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Cooper S, Robles-Navarro A, Smits OR, Schwerdtfeger P. From Hard to Soft Dense Sphere Packings: The Cohesive Energy of Barlow Structures Using Exact Lattice Summations for a General Lennard-Jones Potential. J Phys Chem Lett 2024; 15:8387-8392. [PMID: 39115313 DOI: 10.1021/acs.jpclett.4c01986] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/16/2024]
Abstract
There are infinitely many distinguishable dense sphere packings in dimension three (Barlow structures) with maximum packing density of ρ = π/√18. While Hales [Hales, T. C. Ann. Math. 2005, 162, 1065-1185.] proved that the packing density of the most dense cubic packing cannot be surpassed, it is currently not known how the infinite possibilities of densely packed Barlow structures with different sequences of hexagonal close packed layers are energetically related compared to the well-known face centered cubic (fcc) and hexagonal close packed (hcp) structures. We demonstrate that, for a general Lennard-Jones potential, which includes the hard-sphere model as a limiting case, Barlow packings lie energetically between fcc and hcp. Exceptions to this energy sequence only occur when fcc and hcp are energetically quasi-degenerate.
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Affiliation(s)
- Shaun Cooper
- School of Mathematical and Computational Sciences, Massey University Auckland, Private Bag 102904, Auckland 0745, New Zealand
| | - Andres Robles-Navarro
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Private Bag 102904, 0745 Auckland, New Zealand
| | - Odile R Smits
- The School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
| | - Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Private Bag 102904, 0745 Auckland, New Zealand
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2
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Möller J, Schottelius A, Caresana M, Boesenberg U, Kim C, Dallari F, Ezquerra TA, Fernández JM, Gelisio L, Glaesener A, Goy C, Hallmann J, Kalinin A, Kurta RP, Lapkin D, Lehmkühler F, Mambretti F, Scholz M, Shayduk R, Trinter F, Vartaniants IA, Zozulya A, Galli DE, Grübel G, Madsen A, Caupin F, Grisenti RE. Crystal Nucleation in Supercooled Atomic Liquids. PHYSICAL REVIEW LETTERS 2024; 132:206102. [PMID: 38829060 DOI: 10.1103/physrevlett.132.206102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2023] [Revised: 02/22/2024] [Accepted: 03/28/2024] [Indexed: 06/05/2024]
Abstract
The liquid-to-solid phase transition is a complex process that is difficult to investigate experimentally with sufficient spatial and temporal resolution. A key aspect of the transition is the formation of a critical seed of the crystalline phase in a supercooled liquid, that is, a liquid in a metastable state below the melting temperature. This stochastic process is commonly described within the framework of classical nucleation theory, but accurate tests of the theory in atomic and molecular liquids are challenging. Here, we employ femtosecond x-ray diffraction from microscopic liquid jets to study crystal nucleation in supercooled liquids of the rare gases argon and krypton. Our results provide stringent limits to the validity of classical nucleation theory in atomic liquids, and offer the long-sought possibility of testing nonclassical extensions of the theory.
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Affiliation(s)
- Johannes Möller
- European X-ray Free-Electron Laser Facility, 22869 Schenefeld, Germany
| | - Alexander Schottelius
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, 60438 Frankfurt am Main, Germany
| | - Michele Caresana
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, 60438 Frankfurt am Main, Germany
| | - Ulrike Boesenberg
- European X-ray Free-Electron Laser Facility, 22869 Schenefeld, Germany
| | - Chan Kim
- European X-ray Free-Electron Laser Facility, 22869 Schenefeld, Germany
| | | | - Tiberio A Ezquerra
- Macromolecular Physics Department, Instituto de Estructura de la Materia, IEM-CSIC, 28006 Madrid, Spain
| | - José M Fernández
- Laboratory of Molecular Fluid Dynamics, Instituto de Estructura de la Materia, IEM-CSIC, 28006 Madrid, Spain
| | - Luca Gelisio
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - Andrea Glaesener
- Dipartimento di Fisica "Aldo Pontremoli," Università degli Studi di Milano, 20133 Milano, Italy
| | - Claudia Goy
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - Jörg Hallmann
- European X-ray Free-Electron Laser Facility, 22869 Schenefeld, Germany
| | - Anton Kalinin
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
| | - Ruslan P Kurta
- European X-ray Free-Electron Laser Facility, 22869 Schenefeld, Germany
| | - Dmitry Lapkin
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | | | - Francesco Mambretti
- Dipartimento di Fisica "Aldo Pontremoli," Università degli Studi di Milano, 20133 Milano, Italy
| | - Markus Scholz
