High-resolution small-angle neutron-scattering ͑SANS͒ studies of the vortex lattice ͑VL͒ in single-crystal YNi 2 B 2 C allows us to separate Bragg scattered intensities from the multidomain VL that exists for Bʈc. A precise determination of the VL unit-cell apex angle, ␤, shows that there is a finite transition width associated with the field-driven 45°reorientation of the VL at a field H 1 . Low-and high-field rhombic VL phases coexist over a finite range of applied field with no continuous distortion of the VL between the two phases. The smooth variation in scattered intensity from each phase through the transition indicates a redistribution of domain populations between the low-and high-field vortex structures. Our data supports the notion of a first-order reorientation phase transition in the VL at H 1 in the presence of weak static disorder ͑vortex pinning͒.Type-II superconductivity is characterized by the ''mixed'' or ''vortex'' state where quantized lines of magnetic flux thread the material and form a vortex lattice ͑VL͒. The lowest energy configuration for an array of repulsive magnetic-flux lines is usually a two-dimensional ͑2D͒ hexagonal lattice although the energy difference between hexagonal and square packing configurations is small (Ӎ2%). 1,2 Obst 3 demonstrated that a square VL exists in a low-superconducting Pb-Tl alloy when the magnetic field is orientated along a fourfold symmetry axis due to crystal anisotropy effects. Similar mass anisotropy ͑i.e., penetration depth͒ effects have also been observed in Nb. 4,5 In these lows-wave materials the underlying electronic symmetry can be modified by nonlocal interactions resulting in a fourfold symmetry and ''squaring up'' of the current and field profiles around flux lines. A similar fourfold symmetry can also exist in p-or d-wave superconductors resulting in a square VL in Sr 2 RuO 4 over almost the entire phase diagram. 6 In general, mass anisotropy effects alone cannot describe a square VL configuration but must be combined with details of the anisotropic Fermi surface and underlying crystal symmetry.The discovery 7,8 and successful growth 9 of large, high quality single crystals of the borocarbide superconductors ͓rare earth (RE)]Ni 2 B 2 C has encouraged studies of the VL within them. The RE can be occupied by the nonmagnetic ͑Lu, Y͒ or magnetic ͑Er, Tm, Ho, Dy͒ elements presenting systems that can exhibit both superconductivity and longrange magnetic order at low temperatures. 10,11 The superconducting transition temperature T c varies from about 15 K for RE ϭ Y and Lu to 6 K for Dy, with the Ginzburg-Landau parameter Ͼ5 and upper critical field B c2 as high as 10 T. The normal-state electronic mean free path l is typically an order of magnitude larger than the coherence length ͓l Ӎ300 Å, 0 Ӎ55 Å for YNi 2 B 2 C ͑Ref. 12͒ although will be dependent on sample quality͔, implying that nonlocal interactions are important in describing the properties of these clean superconducting systems. Doping studies, for example, Co into Lu(Ni 1Ϫx Co x ) 2 B 2...