Metals and alloys used in daily applications are submitted to deformations repeated for a very large number of cycles during their lifespan and can break under stresses amplitude lower than their ultimate tensile stress (fatigue of materials). Evaluating the evolution of the microstructure during deformation can provide insights into the mechanisms responsible for the observed mechanical behaviour and produce useful input to design materials ensuring the safety and reliability of the structures throughout their life service. Several techniques, including transmission electron microscopy (TEM), synchrotron x-ray diffraction and neutron diffraction techniques, and electron backscattered diffraction (EBSD), were used to evaluate the dislocation density in plastically deformed materials. However, all these techniques are affected from several limitations in distinguishing the influences of domain size and dislocation density. During the last two decades, Groma et al.[1] developed a new method for the evaluation of the dislocation density and its fluctuation in plastically deformed specimens with the only limitation of the coherent domain size that should be larger than 1μm. This method is based on the asymptotic behavior of the second- and fourth-order restricted moment in the tail portion of the x-ray diffraction peak.
The present research aims to use the variance method for estimating dislocation density when a very large number (~10⁹) cyclic loadings is applied on the single crystal with an applied stress significantly lower than the yield stress so that deformation is almost entirely elastic. The monocrystalline copper specimen was loaded using a 20 kHz ultrasonic fatigue machine mounted on the six-circle diffractometer available at the DiffAbs beamline on the SOLEIL synchrotron facility (France). Since we are interested to investigate the very high cycle fatigue domain, the amplitudes of the cyclic stresses range from 7 to 91 MPa. The diffraction patterns were acquired with a 2D hybrid pixel X-ray detector (XPAD S140) which integration time has been synchronized with the fatigue rig. The diffraction data are analysed with the k-order restricted moments method of the tail portions of individual Bragg peaks, for estimating the microstructure evolution in terms of dislocation density and spatial distribution of the dislocations. The results of these experimental data show an increase in the dislocation density with the external loading. Detailed results will be presented and discussed.

[1] Groma. (1998) Physical Rev. B, 57(13), pp. 7535–7542.

Important advancements in the field of powder X-ray scattering aim at improving the reach and accuracy of pattern analysis methods. Pair distribution function and other methods based on the Debye scattering equation (DSE) are the most straightforward as they directly compute the interference between couples of atoms. All interatomic distances for all grains in the powder have however to be computed. Whole powder pattern and pair distribution function modelling methods solve, instead, the same problem by considering whole objects in place of atoms. Even if not as general, they provide the same result but faster [1, 2].
Common volume functions (CVFs) are used to model the scattering contribution from crystalline domains of any shape. However, CVFs are readily available for a limited set of regular shapes. Allegra and Wilson [3] computed the scattering line profile of deformed shapes applying a linear transformation. Although reprised multiple times, such approach is not suitable for techniques based on the CVF formalism. We generalized the paper of Allegra and Wilson considering the effects on the powder diffraction pattern of a deformation applied to the shape (i), to the underlying lattice (ii) or to both (iii).
Here we discuss the transformation of the CVF to account for the scattering contribution of domain shape and crystal structure deformations (Fig. A), and shape-structure relative orientation (Fig. B). As an example, starting from the CVF for a sphere (cube) domain and a cubic crystal structure, the transformation allows the analysis of (i) ellipsoid (parallelepiped) domains in a cubic lattice, (ii) sphere (cubic) domains in a triclinic lattice and (iii) ellipsoid (parallelepiped) domains in a homologous triclinic lattice. The presence of size and shape deformation dispersions are also considered. The resulting profiles are used to model both the intensity scattering contributions and the small-angle shape function used to correct numerical pair distribution function profiles. Finally, we analysed pattern simulated via DSE to assess the possibility of extracting the deformation information from real powder scattering data.

Nano-structuring is a crucial step in optimizing permanent magnet materials, where both the size and morphology of the individual particles heavily affect the properties of the compacted bulk magnet. The size is tuned to ensure magnetic single-domain particles, which is crucial for optimizing the coercivity of the magnet (the field strength required to flip the magnetic orientation), as this is lowered by the mobility of walls between domains. Generally, the minimum required coercivity of a permanent magnet is half of the saturation magnetization, at which point the remanence (the magnetization at zero field) is the limiting factor. The remanence, in turn, is primarily tuned by the alignment of the particles, i.e. the texture of the bulk magnet.

