[DSRP Evidence](https://dsrpevidence.org/)

# Scaling of Nanoalloy Phase Transitions: Elucidating the Distinct Role of Surface Sites

Leonid Rubinovich, Micha Polak, 2026, Physchem — Chemistry

Patterns: [Distinctions](https://dsrpevidence.org/pattern/distinctions), [Systems](https://dsrpevidence.org/pattern/systems)

## In short

The finding shows that a nanoparticle's overall (whole) phase-transition behavior cannot be captured by a single scaling law but must be decomposed into contributions from geometrically distinct types of surface site (parts), each scaling differently with size.

## What they found (results)

Deviations of nanoparticle critical-temperature shifts from the standard inverse-size finite-size-scaling law were explained by decomposing the shift into separate contributions from face, edge, and vertex surface sites, which scale respectively as n⁻¹, n⁻², and n⁻³ with the number of atomic shells.

## What they set out to do (purpose)

To explain deviations from the standard finite-size-scaling law for phase-separation critical-temperature shifts in nanoparticles by introducing a site-specific model of how different surface-atom types contribute to the shift.

## Abstract

Nano-size-induced shifts in alloy phase-separation critical temperatures (TCnano) are investigated by introducing an atomistic concept of site-specific contributions to the shift (SSCS) associated with different atomic coordination environments in cuboctahedral and truncated-octahedral nanoparticles (NPs). TCnano previously computed using the Free-energy Concentration Expansion Method (FCEM) for the transformation of three small quasi-Janus Pd-Ir NPs into mixed nanophases are extended here to a substantially broader set of 22 NP sizes, ranging from 147 to 49,049 atoms. This dataset provides the basis for the present modeling. The main objective is to elucidate the deviations of the critical-temperature shifts in small NPs from the finite-size-scaling (FSS) inverse-size power law previously proposed on the basis of non-atomistic thermodynamic modeling. Within the SSCS approach, these deviations are described in terms of contributions from face, edge, and vertex sites. The contributions are proportional to the fractions of the corresponding surface-site types and can be approximated by terms proportional to n−1, n−2, and n−3, respectively, where n is the number of nested atomic shells. The SSCS approach can also be applied to other phase transitions in nanoparticles of various shapes and sizes.

These researchers were not testing DSRP. The finding is theirs; the correspondence to DSRP is drawn by this site.

[Source](https://doi.org/10.3390/physchem6030058)