Polychromatic X-ray Microdiffraction Research Articles

In situ analysis of deformation twins within a magnesium polycrystal: (II) twin growth

The process of twin growth is difficult to be captured instantaneously. Synchrotron polychromatic X-ray microdiffraction (micro-XRD) is applied to in situ study twin growth in extruded Mg-3Al-1Zn polycrystal subjected to uniaxial tension. The micro-XRD data is used to map an area of 396 × 200 μm2 under the loading levels from 12 MPa to 73 MPa. The orientations of seven parents and ten resultant twins are determined by indexing Laue patterns, while their morphologies are mapped by the integrated intensities of particular reflections. {101¯2} twins are detected at 64 MPa. The maximum SF criterion for twin variant selection is invalid here. Twin growth rates are deduced from the variation of integrated intensities between 64 MPa and 68 MPa. It is found that twin growth rates in the HCP material are not proportional to active twin's SF values, though the SF value is related to the magnitude of driving resource. Twin growth rate exhibits obvious anisotropy, either for lengthwise growth rate or thickness growth rate. When two twins within a parent belong to the same twin variant, they exhibit similar growth rates. Meanwhile, when two twins within a parent come across, one can block the other and the latter occur shrinking.

In-situ analysis of grain rotation and lattice strain within a magnesium polycrystal based on synchrotron polychromatic X-ray diffraction technique: (I) prior to twin

Hexagonal-close-packed structure aggregates exhibit complicated deformation behaviors, involving different slips and twinning. Synchrotron polychromatic X-ray microdiffraction (micro-XRD) was utilized to study in situ an extruded Mg-3Al-1Zn strip subjected to uniaxial tension. The evolution of grain rotation and lattice strain was analyzed under the load levels from 12 to 73 MPa. The micro-XRD data was used to map an area of 396 × 200 μm within the region of interest. The experimental set-up and X-ray diffraction microscopy in two dimensions allow the morphology, orientation and strain of the target grain to be determined at the submicron size. Results depict local orientation fluctuation, lattice strain evolution, slips system and elastic modulus within the same grain. As the applied load increases, the grain's rotation is accelerated between 46 MPa and 51 MPa at which level of load the grain-scale plastic deformation is activated. The predominantly slip modes prior to twin are identified as the combination of b1→ = (0002) [112¯0] andb3→ = (0002) [2¯110]. During the inspection, all reflection planes displayed an onset of micro yielding at the macro load level of ∼38 MPa. In this work, we confirm that magnesium is nearly elastic isotropic.

In situ synchrotron study of electromigration induced grain rotations in Sn solder joints

Here we report an in situ study of the early stage of microstructure evolution induced by electromigration in a Pb-free β-Sn based solder joint by synchrotron polychromatic X-ray microdiffraction. With this technique, crystal orientation evolution is monitored at intragranular levels with high spatial and angular resolution. During the entire experiment, no crystal growth is detected, and rigid grain rotation is observed only in the two grains within the current crowding region, where high density and divergence of electric current occur. Theoretical calculation indicates that the trend of electrical resistance drop still holds under the present conditions in the grain with high electrical resistivity, while the other grain with low resistivity reorients to align its a-axis more parallel with the ones of its neighboring grains. A detailed study of dislocation densities and subgrain boundaries suggests that grain rotation in β-Sn, unlike grain rotation in high melting temperature metals which undergo displacive deformation, is accomplished via diffusional process mainly, due to the high homologous temperature.

In situ analysis of multi-twin morphology and growth using synchrotron polychromatic X-ray microdiffraction

Synchrotron polychromatic X-ray microdiffraction (micro-XRD) was applied to study in situ deformation twinning of commercially AZ31 (Mg–3Al–1Zn) strip subjected to uniaxial tension. The morphology and growth of twins were analyzed in situ under the load level from 64 to 73 MPa. The X-ray microdiffraction data, collected on beamline 12.3.2 at the Advanced Light Source, were then used to map an area of 396 μm − 200 μm within the region of interest. The experimental set-up and X-ray diffraction microscopy with a depth resolution allow the position and orientation of each illuminated grain to be determined at the submicron size. A list of parent grains sorted by crystallographic orientation were selected to examine their twinning behavior. The results depict twin variant selection, local misorientation fluctuation and mosaic spread for multi-twins within the same parent grain. As load increases, the amplitude of misorientation fluctuation along twin trace keeps increasing. This is attributable to the accumulation of geometrically necessary dislocations.

