Advanced search
Publication Cover
Philosophical Magazine Volume 86, 2006 - Issue 6-8: Proceedings of the 9th International Conference on Quasicrystals, 22–26 May 2005, Part 2 Guest Editors: Cynthia J. Jenks, Daniel J. Sordelet and Patricia Thiel
Submit an article Journal homepage
608
Views
88
CrossRef citations to date
0
Altmetric
Original Articles

Effective potentials for quasicrystals from ab-initio data

P. Brommer Institut für Theoretische und Angewandte Physik, Universität Stuttgart, 70550 Stuttgart, GermanyCorrespondence[email protected]
&
F. Gähler Institut für Theoretische und Angewandte Physik, Universität Stuttgart, 70550 Stuttgart, Germany
Pages 753-758 | Received 11 May 2005, Accepted 26 Aug 2005, Published online: 19 Aug 2006

Citations (88)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (3)

M. Mihalkovič & C.L. Henley. (2011) Energetics and dynamics of caged Zn4 in i-ScZn. Philosophical Magazine 91:19-21, pages 2548-2556.
Read now
P. Brommer, F. GÄhler & M. Mihalkovi[cbreve]. (2007) Ordering and correlation of cluster orientations in CaCd6. Philosophical Magazine 87:18-21, pages 2671-2677.
Read now
M. Mihalkovič & M. Widom. (2006) Canonical cell model of cadmium-based icosahedral alloys. Philosophical Magazine 86:3-5, pages 519-527.
Read now

Articles from other publishers (85)

Sho Hayakawa & Haixuan Xu. (2024) Development of an interatomic potential for L12 precipitates in Fe–Ni–Al alloys. Computational Materials Science 232, pages 112614.
Crossref
Yimei Fang, Yang Sun, Renhai Wang, Feng Zheng, Feng Zhang, Shunqing Wu, Cai-Zhuang Wang, Renata M. Wentzcovitch & Kai-Ming Ho. (2023) Structural prediction of Fe-Mg-O compounds at super-Earth's pressures. Physical Review Materials 7:11.
Crossref
Tianxing Yang, Xiujun Han, Wei Li, Xiaohong Chen & Ping Liu. (2023) Angular dependent potential for Al-Zr binary system to study the initial heterogeneous nucleation behavior of liquid Al on L12-Al3Zr. Computational Materials Science 230, pages 112480.
Crossref
William A. Angermeier, Brett S. Scheiner, Nathaniel R. Shaffer & Thomas G. White. (2023) Disentangling the effects of non-adiabatic interactions upon ion self-diffusion within warm dense hydrogen. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 381:2253.
Crossref
Jiaying Sun, Renhai Wang, Zhiyuan Ding, Xunjiang Zhang, QianRong Zhang, Bingkai Zhang, Huafeng Dong & Fugen Wu. (2023) Layered Li–Co–B as a Low-Potential Anode for Lithium-Ion Batteries. Inorganic Chemistry 62:21, pages 8136-8144.
Crossref
Brendon Waters, Daniel S. Karls, Ilia Nikiforov, Ryan S. Elliott, Ellad B. Tadmor & Brandon Runnels. (2023) Automated determination of grain boundary energy and potential-dependence using the OpenKIM framework. Computational Materials Science 220, pages 112057.
Crossref
Shaodong Zhang, Shuangru Li, Lei Wei, Huadi Zhang, Xuping Wang, Bing Liu, Yuanyuan Zhang, Rui Zhang & Chengcheng Qiu. (2023) Wide-Temperature Tunable Phonon Thermal Switch Based on Ferroelectric Domain Walls of Tetragonal KTN Single Crystal. Nanomaterials 13:3, pages 376.
Crossref
Feng Zheng, Yang Sun, Renhai Wang, Yimei Fang, Feng Zhang, Shunqing Wu, Cai-Zhuang Wang, Vladimir Antropov & Kai-Ming Ho. (2023) Superconductivity in the Li-B-C system at 100 GPa. Physical Review B 107:1.
Crossref
M. W. C. Dharma-wardana, Lucas J. Stanek & Michael S. Murillo. (2022) Yukawa-Friedel-tail pair potentials for warm dense matter applications. Physical Review E 106:6.
