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Explorations of the order-disorder transformation in vortex matter in singlecrystals of tetragonal structured (c/a $\sim$3) borocarbide superconductors,$YNi_2B_2C$ and $LuNi_2B_2C$, reveal that vortex arrays experience differenteffective pinning in different crystallographic directions. We surmise thatcorrelation exists between the large anisotropy in effective pinning/disorderand the differences in the (local) symmetry transition from rhombohedral to(quasi) square vortex lattice(VL). For field along high symmetry directions,like, c-axis and ab-basal plane, the VL symmetry is close to square and theordered state spans a large field interval. When the field is turned away fromthe c-axis towards ab-plane, at intermediate angles, the region of orderedstate shrinks, in response to enhancement in effective pinning. At suchintermediate angles the symmetry of the VL would be far from ideal triangularor square.

Anisotropy in spatial order-disorder transformations and the vortex lattice symmetry transition in $YNi_2B_2C$ and $LuNi_2B_2C$