Spatially Resolved X-ray Diffraction Research Articles

Orientation of a Dispersion of Kaolinite Flowing in a Jet

Orientational alignment in a dilute dispersion of kaolinite particles has been investigated in a flow pattern that combines both shear and elongational stress, namely flow at a jet created by a 2 mm diameter nozzle inserted in a 6 mm diameter pipe. Spatially-resolved X-ray diffraction with synchrotron radiation permits detailed maps of the alignment to be deduced and compared with fluid mechanics calculations of the flow. The angular distribution of diffracted intensity from a given position in the pipe provides information about the orientation distribution of the particles. This is quantified and presented in terms of order parameters. The cone-shaped nozzle provides a jet of liquid giving a high degree of alignment of the particles that is uniform along lines across the conical section and constant in the small straight-sided region at the exit of the nozzle. The vortex motion that arises from the flow with a modest Reynolds number could be determined as well as the tendency for some particles to align with their large faces perpendicular to the overall flow direction at the flat surface of the nozzle outlet.

Spatially resolved x-ray diffraction study of GaSb layers grown laterally on SiO2-masked GaAs substrates

In this work spatially resolved x-ray diffraction (SRXRD) is used to analyze strain in GaSb layers grown by epitaxial lateral overgrowth (ELO) on SiO2-masked (001) GaAs substrates. We show that this heteroepitaxial structure contains local mosaicity in the wing area that cannot be detected by selective etching. While the standard x-ray diffraction measurements only suggest the presence of grain structure of the ELO layer, SRXRD allows examining the microscopic strain distribution in the sample. In particular, size of microblocks and their relative misorientation are determined.

Spatially Resolved X-ray Diffraction Technique for Crystallographic Quality Inspection of Semiconductor Microstructures

There is an increasing demand for techniques that allow detection and visualization of crystalline lattice microdefects. From the many techniques available the X-ray Rocking Curve Imaging (RCI), based on synchrotron X-ray diffraction, has gained much attention recently as a method of wafer defect analysis [1]. However, for most crystal growers laboratory techniques are preferred. Therefore, instead of applying RCI we have developed a microimaging technique based on spatially resolved X-ray diffraction (SRXRD) that makes use of conventional high resolution X-ray diffractometer. Briefly, the size of incident X-ray beam is reduced by a set of slits. Then the sample is moved in small steps while the rest of the system stays fixed. At each sample position X-ray diffraction curve is measured from precisely defined area. Finally, all diffraction curves are collected to construct the X-ray diffraction image of the sample. Both the ω and 2θ/ω scans are performed allowing independent mapping of crystallographic misorientation and lattice parameter distributions across the sample. Spatial resolution offered by the SRXRD technique is smaller than that obtainable with the use of synchrotron radiation based methods. This is due to a limited radiation intensity of conventional X-ray sources. We have checked that in our experimental setup measurable signals can be obtained with the X-ray beam as small as 10/sinθ × 100 μm 2 , where θ is the Bragg angle for the reflection studied. This corresponds to the beam spot size of ~18 × 100 μm 2 for 004 reflections of GaAs and Si. The aim of this report is to present advantages of SRXRD over a standard X-ray diffraction when applied for analysis of crystalline microstructures. First, we focus on SRXRD studies of epitaxial laterally overgrown (ELO) GaAs layers grown by liquid phase epitaxy on SiO2-masked GaAs substrates. ELO layer consists of a few hundreds micrometers wide monocrystalline stripes regularly arranged on a substrate. Since each stripe is strained such samples contain a periodic distribution of strain and/or defects. Thus, they are very suitable to demonstrate potential of the technique. We show that high spatial and angular resolutions of SRXRD allow studying a strong effect of ELO wings tilt towards the mask as well as very fine residual strain caused by dopant concentration inhomogeneity. Direction of the tilt and the distribution of tilt magnitude across width of each wing can be easily determined. In fully overgrown GaAs ELO layers additional strain was observed at a coalescence front where ELO wings grown from adjacent seeds merged. With the use of SRXRD a local structure of the crystal lattice around this coalescence front was studied. In heteroepitaxial GaSb/GaAs ELO layers local mosaicity in the wing area was found. By SRXRD the size of microblocks and their relative misorientation were analyzed. As the final example, we report on strain distribution in thermally oxidized Si wafers. Microscopic curvature of lattice planes confined between two neighboring slip bands was measured allowing its correlation with the dislocation structure. It is noting worthy that all the phenomena presented are difficult to study by standard X-ray diffraction. On the contrary, due to its high spatial resolution the SRXRD technique allows deeper insight into a localized strain fields present in semiconductor microstructures.

