X-ray Diffraction Stress Measurements Research Articles

Microstructure evaluation and crack initiation crack for AZ31 sheet under biaxial stress

In this study, a biaxial tensile test of cruciform specimens containing centre notch was conducted with a miniature biaxial tensile test system in order to clarify the deformation behavior near the crack tip at the early stages of crack initiation when objected to a biaxial stress state. Stress distributions were determined by X-ray diffraction stress measurement, and the crack initiation angle was predicted by modified Dugdale model. The microstructure evolutions were investigated by the electron backscatter diffraction technique. The deformation twins were formed at the biaxial tensile test due to the creation of a large stress field near the crack-tip region. The formation region of deformation twins became small with the equiaxial tension due to the lower stress concentration. Observation of the microstructure reveals that the deformation is dominated by basal slip under equal biaxial tensile loading. The asymmetrical biaxial tensile loading generates deformation twins near the crack tip. These results indicate that deformation twinning in the vicinity of crack tip is more significant in predicting the initial crack growth.

Nonmonotonic crystallite-size dependence of the lattice parameter of nanocrystalline nickel

A nonmonotonic crystallite-size dependence of the lattice parameter of ultrathin, nanocrystalline Ni films, i.e., lattice contraction followed by lattice expansion with decreasing crystallite size, was observed using in situ x-ray diffraction stress measurements combined with a dedicated thermal treatment called “loop annealing.” The expected lattice contraction with decreasing crystallite size was found for nanocrystalline Cu and nanocrystalline Pd.

X-ray diffraction characteristics of five materials for stress measurement

This paper presents the laboratory X-ray diffraction characteristics of five materials: carbon steel (Q235), austenitic stainless steel (1Cr18Ni9Ti), martensitic stainless steel (A335P92), Al alloy (LY12), and Ti alloy (TA15) in X-ray diffraction stress measurement. The difficulty in accurately determining actual stress is illustrated by two diffraction peaks with low diffraction intensity that occur in laboratory X-ray diffraction stress measurement. Stress measurements by both laboratory X-ray diffraction and strain gauges methods were conducted by using uniform strength beams of the five materials. A comparison between measured results and analytical/theoretical results was made to examine laboratory X-ray diffraction characteristics of the five materials for stress measurement. The measurements show that austenitic stainless steel, Al alloy, and Ti alloy present two diffraction peaks in X-ray diffraction stress measurement. Although the CrKα diffraction peak of the {220} plane of austenitic stainless steel is apparent, the stress calculated from this peak does not represent the actual stress; however, the CrKβ diffraction peak of the {311} plane, in spite of the lower peak-back ratio, can be used to obtain the actual stress. For the Al alloy, only the CrKα peak of the {222} plane can represent the material's stress. Two diffraction peaks of the Ti alloy measured by CoK α radiation can be used to calculate its actual stress. Hence attention should be paid to which X-ray diffraction peaks can be used for actual stress determination.

Determination of depth gradients of grain interaction and stress in Cu thin films

Grain-interaction and residual stress depth gradients in a sputter-deposited Cu thin film (thickness 4 µm) were determined by employing X-ray diffraction stress measurements at constant information depths in the range between 200 and about 1500 nm. A novel procedure, which allows the determination of an effective grain-interaction parameter on the basis of thef(ψ,hkl) method and the Voigt and Reuss models of elastic grain interaction, was used. The range of accessible penetration depths was maximized by employing different photon energies using a laboratory diffractometer with Cu Kα radiation and a diffractometer at a synchrotron beamline. The variation of grain interaction with depth could be successfully related to the microstructure of the specimen. The tensile residual stress in the film parallel to its surface decreases with decreasing depth. By measuring the lattice spacing for several reflections at one penetration depth with two different photon energies (i.e.using small and large incident beam angles) it was found that the surface roughness of the specimen counteracts the effect of beam refraction to some degree. As a consequence, irrespective of whether a refraction correction is applied or neglected for the low-incidence angle measurement, erroneous results are obtained for lattice spacings derived from reflections at small incidence angles; reliable grain-interaction and stress analysis requires measurements at high incidence angle.

Driving force for Sn whisker growth in the system Cu–Sn

The evolution of residual stress gradients in Sn thin films on Cu substrates upon aging at ambient temperature has been investigated, for specimens which do exhibit and which do not exhibit Sn whisker growth, by performing x-ray diffraction stress measurements at constant penetration depths. Comparison of the measured near-surface stress-depth profiles for both types of specimens, as function of aging time at ambient temperature, showed that a significant negative stress gradient from the surface toward the Sn∕Cu interface is decisive for Sn whisker growth in the system Cu–Sn.

