Measured Lattice Strain Research Articles

In-situ neutron diffraction study of phase stress evolutions in a Ni-based porous anode solid oxide fuel cells under uniaxial load

Ni/YSZ porous composite is used widely as anode for solid oxide fuel cells. In this study, neutron diffraction patterns were recorded in-situ while a bulk porous Ni-NiO-YSZ anode was loaded under uniaxial compression. Single peak refinement was used to calculate the lattice strains of each phase in the composite, and the local stress state of each phase was derived from the measured lattice strains and the corresponding diffraction elastic constants. An internal triaxial stress state was observed to develop in the bulk of the specimen under plastic deformation, specifically in the Ni phase. Meanwhile, the NiO and YSZ phases are deforming elastically even in the macroscopically plastic regime of deformation. The von Mises equivalent stress was used to quantify the phase stress evolution. A significant stress concentration induced by the presence of pores becomes manifest in all three phase components. The reduction of stress concentration factor in Ni above the yield point of the composite can be attributed to a gradual change of the grains-pores morphology during the plastic deformation.

Residual stress and strain-free lattice-parameter depth profiles in a γ′-Fe4N1-x layer on an α-Fe substrate measured by x-ray diffraction stress analysis at constant information depth

The residual stress and lattice-parameter depth profiles in a γ′-Fe4N1-x layer (6-μm thickness) grown on top of an α-Fe substrate were investigated using x-ray diffraction stress analysis at constant penetration depths. Three different reflections (220, 311, and 222) were recorded at six different penetration depths using three different wavelengths. At each penetration depth, x-ray diffraction stress analysis was performed on the basis of the sin2ψ method. As a result, the residual-stress depth profile was obtained from the measured lattice strains. The lattice spacings measured in the strain-free direction were used to determine the (strain-free) lattice-parameter depth profile. The nitrogen-concentration depth profile in the layer was calculated by applying a relationship between the (strain-free) γ′ lattice parameter and the nitrogen concentration. It was found that the strain-free lattice-parameter depth profile as derived from the 311 reflections is best compatible with nitrogen concentrations at the surface and at the γ′/α interface as predicted on the basis of local thermodynamic equilibrium. It could be shown that the 311 reflection is most suitable for the analysis of lattice-parameter and residual stress depth profiles because the corresponding x-ray elastic constants exhibit the least sensitivity to the type of and changes in grain interaction. The depth-dependence of the grain interaction could be revealed. It was found that the grain interaction changes from Voigt-type near the surface to Reuss-type at the layer/substrate interface.

Tensile Deformation Behavior of Duplex Stainless Steel Studied by In-Situ Time-of-Flight Neutron Diffraction

For a duplex alloy being subjected to deformation, the different mechanical behaviors of its constituent phases may lead to a nonuniform partition of stresses between phases. In addition, the grain-orientation-dependent elastic/plastic anisotropy in each phase may cause grain-to-grain interactions, which further modify the microscopic load partitioning between phases. In the current work, neutron diffraction experiments on the spectrometer for materials research at temperature and stress (SMARTS) were performed on an austenite-ferrite stainless steel for tracing the evolution of various microstresses during tensile loading, with particular emphasis on the load sharing among grains with different crystallographic orientations. The anisotropic elastic/plastic properties of the duplex steel were simulated using a visco-plastic self-consistent (VPSC) model that can predict the phase stress and the grain-orientation-dependent stress. Material parameters used for describing the constitutive laws of each phase were determined from the measured lattice strain distributions for different diffraction {hkl} planes as well as the laboratorial macroscopic stress-strain curve of the duplex steel. The present investigations provide in-depth understanding of the anisotropic micromechanical behavior of the duplex steel during tensile deformation.

