Shu, Yi; Galles, Daniel; Tertuliano, Ottman A.; Mcwilliams, Brandon A.; Yang, Nancy; Cai, Wei; Lew, Adrian J.
The study of microstructure evolution in additive manufacturing of metals would be aided by knowing the thermal history. Since temperature measurements beneath the surface are difficult, estimates are obtained from computational thermo-mechanical models calibrated against traces left in the sample revealed after etching, such as the trace of the melt pool boundary. Here we examine the question of how reliable thermal histories computed from a model that reproduces the melt pool trace are. To this end, we perform experiments in which one of two different laser beams moves with constant velocity and power over a substrate of 17-4PH SS or Ti-6Al-4V, with low enough power to avoid generating a keyhole. We find that thermal histories appear to be reliably computed provided that (a) the power density distribution of the laser beam over the substrate is well characterized, and (b) convective heat transport effects are accounted for. Poor control of the laser beam leads to potentially multiple three-dimensional melt pool shapes compatible with the melt pool trace, and therefore to multiple potential thermal histories. Ignoring convective effects leads to results that are inconsistent with experiments, even for the mild melt pools here.
The localized corrosion of laser surface melted (LSM) 316L stainless steel is investigated by a combination of potentiodynamic anodic polarization in 0.1 M HCl and microscopic investigation of the initiation and propagation of localized corrosion. The pitting potential of LSM 316L is significantly lower than the pitting potential of wrought 316L. The LSM microstructure is highly banded as a consequence of the high laser power density and high linear energy density. The bands are composed of zones of changing modes of solidification, cycling between very narrow regions of primary austenite solidification and very wide regions of primary ferrite solidification. Pits initiate in the outer edge of each band where the mode of solidification is primary austenite plane front solidification and primary austenite cellular solidification. The primary austenite regions have low chromium concentration (and possibly low molybdenum concentration), which explains their susceptibility to pitting corrosion. The ferrite is enriched in chromium, which explains the absence of pitting in the primary ferrite regions. The presence of the low chromium regions of primary austenite solidification explains the lower pitting resistance of LSM 316L relative to wrought 316L. The influence of banding on localized corrosion is applicable to other rapidly solidified processes such as additive manufacturing.
The microstructures of 316 L stainless steel created by rapid solidification are investigated by comparing the similar microstructures of individual hatches of directed energy deposition additive manufacturing (DED-AM) and those of single, laser surface-melted tracks formed on a solid plate. High recoil pressure, which is exponentially dependent on the laser beam power density, induces convection of the melt pool, which causes formation of microstructural bands in the as-solidified microstructure. The microstructural bands are associated with changes in the chromium concentration and are a significant component of the inhomogeneous microstructure of DED-AM.
POur experiments indicated that upon a post-processing anneal, an additively manufactured 316L stainless steel exhibits cubic grains rather than the conventional equiaxed grains. Here, we have used kinetic Monte Carlo simulations to explore the origin of these cubic grains. First, we implemented a new kinetic Monte Carlo model in parallel code SPPARKS to simulate grain growth and recrystallization under a residual energy distribution. Our model incorporates physical properties and real-time, as opposed to generic properties and relative time. We further validated that our SPPARKS simulations reproduced the expected kinetic behavior of single-grain evolution. We then used the validated approach to simulate the anneal of an additively manufactured material under the same conditions used in our experiments. We found that the cubic grains can origin from a periodically varying residual energy that may be present in additively manufactured materials.
To identify the critical issues that affect the evolution of microstructure during additive manufacturing, we investigated the influence of process parameters on the evolution of the dimensional and surface quality, microstructure, internal defects, and mechanical properties in 316L stainless steel (SS) components fabricated using laser engineered net shaping (LENS®), a directed energy deposition (DED) additive manufacturing (AM) technique. The results show that the accumulation of un-melted powder particles on the side walls of deposited sections can be avoided by selecting a laser under-focused condition. Moreover, we report that the variation of melt pool width is more sensitive to laser power than to the depth of the melt pool. The formation of a so-called “hierarchical” microstructure with cellular morphology is attributable to a combination of layer deposition and rapid solidification, which are characteristics of AM. Finally, we discuss microstructure evolution and defect formation, particularly the formation of multiple interfaces and the presence of un-melted powder particles and pores, in light of the dynamic convective fluid flow and rapid solidification that occur in the melt pool. X-ray computed tomography (X-CT) was used to precisely map the spatial distribution of pores in the DED components. The evolution of microstructure during DED is discussed in the context of related thermal phenomena in an effort to provide fundamental insight into the mechanisms that govern defect formation.
