Quantifying the local compositional fluctuation and Shannon entropy inherent in multi-principal element alloys

Multi-principal element alloys (MPEAs), also known as high-entropy alloys, are highly concentrated solid solutions more complex than the initially assumed ideal solid solutions. Using a combination of theoretical predictions and numerical simulations, this study quantitatively evaluates the degree of local compositional fluctuation in MPEAs and maps out how it depends on the number of principal elements and the constituent atomic concentrations. Shannon entropy is introduced as a metric to assess the compositional complexity, which is found to be maximized at the equiatomic composition, emphasizing the impact of balanced elemental proportions. We advocate the Shannon entropy, being more directly related to MPEA properties, as an indicator better than the configurational entropy to carry/capture the "high entropy" concept than configurational entropy.