A side-by-side comparison of the solidification dynamics of quasicrystalline and approximant phases in the Al–Co–Ni system

Han, Insung; Xiao, Xianghui; Sun, Haiping; Shahani, Ashwin J.

doi:10.1107/S2053273318017114

Title: A side-by-side comparison of the solidification dynamics of quasicrystalline and approximant phases in the Al–Co–Ni system

Journal Article · Wed Feb 06 00:00:00 EST 2019 · Acta Crystallographica. Section A, Foundations and Advances (Online)

DOI:https://doi.org/10.1107/S2053273318017114· OSTI ID:1493634

Han, Insung; Xiao, Xianghui; Sun, Haiping; Shahani, Ashwin J.

Quasicrystals and their approximants have triggered widespread interest due to the challenge of solving their complex crystal structures as well as their possibly exceptional properties. The structural motifs of approximants are similar to those of the corresponding quasicrystals, but to what extent are their crystallization pathways the same? Unfortunately, there have been very fewin situexperimental investigations to answer this question. Here, by leveraging the high penetrating power of hard X-rays, synchrotron-based X-ray tomography was conducted in order to capture the nucleation and growth of a decagonal quasicrystal and its related approximant. The combination of data-driven computational analysis with new thermodynamic databases allowed the characterization, with high precision, of the constitutional and kinetic driving forces for crystallization. The experimental results prove that the growth of both crystals from a liquid is dominated by first-order kinetics. Nevertheless, and somewhat surprisingly, significant differences were observed in their rates of nucleation and growth. The reasons for such divergent behaviours are discussed in light of contemporary theories of intermetallic crystallization.

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Research Organization:: Argonne National Lab. (ANL), Argonne, IL (United States); Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-06CH11357; SC0019118

OSTI ID:: 1493634

Alternate ID(s):: OSTI ID: 1530183; OSTI ID: 1657180

Journal Information:: Acta Crystallographica. Section A, Foundations and Advances (Online), Journal Name: Acta Crystallographica. Section A, Foundations and Advances (Online) Vol. 75 Journal Issue: 2; ISSN 2053-2733

Publisher:: International Union of CrystallographyCopyright Statement

Country of Publication:: Denmark

Language:: English

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Cited by: 10 works

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References (86)