One way to control the alignment is through the morphology of the nano-particles, as the right particle shape leads the powder to self-alignment during compaction and sintering into dense pellets, thus optimizing the alignment of the magnetic domains in the resulting bulk magnet^[1].
The overall figure-of-merit for permanent magnets is evaluated from the volume-weighted energy product (a.k.a. the BH_max), reported in kJ/m³ (MGOe in cgs-units). It follows that the density of the final bulk magnet is an important parameter, which again is correlated with the particle microstructure. The combination of crystallite size, texture, and density emphasizes the compaction process when going from powder to bulk, which also often includes a sintering step. Powder diffraction is a powerful technique for studying the compaction and sintering processes, as proper refinement of the data can provide valuable information about phases, crystallite size, texture, and, in the case of neutron diffraction, the magnetic moments, as they develop during the compact. Neutron powder diffraction also comes with the benefit of a large probing volume, which is useful for studying bulk behavior.

The rapid improvements in both detectors and sources allow for faster and faster data collection, but the accompanying large data quantities require robust and efficient data treatment strategies. One such strategy is sequential refinement, where each pattern in the dataset is refined one after the other (typically) in chronological order, using the final model of the previous refinement as a starting model for the next.

Taking it a step further gives us parametric refinement. Here, a single overall model is used to describe an entire dataset simultaneously, while still allowing some individuality between patterns. This is accomplished by describing suitable parameters using functions or constraints across all N patterns. In this way, the remaining unconstrained parameters are allowed to more freely refine towards physically sensible minima. As an example, a given phase formation might be known to follow a certain kinetic model, and so the scale factor can be parameterized to follow that model. Likewise, the unit cell parameters for a compound known to exhibit linear thermal expansion might be described by two parameters (slope and intercept), rather than N times unit cell parameters. This is clearly a significant reduction in the total number of refined parameters, especially for large in situ datasets. The ability to refine across several patterns makes parametric refinement a powerful tool for disentangling correlating parameters such as intensity-dependent parameters or peak profile parameters, as it allows us to impose physically meaningful time-dependent constraints.

Using parametric refinements allows us to get the most out of our neutron powder diffraction data!

^[1] Stingaciu, Marian, et al. "Optimization of magnetic properties in fast consolidated SrFe 12 O 19 nanocrystallites." RSC advances 9.23 (2019): 12968-12976.

Polycrystalline layers of organic perovskites such as CH3NH3PbI3 (MAPbI3) are intensively studied in order to achieve high performance of solar cells. The final efficiency correlates with the defect density, size and morphology of the crystallites. These materials exhibit tendency to form strongly oriented layers with sharp fibre multi-component texture. In order to correlate the relevant physical properties of the layers with their crystallographic orientation, it is highly desirable to easily measure the present texture.

As a classical and well-established approach, one can use pole figure measurement to fully determine the texture of the layers, however here the task is complicated by the fact that the low-symmetry unit cell of this material is rather large. Consequently, the number of observable peaks is high and their diffraction angles are partially overlapping. In order to resolve them, the resolution in diffraction angle has to be increased at the expense of the intensity making the pole figure measurement to be a time consuming. Another specific problem can be a presence of some possible strain influencing the peak positions.

Fortunately, fast 2D detectors are more and more available also in standard laboratory diffractometers that makes it possible to measure reciprocal-space maps very quickly. In this presentation, the measurements with 2D detector placed closely behind the sample are presented. Using the shorter sample-detector distance, the resolution is partially sacrificed while the reciprocal space area observed by the detector is dramatically extended. In this configuration, the continuous theta-2theta scan fully probes a long stripe in a reciprocal space. By measuring several such stripes, it is easy to reveal the full planar cut of the reciprocal space, and surprisingly the total acquisition time can be only tens of minutes for strongly oriented layers. Moreover, such measurement can be performed for different sample azimuth in order to obtain different planar cuts. This is desirable for single-crystal substrates, for which the surface symmetry can be followed.

The obvious advantage of this approach is a possibility to quickly visualise the intensity in reciprocal space and to compare the obtained images with the simulations based on some expected phase/texture model giving semi-quantitative results. Therefore it is very suitable for the first-try characterization of the unknown samples.