X-ray diffraction micro-imaging of strain in laterally overgrown GaAs layers. Part II: analysis of multi-stripe and fully overgrown layers

As a development of our previous analysis of a single GaAs stripe, in this work spatially resolved X-ray diffraction (SRXRD) was applied for micro-imaging of strain in partially and fully overgrown GaAs layers grown by epitaxial lateral overgrowth (ELO) on SiO2-masked GaAs substrates. We show that a standard X-ray diffraction providing information integrated over many stripes leads to overestimation of lattice misorientation in such samples. On the contrary, the SRXRD allows precise measurements of local wing tilts of individual ELO stripes with micrometer-scale spatial resolution. A complex strain field was found in fully overgrown GaAs ELO samples. With the use of the SRXRD technique, the distribution of this strain was measured that allowed reproducing the shape of deformed lattice planes both inside the epitaxial layer as well as in the substrate underneath.

X-ray diffraction micro-imaging of strain in laterally overgrown GaAs layers. Part I: analysis of a single GaAs stripe

Spatially resolved X-ray diffraction (SRXRD) is used for micro-imaging of strain in GaAs:Si layers grown by liquid phase epitaxial lateral overgrowth (ELO) on SiO2-masked GaAs substrates. We show that laterally overgrown parts of the layers (wings) are tilted towards the underlying mask. By SRXRD mapping local wing tilt is easily distinguished from macroscopic sample curvature. The direction of the tilt and distribution of tilt magnitude across the width of each layer can also be readily determined. This allows measuring of the shape of the lattice planes in individual ELO stripes. Downward wing tilt disappears completely when the mask is removed by selective etching. Then residual strain in ELO layers is exposed. In particular, upward tilt is found in free-standing ELO wings. Numerical simulations show that this phenomenon is caused by different concentrations of silicon dopant in vertically and laterally grown parts of the layer.

In-situ phase mapping and direct observations of phase transformations during arc welding of 1045 steel

In-situ spatially resolved X-ray diffraction (SRXRD) experiments were performed during gas tung-sten arc (GTA) welding of AISI 1045 C-Mn steel. Ferrite (α) and austenite (γ) phases were identified and quantified in the weld heat-affected zone (HAZ) from the real time SRXRD data. The results were compiled with weld temperatures calculated using a coupled thermal fluids model to create a phase map of the HAZ. Kinetics of the α → γ transformation during weld heating and the reverse γ → α transformation during weld cooling were extracted from the map. Superheating as high as 250 °C above the A3 temperature was observed for the α → γ phase transformation to reach completion at locations near the fusion zone (FZ) boundary. The SRXRD experiments revealed that the newly created γ phase exists with two distinct lattice parameters, resulting from the inhomogeneous distribution of carbon and manganese in the starting pearlitic/ferritic microstructure. During cooling, the reverse γ → α phase transformation was shown to depend on the HAZ location. In the fine-grained region of the HAZ, the γ → α transformation begins near the A3 temperature and ends near the A1 temperature. In this region, where the cooling rates are below 40 °C/s, the transformation occurs by nucleation and growth of pearlite. In the coarse-grained region of the HAZ, the γ → α transformation requires 200 °C of undercooling for completion. This high degree of undercooling is caused by the large grains coupled with cooling rates in excess of 50 °C/s that result in a bainitic transformation mechanism.