Equilibrium and growth shapes of crystals: how do they differ and why should we care? Sekerka, Robert F. Crystal Research and Technology, Vol. 40, Issue 4-5 https://doi.org/10.1002/crat.200410342	journal	April 2005
How do Quasicrystals Grow? Keys, Aaron S.; Glotzer, Sharon C. Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.235503	journal	December 2007
Metallic Phase with Long-Range Orientational Order and No Translational Symmetry Shechtman, D.; Blech, I.; Gratias, D. Physical Review Letters, Vol. 53, Issue 20, p. 1951-1953 https://doi.org/10.1103/PhysRevLett.53.1951	journal	November 1984
Analytics on large microstructure datasets using two-point spatial correlations: Coarsening of dendritic structures Sun, Yue; Cecen, Ahmet; Gibbs, John W. Acta Materialia, Vol. 132 https://doi.org/10.1016/j.actamat.2017.04.054	journal	June 2017
A model of grain refinement incorporating alloy constitution and potency of heterogeneous nucleant particles Easton, M. A.; StJohn, D. H. Acta Materialia, Vol. 49, Issue 10 https://doi.org/10.1016/S1359-6454(00)00368-2	journal	June 2001
Explaining the formation of thin ice crystal plates with structure-dependent attachment kinetics Libbrecht, Kenneth G. Journal of Crystal Growth, Vol. 258, Issue 1-2 https://doi.org/10.1016/S0022-0248(03)01496-9	journal	October 2003
Total-energy-based prediction of a quasicrystal structure Mihalkovič, M.; Al-Lehyani, I.; Cockayne, E. Physical Review B, Vol. 65, Issue 10 https://doi.org/10.1103/PhysRevB.65.104205	journal	March 2002
Single crystal growth of Al-based intermetallic phases being approximants to quasicrystals Gille, Peter; Bauer, Birgitta; Hahne, Michael Journal of Crystal Growth, Vol. 318, Issue 1 https://doi.org/10.1016/j.jcrysgro.2010.10.021	journal	March 2011
In situ study of nucleation and growth of the irregular α-Al/β-Al5FeSi eutectic by 3-D synchrotron X-ray microtomography Terzi, S.; Taylor, J. A.; Cho, Y. H. Acta Materialia, Vol. 58, Issue 16 https://doi.org/10.1016/j.actamat.2010.06.012	journal	September 2010
Experimental investigation and thermodynamic assessment of the Al-Co-Ni system Wang, Yao; Cacciamani, Gabriele Calphad, Vol. 61 https://doi.org/10.1016/j.calphad.2018.03.008	journal	June 2018
Inclined net plane faceting observed at Czochralski growth of decagonal AlCoNi quasicrystals Gille, P.; Meisterernst, G.; Faber, N. Journal of Crystal Growth, Vol. 275, Issue 1-2 https://doi.org/10.1016/j.jcrysgro.2004.10.088	journal	February 2005
Geometrical Model of the Phase Transformation of Decagonal Al–Co–Ni to its Periodic Approximant Honal, M.; Haibach, T.; Steurer, W. Acta Crystallographica Section A Foundations of Crystallography, Vol. 54, Issue 4 https://doi.org/10.1107/S0108767397018837	journal	July 1998
Structure–property linkages using a data science approach: Application to a non-metallic inclusion/steel composite system Gupta, Akash; Cecen, Ahmet; Goyal, Sharad Acta Materialia, Vol. 91 https://doi.org/10.1016/j.actamat.2015.02.045	journal	June 2015
Anisotropic Conductivity in a Decagonal Quasicrystal of Al ₇₀ Ni ₁₅ Co ₁₅ Shibuya, Tadaharu; Hashimoto, Tatsuo; Takeuchi, Shin Journal of the Physical Society of Japan, Vol. 59, Issue 6 https://doi.org/10.1143/JPSJ.59.1917	journal	June 1990
The time dependent behavior of the ostwald ripening for the finite volume fraction Enomoto, Y.; Kawasaki, K.; Tokuyama, M. Acta Metallurgica, Vol. 35, Issue 4 https://doi.org/10.1016/0001-6160(87)90170-2	journal	April 1987
Structural Characteristics of Al-Co-Ni Decagonal Quasicrystals and Crystalline Approximants Hiraga, Kenji; Ohsuna, Tetsu; Sun, Wei MATERIALS TRANSACTIONS, Vol. 42, Issue 11 https://doi.org/10.2320/matertrans.42.2354	journal	January 2001
Stable Decagonal Al–Co–Ni and Al–Co–Cu Quasicrystals Tsai, An-Pang; Inoue, Akihisa; Masumoto, Tsuyoshi Materials Transactions, JIM, Vol. 30, Issue 7 https://doi.org/10.2320/matertrans1989.30.463	journal	January 1989