Extreme elastic anisotropy of cementite, Fe 3C: First-principles calculations and experimental evidence

First-principles results for the full set of elastic constants (stiffnesses) cij of cementite, Fe3C, revealed an extreme elastic anisotropy with a very small c44 amounting to only about 1/10 of c55 and c66. Synchrotron X-ray diffraction stress measurements were performed on Fe3C layers grown on α-Fe exhibiting a planar state of compressive residual stress. These data exhibit a characteristic hkl-dependence of the stress-induced reflection shifts, and provide experimental proof for the extreme elastic anisotropy of Fe3C.

Interdiffusion and stress development in Cu–Pd thin film diffusion couples

Thin film Cu–Pd diffusion couples (individual sublayer thicknesses: 50 nm) were prepared by direct current magnetron sputtering on silicon substrates coated with amorphous diffusion/reaction barriers (Si 3N 4 on top of SiO 2). The microstructural variations, phase formation and stress evolution during diffusion annealing were investigated employing Auger-electron spectroscopy in combination with sputter-depth profiling, transmission electron microscopy and in-situ X-ray diffraction. Upon annealing at relatively low temperatures (185 °C) for durations up to 17 h, considerable diffusional intermixing occurs. Interdiffusion is accompanied by the formation of a compound phase (ordered Cu 3Pd (α′)). The stress changes in the bilayer system during heating and isothermal annealing were investigated employing in-situ X-ray diffraction stress measurements and were compared to corresponding results obtained for single layers of the components in the Cu–Pd bilayer system, produced under conditions identical to those employed for the sublayers of the diffusion couple. The specific residual stresses that emerge due to diffusion (and reactions) between the (sub)layers in the bilayer could then be identified by comparing the stress evolutions upon annealing of the single layers with those recorded for the sublayers of the bilayer.

Depth dependence of elastic grain interaction and mechanical stress: Analysis by x-ray diffraction measurements at fixed penetration/information depths

Gradients of the type of elastic grain interaction and the (residual) internal state of stress were determined. This was possible by the application of x-ray diffraction stress measurements at various fixed penetration/information depths. The analysis was applied to nickel films of thicknesses 2 and 4μm. Surface anisotropy was considered as source of direction-dependent (anisotropic) elastic grain interaction. It was found that only a small gradient of the state of stress, but a pronounced gradient of the grain interaction constraints, prevails in the investigated specimens. Thereby the evidence for the depth dependence of the so-called surface anisotropy was obtained.

An X-Ray Diffraction Method to Determine Stress at Constant Penetration/Information Depth

A rigorous strategy for (X-ray) diffraction stress measurements at fixed penetration/information depths is described. Thereby errors caused by lack of penetration-depth control in traditional (X-ray) diffraction (sin2ψ) measurements are annulled. The ranges of accessible penetration/information depths and experimental aspects are briefly discussed. The power of the method is illustrated by the analysis of an only small stress gradient in a sputter-deposited nickel layer.

A method for the non-destructive analysis of gradients of mechanical stresses by X-ray diffraction measurements at fixed penetration/information depths

A rigorous measurement strategy for (X-ray) diffraction stress measurements at fixed penetration/information depths has been developed. Thereby errors caused by lack of penetration-depth control in traditional (X-ray) diffraction (sin2ψ) measurements have been annulled. The range of accessible penetration/information depths and experimental aspects have been discussed. As a practical example, the depth gradient of the state of residual stress in a sputter-deposited nickel layer of 2 µm thickness has been investigated by diffraction stress measurements with uncontrolled penetration/information depth and two controlled penetration/information depths corresponding to about one quarter and one tenth of the layer thickness, respectively. The decrease of the planar tensile stress in the direction towards the surface could be well established quantitatively.

Effects of BEOL Stack on Thermal Mechanical Stress of Cu Lines

AbstractThe measurement and control of the stress state in BEOL interconnects are important to ensure structural integrity and long term reliability of integrated circuits. Thermal stress in interconnects is determined by the thermal-mechanical properties of Cu lines, substrate, and dielectric materials. The effect of BEOL stacks on thermal stress characteristics of Cu lines were investigated using X-ray diffraction stress measurements. The stress characteristics of M1 and M4 level interconnects in full low-k and low-k/oxide hybrid dielectric stacks were evaluated, and the results indicated reduced substrate confinement and an increased impact of the dielectric material on in-plane stresses in higher level interconnects. The effects of dielectric stack and material properties were examined and the implication in the stresses of multilevel interconnects are discussed.