Metal hydride films have been observed to crack during production and use, prompting mechanical property studies of scandium deuteride films. The following focuses on elastic modulus, fracture, and size effects observed in the system for future film mechanical behavior modeling efforts. Scandium deuteride films were produced through the deuterium charging of electron beam evaporated scandium films using X-ray diffraction, scanning Auger microscopy, and electron backscatter diffraction to monitor changes in the films before and after charging. Scanning electron microscopy, nanoindentation, and focused ion beam machined micropillar compression tests were used for mechanical characterization of the scandium deuteride films. The micropillars showed a size effect for flow stress, indicating that film thickness is a relevant tuning parameter for film performance, and that fracture was controlled by the presence of grain boundaries. Elastic modulus was determined by both micropillar compression and nanoindentation to be approximately 150 GPa, Fracture studies of bulk film channel cracking as well as compression induced cracks in some of the pillars yielded a fracture toughness around 1.0 MPa-m1/2. Preliminary Weibull distributions of fracture in the micropillars are provided. Despite this relatively low value of fracture toughness, scandium deuteride micropillars can undergo a large degree of plasticity in small volumes and can harden to some degree, demonstrating the ductile and brittle nature of this material
We investigate the process-structure-property relationships for 316L stainless steel prototyping utilizing 3-D laser engineered net shaping (LENS), a commercial direct energy deposition additive manufacturing process. The study concluded that the resultant physical metallurgy of 3-D LENS 316L prototypes is dictated by the interactive metallurgical reactions, during instantaneous powder feeding/melting, molten metal flow and liquid metal solidification. The study also showed 3-D LENS manufacturing is capable of building high strength and ductile 316L prototypes due to its fine cellular spacing from fast solidification cooling, and the well-fused epitaxial interfaces at metal flow trails and interpass boundaries. However, without further LENS process control and optimization, the deposits are vulnerable to localized hardness variation attributed to heterogeneous microstructure, i.e., the interpass heat-affected zone (HAZ) from repetitive thermal heating during successive layer depositions. Most significantly, the current deposits exhibit anisotropic tensile behavior, i.e., lower strain and/or premature interpass delamination parallel to build direction (axial). This anisotropic behavior is attributed to the presence of interpass HAZ, which coexists with flying feedstock inclusions and porosity from incomplete molten metal fusion. The current observations and findings contribute to the scientific basis for future process control and optimization necessary for material property control and defect mitigation.
This work studies the microstructural evolution of nanocrystalline (<1 µm) barium titanate (BaTiO3), and presents high pressure in field-assisted sintering (FAST) as a robust methodology to obtain >100 nm BaTiO3 compacts. Using FAST, two commercial ~50 nm powders were consolidated into compacts of varying densities and grain sizes. Microstructural inhomogeneities were investigated for each case, and an interpretation is developed using a modified Monte Carlo Potts (MCP) simulation. Two recurrent microstructural inhomogeneities are highlighted, heterogeneous grain growth and low-density regions, both ubiqutously present in all samples to varying degrees. In the worst cases, HGG presents an area coverage of 52%. Because HGG is sporadic but homogenous throughout a sample, the catalyst (e.g., the local segregation of species) must be, correspondingly, distributed in a homogenous manner. MCP demonstrates that in such a case, a large distance between nucleating abnormal grains is required—otherwise abnormal grains prematurely impinge on each other, and their size is not distinguishable from that of normal grains. Compacts sintered with a pressure of 300 MPa and temperatures of 900 °C, were 99.5% dense and had a grain size of 90±24 nm. These are unprecedented results for commercial BaTiO3 powders or any starting powder of 50 nm particle size—other authors have used 16 nm lab-produced powder to obtain similar results.
