1、BSI Standards PublicationBS ISO 11775:2015Surface chemical analysis Scanning-probe microscopy Determination of cantilevernormal spring constantsBS ISO 11775:2015 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of ISO 11775:2015.The UK participation in its preparation
2、was entrusted to TechnicalCommittee CII/60, Surface chemical analysis.A list of organizations represented on this committee can beobtained on request to its secretary.This publication does not purport to include all the necessaryprovisions of a contract. Users are responsible for its correctapplicat
3、ion. The British Standards Institution 2015.Published by BSI Standards Limited 2015ISBN 978 0 580 66871 5ICS 71.040.40Compliance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was published under the authority of theStandards Policy and Strategy Committee
4、on 31 October 2015.Amendments/corrigenda issued since publicationDate T e x t a f f e c t e dBS ISO 11775:2015 ISO 2015Surface chemical analysis Scanning-probe microscopy Determination of cantilever normal spring constantsAnalyse chimique des surfaces Microscopie sonde balayage Dtermination de const
5、antes normales en porte-faux de ressortINTERNATIONAL STANDARDISO11775First edition2015-10-01Reference numberISO 11775:2015(E)BS ISO 11775:2015ISO 11775:2015(E)ii ISO 2015 All rights reservedCOPYRIGHT PROTECTED DOCUMENT ISO 2015, Published in SwitzerlandAll rights reserved. Unless otherwise specified
6、, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISOs m
7、ember body in the country of the requester.ISO copyright officeCh. de Blandonnet 8 CP 401CH-1214 Vernier, Geneva, SwitzerlandTel. +41 22 749 01 11Fax +41 22 749 09 47copyrightiso.orgwww.iso.orgBS ISO 11775:2015ISO 11775:2015(E)Foreword ivIntroduction v1 Scope . 12 Normative references 13 Terms and d
8、efinitions . 14 Symbols and abbreviated terms . 25 General information . 45.1 Background information 45.2 Methods for the determination of AFM normal spring constant . 56 Dimensional methods to determine kz56.1 General . 56.2 kzusing formulae requiring 3D geometric information . 56.2.1 Method 56.2.2
9、 Measuring the required dimensions and material properties of the cantilever . 76.2.3 Determining kzfor the rectangular cantilever . 86.2.4 Determining kzfor the V-shaped cantilever . 86.2.5 kzfor the trapezoidal cross-sections 96.2.6 kzto account for coatings . 96.3 kzusing plan view dimensions and
10、 resonant frequency for rectangular tipless cantilevers 106.3.1 Determining kz106.3.2 Uncertainty 117 Static experimental methods to determine kz117.1 General 117.2 Static experimental method with a reference cantilever 117.2.1 Set-up 117.2.2 Determining kz127.2.3 Uncertainty 147.3 Static experiment
11、al method using a nanoindenter 157.3.1 General. 157.3.2 Determining kzfor a tipped or tipless cantilever .157.3.3 Uncertainty 167.4 Measurement methods . 187.4.1 Static deflection calibration. 188 Dynamic experimental methods to determine kz.188.1 General 188.2 Dynamic experimental method using ther
12、mal vibrations using AFM .188.2.1 Determining kz188.2.2 Uncertainty 20Annex A (informative) Inter-laboratory and intra-laboratory comparison of AFM cantilevers 21Bibliography .24 ISO 2015 All rights reserved iiiContents PageBS ISO 11775:2015ISO 11775:2015(E)ForewordISO (the International Organizatio
13、n for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has
14、 the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.The pr
15、ocedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the edito
16、rial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any patent right
17、s identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents).Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement.For an explan
18、ation on the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISOs adherence to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information.The committee responsible for this docum
19、ent is ISO/TC 201, Surface chemical analysis, Subcommittee SC 9, Scanning probe microscopy.iv ISO 2015 All rights reservedBS ISO 11775:2015ISO 11775:2015(E)IntroductionAtomic force microscopy (AFM) is a mode of scanning probe microscopy (SPM) used to image surfaces by mechanically scanning a probe o
20、ver the surface in which the deflection of a sharp tip sensing the surface forces mounted on a compliant cantilever is monitored. It can provide amongst other data, topographic, mechanical, chemical, and electro-magnetic information about a surface depending on the mode of operation and the property
