A6, face-centered tetragonal and Aa, tetragonal close-packed

Structural typeA6, Aa
Common nameA6 – face-centered tetragonal (fct),
Aa – tetragonal close-packed (tcp) or body-centered tetragonal (bct)
DefinitionA6 – tetragonal distortion of fcc,
Aa – tetragonal close-packed deformation of bcc (see the diagram below)
PrototypeA6 – In, Aa – α-Pa
Pearson symboltI2
Space group139 I4/mmm D4h17
Chemical formulaA
Atomic positions A (2a)  0  0  0
2l+8cbc/a<sqrt(2/3)≈0.82out of range
10c/a=sqrt(2/3) δ=sqrt(8)/3≈.94
PDB filesA6 (as fcc), Aa (ideally packed)
ParametersA6 – c/a≈1.41,
Aa – c/a≈0.82
Superstructuresfcc for c/a=sqrt(2),
bcc for c/a=1
SubstancesA6 – In (c/a=1.52), Aa – α-Pa (c/a=0.83)

Like bcc, tcp is not a local maximum in packing – there is a orthorombic deformation which increases the packing continuously transforming to both fcc and hcp. In particular the highest symmetry path to hcp goes through oC4 lattice with space group 63 Cmcm and atoms occupying position (4c)=(0,eta,1/4), where b/a=sqrt(3), eta,c/a=0,sqrt(3) for tcp and 1/12,sqrt(8/3) for hcp. A martensitic bcc-hcp transition in iron goes this way.