Crossref
Feng Zheng, Yang Sun, Renhai Wang, Yimei Fang, Feng Zhang, Bo Da, Shunqing Wu, Cai-Zhuang Wang, Renata M. Wentzcovitch & Kai-Ming Ho. (2022) Structure and motifs of iron oxides from 1 to 3 TPa. Physical Review Materials 6:4.
Crossref
Yimei Fang, Yang Sun, Renhai Wang, Feng Zheng, Shunqing Wu, Cai-Zhuang Wang, Renata M. Wentzcovitch & Kai-Ming Ho. (2021) Unconventional iron-magnesium compounds at terapascal pressures. Physical Review B 104:14.
Crossref
Renhai Wang, Yang Sun, Renata M Wentzcovitch, Feng Zheng, Yimei Fang, Shunqing Wu, Zijing Lin, Cai-Zhuang Wang & Kai-Ming Ho. (2021) Prediction of crystal structures and motifs in the Fe–Mg–O system at Earth’s core pressures. New Journal of Physics 23:6, pages 063050.
Crossref
Lucas J. Stanek, Raymond C. ClayIIIIII, M. W. C. Dharma-wardana, Mitchell A. Wood, Kristian R. C. Beckwith & Michael S. Murillo. (2021) Efficacy of the radial pair potential approximation for molecular dynamics simulations of dense plasmas. Physics of Plasmas 28:3.
Crossref
Bo Lin, Jincheng Wang, Junjie Li & Zhijun Wang. (2020) A neural-network based framework of developing cross interaction in alloy embedded-atom method potentials: application to Zr–Nb alloy. Journal of Physics: Condensed Matter 33:8, pages 084004.
Crossref
Aravind Krishnamoorthy, Ankit Mishra, Deepak Kamal, Sungwook Hong, Ken-ichi Nomura, Subodh Tiwari, Aiichiro Nakano, Rajiv Kalia, Rampi Ramprasad & Priya Vashishta. (2021) EZFF: Python library for multi-objective parameterization and uncertainty quantification of interatomic forcefields for molecular dynamics. SoftwareX 13, pages 100663.
Crossref
Bernd BauerhenneBernd Bauerhenne. 2021. Materials Interaction with Femtosecond Lasers. Materials Interaction with Femtosecond Lasers 275 322 .
Haiyan Wang, Xueyun Gao, Shuming Chen, Yiming Li, Zhongwang Wu & Huiping Ren. (2020) Effects of Al on the precipitation of B2 Cu-rich particles in Fe–Cu ferritic alloy: Experimental and theoretical study. Journal of Alloys and Compounds 846, pages 156386.
Crossref
Bo Lin, Junjie Li, Zhijun Wang & Jincheng Wang. (2020) Dislocation nucleation from Zr–Nb bimetal interfaces cooperating with the dynamic evolution of interfacial dislocations. International Journal of Plasticity 135, pages 102830.
Crossref
D. S. Karls, M. Bierbaum, A. A. Alemi, R. S. Elliott, J. P. Sethna & E. B. Tadmor. (2020) The OpenKIM processing pipeline: A cloud-based automatic material property computation engine. The Journal of Chemical Physics 153:6.
Crossref
Balamurugan Balasubramanian, Masahiro Sakurai, Cai-Zhuang Wang, Xiaoshan Xu, Kai-Ming Ho, James R. Chelikowsky & David J. Sellmyer. (2020) Synergistic computational and experimental discovery of novel magnetic materials. Molecular Systems Design & Engineering 5:6, pages 1098-1117.
Crossref
Renhai Wang, Yang Sun, Volodymyr Gvozdetskyi, Xin Zhao, Feng Zhang, Lin-Han Xu, Julia V. Zaikina, Zijing Lin, Cai-Zhuang Wang & Kai-Ming Ho. (2020) Theoretical search for possible Li–Ni–B crystal structures using an adaptive genetic algorithm. Journal of Applied Physics 127:9.
Crossref
Xin Zhao, Shunqing Wu, Manh Cuong Nguyen, Kai-Ming Ho & Cai-Zhuang Wang. 2020. Handbook of Materials Modeling. Handbook of Materials Modeling 2757 2776 .
