International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 2.3, p. 343

Table 2.3.4.1 

I. Gregoraa*

aInstitute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague 8, Czech Republic
Correspondence e-mail: gregora@fzu.cz

Table 2.3.4.1| top | pdf |
Symmetrized (s) and antisymmetrized (a) sets of trilinear basis functions corresponding to symmetry species of the 4mm class

SpeciesBasis functionsSymmetry
A1 [(x{_1}x{_2}+y{_1}y{_2})z{_3}]; [z{_1}z{_2}z{_3}]; [(x{_1}z{_2}+z{_1}x{_2})x{_3}] [+] [(y{_1}z{_2} +z{_1}y{_2})y{_3}] (s)
[(x{_1}z{_2}-z{_1}x{_2})x{_3}] [+] [(y{_1}z{_2}-z{_1}y{_2})y{_3}] (a)
A2 [(x{_1}z{_2}+z{_1}x{_2})y{_3}][(y{_1}z{_2}+z{_1}y{_2})x{_3}] (s)
[(x{_1}y{_2}-y{_1}x{_2})z{_3}]; [(x{_1}z{_2}-z{_1}x{_2})y{_3}][(y{_1}z{_2}-z{_1}y{_2})x{_3}] (a)
B1 [(x{_1}x{_2}-y{_1}y{_2})z{_3}]; [(x{_1}z{_2}+z{_1}x{_2})x{_3}][(y{_1}z{_2}+z{_1}y{_2})y{_3}] (s)
[(x{_1}z{_2}-z{_1}x{_2})x{_3}][(y{_1}z{_2}-z{_1}y{_2})y{_3}] (a)
B2 [(x{_1}y{_2}+y{_1}x{_2})z{_3}]; [(x{_1}z{_2}+z{_1}x{_2})y{_3}] [+] [(y{_1}z{_2}+z{_1}y{_2})x{_3}] (s)
[(x{_1}z{_2}-z{_1}x{_2})y{_3}] [+] [(y{_1}z{_2}-z{_1}y{_2})x{_3}] (a)
E [[(x{_1}x{_2}+y{_1}y{_2})x{_3},(x {_1}x{_2}+y{_1}y{_2})y{_3}]]; [[z{_1}z{_2}x{_3}, z{_1}z{_2}y{_3}]]; [[(x{_1}z{_2}+z{_1}x{_2})z{_3}, (y{_1}z{_2}+z{_1}y{_2})z{_3}]]; [[(x{_1}x{_2}-y{_1}y{_2})x{_3},] [-(x{_1}x{_2}-y{_1}y{_2})y{_3}]]; [[(x{_1}y{_2}+y{_1}x{_2})y{_3}], [(x{_1}y{_2}+y{_1}x{_2})x{_3}]] (s)
[[(x{_1}z{_2}-z{_1}x{_2})z{_3}, (y{_1}z{_1}-z{_1}y{_2})z{_3}]]; [[(x{_1}y{_2}-y{_1}x{_2})y{_3}], [-(x{_1}y{_2}-y{_1}x{_2})x{_3}]] (a)