Directed energy deposition (DED) is a type of additive manufacturing (AM) process; Laser Engineered Net Shaping (LENS) is a commercial DED process. We are developing LENS technology for printing 316L stainless steel components for structural applications. It is widely known that material properties of AM components are process dependent, attributed to different molten metal incorporation and thermal transport mechanisms. This investigation focuses on process-structure-property relationships for LENS deposits for enabling the process development and optimization to control material property. We observed interactions among powder melting, directional molten metal flow, and the molten metal solidification. The resultant LENS induced microstructure found to be dictated by the process-related characteristics, i.e., interpass boundaries from multi-layer deposition, molten metal flow lines, and solidification dendrite cells. Each characteristic bears the signature of the unique localized thermal history during deposition. Correlation observed between localized thermal transport, resultant microstructure, and its subsequent impact on the mechanical behavior of the current 316L is discussed. We also discuss how the structures of interpass boundaries are susceptible to localized recrystallization, grain growth and/or defect formation, and therefore, heterogeneous mechanical properties due to the adverse presence of unmelted powder inclusions.
Palladium and its alloys are model systems for studying the solid-state storage of hydrogen. Mechanical milling is commonly used to process complex powder systems for solid-state hydrogen storage; however, milling can also be used to evolve nanostructured powder to modify hydrogen sorption characteristics. In the present study, cryomilling (mechanical attrition milling in a cryogenic liquid) is used to produce nanostructured palladium-rhodium alloy powder. Characterization of the cryomilled Pd-10Rh using electron microscopy, X-ray diffraction and surface area analysis reveal that (i) particle morphology evolves from spherical to flattened disk-like particles; while (ii) crystallite size decreases from several microns to less than 100 nm; and (iii) dislocation density increases with increased cryomilling time. Hydrogen absorption and desorption isotherms as well as the time scales for absorption were measured for cryomilled Pd-10Rh, and correlated with observed microstructural changes induced by the cryomilling process. In short, as the microstructure of the Pd-10Rh alloy is refined by cryomilling: (i) the maximum hydrogen concentration in the α-phase increases, (ii) the pressure plateau becomes flatter and (iii) the equilibrium hydrogen capacity increases at pressure of 101.3 kPa. Additionally, the rate of hydrogen absorption was reduced by an order of magnitude compared to non-cryomilled (atomized) powder.
Thermoelectric (TE) generators have very important applications, such as emerging automotive waste heat recovery and cooling applications. However, reliable transport properties characterization techniques are needed in order to scale-up module production and thermoelectric generator design DOE round-robin testing found that literature values for figure of merit (ZT) are sometimes not reproducible in part for the lack of standardization of transport properties measurements. In Sandia National Laboratories (SNL), we have been optimizing transport properties measurements techniques of TE materials and modules. We have been using commercial and custom-built instruments to analyze the perfomance of TE materials and modules We developed a reliable procedure to measure thermal conductivity, seebeck coefficient and resistivity of TE materials to calculate the ZT as function of temperature. We use NIST standards to validate our procedures and measure multiple samples of each specific material to establish consistency. Using these developed thermoelectric capabilities, we studied transport properties of BizTe, based alloys diermal aged up to 2 years. Parallel with analytical and microscopy studies, we correlated transport properties changes with chemical changes. Also, we have developed a resistance mApplng setup to measure the contact resistance of Au contacts on TE materials and TE modules as a whole in a non-destnictive way. The development of novel but reliable characterization techniques has been fundamental to better understand TE materials as fimction of aging hme, temperature and environmental conditions.
Thermoelectric (TE) generators have very important applications, such as emerging automotive waste heat recovery and cooling applications. However, reliable transport properties characterization techniques are needed in order to scale-up module production and thermoelectric generator design DOE round-robin testing found that literature values for figure of merit (ZT) are sometimes not reproducible in part for the lack of standardization of transport properties measurements. In Sandia National Laboratories (SNL), we have been optimizing transport properties measurements techniques of TE materials and modules. We have been using commercial and custom-built instruments to analyze the perfomance of TE materials and modules We developed a reliable procedure to measure thermal conductivity, seebeck coefficient and resistivity of TE materials to calculate the ZT as function of temperature. We use NIST standards to validate our procedures and measure multiple samples of each specific material to establish consistency. Using these developed thermoelectric capabilities, we studied transport properties of BizTe, based alloys diermal aged up to 2 years. Parallel with analytical and microscopy studies, we correlated transport properties changes with chemical changes. Also, we have developed a resistance mApplng setup to measure the contact resistance of Au contacts on TE materials and TE modules as a whole in a non-destnictive way. The development of novel but reliable characterization techniques has been fundamental to better understand TE materials as fimction of aging hme, temperature and environmental conditions.
