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Solid State Chemistry and its Applications. Anthony R. West

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Solid State Chemistry and its Applications - Anthony R. West

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rel="nofollow" href="#fb3_img_img_2536cae6-87a4-5665-b179-7b15579fe3d9.png" alt="bold-italic x overbar bold-italic y overbar one half plus bold-italic z"/>. Special positions with point symmetry 2, 2(a): x, 0, 0; bold-italic x overbar, 0, ½; 2(b): x, ½, 0; x overbar , ½, ½; 2(c): 0, y, one fourth; 0, y overbar, three fourths; 2(d): ½, y, one fourth; ½, y overbar , three fourths

Image described by caption.

       Figure 1.65 Orthorhombic space group F222 (No 22); coordinates of equivalent positions 16(k)

StartLayout 1st Row bold-italic 000 colon bold-italic x y z comma x overbar y overbar z comma x y overbar z overbar comma x overbar y z overbar 2nd Row bold-italic 0 and one half one half colon bold-italic x y plus one half z plus one half comma x overbar one half minus y one half plus z comma x one half minus y one half minus z comma x overbar one half plus y comma one half minus z 3rd Row one half bold-italic 0 and one half colon one half plus bold-italic x y one half plus z comma one half minus x y overbar one half plus z comma one half plus x y overbar one half minus z comma one half minus bold-italic x y one half minus z 4th Row one half one half bold-italic 0 colon one half plus x one half plus bold-italic y z comma one half minus x one half minus bold-italic y z comma one half plus x one half minus y z overbar comma one half minus x one half plus y z overbar EndLayout

      Special positions with point symmetry 222, 4(a): only one position is given as the other three are generated by the face centring; 0, 0, 0; 4(b): 0, 0, ½; 4(c): one fourth, one fourth, one fourth; 4(d): one fourth, one fourth, three fourths; special positions with point symmetry 2, 8(e): x, 0, 0; x overbar , 0, 0; 8(f): 0, y, 0; 0, y overbar, 0; 8(g): 0, 0, z; 0, 0, z overbar; 8(h): one fourth, one fourth, z; one fourth, one fourth, ½ − z; 8(i): one fourth, y, one fourth; one fourth, ½ − y, one fourth; 8(j): x, one fourth, one fourth; ½ − x, one fourth, one fourth .

      There are sixteen general equivalent positions that fall into four groups related by the face‐centring condition. The four sets are related as (0, 0, 0); (½, ½, 0); (½, 0, ½) and (0, ½, ½). Thus, position l, (x, y, z), is related to positions 2–4: (x + ½, у + ½, z); (x + ½, y, z + ½) and (x, y + ½, z + ½). Generation of the remaining equivalent positions by the action of the 2‐fold axes should be straightforward.

       1.18.5.6 Tetragonal I41

Schematic illustration of tetragonal space group I41.

       Figure 1.66 Tetragonal space group I41 (No 80); coordinates of equivalent positions 8(b):

StartLayout 1st Row bold-italic 000 colon bold-italic x y z comma x overbar y overbar z comma y overbar one half plus x one fourth plus z comma y one half minus x one fourth plus z 2nd Row one half one half one half colon x plus one half y plus one half z plus one half comma one half minus x one half minus y one half plus z comma one half minus bold-italic y x three fourths plus z comma one half plus y x overbar three fourths plus z EndLayout

      Special positions with point symmetry 2, 4(a): 0, 0, z; 0, ½,

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