Energy-dispersive Synchrotron X-ray Diffraction Research Articles

Novel bulk triaxial residual stress mapping in an additive manufactured bridge sample by coupling energy dispersive X-ray diffraction and contour method measurements

A novel approach for determining triaxial residual stress states by coupling energy dispersive X-ray diffraction and contour method measurements is provided and validated in a Ti‐5Al‐5V‐5Mo‐3Cr additive manufactured (AM) bridge sample. Synchrotron X-ray diffraction (SXRD) can provide relatively fine spatial resolution (on the order of 10–100 µm) for mapping 3D elastic strain fields within a sample. However, for samples with dimensions larger than one or two centimeters the path length can get prohibitive as both constant wavelength and energy dispersive SXRD are based upon transmission measurements. As an example, for a plate-like sample geometry where the thickness is limited (less than a centimeter) it is trivial to measure the longitudinal and height direction elastic strain components with excellent in-plane spatial resolution (∼100 µm) and a somewhat lower through-thickness resolution (10–15 times larger) but obtaining the through thickness component is often not possible as the beam path must be parallel to one of the large dimensions of the plate. While small samples of low Z-number alloys (e.g., Ti or Al) allow determination of the three elastic strain components, this is often not the case for higher Z alloys (e.g., Fe or Ni) or large samples where some strain components can be indeterminable. To overcome these limitations, this work applies a combination of synchrotron X-ray diffraction and the contour method (a mechanical relaxation technique), to determine the triaxial stress state. This novel combination is demonstrated and validated in a relatively small additive manufactured sample where all three orthogonal strain components are accessible via X-ray diffraction for stress determination. The paper also explores methods for determining the strain-free lattice parameter, typically obtained from a small stress-free reference sample. This work shows that a small size AM sample is not stress free, producing unreliable magnitudes of strain and stress. Instead, a strain-free lattice parameter is determined using residual stress equilibrium conditions, which gives consistent strain and stress trends for both X-ray diffraction (alone) and the new diffraction-contour coupling technique. This demonstrates that the coupling technique can be confidently applied to samples to determine stress when path length (size or Z-number) prohibit determination of three orthogonal strain components via diffraction.

Multicycle flash sintering of cubic Y2O3-stabilized ZrO2: An in situ energy dispersive synchrotron x-ray diffraction study with high temporal resolution

The current induced unit cell volume changes, (111) Bragg peak full width at half maximum (FWHM) and its integrated intensity in 8 % Y2O3 stabilized ZrO2 (8 %YSZ) solid state electrolyte was monitored during a triple-flash sintering experiment by in situ energy dispersive x-ray diffraction using a polychromatic synchrotron probe (max, photon energy 200 keV) with 2 second temporal resolution. The first spontaneous singularity in the unit cell volume (+0.54 %) was observed at 899 °C under 15 V/mm applied field intensity, which was associated with 13 mA/mm2 current draw and an increase in density to 97 %. Following anelastic relaxation of the unit cell volume under open circuit conditions, the same applied field was applied twice in a row which resulted in additional induced singularities at 925 °C (+0.48 %) and 944 °C (+0.42 %). A floating baseline, which was above the thermal expansion baseline, was observed from 833 to 969 °C and was attributed to Joule heating. The singularity at 899 °C is associated with a sharp change in (111) FWHM and a 34 % decrease in integrated peak area that was attributed to changes in the distribution of oxygen vacancies and the changes in their concentration as induced by the applied field in the spontaneous transient stage of flash sintering.

Yüksek Enerjili Senkrotron Işık Kaynağı Kullanarak Al7075 Plakalarda Yerinde Gerilme Ölçümü

In this study, compressive and tensile strain in Al7075 plate have been measured by synchrotron energy-dispersive X-ray diffraction (EDXRD) in conjunction with 4-point bending test under various load up to 1000 lbs(453.6 kg). The compressive and tensile strain are determined by stress related interplanar spacing variation at 111 peak reflection which is considered atomic level strain measurement. The specimen initially shows elastic strain behavior under 400 lbs (181.4 kg) load. However, further load increment applied on sample causes plastic deformation on the regions close edge of the specimen where the biggest stress values in terms of both compression and tension is aroused. Finally, 1000 lbs load is applied on the specimen and major part of the specimen is deformed plastically. Vicinity of body center of sample shows almost no strain formation which is attributed nature of 4-point bending flexural test. Using high energy EDXRD method allow us to reveal precise atomic level strain distribution in Al7075 alloy under different loads.

