The material described by Ba2Sr3CaMg2(SiO4)4 crystallizes in the trigonal P3m1 space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(3), three equivalent O(5), and three equivalent O(7) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(1)O12 cuboctahedra, edges with three equivalent Si(1)O4 tetrahedra, edges with three equivalent Si(3)O4 tetrahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Mg(2)O6 octahedra. In the second Ba site, Ba(2) is bonded to three equivalent O(2), three equivalent O(4), three equivalent O(6), and three equivalent O(8) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(2)O12 cuboctahedra, edges with three equivalent Si(2)O4 tetrahedra, edges with three equivalent Si(4)O4 tetrahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Mg(2)O6 octahedra. There are three inequivalent Sr sites. In the first Sr site, Sr(1) is bonded in a 10-coordinate geometry to one O(2), three equivalent O(5), and six equivalent O(8) atoms. In the second Sr site, Sr(2) is bonded in a 10-coordinate geometry to one O(3), three equivalent O(8), and six equivalent O(5) atoms. In the third Sr site, Sr(3) is bonded in a 10-coordinate geometry to one O(4), three equivalent O(7), and six equivalent O(6) atoms. Ca(1) is bonded in a 10-coordinate geometry to one O(1), three equivalent O(6), and six equivalent O(7) atoms. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(5) and three equivalent O(8) atoms to form MgO6 octahedra that share corners with three equivalent Si(1)O4 tetrahedra, corners with three equivalent Si(4)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(2)O12 cuboctahedra. In the second Mg site, Mg(2) is bonded to three equivalent O(6) and three equivalent O(7) atoms to form MgO6 octahedra that share corners with three equivalent Si(2)O4 tetrahedra, corners with three equivalent Si(3)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(2)O12 cuboctahedra. There are four inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1) and three equivalent O(5) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. In the second Si site, Si(2) is bonded to one O(2) and three equivalent O(6) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. In the third Si site, Si(3) is bonded to one O(3) and three equivalent O(7) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. In the fourth Si site, Si(4) is bonded to one O(4) and three equivalent O(8) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to three equivalent Ba(1), one Ca(1), and one Si(1) atom. In the second O site, O(2) is bonded in a distorted linear geometry to three equivalent Ba(2), one Sr(1), and one Si(2) atom. In the third O site, O(3) is bonded in a distorted linear geometry to three equivalent Ba(1), one Sr(2), and one Si(3) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to three equivalent Ba(2), one Sr(3), and one Si(4) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one Ba(1), one Sr(1), two equivalent Sr(2), one Mg(1), and one Si(1) atom. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one Ba(2), two equivalent Sr(3), one Ca(1), one Mg(2), and one Si(2) atom. In the seventh O site, O(7) is bonded in a 2-coordinate geometry to one Ba(1), one Sr(3), two equivalent Ca(1), one Mg(2), and one Si(3) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one Ba(2), one Sr(2), two equivalent Sr(1), one Mg(1), and one Si(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ba2Sr3CaMg2(SiO4)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.546
_cell_length_b   5.546
_cell_length_c   14.084
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   375.083
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ba  Ba0  1  0.333  0.667  0.251  1.0
  Ba  Ba1  1  0.333  0.667  0.749  1.0
  Sr  Sr2  1  0.667  0.333  0.919  1.0
  Sr  Sr3  1  0.000  0.000  0.082  1.0
  Sr  Sr4  1  0.000  0.000  0.580  1.0
  Ca  Ca5  1  0.667  0.333  0.416  1.0
  Mg  Mg6  1  0.333  0.667  0.001  1.0
  Mg  Mg7  1  0.333  0.667  0.499  1.0
  Si  Si8  1  0.667  0.333  0.138  1.0
  Si  Si9  1  0.667  0.333  0.634  1.0
  Si  Si10  1  0.000  0.000  0.365  1.0
  Si  Si11  1  0.000  0.000  0.865  1.0
  O  O12  1  0.667  0.333  0.254  1.0
  O  O13  1  0.667  0.333  0.748  1.0
  O  O14  1  0.000  0.000  0.250  1.0
  O  O15  1  0.000  0.000  0.750  1.0
  O  O16  1  0.509  0.491  0.090  1.0
  O  O17  1  0.508  0.492  0.587  1.0
  O  O18  1  0.509  0.017  0.090  1.0
  O  O19  1  0.508  0.017  0.587  1.0
  O  O20  1  0.983  0.491  0.090  1.0
  O  O21  1  0.983  0.492  0.587  1.0
  O  O22  1  0.158  0.842  0.411  1.0
  O  O23  1  0.158  0.842  0.912  1.0
  O  O24  1  0.158  0.317  0.411  1.0
  O  O25  1  0.158  0.317  0.912  1.0
  O  O26  1  0.683  0.842  0.411  1.0
  O  O27  1  0.683  0.842  0.912  1.0
[/CIF]
