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Abstract
Experimental discovery of ultralarge elastic deformation in nanoscale diamond and machine learning of its electronic and phonon structures have created opportunities to address new scientific questions. Can diamond, with an ultrawide bandgap of 5.6 eV, be completely metallized, solely under mechanical strain without phonon instability, so that its electronic bandgap fully vanishes? Through first-principles calculations, finite-element simulations validated by experiments, and neural network learning, we show here that metallization/demetallization as well as indirect-to-direct bandgap transitions can be achieved reversibly in diamond below threshold strain levels for phonon instability. We identify the pathway to metallization within six-dimensional strain space for different sample geometries. We also explore phonon-instability conditions that promote phase transition to graphite. These findings offer opportunities for tailoring properties of diamond via strain engineering for electronic, photonic, and quantum applications.
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Affiliation(s)
- Zhe Shi
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
| | - Ming Dao
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139;
| | | | | | - Ju Li
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139;
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
| | - Subra Suresh
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139;
- Nanyang Technological University, 639798 Singapore, Republic of Singapore
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2
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Cao T, Cuffari D, Bongiorno A. First-Principles Calculation of Third-Order Elastic Constants via Numerical Differentiation of the Second Piola-Kirchhoff Stress Tensor. PHYSICAL REVIEW LETTERS 2018; 121:216001. [PMID: 30517818 DOI: 10.1103/physrevlett.121.216001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2018] [Indexed: 06/09/2023]
Abstract
A general method is presented to calculate from first principles the full set of third-order elastic constants of a material of arbitrary symmetry. The method here illustrated relies on a plane-wave density functional theory scheme to calculate the Cauchy stress and the numerical differentiation of the second Piola-Kirchhoff stress tensor to evaluate the elastic constants. It is shown that finite difference formulas lead to a cancellation of the finite basis set errors, whereas simple solutions are proposed to eliminate numerical errors arising from the use of Fourier interpolation techniques. Applications to diamond, silicon, aluminum, magnesium, graphene, and a graphane conformer give results in excellent agreement with both experiments and previous calculations based on fitting energy density curves, demonstrating both the accuracy and generality of our new methodology to investigate nonlinear elastic behaviors of materials.
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Affiliation(s)
- Tengfei Cao
- Department of Chemistry, College of Staten Island, Staten Island, New York 10314, USA
- Advanced Science Research Center, City University of New York, 85 St. Nicholas Terrace, New York, New York 10031, USA
| | - David Cuffari
- Department of Chemistry, College of Staten Island, Staten Island, New York 10314, USA
- Ph.D. Program in Physics, The Graduate Center of the City University of New York, New York, New York 10016, USA
| | - Angelo Bongiorno
- Department of Chemistry, College of Staten Island, Staten Island, New York 10314, USA
- Advanced Science Research Center, City University of New York, 85 St. Nicholas Terrace, New York, New York 10031, USA
- Ph.D. Program in Physics, The Graduate Center of the City University of New York, New York, New York 10016, USA
- Ph.D. Program in Chemistry, The Graduate Center of the City University of New York, New York, New York 10016, USA
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3
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Turneaure SJ, Sharma SM, Volz TJ, Winey JM, Gupta YM. Transformation of shock-compressed graphite to hexagonal diamond in nanoseconds. SCIENCE ADVANCES 2017; 3:eaao3561. [PMID: 29098183 PMCID: PMC5659656 DOI: 10.1126/sciadv.aao3561] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2017] [Accepted: 09/27/2017] [Indexed: 05/13/2023]
Abstract
The graphite-to-diamond transformation under shock compression has been of broad scientific interest since 1961. The formation of hexagonal diamond (HD) is of particular interest because it is expected to be harder than cubic diamond and due to its use in terrestrial sciences as a marker at meteorite impact sites. However, the formation of diamond having a fully hexagonal structure continues to be questioned and remains unresolved. Using real-time (nanosecond), in situ x-ray diffraction measurements, we show unequivocally that highly oriented pyrolytic graphite, shock-compressed along the c axis to 50 GPa, transforms to highly oriented elastically strained HD with the (100)HD plane parallel to the graphite basal plane. These findings contradict recent molecular dynamics simulation results for the shock-induced graphite-to-diamond transformation and provide a benchmark for future theoretical simulations. Additionally, our results show that an earlier report of HD forming only above 170 GPa for shocked pyrolytic graphite may lead to incorrect interpretations of meteorite impact events.
