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The structures, as building-blocks for designing functional nanomaterials, have fueled the development of versatile nanoprobes to understand local structures of noncrystalline specimens. Progresses in analyzing structures of individual specimens with atomic scale accuracy have been notable recently. In most cases, however, only a limited number of specimens are inspected lacking statistics to represent the systems with structural inhomogeneity. Here, by employing single-particle imaging with X-ray free electron lasers and new algorithm for multiple-model 3D imaging, we succeeded in investigating several thousand specimens in a couple of hours, and identified intrinsic heterogeneities with 3D structures. Quantitative analysis has unveiled 3D morphology, facet indices and elastic strains. The 3D elastic energy distribution is further corroborated by molecular dynamics simulations to gain mechanical insight at atomic level. This work establishes a new route to high-throughput characterization of individual specimens in large ensembles, hence overcoming statistical deficiency while providing quantitative information at the nanoscale.