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Rettenmaier C, Herzog A, Casari D, Rüscher M, Jeon HS, Kordus D, Luna ML, Kühl S, Hejral U, Davis EM, Chee SW, Timoshenko J, Alexander DTL, Bergmann A, Cuenya BR. Operando insights into correlating CO coverage and Cu-Au alloying with the selectivity of Au NP-decorated Cu 2O nanocubes during the electrocatalytic CO 2 reduction. EES CATALYSIS 2024; 2:311-323. [PMID: 38222061 PMCID: PMC10782806 DOI: 10.1039/d3ey00162h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 10/20/2023] [Indexed: 01/16/2024]
Abstract
Electrochemical reduction of CO2 (CO2RR) is an attractive technology to reintegrate the anthropogenic CO2 back into the carbon cycle driven by a suitable catalyst. This study employs highly efficient multi-carbon (C2+) producing Cu2O nanocubes (NCs) decorated with CO-selective Au nanoparticles (NPs) to investigate the correlation between a high CO surface concentration microenvironment and the catalytic performance. Structure, morphology and near-surface composition are studied via operando X-ray absorption spectroscopy and surface-enhanced Raman spectroscopy, operando high-energy X-ray diffraction as well as quasi in situ X-ray photoelectron spectroscopy. These operando studies show the continuous evolution of the local structure and chemical environment of our catalysts during reaction conditions. Along with its alloy formation, a CO-rich microenvironment as well as weakened average CO binding on the catalyst surface during CO2RR is detected. Linking these findings to the catalytic function, a complex compositional interplay between Au and Cu is revealed in which higher Au loadings primarily facilitate CO formation. Nonetheless, the strongest improvement in C2+ formation appears for the lowest Au loadings, suggesting a beneficial role of the Au-Cu atomic interaction for the catalytic function in CO2RR. This study highlights the importance of site engineering and operando investigations to unveil the electrocatalyst's adaptations to the reaction conditions, which is a prerequisite to understand its catalytic behavior.
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Affiliation(s)
- Clara Rettenmaier
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - Antonia Herzog
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - Daniele Casari
- Electron Spectrometry and Microscopy Laboratory (LSME), Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne (EPFL) Lausanne CH-1015 Switzerland
| | - Martina Rüscher
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - Hyo Sang Jeon
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - David Kordus
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - Mauricio Lopez Luna
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - Stefanie Kühl
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - Uta Hejral
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - Earl M Davis
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - See Wee Chee
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - Janis Timoshenko
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - Duncan T L Alexander
- Electron Spectrometry and Microscopy Laboratory (LSME), Institute of Physics (IPHYS), École Polytechnique Fédérale de Lausanne (EPFL) Lausanne CH-1015 Switzerland
| | - Arno Bergmann
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
| | - Beatriz Roldan Cuenya
- Department of Interface Science, Fritz-Haber-Institute of the Max-Planck Society Faradayweg 4-6 14195 Berlin Germany
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Maji TK, Vaibhav K, Hawaldar R, Adarsh KV, Pal SK, Karmakar D. Intriguing electronic and optical prospects of FCC bimetallic two-dimensional heterostructures: epsilon near-zero behavior in UV-Vis range. Phys Chem Chem Phys 2020; 22:16314-16324. [PMID: 32647839 DOI: 10.1039/d0cp00951b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A higher superconducting critical temperature and large-area epsilon-near-zero systems are two long-standing goals of the scientific community, having an explicit relationship with the correlated electrons in localized orbitals. Motivated by the recent experimental findings of the strongly correlated phenomena in nanostructures of simple Drude metallic systems, we have theoretically investigated some potential bimetallic FCC combinations having close resemblance with the experimental systems. The explored systems include the large-area interface to the embedded and doped two-dimensional (2D) combinatorial nanostructures. Using different effective single-particle first-principles approaches encompassing density functional theory (DFT), time-dependent DFT (TDDFT), phonon and DFT-coupled quantum transport, we propose some interesting correlated prospects of potential bimetallic nanostructures like Au/Ag and Pt/Pd. For the 2D doped and embedded nanostructures of these systems, the DFT-calculated non-trivial band-structures indicate the interfacial morphology-induced band localization. The calculated Fermi-surface topology of the nanostructures and the corresponding nesting behavior may be emblematic to the presence of instabilities, such as charge density waves. The optical attributes extracted from the TDDFT calculations result in near-zero behavior of both real and imaginary parts of the dynamical dielectric response in the ultra-violet to visible (UV-Vis) optical range. In addition, low-energy intra-band plasmonic oscillations, as present for individual metallic surfaces, are completely suppressed for the embedded and doped nanostructures. The TDDFT-derived electron-energy loss spectra manifest the survival of only inter-band transitions. The presence of soft phonons and dynamic instabilities is observed from the phonon-dispersion of the nanostructured systems. Quantum transport calculations on the simplest possible device made out of these bimetallic systems reveal the generation of highly transmitting pockets over the cross-sectional area for some selected device geometry. We envisage that, if scrutinized experimentally, such systems may unveil many fascinating interdisciplinary aspects of orbital chemistry, physics and optics, promoting their relevant applications in many diverse fields.
