We have performed a kinematically complete measurement of the Coulomb dissociation of 28 MeV/nucleon [sup 11]Li into [sup 9]Li and two neutrons by a Pb target. From the energies and angles of the emitted neutrons and of [sup 9]Li, the excitation energy [ital E] of [sup 11]Li was determined on an event-by-event basis, and the Coulomb dissociation cross section as a function of excitation energy was constructed. The photonuclear cross section [sigma][sub [ital E]1]([ital E]) and the dipole strength function [ital dB]([ital E]1)/[ital dE] were determined from the Coulomb dissociation cross section. [sigma][sub [ital E]1]([ital E]) has a peak at [ital E]=1.0 MeV and a width [Gamma]=0.8 MeV. These parameters are consistent with the picture of a soft dipole mode. However, a significant post-breakup Coulomb acceleration of [sup 9]Li suggests instead a direct breakup. The complete kinematical measurement also allowed neutron and [sup 9]Li momentum distributions to be constructed in the rest frame of the [sup 11]Li. The momentum distributions were fitted with Gaussian functions, yielding width parameters [sigma][sub 9]=18[plus minus]4 MeV/[ital c] and [sigma][sub [ital n]]=13[plus minus]3 MeV/[ital c]. A more general feature of the breakup mechanism of [sup 11]Li could be deduced from these measurements. It was foundmore » that the [sup 9]Li and neutron momentum distributions and the neutron-neutron relative momentum distribution could be reproduced if the [sup 11]Li excitation energy was partitioned between the [sup 9]Li and the neutrons by a three-body phase space distribution. This indicates there is no directional correlation between the halo neutrons, and shows that the halo neutrons do not exist as a dineutron bound to a [sup 9]Li core.« less