Thomas Tsakalakos

Strain field and scattered intensity profiling with energy dispersive x-ray scattering

Two powerful synchrotron x-ray scattering techniques for residual strain depth-profiling and tomography-like scatter-intensity profiling of materials are presented. The techniques utilize energy dispersive x-ray scattering, from a fixed microvolume, with microscanning of the specimen being used to profile its interior. The tomography-like profiles exploit scattering-cross-section variations, and can be contrast enhanced by separately monitoring scattering from different crystal structures. The strain profiling technique is shown to finely chronicle the internal strain variation over several mm of steel. Detailed strain profiling for a cantilever spring demonstrates the interplay of residual and external stresses in elastic/plastic deformation. Since surface compression, by shot peening, is a classic method to fortify against fatigue failure, the strain profile for a shot-peened, surface-toughened material is determined and discussed in terms of a simple elastic–plastic stress/strain model. Finally the lattice strains in a WC/Co coated steel composite material are discussed.

Enhanced elastic modulus in composition modulated copper‐nickel‐iron foils

Young’s modulus was measured by tensile testing on Cu/NiFe thin foils containing short‐wavelength composition modulation of 1.4–10.0 nm. The foils, of 53% Cu/40% Ni‐7% Fe composition, were produced by vapor deposition using a three‐source evaporator. As compared with homogeneous foils of the same average composition, the modulated foils exhibited an appreciable increase (up to 300%) in modulus for two distinct ranges of composition wavelength: 2.1–2.7 and 3.6–4.1 nm. The increase was proportional to the square of the composition amplitude. The stress‐strain curves of the modulated foils displayed a Hookean behavior below 0.2% strain.

Effect of long‐range interaction on diffusion in copper‐nickel composition‐modulated alloys

Vapor deposited Cu–Ni films were produced containing composition modulations with wavelengths between 0.8 to 5.0 nm. The foils, deposited on mica substrates, exhibited a strong 〈111〉 texture and produced satellite peaks in the x‐ray diffraction patterns. The interdiffusivities in the range of 375–450 °C, which were measured from the decay rate of the x‐ray diffraction satellite intensities, yielded an activation energy of 2.7×105 J/mol. This value is in good agreement with that obtained by tracer diffusivities at high temperatures. The effective diffusion coefficient DB at 400 °C [as a function of the dispersion relation B2(h)] showed a minimum at a wavelength of about 1.5 nm in contrast with the linear or monotonic behavior of several other systems. A new formulation of DB in a power series of B2 was developed and the first six interaction energies were calculated from short‐range order parameters.

Anomalous lattice expansion in yttria stabilized zirconia under simultaneous applied electric and thermal fields: A time-resolved in situ energy dispersive x-ray diffractometry study with an ultrahigh energy synchrotron probe

Nonisothermal densification in 8% yttria doped zirconia (8YSZ) particulate matter of 250 nm median particle size was studied under 215 V/cm dc electric field and 9 °C/min heating rate, using time-resolved in-situ high temperature energy dispersive x-ray diffractometry with a polychromatic 200 keV synchrotron probe. Densification occurred in the 876–905 °C range, which resulted in 97% of the theoretical density. No local melting at particle-particle contacts was observed in scanning electron micrographs, implying densification was due to solid state mass transport processes. The maximum current draw at 905 °C was 3 A, corresponding to instantaneous absorbed power density of 570 W/cm3. Densification of 8YSZ was accompanied by anomalous elastic volume expansions of the unit cell by 0.45% and 2.80% at 847 °C and 905 °C, respectively. The anomalous expansion at 905 °C at which maximum densification was observed is characterized by three stages: (I) linear stage, (II) anomalous stage, and (III) anelastic recove...

In situ strain profiling of elastoplastic bending in Ti–6Al–4V alloy by synchrotron energy dispersive x-ray diffraction

Elastic and plastic strain evolution under four-point bending has been studied by synchrotron energy dispersive x-ray diffraction. Measured strain profiles across the specimen thickness showed an increasing linear elastic strain gradient under increasing four-point bending load up to ∼2 kN. The bulk elastic modulus of Ti–6Al–4V was determined as 118 GPa. The onset of plastic deformation was found to set in at a total in-plane strain of ∼0.008, both under tension and compression. Plastic deformation under bending is initiated in the vicinity of the surface and at a stress of 1100 MPa, and propagates inward, while a finite core region remains elastically deformed up to 3.67 kN loading. The onset of the plastic regime and the plastic regime itself has been verified by monitoring the line broadening of the (100) peak of α-Ti. The effective compression/tension stress-strain curve has been obtained from the scaling collapse of strain profile data taken at seven external load levels. A similar multiple load scal...

