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Falin A, Lv H, Janzen E, Edgar JH, Zhang R, Qian D, Sheu HS, Cai Q, Gan W, Wu X, Santos EJG, Li LH. Anomalous isotope effect on mechanical properties of single atomic layer Boron Nitride. Nat Commun 2023; 14:5331. [PMID: 37658077 PMCID: PMC10474280 DOI: 10.1038/s41467-023-41148-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 08/24/2023] [Indexed: 09/03/2023] Open
Abstract
The ideal mechanical properties and behaviors of materials without the influence of defects are of great fundamental and engineering significance but considered inaccessible. Here, we use single-atom-thin isotopically pure hexagonal boron nitride (hBN) to demonstrate that two-dimensional (2D) materials offer us close-to ideal experimental platforms to study intrinsic mechanical phenomena. The highly delicate isotope effect on the mechanical properties of monolayer hBN is directly measured by indentation: lighter 10B gives rise to higher elasticity and strength than heavier 11B. This anomalous isotope effect establishes that the intrinsic mechanical properties without the effect of defects could be measured, and the so-called ultrafine and normally neglected isotopic perturbation in nuclear charge distribution sometimes plays a more critical role than the isotopic mass effect in the mechanical and other physical properties of materials.
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Affiliation(s)
- Alexey Falin
- Institute for Frontier Materials, Deakin University, Geelong Waurn Ponds Campus, Waurn Ponds, Geelong, VIC, 3216, Australia
| | - Haifeng Lv
- Hefei National Laboratory for Physical Sciences at the Microscale, School of Chemistry and Material Sciences, CAS Key Laboratory of Materials for Energy Conversion and CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Eli Janzen
- Tim Taylor Department of Chemical Engineering, Kansas State University, Manhattan, KS, 66506, USA
| | - James H Edgar
- Tim Taylor Department of Chemical Engineering, Kansas State University, Manhattan, KS, 66506, USA
| | - Rui Zhang
- Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, TX, 75080, USA
| | - Dong Qian
- Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, TX, 75080, USA
| | - Hwo-Shuenn Sheu
- National Synchrotron Radiation Research Center, Hsinchu, 300, Taiwan
| | - Qiran Cai
- Institute for Frontier Materials, Deakin University, Geelong Waurn Ponds Campus, Waurn Ponds, Geelong, VIC, 3216, Australia
| | - Wei Gan
- Institute for Frontier Materials, Deakin University, Geelong Waurn Ponds Campus, Waurn Ponds, Geelong, VIC, 3216, Australia
| | - Xiaojun Wu
- Hefei National Laboratory for Physical Sciences at the Microscale, School of Chemistry and Material Sciences, CAS Key Laboratory of Materials for Energy Conversion and CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Elton J G Santos
- Institute for Condensed Matter Physics and Complex Systems, School of Physics and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, UK
- Higgs Centre for Theoretical Physics, The University of Edinburgh, Edinburgh, EH9 3FD, UK
| | - Lu Hua Li
- Institute for Frontier Materials, Deakin University, Geelong Waurn Ponds Campus, Waurn Ponds, Geelong, VIC, 3216, Australia.
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2
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Lee SK, Yi Y, Kim YH, Kim HI, Chow P, Xiao Y, Eng P, Shen G. Imaging of the electronic bonding of diamond at pressures up to 2 million atmospheres. SCIENCE ADVANCES 2023; 9:eadg4159. [PMID: 37205753 DOI: 10.1126/sciadv.adg4159] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 04/17/2023] [Indexed: 05/21/2023]
Abstract
Diamond shows unprecedented hardness. Because hardness is a measure of resistance of chemical bonds in a material to external indentation, the electronic bonding nature of diamond beyond several million atmospheres is key to understanding the origin of hardness. However, probing the electronic structures of diamond at such extreme pressure has not been experimentally possible. The measurements on the inelastic x-ray scattering spectra for diamond up to 2 million atmospheres provide data on the evolution of its electronic structures under compression. The mapping of the observed electronic density of states allows us to obtain a two-dimensional image of the bonding transitions of diamond undergoing deformation. The spectral change near edge onset is minor beyond a million atmospheres, while its electronic structure displays marked pressure-induced electron delocalization. Such electronic responses indicate that diamond's external rigidity is supported by its ability to reconcile internal stress, providing insights into the origins of hardness in materials.
