High energy transmission micro-beam Laue synchrotron X-ray diffraction

Abstract

Synchrotron-based micro-beam Laue diffraction is an experimental technique for the study of intra-granular lattice orientation and elastic strain in individual crystallites of polycrystalline engineering alloys. Traditionally the technique operates in reflection geometry with a polychromatic X-ray beam focused to a sub-micron spot and with photon energy ranging from approximately 5 to 30 keV. This allows the study of material in the near-surface region. In this paper the first feasibility study of extending this technique to a polychromatic beam with significantly higher photon energies from 50 to 300 keV is presented. At these energies, transmission through even thick samples can be achieved and it becomes possible to study deeply buried material volumes. The technique is demonstrated by recording an orientation map of a flat dogbone large-grained Ni sample. Comparison with an optical micrograph shows very good agreement, validating the feasibility of this approach.

Introduction

Micro-beam Laue diffraction is a powerful synchrotron-based diffraction technique which has emerged in recent years. It allows the study of intra-granular variation of lattice orientation, elastic strains, stresses and dislocation microstructure within single crystals or individual crystallites of a polycrystalline material. A polychromatic X-ray beam is used to illuminate a sampling volume considerably smaller than the average grain size. The resulting Laue diffraction pattern recorded on an area detector consists of a number of diffraction spots. Indexation of these spots allows accurate determination of lattice orientation in the sampling volume. By refinement of the exact spot positions, the local deviatoric elastic strain tensor can be found. Spot shape and changes in shape across the pattern provide important information about local lattice orientation spread which can be interpreted in terms of dislocation arrangement [1], [2], [3].

Spatial resolution perpendicular to the incident beam is dictated by the spot size on the sample. Using modern achromatic optics (Kirkpatrick–Baez or KB mirrors) at high brilliance 3rd generation light sources, sub-micron spot sizes are routinely achieved. Currently the smallest focus of a polychromatic beam using KB mirrors is 7 nm [4].

Most micro-beam Laue experiments use reflection geometry with the sample surface forming a 40° or 45° angle with the incident beam and the area detector placed vertically above the sample at 2θ = 90° (angle between the incident beam and the vector from the sample to the detector centre). The photon energy bandpass used depends on the instrument. In general, the lower limit lies between 5 and 10 keV, the upper limit between 22 and 35 keV [5], [6], [7]. A wide range of systems have been studied using this setup. Examples include elastic strains and lattice orientation in thin films [8], [9], Sn whisker growth [10], [11], electro migration-induced stresses [12] and in situ deformation of FIB-machined single crystal micro pillars [13], [14].

In the case of samples where the sample thickness along the beam direction is of the same order as the attenuation length or shorter, such as thin films, the size of the sampling volume in the beam direction is defined by the sample thickness. However, in bulk samples which extend to much greater thickness than the attenuation length, as is the case in measurements in grains on the surface of a polycrystalline material, the size of the scattering volume in the beam direction is limited by absorption and hence not sharply defined. This introduces a convolution effect between real and reciprocal space in the resulting diffraction images. In order to achieve a more clearly defined gauge volume, the differential aperture X-ray microscopy method (DAXM) was developed [15], [16]. Here a tungsten wire is scanned between the detector and the sample. Using ray tracing, the exact depth from which a given reflection originated can be computed. DAXM has found a wide range of applications, in particular in samples with steep lattice rotation gradients. Here depth resolution allows the breaking up of Laue streaks into individual patterns of diffraction spots. Applications include the study of friction stir welded samples [17], metal matrix composites [18] and Sn whisker growth [19].

An alternative method to micro-beam Laue diffraction for the study of microstructure in three dimensions has been developed in the form of 3DXRD [20], [21]. A monochromatic “sheet” beam of around 50 keV is used to illuminate slices of the specimen under investigation. The sample is then rotated about an axis perpendicular to the beam. As individual grains are placed in Bragg condition, diffraction contrast can be observed. This is particularly prominent in highly annealed samples. At the same time, the reflection arising from the crystal in Bragg condition is recorded on a set of area detectors placed at different distances to the sample. Using ray tracing methods, the diffracting grain shape can be reconstructed in the illuminated plane, along with lattice orientation and grain level elastic strain. The rapid data collection possible with this method makes the study of dynamic processes such as re-crystallisation [22] and the mapping of large sample volumes [23] feasible.

The limitations of the methods discussed thus far are, in the case of classical micro-beam Laue diffraction, that investigations are more or less constrained to near-surface regions due to the X-ray energies in use — in Ni, the attenuation length at 20 keV is ∼ 35.5 μm, in Al at 20 keV, the attenuation length is ∼ 1.17 mm. In the case of 3DXRD methods, the need for sample rotation can be a limiting factor, especially where samples of complex shape and with limited access are concerned.

In the ideal case, an even more useful tool for the material scientist and engineer would allow the penetration deep into the bulk of real engineering components, where thicknesses might reach up to several mm, without the need for sample rotation. One way of achieving this non-destructively is to extend the micro-beam Laue diffraction technique to higher photon energies. The idea of extending existing diffraction methods to higher photon energies in order to achieve improved penetration into thick samples is already commonly used in the powder diffraction community. Examples include both the use of monochromatic [24], [25] and energy dispersive [26], [27] high energy X-ray diffraction setups for the determination of lattice strains, micro-strains, microstructure and texture evolution. In the case of micro-beam Laue diffraction, this would potentially allow the study of material buried deep within bulk and through-thickness characterisation of orientation and elastic strains in real engineering components.

Here we present the first feasibility study of a high energy transmission micro-beam Laue diffraction setup developed at beamline ID15A at ESRF, Grenoble. To demonstrate the technique, an orientation map of a 0.3 mm thick dogbone-shaped plate sample of commercially pure Ni was recorded. Very good agreement was found between the grain microstructure from high energy-transmission Laue diffraction and optical micrographs, providing some validation of the method.