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Affiliation(s)
- Stefan J. Turneaure
- Institute for Shock Physics, Washington State University, Pullman, WA 99164, USA
| | - Surinder M. Sharma
- Institute for Shock Physics, Washington State University, Pullman, WA 99164, USA
| | - Travis J. Volz
- Institute for Shock Physics, Washington State University, Pullman, WA 99164, USA
- Department of Physics and Astronomy, Washington State University, Pullman, WA 99164, USA
| | - J. M. Winey
- Institute for Shock Physics, Washington State University, Pullman, WA 99164, USA
| | - Yogendra M. Gupta
- Institute for Shock Physics, Washington State University, Pullman, WA 99164, USA
- Department of Physics and Astronomy, Washington State University, Pullman, WA 99164, USA
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4
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Feng B, Levitas VI. Pressure Self-focusing Effect and Novel Methods for Increasing the Maximum Pressure in Traditional and Rotational Diamond Anvil Cells. Sci Rep 2017; 7:45461. [PMID: 28429723 PMCID: PMC5399457 DOI: 10.1038/srep45461] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Accepted: 03/01/2017] [Indexed: 11/16/2022] Open
Abstract
The main principles of producing a region near the center of a sample, compressed in a diamond anvil cell (DAC), with a very high pressure gradient and, consequently, with high pressure are predicted theoretically. The revealed phenomenon of generating extremely high pressure gradient is called the pressure self-focusing effect. Initial analytical predictions utilized generalization of a simplified equilibrium equation. Then, the results are refined using our recent advanced model for elastoplastic material under high pressures in finite element method (FEM) simulations. The main points in producing the pressure self-focusing effect are to use beveled anvils and reach a very thin sample thickness at the center. We find that the superposition of torsion in a rotational DAC (RDAC) offers drastic enhancement of the pressure self-focusing effect and allows one to reach the same pressure under a much lower force and deformation of anvils.
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Affiliation(s)
- Biao Feng
- Department of Aerospace Engineering, Iowa State University, Ames, Iowa 50011, USA
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Valery I. Levitas
- Departments of Aerospace Engineering, Mechanical Engineering, and Material Science and Engineering, Iowa State University, Ames, Iowa 50011, USA
- Ames Laboratory, Division of Materials Science and Engineering, Ames, Iowa 50011, USA
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Lang JM, Gupta YM. Experimental determination of third-order elastic constants of diamond. PHYSICAL REVIEW LETTERS 2011; 106:125502. [PMID: 21517323 DOI: 10.1103/physrevlett.106.125502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2010] [Indexed: 05/30/2023]
Abstract
To determine the nonlinear elastic response of diamond, single crystals were shock compressed along the [100], [110], and [111] orientations to 120 GPa peak elastic stresses. Particle velocity histories and elastic wave velocities were measured by using laser interferometry. The measured elastic wave profiles were used, in combination with published acoustic measurements, to determine the complete set of third-order elastic constants. These constants represent the first experimental determination, and several differ significantly from those calculated by using theoretical models.
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Affiliation(s)
- J M Lang
- Institute for Shock Physics and Department of Physics, Washington State University, Pullman, Washington 99164, USA
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Diaz JAC, Cağin T. Thermo-mechanical stability and strength of peptide nanostructures from molecular dynamics: self-assembled cyclic peptide nanotubes. NANOTECHNOLOGY 2010; 21:115703. [PMID: 20173235 DOI: 10.1088/0957-4484/21/11/115703] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Peptide nanostructures present a wide range of opportunities for applications in biomedicine and bionanotechnology; hence experimental and theoretical studies aiming at determination of thermo-mechanical stability of peptide-based nanostructures are critical for the design and development of their technological applications. Here, we present a homogeneous deformation method combined with the finite elasticity theory and molecular dynamics simulations (MD) for the calculation of second-order anisotropic elastic constants for a membrane model made up of self-assembled cyclic peptide nanotubes. We have computed the values of all anisotropic elastic constants at 300 K. The value of the engineering Young's modulus (in the z direction) is 19.6 GPa. We observed a yield behavior in the z direction for a strain value of 6%. Furthermore, we also report calculated heat capacity, thermal expansion coefficient and isothermal compressibility of the system under study.