Inhomogeneous deformation behavior in intercrystalline regions in polycrystalline Ni

We report on three-dimensional spatially resolved X-ray microdiffraction measurements of inhomogeneous deformation within individual polycrystalline grains. These measurements provide new insights into the role of grain boundaries. Particularly striking is the qualitatively different mechanical behavior of subgrain volumes near grain boundaries and triple junctions compared to bulk-grain mechanical behavior. These differences are studied by characterizing the evolution of the local orientation distribution in a polycrystalline Ni sample using polychromatic synchrotron X-ray microdiffraction. Dependence of deformation on grain boundary types and triple junctions is determined. Quantitative distinctions in deformation behavior between low-angle boundaries, special low-energy high-angle boundaries, general high-angle boundaries and triple junctions are characterized in terms of spatially resolved misorientation development and extensions of grain boundary effects. In general, larger lattice misorientations are observed near boundaries with higher grain boundary energy. Special high-coincidence grain boundaries exhibit smaller deformation misorientations than general high-angle grain boundaries. These observations are consistent with the observed increases in ductility in grain boundary engineered materials.

In situ X-ray microdiffraction studies inside individual VO2 microcrystals

Synchrotron X-ray microdiffraction provides quantitative structural measurements with submicron spatial resolution, and hence enables investigations of how local microstructural inhomogeneities affect materials’ properties. A combination of polychromatic and monochromatic X-ray microdiffraction was used to investigate domain formation, interface orientations and strain distributions inside individual vanadium dioxide (VO2) microcrystals. Using in situ measurements near the VO2 metal–insulator phase transition, it was found that the observed phase evolution is critically dependent on external strain. Substrate-induced strains or inhomogeneous sample heating can directly alter phase stability and affect the local domain orientations. In different clamped or freely suspended single-crystal samples, all the predicted twin laws for the M2 phase in VO2 were observed, except one. When the rutile and M2 phases coexist, it was found that different interphase boundary orientations can be stabilized by sample size and by interfacial elastic strain. The large variations in phase sequences and domain orientations observed in relatively simple, small single crystals provide insight into the mechanisms responsible for the broad structural and electronic transitions observed in epitaxial VO2 films.

Diffraction Across the Length Scale

This JOM special topic concerns advances in neutron and x-ray diffraction directed toward the study of the structural properties of materials at different length scales. This year, the scientific community is celebrating 100 years since the discovery of x-ray diffraction by Laue, Bragg, and the first experimental diffraction pattern obtained from a crystal by Friedrich and Knipping. After their experiment, it was immediately understood that x-rays could become one of the most powerful tools for material characterization, medicine, etc. During the last century, the importance of diffraction methods utilizing x-rays and later electrons, neutrons, and Mossbauer photons increased enormously, while their area of applicability significantly broadened. For example, compare the first laboratory x-ray tubes of 100 years ago with the ultrabrilliant synchrotron x-ray sources of today that have opened fantastic possibilities for the analysis of structure in a broad spectrum of materials. In the first decades of x-ray science, the studies of regular Laue–Bragg reflections, specifically their positions and intensities, were the primary focus of research. This allowed the characterization of crystallographic structure starting from simple lattices and moving toward complicated organic structures. Diffraction studies became the basis for the development of crystallography, physics, chemistry, etc. Later, the focus of x-ray science moved to the understanding of both static and dynamic lattice defects. In real crystals, thermal vibrations and other defects disturb periodic atomic arrangements and alter the diffracted intensity. Diffraction lines and reflections may broaden, their intensity weakens, and sometimes the so-called diffuse scattering appears around and between the Bragg peaks. The character of the scattered intensity relates to the shortand long-range order, type, and symmetry of defects, the interaction energy between different atoms, the Fermi surface, and phonons, and critical fluctuations near phase transitions, etc. The selected manuscripts present a slice of several x-ray and neutron diffraction applications that are currently the focus of research in different laboratories worldwide. These manuscripts demonstrate the possibilities of materials studies utilizing small local probes providing information about submicron volumes in those materials and larger beams probing statistically averaged properties of those materials. First, three manuscripts titled ‘‘Microscopic Deformation in Individual Grains in an Advanced High-Strength Steel’’ by Zhenzhen Yu, Roziliya Barabash, Oleg Barabash, Wenjun Liu, and Zhili Feng, ‘‘Acquisition, Sharing and Processing of Large Datasets for Strain Imaging: An Example of an Indented Ni3Al/Mo Composite’’ by N.S. McIntyre, R.I. Barabash, J. Qin, M. Kunz, N. Tamura, and H. Bei and ‘‘In Situ Observation of the Dislocation Structure Evolution During a Strain Path Change in Copper’’ by Christian Wejdemann, Henning Friis Poulsen, Ulrich Lienert, and Wolfgang Pantleon present example applications of different versions of x-ray microdiffraction with a beamsize 0.5 lm for in-depth understanding of the mechanical behavior at the mesoscale. Several versions of microdiffraction were developed: Polychromatic x-ray microdiffraction (PXM) and differential aperture x-ray microscopy (DAXM) were developed by Oak Ridge National Laboratory at the microdiffraction beamline 34-IDE at the Advanced Photon Source at Argonne National Laboratory. This method is directly based on Laue diffraction experiments. Modernization of the beam line apparatus and the high brilliance of synchrotron emissions create unusual opportunities to extract the mesoscale information about the materials. A slightly different version of this technique is described by McIntyre et al. where it is employed at the microdiffraction beamline at the Advanced Light Source. The PXM technique utilizes both a monochromatic beam and a white (pink) beam with an energy range of 5–25 keV. It is best suited to study defects in polycrystalline or multiphase materials Rozaliya I. Barabash is the guest editor for the Mechanical Behavior of Materials Committee of the TMS Structural Materials Division, and coordinated the topic Diffraction Studies across the Length Scales in this issue. JOM, Vol. 65, No. 1, 2013