Measuring and modeling distributions of stress state in deforming polycrystals

Crystal stress distributions from synchrotron X-ray diffraction experiments and crystal-based finite element simulations conducted on copper specimens loaded through yielding and the elastic–plastic transition are presented. In the experiments, the lattice strain tensor, ϵ ( R ) , and ultimately the stress tensor, σ ( R ) , for every crystal orientation, R , within the aggregate were determined at discrete load levels during a tension test by inverting measured lattice strain pole figures. The simulation conditions exactly mimicked the experiment and the underlying model employed single-crystal elasticity and restricted-slip plasticity. In the simulation, ϵ ( R ) and σ ( R ) are the average values from all elements at a particular orientation. Significant dependence in the components of σ ( R ) with orientation were found and the σ ( R ) determined from the experiment compared well with the simulation results. In addition we employed a spherical harmonic expansion of each component of stress over orientation space. The coefficients from the experiments compared well with those obtained from the simulation.

Heterogeneous Deformation Behavior Studied by in Situ Neutron Diffraction during Tensile Deformation for Ferrite, Martensite and Pearlite Steels

Tensile behavior was investigated by using in situ TOF neutron diffraction comparatively for ferritic steels; ferrite (F), as-quenched martensite (QM), tempered martensite (TM) and pearlite (P) steels. Changes in lattice spacing, diffraction intensity and FWHM with increasing of the applied stress were measured. Preferential plastic flow takes place depending on crystal orientation, so that intergranular stresses are yielded due to the misfit plastic strains in differently oriented [hkl] family grains for steel F, in blocks for the other steels. Because of the existence of cementite in steels TM and P, phase stresses are superposed upon the intergranular stresses. When the averaged phase strain is subtracted from the measured lattice strain, the trend in generation of intergranular strain in steel TM is similar to that observed in steels F and QM, while that in steel P differs from the other steels. The changes in [hkl] diffraction intensity and FWHM with tensile deformation are similar in steels F, TM and P, while those in steel QM are different from the others. FWHM decreases with tensile deformation suggesting the decrease in dislocation density in steel QM. That is, dislocations induced during martensitic transformation move preferentially and are annihilated by coalescence of dislocations with different signs in the beginning of deformation and hence transformation induced dislocation structure changes to deformation induced one that shows lower dislocation density but higher resistance to tensile flow. The preferential movement of transformation induced dislocations in steel QM leads to a different texture evolution which is recognized from the change in diffraction intensity with tensile deformation.

Intergranular Strain and Phase Transformation in a Cobalt-Based Superalloy

ULTIMET® alloy, a cobalt-based superalloy with good corrosion and wear resistant properties, exhibits a deformation-induced phase transformation from the face-centered-cubic (FCC) phase to the hexagonal-close-packed (HCP) phase. The HCP phase formation during monotonic tensile loading was investigated using in-situ neutron diffraction. The HCP phase is first observed at a stress level of 810 MPa, which is well beyond macroscopic yielding. Strain analysis is performed on the FCC phase diffraction data in order to relate the lattice-strain development with the evolution of the new HCP phase. A method of calculating the effective macroscopic stress associated with the measured lattice strains is presented here. The effective stress can then be compared to the applied macroscopic stress in order to draw conclusions about the load-partitioning behavior of the material as a new phase develops.

高温水素雰囲気中における純ニオブのその場X線回折測定

The Lattice constants of pure niobium metal were measured by in-situ X-ray diffraction method at the temperature of 293 K to 673 K and the hydrogen pressure below 0.3 MPa. The deformation and fracture of niobium metal membrane during hydrogen permeation were treated by the measured lattice strain. The membrane was deformed and fractured easily when about 10% lattice contraction was introduced to it by lowering the hydrogen pressure at 673 K, at which the dehydrogenation reaction progressed smoothly. However, neither deformation nor fracture took place at the temperature lower than 473 K, because the dehydrogenation reaction hardly occurred in such a temperature range. Thus, the principal reason for the deformation or fracture of niobium metal membrane was attributable to the large volumetric contraction during dehydrogenation, the easiness of which, however, depended largely on the temperature.

