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Minkov VS, Bud'ko SL, Balakirev FF, Prakapenka VB, Chariton S, Husband RJ, Liermann HP, Eremets MI. Author Correction: Magnetic field screening in hydrogen-rich high-temperature superconductors. Nat Commun 2023; 14:5322. [PMID: 37658055 PMCID: PMC10474084 DOI: 10.1038/s41467-023-40837-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/03/2023] Open
Affiliation(s)
- V S Minkov
- Max Planck Institute for Chemistry, Hahn Meitner Weg 1, 55128, Mainz, Germany.
| | - S L Bud'ko
- Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames, IA, 50011, USA
- Department of Physics and Astronomy, Iowa State University, Ames, IA, 50011, USA
| | - F F Balakirev
- Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - V B Prakapenka
- Center for Advanced Radiation Sources, University of Chicago, 5640 South Ellis Avenue, Chicago, IL, 60637, USA
| | - S Chariton
- Center for Advanced Radiation Sources, University of Chicago, 5640 South Ellis Avenue, Chicago, IL, 60637, USA
| | - R J Husband
- Photon Science, DESY, Notkestrasse 85, 22607, Hamburg, Germany
| | - H P Liermann
- Photon Science, DESY, Notkestrasse 85, 22607, Hamburg, Germany
| | - M I Eremets
- Max Planck Institute for Chemistry, Hahn Meitner Weg 1, 55128, Mainz, Germany.
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Minkov VS, Bud'ko SL, Balakirev FF, Prakapenka VB, Chariton S, Husband RJ, Liermann HP, Eremets MI. Magnetic field screening in hydrogen-rich high-temperature superconductors. Nat Commun 2022; 13:3194. [PMID: 35680889 PMCID: PMC9184750 DOI: 10.1038/s41467-022-30782-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 05/19/2022] [Indexed: 11/25/2022] Open
Abstract
In the last few years, the superconducting transition temperature, Tc, of hydrogen-rich compounds has increased dramatically, and is now approaching room temperature. However, the pressures at which these materials are stable exceed one million atmospheres and limit the number of available experimental studies. Superconductivity in hydrides has been primarily explored by electrical transport measurements, whereas magnetic properties, one of the most important characteristic of a superconductor, have not been satisfactory defined. Here, we develop SQUID magnetometry under extreme high-pressure conditions and report characteristic superconducting parameters for Im-3m-H3S and Fm-3m-LaH10-the representative members of two families of high-temperature superconducting hydrides. We determine a lower critical field Hc1 of ∼0.82 T and ∼0.55 T, and a London penetration depth λL of ∼20 nm and ∼30 nm in H3S and LaH10, respectively. The small values of λL indicate a high superfluid density in both hydrides. These compounds have the values of the Ginzburg-Landau parameter κ ∼12-20 and belong to the group of "moderate" type II superconductors, rather than being hard superconductors as would be intuitively expected from their high Tcs.
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Affiliation(s)
- V S Minkov
- Max Planck Institute for Chemistry, Hahn Meitner Weg 1, 55128, Mainz, Germany.
| | - S L Bud'ko
- Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames, IA, 50011, USA
- Department of Physics and Astronomy, Iowa State University, Ames, IA, 50011, USA
| | - F F Balakirev
- Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - V B Prakapenka
- Center for Advanced Radiation Sources, University of Chicago, 5640 South Ellis Avenue, Chicago, IL, 60637, USA
| | - S Chariton
- Center for Advanced Radiation Sources, University of Chicago, 5640 South Ellis Avenue, Chicago, IL, 60637, USA
| | - R J Husband
- Photon Science, DESY, Notkestrasse 85, 22607, Hamburg, Germany
| | - H P Liermann
- Photon Science, DESY, Notkestrasse 85, 22607, Hamburg, Germany
| | - M I Eremets
- Max Planck Institute for Chemistry, Hahn Meitner Weg 1, 55128, Mainz, Germany.
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Glazyrin K, Khandarkhaeva S, Fedotenko T, Dong W, Laniel D, Seiboth F, Schropp A, Garrevoet J, Brückner D, Falkenberg G, Kubec A, David C, Wendt M, Wenz S, Dubrovinsky L, Dubrovinskaia N, Liermann HP. Sub-micrometer focusing setup for high-pressure crystallography at the Extreme Conditions beamline at PETRA III. J Synchrotron Radiat 2022; 29:654-663. [PMID: 35510998 PMCID: PMC9070721 DOI: 10.1107/s1600577522002582] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Accepted: 03/07/2022] [Indexed: 06/14/2023]
Abstract
Scientific tasks aimed at decoding and characterizing complex systems and processes at high pressures set new challenges for modern X-ray diffraction instrumentation in terms of X-ray flux, focal spot size and sample positioning. Presented here are new developments at the Extreme Conditions beamline (P02.2, PETRA III, DESY, Germany) that enable considerable improvements in data collection at very high pressures and small scattering volumes. In particular, the focusing of the X-ray beam to the sub-micrometer level is described, and control of the aberrations of the focusing compound refractive lenses is made possible with the implementation of a correcting phase plate. This device provides a significant enhancement of the signal-to-noise ratio by conditioning the beam shape profile at the focal spot. A new sample alignment system with a small sphere of confusion enables single-crystal data collection from grains of micrometer to sub-micrometer dimensions subjected to pressures as high as 200 GPa. The combination of the technical development of the optical path and the sample alignment system contributes to research and gives benefits on various levels, including rapid and accurate diffraction mapping of samples with sub-micrometer resolution at multimegabar pressures.