Adjustment of the Mechanical Properties of Mg2Nd and Mg2Yb by Optimizing Their Microstructures

The deformation behavior of the extruded magnesium alloys Mg2Nd and Mg2Yb was investigated at room temperature. By using in situ energy-dispersive synchrotron X-ray diffraction compression and tensile tests, accompanied by Elasto-Plastic Self-Consistent (EPSC) modeling, the differences in the active deformation systems were analyzed. Both alloying elements change and weaken the extrusion texture and form precipitates during extrusion and subsequent heat treatments relative to common Mg alloys. By varying the extrusion parameters and subsequent heat treatment, the strengths and ductility can be adjusted over a wide range while still maintaining a strength differential effect (SDE) of close to zero. Remarkably, the compressive and tensile yield strengths are similar and there is no mechanical anisotropy when comparing tensile and compressive deformation, which is desirable for industrial applications. Uncommon for Mg alloys, Mg2Nd shows a low tensile twinning activity during compression tests. We show that heat treatments promote the nucleation and growth of precipitates and increase the yield strengths isotopically up to 200 MPa. The anisotropy of the yield strength is reduced to a minimum and elongations to failure of about 0.2 are still achieved. At lower strengths, elongations to failure of up to 0.41 are reached. In the Mg2Yb alloy, adjusting the extrusion parameters enhances the rare-earth texture and reduces the grain size. Excessive deformation twinning is, however, observed, but despite this the SDE is still minimized.

Thermal equation of state study of polymorphic phases of Y2O3

Pressure and temperature dependences of the unit cell volumes of Y2O3’s three polymorphs (cubic, monoclinic, and hexagonal) have been measured by synchrotron energy dispersive x-ray diffraction in conjunction with a cubic anvil technique to pressures and temperatures up to 7.5 GPa and 1073 K, respectively. The measured pressure–volume–temperature (P–V–T) data were used to obtain thermoelastic parameters of the polymorphs by fitting the modified high temperature third-order Birch–Murnaghan equation of state and a thermal pressure approach. The thermoelastic properties that were determined in this study are the ambient bulk modulus with fixed pressure derivative of the bulk modulus (K0′=4.0), the isobaric temperature derivative of the bulk modulus (∂K/∂T)P, the volumetric thermal expansion coefficient along with the isothermal pressure derivative of thermal expansion (∂α/∂P)T, and the isometric temperature derivative of the bulk modulus (∂K/∂T)V. The ambient bulk modulus for cubic [152(7) GPa] and monoclinic [197(9) GPa] polymorphs agrees well with previous reports. There is no precedence for all other thermophysical properties of all three polymorphs of Y2O3 reported in this study. For instance, (∂K/∂T)P is the highest for the monoclinic polymorph, while (∂α/∂P)T and (∂K/∂T)V are the highest for the cubic polymorph. The results of this study add to the stock of knowledge on the thermophysical properties of Y2O3, which is a technologically relevant solid state material.

In Situ Investigations on Stress and Microstructure Evolution in Polycrystalline Ti(C,N)/α-Al2O3 CVD Coatings under Thermal Cycling Loads

The stress behavior and the associated microstructure evolution of industrial Ti(C,N)/α-Al2O3 coatings subjected to thermal cycling are investigated by in situ energy dispersive synchrotron X-ray diffraction and transmission electron microscopy. Temperature-dependent stresses and changes in microstructural parameters (domain size and microstrain) are analyzed by in situ measurements at different temperatures between 25 and 800 °C, both in the heating up and cooling down step, including several thermal cycles. Transmission electron microscopy is used to evaluate defects before and after the thermal treatment. The introduction of high compressive stresses in α-Al2O3 by top-blasting is connected to a high defect density at the basal planes of the alumina layer. The stress relaxation of the alumina layer at high temperatures is associated with a successive annihilation of defects until a reversible temperature-dependent stress condition is set. Top-blasting does not change the initial microstructure and residual stress of the Ti(C,N) layer. Ti(C,N) shows a cyclic stress behavior associated with the heat treatment and an elastic deformation behavior in the temperature range investigated.

