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·Materials Characterization and testing
Quantitative Material Inspection with Coherent X-Ray ScatteringH. Bomsdorf, T. Müller
Fachbereich Physik, Bergische Universität - Gesamthochschule Wuppertal
YXLON International X-Ray GmbH, Hamburg
During the past years an experimental system for coherent scatter measurements on bulk objects was set up at the Physics department of the University of Wuppertal, Germany. The apparatus was designed to allow flexible change of the scatter geometry enabling to assess the applicability of the method with respect to different inspection tasks. This is further supported by a simulation program allowing to predict diffraction patterns based on literature data (Powder Diffraction File, PDF). Both simulation and experiments were applied successfully within a study focussing on the identification of pigments used in ancient paintings . For a broader assessment of the potential of coherent scatter for industrial NDT a collaboration between YXLON International and the University of Wuppertal was established. Currently the investigations are focussing on the following subjects: system optimization by means of simulation, investigations on amorphous substances and liquids and the assessment of new applications. Here we will give some examples of first results obtained within this collaboration.
|Fig 1: Longitudinal section of the circularly symmetric region-of-interest (dotted area) defined by the scatter collimator dimensions and the beam diameter (Dbeam)(drawing not true to scale). The measures of the used collimator were: R1 = 5 mm,R2 = 12.8 mm, A = 0.6 mm, L: depending on the scatter angle (see text)|
Here l is replaced by the photon energy E. Obviously a primary X-ray photon of high energy is scattered under a small scatter angle È for a given lattice spacing d. Since the scatter angle is fixed different lattice spacings characterizing the crystalline structure of the material result in different diffraction peaks within the energy spectrum of the scattered X-ray photons. According to the Bragg-condition the spectrum is shifted along the energy axis if the scatter angle is changed. It will be shown below that the spectral resolution and thus the ability to distinguish different diffraction peaks is strongly influenced by the choice of the scatter angle. In contrast to previous setups the apparatus used here allows flexible change of the scatter collimator dimensions in the experiment for easy system optimization. The energy spectrum of the scattered photons measured by means of a HPGe-detector and a multi-channel analyzer as described in  has to be normalized in order to correct for the energy spectrum of the incident X-ray beam and the influence of sample absorption. For that purpose the scatter spectrum is divided by the absorption spectrum, which is measured in a separate run (measurement with removed beam stop S, see Fig.1). By means of the Bragg-condition (2) the peak positions E within the normalized spectrum can be used to calculate the corresponding lattice spacings d allowing substance identification by comparison with literature data (Powder Diffraction File). On the other hand the peak positions of a material within the energy spectrum measured in this experiment can be predicted from the peaks of the angular dispersive PDF-data using the same equations. The lattice spacings of the investigated material, however, only give the measured peak positions. The broadening of the lines reflecting the energy dependent line resolution of the system is not obtained from the corresponding PDF-data. This is because the line width DE in this experiment is not a function of the (mean) scatter angle Q alone but also of the so-called angular blurring, i.e. the range of scatter angles Q = Q max - Q min (see Fig.1) defined by the opening A of the scatter collimator used in the experiment:
Obviously DQ can not be made negligibly small in a real experiment because a certain width A of the scatter collimator slits is necessary for sensitivity reasons. Fig.1 further shows that the size of A together with the diameter of the X-ray beam Dbeam not only determine the an gular blurring DQ of the system (line resolution) but also the size of the regionofinterest (spatial resolution). From (3) it further follows that the described behavior strongly depends on the chosen scatter angle, which in turn is related to the lattice spacings to be observed. The (mean) angle Q can be varied in the experiment by altering the distance L between the two collimator diaphragms whereas Dbeam is defined by means of the dimensions of a primary collimator (pin hole, not shown in Fig.1). The above statements indicate that proper design of the scatter collimator and optimum choice of the other experimental parameters are crucial in order to balance the requirements of line resolution, spatial resolution and sensitivity. Spatially resolved investigation of a whole object, if necessary, is accomplished by moving it with respect to the apparatus, i.e. the ROI. Thereby, scatter images may be obtained by appropriate 2-dimensional display of the acquired data .
Regarding the obtained material specific information, the above features of the system yield the following consequences:
Although the principle of coherent X-ray scattering allows nondestructive identification, lo calization, quantification and texture analysis of materials within bulk objects the achievable specificity and accuracy is an open question for a given inspection task and each application requires individual optimization of the setup. The main system parameters to be chosen are the scatter angle as well as the scatter collimator slit width and the diameter of the incident pencil beam. Thereby, resolution and sensitivity can be adapted to the needs of the given inspection task. In order to facilitate this process a simulation program was developed at the University of Wuppertal utilizing a ray tracing algorithm to calculate the diffraction pattern of a material with given lattice spacings d to be observed. The d values, known e.g. from PDF-data, together with the given system parameters and the spatial composition of the object serve as input parameters of the program. As a result of the ray tracing evaluation of all possible X-ray paths the blurred diffraction pattern is obtained. By repeating this step with different system parameters the optimum configuration for a given inspection task can be determined without time consuming experiments.
