The Mathcad™ worksheets allow us to compute and visualize various types of hysteresis loops defined in a parametric form. The hysteresis phenomenon is widespread, it requires simple and adequate description. The Mathcad worksheets support building both smooth hysteresis loops and piecewise-linear ones. The approximating model describing the hysteresis loops is based on the results presented in the article Analytical model for the approximation of hysteresis loop and its application to the scanning tunneling microscope (R. V. Lapshin, Rev. Sci. Instrum., vol. 66, no. 9, pp. 4718-4730, 1995). The other valuable source of information is the article titled An improved parametric model for hysteresis loop approximation (R. V. Lapshin, Rev. Sci. Instrum., vol. 91, iss. 6, no. 065106, 31 pp., 2020). Please refer to these articles for model details and explanations. The implemented model of the hysteresis loop is simple and intuitive, it allows to quickly construct hysteresis loops of required type and easily fit their parameters. Because the length restriction, the articles include only widespread loops. If you did not find a required hysteresis loop, it makes sense to search in the worksheets. If you do not have Mathcad software installed, you can use the readable version of the worksheets as a PDF-file. It should be noted that the worksheets are created and tested in Mathcad 2001i Professional. Error-free calculations in the later Mathcad versions are not guaranteed.
This program carries out recognition of atoms or similar simple objects (surface features) on SPM images. The acceptable scans should be plane enough and the surface features should have a small dispersion of the vertical positions. Preliminary subtraction of a surface tilt as well as image smoothing are earnestly recommended. The input scan data should be written in sm2 format (RHK Technology, Inc.). To measure precisely atom positions, automatic search of the best horizontal cutting plane is provided for. Type key “/C” in the MSDOS command line to generated an image file *#.sm2 intended for visual qualitative control of the recognition results and estimation of the cutting plane position.
Features on or near image border are rejected since they either were cut by the border or were distorted by edge scanning effects. Recognition of long threads (streaks) parallel to the fast-scan direction signals that the analyzed topography is contaminated. Undetermined objects are isolated noise peaks, islets, and threads found near image border. The lattice constants of HOPG (a=b=2.464 Å, c=3.354 Å) are set as defaults. The recognition program automatically collects topography statistics (see resume file *.rsm) including such parameters as compactness and continuity.
Compactness shows discrepancy between form of a feature basement and a circle, which form is assumed to be perfect (100% compactness). Compactness Cmp is defined as follows
Continuity is a measure of surface flatness and dispersion of the vertical feature positions. On an atomic topography, approaching to 100% continuity is considered as ideal, it means that the cutting plane is drawn close to the optimal position. Continuity Cnt is defined as follows
Relative coordinates of the features are stored in the so-called chain format (*.chn):
To recognize surface features in case of a complex topography, a program performing feature-oriented scanning (FOS) should be applied either in real or virtual operation mode. Recognition core of the FOS approach uses direct recognition methods instead of the iterative method built-in the Recognizer. At present, the FOS program is under development, it is not yet distributed.
Using the atom coordinates obtained during recognition, the Stylizer builds a hypothetical surface (a ball model of the surface), where atoms are represented as hemispheres. The stylized image rendered has no linear distortions (disproportion) induced by inequality of the calibration coefficients.
Using the recognized atom coordinates, this program determines lateral calibration coefficients and an obliquity angle (nonorthogonality) of the SPM piezoscanner. It should be noted that the larger value of multiple k is set, the higher precision of the sought coefficients will be obtained. On the other hand, the larger value of the multiple k is set, the less number of equilateral triangles are found in the image and therefore, the less averagings of the noise-sensitive calibration coefficients are performed. Thus, in practice, you should balance between the assigned multiple k value and the number of the detected triangles.
For calibration purposes, one should use a rather small-sized scans since they have minimal thermodrift and creep distortions. To eliminate these drifts, either the feature-oriented scanning in real operation mode or a less complex method of counter-scanned images should be applied. In order to check calibration, it is recommended to run the Calibrator on the image processed by the Corrector program intended for removing image disproportion and obliquity. As a result, both calibration coefficients should be approaching to unity and the obliquity angle should be approaching to zero.
The batch file is intended for simplification of the lateral calibration and the subsequent image processing. P7_SPM.exe is an SPM control program distributed by the NT-MDT Co. Instead of the P7_SPM program, any other program capable to generate sm2 data, may be used.
If necessary, more details and references on the automatic SPM scanner calibration can be found in the following works: Automatic lateral calibration of tunneling microscope scanners (R. V. Lapshin, Rev. Sci. Instrum., vol. 69, no. 9, pp. 3268-3276, 1998); Object-oriented scanning for probe microscopy and nanotechnology (R. V. Lapshin, Ph. D. Thesis, the Institute of Physical Problems, Moscow, 2002).
This program corrects image disproportion and obliquity using the calibration coefficients and the obliquity angle determined with the Calibrator. To run the Corrector, one should free maximum conventional memory by commenting all lines in Autoexec.bat and Config.sys except HiMem.sys and EMM386.exe drivers, then reboot computer in MSDOS mode.
This program converts the chain data obtained during scan recognition into plain ASCII 3D array of x, y, z absolute coordinates of the recognized features for subsequent use in Mathcad™, MatLab™ and other software. The units for x, y axes (the 1st and the 2nd columns) are Ångströms, the unit for z axis (the 3rd column) is Ångström, nanoAmpere or nanoNewton depending on the SPM measurement mode applied.
This program converts sm2 scanning data into plain ASCII 1D array of topography heights for subsequent use in Mathcad™, MatLab™ and other software. The 1st topographical height in this array corresponds to the 1st probe position in the 1st raster line, the 2nd height corresponds to the 2nd position in the 1st raster line, and so on for the subsequent probe positions in the raster. The unit is meter, Ampere or Newton depending on the SPM measurement mode applied.