On the influence of heat treatment on microstructure and mechanical behavior of laser powder bed fused Inconel 718

A range of heat treatments have been developed for wrought Inconel 718 to obtain desired properties. For additively manufactured Inconel 718, the recently developed standard ASTM F3301 provides guidance for heat treatment of powder bed fusion specimens. Although this standard is based on standards developed for wrought Inconel 718, it does not include direct aging. Since direct aging reduces the number of processing steps, it can result in a post processing cost reduction if the desired properties are obtained. In this study, we characterized the microstructure and tensile behavior of Inconel 718 specimens produced by a laser powder bed fusion process. The specimens were heat treated according to two different routines after stress relieving: a full heat treatment versus a one-step direct aging process. Differences in the resulting texture and grain morphology were observed. The ex-situ stress-strain behavior was broadly similar. However, a slight increase in yield strength was observed for the direct aged specimen. In order to understand this behavior, investigations with in-situ synchrotron energy dispersive X-ray diffraction tensile testing revealed differences in the load partitioning among different crystal directions. Importantly, the elastic anisotropy expressed by the magnitude of the diffraction elastic constants showed a dependency on the microstructures.

Evolution of substructure in low-interstitial martensitic stainless steel during tempering

The evolution of the substructure and the distribution of interstitial elements in lath martensite during tempering in soft martensitic stainless steel X4CrNiMo16-5-1 was studied with line profile analysis of diffractograms from energy dispersive synchrotron X-ray diffraction, local chemical analysis with atom probe tomography and orientation mapping with electron backscatter and transmission Kikuchi diffraction. Martensite formation occurred below 135 °C without auto-tempering and led to a dislocation density in martensite of 3.8 ∙ 1015 m−2, as determined from X-ray line profile analysis. On tempering, carbon and nitrogen segregated to low-angle and high-angle grain boundaries. Recovery commenced above 550 °C and led to a reduction in dislocation density to a steady value of 4 ∙ 1014 m−2 from 600 to 750 °C. Further tempering led to a second increase in dislocation density at room temperature, owing to the transformation of reverted austenite, formed above 650 °C, into martensite on cooling. It was observed that the recovery of martensite competes with the formation of reverted austenite. The interpretation of the coherently diffracting domain size obtained from X-ray line profile analysis was critically discussed in the context of the internal structure in martensite.

The yielding behavior of SiC under high pressure and temperature conditions

A large volume cubic anvil press integrated with synchrotron energy-dispersive x-ray diffraction was employed to study the yielding behavior of powdered beta silicon carbide (SiC) under high pressure and high temperature conditions up to 7.4 GPa and 1400 °C. During compression and heating, the x-ray pattern was collected at each pressure–temperature point, and, then, via assessing the peak width of the x-ray diffraction pattern, the strains/stresses developed inside the sample under varied pressure–temperature conditions were determined. From the constitutive response of the sample as a function of pressure and temperature, we did not observe the yielding occurrence in SiC at cold compression. In contrast, high temperature induces a yielding at 1100 °C with a constant loading pressure of ∼7.4 GPa. By comparison, we found that this material is the most stable, compared with the other three strong ones (diamond, moissanite, and alfa silicon nitride), in terms of the yielding under high pressure and temperature conditions. Along with its much higher pressure and temperature requirements for phase transition and decomposition, SiC is a competent material for the development of novel tools/devices to be used in the harshly extreme working environment, such as deep drilling, high-speed cutting, and aerospace engineering.

J-integral analysis: An EDXD and DIC comparative study for a fatigue crack

Synchrotron Energy Dispersive X-ray Diffraction (EDXD) and Digital Image Correlation (DIC) have been applied to map simultaneously the 2D elastic strain and displacement fields of a propagating fatigue crack in the HAZ of a welded Cr2Ni4MoV bainitic steel. The position of the crack tip was tracked via a phase congruency analysis of the displacement field, and also by detection of its cyclic plastic zone. Both types of full field data provided independent inputs to finite element/J-integral analyses that directly quantified the elastic cyclic stress intensity factor range applied to the crack. No knowledge was required of the specimen geometry, crack length or applied loads. The agreement between the two analyses in this controlled study shows that strain mapping by synchrotron EDXD can provide a reliable method to study the crack fields in more complex problems, such as interactions between crack closure, residual stresses and applied loading.

