Machine-learning-assisted discovery of empirical rule for inherent brittleness of full Heusler alloys

• The most 6 critical parameters of deciding ductility of X 2 YZ alloys were determined. • Element X in most of alloys with superior ductility was found to have FCC structure. • A formula k = m EWF m + nG m + k 0 that can effectively predict ductility was constructed. • An approach combining ML and analyses to reveal mechanism was exemplified. Brittleness is a critical issue hindering the potential application of the X 2 YZ-type full Heusler alloys in several fields of state-of-the-art technologies. To realize optimization of brittleness or design a ductile Heuser alloy, it is greatly urgent to identify the key materials factors deciding brittleness and establish an empirical rule to effectively evaluate ductility. For this purpose, by using a machine learning and human analysis cooperation approach, the brittleness of the X 2 YZ-type Heusler alloys was systematically studied. Results showed that the ductility is majorly decided by 6 key materials factors in the studied alloys. Using these 6 factors, a machine learning model to predict the Pugh's ratio k was constructed. Further analyses showed that the crystal structure of the X component could be the most critical factor deciding the ductility. The X component has the face-centered cubic (FCC) structure for most of the alloys with superior ductility. To effectively estimate ductility and guide materials design, an empirical formula of k = m EWF m + nG m + k 0 was established based on the known information of electron work function (EWF) and shear modulus ( G ) of the X, Y, and Z elements where the subscript m represents the weight-average value. The coefficients of m (negative) and n (positive) were confirmed to have opposite signs, which can be explained based on the relations between the ductility and the deformation/fracture resistance. This work is expected to deepen the understanding in ductility and promote the design of advanced ductile Heusler alloys.