Structural transformations in Cu, Ag, and Au metal nanoclusters.

Finite-temperature structures of Cu, Ag, and Au metal nanoclusters are calculated in the entire temperature range from 0 K to melting using a computational methodology that we proposed recently [M. Settem et al., Nanoscale 14, 939 (2022)]. In this method, Harmonic Superposition Approximation (HSA) and Parallel Tempering Molecular Dynamics (PTMD) are combined in a complementary manner. HSA is accurate at low temperatures and fails at higher temperatures. PTMD, on the other hand, effectively samples the high temperature region and melts. This method is used to study the size- and system-dependent competition between various structural motifs of Cu, Ag, and Au nanoclusters in the size range 1-2 nm. Results show that there are mainly three types of structural changes in metal nanoclusters, depending on whether a solid-solid transformation occurs. In the first type, the global minimum is the dominant motif in the entire temperature range. In contrast, when a solid-solid transformation occurs, the global minimum transforms either completely to a different motif or partially, resulting in the co-existence of multiple motifs. Finally, nanocluster structures are analyzed to highlight the system-specific differences across the three metals.

Understanding the strain-dependent structure of Cu nanocrystals in Ag-Cu nanoalloys.

The structure of octahedral Ag-Cu nanoalloys is investigated by means of basin hopping Monte Carlo (BHMC) searches involving the optimization of shape and chemical ordering. Due to the significant size mismatch between Ag and Cu, the misfit strain plays a key role in determining the structure of Ag-Cu nanoalloys. At all the compositions, segregated chemical ordering is observed. However, the shape of the Cu nanocrystal and the associated defects are significantly different. At lower amounts of Cu (as little as 2 atom %), defects close to the surface are observed leading to a highly non-compact shape of the Cu nanocrystal which is non-trivial. The number of Cu-Cu bonds is relatively lower in the non-compact shape which is contrary to the preference of bulk Ag-Cu alloys to maximize the homo-atomic bonds. Due to the non-compact shape, {100} Ag-Cu interfaces are observed which are not expected. As the amount of Cu increases, the Cu nanocrystal undergoes a shape transition from non-compact to a compact octahedron. The associated defect structure is also modified. The structural changes due to the strain effects have been explained by calculating the atomic pressure maps and the bond length distributions. The trends relating to the structure have also been verified at larger sizes.

Correction: Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs.

Correction for 'Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs' by Manoj Settem et al., Nanoscale, 2022, 14, 939-952, https://doi.org/10.1039/D1NR05078H.

Charting Nanocluster Structures via Convolutional Neural Networks.

A general method to obtain a representation of the structural landscape of nanoparticles in terms of a limited number of variables is proposed. The method is applied to a large data set of parallel tempering molecular dynamics simulations of gold clusters of 90 and 147 atoms, silver clusters of 147 atoms, and copper clusters of 147 atoms, covering a plethora of structures and temperatures. The method leverages convolutional neural networks to learn the radial distribution functions of the nanoclusters and distills a low-dimensional chart of the structural landscape. This strategy is found to give rise to a physically meaningful and differentiable mapping of the atom positions to a low-dimensional manifold in which the main structural motifs are clearly discriminated and meaningfully ordered. Furthermore, unsupervised clustering on the low-dimensional data proved effective at further splitting the motifs into structural subfamilies characterized by very fine and physically relevant differences such as the presence of specific punctual or planar defects or of atoms with particular coordination features. Owing to these peculiarities, the chart also enabled tracking of the complex structural evolution in a reactive trajectory. In addition to visualization and analysis of complex structural landscapes, the presented approach offers a general, low-dimensional set of differentiable variables that has the potential to be used for exploration and enhanced sampling purposes.

Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs.

A computational approach to determine the equilibrium structures of nanoclusters in the whole temperature range from 0 K to melting is developed. Our approach relies on Parallel Tempering Molecular Dynamics (PTMD) simulations complemented by Harmonic Superposition Approximation (HSA) calculations and global optimization searches, thus combining the accuracy of global optimization and HSA in describing the low-energy part of configuration space, together with the PTMD thorough sampling of high-energy configurations. This combined methodology is shown to be instrumental towards revealing the temperature-dependent structural motifs in Au nanoclusters of sizes 90, 147, and 201 atoms. The reported phenomenology is particularly rich, displaying a size- and temperature-dependent competition between the global energy minimum and other structural motifs. In the case of Au90 and Au147, the global minimum is also the dominant structure at finite temperatures. In contrast, the Au201 cluster undergoes a solid-solid transformation at low temperature (<200 K). Results indicate that PTMD and HSA very well agree at intermediate temperatures, between 300 and 400 K. For higher temperatures, PTMD gives an accurate description of equilibrium, while HSA fails in describing the melting range. On the other hand, HSA is more efficient in catching low-temperature structural transitions. Finally, we describe the elusive structures close to the melting region which can present complex and defective geometries, that are otherwise difficult to characterize through experimental imaging.

Role of core-shell energetics on anti-Mackay, chiral stacking in AgCu nanoalloys and thermally induced transition to chiral stacking.

In AgCu nanoalloys a size-dependent transition to the chiral stacking from the anti-Mackay stacking has been predicted previously. This trend is explained by considering the interplay between the core-shell energetics. Results indicate that the energy changes in the Ag shell alone is not sufficient to explain the stability of the chiral stacking and the energy changes in the Cu core also need to be considered. In addition to this, thermally induced transition to chiral stacking was observed at sizes where anti-Mackay stacking is energetically favourable. On transition to the chiral stacking, the Ag-Ag, Ag-Cu and Cu-Cu bond lengths change significantly. These observations are also applicable for AgCu nanoalloys with incomplete Ag shells.

Influence of supporting amorphous carbon film thickness on measured strain variation within a nanoparticle.

Strain variation within a nanoparticle plays a crucial role in tuning its properties. High Resolution Transmission Electron Microscopy (HRTEM) images of a nanoparticle supported on amorphous carbon film are used to determine the strain variation. Experimental measurements in this present study on a single crystalline silver nanoparticle exhibited an unexpected high strain variation. Generally, the influence of carbon film is not accounted for during interpretation of measured strain variation. However, experimental observations raise the question whether the supporting carbon film alters the measured strain variation. In order to address this, strain variation within a simulated Ag nanoparticle supported on an amorphous carbon is measured with varying film thicknesses. The results show that supporting carbon film thickness introduces an artefact leading to more strain variation than what is present within an unsupported nanoparticle. Moreover, the variation increases with increasing supporting carbon film thickness. This effect is more pronounced in a thinner nanoparticle. Without considering this influence, the interpretation of strain within a nanoparticle may introduce severe errors which in turn will affect the tunability of desirable properties for different applications. Since strain measurement depends on the accuracy of the atomic position, the interpretation of any result using the atomic position from HRTEM images of a nanoparticle should consider the influence of supporting film.