Sarah Longbottom & Peter Brommer. (2019) Uncertainty quantification for classical effective potentials: an extension to potfit . Modelling and Simulation in Materials Science and Engineering 27:4, pages 044001.
Crossref
Yanan Wang, Yongliang Shi, Chuanyu Zhao, Qijing Zheng & Jin Zhao. (2019) Photogenerated carrier dynamics at the anatase/rutile interface . Physical Review B 99:16.
Crossref
Xin Zhao, Shunqing Wu, Manh Cuong Nguyen, Kai-Ming Ho & Cai-Zhuang Wang. 2018. Handbook of Materials Modeling. Handbook of Materials Modeling 1 20 .
Zejin Yang, Shunqing Wu, Xin Zhao, Manh Cuong Nguyen, Shu Yu, Tongqi Wen, Ling Tang, Fuxiang Li, Kai-Ming Ho & Cai-Zhuang Wang. (2018) Structures and magnetic properties of iron silicide from adaptive genetic algorithm and first-principles calculations. Journal of Applied Physics 124:7.
Crossref
Xin Gui, Xin Zhao, Zuzanna Sobczak, Cai-Zhuang Wang, Tomasz Klimczuk, Kai-Ming Ho & Weiwei Xie. (2018) Ternary Bismuthide SrPtBi 2 : Computation and Experiment in Synergism to Explore Solid-State Materials . The Journal of Physical Chemistry C 122:9, pages 5057-5063.
Crossref
S.V. Starikov, L.N. Kolotova, A.Yu. Kuksin, D.E. Smirnova & V.I. Tseplyaev. (2018) Atomistic simulation of cubic and tetragonal phases of U-Mo alloy: Structure and thermodynamic properties. Journal of Nuclear Materials 499, pages 451-463.
Crossref
Haiyan Wang, Zhaofeng Yao, Xueyun Gao, Peng Cui & Huiping Ren. (2018) Molecular Dynamics Investigation of the Effect of Lanthanum on the Diffusivity of Niobium in Austenite. MATERIALS TRANSACTIONS 59:5, pages 706-711.
Crossref
Mingjian Wen, Sharmila N. Shirodkar, Petr Plecháč, Efthimios Kaxiras, Ryan S. Elliott & Ellad B. Tadmor. (2017) A force-matching Stillinger-Weber potential for MoS2: Parameterization and Fisher information theory based sensitivity analysis. Journal of Applied Physics 122:24.
Crossref
Xin Zhao, Cai-Zhuang Wang, Minsung Kim & Kai-Ming Ho. (2017) Fe-Cluster Compounds of Chalcogenides: Candidates for Rare-Earth-Free Permanent Magnet and Magnetic Nodal-Line Topological Material. Inorganic Chemistry 56:23, pages 14577-14583.
Crossref
L. P. Bulat, A. A. Ivanov, V. B. Osvenskii, D. A. Pshenay-Severin & A. I. Sorokin. (2017) Thermal conductivity of Cu2Se taking into account the influence of mobile copper ions. Physics of the Solid State 59:10, pages 2097-2102.
Crossref
K. P. Migdal, P. A. Pokatashkin & A. V. Yanilkin. (2017) Investigation of melting at the uranium γ phase by quantum and classical molecular dynamics methods. High Temperature 55:5, pages 711-717.
Crossref
Pui-Wai Ma, S. L. Dudarev & Jan S. Wróbel. (2017) Dynamic simulation of structural phase transitions in magnetic iron. Physical Review B 96:9.
Crossref
Andrew Rohskopf, Hamid R. Seyf, Kiarash Gordiz, Terumasa Tadano & Asegun Henry. (2017) Empirical interatomic potentials optimized for phonon properties. npj Computational Materials 3:1.
Crossref
Xin Zhao, Shu Yu, Shunqing Wu, Manh Cuong Nguyen, Cai-Zhuang Wang & Kai-Ming Ho. (2017) Structures, phase transitions, and magnetic properties of from first-principles calculations . Physical Review B 96:2.
Crossref
S Q Wu, B Balamurugan, X Zhao, S Yu, Manh Cuong Nguyen, Y Sun, S R Valloppilly, D J Sellmyer, K M Ho & C Z Wang. (2017) Exploring new phases of Fe 3− x Co x C for rare-earth-free magnets . Journal of Physics D: Applied Physics 50:21, pages 215005.