Plastic and elastic strains in short and long cracks in Alloy 600 studied by polychromatic X-ray microdiffraction and electron backscatter diffraction

The microscopic strain distributions were studied for stress corrosion cracks produced electrochemically in C-rings of Alloy 600 (0.65 Ni, 0.16 Cr, 0.08 Fe). The strain data were obtained using polychromatic X-ray microdiffraction (PXM) and (in part) by electron back-scatter diffraction (EBSD). PXM was used to measure plastic and elastic strain distributions around the tip of a short crack, along with the changes to the direction and shape of the diffraction spots (ellipticity). For a sample with a short (30μm) crack, the misorientation map showed a well-defined region of plastic deformation along the grain boundary in advance of the crack tip, extending to the next triple point. For the large crack sample, plastic and elastic stains as well as crystalline order could be measured in high detail with respect to the crack path. However, no correlation between these could be obtained, except for a notable degradation of crystalline order near the crack mouth. A comparable EBSD misorientation map shows strong correlation between misorientation and the crack edges; this may in part reflect the role of sharp edges in the more surface-sensitive approach.

Assessment of Plastic Deformation Induced by Indentation on a Large Grain on Inconel 600 Using Synchrotron Polychromatic X-ray Microdiffraction

A synchrotron-based three-dimensional (3-D) Laue technique called Differential Aperture X-ray microscopy (DAXM) was used to investigate plastic deformation of Inconel 600 induced by indentation. The DAXM technique is capable of probing up to 60 to 100 μm into the Ni alloy, with micron resolution. A conical indenter was used to generate an indent on a large surface grain on Inconel 600. The DAXM Laue images from the uppermost grain exhibited pronounced streaking and splitting of Laue spots, which increased as the grain boundary was approached. Splitting of the Laue patterns correlates with subgrain or dislocation cell formation. A significant amount of dislocation cell formation was found within the 1-μm voxels probed by DAXM. A change in total angle of 8.79 deg was determined for the uppermost grain from the diffraction data from depths 4 to 28 μm, with an average misorientation angle of 2.15 deg between the dislocation cells. The next grain having a different crystallographic orientation continued to rotate in the same direction as the uppermost grain due to the large plastic deformation.

Assessment of deviatoric lattice strain uncertainty for polychromatic X-ray microdiffraction experiments

X-ray microdiffraction is a powerful technique for conducting high-spatial-resolution lattice strain measurements. However, there has been limited validation of the technique to date. An experiment was conducted at the Advanced Light Source to assess the uncertainty of deviatoric lattice strains measured using polychromatic X-ray microdiffraction. It is shown that the measurement uncertainty is different for each component of the deviatoric lattice strain tensor. Monte Carlo simulations of the experiment are used to explain the differences in uncertainty. The simulations point to the existence of spurious deformation modes that arise erroneously in the strain calculation owing to measurement noise and limited pole figure coverage. Methods for reducing measurement uncertainty are proposed.