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Affiliation(s)
- Sung Keun Lee
- School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, Korea
- Institute of Applied Physics, Seoul National University, Seoul, Korea
| | - Yoosoo Yi
- School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, Korea
| | - Yong-Hyun Kim
- School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, Korea
| | - Hyo-Im Kim
- School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, Korea
| | - Paul Chow
- HPCAT, X-ray Science Division, Argonne National Laboratory, Argonne, IL 60439 USA
| | - Yuming Xiao
- HPCAT, X-ray Science Division, Argonne National Laboratory, Argonne, IL 60439 USA
| | - Peter Eng
- Center for Advanced Radiation Sources, The University of Chicago, Chicago, IL 60637, USA
| | - Guoyin Shen
- HPCAT, X-ray Science Division, Argonne National Laboratory, Argonne, IL 60439 USA
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3
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Guo X, Delegan N, Karsch JC, Li Z, Liu T, Shreiner R, Butcher A, Awschalom DD, Heremans FJ, High AA. Tunable and Transferable Diamond Membranes for Integrated Quantum Technologies. NANO LETTERS 2021; 21:10392-10399. [PMID: 34894697 PMCID: PMC8704172 DOI: 10.1021/acs.nanolett.1c03703] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Revised: 12/02/2021] [Indexed: 06/14/2023]
Abstract
Color centers in diamond are widely explored as qubits in quantum technologies. However, challenges remain in the effective and efficient integration of these diamond-hosted qubits in device heterostructures. Here, nanoscale-thick uniform diamond membranes are synthesized via "smart-cut" and isotopically (12C) purified overgrowth. These membranes have tunable thicknesses (demonstrated 50 to 250 nm), are deterministically transferable, have bilaterally atomically flat surfaces (Rq ≤ 0.3 nm), and bulk-diamond-like crystallinity. Color centers are synthesized via both implantation and in situ overgrowth incorporation. Within 110-nm-thick membranes, individual germanium-vacancy (GeV-) centers exhibit stable photoluminescence at 5.4 K and average optical transition line widths as low as 125 MHz. The room temperature spin coherence of individual nitrogen-vacancy (NV-) centers shows Ramsey spin dephasing times (T2*) and Hahn echo times (T2) as long as 150 and 400 μs, respectively. This platform enables the straightforward integration of diamond membranes that host coherent color centers into quantum technologies.
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Affiliation(s)
- Xinghan Guo
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60615, United States
| | - Nazar Delegan
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60615, United States
- Center
for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Jonathan C. Karsch
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60615, United States
| | - Zixi Li
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60615, United States
| | - Tianle Liu
- Department
of Physics, University of Chicago, Chicago, Illinois 60615, United States
| | - Robert Shreiner
- Department
of Physics, University of Chicago, Chicago, Illinois 60615, United States
| | - Amy Butcher
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60615, United States
| | - David D. Awschalom
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60615, United States
- Center
for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
- Department
of Physics, University of Chicago, Chicago, Illinois 60615, United States
| | - F. Joseph Heremans
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60615, United States
- Center
for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Alexander A. High
- Pritzker
School of Molecular Engineering, University
of Chicago, Chicago, Illinois 60615, United States
- Center
for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
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4
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Ultrasound elasticity of diamond at gigapascal pressures. Proc Natl Acad Sci U S A 2021; 118:2118490118. [PMID: 34907019 DOI: 10.1073/pnas.2118490118] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/09/2021] [Indexed: 11/18/2022] Open
Abstract
Diamond is the hardest known material in nature and features a wide spectrum of industrial and scientific applications. The key to diamond's outstanding properties is its elasticity, which is associated with its exceptional hardness, shear strength, and incompressibility. Despite many theoretical works, direct measurements of elastic properties are limited to only ∼1.4 kilobar (kb) pressure. Here, we report ultrasonic interferometry measurements of elasticity of void-free diamond powder in a multianvil press from 1 atmosphere up to 12.1 gigapascal (GPa). We obtained high-accuracy bulk modulus of diamond as K 0 = 439.2(9) GPa, K 0' = 3.6(1), and shear modulus as G 0 = 533(3) GPa, G 0' = 2.3(3), which are consistent with our first-principles simulation. In contrast to the previous experiment of isothermal equation of state, the K 0' obtained in this work is evidently greater, indicating that the diamond is not fully described by the "n-m" Mie-Grüneisen model. The structural and elastic properties measured in this work may provide a robust primary pressure scale in extensive pressure ranges.