The modelling of residual stresses due to surface peening using eigenstrain distributions

The beneficial effect of surface peening (including shot peening, laser shock peening, low plasticity burnishing, etc.) on fatigue resistance of structural alloys is well documented and widely used in industry to improve component life. It is perhaps the most widely used technique that relies on the introduction of residual stresses into the component by direct mechanical means. The resulting stress states are usually evaluated experimentally by X-ray diffraction or other stress measurement techniques. In order for shot peening operations to be effective and reliable, the process of introducing residual stresses and strains into peened components must not only be controlled but also be predictable and quantifiable. The present paper establishes a framework for predictive modelling of the residual stress states due to surface peening. Firstly, uniform (within planes parallel to the surface) plastic deformation of the surface layer taking place during shot peening of a thin plate is simulated using the concept of eigenstrain. As a further demonstration of the capabilities of the proposed approach, flexible plate theory is applied to the analysis of stresses and deformations arising due to local peening within a circular area. The results are of considerable use and significance for the analysis of shot peening and peen forming operations.

Residual stress measurement with focused acoustic waves and direct comparison with X-ray diffraction stress measurements

The technique of measuring small changes in acoustic wave velocity due to external or internal stress has been used for quantitative determination of residual stress in materials during the last decade. Application of similar methodology with focused acoustic waves leads to residual stress measurement with spatial resolution of a few millimeters to a few microns. The high spatial resolution residual stress measurement required development of new methodologies in both the design of acoustic lenses and the instrumentation for acoustic wave velocity determination. This paper presents two new methodologies developed for the measurement of residual stress with spatial resolution of a few millimeters. The design of new type of acoustic lens for achieving higher spatial resolution in residual stress measurement is introduced. Development of instrumentation for high precision local surface wave velocity measurement will be presented. Residual stresses measured around a crack tip in a sample of Ti–6A1–4V using a focused beam will be compared with X-ray diffraction measurements performed on the same region of the sample. Results of residual stress measurements along a direction perpendicular to the electron beam weld in a sample of Ti–6A1–4V, determined using focused acoustic waves and X-ray diffraction technique, are also presented. The spatial resolution and penetration depth of X-rays and focused acoustic beams with reference to residual stress measurements are discussed.

Origin and implications of the observed rhombohedral phase in nominally tetragonal Pb(Zr0.35Ti0.65)O3 thin films

The structural and electrical properties of Pb(Zr0.35Ti0.65)O3 (PZT) thin films ranging in thickness from 700 to 4000 Å have been investigated. These (001)/(100)-textured films were grown by metalorganic chemical vapor deposition on (111)-textured Ir bottom electrodes. It was observed that, in the as-deposited state, the thinnest PZT films are rhombohedral even though bulk PZT of this composition should be tetragonal. Thicker films have a layered structure with tetragonal PZT at the surface and rhombohedral PZT at the bottom electrode interface. In this article we investigate the origin of this structure and its effect of the ferroelectric and dielectric properties of PZT capacitors. It has been suggested that thin films stresses can affect the phase stability regions of single domain PZT. This possibility has been investigated by piezoresponse microscopy and thin film stress measurements. In the as-deposited state the majority of PZT grains contain a single ferroelastic domain, whereas after a high temperature anneal, a large fraction of the grains contain several ferroelastic domains. Wafer curvature measurements in combination with x-ray diffraction stress measurements in the Ir bottom electrode showed that the as-deposited PZT films are, within experimental error, stress free at room temperature. Landau–Ginbzurg–Devonshire formalism was used to explain the origin of the rhombohedral phase as a result of substrate constraint on single domain PZT grains. Annealing was found to affect the relative volume fractions of the rhombohedral and tetragonal phases and the electrical properties of PZT films. Intermediate temperature anneals increased the volume fraction of the rhombohedral phase and the coercive field extracted from the polarization-electric field hysteresis loops. After a high temperature anneal (650 °C) the majority of the grains transformed into a polydomain state, decreasing the volume fraction of the rhombohedral phase and the coercive field. If the high temperature anneal was performed after deposition of the top electrode, the coercive field became independent of the PZT thickness.

Unerwartete Ergebnisse von Barkhausenrauschmessungen an einem Rollenwälzlager nach Trockenlauf

Locally increased amplitudes of Barkhausen Noise are usually due to changes of residual stresses versus tension and/or reduction of mechanical hardness. This rule was found not to be valid for a 5 to 10 μm thick surface layer with microstructural changes similar to friction martensite which was detected in a roller bearing of a helicopter intermediate gear, after running without lubrication for about 20 minutes. Besides of Barkhausen Noise Measurements and conventional Non Destructive Testing, X-Ray Diffraction Analysis and Stress Measurements, Scanning Electron Microscopy, ESCA and metallographic investigations were carried out. It is assumed that rearrangements of dislocations and interstitial atoms in connection with transformation of retained austenite have lead to an increase of the mobility of Bloch Walls and so caused the observed high noise amplitudes.