The study of stress application and corrosion cracking on Ni–16 Cr–9 Fe (Alloy 600) C-ring samples by polychromatic X-ray microdiffraction

Microscopic strains associated with stress corrosion cracks have been investigated in stressed C-rings of Ni–16 Cr–9 Fe (Alloy 600) boiler tubing. Polychromatic X-ray microdiffraction was used to measure deviatoric strain tensors and the distribution of dislocations near cracks that had been propagated in electrochemically accelerated corrosion tests. An associated investigation of the C-ring-induced strains prior to corrosion showed significant tensile strain in the stress axis direction by the torsional closure of the alloy tube section in the C-ring test. Significant grain lattice rotation and pronounced plastic strain at some grain boundaries were noted. Stress-corrosion-cracking-generated intergranular cracks were produced in two Alloy 600 specimens after 6h and 18h tests. The diffraction patterns and resultant strain tensors were mapped around the cracked area to a 1μm spatial resolution. The strain tensor transverse to the crack growth direction showed tensile strain at the intergranular region just ahead of the crack tip for both specimens. Both cracks were found to follow grain boundary pathways that had the lowest angle of misorientation. Dislocation distributions within each grain were qualitatively obtained from the shapes of the diffraction spots and the effect of “hard” and “soft” grains on the crack pathway was explored for both 6h and 18h specimens. The Schmid factor of one of the grains adjacent to the crack at the 6h and 18h initiation sites was found to be the lowest, compared to Schmid factors calculated for surface grains away from the initiation site, and also along the crack path into the bulk.

Nonpercolative metal-insulator transition in VO2single crystals

Detailed temperature-dependent transport, optical microscopy, and synchrotron-based polychromatic x-ray microdiffraction measurements have been carried out in the vicinity of the metal-insulator transition (MIT) temperature of VO${}_{2}$ single crystals. The formation and propagation of a real-space phase boundary along the rutile c axis is monitored during the transition. Pure metallic rutile R, as well as insulating monoclinic M1 phases, is observed at the onset of MIT. The two phases are separated by a sharp-phase boundary. Our findings suggest a nonpercolative nature of the MIT in VO${}_{2.}$

Deformation twinning and residual stress in calcite studied with synchrotron polychromatic X-ray microdiffraction

Microstructures of deformed calcite in marble from the Bergell Alps are studied by using a microfocused polychromatic synchrotron X-ray beam. The high spatial resolution, together with orientation and strain resolutions, reveals twin plane orientation, multiple twin lamellae, and strain distributions associated with the twins. Single and multiple mechanical twins on $$ e = \left\{ {01\overline{1} 8} \right\} $$ systems are confirmed. Residual stresses are derived from the strain tensor that is derived from Laue diffraction patterns. Average lattice strains from several hundred to over one thousand microstrains are detected in a deformed marble from the Bergell Alps. Such strains suggest 60–120 MPa residual stresses. A detailed study of strain components shows that shear stresses on twin planes are completely released.

Evolution of ferroelectric domain structures embedded inside polycrystalline BaTiO3 during heating

The evolution of ferroelectric domains inside a single grain of a polycrystalline BaTiO3 ceramic was investigated under quasistatic heating by using polychromatic scanning x-ray microdiffraction. Four domain orientations were observed, three of which exhibited a classic of ∼90° ferroelastic relationship. The fourth domain orientation was found to be crystallographically related with one of the other orientations by a rotation of either 180.47° or 0.47°. While heating the polycrystalline BaTiO3 from room temperature to above the Curie temperature (125 °C), all four ferroelectric domain orientations rotated toward a paraelectric cubic orientation which was found to be at an intermediate orientation relative to the four domain orientations. The crystallographic relationships of the domains with respect to paraelectric phase were explained using a domain structure model by Nepochatenko.

A comparative EBSD and micro-XRD study of the intergranular grain structure in CP-Ti

Electron Backscatter Diffraction (EBSD) and scanning polychromatic X-ray micro-diffraction (micro-XRD) have been applied to study the intergranular grain structure in CP-Ti strip. Prior to synchrotron experimentation, a polycrystalline CP-Ti sample was electrochemically polished and a series of fiducial markers were placed on the surface to define a 500 μm×500 μm region of interest. Within this area EBSD was used to obtain an orientation map of the grains at the sample surface. Synchrotron polychromatic X-ray micro-diffraction data, collected on beamline 12.3.2 at the Advanced Light Source, was then used to map an area of 200×60 μm 2 within the region of interest. Comparison of the respective grain maps indicated an average grain size of ∼50 μm. Micro-XRD data was initially used to locate the same surface grains determined by EBSD. Based on comparison of the Euler angles, grain orientation maps from the two data sets were found to be in close agreement. The typical rolling texture found in CP-Ti was identified with the basal pole maxima tilted slightly toward the transverse direction. Subsequent 3D analysis of the Laue pattern intensity distribution of the surface grains revealed that some of the large grains identified by EBSD formed sub-cell structures below the sample surface.