We reveal the novel result about the residual strain distribution as a function of depth in alumina/ stainless steel brazing joint using synchrotron XRD in transmission geometry. The evolution of the residual strain distribution in the joint during cooling is in-situ measured using an in-house developed brazing equipment. The residual strain in the joint is low at relatively high temperature and with the decrease of the temperature, the residual strain increases and becomes compressive. The residual strain is found to be increasing from the surface to the interface in a nonlinear fashion. The microstructure of the joint is characterised and the effect of the pores and the fillet on the residual strain distribution is studied by image based modelling.

Electronic devices are becoming more and more present in our daily life and their relevance will increase even more in the future. These gadgets evolve aiming at higher performance, lower energy consumption and better portability. This continuously creates a demand for miniaturised components. Such devices contain many elements whose properties are based on ferroelectricity. Barium titanate is the model ferroelectric system. In addition, its properties are highly temperature and grain size dependent. It has excellent properties with grain sizes of approximately 1 µm, but undergoes marked weakening as the grain size decreases. A wide range of unimodal grain size distribution between 0.4 µm and 15 µm was successfully sintered, avoiding abnormal grain growth. Samples with intermediate grain size, showed excellent electromechanical and dielectric properties. They possess a balance between microstructural strain, existence and mobility of domain walls, which in turn allows the field induced crystal phase transformation. The samples, under application of external electric field, were subjected to in situ high energy X-ray diffraction analysis. To resolve the angular resolution a high‑resolution multianalyser detector was used. By means of STRAP the field induced phase transformations were quantified. This induced phase transformation is stronger in samples whose grain size distribution curve is located around 1 µm. These results contribute to the understanding of fundamental questions about the ferroelectric effect in barium titanate and consequently other similar systems.

In our contribution we will present feasibility of using a high resolution three axis neutron diffractometer performance for elastic and plastic deformation studies of metallic polycrystalline samples. The method consists of unconventional set up employing bent perfect crystal (BPC) monochromator and analyzer with a polycrystalline sample in between (see Fig. 1). After realization of focusing conditions in real and momentum space at the neutron wavelength of 0.162 nm, a high angular resolution down up to FWHM(Δd/d)=2x10^-3 and FWHM(Δd/d)=3x10^-3 which was achieved on the standard α-Fe(110) samples 2 mm diameter in the vertical position and 8 mm diameter for 10 mm irradiated length in the horizontal position, respectively. It opens the possibility for mea-surements of small lattice parameter changes even on bulk samples. The drawback of theperformance shown in Fig. 1 consists in the necessity step-by-step analysis by rocking the BPC-analyzer. However, in the case of residual strain/stress measurements, position sensitive detector can by employed (see Fig. 1b) and partly eliminate the former drawback. In the latter case, bulk samples e.g. in the tension/compression rig can be studied with a high resolution. The feasibility of both instrument performances for macro- and microstrain as well as grain size studies is demonstrated on the polycrystalline samples of standard and low carbon shear deformed steel wires.

Figure 1.

Figure caption:

Fig. 1. Three axis diffractometer set-ups employing BPC monochromator and analyzer as used in the experimental feasibility studies (R_M, R_A - radii of curvature, θ_M, θ_A - Bragg angles) with a point detector – (a) and/or with a position sensitive detector (PSD) – (b).

Due to their excellent mechanical properties and high specific mass, tungsten heavy alloys are used in demanding applications, such as kinetic penetrators, gyroscope rotors, or radiation shielding [1]. However, their composite structure, consisting of hard tungsten particles embedded in a soft matrix [2], makes the deformation processing a challenging task. This study focused on the characterization of deformation behaviour during thermomechanical processing of a W-Ni-Co tungsten heavy alloy (produced by powder metallurgy) via the method of rotary swaging (aimed at still improving properties) at ambient temperature and at 900°C.

Swaging changed mechanical properties, and - as an important step to optimize microstructure and mechanical properties is to understand the underlying processes - the aim of the neutron diffraction study was to determine texture and to characterize microstrain, dislocations as well as the active slip system. The strength of neutron diffraction method lies in the information provision from the bulk of the sample, i.e. not only from its near-surface region. This advantage is still amplified for materials with very high X-ray absorption (like tungsten alloys) and/or with large grains.

