Short- and medium-range orders in Al90Tb10 glass and their relation to the structures of competing crystalline phases

Tang, L.; Yang, Z. J.; Wen, T. Q.; Ho, K. M.; Kramer, M. J.; Wang, C. Z.

doi:10.1016/j.actamat.2020.116513

Title: Short- and medium-range orders in Al90Tb10 glass and their relation to the structures of competing crystalline phases

Abstract

Molecular dynamics simulations using an interatomic potential developed by artificial neural network deep machine learning are performed to study the local structural order in Al90Tb10 metallic glass. We show that more than 80% of the Tb-centered clusters in Al90Tb10 glass have short-range order (SRO) with their 17 first coordination shell atoms stacked in a ‘3661’ or ‘15551’ sequence. Medium-range order (MRO) in Bergman-type packing extended out to the second and third coordination shells is also clearly observed. Analysis of the network formed by the ‘3661’ and ‘15551’ clusters show that ~82% of such SRO units share their faces or vertexes, while only ~6% of neighboring SRO pairs are interpenetrating. Such a network topology is consistent with the Bergman-type MRO around the Tb-centers. Moreover, crystal structure searches using genetic algorithm and the neural network interatomic potential reveal several low-energy metastable crystalline structures in the composition range close to Al₉₀Tb₁₀. Some of these crystalline structures have the ‘3661’ SRO while others have the ‘15551’ SRO. While the crystalline structures with the ‘3661’ SRO also exhibit the MRO very similar to that observed in the glass, the ones with the ‘15551’ SRO have very different atomic packing in the second and third shellsmore »« less

Authors:

^[1]; Yang, Z. J. ^[1]; Wen, T. Q. ^[2]; Ho, K. M. ^[2]; Kramer, M. J. ^[2]; Wang, C. Z. ^[2]

Zhejiang Univ. of Technology, Hangzhou (China)
Ames Lab., Ames, IA (United States); Iowa State Univ., Ames, IA (United States)

Publication Date:: Mon Feb 01 00:00:00 EST 2021

Research Org.:: Ames Lab., Ames, IA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; National Natural Science Foundation of China (NSFC); Natural Science Foundation of Zhejiang Province; USDOE

OSTI Identifier:: 1735847

Alternate Identifier(s):: OSTI ID: 1780024

Report Number(s):: IS-J-10,374
Journal ID: ISSN 1359-6454

Grant/Contract Number:: AC02-07CH11358; 11304279; 11104247; LY18E010 0 07

Resource Type:: Accepted Manuscript

Journal Name:: Acta Materialia

Additional Journal Information:: Journal Volume: 204; Journal ID: ISSN 1359-6454

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE

Citation Formats


                    Tang, L., Yang, Z. J., Wen, T. Q., Ho, K. M., Kramer, M. J., and Wang, C. Z. Short- and medium-range orders in Al90Tb10 glass and their relation to the structures of competing crystalline phases.  United States: N. p., 2021. 
Web.  doi:10.1016/j.actamat.2020.116513.

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                    Tang, L., Yang, Z. J., Wen, T. Q., Ho, K. M., Kramer, M. J., & Wang, C. Z. Short- and medium-range orders in Al90Tb10 glass and their relation to the structures of competing crystalline phases.  United States.  https://doi.org/10.1016/j.actamat.2020.116513

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                    Tang, L., Yang, Z. J., Wen, T. Q., Ho, K. M., Kramer, M. J., and Wang, C. Z. Mon .  
"Short- and medium-range orders in Al90Tb10 glass and their relation to the structures of competing crystalline phases".  United States.  https://doi.org/10.1016/j.actamat.2020.116513.  https://www.osti.gov/servlets/purl/1735847.

