X-RAY DIFFRACTION IMAGING AS A TOOL OF MESOSTRUCTURE ANALYSIS

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X-RAY DIFFRACTION IMAGING AS A TOOL OF MESOSTRUCTURE ANALYSIS

J. Fiala, S. Němeček

Škoda Research Ltd., 316 00 Plzeň, Czech Republic ABSTRACT

In case that some crystallites in the material under study are greater than, say, ten micrometers, the diffraction lines become spotty and the information on the size, shape, orientation and various structural defects of these crystallites can be inferred by measuring x-ray diffraction images from individual crystallites. In our contribution, we refer to a number of cases where we managed to get valuable information on deformation, recrystallization processes using x-ray imaging, which would be unattainable by other methods.

INTRODUCTION

The packing of structural features with a size between 10 µm and 100 µm defines the materials mesostructure. Such features are usually examined under a microscope. But x-ray diffraction is capable of revealing some useful information on the mesostructure that cannot be got by microscopes. E.g., the Figure 1 shows the microstructure of an ordinary low carbon steel (0.16C – 0.39Mn – 0.09Si – 0.020P – 0.027S in wt.%) rolled at 600°C, 700°C, 800°C, and 850°C.

Figure 1. Effect of rolling temperature on microstructure of a mild carbon steel: a) 600°C; b) 700°C; c) 800°C; d) 850°C.

Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol.44 1 Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol.44 24

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The grain, as observed in a microscope, does not change at these temperatures, while the rolling resistance and the hardness of the produced sheet diminish with temperature as shown in Table 1.

This discrepancy was explained by x-ray diffraction which demonstrated that the coherently scattering regions (CSR) increase with rolling temperature (Figure 2). In this case, the mechanical properties (formability and hardness) of the material are determined not by grain, as seen in microscope, but by (CSR) which are invisible in microscope and can be displayed by x-ray diffraction.

Rolling temperature [°C] 600 700 800 850

Rolling resistance [kN] 229 152 133 124

Hardness HV30 190 151 131 127

Table 1. Effect of rolling temperature on rolling resistance and hardness of a mild steel sheet.

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Figure 2. Effect of rolling on the aspect of the (200) diffraction ring of ferrite in a mild carbon steel (Fe-filtered Co radiation in 114.6 mm Bragg-Brentano semifocusing camera with 30°angle of incidence): a) 600°C; b) 700°C; c) 800°C; d) 850°C.

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EXPERIMENTAL PROCEDURE

Unlike the case when coherent scattering regions (CSR) are smaller than, say, hundred nanometers and their size, shape, orientation, strain, and distributions of thereof are determined by traditional (“radial”) diffraction line profile analysis using an ordinary υ-2υ scanning diffractometer [1], in the case under consideration, the size of the CSR is between 10 µm and 100 µm. Therefore, the diffraction lines are split up into individual spots, or reflections. We call this azimutal or lateral diffraction line profile which can be recorded on a film or an electronic area detector (Figure 3). These spots are diffraction images (topographs) of individual CSR which satisfy the Bragg conditions for a given geometry. The information on the size, shape, orientation and various structural defects of these CSR can be inferred from the size, shape, orientation and distribution of diffracted intensity through the corresponding spots (reflections).

This is the principle of the “diffraction imaging” or grain-by-grain method of mesostructure analysis [1-4].

PLASTIC DEFORMATION

X-ray diffraction imaging can be to advantage applied to the description and study of plastic deformation [5] – see Figure 4. Deformation (de-formation) processes change the shape (the form) of crystals, grains, needles, plates, bands, etc., which represent the geometric framework within which microscopy expresses its description of the (meso)structure. In this way, the identity of topographical features of the mesostructure as seen in a micrograph, is concealed.

Crystallographers call this effect pseudomorphism [6]. Due to pseudomorphism, the information provided by microscope becomes uncertain and sometimes even confusing. On the contrary, x- ray diffraction does not identify the individual mesostructural features on the basis of their appearance (which may be severely altered by deformation) but on the basis of their internal crystal structure (which cannot be perceived by means of a microscope); that is why the x-ray diffraction identification of mesostructural features cannot be wrong.

RECRYSTALLIZATION

Another field where x-ray diffraction imaging will be of great value is the study of recrystallization. E.g., Figure 5 shows micrographs and x-ray diffraction patterns of a deformed sheet made of an iron based alloy containing 14 wt% Al and 0.02 wt.% C annealed for 15 min. at 830°C and 890°C. According to micrographs, the grain after annealing at 830°C seem to be smaller than the grains in the deformed sheet which was not annealed. Which is, of course, nonsense. Also, the hardness measurements show that the deformed sheet is harder than the annealed sheet. X-ray diffraction explains this discrepancy. The diffraction patterns indicate clearly that the “grains as seen in micrographs of the deformed unannealed sheet are composed of a large number of small strained crystals (size ~ 0,1 µm); annealing at 830°C caused recrystallization and the crystallites grew up to size ~ 50 µm. Thus, x-ray diffraction imaging provide that crystallites really grew up upon annealing, as expected. After annealing at 890°C the diffraction pattern shows that the crystallites grew even more and reached the size of several hundreds of micrometers. Which is in accordance with what is observed under the microscope.

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Figure 3. Diffraction pattern of austenite taken (a) with an electronic area detector, (b) with a powder camera, and (c) with an ordinary powder diffractometer. Due to mesostructure of austenite, the continuous diffraction ring is split up into individual reflections which cannot be ascertained by diffractometer.