First, phase identification was done from the diffraction patterns. The detected main phase was corresponding to the original tungsten powder grains of bcc structure, the second (in fact matrix) phase, was Ni-Co solid solution with fcc structure [3]. Peak broadening after swaging was visible in the soft matrix phase.

Further, texture measurement using neutron diffraction was done, which shows that the original as sintered material had for the tungsten phase no texture. It also shows that there were very large grains of Ni-Co matrix phase in the as sintered bar, without any clear preferential orientation. During rotary swaging, the large grains of Ni-Co are fractioned to fine-grained microstructure. A strong texture formed in both phases after rotary swaging [4]. Both bcc phase and fcc phase, after rotary swaging, have the same texture type as for wire drawing. It can be thus concluded that the primary deformation mechanism for rotary swaging was the same as for wire drawing. The textures for cold and hot swaging are qualitatively the same, but stronger for cold swaging which indicates that secondary deformation mechanisms are also active for the hot swaging. The deformation was also connected with formation of residual macrostresses [4,5].

The peak broadening was evaluated for the neutron-diffraction peaks of the relatively soft Ni-Co matrix phase [3]. The modified Williamson-Hall plot shows that the microstrain increased approximately 3 times after rotary swaging. In accord with the texture measurement, the edge dislocations with <110> {111} slip system (typical in fcc) provide such contrast factor, that the integral breaths of the individual reflections fit very well to straight lines. Interesting is the Ni-Co matrix in non-deformed as-sintered bar where the contrast factor for screw <111> dislocation fits best with the measured integral breaths. The dislocation densities from the slope of the modified Williamson-Hall plot were estimated. The dislocation density increased approximately 5 times after rotary swaging, which is linked with the mechanical properties: swaged samples exhibited substantial strengthening - primarily caused by the increase in dislocation density. Further, the dislocation density is 15% higher for the sample swaged at room temperature than for the sample deformed at 900°C, which fits the trend observed in stress-strain curve.

[1] Kocich, R.; Kunčická, L.; Dohnalík, D.; Macháčková, A. & Šofer, M. (2016) Int. J. Refract. Met. Hard Mater. 61, 264–272.

[2] Durlu, N.; Caliskan, N.K. & Sakir, B. (2014) Int. J. Refract. Met. Hard Mater 42, 126–131.

[3] Strunz, P.; Kunčická, L.; Beran, P.; Kocich, R. & Hervoches, C. (2020). Materials 13, 208, doi:10.3390/ma13010208

[4] Strunz, P.; Kocich, R.; Canelo-Yubero, D; Macháčková A.; Beran, P. & Krátká, L. (2020) Materials 13, 2869; doi:10.3390/ma13122869

[5] Canelo‑Yubero, D.; Kocich, R.; Hervoches, Ch.; Strunz, P.; Kunčická, L. & Krátká, L. (2021) Metals and Materials International, https://doi.org/10.1007/s12540-020-00963-8

Keywords: tungsten heavy alloys; rotary swaging; neutron diffraction; dislocations; microstrain; texture

The authors acknowledge support for this research by Czech Science Foundation, grant No. 19-15479S. Measurements were carried out at the CANAM infrastructure of the NPI CAS Řež. The presented results were obtained also with the use of infrastructure Reactors LVR-15 and LR-0 financially supported by the Ministry of Education, Youth and Sports - project LM2018120.

Deformation behavior of ZN11 magnesium alloy in a form of extruded profile has been investigated with respect to different loading directions. The samples were compressed at room temperature with a constant strain rate of 10^-3s^-1 along extrusion (ED), transversal (TD) and normal direction (ND). X-ray diffraction technique was employed to follow the development of texture during loading. The twinning activity was studied by the subsequent analysis of microstructure using scanning electron microscopy (BSD, EBSD). The deformation behavior of the extruded profile was also investigated by the acoustic emission (AE) technique, where the AE signal analysis correlates the microstructure and the stress-time curves to the active deformation mechanisms. Compression along the ND (i.e. compression perpendicular to the basal planes) is not favorable for twinning, while during compression along the ED and TD twinning activity is observed.