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@article{osti_1735847,

  title        = {Short- and medium-range orders in Al90Tb10 glass and their relation to the structures of competing crystalline phases},

  author       = {Tang, L. and Yang, Z. J. and Wen, T. Q. and Ho, K. M. and Kramer, M. J. and Wang, C. Z.},

  abstractNote = {Molecular dynamics simulations using an interatomic potential developed by artificial neural network deep machine learning are performed to study the local structural order in Al90Tb10 metallic glass. We show that more than 80% of the Tb-centered clusters in Al90Tb10 glass have short-range order (SRO) with their 17 first coordination shell atoms stacked in a ‘3661’ or ‘15551’ sequence. Medium-range order (MRO) in Bergman-type packing extended out to the second and third coordination shells is also clearly observed. Analysis of the network formed by the ‘3661’ and ‘15551’ clusters show that ~82% of such SRO units share their faces or vertexes, while only ~6% of neighboring SRO pairs are interpenetrating. Such a network topology is consistent with the Bergman-type MRO around the Tb-centers. Moreover, crystal structure searches using genetic algorithm and the neural network interatomic potential reveal several low-energy metastable crystalline structures in the composition range close to Al90Tb10. Some of these crystalline structures have the ‘3661’ SRO while others have the ‘15551’ SRO. While the crystalline structures with the ‘3661’ SRO also exhibit the MRO very similar to that observed in the glass, the ones with the ‘15551’ SRO have very different atomic packing in the second and third shells around the Tb centers from that of the Bergman-type MRO observed in the glassy phase.},

  doi          = {10.1016/j.actamat.2020.116513},

  journal      = {Acta Materialia},

  number       = ,

  volume       = 204,

  place        = {United States},

  year         = {Mon Feb 01 00:00:00 EST 2021},

  month        = {Mon Feb 01 00:00:00 EST 2021}

}

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Works referenced in this record:

‘Crystal Genes’ in Metallic Liquids and Glasses
journal, March 2016

Sun, Yang; Zhang, Feng; Ye, Zhuo
Scientific Reports, Vol. 6, Issue 1
DOI: 10.1038/srep23734

Thermodynamic evaluation and optimization of Al–Gd, Al–Tb, Al–Dy, Al–Ho and Al–Er systems using a Modified Quasichemical Model for the liquid
journal, December 2010

Jin, Liling; Kang, Youn-Bae; Chartrand, Patrice
Calphad, Vol. 34, Issue 4
DOI: 10.1016/j.calphad.2010.08.004

Ageless Aluminum-Cerium-Based Alloys in High-Volume Die Casting for Improved Energy Efficiency
journal, April 2018

Stromme, Eric T.; Henderson, Hunter B.; Sims, Zachary C.
JOM, Vol. 70, Issue 6
DOI: 10.1007/s11837-018-2861-9

On the role of Sm in solidification of Al-Sm metallic glasses
journal, November 2016

Bokas, G. B.; Zhao, L.; Perepezko, J. H.
Scripta Materialia, Vol. 124
DOI: 10.1016/j.scriptamat.2016.06.045

Nucleation-controlled reactions and metastable structures
journal, January 2004

Perepezko, J. H.
Progress in Materials Science, Vol. 49, Issue 3-4
DOI: 10.1016/S0079-6425(03)00028-8

Amorphization and nanostructure synthesis in Al alloys
journal, November 2002

Perepezko, J. H.; Hebert, R. J.; Tong, W. S.
Intermetallics, Vol. 10, Issue 11-12
DOI: 10.1016/S0966-9795(02)00144-9

The role of amorphous precursor in phase selection hierarchy in marginal metallic glasses
journal, December 2016

Yildirim, C.; Kutsal, M.; Ott, R. T.
Materials & Design, Vol. 112
DOI: 10.1016/j.matdes.2016.09.060

Dislocation formation during deformation-induced synthesis of nanocrystals in amorphous and partially crystalline amorphous Al88Y7Fe5 alloy
journal, January 2006

Hebert, R. J.; Perepezko, J. H.; Rösner, H.
Scripta Materialia, Vol. 54, Issue 1
DOI: 10.1016/j.scriptamat.2005.09.013

Nucleation kinetics in Al-Sm metallic glasses
journal, January 2018

Zhao, L.; Bokas, G. B.; Perepezko, J. H.
Acta Materialia, Vol. 142
DOI: 10.1016/j.actamat.2017.09.050

Cooling rate dependence of structural order in Al90Sm10 metallic glass
journal, July 2016

Sun, Yang; Zhang, Yue; Zhang, Feng
Journal of Applied Physics, Vol. 120, Issue 1
DOI: 10.1063/1.4955223

