Using the Global Calibration Initiative

1. CANTILEVERS: Select a cantilever model to be calibrated.

2. DATA ENTRY - Two modes of operation:

1. Enter frequency, quality factor and spring constant measured using the Thermal Method. Press UPLOAD & CALCULATE. The entered data is uploaded to the database and the Sader Method (described in THEORY) gives you a new calculation of your spring constant.

   Standardisation and troubleshooting: Compare your measured spring constant to this new value (which is derived from all other users).

2. Enter the frequency and quality factor only. Press CALCULATE. The Sader Method uses the existing database to calculate your spring constant.

   Approach (i) lets users contribute their data to the international database - providing a global reference point for AFM force measurements.

   (Spring constant with 95% confidence interval is reported)

3. UPLOADED DATA: View and edit your own data (not those of other users).

4. REQUEST CANTILEVER: Request cantilever models to be added to the GCI.

NOTE: Take measurements of the fundamental flexural mode in air - with your cantilever at least 100 µm from the surface.

The GCI reports the static normal spring constant at the imaging tip position.

Reference: Sader et al., Review of Scientific Instruments, 87, 093711 (2016).

Theory

The spring constant, \(k\), is evaluated using the Sader Method (Ref. 1):

\(k_\mathrm{Sader}= \displaystyle A \, Q\, f_R^{1.3}\)

which requires only the resonant frequency, \(f_R\), and quality factor, \(Q\), of the uncalibrated cantilever in air, measured far from any surface.

The coefficient, \(A\), is universal for a particular cantilever geometry, regardless of cantilever thickness or coatings, and is obtained from measurements of a reference cantilever:

\(A = \displaystyle \frac{k_\mathrm{ref}}{Q_\mathrm{ref} \, f_{R, \mathrm{ref}}^{1.3}}\)

where the subscript 'ref' refers to the reference cantilever. Multiple reference cantilevers are used to determine the \(A\)-coefficient (Ref. 2):

\(A= \displaystyle \frac{1}{N} \sum_{i=1}^{N} A_i = \frac{1}{N} \sum_{i=1}^{N} \frac{k_{\mathrm{ref}, i}}{Q_{\mathrm{ref}, i} \, f_{R, \mathrm{ref}, i}^{1.3}}\)

where \(N\) is the total number of measurements and the subscript \(i\) refers to an individual measurement. This average systematically reduces uncertainty in the \(A\)-coefficient which is used to standardise calibration.

The Global Calibration Initiative utilises measured data from the international AFM community to determine the \(A\)-coefficient - seamlessly enabling the standardisation and non-invasive calibration of any cantilever type (which users can specify*).

This is performed from users' measurements of \(f_{R, \mathrm{ref}}\), \(Q_\mathrm{ref}\) and \(k_\mathrm{ref}\) in air obtained using the Thermal Method (which is built into most AFMs).

A histogram of the individual \(A\)-coefficients from users is provided, along with the total number of data samples and users for each cantilever.

Details of the Global Calibration Initiative are in Ref. 3.

* Users can suggest a cantilever type for the Global Calibration Initiative by clicking on the "Request Cantilever" button.

References

1. J. E. Sader et al., Rev. Sci. Instrum. 83, 103705 (2012) [Sec. III D];   85, 116101 (2014).

2. J. E. Sader et al., Rev. Sci. Instrum. 86, 056106 (2015).

3. J. E. Sader et al., Rev. Sci. Instrum. 87, 093711 (2016).