  Stress and strain are important factors in determining the mechanical,
electronic, and optical properties of materials, relating to each other by the
material's elasticity or stiffness. Both are represented by second rank field
tensors with, in general, six independent components. Measurements of these
quantities are usually achieved by measuring a property that depends on the
translational symmetry and periodicity of the crystal lattice, such as optical
phonon energies using Raman spectroscopy, the electronic band gap using
cathodoluminescence, photoelasticity via the optical birefringence, or Electron
Back Scattering Diffraction (EBSD). A reciprocal relationship therefore exists
between the maximum sensitivity of the measurements and the spatial resolution.
Furthermore, of these techniques, only EBSD and off-axis Raman spectroscopy
allow measurement of all six components of the stress tensor, but neither is
able to provide full 3D maps. Here we demonstrate a method for measuring the
full stress tensor in diamond, using the spectral and optical polarization
properties of the photoluminescence from individual nitrogen vacancy (NV)
colour centres. We demonstrate a sensitivity of order 10 MPa, limited by local
fluctuations in the stress in the sample, and corresponding to a strain of
about 10^-5, comparable with the best sensitivity provided by other techniques.
By using the colour centres as built-in local sensors, the technique overcomes
the reciprocal relationship between spatial resolution and sensitivity and
offers the potential for measuring strains as small as 10^-9 at spatial
resolution of order 10 nm. Furthermore it provides a straightforward route to
volumetric stress mapping. Aside from its value in understanding strain
distributions in diamond, this new approach to stress and strain measurement
could be adapted for use in micro or nanoscale sensors.