Direct observations of the α → γ transformation at different input powers in the heat-affected zone of 1045 C-Mn steel arc welds observed by spatially resolved X-ray diffraction

Spatially resolved X-ray diffraction (SRXRD) experiments have been performed during gas tungstenarc (GTA) welding of AISI 1045 C-Mn steel at input powers ranging from 1000 to 3750 W. In-situ diffraction patterns taken at discreet locations across the width of the heat-affected zone (HAZ) near the peak of the heating cycle in each weld show regions containing austenite (γ), ferrite and austenite (α+γ), and ferrite (α). Changes in input power have a demonstrated effect on the resulting sizes of these regions. The largest effect is on the γ phase region, which nearly triples in width with increasing input power, while the width of the surrounding two-phase α+γ region remains relatively constant. An analysis of the diffraction patterns obtained across this range of locations allows the formation of austenite from the base-metal microstructure to be monitored. After the completion of the α → γ transformation, a splitting of the austenite peaks is observed at temperatures between approximately 860 °C and 1290 °C. This splitting in the austenite peaks results from the dissolution of cementite laths originally present in the base-metal pearlite, which remain after the completion of the α → γ transformation, and represents the formation of a second more highly alloyed austenite constituent. With increasing temperatures, carbon, originally present in the cementite laths, diffuses from the second newly formed austenite constituent to the original austenite constituent. Eventually, a homogeneous austenitic microstructure is produced at temperatures of approximately 1300 °C and above, depending on the weld input power.

Optimization of the johnson-mehl-avarami equation parameters for α-ferrite to γ-austenite transformation in steel welds using a genetic algorithm

A nonisothermal Johnson-Mehl-Avarami (JMA) equation with optimized JMA parameters is proposed to represent the kinetics of transformation of α-ferrite to γ-austenite during heating of 1005 steel. The procedure used to estimate the JMA parameters involved a combination of numerical heat-transfer and fluid-flow calculations, the JMA equation for nucleation and growth for nonisothermal systems, and a genetic algorithm (GA) based optimization tool that used a limited volume of experimental kinetic data. The experimental data used in the calculations consisted of phase fraction of γ-austenite measured at several different monitoring locations in the heat-affected zone (HAZ) of a gas tungsten arc (GTA) weld in 1005 steel. These data were obtained by an in-situ spatially resolved X-ray diffraction (SRXRD) technique using synchrotron radiation during welding. The thermal cycles necessary for the calculations were determined for each monitoring location from a well-tested three-dimensional heat-transfer and fluid-flow model. A parent centric recombination (PCX) based generalized generation gap (G3) GA was used to obtain the optimized values of the JMA parameters, i.e., the activation energy, pre-exponential factor, and exponent in the nonisothermal JMA equation. The GA based determination of all three JMA equation parameters resulted in better agreement between the calculated and the experimentally determined austenite phase fractions than was previously achieved.

In situ observations of ferrite – austenite transformations in duplex stainless steel weldments using synchrotron radiation

Ferrite (δ)-austenite (γ) transformations in the heat affected zone (HAZ) of a gas tungsten arc weld in 2205 duplex stainless steel are observed in real time using spatially resolved X-ray diffraction (SRXRD) with high intensity synchrotron radiation. A map showing the locations of the δ and γ phases with respect to the calculated weld pool dimensions has been constructed from a series of SRXRD scans. Regions of liquid, completely transformed γ, a combination of partially transformed γ with untransformed δ, and untransformed γ + δ are identified. Analysis of each SRXRD pattern provides a semiquantitative definition of both the δ/γ phase balance and the extent of annealing, which are mapped for the first time with respect to the calculated weld pool size and shape. A combination of these analyses provides a unique real time description of the progression of phase transformations in the HAZ. Results show that during heating, δ and γ both show signs of annealing as temperatures approach 550 ° C. The δ phase then starts to transform to γ as temperatures approach 700 ° C. Although supported by thermodynamic calculations, this δ → γ transformation during heating has not been directly observed until now. Following this reaction, the HAZ microstructure evolves in three different ways. For peak temperatures less than approximately 1100 ° C, δ retransforms, reverting to its original base metal fraction on cooling. When peak temperatures exceed approximately 1375 ° C, the microstructure completely transforms to δ before retransforming to a mixture of δ and γ during weld cooling. For peak temperatures between 1100 and 1375 ° C, γ is only partially transformed during both heating and cooling. Using these real time observations, important kinetic information about the transformations occurring in duplex stainless steels during both non-isothermal heating and cooling of welding can be determined.

