Unidirectional diagonal order and three-dimensional stacking of charge stripes in orthorhombic ${\mathrm{Pr}}_{1.67}{\mathrm{Sr}}_{0.33}\mathrm{Ni}{\mathrm{O}}_4$ and ${\mathrm{Nd}}_{1.67}{\mathrm{Sr}}_{0.33}\mathrm{Ni}{\mathrm{O}}_4$

The interplay between crystal symmetry and charge stripe order in ${\mathrm{Pr}}_{1.67}{\mathrm{Sr}}_{0.33}\mathrm{Ni}{\mathrm{O}}_4$ and ${\mathrm{Nd}}_{1.67}{\mathrm{Sr}}_{0.33}\mathrm{Ni}{\mathrm{O}}_4$ has been studied by means of single crystal x-ray diffraction. In contrast to tetragonal ${\mathrm{La}}_{1.67}{\mathrm{Sr}}_{0.33}\mathrm{Ni}{\mathrm{O}}_4$, these crystals are orthorhombic. The corresponding distortion of the $\mathrm{Ni}{\mathrm{O}}_2$ planes is found to dictate the direction of the charge stripes, similar to the case of diagonal spin stripes in the insulating phase of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$. In particular, diagonal stripes seem to always run along the short $a$ axis, which is the direction of the octahedral tilt axis. In contrast, no influence of the crystal symmetry on the charge stripe ordering temperature itself was observed, with $T_{\mathrm{CO}}\sim 240\mathrm{K}$ for La, Pr, and Nd. The coupling between lattice and stripe degrees of freedom allows one to produce macroscopic samples with unidirectional stripe order. In samples with stoichiometric oxygen content and a hole concentration of exactly $1∕3$, charge stripes exhibit a staggered stacking order with a period of three $\mathrm{Ni}{\mathrm{O}}_2$ layers, previously only observed with electron microscopy in domains of mesoscopic dimensions. Remarkably, this stacking order starts to melt about $40\mathrm{K}$ below $T_{\mathrm{CO}}$. The melting process can be described by mixing the ground state, which has a three-layer stacking period, with an increasing volume fraction with a two-layer stacking period.