Measurements of interdiffusivities in Cu/NiFe ternary alloy thin films

Abstract Interdiffusivities have been measured in Cu/NiFe ternary alloys containing 53at.% Cu, 40 at.% Ni and 7 at.% Fe. Isothermal anneals were performed at temperatures: 320, 345 and 400°C using thin films containing composition modulations (1.6–4.98 nm) produced by the vapor-phase growth technique. Spinodal decomposition in these films was observed in the X-ray diffraction pattern as indicated by the growth of satellite intensities at 320°C. The diffusivities at each temperature were determined from the growth or decay rate of the composition modulation. A plot of the interdiffusion coefficient D B , versus the dispersion relation B 2 demonstrated anomalous behavior at certain wavelengths at which an enhanced elastic modulus effect is observed. The critical spinodal temperature was estimated and first three gradient energy coefficients were calculated using a nonlinear regression fit to the D B vs B 2 curve.

Formation of fault structures during coalescence and growth of gold particles in a fused silica matrix—I

Abstract The fault structures formed during annealing of gold particles in a fused silica matrix were examined employing transmission electron microscopy. For higher volume fractions of gold and short annealing times at 900°C particle-particle coalescence by bridge formation was observed. After longer annealing times, particles assumed a nearly spherical shape approximately 500 A in diameter. A limited number of planar boundaries were found to have formed as the result of particle-particle coalescences and grain growth. The predominant structural configuration was a series of parallel or nonparallel planar twin boundaries within the gold particles. In the case of intersecting twins a specific planar coincidence lattice boundary was also observed. No evidence of high angle grain boundaries and dislocation structure was observed. It is believed that the various twin structures observed are metastable, with little mobility and may be used to examine mechanisms of grain boundary migration and annealing twin formation.

Elastic and plastic contribution to x-ray line broadening of InGaAsP/InP heterostructures

The coherency state of MOCVD grown InGaAsP/InP double-heterostructure wafers was examined and their effects on the structural properties were determined in this study. Lattice mismatches were measured using {511} asymmetric and (400) symmetric x-ray reflections. The chemical lattice misfit and the elastic strain were also calculated. Misfit dislocations were examined by both x-ray topography and photoluminescence imaging. The x-ray full width at half maximum (FWHM) varied with the degree of mismatch. The largest FWHM was obtained for samples containing the misfit dislocations. It was found that FWHM is influenced not only by the plastic deformation, but also by the elastic strain. To model the dependence of the FWHM, the radius of curvature was measured, and its contribution to the x-ray line broadening was calculated. Also, the contribution from misfit dislocations was taken into account. This model assumes that the dislocations are planar and interact weakly with each other. Good agreement between measured and calculated values was obtained. Thus, it is concluded that the major contribution to x-ray line broadening ofelastically strained sample is the lattice curvature induced by misfit strain, and that the dominant factor affecting x-ray FWHM ofplastically deformed sample is lattice relaxation induced by misfit dislocation.

Nonlinear diffusion in spinodal decomposition: a numerical solution

The numerical solution of the one-dimensional nonlinear diffusion equation with a negative diffusion coefficient (up-hill diffusion) by a five-point approximation central difference scheme is considered. The stability criteria are discussed in detail and a numerical solution is provided for a specific case in which the time evolution of a periodic composition wave is presented with growth eventually leading to a stationary configuration. A critical comparison of the numerical solution with existing analytical solutions is shown. This leads to a simple semi-empirical growth law for studying the kinetics of spinodal decomposition in alloys.

Stress Gradient Induced Strain Localization in Metals: High Resolution Strain Cross Sectioning via Synchrotron X-Ray Diffraction

Strain localization in the presence of a stress gradient is a phenomenon common to many systems described by continuum mechanics. Variations of this complex phenomenon lead to interesting nonlinear effects in materials/engineering science as well as in other fields. Here, the synchrotron based energy dispersive x-ray diffraction (EDXRD) technique is used for high spatial resolution profiling of both compression and tension induced strain localization in important materials/engineering problems. Specifically, compression induced strain localization in shot peened materials and tension induced strain localization in the plastic zones adjoining the faces of a fatigue crack are profiled. The utility of the EDXRD synchrotron technique for nondestructively cross-sectioning strain variations on small length scales (down to 10-20 μm) is described. While the strain field profiling relies on the shift of the Bragg lines, the data show that plastic deformation regions can also consistently be seen in the broadening of the Bragg peaks through the full width at half maximum parameter. Quantitative correlations between the synchrotron based x-ray determined deformations and surface deformations, as measured by optical surface height profiling, are also made.