  Incommensurate crystal structures of spin ladder series Sr14-xCaxCu24O41
(x=3, 7, 11, 12.2) were characterized by powder neutron scattering method and
refined using the superspace group Xmmm(00{\gamma})ss0 (equivalent to
superspace group Fmmm(0,0,1+{\gamma})ss0); X stands for non-standard centering
(0,0,0,0), (0,1/2,1/2,1/2), (1/2,1/2,0,0), (1/2,0,1/2,1/2)) with a modulated
structure model. The Ca doping effects on the lattice parameters, atomic
displacement, Cu-O distances, Cu-O bond angles and Cu bond valence sum were
characterized. The refined results show that the CuO4 planar units in both
chain and ladder sublattices become closer to square shape with an increase of
Ca doping. The Cu bond valence sum calculation provided new evidence for the
charge transfer from the chains to ladders (approximately 0.16 holes per Cu
from x=0 to 12.2). The charge transfer was attributed to two different
mechanisms: (a) the Cu-O bond distance shrinkage on the ladder; (b) increase of
the interaction between two sublattices, resulting in Cu-O bonding between the
chains and ladders. The low temperature structural refinement resulted in the
similar conclusion, with a slight charge backflow to the chains.
