X-ray anomalous scattering investigations on the charge order in ${\alpha }^{\mathrm{\prime }}$-NaV${}_2$O${}_5$

Anomalous x-ray diffraction studies show that the charge ordering in ${\alpha }^{\mathrm{\prime }}$-NaV${}_2$O${}_5$ is of zig-zag type in all vanadium ladders. We have found that there are two models of the stacking of layers along \emph{c-}direction, each of them consisting of 2 degenerated patterns, and that the experimental data is well reproduced if the 2 patterns appears simultaneously. We believe that the low temperature structure contains stacking faults separating regions corresponding to the four possible patterns.