Phase diagrams obtained from first-principles have the potential to reduce time and expense by guiding experimental investigations for materials design applications. However, simply substituting all experimental data with calculated single phase quantities alone has generally shown limited success in the standard CALPHAD modelling of binary or multicomponent systems. In this work, the solid aluminium-nickel system is described using Bragg-Williams-Gorsky approximations in combination with order-disorder partitioning models, where all parameters are obtained directly from first-principles calculation without optimisation considering any phase diagram data. The resulting phase diagram reproduces all major features of the experimentally known phase diagram at a practical application level. This work demonstrates that by careful consideration of the Gibbs energy models and the accuracy of the first-principles calculation, it is possible to obtain a first-principles CALPHAD-type thermodynamic description without conventional optimisation based on experimental data.