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Affiliation(s)
- Tuhin Kumar Maji
- Department of Chemical Biological and Macromolecular Sciences, S.N. Bose National Centre for Basics Sciences, Salt Lake, Sector 3, Kolkata 700106, India
| | - Kumar Vaibhav
- Computer Division, Bhabha Atomic Research Centre, Trombay 400085, India
| | - Ranjit Hawaldar
- Centre for Materials for Electronics Technology, Off Pashan Road, Panchwati, Pune-411008, India
| | - K V Adarsh
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462066, India
| | - Samir Kumar Pal
- Department of Chemical Biological and Macromolecular Sciences, S.N. Bose National Centre for Basics Sciences, Salt Lake, Sector 3, Kolkata 700106, India
| | - Debjani Karmakar
- Technical Physics Division, Bhabha Atomic Research Centre, Trombay 400085, India.
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Asselin J, Boukouvala C, Wu Y, Hopper ER, Collins SM, Biggins JS, Ringe E. Decoration of plasmonic Mg nanoparticles by partial galvanic replacement. J Chem Phys 2019; 151:244708. [PMID: 31893891 DOI: 10.1063/1.5131703] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Plasmonic structures have attracted much interest in science and engineering disciplines, exploring a myriad of potential applications owing to their strong light-matter interactions. Recently, the plasmonic concentration of energy in subwavelength volumes has been used to initiate chemical reactions, for instance by combining plasmonic materials with catalytic metals. In this work, we demonstrate that plasmonic nanoparticles of earth-abundant Mg can undergo galvanic replacement in a nonaqueous solvent to produce decorated structures. This method yields bimetallic architectures where partially oxidized 200-300 nm Mg nanoplates and nanorods support many smaller Au, Ag, Pd, or Fe nanoparticles, with potential for a stepwise process introducing multiple decoration compositions on a single Mg particle. We investigated this mechanism by electron-beam imaging and local composition mapping with energy-dispersive X-ray spectroscopy as well as, at the ensemble level, by inductively coupled plasma mass spectrometry. High-resolution scanning transmission electron microscopy further supported the bimetallic nature of the particles and provided details of the interface geometry, which includes a Mg oxide separation layer between Mg and the other metal. Depending on the composition of the metallic decorations, strong plasmonic optical signals characteristic of plasmon resonances were observed in the bulk with ultraviolet-visible spectrometry and at the single particle level with darkfield scattering. These novel bimetallic and multimetallic designs open up an exciting array of applications where one or multiple plasmonic structures could interact in the near-field of earth-abundant Mg and couple with catalytic nanoparticles for applications in sensing and plasmon-assisted catalysis.
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Affiliation(s)
- Jérémie Asselin
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, United Kingdom
| | - Christina Boukouvala
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, United Kingdom
| | - Yuchen Wu
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, United Kingdom
| | - Elizabeth R Hopper
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, United Kingdom
| | - Sean M Collins
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, United Kingdom
| | - John S Biggins
- Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, United Kingdom
| | - Emilie Ringe
- Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, United Kingdom
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Meischein M, Garzón-Manjón A, Frohn T, Meyer H, Salomon S, Scheu C, Ludwig A. Combinatorial Synthesis of Binary Nanoparticles in Ionic Liquids by Cosputtering and Mixing of Elemental Nanoparticles. ACS COMBINATORIAL SCIENCE 2019; 21:743-752. [PMID: 31614084 DOI: 10.1021/acscombsci.9b00140] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Binary alloy nanoparticles were fabricated by two combinatorial methods: (I) cosputtering from elemental targets into the ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [Bmim][(Tf)2N] and (II) by mixing elemental nanoparticles after sputtering them separately into [Bmim][(Tf)2N]. Both methods lead to the formation of Au-Cu nanoparticles (2.3 nm for cosputtered, 3.6 nm for mixed), however with different resulting compositions: cosputtered nanoparticles show a composition range of Au80-90Cu20-10; mixing of Au- and Cu-loaded ionic liquids leads to the formation of Au75Cu25 nanoparticles. Annealing the binary nanoparticles at 100 °C shows that the mixed nanoparticles grow to sizes of 4.1 nm, whereas the cosputtered nanoparticles grow only to 3 nm.