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Cadelano E, Palla PL, Giordano S, Colombo L. Nonlinear elasticity of monolayer graphene. PHYSICAL REVIEW LETTERS 2009; 102:235502. [PMID: 19658947 DOI: 10.1103/physrevlett.102.235502] [Citation(s) in RCA: 82] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2008] [Indexed: 05/28/2023]
Abstract
By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.
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Affiliation(s)
- John J. Gilman
- a Lawrence Berkeley Laboratory , Berkeley , California , 94720 , USA
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9
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Bradley DK, Eggert JH, Hicks DG, Celliers PM, Moon SJ, Cauble RC, Collins GW. Shock compressing diamond to a conducting fluid. PHYSICAL REVIEW LETTERS 2004; 93:195506. [PMID: 15600850 DOI: 10.1103/physrevlett.93.195506] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2004] [Indexed: 05/24/2023]
Abstract
Laser generated shock reflectance data show that diamond undergoes a continuous transition from optically absorbing to reflecting between Hugoniot pressures 600<P(H)<1000 GPa. The data are consistent with diamond having a thermal population of carriers at P(H) approximately 600 GPa, undergoing band overlap metallization at P(H) approximately 1000 GPa and melting at 800<P(H)<1000 GPa. The results agree well with an equation of state model that predicts that elemental carbon remains solid throughout the interior of Neptune.
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Affiliation(s)
- D K Bradley
- Lawrence Livermore National Laboratory, Livermore, California 94551, USA
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10
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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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11
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Goncharov AF, Gregoryanz E, Hemley RJ, Mao H. Spectroscopic studies of the vibrational and electronic properties of solid hydrogen to 285 GPa. Proc Natl Acad Sci U S A 2001; 98:14234-7. [PMID: 11717391 PMCID: PMC64665 DOI: 10.1073/pnas.201528198] [Citation(s) in RCA: 97] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We report Raman scattering and visible to near-infrared absorption spectra of solid hydrogen under static pressure up to 285 GPa between 20 and 140 K. We obtain pressure dependences of vibron and phonon modes consistent with results previously determined to lower pressures. The results indicate the stability of the ordered molecular phase III to the highest pressure reached and provide constraints on the insulator-to-metal transition pressure.
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Affiliation(s)
- A F Goncharov
- Geophysical Laboratory and Center for High Pressure Research, Carnegie Institution of Washington, 5251 Broad Branch Road NW, Washington, DC 20015, USA
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13
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Chacham H, Kleinman L. Instabilities in diamond under high shear stress. PHYSICAL REVIEW LETTERS 2000; 85:4904-4907. [PMID: 11102147 DOI: 10.1103/physrevlett.85.4904] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2000] [Indexed: 05/23/2023]
Abstract
We investigate, through first-principles calculations, lattice instabilities induced in diamond by the application of high shear stresses. For shear stresses as low as 95 GPa a lattice instability will occur, leading to graphitelike layered structures. This effect is highly anisotropic. The reversal of the direction of the applied shear forces may cause a change of 80 GPa in the shear stress value at which the instability develops. The same reversal also causes different bonds to be broken, resulting in a drastic change in the orientation of the resulting graphitelike structures. We also find that an additional compressive stress of 50 GPa along the (111) direction does not eliminate the shear-induced instability.
