QUICK FACTS
In the recent past, High-Resolution Transmission Electron Microscopy (HRTEM) became a powerful tool for studying the structure and chemical composition of materials at atomic scale. Dr. Fritz Phillipp and his colleagues from the Max Planck Institute developed different methods for analysing the structure of materials. They used PV-WAVE Extreme-Advantage for image processing and to determine the geometry of the projected unit cells.

THE PROBLEM
The investigation of materials structure was previously conducted through a known iterative technique that could only be used on small areas. Further, through this technique, the imaging parameters and a model structure of the object had to be refined until a best match between experimental and simulated images was achieved.

THE SOLUTION
When PV-WAVE was introduced, Max Planck Society metal researchers, Dr. Fritz Phillipp, K. Du, Y. Rau and N. Y. Jin-Phillipp invoked this code [1] to develop their software package, LADIA (Lattice Distortion Analysis). This procedure was developed for coherent structures, i.e., structures without extended defects (e.g. boundaries). Unlike the known iterative technique, this technique does not require the comparison with simulated images during each evaluation process. Further, under favourable conditions, information on lattice strain may be derived directly from the HRTEM micrograph. On these accounts, PV-WAVE has accelerated the analysis of materials structures and is well-suited to the analysis of large area micrographs.

In the research of materials structure, PV-WAVE is essential in the development of LADIA to visualize the data of the simulation results. In the following, the module LADIA is described using a flow-chart.

Direct strain mapping relies on the assumption that a HRTEM micrograph of a coherent structure taken at proper conditions represents the geometry of the crystal lattice. Also, a constant spatial relationship between the image Max/Min and the projected atom columns can be assumed on a local scale. The figure shows the flow-chart of LADIA. Though various image formats can be used as input, the EMS (Electron Microscopy Image Simulation) image format *.ima has been implemented for testing the procedures on simulated images. For the geometrical processing, various tools are provided for selecting the image area of interest, rotating the image and defining the sampling. Because the strain detection limit is influenced by the presence of noise coming from amorphous surface layers, a few filters were implemented, e.g. Wiener filter, Bragg filter and band-pass filter, to reduce the noise. Developers established that strain values calculated from a noise-added image may differ from the true value, which is obtained from the simulated image, by about 3%. Since the deviation of the Wiener filtered image is less than 1%, they decided to implement the Wiener filter into LADIA. As a next step, a template of the contrast pattern motif is extracted from the experimental image by averaging over ca. 20 motives in order to reduce shot noise. To define the position of the image Max/Min, the so called peaks, cross-correlation (comparison) with the template motif is then made. From an area of the image, which shows the undistorted lattice, a reference lattice is then created from the peaks and extrapolated over the entire image. The local displacements of the Max/Min (peaks) position in the experimental image from the reference lattice represent the local lattice distortions (Distortion Analysis). Additionally, tools for determination of the local area of the image unit cells and tetragonal or shear strain are implemented. All the presented tools are part of the PV-WAVE mathematical and statistical libraries and have enabled LADIA to accurately analyze the 2D strain state of a material.

RETURN ON INVESTMENT
LADIA is written in the PV-WAVE language and has been applied for strain mapping in various materials [2-5].

1. K. Du, Y. Rau, N.Y. Jin-Phillipp and F. Phillipp, unpublished.
2. N.Y. Jin-Phillipp and F. Phillipp: J. Microsc, 1999, 194, 161.
3. N.Y. Jin-Phillipp and F. Phillipp: J. Appl. Phys., 2000, 88, 710.
4. N.Y. Jin-Phillipp, M. K. Zundel, K. Du, F. Phillipp and K. Eberl: Microscopy of Semiconducting Materials 1997, Inst. Phys. Conference Series, edited by A. G. Cullis and J. L. Hutchison (IOP, Bristol, 1997), Vol. 157, p.339J
5. M. Chauvaeau, A. Trampert et al, Appl. Phys. Lett. 84, 2505 – 1505 (2004)

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