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Affiliation(s)
- Michael Meischein
- Chair for Materials Discovery and Interfaces, Institute for Materials, Faculty of Mechanical Engineering, Ruhr University Bochum, Universitätsstr. 150, D-44780 Bochum, Germany
| | - Alba Garzón-Manjón
- Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Straße 1, D-40237 Düsseldorf, Germany
| | - Thomas Frohn
- Chair for Materials Discovery and Interfaces, Institute for Materials, Faculty of Mechanical Engineering, Ruhr University Bochum, Universitätsstr. 150, D-44780 Bochum, Germany
| | - Hajo Meyer
- Chair for Materials Discovery and Interfaces, Institute for Materials, Faculty of Mechanical Engineering, Ruhr University Bochum, Universitätsstr. 150, D-44780 Bochum, Germany
| | - Steffen Salomon
- Chair for Materials Discovery and Interfaces, Institute for Materials, Faculty of Mechanical Engineering, Ruhr University Bochum, Universitätsstr. 150, D-44780 Bochum, Germany
| | - Christina Scheu
- Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Straße 1, D-40237 Düsseldorf, Germany
| | - Alfred Ludwig
- Chair for Materials Discovery and Interfaces, Institute for Materials, Faculty of Mechanical Engineering, Ruhr University Bochum, Universitätsstr. 150, D-44780 Bochum, Germany
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Rebello Sousa Dias M, Leite MS. Alloying: A Platform for Metallic Materials with On-Demand Optical Response. Acc Chem Res 2019; 52:2881-2891. [PMID: 31305980 DOI: 10.1021/acs.accounts.9b00153] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Metallic materials with engineered optical properties have the potential to enhance the performance of energy harvesting and storage devices operating at the macro- and nanoscale, such as solar cells, photocatalysts, water splitting, and hydrogen storage systems. For both thin films and subwavelength nanostructures, upon illumination, the coherent oscillation of charge carriers at the interface with a dielectric material gives rise to resonances named surface plasmon polariton (SPP) and localized surface plasmon resonance (LSPR), respectively. These resonances result in unique light absorption, scattering, and transmission responses over the electromagnetic spectrum, which, in turn, can be exploited to tailor the behavior of active metallic components in optoelectronic devices containing Ag, Au, Cu, Al, Mg, among other metals. The wavelength in which the resonances occur primarily depends on the metal itself (i.e., the dielectric function or permittivity), the dielectric medium surrounding the metals, and the size, geometry, and periodicity of the metallic nanostructures. Nevertheless, the aforementioned parameters allow a limited modulation of both SPP and LSPR over a narrow window of frequencies. To overcome this constraint, we have proposed and realized the alloying of metals via physical deposition methods as a paradigm to almost arbitrarily tuning their optical behavior in the UV-NIR, which leads to permittivity values currently not available. Our approach offers an additional knob, chemical composition, to engineer light-matter interactions in metallic materials. This Account highlights recent progress in using alloying as a pathway to control the optical behavior of metallic thin films and nanostructures for energy harvesting and storage applications, including (photo)catalysis, photovoltaics, superabsorbers, hydrogen storage, among other systems. We choose to primarily focus on the optical properties of the metallic mixtures and in their near- to far-field responses in the UV-NIR range of the spectrum as they represent key parameters for materials' selection for the devices above. By alloying, it is possible to obtain metallic materials with LSPR not available for pure metals, which can enable the further control of the electromagnetic spectrum. First, we discuss how the permittivity of binary mixtures of coinage metals (Au, Ag, and Cu) can be tailored based on the chemical composition of their pure counterparts. Second, we present how novel metallic materials can be designed through band structure engineering through density functional theory (DFT), a paradigm that could benefit from artificial intelligence methods. Concerning alloyed thin films, we discuss the promise of earth-abundant metals and provide an example of the superior performance of AlCu in superabsorbers. In the realm of nanostructures, we focus the discussion on physical deposition methods, where we provide a detailed analysis of how chemical composition can affect the far- and near-field responses of metallic building blocks. Finally, we provide a brief outlook of promising next steps in the field.
