  Boron nitride (BN) is a material with outstanding technological promise
because of its exceptional thermochemical stability, structural, electronic and
thermal conductivity properties, and extreme hardness. Yet, the relative
thermodynamic stability of its most common polymorphs (diamond-like cubic and
graphite-like hexagonal) has not been resolved satisfactorily because of the
crucial role played by kinetic factors in the formation of BN phases at high
temperatures and pressures (experiments), and by competing bonding,
electrostatic and many-body dispersion forces in BN cohesion (theory). This
lack of understanding hampers the development of potential technological
applications, and challenges the boundaries of fundamental science. Here, we
use high-level first-principles theories that correctly reproduce all important
electronic interactions (the adiabatic-connection fluctuation-dissipation
theorem in the random phase approximation) to estimate with unprecedented
accuracy the energy differences between BN polymorphs, and thus overcome the
accuracy hurdle that hindered previous theoretical studies. We show that the
ground-state phase of BN is cubic and that the frequently observed hexagonal
polymorph becomes entropically stabilized over the cubic at temperatures
slightly above ambient conditions ($T_{\rm c \to h} = 335 \pm 30$ K). We also
reveal a low-symmetry monoclinic phase that is extremely competitive with the
other low-energy polymorphs and which could explain the origins of the
experimentally observed "compressed h-BN" phase. Our theoretical findings
therefore should stimulate new experimental efforts in bulk BN as well as
promote the use of high-level theories in modelling of technologically relevant
van der Waals materials.
