3D-Analysis of Complex Microstructures
Quantification and Classification by FIB/SEM-Nanotomography
- Fig. 1: Standard series images of the six basic graphite types according to DIN EN ISO 945.
- Fig. 2: Results of FIB/SEM-tomography, 3D reconstructed images of a) nodular
- Fig. 2: Results of FIB/SEM-tomography, 3D reconstructed images of b) temper
- Fig. 2: Results of FIB/SEM-tomography, 3D reconstructed images of c) vermicular
- Fig. 2: Results of FIB/SEM-tomography, 3D reconstructed images of d) flake graphite [4, 5].
- Fig. 3a: Results of the classification of virtual 2D sections through the 3D reconstructed temper graphite particle. The outer small sections don’t carry comprehensive shape information. The simulatetd smooth frequency distribution gives an impression of the expected shape distribution of all virtual 2D sections trough the 3D particle. The misinterpreted 2D sections (section colour different from particle colour) indicate the discrepancy between conventional image analysis results and advanced techniques which follow the smooth frequency function [4, 6].
- Fig. 3b: Results of the classification of virtual 2D sections through the 3D reconstructed temper graphite particle. The outer small sections don’t carry comprehensive shape information. The simulatetd smooth frequency distribution gives an impression of the expected shape distribution of all virtual 2D sections trough the 3D particle. The misinterpreted 2D sections (section colour different from particle colour) indicate the discrepancy between conventional image analysis results and advanced techniques which follow the smooth frequency function [4, 6].
- Fig. 4: Results of online classification with the help of support vector machine. Not only is a decision given for each classified particle but also a quantitative measure of the individual probability to fall into the different types of graphite morphology. The reason, why not always an unambiguous classification could be given (is the unavoidable lack of information in the 2D section which has been proven by representative 3D experiments with nanotomography. The new technique can be used in the web (www.materialography.net) .
A precise design of complex microstructural features calls for adequate 3D characterization. For the example an automatic classification of local graphite morphologies was developed for application of advanced cast iron in high performing functional gradient materials. FIB/SEM Nanotomography was combined with a computer simulation to measure a reliable probability distribution of random 2D sections through reconstructed 3D particles. The procedure is applicable for other complex microstructures.
The 3D nature of materials microstructure is known to be the essential link between the materials processing and its properties. Its adequate quantitative description plays a soaring role for the tailoring of advanced materials such as complex composite or gradient materials . For example the development of advanced cast iron with tailored functional gradients of graphite morphologies is investigated in light weight solutions of internal combustion-engines of cars. It requires an objective classification of graphite morphology rather than the (current) subjective interpretation by experts, which is a well known source of discrepancies . The graphite morphologies are classified into six categories (Fig.1) and diverse subcaterories which are geometrically complex as a consequence of various precipitation scenarios and subtile technologies. This 3D-complexity cannot be fully reflected in the experimental (and only 2D) metallographic section leading to numerous uncertainties even if sophisticated image analysing procedures are applied .
3D Characterisation by Means of FIB/SEM-Nanotomography
Realizing that the uncertainties by the 2D classification are caused by a (so far unknown) 3D complexity we analyzed the 3D shape of typical graphite morphologies. Especially the nanotomography, which uses the focused ion beam (FIB) for the serial sectioning in nanometer dimensions (minimum intersectional distance could practically be as low as 10 nm) and the scanning electron beam (SEM) with its resolution down to 3 nm (FEI StrataDB), provides a spatial resolution for serial sectioning down to 3x3x10 nm3. The maximum sample volume to be analyzed depends on the sputtering capability of the ion beam and thus is limited to about 100x100x100 µm3.
It should be emphasized that in comparison to other tomographic techniques not only the resolution and the maximum sample volume is relevant for the investigation of microstructural aspects but also the availability of practically all SEM contrast phenomena such as secondary electrons, backscattered electrons and their characteristic Bragg pattern (EBSD) as well as the emitted X-rays for the EDX signal .
Figure 2 shows the reconstructed 3D shape of four individual graphite particles. We got a lot of new information about the particle formation and their growth mechanisms due to the precise examination of the graphite morphology and its inner structure as well as the localization and chemical investigation of the nuclei [4, 5].
3D Analysis of the Graphite Morphology
All graphite particles were quantitatively analyzed with the help of 3D characterization software MAVI. The software was developed on the basis of algorithms described in . The characteristic basic parameters like volume (V), surface (S), integral of mean curvature (M) and total curvature (K) as well as shape parameters were determined for all particles of each graphite type and offer clear i.e. unambiguous criteria for graphite classification in 3D. The detailed results for the different types of graphite are published elsewhere .
Analysis of Virtual 2D Sections
Since the scientific goal was the significant improvement of technically relevant 2D image analyzing strategies  - now based on the knowledge of the 3D morphology of graphite precipitations - a computer simulation was performed to section all the 3D reconstructions of graphite particles randomly. These simulated artificial random sections were evaluated with 15 potentially relevant parameters in image analysis of disperse microstructures, and the frequency was detected of each type of planar section. Thus, a probability distribution was acquired for the different planar section types for each category of graphite morphologies, which strongly supports the identification in "real" planar sections of 2D image analysis (Fig. 3). The application of a support vector machine to analyse the sensitivity and the precision of this study enabled the definition of a new image analyzing strategy to classify the graphite categories with highest possible and even calculable precision (Fig. 4) .
The FIB/SEM-Nanotomography by serial sectioning has been proven to be a valuable tool in the evaluation, classification and quantification of several aspects of complex microstructures. This has been shown on the example of graphite morphologies in gradient cast iron materials. The lack of information in conventional 2D-image analysis can be compensated to some extend for an improved classification procedure by the exemplary analysis of representative microstructural elements in 3D followed by measuring the frequencies of virtual 2D sections through the reconstructed 3D particle. Thus the 2D classification reliability can be estimated. On that basis the additional application of the support vector machine opens the mind to recognize the most significant measuring parameters in image analysis.
This approach has been tested to be a general solution for promising 3D quantifications and classifications of many types of complex microstructures not only in cast iron but also in AlSi materials and others.
The authors acknowledge the fruitful cooperation with G. Weikum (MPI Saarbruecken) regarding the support vector machine and with K. Schladitz (ITWM Kaiserslautern) regarding the spatial image analysis, as well as the financial support by BMBF-project 03N3119.
 Ohser J. and Mücklich F.: Statistical Analysis of Microstructures in Materials Science. John Willey & Sons Ltd, Chichester, 2000.
 Ohser J., et al., Practical Metallography. 454-473 (2003).
 Lasagni F., et al.: Advanced Engineering Materials 8, 719-723 (2006).
 Velichko A., et al., Advanced Engineering Materials 9, 39-45 (2007).
 Velichko A., et al., Acta Materialia (2007) submitted.
 Velichko A. and Mücklich F., Practical Metallography 43, 192-207 (2006).
 Richter C.: Classification of Microstructural Images based on Particle Parameters, Saarland University, 2005, Master thesis.