Standard No.:	GB/T 42543-2023
English Name:	Surface chemical analysis—Scanning probe microscopy—Determination of cantilever normal spring constants
Chinese Name:	表面化学分析 扫描探针显微术 悬臂梁法向弹性常数的测定
Chinese Classification:	G04    Basic standards and general methods
Professional Classification:	GB    National Standard
ICS Classification:	71.040.40 71.040.40    Chemical analysis 71.040.40
Source Content Issued by:	SAMR; SAC
Issued on:	2023-05-23
Implemented on:	2023-9-1
Status:	valid
Target Language:	English
File Format:	PDF
Word Count:	14500 words
Translation Price(USD):	435.0
Delivery:	via email in 1~3 business day

Surface chemical analysis - Scanning probe microscopy - Determination of cantilever normal spring constants 1 Scope This International Standard describes five of the methods for the determination of normal spring constants 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. This document is not applicable to an accuracy higher than 5 % to 10 %. For accuracies better than 5 % to 10 %, more sophisticated methods not described here are required. 2 Normative references The 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. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 18115-2:2013 Surface chemical analysis - Vocabulary - Part 2: Terms used in scanning-probe microscopy 3 Terms and definitions For the purposes of this document, the terms and definitions given in ISO 18115-2 and the following apply. 3.1 normal spring constant spring constant force constant DEPRECATED: cantilever stiffness kz quotient of the applied normal force at the probe tip (3.2) by the deflection of the cantilever in that direction at the probe tip position Note 1: See lateral spring constant, torsional spring constant. Note 2: 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: The force is applied normal to the plane of the cantilever to compute or measure the normal force constant, kz. In application, the cantilever in an AFM may be tilted at an angle, θ, 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 studies. 3.2 probe tip tip probe apex structure at the extremity of a probe, the apex of which senses the surface Note: See cantilever apex (3.3). 3.3 cantilever apex end of the cantilever furthest from the cantilever support structure Note: See probe apex (3.2), tip apex (3.2). 4 Symbols and abbreviated terms The following symbols and abbreviated terms apply to this document. The abbreviated terms are: AFM Atomic force microscopy FEA Finite element analysis PSD Power spectral density SEM Scanning electron microscopy SPM Scanning probe microscopy Note: In 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 symbols for use in the formulae are: A amplitude of cantilever at a certain frequency A0 amplitude of a cantilever at its fundamental resonant frequency Awhite mean amplitude of a cantilever associated with white noise BΦ gradient determined from a straight line fit to values of Lx versus Φx1/3 Bk gradient determined from a straight line fit to values of Lx versus (kzLx)-1/3 C1 correction factor for the thermal vibration method described in 8.2 C2 correction factor for the thermal vibration method described in 8.2 d distance between the probe tip and the cantilever apex D height of the probe tip e width of the V-shaped cantilever at a distance L0 from the apex E Young’s modulus of the material of a cantilever EB Young’s modulus of the base material of a cantilever EC Young’s modulus of the coating material on a cantilever f frequency f0 fundamental resonant frequency of a cantilever F force of a nanoindenter h displacement of a nanoindenter i index of Pi, where i = 1 to 5 kB Boltzmann constant kz normal spring constant kzLx normal spring constant at the position Lx along a cantilever kzR normal spring constant of a reference cantilever kzW normal spring constant of a working cantilever kz(tc=0) normal spring constant of a cantilever with a coating thickness of 0 L length of a rectangular cantilever or the effective length of a V-shaped cantilever Lx distance between the base of a cantilever and the effective position of a V-shaped cantilever L0 length of a V-shaped cantilever between the apex and the start of the arms L1 length of a V-shaped cantilever between the base and the start of the arms Pi label of one of the five positions on the reference cantilever axis Q quality factor of a cantilever r term defined by Formula (7) t thickness of a cantilever tB thickness of the bulk material of a cantilever tC thickness of a coating on a cantilever T absolute temperature of the cantilever measured in Kelvins uA0 standard uncertainty in A0 uB standard uncertainty in B uC1 standard uncertainty in C1 uC2 standard uncertainty in C2 ud standard uncertainty in the distance between the probe tip and the cantilever apex uE standard uncertainty in the Young’s modulus of a cantilever uF standard uncertainty due to the calibration of force in the nanoindenter uf0 standard uncertainty in the resonant frequency uh standard uncertainty due to the calibration of displacement in the nanoindenter ukz standard uncertainty in the normal spring constant ukzR standard uncertainty in the normal spring constant of the reference cantilever uL standard uncertainty in the length of a cantilever uQ standard uncertainty in the quality factor of a cantilever ut standard uncertainty in the thickness of a cantilever uT standard uncertainty in the absolute temperature uw standard uncertainty in the width of a cantilever ux1 standard uncertainty in x1 uα1 standard uncertainty in α1 uρ standard uncertainty in the density of a cantilever w width of a cantilever w1 width of one side of a trapezium w2 width of one side of a trapezium wt w cosθ x1 offset to account for the small uncertainty in the true position of the base of the cantilever com-pared to an arbitrary reference point x2 offset to account for the uncertainty in the true position of the probe tip compared to an arbi-trary reference point Z1 term defined by Formula (4) Z2 term defined by Formula (5) α angle of the working cantilever with respect to the reference cantilever or surface α1 numeric constant used in Formula (11) δR average inverse gradient of the force-distance curve obtained with the working cantilever pressing on the reference cantilever or device δW average inverse gradient of the force-distance curve obtained with the working cantilever pressing on a stiff surface υ half angle between the arms of a V-shaped cantilever θ2 term defined by Formula (6) ν Poisson’s ratio of the cantilever material ρ density of a cantilever φx term defined by Formula (16)