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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2019-10-6-642-653</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-820</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>CHEMISTRY AND MATERIALS SCIENCE</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ХИМИЯ И НАУКА О МАТЕРИАЛАХ</subject></subj-group></article-categories><title-group><article-title>On the accuracy of the probe-sample contact stiffness measured by an atomic force microscope</article-title><trans-title-group xml:lang="ru"><trans-title>On the accuracy of the probe-sample contact stiffness measured by an atomic force microscope</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ankudinov</surname><given-names>А. V.</given-names></name><name name-style="western" xml:lang="en"><surname>Ankudinov</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>26 Politekhnicheskaya, Saint-Petersburg 194021</p></bio><bio xml:lang="en"><p>26 Politekhnicheskaya, Saint-Petersburg 194021</p></bio><email xlink:type="simple">Alexander.ankudinov@mail.ioffe.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Ioffe Institute</institution></aff><aff xml:lang="en"><institution>Ioffe Institute</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>13</day><month>08</month><year>2025</year></pub-date><volume>10</volume><issue>6</issue><fpage>642</fpage><lpage>653</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Ankudinov A.V., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Ankudinov А.V.</copyright-holder><copyright-holder xml:lang="en">Ankudinov A.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/820">https://nanojournal.ifmo.ru/jour/article/view/820</self-uri><abstract><p>To improve the accuracy of atomic force microscopy in nanomechanical experiments, an analytical model is proposed to study the static interaction of a cantilever in contact with a sample. The model takes into account: the cantilever probe is clamped by the sample or slides along its surface, the geometric and mechanical characteristics of the sample and the cantilever, their relative orientation. The cantilever console bending and torsion angles as functions of the sample displacements in three orthogonal directions have been measured by atomic force microscopy with an optical beam deflection scheme.The measurements are in good agreement with the simulation.</p></abstract><trans-abstract xml:lang="ru"><p>To improve the accuracy of atomic force microscopy in nanomechanical experiments, an analytical model is proposed to study the static interaction of a cantilever in contact with a sample. The model takes into account: the cantilever probe is clamped by the sample or slides along its surface, the geometric and mechanical characteristics of the sample and the cantilever, their relative orientation. The cantilever console bending and torsion angles as functions of the sample displacements in three orthogonal directions have been measured by atomic force microscopy with an optical beam deflection scheme.The measurements are in good agreement with the simulation.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>AFM</kwd><kwd>cantilever</kwd><kwd>sliding and clamping probesample contact</kwd></kwd-group><kwd-group xml:lang="en"><kwd>AFM</kwd><kwd>cantilever</kwd><kwd>sliding and clamping probesample contact</kwd></kwd-group><funding-group><funding-statement xml:lang="en">The author thanks his colleagues, Dr. M. M. Khalisov and Dr. A. A. Krasilin for constructive criticism of the manuscript</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Binnig G., Quate C.F., Gerber Ch. Atomic Force Microscope. Physical Review Letters, 1986, 56 (9), P. 930–933.</mixed-citation><mixed-citation xml:lang="en">Binnig G., Quate C.F., Gerber Ch. Atomic Force Microscope. Physical Review Letters, 1986, 56 (9), P. 930–933.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Scanning probe based apparatus and methods for low-force profiling of sample surfaces and detection and mapping of local mechanical and electromagnetic properties in non-resonant oscillatory mode. Patent Number: US 9,110,092 B1, USA. Date of Patent: Aug. 18, 2015. Int. Cl.: GOIN I3/6 (2006.01), G0IB 5/28 (2006.01). Inventors: Magonov S., Belikov S., Alexander J.D., Wall C.G., Leesment S., and Bykov V. Assignee: NT-MDT Development Inc., Tempe, AZ (US). Appl. No.: 14/247,041. Filed: Apr. 7, 2014. 10 Claims, 34 Drawing Sheets.</mixed-citation><mixed-citation xml:lang="en">Scanning probe based apparatus and methods for low-force profiling of sample surfaces and detection and mapping of local mechanical and electromagnetic properties in non-resonant oscillatory mode. Patent Number: US 9,110,092 B1, USA. Date of Patent: Aug. 18, 2015. Int. Cl.: GOIN I3/6 (2006.01), G0IB 5/28 (2006.01). Inventors: Magonov S., Belikov S., Alexander J.D., Wall C.G., Leesment S., and Bykov V. Assignee: NT-MDT Development Inc., Tempe, AZ (US). Appl. No.: 14/247,041. Filed: Apr. 7, 2014. 