Crossref
Sergey StarikovAlexey KuksinDaria SmirnovaAlexey DolgodvorovVladimir Ozrin. (2017) Multiscale Modeling of Uranium Mononitride: Point Defects Diffusion, Self-Diffusion, Phase Composition. Defect and Diffusion Forum 375, pages 101-113.
Crossref
Haimen Mu, Bo Xu, Chuying Ouyang & Xueling Lei. (2017) Highly optimized embedding atom method potential for Pt-Cu alloys. Journal of Alloys and Compounds 696, pages 470-480.
Crossref
D.E. Smirnova & S.V. Starikov. (2017) An interatomic potential for simulation of Zr-Nb system. Computational Materials Science 129, pages 259-272.
Crossref
Albert M Iskandarov, Yingna Ding & Yoshitaka Umeno. (2017) Effect of cation dopants in zirconia on interfacial properties in nickel/zirconia systems: an atomistic modeling study. Journal of Physics: Condensed Matter 29:4, pages 045001.
Crossref
Mingjian Wen, Junhao Li, Peter Brommer, Ryan S Elliott, James P Sethna & Ellad B Tadmor. (2017) A KIM-compliant potfit for fitting sloppy interatomic potentials: application to the EDIP model for silicon . Modelling and Simulation in Materials Science and Engineering 25:1, pages 014001.
Crossref
A. S. Rokhmanenkov, A. Yu. Kuksin & A. V. Yanilkin. (2017) Simulation of hydrogen diffusion in TiH x structures. Physics of Metals and Metallography 118:1, pages 28-38.
Crossref
Kirill P. Migdal, Pavel A. Pokatashkin & Alexey V. Yanilkin. Thermodynamic properties and phase transitions of γ and liquid uranium: QMD and classical MD modeling. Thermodynamic properties and phase transitions of γ and liquid uranium: QMD and classical MD modeling.
P. Korotaev, A. Kuksin, P. Pokatashkin & A. Yanilkin. Quantum and classical molecular dynamics simulation of boron carbide behavior under pressure. Quantum and classical molecular dynamics simulation of boron carbide behavior under pressure.
Yongliang Shi, Huijuan Sun, Manh Cuong Nguyen, Caizhuang Wang, Kaiming Ho, Wissam A. Saidi & Jin Zhao. (2017) Structures of defects on anatase TiO 2 (001) surfaces . Nanoscale 9:32, pages 11553-11565.
Crossref
J. Roth, A. Kiselev & H.-R. Trebin. (2016) Studying laser ablation with molecular dynamics simulations: From metals to covalent materials. Studying laser ablation with molecular dynamics simulations: From metals to covalent materials.
Xin Zhao, Liqin Ke, Cai-Zhuang Wang & Kai-Ming Ho. (2016) Metastable cobalt nitride structures with high magnetic anisotropy for rare-earth free magnets. Physical Chemistry Chemical Physics 18:46, pages 31680-31690.
Crossref
P. Wu, S. Q. Wu, X. Lv, X. Zhao, Z. Ye, Z. Lin, C. Z. Wang & K. M. Ho. (2016) Fe–Si networks in Na 2 FeSiO 4 cathode materials . Physical Chemistry Chemical Physics 18:34, pages 23916-23922.
Crossref
Alexander Kiselev, Johannes Roth & Hans-Rainer Trebin. 2016. High Performance Computing in Science and Engineering ´16. High Performance Computing in Science and Engineering ´16 189 202 .
Ning Wang, Jie Tian, Tao Jiang, Yanqiu Yang, Sheng Hu, Shuming Peng & Liuming Yan. (2015) Energetics of gaseous and volatile fission products in molten U–10Zr alloy: A density functional theory study. Journal of Nuclear Materials 466, pages 583-587.
Crossref
Peter Brommer, Alexander Kiselev, Daniel Schopf, Philipp Beck, Johannes Roth & Hans-Rainer Trebin. (2015) Classical interaction potentials for diverse materials from ab initio data: a review of potfit . Modelling and Simulation in Materials Science and Engineering 23:7, pages 074002.
Crossref
Xin Zhao, Liqin Ke, Manh Cuong Nguyen, Cai-Zhuang Wang & Kai-Ming Ho. (2015) Structures and magnetic properties of Co-Zr-B magnets studied by first-principles calculations. Journal of Applied Physics 117:24.