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Affiliation(s)
| | - Marina S. Leite
- Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, United States
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, United States
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Chang JH, Kleiven D, Melander M, Akola J, Garcia-Lastra JM, Vegge T. CLEASE: a versatile and user-friendly implementation of cluster expansion method. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:325901. [PMID: 31013487 DOI: 10.1088/1361-648x/ab1bbc] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Materials exhibiting a substitutional disorder such as multicomponent alloys and mixed metal oxides/oxyfluorides are of great importance in many scientific and technological sectors. Disordered materials constitute an overwhelmingly large configurational space, which makes it practically impossible to be explored manually using first-principles calculations such as density functional theory due to the high computational costs. Consequently, the use of methods such as cluster expansion (CE) is vital in enhancing our understanding of the disordered materials. CE dramatically reduces the computational cost by mapping the first-principles calculation results on to a Hamiltonian which is much faster to evaluate. In this work, we present our implementation of the CE method, which is integrated as a part of the atomic simulation environment (ASE) open-source package. The versatile and user-friendly code automates the complex set up and construction procedure of CE while giving the users the flexibility to tweak the settings and to import their own structures and previous calculation results. Recent advancements such as regularization techniques from machine learning are implemented in the developed code. The code allows the users to construct CE on any bulk lattice structure, which makes it useful for a wide range of applications involving complex materials. We demonstrate the capabilities of our implementation by analyzing the two example materials with varying complexities: a binary metal alloy and a disordered lithium chromium oxyfluoride.
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Affiliation(s)
- Jin Hyun Chang
- Department of Energy Conversion and Storage, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
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7
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Xie Y, Dimitrov N. Highly Active and Durable Cu x Au (1-x) Ultrathin-Film Catalysts for Nitrate Electroreduction Synthesized by Surface-Limited Redox Replacement. ACS OMEGA 2018; 3:17676-17686. [PMID: 31458367 PMCID: PMC6643547 DOI: 10.1021/acsomega.8b02148] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/23/2018] [Accepted: 12/03/2018] [Indexed: 06/10/2023]
Abstract
Cu x Au(1-x) bimetallic ultrathin-film catalysts for nitrate electroreduction have been synthesized using electrochemical atomic layer deposition by surface-limited redox replacement of Pb underpotentially deposited layer. Controlled by the ratio of [Cu2+] ions and [AuCl4 -] complex in the deposition solution, the alloy film composition (atomic fraction, x in the range of 0.5-1) has been determined by X-ray photoelectron spectroscopy and indirectly estimated by anodic stripping voltammetry. The catalytic activity and durability of Cu x Au(1-x) thin films, Cu thin film, and bulk Cu have been studied by one- and multiple-cycle voltammetry. The synthesized Cu x Au(1-x) thin films feature up to two times higher nitrate electroreduction activity in acidic solution compared to bulk and thin-film Cu counterparts. Highest activity has been measured with a Cu0.70Au0.30 catalyst. Durability tests have demonstrated that Cu thin films undergo rapid deactivation losing 65% of its peak activity for 92 cycles, whereas Cu0.70Au0.30 catalysts lose only 45% of their top performance. The significantly better durability of alloy films can be attributed to effective resistance to poisoning and/or hindered dissolution of Cu active centers. It has been also found that both Cu x Au(1-x) and pure Cu thin films show best electroreduction activity at lowest pH.
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8
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Pischetola C, Collado L, Keane MA, Cárdenas-Lizana F. Gas Phase Hydrogenation of Furaldehydes via Coupling with Alcohol Dehydrogenation over Ceria Supported Au-Cu. Molecules 2018; 23:E2905. [PMID: 30405073 PMCID: PMC6278317 DOI: 10.3390/molecules23112905] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2018] [Revised: 11/04/2018] [Accepted: 11/05/2018] [Indexed: 11/16/2022] Open
Abstract
We have investigated the synthesis and application of Au-Cu/CeO₂ (Cu: Au = 2) in the continuous gas phase (P = 1 atm; T = 498 K) coupled hydrogenation of 5-hydroxymethyl-2-furaldehyde (HMF) with 2-butanol dehydrogenation. STEM-EDX analysis revealed a close surface proximity of both metals in Au-Cu/CeO₂ post-TPR. XPS measurements suggest (support → metal) charge transfer to form Auδ- and strong metal-support interactions to generate Cu⁰ and Cu⁺. Au-Cu/CeO₂ promoted the sole formation of 2,5-dihydroxymethylfuran (DHMF) and 2-butanone in the HMF/2-butanol coupling with full hydrogen utilisation. Under the same reaction conditions, Au/CeO₂ was fully selective to DHMF in standard HMF hydrogenation (using an external hydrogen supply), but delivered a lower production rate and utilised less than 0.2% of the hydrogen supplied. Exclusive -C=O hydrogenation and -OH dehydrogenation is also demonstrated for the coupling of a series of m-substituted (-CH₃, -CH₂CH₃, -CH₂OH, -CF₃, -N(CH₃)₂, -H) furaldehydes with alcohol (1-propanol, 1-butanol, 2-propanol, 2-butanol, cyclohexanol) dehydrogenation over Au-Cu/CeO₂, consistent with a nucleophilic mechanism. In each case, we observed a greater hydrogenation rate and hydrogen utilisation efficiency with a 3⁻15 times lower E-factor in the coupling process relative to standard hydrogenation. Our results demonstrate the feasibility of using hydrogen generated in situ through alcohol dehydrogenation for the selective hydrogenation of m-furaldehydes with important industrial applications.