Discussion on clusters, phasons and quasicrystal stabilisation Henley, C. L.; de Boissieu, M.; Steurer, W. Philosophical Magazine, Vol. 86, Issue 6-8 https://doi.org/10.1080/14786430500419395	journal	February 2006
Total-energy-based structure prediction for d(AlNiCo) Henley, C. L.; Mihalkovič, M.; Widom, M. Journal of Alloys and Compounds, Vol. 342, Issue 1-2 https://doi.org/10.1016/S0925-8388(02)00199-8	journal	August 2002
Solid–liquid interface in the growth of a decagonal Al-72Co-16Ni-12 quasicrystal Guo, J. Q.; Sato, T. J.; Hirano, T. Journal of Crystal Growth, Vol. 197, Issue 4 https://doi.org/10.1016/S0022-0248(98)01165-8	journal	March 1999
Electrically enhanced free dendrite growth in polar and non-polar systems Libbrecht, K. G.; Crosby, T.; Swanson, M. Journal of Crystal Growth, Vol. 240, Issue 1-2 https://doi.org/10.1016/S0022-0248(01)02089-9	journal	April 2002
Structural relationships between decagonal Al-Co-Ni and its approximants Steurer, Walter Ferroelectrics, Vol. 250, Issue 1 https://doi.org/10.1080/00150190108225105	journal	February 2001
Structure solution of the basic decagonal Al–Co–Ni phase by the atomic surfaces modelling method Cervellino, Antonio; Haibach, Torsten; Steurer, Walter Acta Crystallographica Section B Structural Science, Vol. 58, Issue 1 https://doi.org/10.1107/S0108768101018936	journal	January 2001
Phase-field simulation of the columnar-to-equiaxed transition in alloy solidification Badillo, Arnoldo; Beckermann, Christoph Acta Materialia, Vol. 54, Issue 8 https://doi.org/10.1016/j.actamat.2005.12.025	journal	May 2006
Highly perfect decagonal Al-Co-Ni quasicrystals Ritsch, S. Philosophical Magazine Letters, Vol. 74, Issue 2 https://doi.org/10.1080/095008396180452	journal	August 1996
The microstructure of rapidly solidified Al6Mn Shechtman, D.; Blech, I. A. Metallurgical Transactions A, Vol. 16, Issue 6 https://doi.org/10.1007/BF02811670	journal	June 1985
Non-equilibrium solidification of undercooled metallic metls Herlach, D. Materials Science and Engineering: R: Reports, Vol. 12, Issue 4-5 https://doi.org/10.1016/0927-796X(94)90011-6	journal	August 1994
An Analytical Model for Solute Segregation at Liquid Metal/Solid Substrate Interface Men, Hua; Fan, Zhongyun Metallurgical and Materials Transactions A, Vol. 45, Issue 12 https://doi.org/10.1007/s11661-014-2525-5	journal	August 2014
Quasicrystal structure and growth models: discussion of the status quo and the still open questions Steurer, Walter Journal of Physics: Conference Series, Vol. 809 https://doi.org/10.1088/1742-6596/809/1/012001	journal	February 2017
In-situ solute measurements with a laboratory polychromatic microfocus X-ray source during equiaxed solidification of an Al-Ge alloy Becker, M.; Klein, S.; Kargl, F. Scripta Materialia, Vol. 124 https://doi.org/10.1016/j.scriptamat.2016.06.032	journal	November 2016
Theory for the trapping of disorder and solute in intermetallic phases by rapid solidification Boettinger, W. J.; Aziz, M. J. Acta Metallurgica, Vol. 37, Issue 12 https://doi.org/10.1016/0001-6160(89)90210-1	journal	December 1989
Developments in synchrotron x-ray computed microtomography at the National Synchrotron Light Source Dowd, Betsy A.; Campbell, Graham H.; Marr, Robert B. SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, SPIE Proceedings https://doi.org/10.1117/12.363725	conference	September 1999
II—mean curvature and weighted mean curvature Taylor, J. E. Acta Metallurgica et Materialia, Vol. 40, Issue 7 https://doi.org/10.1016/0956-7151(92)90091-R	journal	July 1992
Energy-based structure prediction for d (Al ₇₀ Co ₂₀ Ni ₁₀ ) Gu, N.; Mihalkovič, M.; Henley, C. L. Philosophical Magazine Letters, Vol. 87, Issue 12 https://doi.org/10.1080/09500830701581775	journal	December 2007