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Figure 4. Effect of deformation on the aspect of the (211) ferrite diffraction ring of tensile tested mild steel (0.04C – 0.08Mn – 0.01Si – 0.01P – 0.008S in wt.%). Tensile deformation 0% (a), 7%

(b), 11% (c), and 20% (d). Back-reflection camera, 43 mm sample-to-film distance, Cr-anode.

With microscope unfortunately we can recognize only the late stages of recrystallization when the grain grows coarse to such a degree that the material becomes useless. These are the early stages of recrystallization, the monitoring of which is of great technological interest. While they seldom can be recognized under the microscope, x-ray diffraction imaging is very sensitive to the early stages of recrystallization.

LOW TEMPERATURE RELAXATION

The materials structure changes not only upon heating but also at ambient temperature (or at temperatures which are deeply below the recrystallization temperature) after some time. We speak on low temperature relaxation. An example of such a process are changes we noticed in the mesostructure of a steel containing 0.6 wt.% C and 6 wt.% Mn at room temperature during 31years (Figure 6). In the spring 1968, we applied different heat treatments for a dozen of pieces of this steel in order to get a variety of structures ranging from pure ferrite to pure austenite. In the course of the following 31 years, we lent these samples to a number of laboratories where they served as calibrating standards for determination of ferrite-to-austenite ratio. In the meantime, these samples were deposited in our laboratory at room temperature. In 1999 we took again the diffraction patterns of these samples with the same 114.6 mm Bragg-Brentano semifocusing camera we had used 31 year ago. The difference between the diffraction patterns of individual samples taken in 1968 and in 1999 proves that their mesostructure changed; the crystallites (CSR, mosaic blocks, diffraction cells) forming the individual grains in 1968 grew larger and diversified by misorientation.

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Figure 5. Effect of recrystallization annealing on the microstructure (100x) and on the aspect of the (110) and (200) ferrite diffraction rings of a heat-resistant iron based alloy containing 14 wt.% Cr, 4 wt.% Al and 0.02 wt.%C: (a) no annealing; (b) annealed for 15 min at 830°C; (c) annealed for 15 min at 890°C (Co-Kα-radiation, 114.6 mm Bragg-Brentano semifocusing camera, 30°angle of incidence).

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X-ray diffraction imaging is very sensitive to the changes of mesostructure resulting from low temperature relaxation. It will be to advantage applied to monitor various degrading processes in the material of the critical engineering components (power stations, chemical industry) on service and to assess their residual life-time.

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Figure 6. Changes in the diffraction pattern of a steel sample containing 0.6 wt.% C and 6 wt.%

Mn, caused by low-temperature relaxation in course of 31 years at ambient temperature: (a) year 1968; (b) year 1999 (Co-Kα radiation, 114.6 mm Bragg-Brentano semifocusing camera, 30°angle of incidence).

FUTURE DEVELOPMENTS

Electronic area position sensitive detectors are very efficient. They allow one to shorten the data collection time for the whole pattern down to tens of seconds and to take a large number of diffraction pattern within a short time. It is important in case of inhomogeneous materials and in the fieldwork. In contrary to the photographic recording, the use of electron area detectors eliminates processing of films and photometry. Diffraction images collected by area detector are immediately passed to computer for display and processing with picture analysis software [7].

Doing two-dimensional Fourier transform of the diffraction images (Figure 7) opens the door for their examination from quite a new point of view.

CONCLUSIONS

1. For the most part, materials contain some crystallites which are greater than 10 µm.

Therefore, we should verify how the lateral (azimutal) profile of the diffraction lines looks like before analysing their radial profile (broadening).

2. Lateral profile of the diffraction lines brings information on the materials mesostructure which is not seen in micrographs and cannot be deduced from line broadening analysis.

3. X-ray diffraction imaging enables one to monitor degrading processes in the material of the critical engineering components on service which cannot be detected with ultrasound or radiography.

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Figure 7. Photographs of four different diffraction rings and their (two-dimensional) Fourier transforms.

ACKNOWLEDGEMENTS

It is a pleasure to acknowledge that this work was supported by grant no. LN00B084 of Ministry of Education of the Czech Republic.

REFERENCES

[1] Snyder, R.L.; Fiala, J.; Bunge, H.J., Defect and Microstructure Analysis by Diffraction, Oxford University Press: Oxford, 1999, 1-15.

[2] Black, D.R.; Burdette, H.E.; Kuriyama, M.; Spal, R.D., Journal of Materials Research, 1991, 6, 1469-1476.

[3] Weissmann, S.; Lee, L.H., Progress in Crystal Growth and Characterization, 1989, 18, 205- 226.

[4] Weissmann, S., Advances in X-ray Analysis, 1992, 35, 221-237.

[5] Tschegg, E.; Faltin, Ch.; Stanzl, S., Journal of Materials Science, 1980, 15, 131-138.

[6] Winkler, G.G., Die Pseudomorfosen des Mineralreiches, Joh.Palm´s Hofbuchhandlung:

Munchen, 1855, 29-58.

[7] Huang, T.S., ed., Picture Processing and Digital Filtering, Springer: Berlin, 1975, 21-68.

X-RAY DIFFRACTION IMAGING AS A TOOL OF MESOSTRUCTURE ANALYSIS