Satellite- and aircraft-based mid-infrared measurements of polar stratospheric clouds (PSCs) have provided spectroscopic evidence for the presence of β-NAT (nitric acid trihydrate) particles. Metastable nitric acid hydrate phases such as α-NAT and α-NAD (nitric acid dihydrate) have been frequently observed in laboratory experiments but not yet detected as a constituent of PSCs in atmospheric measurements. As for the β-NAD modification, its formation was first observed in X-ray diffraction measurements when the low-temperature α-NAD phase was warmed to a temperature above 210 K. Its infrared spectrum has been reported, but so far no optical constants have been derived that could be used as input for infrared retrievals of PSC composition. In this work, we show that β-NAD particles were efficiently formed in isothermal heterogeneous crystallisation experiments at 190 K from supercooled HNO3/H2O solution droplets containing an embedded mineral dust or meteoric smoke particle analogue. An inversion algorithm based on a T-matrix optical model was used to derive for the first time the mid-infrared complex refractive indices of the β-NAD modification from the measured extinction spectrum of the particles. In contrast to the heterogeneous crystallisation experiments, the α-NAD phase was formed when the HNO3/H2O solution droplets did not contain a solid nucleus and crystallised homogeneously. Using a light-scattering detector that recorded two-dimensional scattering patterns of the crystallised NAD particles, we were able to determine predominant shapes of the α- and β-NAD crystals. We found that α-NAD grew into elongated, needle-shaped crystals, while β-NAD particles were compact in shape. This agrees with previously reported images of α- and β-NAD particles grown on the cryo-stage of an environmental scanning electron microscope. While direct evidence for the existence of metastable NAD in the polar stratosphere is still lacking, our experiments add to the wealth of previous laboratory studies that have identified various conditions for the rapid growth of metastable compositions. In the atmosphere, these could be intermediate states that transform into thermodynamically stable NAT on longer timescales in aged PSCs.