  Small volume nuclear magnetic resonance spectroscopy (NMR) has recently made
considerable progress due to rapid developments in the field of quantum sensing
using nitrogen vacancy (NV) centers. These optically active defects in the
diamond lattice have been used to probe unprecedented small volumes on the
picoliter range with high spectral resolution. However, the NMR signal size
depends strongly on both the diamond sensor's and sample's geometry. Using
Monte-Carlo integration of sample spin dipole moments, the magnetic field
projection along the orientation of the NV center for different geometries has
been analysed. We show that the NMR signal strongly depends on the NV-center
orientation with respect to the diamond surface. While the signal of currently
used planar diamond sensors converges as a function of the sample volume, more
optimal geometries lead to a logarithmically diverging signal. Finally, we
simulate the expected signal for spherical, cylindrical and nearly-2D sample
volumes, covering relevant geometries for interesting applications in NV-NMR
such as single-cell biology or NV-based hyperpolarization. The results provide
a guideline for NV-NMR spectroscopy of microscopic objects. Keywords: Nitrogen
vacancy center, nuclear magnetic resonance, Monte-Carlo, quantum sensing,
sample geometry, small volume NMR.
