Short-range order (SRO) in alloys refers to deviations from a perfectly random distribution of atoms in lattice sites within a short distance. Conventionally, the degree of the deviations has been quantified using an average SRO parameter, but such a coarse-grained description does not reflect how the deviations occur at a finer level. Here we show the distribution of the local atomic SRO parameter, which describes the occurring frequency of a local structural motif, carries the crucial information for both structures and properties in Si-Ge-Sn alloy system. This is demonstrated through the fact that distinct SRO structures can exhibit the same average SRO parameter but very different distributions and disparate electronic structures. By deliberately creating special structures that explicitly match the structural information at different levels, we show the distribution of local atomic SRO parameters contain critical structural features that are missing in the average SRO parameter but can substantially contribute to material's properties. Our finding thus calls for the need for considering the finer structural details to effectively describe alloys' structures and properties.

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• Structural properties
• Disordered alloys
• Elemental semiconductors
• First-principles calculations
• Metropolis algorithm
• Monte Carlo methods