Microstructure and mechanical properties of annealed, quenched and suction cast Ti-6Al-4V

The effect of heat treatment or processing method on microstructure, mechanical properties and phase formation in Ti-6Al-4V alloys has been researched. The alloys in as-delivered, annealed, quenched and suction cast conditions were investigated using scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX) and synchrotron X-ray diffraction (SXRD) analysis. The different processing- or heat treatment routes lead to significant changes in the phase composition. The quenched and suction cast alloys exhibited a mixture of martensitic α′ / α″ and BCC β phase. In annealed and as-delivered alloys α′ + β phase mixtures was detected. The properties of alloys strongly depend on heat treatment and / or processing route.

Internal load transfer in an interpenetrating metal/ceramic composite material studied using energy dispersive synchrotron X-ray diffraction

The mechanism of internal load transfer in a newly developed interpenetrating metal/ceramic composite is studied for the first time in this work using energy dispersive synchrotron X-ray diffraction. The composite was fabricated by infiltration of Al12Si melt in an open porous alumina preform, fabricated using a mixture of two different polymer waxes as pore formers, by gas pressure infiltration. Several diffraction planes of all three crystalline phases of the composite – alumina, silicon and aluminum solid solution are investigated. Lattice strains, both along and transverse to the loading direction, in each phase are calculated from the shifts in the measured diffraction peak positions. Results show that until about 100 MPa applied compressive stress, all three phases undergo elastic deformation. At higher applied stresses aluminum undergoes plastic deformation and correspondingly load is transferred to alumina. The load carrying capability of alumina is however limited by incipient damage in this phase. At applied compressive stresses higher than 187 MPa, load carried by the alumina phase continuously decreases and correspondingly more load is again carried by the aluminum solid solution. Throughout, the fraction of load carried by silicon remains almost constant, suggesting no significant load transfer within the metallic alloy itself.

Quantifying fatigue overload retardation mechanisms by energy dispersive X-ray diffraction

The fatigue crack retardation mechanisms operating after an overload event are investigated for a bainitic steel using high spatial resolution energy dispersive synchrotron X-ray diffraction. The elastic crack-tip strain fields are mapped at mid-thickness of compact tension samples at R-ratios of 0.1 and 0.4. The same overload stress intensity factor (KOL = 60 MPa m1/2) is applied in each case with the cracks then propagating under the same applied stress intensity range, ΔKapp = 27 MPa m1/2. The competing retardation mechanisms are directly quantified and separated, with the associated fatigue crack growth (FCG) rates then being predicted according to a 2-parameter Walker-type assessment and validated against those measured. The stress intensity factor associated with the overload residual stress field is calculated using a weight function approach. For R=0.1, shielding from residual stress controls retardation when crack growth through the overload plastic zone, rpOL, is small (specifically <0.6rpOL). For more extensive crack growth, discontinuous crack closure controls the retardation behaviour, with significant load transfer across opposing crack faces being observed at minimum load (for R=0.1). These crack face tractions are associated with the plastic asperity created during overload. The traction forces holding the crack faces open at minimum load are, for the first time, used to directly quantify the associated stress intensity factor, Kmintract as a function of crack growth. While no crack shielding is expected, nor observed, for R=0.4, the variation in FCG rate after overload is explained by changes in effective R-ratio.