Crossref
P Pokatashkin, A Kuksin & A Yanilkin. (2015) Angular dependent potential for α -boron and large-scale molecular dynamics simulations . Modelling and Simulation in Materials Science and Engineering 23:4, pages 045014.
Crossref
D.E. Smirnova, A.Yu. Kuksin & S.V. Starikov. (2015) Investigation of point defects diffusion in bcc uranium and U–Mo alloys. Journal of Nuclear Materials 458, pages 304-311.
Crossref
Hua Y. Geng. (2015) Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface. Journal of Computational Physics 283, pages 299-311.
Crossref
Albert M Iskandarov, Atsushi Kubo & Yoshitaka Umeno. (2015) Development of a new dipole model: interatomic potential for yttria-stabilized zirconia for bulk and surface. Journal of Physics: Condensed Matter 27:1, pages 015005.
Crossref
Ning Wang, Tao Jiang, Yanqiu Yang, Jie Tian, Sheng Hu, Shuming Peng & Liuming Yan. (2015) Embedded atom model for the liquid U–10Zr alloy based on density functional theory calculations. RSC Advances 5:76, pages 61495-61501.
Crossref
Feng Zhang, Min Ji, Xiao-Wei Fang, Yang Sun, Cai-Zhuang Wang, Mikhail I. Mendelev, M.J. Kramer, Ralph E. Napolitano & Kai-Ming Ho. (2014) Composition-dependent stability of the medium-range order responsible for metallic glass formation. Acta Materialia 81, pages 337-344.
Crossref
S. V. Starikov, A. Ya. Faenov, T. A. Pikuz, I. Yu. Skobelev, V. E. Fortov, S. Tamotsu, M. Ishino, M. Tanaka, N. Hasegawa, M. Nishikino, T. Kaihori, T. Imazono, M. Kando & T. Kawachi. (2014) Soft picosecond X-ray laser nanomodification of gold and aluminum surfaces. Applied Physics B 116:4, pages 1005-1016.
Crossref
Daniel Schopf, Holger Euchner & Hans-Rainer Trebin. (2014) Effective potentials for simulations of the thermal conductivity of type-I semiconductor clathrate systems. Physical Review B 89:21.
Crossref
Xin Zhao, Qiang Shu, Manh Cuong Nguyen, Yangang Wang, Min Ji, Hongjun Xiang, Kai-Ming Ho, Xingao Gong & Cai-Zhuang Wang. (2014) Interface Structure Prediction from First-Principles. The Journal of Physical Chemistry C 118:18, pages 9524-9530.
Crossref
S Q Wu, M Ji, C Z Wang, M C Nguyen, X Zhao, K Umemoto, R M Wentzcovitch & K M Ho. (2014) An adaptive genetic algorithm for crystal structure prediction. Journal of Physics: Condensed Matter 26:3, pages 035402.
Crossref
X. Zhao, M. C. Nguyen, W. Y. Zhang, C. Z. Wang, M. J. Kramer, D. J. Sellmyer, X. Z. Li, F. Zhang, L. Q. Ke, V. P. Antropov & K. M. Ho. (2014) Exploring the Structural Complexity of Intermetallic Compounds by an Adaptive Genetic Algorithm. Physical Review Letters 112:4.
Crossref
Manh Cuong Nguyen, Jin-Ho Choi, Xin Zhao, Cai-Zhuang Wang, Zhenyu Zhang & Kai-Ming Ho. (2013) New Layered Structures of Cuprous Chalcogenides as Thin Film Solar Cell Materials: and . Physical Review Letters 111:16.
Crossref
Manh Cuong Nguyen, Liqin Ke, Xin Zhao, Vladimir Antropov, Cai-Zhuang Wang & Kai-Ming Ho. (2013) Atomic Structure and Magnetic Properties of HfCo$_{7}$ Alloy. IEEE Transactions on Magnetics 49:7, pages 3281-3283.
Crossref
D E Smirnova, A Yu Kuksin, S V Starikov, V V Stegailov, Z Insepov, J Rest & A M Yacout. (2013) A ternary EAM interatomic potential for U–Mo alloys with xenon. Modelling and Simulation in Materials Science and Engineering 21:3, pages 035011.