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Affiliation(s)
- H Chacham
- Department of Physics, University of Texas, Austin, Texas 78712 and Departamento de Fisica, ICEx, Universidade Federal de Minas Gerais, CP 702, 30123-970, Belo Horizonte, MG, Brazil
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14
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Karch K, Dietrich T, Windl W, Pavone P, Mayer AP, Strauch D. Contribution of quantum and thermal fluctuations to the elastic moduli and dielectric constants of covalent semiconductors. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:7259-7266. [PMID: 9982173 DOI: 10.1103/physrevb.53.7259] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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15
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Clark SJ, Ackland GJ, Crain J. Theoretical stability limit of diamond at ultrahigh pressure. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:15035-15038. [PMID: 9980844 DOI: 10.1103/physrevb.52.15035] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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16
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Muinov M, Kanda H, Stishov SM. Raman scattering in diamond at high pressure: Isotopic effects. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:13860-13862. [PMID: 9975600 DOI: 10.1103/physrevb.50.13860] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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17
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Hebbache M. Elastic phase transition in germanium and silicon. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:6522-6527. [PMID: 10009369 DOI: 10.1103/physrevb.49.6522] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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18
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Pavone P, Karch K, Schütt O, Strauch D, Windl W, Giannozzi P, Baroni S. Ab initio lattice dynamics of diamond. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:3156-3163. [PMID: 10008738 DOI: 10.1103/physrevb.48.3156] [Citation(s) in RCA: 123] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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19
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Surh MP, Louie SG, Cohen ML. Band gaps of diamond under anisotropic stress. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:8239-8247. [PMID: 10000654 DOI: 10.1103/physrevb.45.8239] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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20
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Chetty N, Martin RM. First-principles energy density and its applications to selected polar surfaces. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:6074-6088. [PMID: 10000352 DOI: 10.1103/physrevb.45.6074] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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21
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Lambrecht WR, Segall B, Methfessel M. Calculated elastic constants and deformation potentials of cubic SiC. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:3685-3694. [PMID: 9999997 DOI: 10.1103/physrevb.44.3685] [Citation(s) in RCA: 63] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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23
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Hanfland M, Hemley RJ, Mao HK. Optical absorption measurements of hydrogen at megabar pressures. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:8767-8770. [PMID: 9996542 DOI: 10.1103/physrevb.43.8767] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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24
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Fukumoto A. First-principles pseudopotential calculations of the elastic properties of diamond, Si, and Ge. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:7462-7469. [PMID: 9994891 DOI: 10.1103/physrevb.42.7462] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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25
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Hanfland M, Beister H, Syassen K. Graphite under pressure: Equation of state and first-order Raman modes. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:12598-12603. [PMID: 9948126 DOI: 10.1103/physrevb.39.12598] [Citation(s) in RCA: 208] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Pickett WE. Thin superlattices and band-gap discontinuities: The (110) diamond-boron nitride interface. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:1316-1322. [PMID: 9946392 DOI: 10.1103/physrevb.38.1316] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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28
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Weyrich KH, Brey L, Christensen NE. Full-potential linear-muffin-tin-orbital calculation of phonon frequencies in semiconductors. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:1392-1396. [PMID: 9946402 DOI: 10.1103/physrevb.38.1392] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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29
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Fahy S, Louie SG. High-pressure structural and electronic properties of carbon. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 36:3373-3385. [PMID: 9943253 DOI: 10.1103/physrevb.36.3373] [Citation(s) in RCA: 70] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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30
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Brey L, Christensen NE, Cardona M. Deformation potentials at the valence-band maximum in semiconductors. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 36:2638-2644. [PMID: 9943148 DOI: 10.1103/physrevb.36.2638] [Citation(s) in RCA: 31] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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31
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Christensen NE, Satpathy S, Pawlowska Z. Bonding and ionicity in semiconductors. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 36:1032-1050. [PMID: 9942909 DOI: 10.1103/physrevb.36.1032] [Citation(s) in RCA: 145] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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32
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Biswas R, Martin RM, Needs RJ, Nielsen OH. Stability and electronic properties of complex structures of silicon and carbon under pressure: Density-functional calculations. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 35:9559-9568. [PMID: 9941381 DOI: 10.1103/physrevb.35.9559] [Citation(s) in RCA: 50] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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33
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Wickboldt P, Anastassakis E, Sauer R, Cardona M. Raman phonon piezospectroscopy in GaAs: Infrared measurements. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 35:1362-1368. [PMID: 9941542 DOI: 10.1103/physrevb.35.1362] [Citation(s) in RCA: 67] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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