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The material described by Ba2Sr3CaMg2(SiO4)4 crystallizes in the trigonal P3m1 space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1), three equivalent O(3), three equivalent O(5), and three equivalent O(7) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(1)O12 cuboctahedra, edges with three equivalent Si(1)O4 tetrahedra, edges with three equivalent Si(3)O4 tetrahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Mg(2)O6 octahedra. In the second Ba site, Ba(2) is bonded to three equivalent O(2), three equivalent O(4), three equivalent O(6), and three equivalent O(8) atoms to form BaO12 cuboctahedra that share edges with six equivalent Ba(2)O12 cuboctahedra, edges with three equivalent Si(2)O4 tetrahedra, edges with three equivalent Si(4)O4 tetrahedra,  a faceface with one Mg(1)O6 octahedra, and  a faceface with one Mg(2)O6 octahedra. There are three inequivalent Sr sites. In the first Sr site, Sr(1) is bonded in a 10-coordinate geometry to one O(2), three equivalent O(5), and six equivalent O(8) atoms. In the second Sr site, Sr(2) is bonded in a 10-coordinate geometry to one O(3), three equivalent O(8), and six equivalent O(5) atoms. In the third Sr site, Sr(3) is bonded in a 10-coordinate geometry to one O(4), three equivalent O(7), and six equivalent O(6) atoms. Ca(1) is bonded in a 10-coordinate geometry to one O(1), three equivalent O(6), and six equivalent O(7) atoms. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(5) and three equivalent O(8) atoms to form MgO6 octahedra that share corners with three equivalent Si(1)O4 tetrahedra, corners with three equivalent Si(4)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(2)O12 cuboctahedra. In the second Mg site, Mg(2) is bonded to three equivalent O(6) and three equivalent O(7) atoms to form MgO6 octahedra that share corners with three equivalent Si(2)O4 tetrahedra, corners with three equivalent Si(3)O4 tetrahedra,  a faceface with one Ba(1)O12 cuboctahedra, and  a faceface with one Ba(2)O12 cuboctahedra. There are four inequivalent Si sites. In the first Si site, Si(1) is bonded to one O(1) and three equivalent O(5) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. In the second Si site, Si(2) is bonded to one O(2) and three equivalent O(6) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. In the third Si site, Si(3) is bonded to one O(3) and three equivalent O(7) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. In the fourth Si site, Si(4) is bonded to one O(4) and three equivalent O(8) atoms to form SiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 13°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to three equivalent Ba(1), one Ca(1), and one Si(1) atom. In the second O site, O(2) is bonded in a distorted linear geometry to three equivalent Ba(2), one Sr(1), and one Si(2) atom. In the third O site, O(3) is bonded in a distorted linear geometry to three equivalent Ba(1), one Sr(2), and one Si(3) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to three equivalent Ba(2), one Sr(3), and one Si(4) atom. In the fifth O site, O(5) is bonded in a 2-coordinate geometry to one Ba(1), one Sr(1), two equivalent Sr(2), one Mg(1), and one Si(1) atom. In the sixth O site, O(6) is bonded in a 2-coordinate geometry to one Ba(2), two equivalent Sr(3), one Ca(1), one Mg(2), and one Si(2) atom. In the seventh O site, O(7) is bonded in a 2-coordinate geometry to one Ba(1), one Sr(3), two equivalent Ca(1), one Mg(2), and one Si(3) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to one Ba(2), one Sr(2), two equivalent Sr(1), one Mg(1), and one Si(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ba2Sr3CaMg2(SiO4)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.546
_cell_length_b   5.546
_cell_length_c   14.084
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   375.083
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ba  Ba0  1  0.333  0.667  0.251  1.0
  Ba  Ba1  1  0.333  0.667  0.749  1.0
  Sr  Sr2  1  0.667  0.333  0.919  1.0
  Sr  Sr3  1  0.000  0.000  0.082  1.0
  Sr  Sr4  1  0.000  0.000  0.580  1.0
  Ca  Ca5  1  0.667  0.333  0.416  1.0
  Mg  Mg6  1  0.333  0.667  0.001  1.0
  Mg  Mg7  1  0.333  0.667  0.499  1.0
  Si  Si8  1  0.667  0.333  0.138  1.0
  Si  Si9  1  0.667  0.333  0.634  1.0
  Si  Si10  1  0.000  0.000  0.365  1.0
  Si  Si11  1  0.000  0.000  0.865  1.0
  O  O12  1  0.667  0.333  0.254  1.0
  O  O13  1  0.667  0.333  0.748  1.0
  O  O14  1  0.000  0.000  0.250  1.0
  O  O15  1  0.000  0.000  0.750  1.0
  O  O16  1  0.509  0.491  0.090  1.0
  O  O17  1  0.508  0.492  0.587  1.0
  O  O18  1  0.509  0.017  0.090  1.0
  O  O19  1  0.508  0.017  0.587  1.0
  O  O20  1  0.983  0.491  0.090  1.0
  O  O21  1  0.983  0.492  0.587  1.0
  O  O22  1  0.158  0.842  0.411  1.0
  O  O23  1  0.158  0.842  0.912  1.0
  O  O24  1  0.158  0.317  0.411  1.0
  O  O25  1  0.158  0.317  0.912  1.0
  O  O26  1  0.683  0.842  0.411  1.0
  O  O27  1  0.683  0.842  0.912  1.0
[/CIF]
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