First X-Ray Scattering Studies on Electrostatically Levitated Metallic Liquids: Demonstrated Influence of Local Icosahedral Order on the Nucleation Barrier Kelton, K. F.; Lee, G. W.; Gangopadhyay, A. K. Physical Review Letters, Vol. 90, Issue 19 https://doi.org/10.1103/PhysRevLett.90.195504	journal	May 2003
Quasicrystal with One-Dimensional Translational Symmetry and a Tenfold Rotation Axis Bendersky, L. Physical Review Letters, Vol. 55, Issue 14 https://doi.org/10.1103/PhysRevLett.55.1461	journal	September 1985
Mapping single-crystal dendritic microstructure and defects in nickel-base superalloys with synchrotron radiation Husseini, Naji S.; Kumah, Divine P.; Yi, Jian Z. Acta Materialia, Vol. 56, Issue 17 https://doi.org/10.1016/j.actamat.2008.05.041	journal	October 2008
Formation of Crystal Nuclei in Liquid Metals Turnbull, D. Journal of Applied Physics, Vol. 21, Issue 10 https://doi.org/10.1063/1.1699435	journal	October 1950
Metastable quasicrystal-induced nucleation in a bulk glass-forming liquid Kurtuldu, Güven; Shamlaye, Karl F.; Löffler, Jörg F. Proceedings of the National Academy of Sciences, Vol. 115, Issue 24 https://doi.org/10.1073/pnas.1717941115	journal	May 2018
Crystallization behavior of iron-containing intermetallic compounds in 319 aluminum alloy Narayanan, L. Anantha; Samuel, F. H.; Gruzleski, J. E. Metallurgical and Materials Transactions A, Vol. 25, Issue 8 https://doi.org/10.1007/BF02668540	journal	August 1994
Thermo-Calc & DICTRA, computational tools for materials science Andersson, J-O; Helander, Thomas; Höglund, Lars Calphad, Vol. 26, Issue 2 https://doi.org/10.1016/S0364-5916(02)00037-8	journal	June 2002
Probing the growth and melting pathways of a decagonal quasicrystal in real-time Han, Insung; Xiao, Xianghui; Shahani, Ashwin J. Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-17821-0	journal	December 2017
Interfacial energies and mass transport in the Ni(Al)–Al2O3 system: The implication of very low oxygen activities Ni, Na; Kaufmann, Yaron; Kaplan, Wayne D. Acta Materialia, Vol. 64 https://doi.org/10.1016/j.actamat.2013.10.041	journal	February 2014
Atomic structure of a decagonal Al-Co-Ni quasicrystal Yamamoto, Akiji; Kato, Katsuo; Shibuya, Tadaharu Physical Review Letters, Vol. 65, Issue 13 https://doi.org/10.1103/PhysRevLett.65.1603	journal	September 1990
In situ imaging of microstructure formation in electronic interconnections Salleh, M. A. A. Mohd; Gourlay, C. M.; Xian, J. W. Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/srep40010	journal	January 2017
Anisotropic magnetic and transport properties of orthorhombic ${Al}_{13} {Co}_{4}$ Dolinšek, J.; Komelj, M.; Jeglič, P. Physical Review B, Vol. 79, Issue 18 https://doi.org/10.1103/PhysRevB.79.184201	journal	May 2009
Ostwald ripening of faceted Si particles in an Al-Si-Cu melt Shahani, A. J.; Xiao, X.; Skinner, K. Materials Science and Engineering: A, Vol. 673 https://doi.org/10.1016/j.msea.2016.06.077	journal	September 2016
TomoPy: a framework for the analysis of synchrotron tomographic data Gürsoy, Dogˇa; De Carlo, Francesco; Xiao, Xianghui Journal of Synchrotron Radiation, Vol. 21, Issue 5 https://doi.org/10.1107/S1600577514013939	journal	August 2014
The evolution of growth modes and activity of growth sources on canavalin investigated by in situ atomic force microscopy Land, Terry A.; De Yoreo, James J. Journal of Crystal Growth, Vol. 208, Issue 1-4 https://doi.org/10.1016/S0022-0248(99)00470-4	journal	January 2000
Anomalously slow crystal growth of the glass-forming alloy CuZr Tang, Chunguang; Harrowell, Peter Nature Materials, Vol. 12, Issue 6 https://doi.org/10.1038/nmat3631	journal	April 2013
Anisotropic magnetic, electrical, and thermal transport properties of the Y-Al-Ni-Co decagonal approximant Smontara, Ana; Smiljanić, I.; Ivkov, J. Physical Review B, Vol. 78, Issue 10 https://doi.org/10.1103/PhysRevB.78.104204	journal	September 2008
