Σ3 Twin Research Articles

Experimental quantification of mechanically induced boundary migration in nanocrystalline copper films

A new experimental technique is presented that combines in situ straining with transmission electron microscope-based automated crystal orientation mapping to document microstructural evolution with nanoscale resolution at sequential stages of deformation. Orientation maps of freestanding annealed nanocrystalline Cu films have been collected, and the resultant datasets provide direct measures of grain size, shape and orientation as well as local grain boundary character and position at various stages of applied strain. Numerous examples of stress-driven grain boundary and twin boundary migration were recorded and studied. Detailed analysis of the misorientation of mobile and immobile grain boundaries provided clear experimental evidence that a broad range of grain boundaries are susceptible to stress-assisted migration; no general correlation between grain boundary misorientation and mobility was detected. Incoherent Σ3 boundaries were observed to be significantly more mobile than coherent Σ3 twin boundaries. Nevertheless, deformation twins were observed to nucleate and grow from grain boundaries and triple points.

Preferred diffusion paths for copper electromigration by in situ transmission electron microscopy

Ionic transport in the reverse direction of an electric field is caused by momentum transfer from free electrons to metal ions, i.e., electromigration (EM), which is a critical factor leading to copper (Cu) interconnect failure in integrated circuits under extreme operating conditions. We investigated Cu self-diffusion paths under electrical bias using in situ transmission electron microscopy (TEM). An electric current was applied to multigrain Cu lines in the TEM instrument for durations of up to the order of 104s to trace EM-induced Cu movement around voids and hillocks. Combining this approach with scanning nanobeam diffraction, we observed that high-angle grain boundaries exposed to the free surface are the most favored paths for Cu EM, rather than a specific orientation within the grain. On hillocks of accumulated Cu atoms, we directly observed grain growth, accompanied by the formation of Σ7 high-mobile and Σ3 twin coincidence site lattice boundaries for effective growth. This study provides insight into the EM mechanism to improve the reliability of metal interconnect design.

Understanding the Effect of Grain Boundary Character on Dynamic Recrystallization in Stainless Steel 316L

Dynamic recrystallization (DRX) occurs during high-temperature deformation in metals and alloys with low to medium stacking fault energies. Previous simulations and experimental research have shown the effect of temperature and grain size on DRX behavior, but not the effect of the grain boundary character distribution. To investigate the effects of the distribution of grain boundary types, experimental testing was performed on stainless steel 316L specimens with different initial special boundary fractions (SBF). This work was completed in conjunction with computer simulations that used a modified Monte Carlo method which allowed for the addition of anisotropic grain boundary energies using orientation data from electron backscatter diffraction (EBSD). The correlation of the experimental and simulation work allows for a better understanding of how the input parameters in the simulations correspond to what occurs experimentally. Results from both simulations and experiments showed that a higher fraction of so-called “special” boundaries (e.g., Σ3 twin boundaries) delayed the onset of recrystallization to larger strains and that it is energetically favorable for nuclei to form on triple junctions without these so-called “special” boundaries.

Microcrack propagation in Cu metal films on a flexible PI substrate during cyclic-bend testing

Cyclic-bend testing of flexible copper clad laminate (FCCL) was conducted to investigate microcrack propagation in electroplated Cu metal films on a flexible polyimide (PI) substrate. During the cyclic-bend testing process, a zigzag pattern of microcracks was developed perpendicular to the loading direction. Electron backscattered diffraction (EBSD) analysis was conducted on the surface planes of un-deformed (i.e. as-received) and deformed Cu metal films to obtain the crystallographic orientation mappings. EBSD analysis revealed that an intergranular type of microcrack propagation was predominant during the cyclic-bend testing. Most of the microcracks were propagated along the high angle grain boundaries (HAGBs) instead of the Σ3 twin boundaries (TBs). EBSD analysis also revealed that microcracks tended to propagate into the HAGBs separating neighboring grains with a high Schmid factor (SF).