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Affiliation(s)
- Chiara Pischetola
- Chemical Engineering, School of Engineering and Physical Sciences, Heriot Watt University, Edinburgh EH14 4AS, Scotland, UK.
| | - Laura Collado
- Chemical Engineering, School of Engineering and Physical Sciences, Heriot Watt University, Edinburgh EH14 4AS, Scotland, UK.
| | - Mark A Keane
- Chemical Engineering, School of Engineering and Physical Sciences, Heriot Watt University, Edinburgh EH14 4AS, Scotland, UK.
| | - Fernando Cárdenas-Lizana
- Chemical Engineering, School of Engineering and Physical Sciences, Heriot Watt University, Edinburgh EH14 4AS, Scotland, UK.
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9
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Structure and Reactivity of Cu-doped Au(111) Surfaces. E-JOURNAL OF SURFACE SCIENCE AND NANOTECHNOLOGY 2018. [DOI: 10.1380/ejssnt.2018.163] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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10
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Tian LY, Levämäki H, Ropo M, Kokko K, Nagy Á, Vitos L. Exchange-Correlation Catastrophe in Cu-Au: A Challenge for Semilocal Density Functional Approximations. PHYSICAL REVIEW LETTERS 2016; 117:066401. [PMID: 27541469 DOI: 10.1103/physrevlett.117.066401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2016] [Indexed: 06/06/2023]
Abstract
Semilocal density functional approximations occupy the second rung of the Jacob's ladder model and are thus expected to have certain limits to their applicability. A recent study [Y. Zhang, G. Kresse, and C. Wolverton, Phys. Rev. Lett. 112, 075502 (2014)] hypothesizes that the formation energy, being one of the key quantities in alloy theory, would be beyond the grasp of semilocal density functional theory (DFT). Here, we explore the physics of semilocal DFT formation energies and shed light on the connection between the accuracy of the formation energy and the ability of a semilocal approximation to produce accurate lattice constants. We demonstrate that semilocal functionals designed to perform well for alloy constituents can concomitantly solve the problem of alloy formation energies.
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Affiliation(s)
- Li-Yun Tian
- Applied Materials Physics, Department of Materials Science and Engineering, Royal Institute of Technology, Stockholm SE-100 44, Sweden
- Key Laboratory of Materials Modification by Laser, Ion, and Electron Beams of Ministry of Education, Dalian University of Technology, Dalian 116024, China
| | - Henrik Levämäki
- Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland
- Turku University Centre for Materials and Surfaces (MatSurf), FI-20014 Turku, Finland
| | - Matti Ropo
- Tampere University of Technology, Department of Physics, FI-33101 Tampere, Finland
- COMP/Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto, Finland
| | - Kalevi Kokko
- Department of Physics and Astronomy, University of Turku, FI-20014 Turku, Finland
- Turku University Centre for Materials and Surfaces (MatSurf), FI-20014 Turku, Finland
| | - Ágnes Nagy
- Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, Hungary
| | - Levente Vitos
- Applied Materials Physics, Department of Materials Science and Engineering, Royal Institute of Technology, Stockholm SE-100 44, Sweden
- Department of Physics and Astronomy, Division of Materials Theory, Uppsala University, Box 516, SE-75121 Uppsala, Sweden
- Research Institute for Solid State Physics and Optics, Wigner Research Center for Physics, Budapest H-1525, P.O. Box 49, Hungary
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12
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Najdovski I, Selvakannan PR, O'Mullane AP. Cathodic Corrosion of Cu Substrates as a Route to Nanostructured Cu/M (M=Ag, Au, Pd) Surfaces. ChemElectroChem 2014. [DOI: 10.1002/celc.201402259] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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13
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Zhang Y, Kresse G, Wolverton C. Nonlocal first-principles calculations in Cu-Au and other intermetallic alloys. PHYSICAL REVIEW LETTERS 2014; 112:075502. [PMID: 24579611 DOI: 10.1103/physrevlett.112.075502] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2013] [Indexed: 06/03/2023]
Abstract
Cu-Au is the prototypical alloy system used to exemplify ordering and compound formation, and it serves as a testbed for all new alloy theory methods. Yet, despite the importance of this system, conventional density functional theory (DFT) calculations with semilocal approximations have two dramatic failures in describing the energies of this system: (1) DFT formation energies of the observed Cu3Au and CuAu compounds are nearly a factor of 2 smaller in magnitude than experimental values, and (2) DFT predicts incorrect ordered ground states ground states for Au-rich compositions. Here, we show how modern extensions of DFT based on nonlocal interactions can rectify both of these failures. Our corrections shed light on improving the theoretical predictions for alloy systems to determine accurate formation energies, order-disorder critical temperatures, phase diagrams, and high-throughput computations.