Atomic structure of an $Al - Co - Ni$ decagonal quasicrystalline surface Yuhara, J.; Klikovits, J.; Schmid, M. Physical Review B, Vol. 70, Issue 2 https://doi.org/10.1103/PhysRevB.70.024203	journal	July 2004
Self diffusion in liquid aluminium Kargl, F.; Weis, H.; Unruh, T. Journal of Physics: Conference Series, Vol. 340 https://doi.org/10.1088/1742-6596/340/1/012077	journal	February 2012
A thermodynamic description of the Al–Co–Ni system and site occupancy in Co + AlNi3 composite binder phase Wang, Yaru; Zhou, Peng; Peng, Yingbiao Journal of Alloys and Compounds, Vol. 687 https://doi.org/10.1016/j.jallcom.2016.06.002	journal	December 2016
Quasicrystals: What do we know? What do we want to know? What can we know? Steurer, Walter Acta Crystallographica Section A Foundations and Advances, Vol. 74, Issue 1 https://doi.org/10.1107/S2053273317016540	journal	January 2018
Phase Diagram Determination For Modifications Of The D Phase In The Al-AlCo-AINi System Lück, R.; Scheffer, M.; Gödecke, T. MRS Proceedings, Vol. 553 https://doi.org/10.1557/PROC-553-25	journal	January 1998
Experimental Observation of Quasicrystal Growth Nagao, Keisuke; Inuzuka, Tomoaki; Nishimoto, Kazue Physical Review Letters, Vol. 115, Issue 7 https://doi.org/10.1103/PhysRevLett.115.075501	journal	August 2015
On the kinetic and equilibrium shapes of icosahedral Al71Pd19Mn10 quasicrystals Senabulya, Nancy; Xiao, Xianghui; Han, Insung Scripta Materialia, Vol. 146 https://doi.org/10.1016/j.scriptamat.2017.11.049	journal	March 2018
Preparation of Decagonal Al–Ni–Co Single Quasicrystal by Czochralski Method Yokoyama, Y.; Note, R.; Kimura, S. Materials Transactions, JIM, Vol. 38, Issue 11 https://doi.org/10.2320/matertrans1989.38.943	journal	January 1997
X-ray diffraction study and theoretical calculations on the X-phase, Al ₉ (Co, Ni) ₄ Katrych, S.; Mihalkovic, M.; Gramlich, V. Philosophical Magazine, Vol. 86, Issue 3-5 https://doi.org/10.1080/14786430500268693	journal	January 2006
-Al13Co4, a new quasicrystal approximant Fleischer, F.; Weber, T.; Jung, D. Y. Journal of Alloys and Compounds, Vol. 500, Issue 2 https://doi.org/10.1016/j.jallcom.2010.03.188	journal	June 2010
A new crystalline phase related to an Al–Ni–Co decagonal phase Hiraga, Kenji; Ohsuna, Tetsu; Nishimura, Sinya Journal of Alloys and Compounds, Vol. 325, Issue 1-2 https://doi.org/10.1016/S0925-8388(01)01364-0	journal	July 2001
Low-Temperature Thermodynamic and Thermal-Transport Properties of Decagonal A $l_{65}$ C $u_{20}$ C $o_{15}$ Edagawa, K.; Chernikov, M. A.; Bianchi, A. D. Physical Review Letters, Vol. 77, Issue 6 https://doi.org/10.1103/PhysRevLett.77.1071	journal	August 1996
Crystal growth in undercooled melts of the intermetallic compounds FeSi and CoSi Barth, M.; Wei, B.; Herlach, D. M. Physical Review B, Vol. 51, Issue 6 https://doi.org/10.1103/PhysRevB.51.3422	journal	February 1995
Finite volume fraction effects on coarsening—II. Interface-limited growth Enomoto, Y. Acta Metallurgica et Materialia, Vol. 39, Issue 8 https://doi.org/10.1016/0956-7151(91)90170-6	journal	August 1991
Finite volume fraction effects on Ostwald ripening Enomoto, Y.; Tokuyama, M.; Kawasaki, K. Acta Metallurgica, Vol. 34, Issue 11 https://doi.org/10.1016/0001-6160(86)90157-4	journal	November 1986
Stripe and ring artifact removal with combined wavelet—Fourier filtering Münch, Beat; Trtik, Pavel; Marone, Federica Optics Express, Vol. 17, Issue 10 https://doi.org/10.1364/OE.17.008567	journal	January 2009
Ordered Liquid Aluminum at the Interface with Sapphire Oh, S. H. Science, Vol. 310, Issue 5748 https://doi.org/10.1126/science.1118611	journal	October 2005
XX. On the velocity of solidification and viscosity of super-cooled liquids Wilson, Harold W. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 50, Issue 303 https://doi.org/10.1080/14786440009463908	journal	August 1900
