Short-range order analysis: A data-volume threshold criterion and the potential role of atom probe tomography

Short-range order (SRO) is a fundamental feature of atomic arrangements in materials, long studied in conventional alloys, ceramics, and minerals. Interest in SRO has intensified with the development of medium- and high-entropy alloys, where local chemical environments can be tuned and exert a direct influence on phase stability and mechanical properties. Yet, quantitative results often diverge across diffraction, electron microscope, atom probe tomography (APT), and simulations, reflecting the unresolved role of analysis volume. Here, we combine large-scale lattice simulations with APT experiments to clarify how data volume governs the reliability of SRO statistics. Large lattice models in simple cubic, body-centred cubic, and face-centred cubic structures are first constructed to establish reference values. By progressively reducing the sampled volume, we demonstrate how finite-size effects emerge: With decreasing number of atoms, the measured SRO values deviate from the reference, showing larger variations that reflect local chemical fluctuations, ordering, clustering, or incipient phase formation. As the sample size increases, these deviations diminish, following the N −1/2 scaling expected for sampling statistics. Reliable quantification requires datasets on the order of ∼2.5 × 10 5 atoms. Extension to binary and ternary alloys demonstrates the generality of this volume effect. APT experiments on CoCrNi alloys confirm the simulations, highlighting the practical importance of data volume thresholds in real materials. These findings establish a quantitative framework for SRO analysis across complementary microscopy techniques. X-ray diffraction provides statistically robust global averages, the electron microscope reveals local structural features and chemical variations, and APT provides three-dimensional, chemically resolved information from statistically meaningful volumes to localised fluctuations.