OpenWrite::noopen: Cannot open /stmp/mathematica/tmp_147336.txt. Content-type: text/html MGROUPS
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The magnetic space groups derived from the Fedorov space group: 034 > 034 (id = 22543)HHHHRead tr. matrix for the supergroup from /tmp/wp-supertrm22543.trnHHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHinverted:HHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHRead tr. matrix for the subgroup from /tmp/wp-subtrm22543.trnHHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHinverted:HHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHRead tr. matrix from /tmp/wp-trm22543.trnHHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 5.000000 0.000000 4.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHTransformation matrix:HHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 5.000000 0.000000 4.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHdeterminant: 5.000000(det-ONE=4.000000)HHHHInverted of the transformation matrix:HHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 0.200000 0.000000 -0.800000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHSubgroup generators: 2, general positions: 4HHHH(x,y,z)HHHH(-x, -y,z)HHHH(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHH(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHHSubgroup Wyckoff positions:HHHHList of Wyckoff positions:HHHHOrbit No:0HHHHMultiplicity:4HHHHLetter:cHHHH(x,y,z)HHHH(-x, -y,z)HHHH(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHH(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHHOrbit No:1HHHHMultiplicity:2HHHHLetter:bHHHH(0.000000, 0.500000,z)HHHH(0.500000, 0.000000, 0.500000 +z)HHHHOrbit No:2HHHHMultiplicity:2HHHHLetter:aHHHH(0.000000, 0.000000,z)HHHH(0.500000, 0.500000, 0.500000 +z)HHHHtr. matrix:(x, 4.000000 + 5.000000y,z)HHHHdet = 5.000000HHHHSupergroup is transformed to unconventional setting.HHHHtake memory for 9 cells.HHHHtr. matrix:(x, 4.000000 + 5.000000y,z)HHHHNumber of gen. pos. = 4, det = 5.000000. New number of general positions: 20HHHHchange the basis with the matrix (x, 4.000000 + 5.000000y,z)HHHHAfter checking group we obtain 20 elementsHHHH000HHHHBefore expanding:HHHH(x,y,z)HHHH(-x, 0.400000 - y,z)HHHH(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH(0.500000 - x, 0.100000 +y, 0.500000 +z)HHHHAfter expanding general positions: number of cells: 1HHHHNumber of gen. pos. = 0, det = 5.000000. New number of general positions: 0HHHH(x,y,z)HHHH(x, 0.200000 +y,z)HHHH(x, 0.400000 +y,z)HHHH(x, 0.600000 +y,z)HHHH(x, 0.800000 +y,z)HHHH(-x, 0.400000 - y,z)HHHH(-x, 0.600000 - y,z)HHHH(-x, 0.800000 - y,z)HHHH(-x, -y,z)HHHH(-x, 0.200000 - y,z)HHHH(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.700000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.900000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.100000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.300000 - y, 0.500000 +z)HHHH(0.500000 - x, 0.100000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.300000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.700000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.900000 +y, 0.500000 +z)HHHH000HHHHSupergroup is transformed (20 gen.pos.)->return the new group.HHHH(x,y,z)HHHH(x, 0.200000 +y,z)HHHH(x, 0.400000 +y,z)HHHH(x, 0.600000 +y,z)HHHH(x, 0.800000 +y,z)HHHH(-x, 0.400000 - y,z)HHHH(-x, 0.600000 - y,z)HHHH(-x, 0.800000 - y,z)HHHH(-x, -y,z)HHHH(-x, 0.200000 - y,z)HHHH(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.700000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.900000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.100000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.300000 - y, 0.500000 +z)HHHH(0.500000 - x, 0.100000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.300000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.700000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.900000 +y, 0.500000 +z)HHHHSupergroup is transformed to the subgroup basis. there are 20 general positionsHHHHSupergroup generators: xxx, general positions:20HHHHSubgroup basis:HHHH(x,y,z)HHHH(x, 0.200000 +y,z)HHHH(x, 0.400000 +y,z)HHHH(x, 0.600000 +y,z)HHHH(x, 0.800000 +y,z)HHHH(-x, 0.400000 - y,z)HHHH(-x, 0.600000 - y,z)HHHH(-x, 0.800000 - y,z)HHHH(-x, -y,z)HHHH(-x, 0.200000 - y,z)HHHH(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.700000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.900000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.100000 - y, 0.500000 +z)HHHH(0.500000 +x, 0.300000 - y, 0.500000 +z)HHHH(0.500000 - x, 0.100000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.300000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.700000 +y, 0.500000 +z)HHHH(0.500000 - x, 0.900000 +y, 0.500000 +z)HHHHnumber of cells: 1HHHH000HHHHSupergroup Wyckoff positions:HHHHOwn basis.HHHHList of Wyckoff positions:HHHHOrbit No:0HHHHMultiplicity:4HHHHLetter:cHHHH(x,y,z)HHHHOrbit No:1HHHHMultiplicity:2HHHHLetter:bHHHH(0.000000, 0.500000,z)HHHHOrbit No:2HHHHMultiplicity:2HHHHLetter:aHHHH(0.000000, 0.000000,z)HHHHSubgroup basis.HHHHList of Wyckoff positions:HHHHOrbit No:0HHHHMultiplicity:4HHHHLetter:cHHHH(x, 1.000000 + 0.200000 (-4.000000 +y),z)HHHHOrbit No:1HHHHMultiplicity:2HHHHLetter:bHHHH(0.000000, 0.300000,z)HHHHOrbit No:2HHHHMultiplicity:2HHHHLetter:aHHHH(0.000000, 0.200000,z)HHHHindex : 5HHHHSplitting of the general