Pd and Pd alloys are candidate material systems for Tr or H storage. We have actively engaged in material synthesis and studied the material science of hydrogen storage for Pd-Rh alloys. In collaboration with UC Davis, we successfully developed/optimized a supersonic gas atomization system, including its processing parameters, for Pd-Rh-based alloy powders. This optimized system and processing enable us to produce {le} 50-{mu}m powders with suitable metallurgical properties for H-storage R&D. In addition, we studied hydrogen absorption-desorption pressure-composition-temperature (PCT) behavior using these gas-atomized Pd-Rh alloy powders. The study shows that the pressure-composition-temperature (PCT) behavior of Pd-Rh alloys is strongly influenced by its metallurgy. The plateau pressure, slope, and H/metal capacity are highly dependent on alloy composition and its chemical distribution. For the gas-atomized Pd-10 wt% Rh, the absorption plateau pressure is relatively high and consistent. However, the absorption-desorption PCT exhibits a significant hysteresis loop that is not seen from the 30-nm nanopowders produced by chemical precipitation. In addition, we observed that the presence of hydrogen introduces strong lattice strain, plastic deformation, and dislocation networking that lead to material hardening, lattice distortions, and volume expansion. The above observations suggest that the H-induced dislocation networking is responsible for the hysteresis loop seen in the current atomized Pd-10 wt% Rh powders. This conclusion is consistent with the hypothesis suggested by Flanagan and others (Ref 1) that plastic deformation or dislocations control the hysteresis loop.
We are developing a low-emissivity thermal management coating system to minimize radiative heat losses under a high-vacuum environment. Good adhesion, low outgassing, and good thermal stability of the coating material are essential elements for a long-life, reliable thermal management device. The system of electroplated Au coating on the adhesion-enhancing Wood's Ni strike and 304L substrate was selected due to its low emissivity and low surface chemical reactivity. The physical and chemical properties, interface bonding, thermal aging, and compatibility of the above Au/Ni/304L system were examined extensively. The study shows that the as-plated electroplated Au and Ni samples contain submicron columnar grains, stringers of nanopores, and/or H{sub 2} gas bubbles, as expected. The grain structure of Au and Ni are thermally stable up to 250 C for 63 days. The interface bonding is strong, which can be attributed to good mechanical locking among the Au, the 304L, and the porous Ni strike. However, thermal instability of the nanopore structure (i.e., pore coalescence and coarsening due to vacancy and/or entrapped gaseous phase diffusion) and Ni diffusion were observed. In addition, the study also found that prebaking 304L in the furnace at {ge} 1 x 10{sup -4} Torr promotes surface Cr-oxides on the 304L surface, which reduces the effectiveness of the intended H-removal. The extent of the pore coalescence and coarsening and their effect on the long-term system integrity and outgassing are yet to be understood. Mitigating system outgassing and improving Au adhesion require a further understanding of the process-structure-system performance relationships within the electroplated Au/Ni/304L system.
This study investigates a pathway to nanoporous structures created by hydrogen and helium implantation in aluminum. Previous experiments for fusion applications have indicated that hydrogen and helium ion implantations are capable of producing bicontinuous nanoporous structures in a variety of metals. This study focuses specifically on implantations of hydrogen and helium ions at 25 keV in aluminum. The hydrogen and helium systems result in remarkably different nanostructures of aluminum at the surface. Scanning electron microscopy, focused ion beam, and transmission electron microscopy show that both implantations result in porosity that persists approximately 200 nm deep. However, hydrogen implantations tend to produce larger and more irregular voids that preferentially reside at defects. Implantations of helium at a fluence of 10{sup 18} cm{sup -2} produce much smaller porosity on the order of 10 nm that is regular and creates a bicontinuous structure in the porous region. The primary difference driving the formation of the contrasting structures is likely the relatively high mobility of hydrogen and the ability of hydrogen to form alanes that are capable of desorbing and etching Al (111) faces.