結晶方位分布関数を用いたＴｉＣＮ配向膜のＸ線応力測定

The X-ray stress measurement is an effective method of nondestructive inspection for the residual stress in the surface layer of steel materials. However, the sin2ψ method, which is commonly used as X-ray stress measurement, is inapplicable to such anisotropic materials as textured materials because the theory supposes isotropic elastic polycrystalline materials as sample.The applicable X-ray stress measurement to textured materials was investigated on the assumption that information about each crystallite orientation was deduced by crystallite orientation distribution (ODF). Applied to measure the stress of the titanium carbide nitride (TiCN) film with the ‹111› preferred orientation, the residual stress value was determined from the measured lattice strain. The strong compressive stress value was observed in the film. Compared with methods of other models, the result indicated a small difference from the ‹111› ideal fiber texture model and was situated between the texture model and sin2ψ method.

X-Ray Elastic Constants of Polycrystalline Materials with Arbitrary Crystal Structure

The X-ray diffraction technique for stress measurement can nondestructively determine residual stress in a localized surface layer of polycrystalline materials. In this method, the stress is determined from measured lattice strains using the X-ray elastic constants. Since the lattice strains of a particular lattice plane in the crystal grains are measured selectively, the X-ray elastic constants are different from the macroscopic constants of isotropic materials. The equations are derived for calculating the X-ray elastic constants for polycrystalline materials having arbitrary crystal structures from single crystal data. The Reus and Kroner models are used for the premise on the deformation of polycrystal. Measured X-ray elastic constants of steel, α-silicon carbide and α-alumina, which have cubic, hexagonal and trigonal structures respectively, were compared with the theoretical values. The values calculated using the Kroner model agreed most closely with the measured values.

The determination of stresses in thin films; modelling elastic grain interaction

X-ray diffraction is frequently employed for the analysis of mechanical stresses in polycrystalline specimens. To this end, suitable so-called diffraction elastic constants are needed for determining the components of the mechanical stress tensor from measured lattice strains. These diffraction elastic constants depend on the single-crystal elastic constants of the material considered and the so-called grain interaction, describing the distribution of stresses and strains over the crystallographically differently oriented crystallites composing the specimen. Well-known grain interaction models, as due to Voigt, to Reuss, to Neerfeld and Hill and to Eshelby and Kröner, may be applied to bulk specimens, but they are generally not suitable for thin films. In this paper, an average 'effective' grain interaction model is proposed that consists of a linear combination of basic extreme models including new models specially suited to thin films. Experimental verification has been achieved by X-ray diffraction strain measurements performed on a sputter-deposited copper film. This is the first time that anisotropic grain interaction has been analysed quantitatively.

Strength and elasticity of SiO2 across the stishovite-CaCl2-type structural phase boundary.

Radial x-ray diffraction experiments were conducted under nonhydrostatic compression on SiO2 to 60 GPa in a diamond anvil cell. This ratio of differential stress to shear modulus t/G is 0.019(3)-0.037(5) at P=15-60 GPa. The ratio for octahedrally coordinated stishovite is lower by a factor of about 2 than observed in four-coordinated silicates. Using a theoretical model for the shear modulus, the differential stress of stishovite is found to be 4.5(1.5) GPa below 40 GPa and to decrease sharply as the stishovite-CaCl2-type phase transition boundary is approached. Inversion of measured lattice strains provides direct experimental evidence for softening of C11-C12.

Load Partition in NiTi Shape Memory Alloy Polycrystals Investigated by In-Situ Neutron Diffraction and Micromechanics Modelling

Neutron diffraction experiments on NiTi polycrystals transforming in mechanical loads at constant temperature. The observed asymmetries between diffraction records of the martensite phase in tension and compression are interpreted as being due to the stress induced martensite texture caused by preferential martensite variant selection under stress. The evolution of the experimentally measured lattice strains and integral intensities of austenite and martensite reflections during compression pseudoelastic load cycle are interpreted with the help of the micromechanics model simulation of the NiTi polycrystal transformation. An information on the load partition mechanism in pseudoelastically transforming NiTi polycrystals is deduced.