Crossref
Cristian V. Ciobanu, Cai‐Zhuang Wang & Kai‐Ming Ho. 2013. Atomic Structure Prediction of Nanostructures, Clusters and Surfaces. Atomic Structure Prediction of Nanostructures, Clusters and Surfaces 37 69 .
G. E. Norman, S. V. Starikov, V. V. Stegailov, I. M. Saitov & P. A. Zhilyaev. (2013) Atomistic Modeling of Warm Dense Matter in the Two-Temperature State. Contributions to Plasma Physics 53:2, pages 129-139.
Crossref
Xin Zhao, Manh Cuong Nguyen, Cai-Zhuang Wang & Kai-Ming Ho. (2013) Structures and stabilities of alkaline earth metal peroxides XO2 (X = Ca, Be, Mg) studied by a genetic algorithm. RSC Advances 3:44, pages 22135.
Crossref
Philipp Beck, Peter Brommer, Johannes Roth & Hans-Rainer Trebin. (2012) Influence of polarizability on metal oxide properties studied by molecular dynamics simulations. Journal of Physics: Condensed Matter 24:48, pages 485401.
Crossref
D. E. Smirnova, S. V. Starikov & V. V. Stegailov. (2012) New interatomic potential for computation of mechanical and thermodynamic properties of uranium in a wide range of pressures and temperatures. The Physics of Metals and Metallography 113:2, pages 107-116.
Crossref
Daniel Schopf, Peter Brommer, Benjamin Frigan & Hans-Rainer Trebin. (2012) Embedded atom method potentials for Al-Pd-Mn phases. Physical Review B 85:5.
Crossref
D E Smirnova, S V Starikov & V V Stegailov. (2012) Interatomic potential for uranium in a wide range of pressures and temperatures. Journal of Physics: Condensed Matter 24:1, pages 015702.
Crossref
Philipp Beck, Peter Brommer, Johannes Roth & Hans-Rainer Trebin. (2011) Ab initio based polarizable force field generation and application to liquid silica and magnesia . The Journal of Chemical Physics 135:23.
Crossref
Min Ji, Koichiro Umemoto, Cai-Zhuang Wang, Kai-Ming Ho & Renata M. Wentzcovitch. (2011) Ultrahigh-pressure phases of H O ice predicted using an adaptive genetic algorithm . Physical Review B 84:22.
Crossref
Wang Zhao-Ke, Wu Yong-Quan, Shen Tong, Liu Yi-Hu & Jiang Guo-Chang. (2011) Long-range Finnis-Sinclair potential for Zn-Mg alloy. Acta Physica Sinica 60:8, pages 086105.
Crossref
Lee-Ping Wang & Troy Van Voorhis. (2010) Communication: Hybrid ensembles for improved force matching. The Journal of Chemical Physics 133:23.
Crossref
Michael Engel, Masahiro Umezaki, Hans-Rainer Trebin & Takashi Odagaki. (2010) Dynamics of particle flips in two-dimensional quasicrystals. Physical Review B 82:13.
Crossref
S. Sonntag, J. Roth & H.-R. Trebin. (2010) Molecular dynamics simulations of laser induced surface melting in orthorhombic Al13Co4. Applied Physics A 101:1, pages 77-80.
Crossref
Michael R. Fellinger, Hyoungki Park & John W. Wilkins. (2010) Force-matched embedded-atom method potential for niobium. Physical Review B 81:14.
Crossref
Peter Brommer & Franz Gähler. (2007) Potfit: effective potentials from ab initio data . Modelling and Simulation in Materials Science and Engineering 15:3, pages 295-304.
Crossref
Erik Bitzek, Pekka Koskinen, Franz Gähler, Michael Moseler & Peter Gumbsch. (2006) Structural Relaxation Made Simple. Physical Review Letters 97:17.
Crossref
Frohmut Rösch, Hans-Rainer Trebin & Peter Gumbsch. (2006) Interatomic potentials and the simulation of fracture: C15 NbCr2. International Journal of Fracture 139:3-4, pages 517-526.
Crossref
Franz Gähler & Katharina Benkert. 2006. High Performance Computing on Vector Systems. High Performance Computing on Vector Systems 173 186 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.