Long-range atomic order and grain boundary ensemble in alloys with L12 superstructure

It is found experimentally that in the Ni3Mn and Pd3Fe alloys with superstructure L12, ordered through a two-phase region A1 + L12, an increase in the degree of long range atomic order is accompanied by a reduction in the special and twin boundaries’ angle of deviation from the special boundaries in the CSL model, and by a change in the special boundaries’ spectrum and its average energy. The dependence of the proportion of Σ3 twin boundaries within the spectrum of special boundaries and the average energy of special boundaries on the degree of long range atomic order is determined by the dependence of these parameters on the mean square displacement and probability of antiphase grain boundaries being superimposed on the boundary planes, and on the presence of second phases on special boundaries.

Effect of atomic ordering on the role of grain boundaries in the plastic deformation of Ni3Fe alloy

The structure of dislocations and the defect structure of grain boundaries and their parameters in Ni3Fe alloy with short-range order (SRO) and long–range order (LRO) at different stages of plastic deformation are studied by means of transmission diffraction electron microscopy using thin foils and replicas. It is found that atomic ordering reduces the Σ3 twins plasticizing effect, increases the density of grain boundary defects, slows their annihilation during deformation, and intensifies the microstrains at the triple junctions of grain boundaries.

Grain Boundary Engineering of a Low Stacking Fault Energy Ni-based Superalloy

The effects of thermo-mechanical processing parameters on the resulting microstructure of an experimental Nickel-based superalloy containing 24 wt pct Co were investigated. Hot compression tests were performed at temperatures ranging from 1293 K to 1373 K (1020 to 1100 °C) and strain rates ranging from 0.0005 to 0.1/s. The mechanically deformed samples were also subject to annealing treatments at sub-solvus 1388 K (1115 °C) and super-solvus 1413 K (1140 °C) temperatures. This investigation sought to quantify and subsequently understand the behavior and evolution of both the grain boundary structure and length fraction of Σ3 twin boundaries in the low stacking fault energy superalloy. Over the range of deformation parameters investigated, the corresponding deformation mechanism map revealed that dynamic recrystallization or dynamic recovery was dominant. These conditions largely promoted post-deformation grain refinement and the formation of annealing twins following annealing. Samples deformed at strain rates of 0.0005 and 0.001/s at 1333 K and 1373 K (1060 °C and 1100 °C) exhibited extensive grain boundary sliding/rotation associated with superplastic flow. Upon annealing, deformation conditions that resulted predominately in superplastic flow were found to provide negligible enhancement of twin boundaries and produced little to no post-deformation grain refinement.

Dislocation and twinning mechanisms for dynamic recrystallization of as-cast Mn18Cr18N steel

Hot deformation behavior and microstructure evolution of as-cast Mn18Cr18N austenitic stainless steel were studied by uniaxial compression experiments at temperatures from 1123K to 1473K under strain rates of 0.001–1s−1 up to the true strain of 0.69. The true stress-strain curves, characterized by hardening and subsequent softening, varied with temperatures and strain rates. By multiple linear regressions of the flow stress-strain data, the hyperbolic sine constitutive equation for the steel was developed and the hot deformation activation energy is calculated to be 672KJmol−1, which implies that the recrystallization is sluggish during hot deformation. Furthermore, two dynamic recrystallization mechanisms, dislocation and twinning, were demonstrated. At higher temperatures and lower strain rates, the dynamic recrystallization was controlled by dislocation slip and climbing. The fully recrystallized grains, composed of sub-grains and various dislocation configurations, can be obtained at 1473K and 0.001s−1 up to the true strain of 0.69. However, the dynamic recrystallization was controlled by twinning at higher strain rates and lower temperatures. Most of recrystallized grains are composed of twins, micro-twins and dislocation cells in twins. It suggests that twinning plays an important role during nucleation and progress of DXR by inducing separation of bulged grain boundaries and accelerating the expansion of migratory boundaries. The uniformly refined recrystallized grains with a large number of Σ3 twins were obtained at 1373K and 1s−1 up to the true strain of 0.69.