Mesure par diffraction des rayons X des microdéformations dans des films minces texturés d'Au

Microdistorsion analysis in Au 150 nm thin films is presented in this study. Applying the method of the «integral width», known and employed in bulk materials, we have shown its feasibility and its interest in the case of thin films. Furthermore, in relation with X-Ray diffraction stress measurement, we found important effects of the deposition conditions on the films microstructure

Stress analysis and failure possibility assessment of multilayer physically vapour deposited coatings

A mathematical model for stress analysis and failure possibility assessment of multilayer coatings produced by ion-assisted physical vapour deposition (PVD) is proposed. Stresses in coating layers are divided into thermal, intrinsic and operational stresses. Calculations of thermal stresses and intrinsic stresses caused by interstitials are performed for TiN and titanium layers on stainless steel substrates. Coating failures as a result of a single layer failure, interface crack propagation and peeling above an area with imperfect adhesion are discussed. The model enables the determination of optimal thicknesses and deposition conditions of layers. X-ray diffraction stress measurements make it possible to estimate the model errors, which are found to be 15%–20%. As an example, calculations for PVD coatings with TiN and titanium layers are carried out. It is concluded that it is useful to interpose the ceramic and metal layers to reduce interface shear forces.

Enhanced Gate Oxide Reliability through Fluorine Incorporation and the Influence of Polysilicon Process Variations

ABSTRACTThere has been some uncertainty as to the impact of fluorine (F) on SiO2 quality and reliability. Several laboratories have shown greatly enhanced quality and reliability with fluorinated oxides, while others have been unable to repeat the results. In addition, the laboratories which have shown enhanced reliability with the fluorinated oxides have differed in their interpretation of the mechanism by which the enhancement occurs. X-ray diffraction stress measurements, partial time dependent dielectric breakdown (TDDB) measurements, SIMS depth profiling, transmission electron microscopy, standard high/low frequency C-V measurements, and hot-carrier aging of variously processed MOSFETs have been used to investigate a variety of fluorinated films. We believe that the apparent lack of consistency of the effects of fluorine on MOSFET reliability between laboratories may be explained by slight variations in the gate polysilicon processing which result in variations in polysilicon morphology. The polysilicon morphology determines both mechanical stress and F diffusion which ultimately impacts interface state density and thus hot carrier reliability.

Growth Characteristics of Co-Cr Thin Films for Magnetic Recording

AbstractThe growth characteristics of magnetron sputtered Co-22%Cr thin films on amorphous glass or carbon substrates have been investigated utilizing transmission electron microscopy,. X-ray diffraction, electrical resisivity and in-plane stress measurements. Results indicate that the initial deposit is “amorphous”, but that isolated islands of small crystallites form before the film reaches 5nm film thickness. By 10nm, well oriented grains with hcp c axis perpendicular to the film plane develop, and by 50nm, a twinned columnar microstructure is evident. As this occurs, the in-plane film stress becomes constant. Also, we have observed a distinct subgrain structure in the thinner films (10–50 nm), and this is reflected in the electrical resistivity. This cannot be accounted for by an “evolutionary selection” growth scenario, but must be related to the low surface mobility of adatoms at these low substrate deposition temperatures.

A Comparison of X-Ray Diffraction Residual Stress Measurement Methods on Machined Surfaces

The two-angle and Sin2ψ methods of x-ray diffraction, residual stress measurement have been shown to yield anomalous results When applied to samples which have been plastically deformed uniaxially in tension or by rolling. These anomalous stresses, which are not true mechanical macrostresses, have been shown to arise from a nonlinear dependence,of d, the interplanar spacing employed for stress measurement, upon Sin2 ψ. A new method of x-ray diffraction stress measurement has been developed by Marion and Cohen which aLlows the separation of the Linear and nonlinear components of the dependence of d upon Sin2 ψ.The two-angle and the Marion-Cohen x-ray diffraction methods are applied to the measurement of residual stresses in the machined and shot peened surfaces of steel and aluminum samples. The results indicate that machining deformation results in a nearly linear dependence of d upon Sin2ψ , and onLy a slight deformation texture. The two x-ray methods yield stress values in ground, turned, and shot peened steel and aluminum samples which agree within the estimated experimental error. Previous results are sighted showing agreement between the two-angle method and a mechanical stress measurement technique. The results indicate that, at least in steels, the multiaxial plastic deformation produced by machining does not significantly effect the accuracy of the two-angle x-ray diffraction stress mea surement method.