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Affiliation(s)
- Yongsheng Zhang
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
| | - Georg Kresse
- Faculty of Physics, Center for Computational Materials Science, Universität Wien, Sensengasse 8/12, A-1090 Wien, Austria
| | - C Wolverton
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
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14
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Duda JC, English TS, Jordan DA, Norris PM, Soffa WA. Reducing thermal conductivity of binary alloys below the alloy limit via chemical ordering. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:205401. [PMID: 21540497 DOI: 10.1088/0953-8984/23/20/205401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Substitutional solid solutions that exist in both ordered and disordered states will exhibit markedly different physical properties depending on their exact crystallographic configuration. Many random substitutional solid solutions (alloys) will display a tendency to order given the appropriate kinetic and thermodynamic conditions. Such order-disorder transitions will result in major crystallographic reconfigurations, where the atomic basis, symmetry, and periodicity of the alloy change dramatically. Consequently, the dominant scattering mechanism in ordered alloys will be different than that in disordered alloys. In this study, we present a hypothesis that ordered alloys can exhibit lower thermal conductivities than their disordered counterparts at elevated temperatures. To validate this hypothesis, we investigate the phononic transport properties of disordered and ordered AB Lennard-Jones alloys via non-equilibrium molecular dynamics and harmonic lattice dynamics calculations. It is shown that the thermal conductivity of an ordered alloy is the same as the thermal conductivity of the disordered alloy at ≈0.6T(melt) and lower than that of the disordered alloy above 0.8T(melt).
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Affiliation(s)
- John C Duda
- Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904, USA.
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15
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Becker J, Sanchez J, Tien J. First-Principles Calculations of Phase Stability for High Temperature Intermetallics. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-213-113] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTTotal energy electronic structure calculations are performed for the elements and selected binary ordered compounds of the ternary system Nb-Ru-Zr. These calculations provide binding energies, atomic volumes, bulk moduli, Debye temperatures, and Grüneiesen constants for the selected structures and compounds. Volume dependent pair and many-body chemical interactions are also obtained from the total energy results which, in turn, are used to study partially ordered alloys at finite temperatures. The stability of all the binary intermetallic compounds experimentally observed at low temperatures is correctly predicted by the first-principles calculations. The solid state portion of the Nb-Ru binary phase diagram is calculated using the chemical interactions obtained from the total energy calculations, a Debye-Grüneisen model for the vibrational free energy and the cluster variation method (CVM) for the configurational entropy with a local volume relaxation scheme. The calculations reproduce the experimentally observed ordering temperature of the NbRu3 intermetallic to within 2%.