10 Claims, 34 Drawing Sheets.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Jumping probe microscope. Patent Number: 5,229,606, USA. Date of Patent: Jul. 20, 1993. Int. Cl.: H01J 37/26. Inventors: Elings V., Gurley J. Assignee: Digital Instruments, Inc., Santa Barbara, Calif. Appl. No.: 361,545. Filed: Jun. 5, 1989. 30 Claims, 4 Drawing Sheets.</mixed-citation><mixed-citation xml:lang="en">Jumping probe microscope. Patent Number: 5,229,606, USA. Date of Patent: Jul. 20, 1993. Int. Cl.: H01J 37/26. Inventors: Elings V., Gurley J. Assignee: Digital Instruments, Inc., Santa Barbara, Calif. Appl. No.: 361,545. Filed: Jun. 5, 1989. 30 Claims, 4 Drawing Sheets.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">de Pablo P.J., Colchero J., Gomez-Herrero J., and Baro A.M. Jumping mode scanning force microscopy. Applied Physics Letters, 1998, 73 (22), P. 3300–3302.</mixed-citation><mixed-citation xml:lang="en">de Pablo P.J., Colchero J., Gomez-Herrero J., and Baro A.M. Jumping mode scanning force microscopy. Applied Physics Letters, 1998, 73 (22), P. 3300–3302.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Kalinin A.S. PhD thesis. National Research Center “Kurchatov Institute”, Moscow, 2017, 102 p.</mixed-citation><mixed-citation xml:lang="en">Kalinin A.S. PhD thesis. National Research Center “Kurchatov Institute”, Moscow, 2017, 102 p.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Sarid D. Exploring scanning probe microscopy with MATHEMATICA. 2nd ed. Weinheim: WILEY-VCH Verlag, 2007, 310 p.</mixed-citation><mixed-citation xml:lang="en">Sarid D. Exploring scanning probe microscopy with MATHEMATICA. 2nd ed. Weinheim: WILEY-VCH Verlag, 2007, 310 p.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Ankudinov A.V., Khalisov M.M., et al. The Probe Length Effect on the Cantilever of an Atomic Force Microscope in Measuring the Mechanical Properties of Living Neurons. Tech. Phys. Lett., 2018, 44 (8), P. 671–674.</mixed-citation><mixed-citation xml:lang="en">Ankudinov A.V., Khalisov M.M., et al. The Probe Length Effect on the Cantilever of an Atomic Force Microscope in Measuring the Mechanical Properties of Living Neurons. Tech. Phys. Lett., 2018, 44 (8), P. 671–674.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Alexander S., Hellemans L., et al. An atomicresolution atomicforce microscope implemented using an optical lever. J. of Appl. Phys., 1989, 65 (1), P. 164–167.</mixed-citation><mixed-citation xml:lang="en">Alexander S., Hellemans L., et al. An atomicresolution atomicforce microscope implemented using an optical lever. J. of Appl. Phys., 1989, 65 (1), P. 164–167.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Fujisawa S., Ohta M., et al. Difference between the forces measured by an optical lever deflection and by an optical interferometer in an atomic force microscope. Rev. Sci. Instrum, 1994, 65 (3), P. 644–647.</mixed-citation><mixed-citation xml:lang="en">Fujisawa S., Ohta M., et al. Difference between the forces measured by an optical lever deflection and by an optical interferometer in an atomic force microscope. Rev. Sci. Instrum, 1994, 65 (3), P. 644–647.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Kawakatsu H., Bleuler H., Saito T., Hiroshi K. Dual Optical Levers for Atomic Force Microscopy. Jpn. J. Appl. Phys., 1995, 34, 1 (6B), P. 3400–3402.</mixed-citation><mixed-citation xml:lang="en">Kawakatsu H., Bleuler H., Saito T., Hiroshi K. Dual Optical Levers for Atomic Force Microscopy. Jpn. J. Appl. Phys., 1995, 34, 1 (6B), P. 3400–3402.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Asylum Research Quantifies the “Last Axis” in Atomic Force Microscopy, 2018, URL: https://www.oxford-instruments.com.</mixed-citation><mixed-citation xml:lang="en">Asylum Research Quantifies the “Last Axis” in Atomic Force Microscopy, 2018, URL: https://www.oxford-instruments.com.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Labuda A., Proksch R. Quantitative measurements of electromechanical response with a combined optical beam and interferometric atomic force microscope. Appl. Phys. Lett., 2015, 106 (25), 253103.</mixed-citation><mixed-citation xml:lang="en">Labuda A., Proksch R. Quantitative measurements of electromechanical response with a combined optical beam and interferometric atomic force microscope. Appl. Phys. Lett., 2015, 106 (25), 253103.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Mironov V.L. Fundamentals of the Scanning Probe Microscopy. The Russian Academy of Sciences Institute of Physics of Microsructures, Nizhniy Novgorod, 2004, 97 p.