Engineering the grain boundary network of thin films via ion-irradiation: Towards improved electromigration resistance

Controlling the grain boundary network of small-scale materials—such as coatings and thin films—is an ambitious goal that would ultimately enable the production of components with tailored properties and improved reliability. In this work we present a new technique—which we term ion-induced grain boundary engineering (iGBE)—to engineer the character distribution and connectivity of grain boundaries in gold films in situ, as they are being deposited. iGBE consists of a repeated sequence of ion-induced material removal and material deposition which results in the selection and growth of crystal grains in twinned relationship. This phenomenon yields a substantial increase in the density and connectivity of Σ3 twin boundaries, which have renowned beneficial effects on the material's resistance to intergranular degradation. We confirm the improved reliability of iGBE microstructures by assessing their resistance to electromigration—one of the most common causes of failure in integrated circuit interconnects. We find that, through iGBE, interconnect lifetime increases by three orders of magnitude at standard operating conditions. Since iGBE is material-insensitive and compatible with standard microfabrication technology, we expect it to have significant impact on microelectronics industry.

Measuring Grain Boundary Character Distributions in Ni-Base Alloy 725 Using High-Energy Diffraction Microscopy

We use high-energy X-ray diffraction microscopy (HEDM) to characterize the microstructure of Ni-base alloy 725. HEDM is a non-destructive technique capable of providing three-dimensional reconstructions of grain shapes and orientations in polycrystals. The present analysis yields the grain size distribution in alloy 725 as well as the grain boundary character distribution (GBCD) as a function of lattice misorientation and boundary plane normal orientation. We find that the GBCD of Ni-base alloy 725 is similar to that previously determined in pure Ni and other fcc-base metals. We find an elevated density of Σ9 and Σ3 grain boundaries. We also observe a preponderance of grain boundaries along low-index planes, with those along (1 1 1) planes being the most common, even after Σ3 twins have been excluded from the analysis.

Crack initiation sensitivity of wrought direct aged alloy 718 in the very high cycle fatigue regime: the role of non-metallic inclusions

Fatigue crack initiation in the direct aged version of the nickel-based superalloy Inconel 718 has been investigated at room temperature in the low stress/very high cycle regime via ultrasonic fatigue testing. Three different microstructures have been examined at the same strain amplitude in order to understand the influence of non-metallic inclusions (NMIs), i.e. carbides, carbonitrides and nitrides, and Σ3 twin boundary density on lifetime and failure mode. A slight refinement in grain structure and a higher Σ3 twin boundary density is associated with substantial reductions in lifetime. Decreasing Σ3 twin boundary density for fine grain microstructures results in a change in crack initiation mechanism from strain localization within grains at the high end of the grain size distribution to cracking of NMIs. To study the early stages of crack initiation and growth, specimens with pre-cracked NMIs were also tested in order to examine the role of the surrounding grain structure. Pre-cracked NMIs mainly result in macroscopic failure initiation at NMIs independent of the wrought microstructure. However, pre-loading specimens within the plastic domain highlighted the competition in crack initiation mode between cracked-NMIs and favorably oriented twin boundaries. Crack arrest from most of the pre-cracked NMIs demonstrates that surrounding grain structure (grain orientation, local plasticity and roughness in the vicinity of crack tip due to pre-straining) play a key role in the fatigue life of components stressed in the nominal elastic regime.

Formation mechanism and properties of twinned structures in (111) seeded directionally solidified solar grade silicon

The growth structure of photovoltaic multicrystalline silicon formed by directional solidification presents a high fraction of Σ3 and higher order twins. Previous studies proposed that these complex structures are formed by a succession of 2D nucleation events of Σ3 twins on {111} growth facets at the triple line formed by their intersection with the crucible wall, another crystal, or the surface. In this work, we report the reproducible formation of multiple twinned domains inside solar grade Si single crystals grown by directional solidification above a (111) seed. These domains start on a Σ3 twin nucleated inside the crystal bulk, and systematically develop into similar twinned structures characterized by a ternary arrangement of grains in Σ3, Σ9, and Σ27 relationship. The mechanism of formation of the initial twin nucleus is discussed, and a scenario is proposed for the processes of subsequent multiple twinning. The growth competition between twin grains is shown to promote the appearance of incoherent twin boundaries, and dislocations near grain boundaries and in the twin grains themselves. The electrical activity of Σ-boundaries is measured, and the correlation between the structure of the defects and the resulting detrimental electrical activity is then discussed.