In situ mapping of normal strains in the field of a growing fatigue crack in a steel weld using digital image correlation and energy dispersive synchrotron X-ray diffraction

Fatigue crack growth in the Heat Affected Zone (HAZ) of a welded CrNiMoV steel has been investigated, in situ, using Digital Image Correlation (DIC) and Energy Dispersive X-ray Diffraction (EDXD). Compact tension specimens of welded joint were loaded under tension–tension cyclic loading. The crack tip position and the evolution of the near-tip strains normal to the crack plane were tracked at selected positions for a growing fatigue crack both on the specimen surface using DIC and in the bulk of the specimen using EDXD of synchrotron X-rays. The uncertainty and quality of the DIC measurements were examined with regard to some of the key data processing parameters, including subset size and the size of measurement window; whilst the measurement errors in the EDXD measurements were also estimated. A “characteristic” strain was estimated, in the bulk of the specimen and on the specimen surface, from the average strains captured at selected positions when the propagating fatigue crack tip reached these positions.

In Situ Investigation of the Evolution of Lattice Strain and Stresses in Austenite and Martensite During Quenching and Tempering of Steel

Energy dispersive synchrotron X-ray diffraction was applied to investigate in situ the evolution of lattice strains and stresses in austenite and martensite during quenching and tempering of a soft martensitic stainless steel. In one experiment, lattice strains in austenite and martensite were measured in situ in the direction perpendicular to the sample surface during an austenitization, quenching, and tempering cycle. In a second experiment, the sin2 ψ method was applied in situ during the austenite-to-martensite transformation to distinguish between macro- and phase-specific micro-stresses and to follow the evolution of these stresses during transformation. Martensite formation evokes compressive stress in austenite that is balanced by tensile stress in martensite. Tempering to 748 K (475 °C) leads to partial relaxation of these stresses. Additionally, data reveal that (elastic) lattice strain in austenite is not hydrostatic but hkl dependent, which is ascribed to plastic deformation of this phase during martensite formation and is considered responsible for anomalous behavior of the 200 γ reflection.

Kinetics analysis of two-stage austenitization in supermartensitic stainless steel

The martensite-to-austenite transformation in X4CrNiMo16-5-1 supermartensitic stainless steel was followed in-situ during isochronal heating at 2, 6 and 18Kmin−1 applying energy-dispersive synchrotron X-ray diffraction at the BESSY II facility. Austenitization occurred in two stages, separated by a temperature region in which the transformation was strongly decelerated. The region of limited transformation was more concise and occurred at higher austenite phase fractions and temperatures for higher heating rates. The two-step kinetics was reproduced by kinetics modeling in DICTRA. The model indicates that the austenitization kinetics is governed by Ni-diffusion and that slow transformation kinetics separating the two stages is caused by soft impingement in the martensite phase. Increasing the lath width in the kinetics model had a similar effect on the austenitization kinetics as increasing the heating-rate.

Anisotropic Thermal Expansion of Zirconium Diboride: An Energy-Dispersive X-Ray Diffraction Study

Zirconium diboride (ZrB2) is an attractive material due to its thermal and electrical properties. In recent years, ZrB2 has been investigated as a superior replacement for sapphire when used as a substrate for gallium nitride devices. Like sapphire, ZrB2 has an anisotropic hexagonal structure which defines its directionally dependent properties. However, the anisotropic behavior of ZrB2 is not well understood. In this paper, we use energy-dispersive synchrotron X-ray diffraction to measure the thermal expansion of polycrystalline ZrB2 powder from 300 to 1150 K. Nine Bragg reflections are fit using Pseudo-Voigt peak profiles and used to compute the a and c lattice parameters using a nonlinear least-squares approximation. The temperature-dependent instantaneous thermal expansion coefficients are determined for each a-axis and c-axis direction and are described by the following equations: αa = (4.1507×10-6 + 5.1086 × 10-9(T-293.15))/(1+4.1507 × 10-6(T-293.15) + 2.5543×10-9(T-293.15)2) and αc = (4.5374×10-6 + 4.3004×10-9(T-293.15))/(1+4.5374×10-6(T-293.15) + 2.1502×10-9(T-293.15)2). Our results are within range of previously reported values but describe the temperature anisotropy in more detail. We show that anisotropic expansion coefficients converge to the same value at about 780 K and diverge at higher temperatures. Results are compared with other reported values.

