[en] The perfect double-crystal small-angle diffraction technique enables measurement of scattering angles to within 0.3 arc sec. accuracy. At a wavelength of 2.55 A, this provides a resolution of 3 x 10^-6 A^-1 in the scattering vector. This technique has been used to study the anisotropic behavior of the critical parameters B₀ and H/sub c1/, characteristic of the first-order magnetic phase transition which occurs in low-kappa type-II superconductors. Magnetic fields were applied parallel to several crystal axes of a large single-crystal sphere of pure niobium, resulting in well-defined flux-line lattices (FLL). Measurement of the FLL cell area in the intermediate mixed state field region gives the equilibrium flux density B₀, which results from an attractive interaction between fluxoids. In addition, field variation of the scattered neutron intensity allows measurement of the transition field between the mixed state and intermediate mixed state. This transition field is related to the lower critical field H/sub c1/ and enables its determination to a precision 0.2%. Data at T = 4.3 K display a small anisotropic effect of about 2% in B₀ and 1% in H/sub c1/. Although orientation effects of this magnitude are difficult to resolve by bulk measurements, the neutron data are in accord with magnetization data. Observations regarding the temperature dependence of these parameters also will be presented, and comparisons made with current theoretical models