Grain-boundary character distribution and correlations with electrical and optoelectronic properties of CuInSe2 thin films

Thin-film solar cells based on polycrystalline Cu(In,Ga)Se2 absorbers exhibit record conversion efficiencies of up to 22.6%. There is still a lack of a quantitative connection between the grain-boundary character distribution (GBCD) and the corresponding electrical and optoelectronic properties. The present work uses microstructural data from a CuInSe2 thin film acquired by electron backscatter diffraction (EBSD) to evaluate the GBCD. The most prominent features of the GBCD of CuInSe2 are Σ3 twin boundaries and the Σ9 and Σ27a symmetric tilt grain boundaries. Moreover, combining EBSD with electron-beam-induced current and cathodoluminescence (measurements on the same identical area) on a CuInSe2/Mo/glass stack provide the means to relate the grain-boundary character with the corresponding electrical and optoelectronic signals across the grain boundary. In part, determining this relationship is accomplished by means of correlation analysis using measurement data from more than 100 grain boundaries. However, the crystallographic, electrical and optoelectronic data showed no strong correlations, which is attributed to atomic reconstruction found in atomic planes adjacent to planar defects in polycrystalline CuInSe2 thin films and corresponding reductions of excess charge densities at these defects.

Σ3 twin boundaries and texture in FCC solid solutions and alloys with L12 superstructure

Crystallographic textures in solid solutions (Cu–Al, Cu–Mn) with face-centered cubic lattice, and in alloys (Ni3Mn, Pd3Fe) with L12 superstructure, are investigated by means of scanning electron microscopy with back-scattered electron diffraction. It is found that an increase in the portion of S3 twin boundaries in a special type of boundary spectrum is accompanied by a strengthening of texture.

Correlation of the crystal orientation and electrical properties of silicon thin films on glass crystallized by line focus diode laser

In this work, crystallographic orientation of polycrystalline silicon films on glass formed by continuous wave diode laser crystallization was studied. Most of the grain boundaries were coincidence lattice Σ3 twin boundaries and other types of boundaries such as, Σ6, Σ9, and Σ21 were also frequently observed. The highest photoluminescence signal and mobility were observed for a grain with (100) orientation in the normal direction. X-ray diffraction results showed the highest occupancies between 41 and 70% along the (110) orientation. However, the highest occupancies changed to (100) orientation when a 100nm thick SiOx capping layer was applied. Suns-Voc measurement and photoluminescence showed that higher solar cell performance is obtained from the cell crystallized with the capping layer, which is suspected from increased occupancies of (100) orientation.

Formation of Nanotwin Networks during High-Temperature Crystallization of Amorphous Germanium.

Germanium is an extremely important material used for numerous functional applications in many fields of nanotechnology. In this paper, we study the crystallization of amorphous Ge using atomistic simulations of critical nano-metric nuclei at high temperatures. We find that crystallization occurs by the recurrent transfer of atoms via a diffusive process from the amorphous phase into suitably-oriented crystalline layers. We accompany our simulations with a comprehensive thermodynamic and kinetic analysis of the growth process, which explains the energy balance and the interfacial growth velocities governing grain growth. For the 〈111〉 crystallographic orientation, we find a degenerate atomic rearrangement process, with two zero-energy modes corresponding to a perfect crystalline structure and the formation of a Σ3 twin boundary. Continued growth in this direction results in the development a twin network, in contrast with all other growth orientations, where the crystal grows defect-free. This particular mechanism of crystallization from amorphous phases is also observed during solid-phase epitaxial growth of 〈111〉 semiconductor crystals, where growth is restrained to one dimension. We calculate the equivalent X-ray diffraction pattern of the obtained nanotwin networks, providing grounds for experimental validation.