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Affiliation(s)
- K. Glazyrin
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - S. Khandarkhaeva
- Bayerisches Geoinstitut, University of Bayreuth, Universitätsstrasse 30, 95440 Bayreuth, Germany
- Material Physics and Technology at Extreme Conditions, Laboratory of Crystallography, University of Bayreuth, Universitätsstrasse 30, 95440 Bayreuth, Germany
| | - T. Fedotenko
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
- Material Physics and Technology at Extreme Conditions, Laboratory of Crystallography, University of Bayreuth, Universitätsstrasse 30, 95440 Bayreuth, Germany
| | - W. Dong
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - D. Laniel
- Material Physics and Technology at Extreme Conditions, Laboratory of Crystallography, University of Bayreuth, Universitätsstrasse 30, 95440 Bayreuth, Germany
| | - F. Seiboth
- Center for X-ray and Nano Science CXNS, Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - A. Schropp
- Center for X-ray and Nano Science CXNS, Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
- Helmholtz Imaging Platform, Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - J. Garrevoet
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - D. Brückner
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
- Department Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- Ruhr-Universität Bochum, Universitätsstrasse 150, 44801 Bochum, Germany
| | - G. Falkenberg
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - A. Kubec
- Laboratory for Micro- and Nanotechnology, Paul Scherrer Institut, Forschungsstrasse 111, 5232 Villigen-PSI, Switzerland
| | - C. David
- Laboratory for Micro- and Nanotechnology, Paul Scherrer Institut, Forschungsstrasse 111, 5232 Villigen-PSI, Switzerland
| | - M. Wendt
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - S. Wenz
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - L. Dubrovinsky
- Bayerisches Geoinstitut, University of Bayreuth, Universitätsstrasse 30, 95440 Bayreuth, Germany
| | - N. Dubrovinskaia
- Material Physics and Technology at Extreme Conditions, Laboratory of Crystallography, University of Bayreuth, Universitätsstrasse 30, 95440 Bayreuth, Germany
- Department of Physics, Chemistry and Biology (IFM), Linköping University, Campus Valla, Fysikhuset F310, SE-581 83 Linköping, Sweden
| | - H.-P. Liermann
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
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Jenei Z, Liermann HP, Husband R, Méndez ASJ, Pennicard D, Marquardt H, O'Bannon EF, Pakhomova A, Konopkova Z, Glazyrin K, Wendt M, Wenz S, McBride EE, Morgenroth W, Winkler B, Rothkirch A, Hanfland M, Evans WJ. New dynamic diamond anvil cells for tera-pascal per second fast compression x-ray diffraction experiments. Rev Sci Instrum 2019; 90:065114. [PMID: 31255042 DOI: 10.1063/1.5098993] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2019] [Accepted: 05/27/2019] [Indexed: 06/09/2023]
Abstract
Fast compression experiments performed using dynamic diamond anvil cells (dDACs) employing piezoactuators offer the opportunity to study compression-rate dependent phenomena. In this paper, we describe an experimental setup which allows us to perform time-resolved x-ray diffraction during the fast compression of materials using improved dDACs. The combination of the high flux available using a 25.6 keV x-ray beam focused with a linear array of compound refractive lenses and the two fast GaAs LAMBDA detectors available at the Extreme Conditions Beamline (P02.2) at PETRA III enables the collection of x-ray diffraction patterns at an effective repetition rate of up to 4 kHz. Compression rates of up to 160 TPa/s have been achieved during the compression of gold in a 2.5 ms fast compression using improved dDAC configurations with more powerful piezoactuators. The application of this setup to low-Z compounds at lower compression rates is described, and the high temporal resolution of the setup is demonstrated. The possibility of applying finely tuned pressure profiles opens opportunities for future research, such as using oscillations of the piezoactuator to mimic propagation of seismic waves in the Earth.