|Fig 2: Normalized diffraction patterns measured from an Al/Si-composite. The reflecting atomic planes are denoted by Miller indices. The mean scatter angle is changed from (approx.) 3.3° to 5.7° leading to a strong increase in line resolution and a larger number of observable diffraction peaks.|
|Fig 3: Normalized diffraction patterns at a mean scatter angle of 5.7°: Measurement of the Al/Si-composite (upper trace), reference data (simulated from PDF) from Al and Si (lower traces). The peaks observed within the composite pattern are verified by the simulated reference data.|
The reflecting atomic planes are denoted by Miller indices.In Fig.2 the significant increase in measured line resolution resulting from a change in the scatter angle from 3.3° to 5.7° (approximate values) is demonstrated (see e.g. the peaks (220) of Si and (200) of Al). Furthermore, the number of scatter peaks observed within the energy range of the primary X-ray spectrum is strongly enhanced. For the purpose of demonstration all spectra shown were acquired using long sampling times (several hundred seconds for the scatter spectra) aiming at a high signaltonoise ratio. These times do not reflect the experimental conditions within a real inspection application which will depend on the individual task, the used X-ray source, scatter geometry and data processing. As explained above system optimization can be accomplished or facilitated by means of simulation.
The diffraction pattern of the Al/Si-composite is shown again in Fig.3 together with patterns from its major constituents, Al and Si, calculated by means of the simulation program based on their PDF data.The peak positions in the observed sum spectrum (upper trace) are clearly identified within the calculated individual spectra of Al and Si. Apart from the peak energies the widths of the measured spectral lines turn out to be in good coincidence with the simulated data, demonstrating the performance of the simulation program. Reference data may also be obtained from measurements. This is demonstrated in Fig.4. displaying the scatter pattern of an aluminum matrix composite containing 20% ceramic particulate (SiC) reinforcements. The diffraction data were taken at a scatter angle of 5.7° and compared with reference measurements from pure Al and pure SiC samples. Again the two constituents are clearly identified in the sum spectrum. According to the specifications of the material a smaller percentage (<10%) of Si should be part of the matrix alloy. This may be indicated by the enhancement of the peak observed at 40 keV (Si (111)) within the measured spectrum. Provided that the influence of texture can be neglected the percentages of Al and SiC within the composite may be determined from the individual peak areas by comparison with reference data taken from samples of equal size and position. Calculations based on the major scatter peaks shown in Fig.4 gave a percentage of 18% to 23.6% for the SiC content in the composite depending on the investigated point within the object and the peaks included in the evaluation. Apart from the relatively large deviation and taking into account a potentially inappropriate choice of the reference materials the result is in good agreement with the value of 20% specified for the material.
This indicates the potential of coherent X-ray scattering to give localized quantitative information on the composition of bulk objects. Within a real inspection task several experimental parameters may be improved and a significant increase in accuracy can be expected:
Firstly, based on exact knowledge on the production process a better choice of the reference materials can be made. Secondly, existing data concerning the (wanted or unwanted) texture within the material may be used in the evaluation. If the investigated material exhibits significant unknown texture, however, the measured relative peak heights may unpredictably differ from those obtained from simulations or reference measurements. This must be regarded as a disadvantage with respect to material identification or quantitative material inspection. On the other hand it allows to study the orientation of material constituents within the lattice, which might turn out to be a helpful additional source of information in the context of specific inspection tasks, e.g. in the field of process development.
|Fig 4: Normalized diffraction patterns measured at a mean scatter angle of 5.7°:Al/SiC-composite (upper trace), reference measurements from Al and SiC (lower traces). The peaks observed within the composite pattern are verified by the reference data.|
Although X-ray diffraction is a technique, which is primarily suited for the analysis of crystalline structures, characteristic patterns are also obtained from amorphous substances and liquids. Due to the absence of fixed lattice spacings no distinct peaks appear in the energy spectrum but the observed broad diffraction patterns display characteristic shapes depending on the investigated material, too. Although these are less specific compared with that of crystalline substances they may still allow identification especially in cases where only a selection between a few possible constituents of the object has to be made. As a further complication, the prediction of diffraction patterns from liquids and amorphous materials is much more difficult as compared to crystalline substances since simulations on the molecular dynamics have to be performed in order to determine the pair correlation function for each combination of the different elements present . The obtained data allow calculation of the diffraction pattern of the substance for comparison with the experiment. An example demonstrating the possibility to discriminate two liquids based on scatter measurements is shown in Fig.5. The honeycomb structure representing a part of an aircraft wing was prepared with two different liquids (water and kerosene) each filling one of the honeycombs. Obviously the difference can not be identified within the conventional X-ray image (left). The diffraction patterns taken from points A and B shown in the right part of the figure, on the other hand, clearly indicate which of the fluids is present in the corresponding honeycomb.
|Fig 5: X-ray image of a honeycomb structure representing a part of an aircraft wing (left).Two honeycombs were filled with different liquids (water and kerosene). Normalized diffraction patterns from points A and B of the object observed at a mean scatter angle of 3.3° (right) allow to distinguish water from kerosene. Additional peaks result from the aluminum structure.|
|Fig 6: Normalized scatter patterns observed at a mean scatter angle of 3.3°: carbon fiber epoxy composite (upper trace), reference measurements: carbon fiber and epoxy (lower traces). The main characteristics of the scatter patterns from both constituents are found within the composite pattern.|
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