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Cohen R, Nikolaevsky M, Salem R, Frydman A. Setup for pressurizing thin films through the superconductor-insulator transition. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2021; 92:083903. [PMID: 34470441 DOI: 10.1063/5.0053906] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 07/25/2021] [Indexed: 06/13/2023]
Abstract
We describe an experimental setup designed for transport measurement of thin disordered superconducting films as a function of pressure up to several GPa. We use a specially designed single screw diamond anvil cell that allows the gradual increase of high pressure at cryogenic temperatures. By depositing amorphous films of disordered superconducting indium oxide directly on the diamond, we avoid the effect of pressure-induced structural changes in the substrate. Using this technique, we are able to drive thin films through a pressure tuned superconductor-insulator transition.
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Affiliation(s)
- R Cohen
- Department of Physics, Jack and Pearl Resnick Institute and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - M Nikolaevsky
- Department of Physics, Jack and Pearl Resnick Institute and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - R Salem
- Physics Department, Nuclear Research Centre - Negev, P.O. Box 9001, 84190 Beer Sheva, Israel
| | - A Frydman
- Department of Physics, Jack and Pearl Resnick Institute and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
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6
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Getmanskii IV, Zaitsev SA, Koval VV, Minyaev RM, Minkin VI. Computationally Designed Crystal Structures of the Supertetrahedral Ga 4C and Ga 4Si Solids. J Phys Chem A 2021; 125:6556-6561. [PMID: 34291645 DOI: 10.1021/acs.jpca.1c02687] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The structural, mechanical, electrical, and optical properties of new supertetrahedral structures cF-Ga4X (X = C, Si) were studied by using a solid state DFT calculation. The crystal structures of cF-Ga4X are built based on a diamond crystal lattice, in which pairs of adjacent carbon atoms are replaced by Ga4X fragments, where Ga4 is a tetrahedron of gallium atoms. Calculations have shown that new mixed-type supertetrahedral structures are dynamically stable, have densities of 3.49 g/cm3 (X = C) and 2.65 g/cm3 (X = Si), and are narrow band gap semiconductors. From the performed molecular dynamics calculations, it follows that the homogeneous melting temperature of the gallium-carbon structure is in the range from 600 to 700 K and that of the gallium-silicon structure is in the range from 400 to 500 K.
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Affiliation(s)
- Iliya V Getmanskii
- Institute of Physical and Organic Chemistry, Southern Federal University, Rostov-on-Don 344090, Russian Federation
| | - Stanislav A Zaitsev
- Institute of Physical and Organic Chemistry, Southern Federal University, Rostov-on-Don 344090, Russian Federation
| | - Vitaliy V Koval
- Institute of Physical and Organic Chemistry, Southern Federal University, Rostov-on-Don 344090, Russian Federation
| | - Ruslan M Minyaev
- Institute of Physical and Organic Chemistry, Southern Federal University, Rostov-on-Don 344090, Russian Federation
| | - Vladimir I Minkin
- Institute of Physical and Organic Chemistry, Southern Federal University, Rostov-on-Don 344090, Russian Federation
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7
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Sun H, Sang L, Wu H, Zhang Z, Teraji T, Li TF, You JQ, Toda M, Koizumi S, Liao M. Effect of Deep-Defects Excitation on Mechanical Energy Dissipation of Single-Crystal Diamond. PHYSICAL REVIEW LETTERS 2020; 125:206802. [PMID: 33258634 DOI: 10.1103/physrevlett.125.206802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2020] [Accepted: 10/15/2020] [Indexed: 06/12/2023]
Abstract
The ultrawide band gap of diamond distinguishes it from other semiconductors, in that all known defects have deep energy levels that are less active at room temperature. Here, we present the effect of deep defects on the mechanical energy dissipation of single-crystal diamond experimentally and theoretically up to 973 K. Energy dissipation is found to increase with temperature and exhibits local maxima due to the interaction between phonons and deep defects activated at specific temperatures. A two-level model with deep energies is proposed to explain well the energy dissipation at elevated temperatures. It is evident that the removal of boron impurities can substantially increase the quality factor of room-temperature diamond mechanical resonators. The deep energy nature of the defects bestows single-crystal diamond with outstanding low intrinsic energy dissipation in mechanical resonators at room temperature or above.
