Ice clouds in the Earth's upper troposphere can form via homogeneous nucleation of ice in aqueous droplets. In this study we investigate the crystallisation, or lack of crystallisation, of the solute phase and ice in aqueous (NH(4))(3)H(SO(4))(2)/H(2)O and NH(4)HSO(4)/H(2)O droplets. This is done using in situ X-ray diffraction of emulsified solution droplets mounted on a cold stage. From the diffraction patterns we are able to identify the phases of crystalline solute and ice that form after homogeneous freezing in micrometer sized droplets. An important finding from this study is that crystallisation of the solute does not always occur, even when crystallisation is strongly thermodynamically favoured. The nucleation and growth of solute phase crystals becomes inhibited since the viscosity of the aqueous brine most likely increases dramatically as the brine concentration increases and temperature decreases. If ice nucleates below a threshold freezing temperature, the brine appears to rapidly become so viscous that solute crystallisation is inhibited. This threshold temperature is 192 K and 180 K, in (NH(4))(3)H(SO(4))(2) and NH(4)HSO(4), respectively. We also speculate that the formation of cubic ice within a highly viscous brine blocks the solvent mediated cubic to hexagonal phase transformation, thus stabilising the metastable cubic ice in the most concentrated solution droplets.