Spatially resolved X-ray diffraction mapping of phase transformations in the heat-affected zone of carbon-manganese steel arc welds

Phase transformations that occur in the heat-affected zone (HAZ) of gas tungsten arc welds in AISI 1005 carbon-manganese steel were investigated using spatially resolved X-ray diffraction (SRXRD) at the Stanford Synchrotron Radiation Laboratory. In situ SRXRD experiments were performed to probe the phases present in the HAZ during welding of cylindrical steel bars. These real-time observations of the phases present in the HAZ were used to construct a phase transformation map that identifies five principal phase regions between the liquid weld pool and the unaffected base metal: (1) α-ferrite that is undergoing annealing, recrystallization, and/or grain growth at subcritical temperatures, (2) partially transformed α-ferrite co-existing with γ-austenite at intercritical temperatures, (3) single-phase γ-austenite at austenitizing temperatures, (4) δ-ferrite at temperatures near the liquidus temperature, and (5) back transformed α-ferrite co-existing with residual austenite at subcritical temperatures behind the weld. The SRXRD experimental results were combined with a heat flow model of the weld to investigate transformation kinetics under both positive and negative temperature gradients in the HAZ. Results show that the transformation from ferrite to austenite on heating requires 3 seconds and 158°C of superheat to attain completion under a heating rate of 102°C/s. The reverse transformation from austenite to ferrite on cooling was shown to require 3.3 seconds at a cooling rate of 45 °C/s to transform the majority of the austenite back to ferrite; however, some residual austenite was observed in the microstructure as far as 17 mm behind the weld.

Investigation of Real-Time Microstructure Evolution in Steep Thermal Gradients Using in-Situ Spatially Resolved X-ray Diffraction: A Case Study for Ti Fusion Welds

A recently developed spatially resolved X-ray diffraction (SRXRD) technique utilizing intense synchrotron radiation has been refined to yield phase and microstructural information down to 200 {micro}m in spatial extent in materials subjected to steep thermal gradients during processing. This SRXRD technique has been applied to map completely the phases and their solid-state transformation in the so-called heat-affected zone (HAZ) in titanium fusion welds in situ during the welding process. Detailed profile analysis of the SRXRD patterns revealed four principal microstructural regions at temperature in the vicinity of the HAZ surrounding the liquid weld pool: (i) a completely transformed {beta}-Ti zone 2--3 mm adjacent to the liquid weld pool; (ii) a mixed {alpha} + {beta}-it region surrounding the pure {beta}-Ti zone, (iii) a back-transformed {alpha}-Ti zone on the backside of the HAZ where pure {beta}-Ti once existed at temperature well above the {alpha} {r_arrow} {beta} transformation isotherm, and (iv) a more diffused region outside the HAZ where annealing and recrystallization of the {alpha}-it base metal occur. The high-temperature microstructures so derived corroborate well the expected transformation kinetics in pure titanium, and the observed phase transformation boundaries are in good agreement with those predicted from the transformation isotherms calculated from a simplifiedmore » heat-flow model. Based on a detailed assessment of the SRXRD setup employed, improved experimentations such as a smaller beam spot emitted from third generation synchrotron sources, better mechanical stability (tighter scattering geometry), and use of an area detector would enable more quantitative structural information for future phase dynamics studies exemplified by this work.« less

Spatially resolved X-ray diffraction phase mapping and α → β → α transformation kinetics in the heat-affected zone of commercially pure titanium arc welds

