# Computational Investigation of the Size Evolution of (La2 B 2O7) n Nanoclusters (B = Ce, Ti, Zr)

## TL;DR

This paper uses computational methods to study how the size of nanoclusters affects their structure and properties, focusing on mixed-oxide materials used in catalysis.

## Contribution

The study provides new insights into the size-dependent structural and electronic behavior of (La2B2O7)n nanoclusters using density functional theory.

## Key findings

- Small clusters (n = 2, 4) show structural diversity with all atoms on the surface, while larger clusters (n ≥ 6) develop bulk-like core features.
- Zr-based nanoclusters show the strongest bonding and highest stability due to increased binding energy per atom with size.
- Oxygen vacancies are more stable on the surface than in the core, with vacancy-induced properties varying significantly based on the B cation.

## Abstract

Mixed-oxide particles
are commonly used to promote chemical reactions
in catalysis. However, our atomistic understanding of how particle
size and oxygen vacancies influence their physicochemical characteristics
remains limited. To address this issue, we use density functional
theory calculations to investigate (La2
B
2O7)
n
nanoclusters,
where B = Ti, Zr, Ce, and n = 2,
4, 6, 8, 10. Our findings and analysis reveal the following: (i) particle
size plays a critical role in determining structural motifs, with
all atoms in small particles (n = 2, 4) being entirely
surface-exposed and exhibiting structural diversity, whereas larger
clusters (n ≥ 6) develop bulk-like features
in the core region with B cations located in the
core and La segregating to the surface region; (ii) binding energy
per atom increases with size, indicating enhanced stability resultant
from diminished surface effects and compact structural motifs, with
Zr-based nanoclusters demonstrating the strongest bonding; (iii) electronic
band gaps decrease with increasing size, consistent with quantum confinement,
although Ti- and Zr-based nanoclusters exhibit anomalies at intermediate
sizes due to structural rearrangements; (iv) electrostatic potential
analysis highlights highly positive cores in larger nanoclusters,
elucidating their increased stability, while regions of low potential
on the surface emerge as preferential sites for defect formation;
(v) the formation of oxygen vacancy energetics follow to the hierarchy
La2Ce2O7 < La2Ti2O7 < La2Zr2O7, with surface vacancies generally more stable than core ones, particularly
in Ce-based nanoclusters; and (vi) vacancy-induced electronic and
magnetic responses are significantly influenced by the B cation: Ce-based nanoclusters exhibit localized f-electron reduction and stable magnetic moments, Ti-based systems
exhibit a mix of itinerant and polaronic behavior, and Zr-based clusters
remain nonreducible and nonmagnetic.