Crystallization behaviour of Al-based metallic glasses below and above the glass-transition temperature
journal, December 2002

Louzguine, D. V.; Inoue, A.
Journal of Non-Crystalline Solids, Vol. 311, Issue 3
DOI: 10.1016/S0022-3093(02)01375-3

Comparative study of the effect of cold rolling on the structure of Al–RE–Ni–Co (RE=rare-earth metals) amorphous and glassy alloys
journal, October 2006

Louzguine-Luzgin, D. V.; Inoue, A.
Journal of Non-Crystalline Solids, Vol. 352, Issue 36-37
DOI: 10.1016/j.jnoncrysol.2006.06.022

Amorphous, nanoquasicrystalline and nanocrystalline alloys in Al-based systems
journal, December 1998

Inoue, Akihisa
Progress in Materials Science, Vol. 43, Issue 5
DOI: 10.1016/S0079-6425(98)00005-X

Local chemical and topological order in Al–Tb and its role in controlling nanocrystal formation
journal, February 2012

Kalay, Y. E.; Kalay, I.; Hwang, Jinwoo
Acta Materialia, Vol. 60, Issue 3
DOI: 10.1016/j.actamat.2011.11.008

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995

Plimpton, Steve
Journal of Computational Physics, Vol. 117, Issue 1
DOI: 10.1006/jcph.1995.1039

Amorphous aluminum alloys—synthesis and stability
journal, March 2002

Perepezko, John H.; Hebert, Rainer J.
JOM, Vol. 54, Issue 3
DOI: 10.1007/BF02822618

Aluminum nanoscale order in amorphous Al92Sm8 measured by fluctuation electron microscopy
journal, April 2005

Stratton, W. G.; Hamann, J.; Perepezko, J. H.
Applied Physics Letters, Vol. 86, Issue 14
DOI: 10.1063/1.1897830

Development of interatomic potentials appropriate for simulation of devitrification of Al ₉₀ Sm ₁₀ alloy
journal, April 2015

Mendelev, M. I.; Zhang, F.; Ye, Z.
Modelling and Simulation in Materials Science and Engineering, Vol. 23, Issue 4
DOI: 10.1088/0965-0393/23/4/045013

Molecular Geometry Optimization with a Genetic Algorithm
journal, July 1995

Deaven, D. M.; Ho, K. M.
Physical Review Letters, Vol. 75, Issue 2
DOI: 10.1103/PhysRevLett.75.288

Canonical dynamics: Equilibrium phase-space distributions
journal, March 1985

Hoover, William G.
Physical Review A, Vol. 31, Issue 3
DOI: 10.1103/PhysRevA.31.1695

Rare earth based bulk metallic glasses
journal, May 2009

Luo, Q.; Wang, W. H.
Journal of Non-Crystalline Solids, Vol. 355, Issue 13
DOI: 10.1016/j.jnoncrysol.2009.02.006

DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics
journal, July 2018

Wang, Han; Zhang, Linfeng; Han, Jiequn
Computer Physics Communications, Vol. 228
DOI: 10.1016/j.cpc.2018.03.016

The atomic structure of aluminum based metallic glasses and universal criterion for glass formation
journal, October 1996

Egami, T.
Journal of Non-Crystalline Solids, Vol. 205-207
DOI: 10.1016/S0022-3093(96)00277-3

In situ Synchrotron Study of Phase Transformation Behaviors in Bulk Metallic Glass by Simultaneous Diffraction and Small Angle Scattering
journal, December 2003

Wang, X. -L.; Almer, J.; Liu, C. T.
Physical Review Letters, Vol. 91, Issue 26
DOI: 10.1103/PhysRevLett.91.265501

Influence of substitution of La by Gd on crystallization behavior of Al-Ni-La metallic glasses
journal, June 2019

Li, X. M.; Wang, Y.; Yi, J. J.
Journal of Alloys and Compounds, Vol. 790
DOI: 10.1016/j.jallcom.2019.03.190

Synthesis and Properties of Metallic Glasses That Contain Aluminum
journal, September 1988

He, Y.; Poon, S. J.; Shiflet, G. J.
Science, Vol. 241, Issue 4873
DOI: 10.1126/science.241.4873.1640

