Citation: Ojovan, M.I.;
Louzguine-Luzgin, D.V. On
Structural Rearrangements during
the Vitrification of Molten Copper.
Materials 2022, 15, 1313. https://
doi.org/10.3390/ma15041313
Academic Editors: George Wardeh
and Michele Bacciocchi
Received: 26 December 2021
Accepted: 7 February 2022
Published: 10 February 2022
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materials
Article
On Structural Rearrangements during the Vitrification of
Molten Copper
Michael I. Ojovan
1,2,
* and Dmitri V. Louzguine-Luzgin
3,4
1
Department of Materials, South Kensington Campus, Imperial College London, Exhibition Road,
London SW7 2AZ, UK
2
Department of Radiochemistry, Faculty of Chemistry, Lomonosov Moscow State University, Leninskie Gory 1,
Bd. 3, 119991 Moscow, Russia
3
Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai 980-8577, Japan;
dml@wpi-aimr.tohoku.ac.jp
4
MathAM-OIL, National Institute of Advanced Industrial Science and Technology (AIST),
Sendai 980-8577, Japan
* Correspondence: m.ojovan@imperial.ac.uk
Abstract: We utilise displacement analysis of Cu-atoms between the chemical bond-centred Voronoi
polyhedrons to reveal structural changes at the glass transition. We confirm that the disordered
congruent bond lattice of Cu loses its rigidity above the glass transition temperature (T
g
) in line
with Kantor–Webman theorem due to percolation via configurons (broken Cu-Cu chemical bonds).
We reveal that the amorphous Cu has the T
g
= 794 ± 10 K at the cooling rate q = 1 × 10
13
K/s and
that the determination of T
g
based on analysis of first sharp diffraction minimum (FDSM) is sharper
compared with classical Wendt–Abraham empirical criterion.
Keywords: amorphous copper; vitrification; glass transition; molecular dynamic simulation; Voronoi
polyhedrons; congruent bond lattice; configuron; percolation; Hausdorff–Besicovitch dimensionality;
set theory
1. Introduction
Spatial distributions and displacement analysis through and between Voronoi poly-
hedrons are widely used to reveal structural changes in various materials in wide ranges
of temperature and composition utilising molecular dynamic (MD) simulations [1,2].
The Voronoi polyhedrons are constructed using tessellations (honeycombs)-atomic centred
polyhedrons which are regular or semiregular polyhedrons in crystalline materials and
irregular polyhedrons in amorphous materials which are characterised by topological
disorder. MD simulations are particularly effective in detecting changes that occur on
vitrification of melts or melting of glasses (glass transition). Pure metals having only one
sort of atoms are attractive as they enable a simplified approach compared to multiatomic
compounds or metallic alloys. There are several ways in which amorphous materials
including metallic systems can be produced. These include enough rapid cooling of
melts, physical vapor deposition, solid-state reactions, irradiation- and pressure-induced
amorphization. Amorphous Cu was produced both by extra-rapid cooling and ultrahigh
pressure 14 GPa [3,4]. Many researchers utilise MD simulations to investigate its behaviour
and properties [5]. The most intriguing question is about structural changes at the glass
transition which was analysed using MD simulations for Fe [6,7], Ni [8,9], Cu [10], Al [11] as
well as for other metals [12]. We aim here to analyse the glass transition (vitrification) of Cu
revealing the structural differences below and above the glass transition temperature (T
g
)
and utilising the pair distribution functions, mainly their first sharp diffraction minimum
(FSDM) as a tool to identify the T
g
.
Materials 2022, 15, 1313. https://doi.org/10.3390/ma15041313 https://www.mdpi.com/journal/materials