New approach to stress analysis based on grazing-incidence X-ray diffraction

A new development in the determination of residual stresses in thin surface layers and coatings is presented. The procedure, based on the grazing-incidence X-ray diffraction geometry (referred to here as the `g-sin2 ψ' geometry), enables non-destructive measurement at a chosen depth below the sample surface. The penetration depth of the X-ray radiation is well defined and does not change during the experiment. The method is particularly useful for the analysis of non-uniform stresses in near-surface layers. The g-sin2 ψ geometry was applied for measurements of the residual stresses in TiN coatings. Anisotropic diffraction elastic constants of textured material were used to determine the stress value from the measured lattice strains. A new method of data treatment enables reference-free measurements of residual stresses.

Diffraction stress analysis of thin films: Modeling and experimental evaluation of elastic constants and grain interaction

Well-known grain interaction models for the description of macroscopic elastic behavior of polycrystalline specimens, as due to Voigt, Reuss, Neerfeld–Hill, and Eshelby–Kröner, may be successfully applied to bulk specimens, but are shown to be less suited for thin films. An elaboration of a proposal due to Vook and Witt for grain interaction is given. It is assumed that the strain parallel to the specimen surface is equal in all crystallites and that the stress perpendicular to the specimen surface is zero in all crystallites. It is shown that these assumptions give rise to elastic anisotropy of the specimen on the macroscopic scale. It is also shown that in this case the dependence of the measured lattice strain (in a diffraction experiment) on the squared sine of the specimen tilt angle ψ (cf. the sin2 ψ method), is nonlinear, contrary to what is predicted by the bulk grain interaction models. This is the first time that nonlinear sin2 ψ plots have been calculated using an elastic grain interaction model, in the absence of crystallographic texture. Experimental verification has been achieved by x-ray diffraction strain measurements performed on a vapor deposited nickel film. The experimental results are in good accordance with the Vook–Witt [J. Appl. Phys. 7, 2169 (1965)] grain interaction model. This is the first experimental evidence of direction dependent grain interaction in thin films.

The effect of ion irradiation on the thermal stability of GeSi/Si strained-layer heterostructures

Double Crystal X-ray Diffraction (DCXRD), Transmission Electron Microscopy (TEM), and Rutherford Backscattering Spectrometry and Channelling (RBS-C) are used to study the effect of ion irradiation on the strain and strain relaxation of metastable Ge x Si 1−x Si strained layers. Room temperature irradiation within the alloy layer is shown to increase the measured lattice strain, behaviour which is well modelled by assuming a strain profile which is based on the excess interstitial distribution created by the irradiation. During annealing to 650°C the radiation damage evolves into intermediate defect complexes and dislocation loops, and misfit dislocations nucleate and grow. The interactions between these different defects can result in a complex strain relaxation sequence which depends on the relative strain contributions of the defects and their relative nucleation and growth behaviour. Strain relaxation can therefore be enhanced or retarded by the ion-irradiation depending on the irradiation fluence and annealing temperature. Evolution of strain in irradiated Ge x Si 1−x Si alloy layers is discussed with reference to the defect microstructure after irradiation and annealing.

Relation between lattice strain and anomalous oxygen precipitation in a Czochralski-grown silicon

Spatial fluctuations of lattice strain in an as-grown Czochralski-grown silicon wafer, in which a ring-shaped region of densely distributed oxidation-induced stacking faults appears after oxidation thermal treatment, are measured by double-crystal reflection topography with synchrotron radiation. The measured lattice strain is isolated into local variations in lattice dilation and inclination angle from an average plane. The variation profile of the lattice spacing shows a small valley in the ring-shaped region, while showing a peak just outside the ring-shaped region. The relation between the lattice strain and anomalous oxygen precipitation is discussed.