Versatile algorithms for the computation of 2-point spatial correlations in quantifying material structure Cecen, Ahmet; Fast, Tony; Kalidindi, Surya R. Integrating Materials and Manufacturing Innovation, Vol. 5, Issue 1 https://doi.org/10.1186/s40192-015-0044-x	journal	January 2016
Observation of the undercoolability of quasicrystal-forming alloys by electromagnetic levitation Holland-Moritz, D.; Herlach, D. M.; Urban, K. Physical Review Letters, Vol. 71, Issue 8 https://doi.org/10.1103/PhysRevLett.71.1196	journal	August 1993
Dendrite Growth Kinetics in Undercooled Melts of Intermetallic Compounds Herlach, Dieter Crystals, Vol. 5, Issue 3 https://doi.org/10.3390/cryst5030355	journal	September 2015
The role of oxides in the formation of primary iron intermetallics in an Al-11.6Si-0.37Mg alloy Miller, D. N.; Lu, L.; Dahle, A. K. Metallurgical and Materials Transactions B, Vol. 37, Issue 6 https://doi.org/10.1007/BF02735008	journal	December 2006
Simulations of microstructural evolution: anisotropic growth and coarsening Roosen, Andrew R.; Carter, W. Craig Physica A: Statistical Mechanics and its Applications, Vol. 261, Issue 1-2 https://doi.org/10.1016/S0378-4371(98)00377-X	journal	December 1998
Co-rich decagonal Al–Co–Ni: predicting structure, orientational order and puckering Gu, N.; Henley, C. L.; Mihalkovič, M. Philosophical Magazine, Vol. 86, Issue 3-5 https://doi.org/10.1080/14786430500263405	journal	January 2006
Single-crystal growth of the decagonal Al–Ni–Co quasicrystal Sato, Taku J.; Hirano, Toshiyuki; Tsai, An Pang Journal of Crystal Growth, Vol. 191, Issue 3 https://doi.org/10.1016/S0022-0248(98)00164-X	journal	July 1998
Structural transformations at the surface of the decagonal quasicrystal ${Al}_{70} {Co}_{15} {Ni}_{15}$ Zurkirch, M.; Bolliger, B.; Erbudak, M. Physical Review B, Vol. 58, Issue 21 https://doi.org/10.1103/PhysRevB.58.14113	journal	December 1998
First-principles calculations of cohesive energies in the $Al − Co$ binary alloy system Mihalkovič, M.; Widom, M. Physical Review B, Vol. 75, Issue 1 https://doi.org/10.1103/PhysRevB.75.014207	journal	January 2007
The Materials Data Facility: Data Services to Advance Materials Science Research Blaiszik, B.; Chard, K.; Pruyne, J. JOM, Vol. 68, Issue 8 https://doi.org/10.1007/s11837-016-2001-3	journal	July 2016
Relative roles of heat transport and interface rearrangement rates in the rapid growth of crystals in undercooled melts Coriell, S. R.; Turnbull, D. Acta Metallurgica, Vol. 30, Issue 12 https://doi.org/10.1016/0001-6160(82)90134-1	journal	December 1982
Stability range of the ternary W-phase in the system Al–Co–Ni Katrych, S.; Steurer, W. Journal of Alloys and Compounds, Vol. 481, Issue 1-2 https://doi.org/10.1016/j.jallcom.2009.03.096	journal	July 2009
The existence regions of structural modifications in decagonal Al-Co-Ni Ritsch, S.; Beeli, C.; Nissen, H. U. Philosophical Magazine Letters, Vol. 78, Issue 2 https://doi.org/10.1080/095008398178048	journal	August 1998
Microstructure informatics using higher-order statistics and efficient data-mining protocols Kalidindi, Surya R.; Niezgoda, Stephen R.; Salem, Ayman A. JOM, Vol. 63, Issue 4 https://doi.org/10.1007/s11837-011-0057-7	journal	April 2011
The shape of crystals to come Villain, J. Nature, Vol. 350, Issue 6316 https://doi.org/10.1038/350273a0	journal	March 1991
Structure model of the Al-Cu-Co decagonal quasicrystal Burkov, S. E. Physical Review Letters, Vol. 67, Issue 5 https://doi.org/10.1103/PhysRevLett.67.614	journal	July 1991
Numerical Computation of the Schwarz–Christoffel Transformation Trefethen, Lloyd N. SIAM Journal on Scientific and Statistical Computing, Vol. 1, Issue 1 https://doi.org/10.1137/0901004	journal	March 1980

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Title: A side-by-side comparison of the solidification dynamics of quasicrystalline and approximant phases in the Al–Co–Ni system

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