Phase separation mediated devitrification of Al88Y7Fe5 glasses
journal, July 2010

Sahu, K. K.; Mauro, N. A.; Longstreth-Spoor, L.
Acta Materialia, Vol. 58, Issue 12
DOI: 10.1016/j.actamat.2010.04.011

A unified formulation of the constant temperature molecular dynamics methods
journal, July 1984

Nosé, Shuichi
The Journal of Chemical Physics, Vol. 81, Issue 1
DOI: 10.1063/1.447334

Mechanisms for nanocrystal formation in metallic glasses
journal, March 2003

Kelton, K. F.; Croat, T. K.; Gangopadhyay, A. K.
Journal of Non-Crystalline Solids, Vol. 317, Issue 1-2
DOI: 10.1016/S0022-3093(02)02004-5

Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics
journal, April 2018

Zhang, Linfeng; Han, Jiequn; Wang, Han
Physical Review Letters, Vol. 120, Issue 14
DOI: 10.1103/PhysRevLett.120.143001

The effect of phase separation on subsequent crystallization in Al88Gd6La2Ni4
journal, October 2000

Gangopadhyay, A. K.; Croat, T. K.; Kelton, K. F.
Acta Materialia, Vol. 48, Issue 16
DOI: 10.1016/S1359-6454(00)00196-8

Spatially Resolved Distribution Function and the Medium-Range Order in Metallic Liquid and Glass
journal, December 2011

Fang, X. W.; Wang, C. Z.; Hao, S. G.
Scientific Reports, Vol. 1, Issue 1
DOI: 10.1038/srep00194

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Title: Short- and medium-range orders in Al90Tb10 glass and their relation to the structures of competing crystalline phases

Abstract

Citation Formats

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Thermodynamic evaluation and optimization of Al–Gd, Al–Tb, Al–Dy, Al–Ho and Al–Er systems using a Modified Quasichemical Model for the liquid journal, December 2010

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Nucleation kinetics in Al-Sm metallic glasses journal, January 2018

Cooling rate dependence of structural order in Al90Sm10 metallic glass journal, July 2016

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Amorphous, nanoquasicrystalline and nanocrystalline alloys in Al-based systems journal, December 1998

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Molecular Geometry Optimization with a Genetic Algorithm journal, July 1995

Canonical dynamics: Equilibrium phase-space distributions journal, March 1985

Rare earth based bulk metallic glasses journal, May 2009

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The atomic structure of aluminum based metallic glasses and universal criterion for glass formation journal, October 1996

In situ Synchrotron Study of Phase Transformation Behaviors in Bulk Metallic Glass by Simultaneous Diffraction and Small Angle Scattering journal, December 2003

Influence of substitution of La by Gd on crystallization behavior of Al-Ni-La metallic glasses journal, June 2019

Synthesis and Properties of Metallic Glasses That Contain Aluminum journal, September 1988

Phase separation mediated devitrification of Al88Y7Fe5 glasses journal, July 2010

A unified formulation of the constant temperature molecular dynamics methods journal, July 1984

Mechanisms for nanocrystal formation in metallic glasses journal, March 2003

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The effect of phase separation on subsequent crystallization in Al88Gd6La2Ni4 journal, October 2000

Spatially Resolved Distribution Function and the Medium-Range Order in Metallic Liquid and Glass journal, December 2011

‘Crystal Genes’ in Metallic Liquids and Glasses
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Thermodynamic evaluation and optimization of Al–Gd, Al–Tb, Al–Dy, Al–Ho and Al–Er systems using a Modified Quasichemical Model for the liquid
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Ageless Aluminum-Cerium-Based Alloys in High-Volume Die Casting for Improved Energy Efficiency
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On the role of Sm in solidification of Al-Sm metallic glasses
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Nucleation-controlled reactions and metastable structures
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The role of amorphous precursor in phase selection hierarchy in marginal metallic glasses
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Dislocation formation during deformation-induced synthesis of nanocrystals in amorphous and partially crystalline amorphous Al88Y7Fe5 alloy
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Nucleation kinetics in Al-Sm metallic glasses
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Cooling rate dependence of structural order in Al90Sm10 metallic glass
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