- European X-ray Free-Electron Laser Facility, 22869 Schenefeld, Germany
| | - Roman Shayduk
- European X-ray Free-Electron Laser Facility, 22869 Schenefeld, Germany
| | - Florian Trinter
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, 60438 Frankfurt am Main, Germany
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
- Molecular Physics, Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany
| | | | - Alexey Zozulya
- European X-ray Free-Electron Laser Facility, 22869 Schenefeld, Germany
| | - Davide E Galli
- Dipartimento di Fisica "Aldo Pontremoli," Università degli Studi di Milano, 20133 Milano, Italy
| | - Gerhard Grübel
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Anders Madsen
- European X-ray Free-Electron Laser Facility, 22869 Schenefeld, Germany
| | - Frédéric Caupin
- Institut Lumière Matière, Université Claude Bernard Lyon 1, CNRS, Institut Universitaire de France, 69622 Villeurbanne, France
| | - Robert E Grisenti
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, 60438 Frankfurt am Main, Germany
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
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Schwerdtfeger P, Wales DJ. 100 Years of the Lennard-Jones Potential. J Chem Theory Comput 2024; 20:3379-3405. [PMID: 38669689 DOI: 10.1021/acs.jctc.4c00135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/28/2024]
Abstract
It is now 100 years since Lennard-Jones published his first paper introducing the now famous potential that bears his name. It is therefore timely to reflect on the many achievements, as well as the limitations, of this potential in the theory of atomic and molecular interactions, where applications range from descriptions of intermolecular forces to molecules, clusters, and condensed matter.
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Affiliation(s)
- Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Private Bag 102904, Auckland 0745, New Zealand
| | - David J Wales
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
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Robles-Navarro A, Jerabek P, Schwerdtfeger P. Tipping the Balance Between the bcc and fcc Phase Within the Alkali and Coinage Metal Groups. Angew Chem Int Ed Engl 2024; 63:e202313679. [PMID: 37877444 DOI: 10.1002/anie.202313679] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Revised: 10/24/2023] [Accepted: 10/25/2023] [Indexed: 10/26/2023]
Abstract
Why the Group 1 elements crystallize in the body-centered cubic (bcc) structure, and the iso-electronic Group 11 elements in the face-centered cubic (fcc) structure, remains a mystery. Here we show that a delicate interplay between many-body effects, vibrational contributions and dispersion interactions obtained from relativistic density functional theory offers an answer to this long-standing controversy. It also sheds light on the Periodic Table of Crystal Structures. A smooth diffusionless transition through cuboidal lattices gives a detailed insight into the bcc→fcc phase transition for the Groups 1 and 11 elements.
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Affiliation(s)
- Andrés Robles-Navarro
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study (NZIAS), Massey University Albany, Private Bag 102904, Auckland, 0745, New Zealand
| | - Paul Jerabek
- Institute of Hydrogen Technology, Helmholtz-Zentrum Hereon, Max-Planck-Str. 1, 21502, Geesthacht, Germany
| | - Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study (NZIAS), Massey University Albany, Private Bag 102904, Auckland, 0745, New Zealand
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Burrows A, Cooper S, Schwerdtfeger P. Lattice sum for a hexagonal close-packed structure and its dependence on the c/a ratio of the hexagonal cell parameters. Phys Rev E 2023; 107:065302. [PMID: 37464642 DOI: 10.1103/physreve.107.065302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2023] [Accepted: 05/17/2023] [Indexed: 07/20/2023]
Abstract
We continue the work by Lennard-Jones and Ingham, and later by Kane and Goeppert-Mayer, and present a general lattice sum formula for the hexagonal close packed (hcp) structure with different c/a ratios for the two lattice parameters a and c of the hexagonal unit cell. The lattice sum is expressed in terms of fast converging series of Bessel functions. This allows us to analytically examine the behavior of a Lennard-Jones potential as a function of the c/a ratio. In contrast to the hard-sphere model, where we have the ideal ratio of c/a=sqrt[8/3] with 12 kissing spheres around a central atom, we observe the occurrence of a slight symmetry-breaking effect and the appearance of a second metastable minimum for the (12,6) Lennard-Jones potential around the ratio c/a=2/3. We also show that the analytical continuation of the (n,m) Lennard-Jones potential to the domain n,m<3 such as the Kratzer potential (n=2,m=1) gives unphysical results.