Cyclic-loading-induced accumulation of geometrically necessary dislocations near grain boundaries in an Ni-based superalloy

In this study, the fatigue-induced microstructure produced in a nickel-based polycrystalline superalloy that was subjected to cyclic loading was characterized by polychromatic x-ray microdiffraction (PXM) together with in-situ neutron diffraction and transmission-electron microscopy (TEM). In-situ neutron-diffraction measurements reveal two distinct stages of the fatigue damage: cyclic hardening followed by cyclic softening. Three-dimensional spatially resolved PXM micro-Laue measurements find an increase in the density of geometrically necessary dislocations near the grain boundaries, which is accompanied by lattice rotations and grain subdivisions. The PXM results are in agreement with the in-situ neutron-diffraction and TEM results.

Study of residual elastic- and plastic-deformation in uniaxial tensile strained nickel-based Alloy 600 samples by polychromatic X-ray microdiffraction (PXM) and neutron diffraction methods

In order to assess the reliability of the relatively new polychromatic X-ray microdiffraction (PXM) method for measuring the magnitude and distribution of mechanical strains, PXM and the traditional technique—neutron diffraction measurements were made on the gauge section of an uniaxially 1% strained Alloy 600 tensile specimen and an unstressed sample of the same alloy. The average strain magnitudes for the grains analyzed by PXM were found to be similar with those measured from neutron diffraction within the large experimental uncertainty. Of particular interest was the behavior of dislocations in opposing grains across grain boundaries of differing orientations, which was studied by comparing the elongation and splitting of PXM spots. Similar dislocation densities, operating on the similar slip systems, were found on both sides of 60° boundaries, while considerable differences in the degree of elongation and splitting of diffraction spots occurred between grains with other misorientation angles.

Neutron and X-ray Microbeam Diffraction Studies around a Fatigue-Crack Tip after Overload

An in-situ neutron diffraction technique was used to investigate the lattice-strain distributions and plastic deformation around a crack tip after overload. The lattice-strain profiles around a crack tip were measured as a function of the applied load during the tensile loading cycles after overload. Dislocation densities calculated from the diffraction peak broadening were presented as a function of the distance from the crack tip. Furthermore, the crystallographic orientation variations were examined near a crack tip using polychromatic X-ray microdiffraction combined with differential aperture microscopy. Crystallographic tilts are considerably observed beneath the surface around a crack tip, and these are consistent with the high dislocation densities near the crack tip measured by neutron peak broadening.

Neutron and X-ray diffraction studies and cohesive interface model of the fatigue crack deformation behavior

The crack-tip deformation behavior during a single overload, fatigue test of ferritic stainless steel, and Ni-based HAYNES 230 superalloy is studied at different structural levels using (1) neutron-diffraction, from which both the elastic-lattice strain and volume-averaged total dislocation densities are obtained, (2) polychromatic X-ray microdiffraction to probe the geometrically necessary dislocations and boundaries distribution, and (3) an irreversible and hysteretic cohesive interface model which has been implemented into a finite element framework to simulate the stress/strain evolution near the fatigue crack tip. Neutron strain measurements and finite element simulations are in qualitative agreement on the macroscopic length scale. Large plastic deformation induced by the overload and the resulting compressive residual strains are observed in front of the crack tip after the overload, and are the principal reason for the fatigue-crack-growth retardation. Strong strain gradients surrounding the crack propagation result in the formation of a high density of geometrically necessary dislocations near the fractured surface and cause local lattice rotations on the submicron level.

Plastic deformation in Al (Cu) interconnects stressed by electromigration and studied by synchrotron polychromatic x-ray microdiffraction

We report here an in-depth synchrotron radiation based white beam x-ray microdiffraction study of plasticity in individual grains of an Al (Cu) interconnect during the early stage of electromigration (EM). The study shows a rearrangement of the geometrically necessary dislocations (GNDs) in bamboo typed grains during that stage. We find that about 90% of the GNDs are oriented so that their line direction is the closest to the current flow direction. In nonbamboo typed grains, the Laue peak positions shift, indicating that the grains rotate. An analysis in terms of force directions has been carried out and is consistent with observed EM induced grain rotation and bending.