21、 of the tip. Accurate force measurements are needed for a wide variety of applications, from measuring the unbinding force of protein and other molecules to determining the elastic modulus of materials, such as organics and polymers at surfaces. For such force measurements, the value of the AFM cant
22、ilever normal spring constant, kz, is required. The manufacturers nominal values of kzhave been found to be up to a factor of three in error, therefore practical methods to calibrate kzare required.This International Standard describes five of the simplest methods in three categories for the determi
23、nation of normal spring constants for atomic force microscope cantilevers. The methods are in one of the three categories of dimensional, static experimental, and dynamic experimental methods. The method chosen depends on the purpose and convenience to the analyst. Many other methods may also be fou
24、nd in the literature. ISO 2015 All rights reserved vBS ISO 11775:2015BS ISO 11775:2015Surface chemical analysis Scanning-probe microscopy Determination of cantilever normal spring constants1 ScopeThis International Standard describes five of the methods for the determination of normal spring constan
25、ts for atomic force microscope cantilevers to an accuracy of 5 % to 10 %. Each method is in one of the three categories of dimensional, static experimental, and dynamic experimental methods. The method chosen depends on the purpose, convenience, and instrumentation available to the analyst. For accu
26、racies better than 5 % to 10 %, more sophisticated methods not described here are required.2 Normative referencesThe following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies.
27、For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 18115-2, Surface chemical analysis Vocabulary Part 2: Terms used in scanning-probe microscopy3 Terms and definitionsFor the purposes of this document, the terms and definitions given in ISO 1
28、8115-2 and the following apply.3.1normal spring constantspring constantforce constantDEPRECATED: cantilever stiffnesskzquotient of the applied normal force at the probe tip (3.2) by the deflection of the cantilever in that direction at the probe tip positionNote 1 to entry: See lateral spring consta
29、nt, torsional spring constant.Note 2 to entry: The normal spring constant is usually referred to as the spring constant. The full term is used when it is necessary to distinguish it from the lateral spring constant.Note 3 to entry: The force is applied normal to the plane of the cantilever to comput
30、e or measure the normal force constant, kz. In application, the cantilever in an AFM may be tilted at an angle, , to the plane of the sample surface and the plane normal to the direction of approach of the tip to the sample. This angle is important in applying the normal spring constant in AFM studi
31、es.3.2probe tiptipprobe apexstructure at the extremity of a probe, the apex of which senses the surfaceNote 1 to entry: See cantilever apex (3.3).3.3cantilever apexend of the cantilever furthest from the cantilever support structureNote 1 to entry: See probe apex (3.2), tip apex (3.2).INTERNATIONAL
32、STANDARD ISO 11775:2015(E) ISO 2015 All rights reserved 1BS ISO 11775:2015ISO 11775:2015(E)4 Symbols and abbreviated termsIn the list of abbreviated terms below, note that the final “M”, given as “Microscopy”, may be taken equally as “Microscope” depending on the context. The abbreviated terms are:A
33、FM Atomic force microscopyFEA Finite element analysisPSD Power spectral densitySEM Scanning electron microscopySPM Scanning probe microscopyThe symbols for use in the formulae and as abbreviated terms in the text are:A amplitude of cantilever at a certain frequencyA0amplitude of a cantilever at its
34、fundamental resonant frequencyAwhitemean amplitude of a cantilever associated with white noiseBgradient determined from a straight line fit to values of Lxversus x1/3Bkgradient determined from a straight line fit to values of LxversuszxLk( )13/C1correction factor for the thermal vibration method des
35、cribed in 8.2C2correction factor for the thermal vibration method described in 8.2d distance between the probe tip and the cantilever apexD height of the probe tipe width of the V-shaped cantilever at a distance L0from the apexE Youngs modulus of the material of a cantileverEBYoungs modulus of the b
