Aluminium (Al) alloys are excellent candidates for lightweight applications due to their outstanding strength-to-weight ratio. Age-hardenable Al alloys benefit from precipitation strengthening through complex mechanisms that impede the motion of dislocation. Adding Copper (Cu) and Lithium (Li) to pure Al will introduce a range of possible precipitates, where the stoichiometric T1 (Al2CuLi) precipitate is considered to contribute the most to the bulk strengthening of most Al-Cu-Li alloys [1]. The size, frequency and morphology of these precipitates that determine the effective hardening are dependent on thermodynamics and diffusion kinetics. Phase-field modelling is a powerful method that allows to quantify competing thermodynamic, kinetic and elastic effects in precipitate evolution of metallic alloys in a thermodynamically consistent manner. Most of the existing phase-field models, like the Kim-Kim-Suzuki model [2], approximate the free energy of stoichiometric precipitate phase using a parabolic function with arbitrary curvature. This leads to inaccurate equilibrium compositions that deviate from ideal stoichiometry and limits the possible validation using experimental findings. Here, we seek an alternative phase-field formalism that was recently proposed by Ji and Chen [3]. The governing Cahn-Hilliard [4] and Allen-Cahn [5] evolution equations are derived from fundamental equations of thermodynamics and are applied to the ternary stoichiometric reaction of T1 precipitation. This allows the free energy of the stoichiometric phase to be described by function that is independent of composition. Elastic properties and interfacial energies are derived from DFT calculations and contribute to the total free energy of the system. The chemical free energies and diffusion coefficients are extracted from CALPHAD and diffusion databases, respectively. The model is discretized using a semi-implicit Fourier-spectral formalism [6] and is accelerated using CUDA and cuFFT for computations on GPUs. In this work, we aim to quantify the role of elasticity and interfacial energy to the equilibrium shape of T1 precipitates for different Al-Cu-Li alloys.