  We examine the fluid phase behaviour of the binary mixture of hard
superellipses using the scaled particle theory The superellipse is a general
two dimensional convex object which can be tuned between circular and
rectangular shapes continuously at a given aspect ratio. We find that the shape
of the particle affects strongly the stability of isotropic nematic and
tetratic phases even if the aspect ratios of both species are fixed. While the
isotropic isotropic demixing transition can be ruled out using the scaled
particle theory the first order isotropic nematic and the nematic nematic
demixing transition can be stabilized with strong fractionation between the
components. It is observed that the demixing tendency is strongest in small
rectangle large ellipse mixtures. Interestingly, it is possible to stabilize
the tetratic order at lower densities in the mixture of hard squares and
rectangles where the long rectangles form nematic phase, while the squares stay
in tetratic order.