Effect of Multiple Cation Electrolyte Mixtures on Rechargeable Zn–MnO2 Alkaline Battery

A Bi2O3 in β-MnO2 composite cathode material has been synthesized using a simple hydrothermal method and cycled in a mixed KOH–LiOH electrolyte with a range of concentrations. We show that, at a KOH:LiOH molar ratio of 1:3, both proton insertion and lithium insertion occur, allowing access to a higher fraction of the theoretical capacity of the MnO2 while preventing the formation of ZnMn2O4. This enables a capacity of 360 mAh/g for over 60 cycles, with cycling limited more by anode properties than traditional cathodic failure mechanisms. The structural changes occurring during cycling are characterized using electron microscopy and in situ synchrotron energy-dispersive X-ray diffraction (EDXRD) techniques. This mixed electrolyte shows exceptional cyclability and capacity and can be used as a drop-in replacement for current alkaline batteries, potentially drastically improving their cycle life and creating a wide range of new applications for this energy storage technology.

Elastic wave velocities in polycrystalline Mg3Al2Si3O12-pyrope garnet to 24 GPa and 1300 K

The mantle transition zone, at depths between 410 to 660 km, is characterized by two prominent discontinuities in seismic-wave velocity in addition to a relatively steep velocity gradient. Throughout this region garnet will be an abundant mineral, the composition of which will change depending on both depth and lithology. It is important, therefore, to be able to characterize the effects of these changes on seismic velocities, which means that models must incorporate reliable elasticity data on the dominant mineral end-members that can be accurately employed at mantle conditions. In this study elastic wave velocities of synthetic polycrystalline pyrope garnet (Mg3Al2Si3O12) have been measured using ultrasonic interferometry combined with energy-dispersive synchrotron X-ray diffraction in a 1000-ton multi-anvil press. Measurements were performed at pressures up to 24 GPa, conditions compatible with the base of the transition zone, and at temperatures up to 1300 K. Least-squares refinement of the ambient-temperature data to a third-order finite strain equation yields values for the bulk and shear moduli and their pressure derivatives of K S0 = 172.0 ±1.6 GPa, G = 89.1 ±0.5 GPa, δ K S / δ P = 4.38 ±0.08, and δ G/ δ P = 1.66 ±0.05. The determined temperature derivatives are δ K S/δ T = −17.8 ±2.0 MPa/K and δ G/ δ T = −7.9 ±1.0 MPa/K. High-temperature data were fitted to extract parameters for a thermodynamic model. As several high-pressure and -temperature studies have been performed on pyrope, fitting all of the available data provides a more robust assessment of the accuracy of velocity measurements and allows the uncertainties that are inherent in the various methodologies to be realized. When this model is used to determine pyrope velocities at transition zone conditions the propagated uncertainties are approximately 1.5 and 2.5% for v p and v s, respectively. To reduce these uncertainties it is important not only to measure velocities as close as possible to mantle temperatures but also to understand what causes the difference in velocities between studies. Pyrope v P and v S at mantle transition zone conditions are found to be approximately 2.4 and 3.7%, respectively, larger than recent determinations of majoritic garnet at the same conditions, implying a significant variation with chemistry that is mainly realized at high temperatures.

In-situ high temperature stress analysis of Ti(C,N) coatings on functionally graded cemented carbides by energy dispersive synchrotron X-ray diffraction

We report on in-situ high temperature X-ray thermal stress analysis of chemically graded Ti(C,N) coatings deposited on functionally graded cemented carbide substrates by chemical vapor deposition. The in-situ analyses were performed by energy dispersive X-ray diffraction using synchrotron radiation. The samples were subjected to one individual thermal cycle from room temperature to 800°C and cooled down to room temperature again. The stresses were determined using the sin2ψ method in the Ψ geometry combined with scattering vector measurements in order to unravel the compositional influences on the lattice strain distributions. It was found that the Ti(C,N) thin film presents a cycling residual stress behavior (tensile–compressive–tensile) connected to the temperature cycle. If top-blasting is applied on the thin film layer after the coating process, compressive stresses are generated. These compressive stresses induced by top-blasting are partially released after the high temperature thermal cycle. The functionalization of the cemented carbide substrate influences the level of stresses developed in the coating. The stress behavior as a function of temperature is discussed with the support of finite element modeling by introducing a bi-linear plasticity model to calculate strain relationships which is in agreement with the synchrotron measurements.