Reconstruction of the 3D atomic structures of multi-element nanoparticles requires strategies tailored to their structural characteristics. Ordered multi-element nanoparticles, such as wurtzite CdSe and rocksalt PbSe, have ordered lattice structures with periodic arrangements of the constituent atoms. Disordered multi-element nanoparticles also have a periodic lattice, but different types of atoms randomly occupy sites in the lattice. Examples of disordered multi-element nanoparticles include alloy FePt, preserving fcc-like crystal structure. The procedure for 3D reconstruction of ordered and disordered multi-element nanoparticles is summarized in Fig. 1.

As an initial step, low-frequency components originating from the liquid background are removed by averaging consecutive frames of *in-situ* TEM data, defined as moving averaging hereafter. Nanoparticles in consecutive frames of *in-situ* TEM data usually have very similar projection direction, thus moving averaging reduces the low-frequency liquid noise and enhances the signal to noise ratio (SNR). 3D reconstruction is initiated with an initial 3D model, and it guides finding the first relative 3D orientations of the 2D images that are subsequently refined. Different types of initial 3D models are used for ordered and disordered multi-element systems. In the ordered systems, an initial 3D model which has the same crystal structure and compositional arrangement as the targeting material is used. In the case of disordered systems, a probabilistic initial 3D model is generated by using PRIME35. Next, 3D reconstruction of the two different systems is conducted by different low-pass filtering strategies to control the frequency range used for matching reprojections of the 3D density with the 2D views. The low-pass filtering strategy for reconstructing the ordered systems is referred to as single-step reconstruction, since a single cut-off frequency of the low-pass filter is applied to include the majority of peaks in reciprocal space. Two-step reconstruction is suggested for 3D reconstruction of disordered multi-element systems. In the first step of two-step reconstruction, the cut-off frequency of the low-pass filter is set below the frequency of the peaks in reciprocal space, excluding lattice information. The second step utilizes lattice information by setting the cut-off frequency of the low-pass filter to include the peaks. Successful reconstruction of high-resolution 3D Coulomb density maps allows the 3D atomic positions to be assigned by identifying local maxima in the 3D density map. Plotting the intensity of the assigned atomic positions against the distance from the center of mass of the nanoparticle displays groups of points with different intensity, allowing classification of the different types of atoms.

3D reconstruction of multi-element nanoparticles is nontrivial, because the introduction of heteroatoms in the host crystal structure complicates the signal in reciprocal space. To understand the effect of the introduction of heteroatoms in the power spectrum of single-element, ordered multi-element, and disordered multi-element nanoparticles, we simulated those systems using 1D models constructed with the same period. From the 1D model systems, the intensity profile and power spectrum were obtained (Fig. 2a). As seen in the 1D intensity profiles and their power spectra, multi-element systems have additional information due to the distribution of heteroatoms, which is lacking in single-element systems.

The intensity profile of the 1D model for single-element systems shows a repeating array of peaks with identical intensity (Fig. 2a, top) and a power spectrum with a peak at frequency zero as well as additional peaks separated according to the reciprocal lattice parameter. The intensity profile of the 1D model for ordered multi-element systems, with a motif consisting of two elements, shows a repeating pattern of two peaks with different intensity (Fig. 2a, middle). The peak positions are the same as for the single-element systems, because the 1D models used in these two cases have the same periodicity. The power spectral density distributions of the two systems are expected to be different because the introduction of heteroatoms modifies the Fourier structure factors36. The 1D model for disordered multi-element systems has elements of two atomic species randomly distributed with uniform interatomic distance. It results in a richer intensity profile and power spectrum (Fig. 2a, bottom). We verified that introduction of heteroatoms modifies the low-frequency signal in 2D by comparing the TEM images of Pt and FePt nanoparticles obtained by experiment and simulation (Figure S1 and S2), suggesting that careful experimentation with the low-pass frequency limit used in the initial stages of 3D reconstruction is likely to be as important as the production of an appropriate initial 3D model.

The initial 3D model is important for robust convergence of the 3D reconstruction process for multi- and single-element nanoparticles (Fig. 1). We argue that different initial 3D model approaches should be used for ordered and disordered multi-element systems. An initial 3D model embedding lattice information, which has the same phase and composition as the target material system, is suitable for 3D reconstruction of ordered multi-element systems37. For disordered multi-element systems, the situation is similar to that of 3D reconstruction of proteins by cryo-EM and single-particle analysis, where *ab-initio* initial 3D models are generated using a probabilistic approach35.

TEM images obtained from a GLC include significant background from the encapsulated liquid pocket, which needs to be reduced for successful 3D reconstruction. We compared nanoparticles contained in the GLC with those in vacuum through TEM simulation to study the effect of the low-frequency signal introduced by the GLC (Figs. 2b and 2c). The GLC creates a halo-ring effect in the low-frequency region, as shown in the power spectrum images of simulated TEM images and their corresponding line profiles (Fig. 2b and 2c). The intensity distribution of power spectrum peaks (ordered multi-element systems) or more complex signal distribution patterns (disordered multi-element systems) can be obscured by the low-frequency “noise” from the GLC. 3D structures reconstructed from simulated TEM images with GLC-induced low-frequency noise confirm that GLC-induced noise can interrupt high-resolution reconstruction (Figure S3 and S4).

Averaging a series of TEM images that represents a nanoparticle, maintaining constant projection direction, in fluctuating liquid environment can be an efficient strategy to reduce GLC background noise. To validate this strategy, ten simulated TEM images of a nanoparticle with a fixed orientation were generated with ten different liquid coordinates and averaged into one image. Averaging diminishes GLC-induced low-frequency noise, as confirmed by the reduced intensity of the halo ring effect in the power spectrum of the averaged image (Fig. 2b and 2c). Moving averaging of *in-situ* TEM images is likely an effective way to remove undesirable GLC signals, considering that nanoparticles can maintain the same projection direction in a few consecutive *in-situ* TEM images. Beam-induced anisotropic motion is also commonly used for *in-situ* TEM images and weighted time window averaging in conjunction with anisotropic motion correction will further assist in the successful 3D reconstruction of multi-element nanoparticles from experimental data37,38.