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Liu JZ, Zunger A. Thermodynamic theory of epitaxial alloys: first-principles mixed-basis cluster expansion of (In, Ga)N alloy film. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:295402. [PMID: 21828531 DOI: 10.1088/0953-8984/21/29/295402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Epitaxial growth of semiconductor alloys onto a fixed substrate has become the method of choice to make high quality crystals. In the coherent epitaxial growth, the lattice mismatch between the alloy film and the substrate induces a particular form of strain, adding a strain energy term into the free energy of the alloy system. Such epitaxial strain energy can alter the thermodynamics of the alloy, leading to a different phase diagram and different atomic microstructures. In this paper, we present a general-purpose mixed-basis cluster expansion method to describe the thermodynamics of an epitaxial alloy, where the formation energy of a structure is expressed in terms of pair and many-body interactions. With a finite number of first-principles calculation inputs, our method can predict the energies of various atomic structures with an accuracy comparable to that of first-principles calculations themselves. Epitaxial (In, Ga)N zinc-blende alloy grown on GaN(001) substrate is taken as an example to demonstrate the details of the method. Two (210) superlattice structures, (InN)(2)/(GaN)(2) (at x = 0.50) and (InN)(4)/(GaN)(1) (at x = 0.80), are identified as the ground state structures, in contrast to the phase-separation behavior of the bulk alloy.
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Lu ZW, Klein BM, Zunger A. Ordering tendencies in Pd-Pt, Rh-Pt, and Ag-Au alloys. ACTA ACUST UNITED AC 2007. [DOI: 10.1007/bf02646247] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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18
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Purton JA, Barrera GD, Allan NL, Blundy JD. Monte Carlo and Hybrid Monte Carlo/Molecular Dynamics Approaches to Order−Disorder in Alloys, Oxides, and Silicates. J Phys Chem B 1998. [DOI: 10.1021/jp9804897] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- John A. Purton
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom, and CETSEI, Department of Geology, University of Bristol, Wills Memorial Building, Bristol BS8 1RJ, United Kingdom
| | - Gustavo D. Barrera
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom, and CETSEI, Department of Geology, University of Bristol, Wills Memorial Building, Bristol BS8 1RJ, United Kingdom
| | - Neil L. Allan
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom, and CETSEI, Department of Geology, University of Bristol, Wills Memorial Building, Bristol BS8 1RJ, United Kingdom
| | - Jon D. Blundy
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom, and CETSEI, Department of Geology, University of Bristol, Wills Memorial Building, Bristol BS8 1RJ, United Kingdom
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Wolverton C, Zunger A, Froyen S, Wei S. Point-charge electrostatics in disordered alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:7843-7856. [PMID: 9984459 DOI: 10.1103/physrevb.54.7843] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Asta M, Foiles SM. Embedded-atom-method effective-pair-interaction study of the structural and thermodynamic properties of Cu-Ni, Cu-Ag, and Au-Ni solid solutions. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:2389-2404. [PMID: 9983741 DOI: 10.1103/physrevb.53.2389] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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21
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Wang Y, Sun SN, Chou MY. Total-energy study of hydrogen ordering in PdHx (0 <~ x <~ 1). PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:1-4. [PMID: 9981925 DOI: 10.1103/physrevb.53.1] [Citation(s) in RCA: 49] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ruban AV, Abrikosov IA, Skriver HL. Ground-state properties of ordered, partially ordered, and random Cu-Au and Ni-Pt alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:12958-12968. [PMID: 9978090 DOI: 10.1103/physrevb.51.12958] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lu ZW, Zunger A. Unequal wave vectors in short- versus long-range ordering in intermetallic compounds. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:6626-6636. [PMID: 9974616 DOI: 10.1103/physrevb.50.6626] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lu ZW, Laks DB, Wei S, Zunger A. First-principles simulated-annealing study of phase transitions and short-range order in transition-metal and semiconductor alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:6642-6661. [PMID: 9974618 DOI: 10.1103/physrevb.50.6642] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wang Y, Chou MY. Energetics and lattice contraction of beta -phase YH2+x. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:10731-10734. [PMID: 10009902 DOI: 10.1103/physrevb.49.10731] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Chakraborty B. Dynamics of ordering in alloys with modulated phases. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:8608-8614. [PMID: 10009639 DOI: 10.1103/physrevb.49.8608] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sun SN, Wang Y, Chou MY. First-principles study of hydrogen ordering in beta -YH2+x. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:6481-6489. [PMID: 10009364 DOI: 10.1103/physrevb.49.6481] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kuhn M, Sham TK. Charge redistribution and electronic behavior in a series of Au-Cu alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:1647-1661. [PMID: 10010954 DOI: 10.1103/physrevb.49.1647] [Citation(s) in RCA: 48] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Dreyssé H, Wille LT. Self-consistent ordering energies and segregation profiles at binary-alloy surfaces. