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Thermodynamics at the nanoscale: Phase diagrams of nickel–carbon nanoclusters and equilibrium constants for phase transition

Evidence and attribution

Authority of statements

The corpus PDF is a Royal Society of Chemistry Accepted Manuscript with placeholder metadata in the header; summaries follow the abstract block in the extract. Confirm volume/pages from the final Nanoscale issue.

Summary

Catalytic chemical vapor deposition (CCVD) of carbon nanotubes depends on Ni–C catalyst particles that may be solid, molten, or partially molten during growth; inferring the actual phase from experiments alone is nontrivial for nanoscale clusters. Engelmann, Bogaerts, and Neyts simulate Ni–C nanoclusters with ReaxFF reactive MD, comparing icosahedral and Wulff morphologies as model catalyst shapes. They construct temperature-dependent phase diagrams using both a Lindemann index (Eq. 1 in the manuscript) and potential energy traces, then derive equilibrium constants and solid/liquid fractions during melting so that melting points are less sensitive to a single arbitrary Lindemann cutoff—a common pain point in nanoscale melting diagnostics.

Methods

Reactive MD model (Ni–C clusters)

  • ReaxFF simulations include C–Ni bonding and carbon dissolution into nickel as temperature increases (Summary).

Morphology comparisons

  • Icosahedral vs Wulff Ni–C nanoclusters probe how particle shape influences melting and phase coexistence (Summary).

Melting diagnostics

  • Lindemann index (Eq. 1 in manuscript) and mean potential energy vs temperature track disordering/melting (Summary).

Thermodynamic post-processing

  • Analytic expressions for equilibrium constants and solid/liquid fractions reduce sensitivity to a single arbitrary Lindemann cutoff (Summary).

Ingest note

Corpus PDF is a Nanoscale Accepted Manuscript (papers/ReaxFF_others/Neyts_coworkers_NiC_Lindemann_2014.pdf); verify volume/pages against the final issue before citing figure numbers.

1 — MD application (atomistic dynamics)

normalized/extracts/2014neyts-venue-paper_p1-2.txt is abstract-level for this slug; detailed MD settings require the typeset Nanoscale article.

  • Engine / code: ReaxFF molecular dynamics of Ni–C nanoclusters (abstract); N/A — MD package not in the indexed excerpt.
  • System size & composition: N/A — atom counts not in p1–2 excerpt (clusters described qualitatively as icosahedral vs Wulff morphologies in wiki summary).
  • Boundaries / periodicity: N/A — not stated in the indexed excerpt.
  • Ensemble: NVT is the plausible default for isolated nanocluster heating scans, but N/A — explicit ensemble not confirmed in p1–2 text—verify in Nanoscale 10.1039/C4NR02354D.
  • Timestep / duration / thermostat / barostat: N/A — not stated in the indexed excerpt.
  • Temperature: temperature-dependent melting diagnostics (Lindemann index, mean potential energy) are central to the abstract narrative.
  • Pressure: N/A — not stated in the excerpt.
  • Electric field: N/A — not stated.
  • Replica / enhanced sampling: N/A — not stated.

2 — Force-field training

N/A — application paper using ReaxFF for Ni–C CCVD catalyst modeling rather than a new fit documented on this slug.

Findings

Outcomes and mechanisms

The abstract-level summary on file emphasizes melting/phase behavior of Ni–C nanoclusters and analytic reductions (equilibrium constants, solid/liquid fractions) meant to reduce Lindemann cutoff arbitrariness when estimating melting temperatures.

Comparisons

Contrasts icosahedral vs Wulff morphology effects on apparent melting behavior in the manuscript framing summarized on this page.

Sensitivity

Temperature sweeps and morphology choice are the main sensitivity knobs discussed at abstract depth.

Limitations and corpus honesty

Accepted manuscript PDF; cluster models omit full CCVD reactor chemistry and support interactions. Cite the final Nanoscale PDF for authoritative numbers and figure labels.

Limitations

Accepted manuscript PDF; partial extract; cluster models omit full CCVD fluid environment.

Relevance to group

Ni–C ReaxFF thermodynamics relevant to catalytic carbon nanostructure formation—complements CNT growth and fuel chemistry entries.

Citations and evidence anchors

  • https://doi.org/10.1039/C4NR02354D — Nanoscale article landing page.