This study investigates a pathway to nanoporous structures created by hydrogen implantation in aluminum. Previous experiments for fusion applications have indicated that hydrogen and helium ion implantations are capable of producing bicontinuous nanoporous structures in a variety of metals. This study focuses specifically on hydrogen and helium implantations of aluminum, including complementary experimental results and computational modeling of this system. Experimental results show the evolution of the surface morphology as the hydrogen ion fluence increases from 10{sup 17} cm{sup -2} to 10{sup 18} cm{sup -2}. Implantations of helium at a fluence of 10{sup 18} cm{sup -2} produce porosity on the order of 10 nm. Computational modeling demonstrates the formation of alanes, their desorption, and the resulting etching of aluminum surfaces that likely drives the nanostructures that form in the presence of hydrogen.
Bi-Te-based thermoelectric (TE) alloys are excellent candidates for power generation modules. We are interested in reliable TE modules for long-term use at or below 200 C. It is known that the metallurgical characteristics of TE materials and of interconnect components affect the performance of TE modules. Thus, we have conducted an extensive scientific investigation of several commercial TE modules to determine whether they meet our technical requirements. Our main focus is on the metallurgy and thermal stability of (Bi,Sb){sup 2}(Te,Se){sup 3} TE compounds and of other materials used in TE modules in the temperature range between 25 C and 200 C. Our study confirms the material suite used in the construction of TE modules. The module consists of three major components: AlN cover plates; electrical interconnects; and the TE legs, P-doped (Bi{sub 8}Sb{sub 32})(Te{sub 60}) and N-doped (Bi{sub 37}Sb{sub 3})(Te{sub 56}Se{sub 4}). The interconnect assembly contains Sn (Sb {approx} 1wt%) solder, sandwiched between Cu conductor with Ni diffusion barriers on the outside. Potential failure modes of the TE modules in this temperature range were discovered and analyzed. The results show that the metallurgical characteristics of the alloys used in the P and N legs are stable up to 200 C. However, whole TE modules are thermally unstable at temperatures above 160 C, lower than the nominal melting point of the solder suggested by the manufacture. Two failure modes were observed when they were heated above 160 C: solder melting and flowing out of the interconnect assembly; and solder reacting with the TE leg, causing dimensional swelling of the TE legs. The reaction of the solder with the TE leg occurs as the lack of a nickel diffusion barrier on the side of the TE leg where the displaced solder and/or the preexisting solder beads is directly contact the TE material. This study concludes that the present TE modules are not suitable for long-term use at temperatures above 160 C due to the reactivity between the Sn-solder and the (Bi,Sb){sup 2}(Te,Se){sup 3} TE alloys. In order to deploy a reliable TE power generator for use at or below 200 C, alternate interconnect materials must be used and/or a modified module fabrication technique must be developed.
The mechanical properties of some materials (Cu, Ni, Ag, etc.) have been shown to develop strong dependence on the geometric dimensions, resulting in a size effect. Several theories have been proposed to model size effects, but have been based on very few experiments conducted at appropriate scales. Some experimental results implied that size effects are caused by increasing strain gradients and have been used to confirm many strain gradient theories. On the other hand, some recent experiments show that a size effect exists in the absence of strain gradients. This report describes a brief analytical and experimental study trying to clarify the material and experimental issues surrounding the most influential size-effect experiments by Fleck et al (1994). This effort is to understand size effects intended to further develop predictive models.
Electrical resistance anomalies noted in EPDM gaskets have been attributed to zinc-enriched surface sublayers, about 10-{micro}m thick, in the sulfur cured rubber material. Gasket over-compression provided the necessary connector pin contact and was also found to cause surprising morphological changes on the gasket surfaces. These included distributions of zinc oxide whiskers in high pressure gasket areas and cone-shaped features rich in zinc, oxygen, and sulfur primarily in low pressure protruding gasket areas. Such whiskers and cones were only found on the pin side of the gaskets in contact with a molded plastic surface and not on the back side in contact with an aluminum surface. The mechanisms by which such features are formed have not yet been defined.
Resist substrates used in the LIGA process must provide high initial bond strength between the substrate and resist, little degradation of the bond strength during x-ray exposure, acceptable undercut rates during development, and a surface enabling good electrodeposition of metals. Additionally, they should produce little fluorescence radiation and give small secondary doses in bright regions of the resist at the substrate interface. To develop a new substrate satisfying all these requirements, we have investigated secondary resist doses due to electrons and fluorescence, resist adhesion before exposure, loss of fine features during extended development, and the nucleation and adhesion of electrodeposits for various substrate materials. The result of these studies is a new anodized aluminum substrate and accompanying methods for resist bonding and electrodeposition. We demonstrate successful use of this substrate through all process steps and establish its capabilities via the fabrication of isolated resist features down to 6 {micro}m, feature aspect ratios up to 280 and electroformed nickel structures at heights of 190 to 1400 {micro}m. The minimum mask absorber thickness required for this new substrate ranges from 7 to 15 {micro}m depending on the resist thickness.
