Accurate determination of the 3D atomic structure of amorphous materials

Amorphous materials—solids lacking long-range order—underpin technologies from thin-film electronics¹, solar cells² and phase-change memory³ to magnetic components⁴, medical devices⁵ and quantum technologies^6,7,8. Yet the absence of periodicity fundamentally limits determination of their three-dimensional (3D) structure at atomic resolution. Despite major theoretical, experimental, and computational advances in characterizing short- and medium-range order^{9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24}, quantitative determination of complete 3D atomic arrangements in amorphous materials remains experimentally demanding. Atomic electron tomography (AET) now provides a pathway to direct 3D atomic mapping in these materials^25,26,27. Here we present a quantitative analysis of AET, showing how robust image preprocessing, denoising, projection alignment and normalization, advanced tomographic reconstruction, atom tracing, elemental classification and atomic position refinement collectively enable reliable determination of 3D atomic coordinates and elemental identities in amorphous materials. Using multislice-simulated datasets of amorphous Si, SiGeSn and CoPdPt nanoparticles under varying noise levels, our workflow outperforms an alternative approach²⁸ in both positional precision and classification accuracy. For CoPdPt, we identify 95.1% of Co, 99.0% of Pd and 100% of Pt atoms, with corresponding 3D positional precisions of 29 pm, 12 pm and 6 pm, respectively, under realistic dose conditions. These results establish practical guidelines and quantitative benchmarks for achieving accurate AET of non-crystalline materials, and the underlying framework can be broadly applied to other tomographic imaging modalities for high-fidelity 3D reconstruction.