</mixed-citation><mixed-citation xml:lang="en">Mironov V.L. Fundamentals of the Scanning Probe Microscopy. The Russian Academy of Sciences Institute of Physics of Microsructures, Nizhniy Novgorod, 2004, 97 p.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">URL: https://www.ntmdt-si.ru/resources/spm-theory/theoretical-background-of-spm.</mixed-citation><mixed-citation xml:lang="en">URL: https://www.ntmdt-si.ru/resources/spm-theory/theoretical-background-of-spm.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Landau L.D., Lifshitz E.M. Theory of Elasticity. Oxford, Pergamon Press Ltd., 1970, 177 p.</mixed-citation><mixed-citation xml:lang="en">Landau L.D., Lifshitz E.M. Theory of Elasticity. Oxford, Pergamon Press Ltd., 1970, 177 p.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Dunaevskiy M., Geydt P., et al. Youngs Modulus of Wurtzite and Zinc Blende InP Nanowires. Nano Letters, 2017, 17 (6), P. 3441–3446.</mixed-citation><mixed-citation xml:lang="en">Dunaevskiy M., Geydt P., et al. Youngs Modulus of Wurtzite and Zinc Blende InP Nanowires. Nano Letters, 2017, 17 (6), P. 3441–3446.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Popov V.L., Heß M., Willert E. Handbook of Contact Mechanics. Exact Solutions of Axisymmetric Contact Problems, 2019. Translation from the German Language edition: Popov et al: Handbuch der Kontaktmechanik. Springer-Verlag GmbH Deutschland, 2018, 347 p.</mixed-citation><mixed-citation xml:lang="en">Popov V.L., Heß M., Willert E. Handbook of Contact Mechanics. Exact Solutions of Axisymmetric Contact Problems, 2019. Translation from the German Language edition: Popov et al: Handbuch der Kontaktmechanik. Springer-Verlag GmbH Deutschland, 2018, 347 p.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Heim L.-O., Kappl M., Butt H.-J. Tilt of Atomic Force Microscope Cantilevers: Effect on Spring Constant and Adhesion Measurements. Langmuir, 2004, 20, P. 2760–2764.</mixed-citation><mixed-citation xml:lang="en">Heim L.-O., Kappl M., Butt H.-J. Tilt of Atomic Force Microscope Cantilevers: Effect on Spring Constant and Adhesion Measurements. Langmuir, 2004, 20, P. 2760–2764.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Hutter J.L. Comment on Tilt of Atomic Force Microscope Cantilevers: Effect on Spring Constant and Adhesion Measurements. Langmuir, 2005, 21, P. 2630–2632.</mixed-citation><mixed-citation xml:lang="en">Hutter J.L. Comment on Tilt of Atomic Force Microscope Cantilevers: Effect on Spring Constant and Adhesion Measurements. Langmuir, 2005, 21, P. 2630–2632.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Timoshchuk K.I., Khalisov M.M., et al. Mechanical characteristics of intact fibroblasts studied by atomic force microscopy. Tech. Phys. Lett., 2019, 45 (9), P. 947–950.</mixed-citation><mixed-citation xml:lang="en">Timoshchuk K.I., Khalisov M.M., et al. Mechanical characteristics of intact fibroblasts studied by atomic force microscopy. Tech. Phys. Lett., 2019, 45 (9), P. 947–950.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Bhushan B. (Ed.) Nanotribology and Nanomechanics. An Introduction. Springer-Verlag, Berlin, Heidelberg, 2005, 1148 p.</mixed-citation><mixed-citation xml:lang="en">Bhushan B. (Ed.) Nanotribology and Nanomechanics. An Introduction. Springer-Verlag, Berlin, Heidelberg, 2005, 1148 p.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">URL: http://nanoprobes.aist-nt.com.</mixed-citation><mixed-citation xml:lang="en">URL: http://nanoprobes.aist-nt.com.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Sader J.E., Chon J.W.M., Mulvaney P. Calibration of rectangular atomic force microscope cantilever. Rev. Sci. Instrum., 1999, 70, P. 3967– 3969.</mixed-citation><mixed-citation xml:lang="en">Sader J.E., Chon J.W.M., Mulvaney P. Calibration of rectangular atomic force microscope cantilever. Rev. Sci. Instrum., 1999, 70, P. 3967– 3969.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Mate C.M., McClelland G.M., Erlandsson R., Chiang S. Atomic-scale friction of a tungsten tip on a graphite surface. Phys. Rev. Lett., 1987, 59, P. 1942–1945.</mixed-citation><mixed-citation xml:lang="en">Mate C.M., McClelland G.M., Erlandsson R., Chiang S. Atomic-scale friction of a tungsten tip on a graphite surface. Phys. Rev. Lett., 1987, 59, P. 1942–1945.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Salvetat J.-P., Briggs G.A.D., et al. Elastic and Shear Moduli of Single-Walled Carbon Nanotube Ropes. Phys. Rev. Lett., 1999, 82, P. 944–947.</mixed-citation><mixed-citation xml:lang="en">Salvetat J.-P., Briggs G.A.D., et al. Elastic and Shear Moduli of Single-Walled Carbon Nanotube Ropes. Phys. Rev. Lett., 1999, 82, P. 944–947.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
