  Crystallography, the primary method for determining the three-dimensional
(3D) atomic positions in crystals, has been fundamental to the development of
many fields of science. However, the atomic positions obtained from
crystallography represent a global average of many unit cells in a crystal.
Here, we report, for the first time, the determination of the 3D coordinates of
thousands of individual atoms and a point defect in a material by electron
tomography with a precision of ~19 picometers, where the crystallinity of the
material is not assumed. From the coordinates of these individual atoms, we
measure the atomic displacement field and the full strain tensor with a 3D
resolution of ~1nm^3 and a precision of ~10^-3, which are further verified by
density functional theory calculations and molecular dynamics simulations. The
ability to precisely localize the 3D coordinates of individual atoms in
materials without assuming crystallinity is expected to find important
applications in materials science, nanoscience, physics and chemistry.