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Affiliation(s)
- Antony Burrows
- Centre for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study (NZIAS), Massey University Albany, Private Bag 102904, Auckland 0745, New Zealand
| | - Shaun Cooper
- School of Mathematical and Computational Sciences, Massey University Albany, Private Bag 102904, Auckland 0745, New Zealand
| | - Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study (NZIAS), Massey University Albany, Private Bag 102904, Auckland 0745, New Zealand
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6
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Burrows A, Cooper S, Schwerdtfeger P. Instability of the body-centered cubic lattice within the sticky hard sphere and Lennard-Jones model obtained from exact lattice summations. Phys Rev E 2021; 104:035306. [PMID: 34654145 DOI: 10.1103/physreve.104.035306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Accepted: 09/08/2021] [Indexed: 11/07/2022]
Abstract
A smooth path of rearrangement from the body-centered cubic (bcc) to the face-centered cubic (fcc) lattice is obtained by introducing a single parameter to lattice vectors of a cuboidal unit cell. As a result, we obtain analytical expressions in terms of lattice sums for the cohesive energy where the interaction is described by a Lennard-Jones (LJ) interaction potential or a sticky hard-sphere (SHS) model with a r^{-n} long-range attractive term. These lattice sums are evaluated to computer precision by expansions in terms of a fast converging Bessel function series. Applying the whole range of lattice parameters for the SHS and LJ potentials we prove that the bcc phase is unstable (or, at best, metastable) toward distortion into the fcc phase in the low temperature and pressure limit. Even if more accurate potentials are used, such as the extended LJ potential for argon or chromium, the bcc phase remains unstable. This strongly indicates that the appearance of a low temperature bcc phase for several elements in the periodic table is due to higher than two-body forces in atomic interactions.
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Affiliation(s)
- Antony Burrows
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Private Bag 102904, 0632 Auckland, New Zealand
| | - Shaun Cooper
- School of Natural and Computational Sciences, Massey University Auckland, Private Bag 102904, 0632 Auckland, New Zealand
| | - Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Private Bag 102904, 0632 Auckland, New Zealand
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Correa E, Albernaz AF, Barreto PR, Aquilanti V. Long-range strength and anisotropies of molecule-molecule interactions: Ab initio calculations, spherical harmonics expansions, and the second virial coefficient for the H2⋯F2 gaseous mixture. Chem Phys Lett 2021. [DOI: 10.1016/j.cplett.2021.138845] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Dewaele A, Rosa AD, Guignot N, Andrault D, Rodrigues JEFS, Garbarino G. Stability and equation of state of face-centered cubic and hexagonal close packed phases of argon under pressure. Sci Rep 2021; 11:15192. [PMID: 34312417 PMCID: PMC8313556 DOI: 10.1038/s41598-021-93995-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 06/23/2021] [Indexed: 11/08/2022] Open
Abstract
The compression of argon is measured between 10 K and 296 K up to 20 GPa and and up to 114 GPa at 296 K in diamond anvil cells. Three samples conditioning are used: (1) single crystal sample directly compressed between the anvils, (2) powder sample directly compressed between the anvils, (3) single crystal sample compressed in a pressure medium. A partial transformation of the face-centered cubic (fcc) phase to a hexagonal close-packed (hcp) structure is observed above 4.2-13 GPa. Hcp phase forms through stacking faults in fcc-Ar and its amount depends on pressurizing conditions and starting fcc-Ar microstructure. The quasi-hydrostatic equation of state of the fcc phase is well described by a quasi-harmonic Mie-Grüneisen-Debye formalism, with the following 0 K parameters for Rydberg-Vinet equation: [Formula: see text] = 38.0 Å[Formula: see text]/at, [Formula: see text] = 2.65 GPa, [Formula: see text] = 7.423. Under the current experimental conditions, non-hydrostaticity affects measured P-V points mostly at moderate pressure ([Formula: see text] 20 GPa).
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Affiliation(s)
- Agnès Dewaele
- CEA, DAM, DIF, 91297, Arpajon, France.
- Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, 91680, Bruyères-le-Châtel, France.
| | | | | | - Denis Andrault
- Université Clermont Auvergne, CNRS, IRD, OPGC, LMV, Clermont-Ferrand, France
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