Flux-Line Lattice Structures in Untwinned<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>YBa</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>7</mml:mn><mml:mo>−</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>

A small angle neutron scattering study of the flux-line lattice in a large untwinned single crystal of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ is presented. In fields parallel to the $c$ axis, diffraction spots are observed corresponding to four orientations of a hexagonal lattice, distorted by the $a\ensuremath{-}b$ anisotropy. A value for the anisotropy, the penetration depth ratio, of ${\ensuremath{\lambda}}_{a}/{\ensuremath{\lambda}}_{b}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.18\left(2\right)$ was obtained. The high quality of the data is such that second-order diffraction is observed, indicating a well ordered FLL. With the field at 33\ifmmode^\circ\else\textdegree\fi{} to $c$, a field dependent reorientation of the lattice is observed around 3 T.