position of the supergroup...HHHHThe general position splits into 5 suborbits.HHHH&Splitting of all positions:HHHHGGGG4c: 4c 4c 4c 4c 4cHHHH2b: 4c 2b 4cHHHH2a: 4c 4c 2aHHHH&Splitting of Wyckoff position 4c: 4c 4c 4c 4c 4cHHHHOrbit 0:HHHH[0]TTTT(x,y,z)TTTT(x, 0.200000 (-4.000000 +y),z)TTTT4cTTTT(x,y,z)HHHH[1]TTTT(-x, 3.000000 - y,z)TTTT(-x, 0.200000 (-1.000000 - y),z)TTTT4cTTTT(-x, -y,z)HHHH[2]TTTT(0.500000 +x, 0.500000 - y, 0.500000 +z)TTTT(0.500000 +x, 0.100000 (-7.000000 - 2.000000y), 0.500000 +z)TTTT4cTTTT(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH[3]TTTT(0.500000 - x, 2.500000 +y, 0.500000 +z)TTTT(0.500000 - x, 0.100000 (-3.000000 + 2.000000y), 0.500000 +z)TTTT4cTTTT(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHHOrbit 1:HHHH[0]TTTT(x, 1.000000 +y,z)TTTT(x, 0.200000 (-3.000000 +y),z)TTTT4cTTTT(x,y,z)HHHH[1]TTTT(-x, 2.000000 - y,z)TTTT(-x, 0.200000 (-2.000000 - y),z)TTTT4cTTTT(-x, -y,z)HHHH[2]TTTT(0.500000 +x, -0.500000 - y, 0.500000 +z)TTTT(0.500000 +x, 0.100000 (-9.000000 - 2.000000y), 0.500000 +z)TTTT4cTTTT(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH[3]TTTT(0.500000 - x, 3.500000 +y, 0.500000 +z)TTTT(0.500000 - x, 0.100000 (-1.000000 + 2.000000y), 0.500000 +z)TTTT4cTTTT(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHHOrbit 2:HHHH[0]TTTT(x, 2.000000 +y,z)TTTT(x, 0.200000 (-2.000000 +y),z)TTTT4cTTTT(x,y,z)HHHH[1]TTTT(-x, 1.000000 - y,z)TTTT(-x, 0.200000 (-3.000000 - y),z)TTTT4cTTTT(-x, -y,z)HHHH[2]TTTT(0.500000 +x, 3.500000 - y, 0.500000 +z)TTTT(0.500000 +x, 0.100000 (-1.000000 - 2.000000y), 0.500000 +z)TTTT4cTTTT(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH[3]TTTT(0.500000 - x, -0.500000 +y, 0.500000 +z)TTTT(0.500000 - x, 0.100000 (-9.000000 + 2.000000y), 0.500000 +z)TTTT4cTTTT(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHHOrbit 3:HHHH[0]TTTT(x, 3.000000 +y,z)TTTT(x, 0.200000 (-1.000000 +y),z)TTTT4cTTTT(x,y,z)HHHH[1]TTTT(-x, -y,z)TTTT(-x, 0.200000 (-4.000000 - y),z)TTTT4cTTTT(-x, -y,z)HHHH[2]TTTT(0.500000 +x, 2.500000 - y, 0.500000 +z)TTTT(0.500000 +x, 0.100000 (-3.000000 - 2.000000y), 0.500000 +z)TTTT4cTTTT(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH[3]TTTT(0.500000 - x, 0.500000 +y, 0.500000 +z)TTTT(0.500000 - x, 0.100000 (-7.000000 + 2.000000y), 0.500000 +z)TTTT4cTTTT(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHHOrbit 4:HHHH[0]TTTT(x, -1.000000 +y,z)TTTT(x, 0.200000 (-5.000000 +y),z)TTTT4cTTTT(x,y,z)HHHH[1]TTTT(-x, -1.000000 - y,z)TTTT(-x, -1.000000 - 0.200000y,z)TTTT4cTTTT(-x, -y,z)HHHH[2]TTTT(0.500000 +x, 1.500000 - y, 0.500000 +z)TTTT(0.500000 +x, -0.500000 - 0.200000y, 0.500000 +z)TTTT4cTTTT(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH[3]TTTT(0.500000 - x, 1.500000 +y, 0.500000 +z)TTTT(0.500000 - x, -0.500000 + 0.200000y, 0.500000 +z)TTTT4cTTTT(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHHGGGG$Splitting of Wyckoff position 2b: 4c 2b 4cHHHHOrbit 0:HHHH[0]TTTT(0.000000, 0.500000,z)TTTT(0.000000, -0.700000,z)TTTT4cTTTT(x,y,z)HHHH[1]TTTT(0.000000, 2.500000,z)TTTT(0.000000, -0.300000,z)TTTT4cTTTT(-x, -y,z)HHHH[2]TTTT(0.500000, 0.000000, 0.500000 +z)TTTT(0.500000, -0.800000, 0.500000 +z)TTTT4cTTTT(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH[3]TTTT(0.500000, 3.000000, 0.500000 +z)TTTT(0.500000, -0.200000, 0.500000 +z)TTTT4cTTTT(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHHOrbit 1:HHHH[0]TTTT(0.000000, 1.500000,z)TTTT(0.000000, -0.500000,z)TTTT2bTTTT(0.000000, 0.500000,z)HHHH[1]TTTT(0.500000, -1.000000, 0.500000 +z)TTTT(0.500000, -1.000000, 0.500000 +z)TTTT2bTTTT(0.500000, 0.000000, 0.500000 +z)HHHHOrbit 2:HHHH[0]TTTT(0.000000, 3.500000,z)TTTT(0.000000, -0.100000,z)TTTT4cTTTT(x,y,z)HHHH[1]TTTT(0.000000, -0.500000,z)TTTT(0.000000, -0.900000,z)TTTT4cTTTT(-x, -y,z)HHHH[2]TTTT(0.500000, 2.000000, 0.500000 +z)TTTT(0.500000, -0.400000, 0.500000 +z)TTTT4cTTTT(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH[3]TTTT(0.500000, 1.000000, 0.500000 +z)TTTT(0.500000, -0.600000, 0.500000 +z)TTTT4cTTTT(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHHGGGG$Splitting of Wyckoff position 2a: 4c 4c 2aHHHHOrbit 0:HHHH[0]TTTT(0.000000, 0.000000,z)TTTT(0.000000, -0.800000,z)TTTT4cTTTT(x,y,z)HHHH[1]TTTT(0.000000, 3.000000,z)TTTT(0.000000, -0.200000,z)TTTT4cTTTT(-x, -y,z)HHHH[2]TTTT(0.500000, 0.500000, 0.500000 +z)TTTT(0.500000, -0.700000, 0.500000 +z)TTTT4cTTTT(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH[3]TTTT(0.500000, 2.500000, 0.500000 +z)TTTT(0.500000, -0.300000, 0.500000 +z)TTTT4cTTTT(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHHOrbit 1:HHHH[0]TTTT(0.000000, 1.000000,z)TTTT(0.000000, -0.600000,z)TTTT4cTTTT(x,y,z)HHHH[1]TTTT(0.000000, 2.000000,z)TTTT(0.000000, -0.400000,z)TTTT4cTTTT(-x, -y,z)HHHH[2]TTTT(0.500000, -0.500000, 0.500000 +z)TTTT(0.500000, -0.900000, 0.500000 +z)TTTT4cTTTT(0.500000 +x, 0.500000 - y, 0.500000 +z)HHHH[3]TTTT(0.500000, 3.500000, 0.500000 +z)TTTT(0.500000, -0.100000, 0.500000 +z)TTTT4cTTTT(0.500000 - x, 0.500000 +y, 0.500000 +z)HHHHOrbit 2:HHHH[0]TTTT(0.000000, -1.000000,z)TTTT(0.000000, -1.000000,z)TTTT2aTTTT(0.000000, 0.000000,z)HHHH[1]TTTT(0.500000, 1.500000, 0.500000 +z)TTTT(0.500000, -0.500000, 0.500000 +z)TTTT2aTTTT(0.500000, 0.500000, 0.500000 +z)HHHHGGGG&{{4, c}, {2, b}, {2, a}}${{{4, c}, {4, c}, {4, c}, {4, c}, {4, c}}, {{4, c}, {2, b}, {4, c}}, {{4, c}, {4, c}, {2, a}}}${{{{x, y, z}, {-x, 3 - y, z}, {1/2 + x, 1/2 - y, 1/2 + z}, {1/2 - x, 5/2 + y, 1/2 + z}}, {{x, 1 + y, z}, {-x, 2 - y, z}, {1/2 + x, -1/2 - y, 1/2 + z}, {1/2 - x, 7/2 + y, 1/2 + z}}, {{x, 2 + y, z}, {-x, 1 - y, z}, {1/2 + x, 7/2 - y, 1/2 + z}, {1/2 - x, -1/2 + y, 1/2 + z}}, {{x, 3 + y, z}, {-x, -y, z}, {1/2 + x, 5/2 - y, 1/2 + z}, {1/2 - x, 1/2 + y, 1/2 + z}}, {{x, -1 + y, z}, {-x, -1 - y, z}, {1/2 + x, 3/2 - y, 1/2 + z}, {1/2 - x, 3/2 + y, 1/2 + z}}}, {{{0, 1/2, z}, {0, 5/2, z}, {1/2, 0, 1/2 + z}, {1/2, 3, 1/2 + z}}, {{0, 3/2, z}, {1/2, -1, 1/2 + z}}, {{0, 7/2, z}, {0, -1/2, z}, {1/2, 2, 1/2 + z}, {1/2, 1, 1/2 + z}}}, {{{0, 0, z}, {0, 3, z}, {1/2, 1/2, 1/2 + z}, {1/2, 5/2, 1/2 + z}}, {{0, 1, z}, {0, 2, z}, {1/2, -1/2, 1/2 + z}, {1/2, 7/2, 1/2 + z}}, {{0, -1, z}, {1/2, 3/2, 1/2 + z}}}}${{{{x, (-4 + y)/5, z}, {-x, (-1 - y)/5, z}, {1/2 + x, (-7 - 2*y)/10, 1/2 + z}, {1/2 - x, (-3 + 2*y)/10, 1/2 + z}}, {{x, (-3 + y)/5, z}, {-x, (-2 - y)/5, z}, {1/2 + x, (-9 - 2*y)/10, 1/2 + z}, {1/2 - x, (-1 + 2*y)/10, 1/2 + z}}, {{x, (-2 + y)/5, z}, {-x, (-3 - y)/5, z}, {1/2 + x, (-1 - 2*y)/10, 1/2 + z}, {1/2 - x, (-9 + 2*y)/10, 1/2 + z}}, {{x, (-1 + y)/5, z}, {-x, (-4 - y)/5, z}, {1/2 + x, (-3 - 2*y)/10, 1/2 + z}, {1/2 - x, (-7 + 2*y)/10, 1/2 + z}}, {{x, (-5 + y)/5, z}, {-x, -1 - y/5, z}, {1/2 + x, -1/2 - y/5, 1/2 + z}, {1/2 - x, -1/2 + y/5, 1/2 + z}}}, {{{0, -7/10, z}, {0, -3/10, z}, {1/2, -4/5, 1/2 + z}, {1/2, -1/5, 1/2 + z}}, {{0, -1/2, z}, {1/2, -1, 1/2 + z}}, {{0, -1/10, z}, {0, -9/10, z}, {1/2, -2/5, 1/2 + z}, {1/2, -3/5, 1/2 + z}}}, {{{0, -4/5, z}, {0, -1/5, z}, {1/2, -7/10, 1/2 + z}, {1/2, -3/10, 1/2 + z}}, {{0, -3/5, z}, {0, -2/5, z}, {1/2, -9/10, 1/2 + z}, {1/2, -1/10, 1/2 + z}}, {{0, -1, z}, {1/2, -1/2, 1/2 + z}}}}${{{{x, y, z}, {-x, -y, z}, {1/2 + x, 1/2 - y, 1/2 + z}, {1/2 - x, 1/2 + y, 1/2 + z}}, {{x, y, z}, {-x, -y, z}, {1/2 + x, 1/2 - y, 1/2 + z}, {1/2 - x, 1/2 + y, 1/2 + z}}, {{x, y, z}, {-x, -y, z}, {1/2 + x, 1/2 - y, 1/2 + z}, {1/2 - x, 1/2 + y, 1/2 + z}}, {{x, y, z}, {-x, -y, z}, {1/2 + x, 1/2 - y, 1/2 + z}, {1/2 - x, 1/2 + y, 1/2 + z}}, {{x, y, z}, {-x, -y, z}, {1/2 + x, 1/2 - y, 1/2 + z}, {1/2 - x, 1/2 + y, 1/2 + z}}}, {{{x, y, z}, {-x, -y, z}, {1/2 + x, 1/2 - y, 1/2 + z}, {1/2 - x, 1/2 + y, 1/2 + z}}, {{0, 1/2, z}, {1/2, 0, 1/2 + z}}, {{x, y, z}, {-x, -y, z}, {1/2 + x, 1/2 - y, 1/2 + z}, {1/2 - x, 1/2 + y, 1/2 + z}}}, {{{x, y, z}, {-x, -y, z}, {1/2 + x, 1/2 - y, 1/2 + z}, {1/2 - x, 1/2 + y, 1/2 + z}}, {{x, y, z}, {-x, -y, z}, {1/2 + x, 1/2 - y, 1/2 + z}, {1/2 - x, 1/2 + y, 1/2 + z}}, {{0, 0, z}, {1/2, 1/2, 1/2 + z}}}}&OK! (#)

Listed with respect to the BNS setting:


Listed with respect to the OG setting:



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