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:62-75. [PMID: 10004416 DOI: 10.1103/physrevb.47.62] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kuhnen CA. Magnetic properties and calculated electronic structure of iron-palladium alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:8915-8925. [PMID: 10002676 DOI: 10.1103/physrevb.46.8915] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bozzolo G, Ferrante J. Heats of formation of bcc binary alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:12191-12197. [PMID: 10001252 DOI: 10.1103/physrevb.45.12191] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bozzolo G, Ferrante J. Lattice parameters of fcc binary alloys using a new semiempirical method. ACTA ACUST UNITED AC 1992. [DOI: 10.1016/0956-716x(92)90576-z] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Chakraborty B, Xi Z. Atomistic Landau theory of ordering and modulated phases in Cu-Au alloys. PHYSICAL REVIEW LETTERS 1992; 68:2039-2042. [PMID: 10045288 DOI: 10.1103/physrevlett.68.2039] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Schönfeld B, Traube J, Kostorz G. Short-range order and pair potentials in Au-Ag. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:613-621. [PMID: 10001099 DOI: 10.1103/physrevb.45.613] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bozzolo G, Ferrante J, Smith JR. Method for calculating alloy energetics. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:493-496. [PMID: 10000212 DOI: 10.1103/physrevb.45.493] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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37
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Lee KY, Schober HR, Oates WA. Pair Potential and Pair Functional Models of Metal-Hydrogen Alloys*. Z PHYS CHEM 1992. [DOI: 10.1524/zpch.1992.1.1.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Magri R, Zunger A. Real-space description of semiconducting band gaps in substitutional systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:8672-8684. [PMID: 9998823 DOI: 10.1103/physrevb.44.8672] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sanchez JM, Stark JP, Moruzzi VL. First-principles calculation of the Ag-Cu phase diagram. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:5411-5418. [PMID: 9998371 DOI: 10.1103/physrevb.44.5411] [Citation(s) in RCA: 57] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lu ZW, Wei S, Zunger A, Frota-Pessoa S, Ferreira LG. First-principles statistical mechanics of structural stability of intermetallic compounds. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:512-544. [PMID: 9999151 DOI: 10.1103/physrevb.44.512] [Citation(s) in RCA: 126] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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41
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Krishnamurthy CV, Murti YV. Solid solutions of alkali halide compounds. I. Configurational and vibrational contributions. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:14206-14218. [PMID: 9997291 DOI: 10.1103/physrevb.43.14206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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42
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First-principles study of short range order and instabilities in AuCu, AuAg and AuPd alloys. ACTA ACUST UNITED AC 1991. [DOI: 10.1016/0956-7151(91)90117-j] [Citation(s) in RCA: 49] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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43
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Takizawa S, Blügel S, Terakura K, Oguchi T. Theoretical study of the structural stability of CuPd and CuPt alloys: Pressure-induced phase transition of CuPt alloy. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:947-955. [PMID: 9996289 DOI: 10.1103/physrevb.43.947] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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44
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Wei S, Ferreira LG, Bernard JE, Zunger A. Electronic properties of random alloys: Special quasirandom structures. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:9622-9649. [PMID: 9995203 DOI: 10.1103/physrevb.42.9622] [Citation(s) in RCA: 134] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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45
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Wei S, Ferreira LG, Zunger A. First-principles calculation of temperature-composition phase diagrams of semiconductor alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:8240-8269. [PMID: 9993147 DOI: 10.1103/physrevb.41.8240] [Citation(s) in RCA: 106] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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46
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Lu ZW, Wei S, Zunger A. Absence of volume metastability in bcc copper. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:2699-2703. [PMID: 9994035 DOI: 10.1103/physrevb.41.2699] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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47
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Ferreira LG, Wei SH, Zunger A. First-principles calculation of alloy phase diagrams: The renormalized-interaction approach. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:3197-3231. [PMID: 9992258 DOI: 10.1103/physrevb.40.3197] [Citation(s) in RCA: 121] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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48
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Takizawa S, Terakura K, Mohri T. Electronic theory for phase stability of nine AB binary alloys, with A=Ni, Pd, or Pt and B=Cu, Ag, or Au. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:5792-5797. [PMID: 9948997 DOI: 10.1103/physrevb.39.5792] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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49
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Wood DM, Zunger A. Composition pinning in epitaxial alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:12756-12759. [PMID: 9946241 DOI: 10.1103/physrevb.38.12756] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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50
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Wood DM, Zunger A. Epitaxial effects on coherent phase diagrams of alloys. PHYSICAL REVIEW LETTERS 1988; 61:1501-1504. [PMID: 10038814 DOI: 10.1103/physrevlett.61.1501] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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