X‐ray modulus and strain distribution in single fibers of polyethylene

AbstractSynchrotron x‐ray radiation was used to study structural changes during deformation of a single high‐modulus, high‐strength fiber of polyethylene (Spectra 1000, Allied Corp.) 20–40 μm in diameter. The high brightness of the synchrotron beam allowed x‐ray diffraction patterns to be obtained from 0.5 μg fiber samples in ca. 1 min. The (002) chain axis reflection shifted and broadened when the fiber was loaded in tension. When a model of crystals and disordered material in series was used for the fiber, the measured lattice strain at stresses up to 1 GPa gave a crystal modulus of 250 GPa. At stresses above 1 GPa the (002) reflection no longer shifted with increasing load. A noncrystalline part of the material deforms and takes up the load; this effect has been observed by Raman spectroscopy. The (002) peak also broadens under stress. When fiber bundles were used as samples, broadening could be due to uneven loading of fibers, but with a single fiber sample, one can be sure that the loading at the fiber level is uniform. Broadening of the (002) reflection then indicates inhomogeneities within the fiber. Deconvolution with the line profile of the fiber at zero stress should give the distribution of crystal strains. The strain distributions are symmetric and during loading the full width at half maximum (fwhm) is approximately equal to the mean strain. With an assumed constant crystal modulus this describes the stress distribution as extending from zero to twice the mean stress.

Residual stress evaluation with X-rays in steels having preferred orientation

Two phenomena limit the use of X-ray stress evaluation in practice: preferred orientation and coarse grained materials. Measurements with Cr-radiation and the (211)-peak showed nonlinearD vs sin 2 ψ distributions in the case of a 75 pct cold-rolled steel, due to preferred orientation, and for a deep-drawing steel spotty diffraction rings on a film exposed in front of the detector, due to large grain size, were observed. However, when Mo-radiation and the (732 + 651)-peak were used, theD vs sin2 ψ distributions proved to be linear, so that residual stresses could be determined. The X-ray elastic constants (XEC) needed to compute the stresses from the measured lattice strains were determined under uniaxial load using samples cut at various angles with respect to the rolling direction. For the deep drawing steel in particular, the XEC differ from the values calculated for Fe-materials having randomly oriented crystallites. Furthermore, the XEC for the two investigated steels proved to depend on the angle of sample cut with respect to the rolling direction.

Lattice distortion and volume change in a dilute heterovalent alloy:AlLi

A theoretical and experimental study of the lattice strain and volume change in the dilute solid solution $\mathrm{Al}\mathrm{Li}$ is presented. The experimental data were obtained by diffuse elastic neutron scattering in Al single crystals containing 0.26 and 0.88 at.% $^{7}\mathrm{Li}$, respectively. The isotope $^{7}\mathrm{Li}$ was used because of the small absorption and the known incoherent cross section of this nucleus. The theoretical method to calculate the volume change, the lattice distortion, and the heat of solution for a heterovalent substitutional impurity is developed within the framework of the perturbed electron-liquid pseudopotential formalism. It is shown that in determining the long-range part of the lattice displacement in a heterovalent dilute alloy such as $\mathrm{Al}\mathrm{Li}$, third- and fourth-order nonlinear screening contributions to the distorting force are equally significant in addition to the traditional linear screening term. This is in contrast to the case of a homovalent solution, where fourth-order nonlinear screening can be ignored. The numerical calculation is based on the ion-electron potentials for pure Al and Li that have been determined by using lattice-constant and elastic or phonon data for each of the pure constituents. The agreement is reasonably good with both the observed anomalous, negative volume change and with the measured lattice strain. The inadequacy of Vegard's rule to predict even the sign of the volume change in this alloy is discussed.