36、ase material of a cantileverECYoungs modulus of the coating material on a cantileverf frequencyf0fundamental resonant frequency of a cantileverF force of a nanoindenterh displacement of a nanoindenteri index of Pi, where i = 1 to 5kBBoltzmann constantkznormal spring constantzxLknormal spring constan
37、t at the position Lxalong a cantilever2 ISO 2015 All rights reservedBS ISO 11775:2015ISO 11775:2015(E)kzRnormal spring constant of a reference cantileverkzWnormal spring constant of a working cantileverkz(tc=0)normal spring constant of a cantilever with a coating thickness of 0L length of a rectangu
38、lar cantilever or the effective length of a V-shaped cantileverLxdistance between the base of a cantilever and the effective position of a V-shaped cantileverL0length of a V-shaped cantilever between the apex and the start of the armsL1length of a V-shaped cantilever between the base and the start o
39、f the armsPilabel of one of the five positions on the reference cantilever axisQ quality factor of a cantileverr term defined by Formula (7)t thickness of a cantilevertBthickness of the bulk material of a cantilevertCthickness of a coating on a cantileverT absolute temperature of the cantilever meas
40、ured in KelvinsuA0standard uncertainty in A0uBstandard uncertainty in BuC1standard uncertainty in C1uC2standard uncertainty in C2udstandard uncertainty in the distance between the probe tip and the cantilever apexuEstandard uncertainty in the Youngs modulus of a cantileveruFstandard uncertainty due
41、to the calibration of force in the nanoindenteruf0standard uncertainty in the resonant frequencyuhstandard uncertainty due to the calibration of displacement in the nanoindenterukzstandard uncertainty in the normal spring constantukzRstandard uncertainty in the normal spring constant of the referenc
42、e cantileveruLstandard uncertainty in the length of a cantileveruQstandard uncertainty in the quality factor of a cantileverutstandard uncertainty in the thickness of a cantileveruTstandard uncertainty in the absolute temperatureuwstandard uncertainty in the width of a cantileverux1standard uncertai
43、nty in x1 ISO 2015 All rights reserved 3BS ISO 11775:2015ISO 11775:2015(E)u1standard uncertainty in 1ustandard uncertainty in the density of a cantileverw width of a cantileverw1width of one side of a trapeziumw2width of one side of a trapeziumwtwcosx1offset to account for the small uncertainty in t
44、he true position of the base of the cantilever com-pared to an arbitrary reference pointx2offset to account for the uncertainty in the true position of the probe tip compared to an arbi-trary reference pointZ1term defined by Formula (4)Z2term defined by Formula (5) angle of the working cantilever wi
45、th respect to the reference cantilever or surface1numeric constant used in Formula (11)Raverage inverse gradient of the force-distance curve obtained with the working cantilever pressing on the reference cantilever or deviceWaverage inverse gradient of the force-distance curve obtained with the work
46、ing cantilever pressing on a stiff surface half angle between the arms of a V-shaped cantilever2term defined by Formula (6) Poissons ratio of the cantilever material density of a cantileverxterm defined by Formula (16)5 General information5.1 Background informationThe spring constant, kz, of an AFM
47、cantilever is needed for quantitative force measurement. It is used to convert the deflection of the cantilever into a force. Applications that need this include the measurement of material properties at the nanoscale, such as elastic modulus, adhesive forces, and for studying the breaking of covale
48、nt bonds and protein unfolding. Depending on the application, kzwill be chosen to be in the range between 0,005 Nm1and 200 Nm1. There are two main shapes of cantilever: the rectangular “diving board” shape and the V-shaped. Both types vary slightly in basic shape and design between manufacturers and
49、 can be rectangular or trapezoidal in cross-section. Some cantilevers are also coated with a thin metallic layer. These factors all influence the value of kz.Many manufacturers provide data sheets for their cantilevers giving nominal values of kz. Unfortunately, these values can be routinely in error by up to a factor of 3. One reason why similar cantilevers have very different values of kzis that the spring constant is proportional to the thickness cubed and the thickness 4 ISO 2015 All rights reservedBS ISO
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