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Affiliation(s)
- Zs Jenei
- High Pressure Physics Group, Lawrence Livermore National Laboratory, 7000 East Avenue, L-041, Livermore, California 94550, USA
| | - H P Liermann
- Photon Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - R Husband
- Photon Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - A S J Méndez
- Photon Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - D Pennicard
- Photon Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - H Marquardt
- Department of Earth Sciences, University of Oxford, South Parks Road, OX1 3AN Oxford, United Kingdom
| | - E F O'Bannon
- High Pressure Physics Group, Lawrence Livermore National Laboratory, 7000 East Avenue, L-041, Livermore, California 94550, USA
| | - A Pakhomova
- Photon Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - Z Konopkova
- Photon Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - K Glazyrin
- High Pressure Physics Group, Lawrence Livermore National Laboratory, 7000 East Avenue, L-041, Livermore, California 94550, USA
| | - M Wendt
- Photon Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - S Wenz
- Photon Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - E E McBride
- Photon Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - W Morgenroth
- Arbeitsgruppe Kristallographie, Department of Geoscience, University of Frankfurt, 60438 Frankfurt, Germany
| | - B Winkler
- Arbeitsgruppe Kristallographie, Department of Geoscience, University of Frankfurt, 60438 Frankfurt, Germany
| | - A Rothkirch
- Photon Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - M Hanfland
- ESRF, The European Synchrotron, 71 Avenue des Martyrs, 38000 Grenoble, France
| | - W J Evans
- High Pressure Physics Group, Lawrence Livermore National Laboratory, 7000 East Avenue, L-041, Livermore, California 94550, USA
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5
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Hirsch A, Kegler P, Alencar I, Ruiz-Fuertes J, Shelyug A, Peters L, Schreinemachers C, Neumann A, Neumeier S, Liermann HP, Navrotsky A, Roth G. Structural, vibrational, and thermochemical properties of the monazite-type solid solution La1–Pr PO4. J SOLID STATE CHEM 2017. [DOI: 10.1016/j.jssc.2016.09.032] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Gorman MG, Briggs R, McBride EE, Higginbotham A, Arnold B, Eggert JH, Fratanduono DE, Galtier E, Lazicki AE, Lee HJ, Liermann HP, Nagler B, Rothkirch A, Smith RF, Swift DC, Collins GW, Wark JS, McMahon MI. Direct Observation of Melting in Shock-Compressed Bismuth With Femtosecond X-ray Diffraction. Phys Rev Lett 2015; 115:095701. [PMID: 26371663 DOI: 10.1103/physrevlett.115.095701] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2014] [Indexed: 06/05/2023]
Abstract
The melting of bismuth in response to shock compression has been studied using in situ femtosecond x-ray diffraction at an x-ray free electron laser. Both solid-solid and solid-liquid phase transitions are documented using changes in discrete diffraction peaks and the emergence of broad, liquid scattering upon release from shock pressures up to 14 GPa. The transformation from the solid state to the liquid is found to occur in less than 3 ns, very much faster than previously believed. These results are the first quantitative measurements of a liquid material obtained on shock release using x-ray diffraction, and provide an upper limit for the time scale of melting of bismuth under shock loading.
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Affiliation(s)
- M G Gorman
- SUPA, School of Physics & Astronomy, and Centre for Science at Extreme Conditions, The University of Edinburgh, Edinburgh EH9 3FD, UK
| | - R Briggs
- SUPA, School of Physics & Astronomy, and Centre for Science at Extreme Conditions, The University of Edinburgh, Edinburgh EH9 3FD, UK
| | - E E McBride
- SUPA, School of Physics & Astronomy, and Centre for Science at Extreme Conditions, The University of Edinburgh, Edinburgh EH9 3FD, UK
- DESY Photon Science, Notkestr. 85, D-22607 Hamburg, Germany
| | - A Higginbotham
- Department of Physics, Clarendon Laboratory, Parks Road, University of Oxford, Oxford OX1 3PU, UK
| | - B Arnold
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - J H Eggert
- Lawrence Livermore National Laboratory, 6000 East Avenue, Livermore, California 94500, USA
| | - D E Fratanduono
- Lawrence Livermore National Laboratory, 6000 East Avenue, Livermore, California 94500, USA
| | - E Galtier
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - A E Lazicki
- Lawrence Livermore National Laboratory, 6000 East Avenue, Livermore, California 94500, USA
| | - H J Lee
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - H P Liermann
- DESY Photon Science, Notkestr. 85, D-22607 Hamburg, Germany
| | - B Nagler
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - A Rothkirch
- DESY Photon Science, Notkestr. 85, D-22607 Hamburg, Germany
| | - R F Smith
- Lawrence Livermore National Laboratory, 6000 East Avenue, Livermore, California 94500, USA
| | - D C Swift
- Lawrence Livermore National Laboratory, 6000 East Avenue, Livermore, California 94500, USA
| | - G W Collins
- Lawrence Livermore National Laboratory, 6000 East Avenue, Livermore, California 94500, USA
| | - J S Wark
- Department of Physics, Clarendon Laboratory, Parks Road, University of Oxford, Oxford OX1 3PU, UK
| | - M I McMahon
- SUPA, School of Physics & Astronomy, and Centre for Science at Extreme Conditions, The University of Edinburgh, Edinburgh EH9 3FD, UK