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Affiliation(s)
- Huanying Sun
- Quantum Physics and Quantum Information Division, Beijing Computational Science Research Center, Beijing 100193, China
- Research Center for Materials Center, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Liwen Sang
- International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Haihua Wu
- Research Center for Materials Center, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Zilong Zhang
- Research Center for Materials Center, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Tokuyuki Teraji
- Research Center for Materials Center, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Tie-Fu Li
- Institute of Microelectronics and Frontier Science Center for Quantum Information, Tsinghua University, Beijing 100084, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - J Q You
- Interdisciplinary Center of Quantum Information and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics and State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China
| | - Masaya Toda
- Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan
| | - Satoshi Koizumi
- Research Center for Materials Center, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Meiyong Liao
- Research Center for Materials Center, National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
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8
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Abstract
The incipient plasticity of diamond is probed, and is shown to result from the propagation of dislocations and structural phase transitions.
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Affiliation(s)
- Chao Xu
- College of Science
- Wuhan University of Science and Technology
- Wuhan 430081
- China
| | - Chunmei Liu
- College of Science
- Wuhan University of Science and Technology
- Wuhan 430081
- China
| | - Haikuo Wang
- College of Materials Science and Engineering
- Henan University of Technology
- Zhengzhou 450007
- China
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9
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Zhou XW, Ward DK, Foster ME. An analytical bond‐order potential for carbon. J Comput Chem 2015; 36:1719-35. [DOI: 10.1002/jcc.23949] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2014] [Revised: 01/13/2015] [Accepted: 02/08/2015] [Indexed: 11/05/2022]
Affiliation(s)
- X. W. Zhou
- Mechanics of Materials DepartmentSandia National LaboratoriesLivermore California94550
| | - D. K. Ward
- Radiation and Nuclear Detection Materials and Analysis DepartmentSandia National LaboratoriesLivermore California94550
| | - M. E. Foster
- Materials Chemistry DepartmentSandia National LaboratoriesLivermore California94550
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10
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Synthesis of Binary Transition Metal Nitrides, Carbides and Borides from the Elements in the Laser-Heated Diamond Anvil Cell and Their Structure-Property Relations. MATERIALS 2011; 4:1648-1692. [PMID: 28824101 PMCID: PMC5448873 DOI: 10.3390/ma4101648] [Citation(s) in RCA: 91] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/15/2011] [Revised: 09/13/2011] [Accepted: 09/16/2011] [Indexed: 11/23/2022]
Abstract
Transition metal nitrides, carbides and borides have a high potential for industrial applications as they not only have a high melting point but are generally harder and less compressible than the pure metals. Here we summarize recent advances in the synthesis of binary transition metal nitrides, carbides and borides focusing on the reaction of the elements at extreme conditions generated within the laser-heated diamond anvil cell. The current knowledge of their structures and high-pressure properties like high-(p,T) stability, compressibility and hardness is described as obtained from experiments.
