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Tepsic S, Gruber G, Møller CB, Magén C, Belardinelli P, Hernández ER, Alijani F, Verlot P, Bachtold A. Interrelation of Elasticity and Thermal Bath in Nanotube Cantilevers. Phys Rev Lett 2021; 126:175502. [PMID: 33988423 DOI: 10.1103/physrevlett.126.175502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 03/16/2021] [Indexed: 06/12/2023]
Abstract
We report the first study on the thermal behavior of the stiffness of individual carbon nanotubes, which is achieved by measuring the resonance frequency of their fundamental mechanical bending modes. We observe a reduction of the Young's modulus over a large temperature range with a slope -(173±65) ppm/K in its relative shift. These findings are reproduced by two different theoretical models based on the thermal dynamics of the lattice. These results reveal how the measured fundamental bending modes depend on the phonons in the nanotube via the Young's modulus. An alternative description based on the coupling between the measured mechanical modes and the phonon thermal bath in the Akhiezer limit is discussed.
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Affiliation(s)
- S Tepsic
- ICFO-Institut De Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - G Gruber
- ICFO-Institut De Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - C B Møller
- ICFO-Institut De Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - C Magén
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain
- Laboratorio de Microscopías Avanzadas (LMA), Universidad de Zaragoza, 50018 Zaragoza, Spain
| | - P Belardinelli
- DICEA, Polytechnic University of Marche, 60131 Ancona, Italy
| | - E R Hernández
- Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), 28049 Madrid, Spain
| | - F Alijani
- Department of Precision and Microsystems Engineering, 3ME, Mekelweg 2, (2628 CD) Delft, The Netherlands
| | - P Verlot
- School of Physics and Astronomy-The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - A Bachtold
- ICFO-Institut De Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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Gruber G, Urgell C, Tavernarakis A, Stavrinadis A, Tepsic S, Magén C, Sangiao S, de Teresa JM, Verlot P, Bachtold A. Mass Sensing for the Advanced Fabrication of Nanomechanical Resonators. Nano Lett 2019; 19:6987-6992. [PMID: 31478676 PMCID: PMC6788197 DOI: 10.1021/acs.nanolett.9b02351] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2019] [Revised: 08/07/2019] [Indexed: 06/01/2023]
Abstract
We report on a nanomechanical engineering method to monitor matter growth in real time via e-beam electromechanical coupling. This method relies on the exceptional mass sensing capabilities of nanomechanical resonators. Focused electron beam-induced deposition (FEBID) is employed to selectively grow platinum particles at the free end of singly clamped nanotube cantilevers. The electron beam has two functions: it allows both to grow material on the nanotube and to track in real time the deposited mass by probing the noise-driven mechanical resonance of the nanotube. On the one hand, this detection method is highly effective as it can resolve mass deposition with a resolution in the zeptogram range; on the other hand, this method is simple to use and readily available to a wide range of potential users because it can be operated in existing commercial FEBID systems without making any modification. The presented method allows one to engineer hybrid nanomechanical resonators with precisely tailored functionalities. It also appears as a new tool for studying the growth dynamics of ultrathin nanostructures, opening new opportunities for investigating so far out-of-reach physics of FEBID and related methods.
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Affiliation(s)
- G. Gruber
- ICFO
- Institut de Ciencies Fotoniques, The Barcelona
Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - C. Urgell
- ICFO
- Institut de Ciencies Fotoniques, The Barcelona
Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - A. Tavernarakis
- ICFO
- Institut de Ciencies Fotoniques, The Barcelona
Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - A. Stavrinadis
- ICFO
- Institut de Ciencies Fotoniques, The Barcelona
Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - S. Tepsic
- ICFO
- Institut de Ciencies Fotoniques, The Barcelona
Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - C. Magén
- Instituto
de Ciencia de Materiales de Aragón (ICMA), Universidad de Zaragoza-CSIC, 50009 Zaragoza, Spain
- Laboratorio
de Microscopías Avanzadas (LMA), Instituto de Nanociencia de
Aragón (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain
| | - S. Sangiao
- Instituto
de Ciencia de Materiales de Aragón (ICMA), Universidad de Zaragoza-CSIC, 50009 Zaragoza, Spain
- Laboratorio
de Microscopías Avanzadas (LMA), Instituto de Nanociencia de
Aragón (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain
| | - J. M. de Teresa
- Instituto
de Ciencia de Materiales de Aragón (ICMA), Universidad de Zaragoza-CSIC, 50009 Zaragoza, Spain
- Laboratorio
de Microscopías Avanzadas (LMA), Instituto de Nanociencia de
Aragón (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain
| | - P. Verlot
- School
of Physics and Astronomy, The University
of Nottingham, University Park, Nottingham NG7 2RD, United
Kingdom
| | - A. Bachtold
- ICFO
- Institut de Ciencies Fotoniques, The Barcelona
Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
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