How can I find the eutectic point of gallium and aluminum?
The Al-Ga system is reasonably well studied, and there are a number of articles in the Calphad (Calculation of Phase Diagrams) literature. For example, Al-Ga-Zn System: Reassessments of the Three Binary Systems and Discussion on Possible Estimations and on Optimisation of the Ternary System, M. Mathon et al., CALPHAD 24(3) 253-284 (2000) has the thermodynamic analysis yielding the fairly simple model for the Al-Ga system. These parameters may be used in one of the many phase diagram software packages, such as ThermoCalc. Or, one could write a simple simulator in Python, yielding something like:



The eutectic is way over on the Ga side. The paper listed above also references a number of experimental papers with measured eutectic points.

For other systems of interest, one easy place to start is the ASM Alloy Phase Diagram Database, assuming your institution has access. The phase diagram entries have a set of references, often containing both experiment and calculation papers. If you have access to Calphad, Journal of Alloys and Compounds, and Journal of Phase Equilibria and Diffusion, those are good places to search for a given binary or ternary system.