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7
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Liermann HP, Konôpková Z, Morgenroth W, Glazyrin K, Bednarčik J, McBride EE, Petitgirard S, Delitz JT, Wendt M, Bican Y, Ehnes A, Schwark I, Rothkirch A, Tischer M, Heuer J, Schulte-Schrepping H, Kracht T, Franz H. The Extreme Conditions Beamline P02.2 and the Extreme Conditions Science Infrastructure at PETRA III. J Synchrotron Radiat 2015; 22:908-24. [PMID: 26134794 PMCID: PMC4489534 DOI: 10.1107/s1600577515005937] [Citation(s) in RCA: 57] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2014] [Accepted: 03/24/2015] [Indexed: 05/18/2023]
Abstract
A detailed description is presented of the Extreme Conditions Beamline P02.2 for micro X-ray diffraction studies of matter at simultaneous high pressure and high/low temperatures at PETRA III, in Hamburg, Germany. This includes performance of the X-ray optics and instrumental resolution as well as an overview of the different sample environments available for high-pressure studies in the diamond anvil cell. Particularly emphasized are the high-brilliance and high-energy X-ray diffraction capabilities of the beamline in conjunction with the use of fast area detectors to conduct time-resolved compression studies in the millisecond time regime. Finally, the current capability of the Extreme Conditions Science Infrastructure to support high-pressure research at the Extreme Conditions Beamline and other PETRA III beamlines is described.
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Affiliation(s)
- H.-P. Liermann
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
- Correspondence e-mail:
| | - Z. Konôpková
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - W. Morgenroth
- Department of Crystallography, University of Frankfurt, Frankfurt, Germany
| | - K. Glazyrin
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - J. Bednarčik
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - E. E. McBride
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - S. Petitgirard
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
- Bayrisches Geoinstitut, University of Bayreuth, Bayreuth, Germany
| | - J. T. Delitz
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - M. Wendt
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - Y. Bican
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - A. Ehnes
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - I. Schwark
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - A. Rothkirch
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - M. Tischer
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - J. Heuer
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | | | - T. Kracht
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
| | - H. Franz
- Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
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Magdysyuk OV, Adams F, Liermann HP, Spanopoulos I, Trikalitis PN, Hirscher M, Morris RE, Duncan MJ, McCormick LJ, Dinnebier RE. Understanding the adsorption mechanism of noble gases Kr and Xe in CPO-27-Ni, CPO-27-Mg, and ZIF-8. Phys Chem Chem Phys 2014; 16:23908-14. [DOI: 10.1039/c4cp03298e] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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Yamanaka T, Kuribayashi T, Mao HK, Hemley R, Shu J, Liermann H, Yang W, Xiao YM, Dera P, Mao W. Ferroelectric and high–low spin transition by MEM using single-crystal and X-ray emission to 100 Gpa. Acta Crystallogr A 2008. [DOI: 10.1107/s010876730808046x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
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Singh AK, Liermann HP, Saxena SK, Mao HK, Devi SU. Nonhydrostatic compression of gold powder to 60 GPa in a diamond anvil cell: estimation of compressive strength from x-ray diffraction data. J Phys Condens Matter 2006; 18:S969-S978. [PMID: 22611106 DOI: 10.1088/0953-8984/18/25/s05] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Two gold powder samples, one with average crystallite size of ≈30 nm (n-Au) and another with ≈120 nm (c-Au), were compressed under nonhydrostatic conditions in a diamond anvil cell to different pressures up to ≈60 GPa and the x-ray diffraction patterns recorded. The difference between the axial and radial stress components (a measure of the compressive strength) was estimated from the shifts of the diffraction lines. The maximum micro-stress in the crystallites (another measure of the compressive strength) and grain size (crystallite size) were obtained from analysis of the line-width data. The strengths obtained by the two methods agreed well and increased with increasing pressure. Over the entire pressure range, the strength of n-Au was found to be significantly higher than that of c-Au. The grain sizes of both n-Au and c-Au decreased under pressure. This decrease was much larger than expected from the compressibility effect and was found to be reversible. An equation derived from the dislocation theory that predicts the dependence of strength on the grain size and the shear modulus was used to interpret the strength data. The strength derived from the published grain size versus hardness data agreed well with the present results.
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Affiliation(s)
- A K Singh
- Materials Science Division, National Aerospace Laboratories, Bangalore 560 017, India
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