Spatially resolved X-ray diffraction (SRXRD) is used to map the α → β → α phase transformation in the heat-affected zone (HAZ) of commercially pure titanium gas tungsten arc welds. In situ SRXRD experiments were conducted using a 180-µm-diameter X-ray beam at the Stanford Synchrotron Radiation Laboratory (SSRL) (Stanford, CA) to probe the phases present in the HAZ of a 1.9 kW weld moving at 1.1 mm/s. Results of sequential linear X-ray diffraction scans made perpendicular to the weld direction were combined to construct a phase transformation map around the liquid weld pool. This map identifies six HAZ microstructural regions between the liquid weld pool and the base metal: (1) α-Ti that is undergoing annealing and recrystallization; (2) completely recrystallized α-Ti; (3) partially transformed α-Ti, where α-Ti and β-Ti coexist; (4) single-phase β-Ti; (5) back-transformed α-Ti; and (6) recrystallized α-Ti plus back-transformed α-Ti. Although the microstructure consisted predominantly of α-Ti, both prior to and after the weld, the crystallographically textured starting material was altered during welding to produce different α-Ti textures within the resulting HAZ. Based on the travel speed of the weld, the α → β transformation was measured to take 1.83 seconds during heating, while the β → α transformation was measured to take 0.91 seconds during cooling. The α → β transformation was characterized to be dominated by long-range diffusional growth on the leading (heating) side of the weld, while the β → α transformation was characterized to be predominantly massive on the trailing (cooling) side of the weld, with a massive growth rate on the order of 100 µm/s.

In-situ phase mapping and transformation study in fusion welds

Spatially resolved X-ray diffraction (SRXRD) technique has been applied using synchrotron radiation to map the phases present in fusion welds in situ with a sub-millimetre resolution. For titanium, exhibiting an allotropic transformation from a hcp α-phase to a bcc β-phase at ∼922°C, the following results have been obtained for the heat-affected zone (HAZ). (i) Co-existence of both α- and β-Ti phases in the HAZ as derived from the phase concentration profiles. (ii) The width of the HAZ was found to be 3.33±0.33 mm as defined by the existence of the high-temperature bcc phase in this zone. (iii) Peak profile and ex-situ post-weld ESCA analyses revealed additional hcp patterns attributable to two TiOx phases formed in an overlayer during the welding process by oxygen diffusion from the ambient at high temperature. The thickness of this TiOx overlayer varied from 50–85 nm, increasing towards the weld pool. The SRXRD technique provides real-time chemical dynamics and in situ phase mapping data for modelling of kinetics of phase transformation and microstructural evolution in allotropic and other more complex systems, under steep thermal gradients and non-isothermal materials processing conditions.

Analysis of heat-affected zone phase transformations usingin situ spatially resolved x-ray diffraction with synchrotron radiation

Spatially resolved X-ray diffraction (SRXRD) consists of producing a submillimeter size X-ray beam from an intense synchrotron radiation source to perform real-time diffraction measurements on solid materials. This technique was used in this study to investigate the crystal phases surrounding a liquid weld pool in commercial purity titanium and to determine the location of the phase boundary separating the high-temperature body-centered-cubic (bcc) β phase from the low-temperature hexagonalclose-packed (hcp) α phase. The experiments were carried out at the Stanford Synchrotron Radiation Laboratory (SSRL) using a 0.25 × 0.50 mm X-ray probe that could be positioned with 10-µm precision on the surface of a quasistationary gas tungsten arc weld (GTAW). The SRXRD patterns were collected using a position-sensitive photodiode array in a φ-2φ geometry. For this probe size, integration times of 10 s/scan at each location on the specimen were found adequate to produce high signal-to-noise (S/N) ratios and quality diffraction patterns for phase identification, thus allowing real-time diffraction measurements to be made during welding. The SRXRD results showed characteristic hcp, bcc, and liquid diffraction patterns at various points along the sample, starting from the base metal through the heat-affected zone (HAZ) and into the weld pool, respectively. Analyses of the SRXRD data show the coexistence of bcc and hcp phases in the partially transformed (outer) region of the HAZ and single-phase bcc in the fully transformed (inner) region of the HAZ. Postweld metallographic examinations of the HAZ, combined with a conduction-based thermal model of the weld, were correlated with the SRXRD results. Finally, analysis of the diffraction intensities of the hcp and bcc phases was performed on the SRXRD data to provide additional information about the microstructural conditions that may exist in the HAZ at temperature during welding. This work represents the first directin situ mapping of phase boundaries in fusion welds.