Twin boundary characters established during dynamic recrystallization in a nickel alloy

For the purpose of providing fundamentals for grain boundary engineering design for high-temperature alloys, twin boundary characters are studied quantitatively in a nickel alloy during DRX to improve the understanding of twin boundary evolution during hot deformation. The nickel alloy samples were hot compressed at temperatures of 1120–1180°C and strain rates of 0.1s−1 and 1s−1 to a fixed true strain of 1.1. Refined equiaxed grain structure is obtained with abundant twin boundaries. Most of the twin boundaries form inside the grains, being highly coherent and showing rather limited mutual interaction. An inversely proportional relationship is found between Σ3 twin boundary length density (BLDΣ3) and DRX grain size (DDRX). An analytical model is derived here, in good agreement with current experimental results, indicating that the stored strain energy difference across grain boundary is the main driving force for grain boundary migration and determines the annealing twin formation during DRX. Σ3 twin boundary length density (BLFΣ3) developed in DRX was found varying within a small range of 44%–48%, which is shown to result from the inverse proportionality between grain boundary length density (BLDGB) and DDRX as well as the inverse proportionality between BLDΣ3 and DDRX.

Mechanics of fatigue crack initiation in submicron-thick freestanding copper films

The mechanics of fatigue crack initiation in roughly 500-nm-thick freestanding copper (Cu) films were investigated by using single-side-edge-notched specimens and elastic finite element method (FEM) analyses. By applying cyclic loading at a stress ratio R=0, an intrusion/extrusion was formed near a notch root, and a fatigue crack then initiated at the intrusion/extrusion, which penetrated the film in the thickness direction on a slip plane parallel to a Σ3 twin boundary. Local stress distributions were evaluated by three-dimensional FEM analyses, taking account of the individual grain shape and crystal orientation around the fatigue crack initiation sites. The results revealed that a fatigue crack was initiated on slip systems where (i) the slip deformation penetrated the film in the thickness direction without being blocked by grain boundaries or twin boundaries, and (ii) a high resolved shear stress occurred under the conditions in (i). The number of cycles to fatigue crack initiation increased as the intensity of the resolved shear stress field at the fatigue crack initiation site decreased. The resolved shear stress required for fatigue crack initiation in the Cu films is roughly one order of magnitude higher than that in a bicrystal or single-crystal bulk Cu of 30–35MPa.

Microstructure and microhardness of OFHC copper processed by high-pressure torsion

An ultra-high purity oxygen free high conductivity (OFHC) Cu was investigated to determine the evolution of microstructure and microhardness during processing by high-pressure torsion (HPT). Disks were processed at ambient temperature, the microstructures were observed at the center, mid-radius and near-edge positions and the Vickers microhardness was recorded along radial directions. At low strains, Σ3 twin boundaries are formed due to dynamic recrystallization before microstructural refinement and ultimately a stabilized ultrafine grain structure is formed in the near-edge position with an average grain size of ~280nm after 10 turns. Measurements show the microhardness initially increases to ~150Hv at an equivalent strain of ~2, then falls to about ~80Hv during dynamic recrystallization up to a strain of ~8 and thereafter increases again to a saturated value of ~150Hv at strains above ~22. The delay in microstructure and microhardness homogeneity by dynamic recrystallization is attributed to the high purity of Cu that enhances dislocation mobility and causes dynamic softening during the early stages of straining.

Effect of atomic displacement on the parameters of the grain boundary ensemble in nickel-based alloys with L12 superstructure

The effect complex stacking fault energy and mean-square atomic displacement have on the parameters of the grain boundary ensemble in nickel-based alloys with L12 superstructure is established experimentally. The higher the complex stacking fault energy, the lower the average number of special grain boundaries per parent grain. The lower the mean-square atomic displacement, the smaller the proportion of the Σ3 twins in the special grain boundary spectrum.