)
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!Displacement due to solid angle
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omega = omega + SolidAngle(xA, xB, xC)
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!Displacement due to elasticity
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u(:) = u(:) + DisloSeg_displacement_iso(xA, xB, burgers(:), poisson)
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end do
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!Total displacement
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u=u(:) + burgers(:) * omega
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!Apply displacement to atom
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r_node(:,ibasis,inod,i) = r_node(:,ibasis,inod,i) + u(:)
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end do
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end do
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end do
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return
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end subroutine
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!********************************************************
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! SOLIDANGLE
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! Calculate solid angle (normalized by 4*pi) used to obtain the
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! displacement created by a dislocation triangle loop ABC at the origin
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! (field point = origin)
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! Ref.: Van Oosterom, A. and Strackee, J.,
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! The Solid Angle of a Plane Triangle,
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! IEEE Transactions on Biomedical Engineering BME-30, 125 (1983).
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!********************************************************
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FUNCTION SolidAngle(xA, xB, xC) RESULT(Omega)
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!
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IMPLICIT NONE
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!
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! Extremities of the triangle loop
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REAL(dp),DIMENSION(3),INTENT(IN) :: xA, xB, xC
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!
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! Solid angle (normalized by 4*pi)
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REAL(dp):: omega
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REAL(dp),PARAMETER:: factor=1.d0/(2.d0*pi)
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!
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REAL(dp) :: rA, rB, rC, numerator, denominator
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!
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rA = norm2(xA)
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rB = norm2(xB)
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rC = norm2(xC)
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!
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numerator = TRIPLE_PRODUCT( xA, xB, xC )
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denominator = rA*rB*rC + DOT_PRODUCT( xA, xB )*rC &
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& + DOT_PRODUCT( xB, xC )*rA + DOT_PRODUCT( xC, xA )*rB
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!
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omega = factor*ATAN2( numerator, denominator )
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!
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END FUNCTION SolidAngle
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!********************************************************
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! DISLOSEG_DISPLACEMENT_ISO
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! Calculate displacement created by dislocation segment AB
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! once the solid angle part has been removed
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! Isotropic elastic calculation with nu Poisson coef.
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! Ref.: Eq. (1) in Barnett, D. M.
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! The Displacement Field of a Triangular Dislocation Loop
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! Philos. Mag. A, 1985, 51, 383-387
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!********************************************************
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FUNCTION DisloSeg_displacement_iso(xA, xB, b, nu) RESULT(u)
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!
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IMPLICIT NONE
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REAL(dp),DIMENSION(3),INTENT(IN):: xA, xB ! Extremities of the segment
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REAL(dp),DIMENSION(3),INTENT(IN):: b ! Burgers vector
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REAL(dp),INTENT(IN):: nu ! Poisson coefficient
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REAL(dp),DIMENSION(3):: u ! Displacement
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REAL(dp):: rA, rB
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REAL(dp),DIMENSION(1:3):: tAB, nAB
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!
|
||||
rA = norm2(xA)
|
||||
rB = norm2(xB)
|
||||
!
|
||||
! Tangent vector
|
||||
tAB(:) = xB(:) - xA(:)
|
||||
tAB(:) = tAB(:)/norm2(tAB)
|
||||
!
|
||||
! Normal vector
|
||||
nAB(:) = CROSS_PRODUCT(xA,xB)
|
||||
nAB(:) = nAB(:)/norm2(nAB)
|
||||
!
|
||||
u(:) = ( -(1.d0-2.d0*nu)*CROSS_PRODUCT(b, tAB)* &
|
||||
& LOG( (rB + DOT_PRODUCT(xB,tAB))/(rA + DOT_PRODUCT(xA,tAB)) ) &
|
||||
& + DOT_PRODUCT(b,nAB)*CROSS_PRODUCT(xB/rB-xA/rA,nAB) ) &
|
||||
& /(8.d0*pi*(1.d0-nu))
|
||||
!
|
||||
END FUNCTION DisloSeg_displacement_iso
|
||||
!
|
||||
!This code simply creates a planar vacancy cluster and does not apply the dislocation loop displacement field.
|
||||
! subroutine disloop
|
||||
! !This subroutine actually creates the dislocation loop.
|
||||
|
||||
! real(kind=dp) :: neighbor_dis(loop_size), temp_box(6), dis
|
||||
! integer :: i, j, index(loop_size)
|
||||
|
||||
! neighbor_dis(:) = HUGE(1.0_dp)
|
||||
! index(:) = 0
|
||||
|
||||
! !First find the nearest atom to the centroid
|
||||
! do i = 1, atom_num
|
||||
! if(norm2(r_atom(:,i) - centroid) < neighbor_dis(1)) then
|
||||
! neighbor_dis(1) = norm2(r_atom(:,i) - centroid)
|
||||
! index(1) = i
|
||||
! end if
|
||||
! end do
|
||||
|
||||
! !Define a new box, this box tries to isolate all atoms on the plane of the atom
|
||||
! !closest to the user defined centroid.
|
||||
! temp_box(:) = box_bd(:)
|
||||
! temp_box(2*loop_normal) = r_atom(loop_normal,index(1)) + 10.0_dp**(-2.0_dp)
|
||||
! temp_box(2*loop_normal-1) = r_atom(loop_normal,index(1)) - 10.0_dp**(-2.0_dp)
|
||||
|
||||
! !Now reset the list for the scanning algorithm
|
||||
! index(1) = 0
|
||||
! neighbor_dis(1) = HUGE(1.0_dp)
|
||||
|
||||
! !Now scan over all atoms again and find the closest loop_size number of atoms to the initial atom
|
||||
! !that reside on the same plane.
|
||||
|
||||
! do i = 1, atom_num
|
||||
! !Check to see if it is on the same plane
|
||||
! if (in_block_bd(r_atom(:,i), temp_box)) then
|
||||
! dis = norm2(r_atom(:,i) - centroid)
|
||||
! do j = 1, loop_size
|
||||
! !Check to see if it is closer than other atoms
|
||||
! if (dis < neighbor_dis(j)) then
|
||||
! !Move values in the neighbor array and add the new neighbor
|
||||
! if(j < loop_size) then
|
||||
! neighbor_dis(j+1:loop_size) = neighbor_dis(j:loop_size-1)
|
||||
! index(j+1:loop_size) = index(j:loop_size-1)
|
||||
! end if
|
||||
! neighbor_dis(j) = dis
|
||||
! index(j) = i
|
||||
! exit
|
||||
! end if
|
||||
! end do
|
||||
! end if
|
||||
! end do
|
||||
|
||||
! !Now delete the atoms
|
||||
! call delete_atoms(loop_size, index)
|
||||
|
||||
! return
|
||||
! end subroutine disloop
|
||||
|
||||
end module opt_disl
|
||||
Loading…
Reference in new issue