Reversed size-dependent stabilization of ordered nanophases

Abstract

The size increase of a nanoscale material is commonly associated with the increased stability of its ordered phases. Here we give a counterexample to this trend by considering the formation of the defect-free L1₁ ordered phase in AgPt nanoparticles, and showing that it is better stabilized in small nanoparticles (up to 2.5 nm) than in larger ones, in which the ordered phase breaks in multiple domains or is interrupted by faults. The driving force for the L1₁ phase formation in small nanoparticles is the segregation of a monolayer silver shell (an Ag-skin) which prevents the element with higher surface energy (Pt) from occupying surface sites. With increasing particle size, the Ag-skin causes internal stress in the L1₁ domains which cannot thus exceed the critical size of ~2.5 nm. A multiscale modelling approach using full-DFT global optimization calculations and atomistic modelling is used to interpret the findings.

Fig. 1

As-grown room temperature AgPt sample (flux 3.2 × 10¹⁵ at cm⁻²). a HRTEM images and in the inset, the total Fourier transform. b Zoom (×2) showing crystal twinning. c STEM-HAADF image with homogeneous contrast. High-resolution STEM-HAADF image and the corresponding FFT for d experimental NP along the [01$\overline{1}$] zone axis and the corresponding simulated images e for a random solid solution and f for an L1₁ ordered structure. HRTEM high resolution in TEM, STEM-HAADF high angle annular dark field in scanning transmission electron microscope, NP nanoparticle

Fig. 2

AgPt NPs after annealing at 400 °C. a STEM-HAADF image; b a zoom on one NP oriented along the [01$\overline{1}$] zone axis showing the L1₁ phase with alternating planes of Ag and Pt and its corresponding FFT showing the superstructure reflections. c, d Simulated STEM-HAADF images along the [01$\overline{1}$] zone axis for an L1₁ structure and a random solid solution respectively. e–g show multidomains, twin and a stacking fault for L1₁ NPs (Pt atoms are in red and Ag atoms in grey). The scale is the same for b–g. NP nanoparticle, FFT fast Fourier Ttransform, STEM-HAADF high angle annular dark field in scanning transmission electron microscope

Fig. 3

L1₁@Ag-skin nanoparticle. a–d High-resolution STEM-HAADF image of a 2.8 nm NP in the [01$\overline{1}$] zone axis with its corresponding intensity profile lines. e–h, i–l and m–p show the model 1, 2, and 3 in the [01$\overline{1}$] zone axis, respectively, with their corresponding intensity profile lines. The intensity profiles were done for three different locations: along the (1$\overline{1}\overline{1}$) plane close to the centre of the NP (AA′), along the (1$\overline{1}\overline{1}$) plane at the NP surface (BB′) and along the (100) plane at the NP surface (CC′). STEM-HAADF high angle annular dark field in scanning transmission electron microscope, NP nanoparticle

Fig. 4

DFT results. a The truncated octahedron of 79 atoms. This structure has 19 internal sites, i.e. 18 subsurface sites plus the central site. b–g Structures of Ag₆₇Pt₁₂. Each cluster is shown in two views. Pt atoms are in red and Ag atoms in grey. Pt and Ag atoms are shown as large and small spheres, respectively, with the exception of the left view of (e), in which all atoms are shown as large spheres. In (b), the perfect L1₁@Ag-skin phase is shown. The numbers give the DFT energy differences from the lowest-energy homotops, which are the perfect L1₁@Ag-skin structure shown in (b) and the structure in (c). DFT density functional theory

Fig. 5

Theoretical predictions of L1₁ nanophases. L1₁@Ag core/shell and L1₁@Pt@Ag core/subshell/shell structures for the TOh₁₂₈₉ (Pt atoms in red, Ag atoms in grey) and their associated stress map in colour code from −6 GPa for tensile stress to 15 GPa for compressive stress. The graph on the bottom right illustrates the stress distribution inside the TOh₁₂₈₉ with the two structures and the graph on top shows the energy difference between the L1₁@Ag and the L1₁@Pt@Ag structures: positive sign means the L1₁@Pt@Ag is the stable structure