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11
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Beghi MG, Di Fonzo F, Pietralunga S, Ubaldi C, Bottani CE. Precision and accuracy in film stiffness measurement by Brillouin spectroscopy. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2011; 82:053107. [PMID: 21639492 DOI: 10.1063/1.3585980] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
The interest in the measurement of the elastic properties of thin films is witnessed by a number of new techniques being proposed. However, the precision of results is seldom assessed in detail. Brillouin spectroscopy (BS) is an established optical, contactless, non-destructive technique, which provides a full elastic characterization of bulk materials and thin films. In the present work, the whole process of measurement of the elastic moduli by BS is critically analyzed: experimental setup, data recording, calibration, and calculation of the elastic moduli. It is shown that combining BS with ellipsometry a fully optical characterization can be obtained. The key factors affecting uncertainty of the results are identified and discussed. A procedure is proposed to discriminate factors affecting the precision from those affecting the accuracy. By the characterization of a model transparent material, silica in bulk and film form, it is demonstrated that both precision and accuracy of the elastic moduli measured by BS can reach 1% range, qualifying BS as a reference technique.
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Affiliation(s)
- M G Beghi
- Energy Department and NEMAS Center, Politecnico di Milano, Via Ponzio 34∕3, 20133 Milano, Italy
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12
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Beghi MG, Bottani CE. Low-frequency Raman and Brillouin spectroscopy from graphite, diamond and diamond-like carbons, fullerenes and nanotubes. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2004; 362:2513-2535. [PMID: 15482989 DOI: 10.1098/rsta.2004.1450] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Inelastic light scattering by acoustic phonons (Brillouin scattering) is a useful tool for probing material properties at the submicrometre scale. In media which are statistically homogeneous at this scale, it gives access to the acoustic properties and the elastic moduli. In nanostructures it probes the vibrational properties at the mesoscopic scale. Applications to carbonaceous materials are reviewed.
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Affiliation(s)
- M G Beghi
- Nuclear Engineering Department and NEMAS Center, Politecnico di Milano, Via Ponzio 34/3, 20133 Milan, Italy.
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13
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Occelli F, Loubeyre P, LeToullec R. Properties of diamond under hydrostatic pressures up to 140 GPa. NATURE MATERIALS 2003; 2:151-154. [PMID: 12612670 DOI: 10.1038/nmat831] [Citation(s) in RCA: 125] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2002] [Accepted: 01/06/2003] [Indexed: 05/24/2023]
Abstract
Diamond is the archetypal covalent material. Each atom in an sp(3) configuration is bonded to four nearest neighbours. Because of its remarkable properties, diamond has been extensively studied. And yet our knowledge of the properties of diamond under very high pressure is still incomplete. Although diamond is known to be the preferred allotrope of carbon at high pressure, the possibility of producing under pressure high-density polymorphs of diamond, including metallic forms, has been discussed. Structural changes have already been reported in diamond under non-hydrostatic pressures around 150 GPa and large deformation. However, measurements of the properties of diamond under hydrostatic pressure have been limited to below 40 GPa. Here, we report accurate measurements of the volume and of the optical phonon frequency of diamond under hydrostatic pressure up to 140 GPa. We show that diamond is more compressible than currently expected. By combining the volume and the frequency pressure shifts, we deduce that diamond remains very stable under pressure: it is a Gruneisen solid up to at least 140 GPa, and the covalent bond is even slightly strengthened under pressure. Finally, the optical phonon frequency versus pressure is calibrated here to be used as a pressure gauge for diamond anvil cell studies in the multi-megabar range.
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Affiliation(s)
- Florent Occelli
- Département de Physique Théorique et Appliquée, CEA/DAM/DIF, 91680 Bruyères-le-Châtel, France
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14
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Arridge RGC, Lang AR, Makepeace APW. Elastic deformation in a crystal plate where lattice–parameter mismatch is present between adjacent growth sectors. I. Anisotropic elasticity theory, with application to lattice-parameter measurements. Proc Math Phys Eng Sci 2002. [DOI: 10.1098/rspa.2002.0988] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- R. G. C. Arridge
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
| | - A. R. Lang
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
| | - A. P. W. Makepeace
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
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15
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16
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17
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Faurskov Nielsen O. Chapter 3. Low-frequency spectroscopic studies and intermolecular vibrational energy transfer in liquids. ACTA ACUST UNITED AC 1997. [DOI: 10.1039/pc093057] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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