Adhesion is an important factor in controlling properties and performance of thin film devices. It is a critical factor in hybrid microcircuits with multilayer films and dissimilar metal interconnects where diffusion of copper from leads during processing and environmental effects during service can modify the adhesion strength of the gold conductive films. Previous work using gold and gold-copper alloy films to simulate different stages of processing and service showed that copper in solution improved film adhesion. More importantly, it took a combination of stressed overlayers and nanoindentation to trigger interfacial fracture of the gold-copper alloy films. The improvement in performance scaled directly with an increase in film strength. However, during two years air exposure telephone cord buckles formed at the gold-copper alloy film edges, grew slowing across the film surface, and eventually covered the sample. Formation of these buckles shows that a significant degradation in interfacial fracture strength had occurred in these films. We characterized the size and shape of the blisters that formed during nanoindentation of the as-deposited films and in the films following aging. These measurements were then combined with mechanics-based models to determine residual stresses and interfacial fracture energies. This analysis shows that air aging decreased the mode I interfacial fracture energy for the gold-copper alloy film from 3.2 J/m{sup 2} to 1.5 J/m{sup 2}. A similar decrease in fracture energy has been observed for many systems exposed to hydrogen from processing and environmental exposure, including copper films, beryllium films, steels and iron- and nickel-based superalloys. This paper describes the effect of environment on resistance of gold-copper alloy film systems to premature interfacial failure, and by comparison with previous studies shows it can be attributed to hydrogen embrittlement.
An Al{sub 85}Ni{sub 10}La{sub 5} amorphous alloy, produced via gas atomization, was selected to study the mechanisms of nanocrystallization induced by thermal exposure. High resolution transmission electron microscopy results indicated the presence of quenched-in Al nuclei in the amorphous matrix of the atomized powder. However, a eutectic-like reaction, which involved the formation of the Al, Al{sub 11}La{sub 3}, and Al{sub 3}Ni phases, was recorded in the first crystallization event (263 C) during differential scanning calorimetry continuous heating. Isothermal annealing experiments conducted below 263 C revealed that the formation of single fcc-Al phase occurred at 235 C. At higher temperatures, growth of the Al crystals occurred with formation of intermetallic phases, leading to a eutectic-like transformation behavior at 263 C. During the first crystallization stage, nanocrystals were developed in the size range of 5 - 30 nm. During the second crystallization event (283 C), a bimodal size distribution of nanocrystals was formed with the smaller size in the range of around 10 - 30 nm and the larger size around 100 nm. The influence of pre-existing quenched-in Al nuclei on the microstructural evolution in the amorphous Al{sub 85}Ni{sub 10}La{sub 5} alloy is discussed and the effect of the microstructural evolution on the hardening behavior is described in detail.
Twinning is ubiquitous in electroplated metals. Here, we identify and discuss unique aspects of twinning found in electrodeposited Ni-Mn alloys. Previous reports concluded that the twin boundaries effectively refine the grain size, which enhances mechanical strength. Quantitative measurements from transmission electron microscopy (TEM) images show that the relative boundary length in the as-plated microstructure primarily comprises twin interfaces. Detailed TEM characterization reveals a range of length scales associated with twinning beginning with colonies ({approx}1000 nm) down to the width of individual twins, which is typically <50 nm. We also consider the connection between the crystallographic texture of the electrodeposit and the orientation of the twin planes with respect to the plating direction. The Ni-Mn alloy deposits in this work possess a 110-fiber texture. While twinning can occur on {l_brace}111{r_brace} planes either perpendicular or oblique to the plating direction in {l_brace}110{r_brace}-oriented grains, plan-view TEM images show that twins form primarily on those planes parallel to the plating direction. Therefore, grains enclosed by twins and multiply twinned particles are produced. Another important consequence of a high twin density is the formation of large numbers of twin-related junctions. We measure an area density of twin junctions that is comparable to the density of dislocations in a heavily cold-worked metal.
