DATA PROCESSING

The 2D diffraction images were stored using a standard ESRF file format. Each file contained the array of intensities, together with metadata such as an acquisition time stamp, run number, etc. These diffraction images contain texture information from two sources: the first is a systematic variation of intensity along a single ring corresponding to a given reflection, and the second is the correlation of intensity variations between several reflections from the same image. With area X-ray detectors, multiple incomplete experimental pole figures are sampled simultaneously, since diffraction rings belonging to several sets of planes are captured at once.

Measurements were carried out using radial diffraction geometry, meaning that there were some important instrument parameters to take into account for the refinement of the data. The actual wavelength, the centre of the image, the sample to detector distance, and the tilting of the detector had to be determined. In this particular

Texture Evolution during -quenching of a Zirconium Alloy 147 experiment, these parameters were kept constant and were calibrated through measurements on a standard aluminium powder of known lattice parameters at different sample to detector distances. From the differences between the distances, the absolute values can be determined. Figure 4.10 compares the diffraction images of the aluminium standard and a sample of Zircaloy-2 in as-rolled condition. The standard should not have signs of texture, i.e. the intensity along each ring should be constant.

Figure 4.10 Diffraction images from (a) aluminium powder standard and (b) as-rolled Zircaloy-2.

The calibration of geometric parameters was carried out using the software FIT2D (Hammersley 1998). FIT2D is a general-purpose program for analysis of X-ray diffraction data in one and two dimensions. It has become a standard in most of the beamlines of the ESRF and in many other crystallography research groups. Calibration and correction of detector distortions are precisely amongst the most important uses of FIT2D. Normally the first step when calibrating a 2D diffraction image is the correction of dark field, flat field and spatial distortions. With the Pixium detector, the dark-field

correction was performed applying a function built into the detector hardware while there was not incident radiation. The geometrical parameters obtained after analysing the calibration images are listed in Table 4.5.

Table 4.5 Calibration parameters for synchrotron experiment

Wavelength (Å) 0.141582

Image centre (pixels) x: 1326.558 y: 960.724 Image centre (mm) x: 204.290 y: 148.106

Detector distance (mm) 697.831

Tilt axis (°) -48.18

Tilt angle (°) -0.13

The next step is to determine the diffraction intensities of all the reflections as a function of the polar angle in the Debye ring (normally denoted as η). For this purpose the diffraction image is sliced in polar angular sections, and the intensity within each slice is integrated. When the number of grains sampled is high and the diffraction rings appear smooth, angular sections of 5 are normally used. If the intensity along the rings appears more scattered, then larger angles may be chosen. For this particular experiment, the maximum angular section used was 10. The integration process converts the diffraction image into a set of 2-theta diffraction spectra at different polar angles (36 or 72 spectra depending on the section size).

For the integration of the diffraction images acquired during the thermal tests, the calibration parameters are critical. Therefore, the calibration must be checked beforehand. This can be done by examining an integrated diffraction image from the calibration standard. Figure 4.11 shows a diffraction image from the aluminium calibration standard after integration. Since the aluminium standard is a powder, neither

Texture Evolution during -quenching of a Zirconium Alloy 149 texture nor residual stresses should be present. Therefore, the integrated rings should not exhibit shifts in the diffraction angle or changes in intensity along each reflection. In Figure 4.11, the rings appear as straight vertical lines with constant intensity, which evidences a satisfactory calibration.

Figure 4.11 Integrated diffraction image from the aluminium standard

The integrated intensities obtained from FIT2D were exported to be analysed using the Rietveld (Rietveld 1969) method as implemented in the software MAUD (Lutterotti et al. 1997). MAUD is a general diffraction analysis program that has many advantages for its application in this project. It is very versatile and can analyse multiple spectra, it supports different instruments and techniques and includes many useful functions such as texture and residual stresses calculations. However, being so general, it takes many parameters into account, which makes the fitting process very laborious. In addition, MAUD is closed-source so it is not possible to know exactly what algorithms are used.

The raw files obtained from the beamline were converted into sets of 2-theta spectra and loaded into MAUD. For the aluminium calibration standard, the crystal and all the

geometrical parameters were known. All the other instrument parameters available in MAUD such as peak shape parameters, 2-theta offset, etc. were refined at this point until the calculated diffraction spectra matched the experimental data. This refinement was a laborious process, especially when multiple phases were present and the diffraction peaks overlapped. The parameters were normally refined in the following order: (1) incident intensity and background, (2) cell parameters, crystallite size and microstrain, and (3) volume fraction of phases. At this stage, the background, the peak position and the peak profiles showed a good agreement with the experimental data, and the texture could be introduced to match the changes in intensity. The texture was included in the Rietveld refinement using 10 iterations of the enhanced E-WIMV (Matthies and Vinel 1982) discrete algorithm implemented in MAUD. For the fitting, intensities from the spectra were extracted using the LeBail method (Le Bail et al.

1988). An incomplete pole figure was extracted from each diffraction ring and the E-WIMV algorithm was used to calculate ODFs from these pole figures. The resolution of all the ODFs obtained from synchrotron data was set to 10 and no sample symmetry was imposed. Once the refinement of the ODFs was finished for each diffraction image analysed, complete pole figures were recalculated.

For the refinement of actual data, most of the instrument parameters obtained from the standard were used. However, since the incident intensity, the background and the image centre may change during the measurements, they were refined again for each diffraction image. Figure 4.12 shows the results of the Rietveld analysis in MAUD for a

Texture Evolution during -quenching of a Zirconium Alloy 151 diffraction image from a Zircaloy-2 specimen in as-rolled condition. Thanks to the resolution of the detector and an adequate sample to detector distance, it was possible to capture a reasonable number of Debye-Scherrer rings, which maximised the amount of information available for ODF calculations. Up to 46 and 13 diffraction rings were captured for the  and  phases respectively, within a 2-theta range between 2 and 10.

Figure 4.12 Results of fitting a set of synchrotron X-ray spectra, corresponding to the as-rolled condition.

Sum of all spectra at the top and comparison of intensity 2D views at the bottom.