Σ3 Grain Research Articles

Combined in situ and EBSD studies of discontinuous precipitation in Al-22 at.%Zn alloy

For the first time, the in-situ observation combined with Electron back scatter diffraction (EBSD) measurements were applied to discontinuous precipitation (DP) in the Al-22 at.% Zn alloy. So far, all the studies were restricted to “frozen” images of grain boundaries (GBs) after certain time of ageing. This did not allow the precise estimation of the incubation period preceding the initiation and growth discontinuous precipitates, as well it was not possible to distinguish still growing cells from those for which the growth was terminated. New approach permitted to determine that a large fraction of GBs does not undergo DP process. This was especially true for low angle GBs with misorientations below 19°. Growth in one direction occurred for a relatively large fraction of GBs. However, no correlation was found for the relationship between misorientation angle and growth rate on one and both sides of the GB as well for incubation period versus growth rate. Only few GBs were characterised with special CSL misorientation and they showed the growth in one direction with an exception of Σ3 grain boundary (no growth). Moreover, there was no evidence that the GBs close to the special Σ misorientations exhibited a very low DP reaction rate.

Exploration of the sliding behavior of a Σ11 grain boundary with precipitates in Ni–Al system using molecular dynamics

Molecular dynamics (MD) was used to gain insights into grain boundary (GB) shear mechanisms in alloys that require GB mobility in a field of coherent precipitates. The area fraction of the Σ11 affected by the γ′ was systematically varied to explore how GB shear mechanisms change with increased number of precipitates. Without precipitates, local atomic shuffling accommodates the Σ11 GB shear; above an area-fraction threshold, GB shear required dislocation emission. In addition to precipitate area fraction, the transition in GB shear mechanisms may also depend on precipitate shape/size, temperature, and GB misorientation. These factors will be investigated in future work.

The effect of Cr on He segregation and diffusion at Σ3(1 1 2) grain boundary in α-Fe

The effect of Cr on He segregation and diffusion properties at Σ3(1 1 2) grain boundary (GB) of α-Fe alloys was investigated using first-principles calculations. The results show that as the increase of Cr-segregated concentration at GB, the grain boundary energy first decreases to the minimum 0.42 J/m2 and then increases to the maximum 0.49 J/m2. As for the effect of Cr on He segregation, the Cr atoms at GB increase effectively the He solution and segregation energies, suggesting that Cr atoms can inhibit He segregation. As for the effect of Cr on He diffusion, Cr can increase or decrease the He migration energy barriers along GB according to the Cr-segregated concentration at GB. It is worth noting that the He migration energy barriers along Cr-segregated GB are still considerably high, compared with He diffusion in Fe bulk. Consequently, the He diffusion along GB is inhabited at Cr-segregated GB in α-Fe alloys.

Chemisorption enhancement of single carbon and oxygen atoms near the grain boundary on Fe surface: ab initio study

The chemisorption of single carbon and oxygen atoms on an iron surface with a Σ3(111) grain boundary has been studied by means of first principles modeling. It is shown that adsorption sites close to the grain boundary have higher adsorbability than any site at clean Fe (100), (110), and (111) surfaces. To reveal the mechanism of chemisorption enhancement, several properties are discussed, such as the rearrangement of iron surface atoms, changes in the electronic densities of states, and the spacial charge density differences caused by adsorbates. Due to the higher movability of atoms on the surface near the grain boundary, the chemical bonding of adsorbate to iron atoms in the vicinity of the grain boundary leads to large displacements of surface atoms. The change of the partial density of states of Fe in the vicinity of adsorption sites induced by such rearrangement suggests that the adsorption properties enhancement of the surface is related to the increase of density of states at Fermi level.

The effect of grain boundaries on instability at the crystal/melt interface during the unidirectional growth of Si

The instability of crystal/melt interfaces including numerous Σ3, small-angle and large-angle grain boundaries during the unidirectional growth of Si was investigated, using an in situ observation system. Planar crystal/melt interfaces including Σ3 or small-angle grain boundaries were found to undergo local morphological transformation at the grain-boundary positions during high-velocity growth. The data also confirmed that the critical growth velocity for the appearance of instability at a crystal/melt interface including grain boundaries is significantly lower than that for a single crystal Si/melt interface. The ambient temperature field at the crystal/melt interface was calculated, taking into account the effective thermal conductivities of grain boundaries and the results show that a negative temperature gradient readily forms in the case that grain boundaries are present.

Correlation among grain boundary character, carbide precipitation and deformation in Alloy 690

ABSTRACTThe correlation among grain boundary character, carbide precipitation and deformation in the grain boundary engineering (GBE) treated Alloy 690 samples with and without pre-deformation aged at 715oC for 15 h was analysed by scanning electron microscopy and electron backscatter diffraction. The fraction of low Σ coincidence site lattice (CSL) grain boundary was enhanced by GBE treatment. The fraction of Σ3 grain boundary decreased, and most of Σ9 and Σ27 grain boundaries disappeared in the deformed GBE samples. After aging treatment, bigger carbide precipitated at coherent Σ3 grain boundary, however, most of plate-like carbide precipitated at incoherent Σ3 grain boundary disappeared in the pre-deformed GBE samples. The larger carbide precipitated on the random grain boundary in the 5% pre-deformed sample, while smaller carbide can be observed in the 15% pre-deformed sample. During the in situ tensile test of the aged GBE samples, grain boundary carbide migrated with the grain boundary migration. The slip bands go across Σ3 grain boundary directly, but cannot go across other grain boundaries. The high density of carbide plate precipitated near incoherent Σ3 and Σ9 grain boundaries can resist the evolution of slip bands. Compared to the Σ3 and Σ9 grain boundaries, Σ27 and random grain boundaries are more easily to form microcrack during deformation. The initiation of grain boundary microcrack not only related to the character of grain boundary but also related to the character of nearby grain boundaries. The phase interface of carbide and matrix is another region to initiate the microcrack.

Designing functional Σ13 grain boundaries at seed junctions for high-quality cast quasi-single crystalline silicon

Dislocation clusters and sub-grain boundaries (Sub-GBs) induced by the misorientation between adjacent seeds are destructive to the quasi-single crystal (QSC) Si ingot quality and the solar cell efficiency. Here, we have designed an artificial Σ13 GB between two adjacent <100>-oriented seeds at the crucible bottom. It is found that the generation of dislocation clusters and sub-GBs from the seed junctions is significantly suppressed owing to the low energy barrier potential of the Σ13 GB. Although some twins could generate from the vertical Σ13 GB, they will not give a bad influence on the ingot quality. The efficiency of solar cells is absolutely high in industrial circles, with an average value of 20.1%. These results pave a new way to the fabrication of high quality QSC-Si ingots for photovoltaic application.

Hydrogen-enhanced decohesion mechanism of the special [formula omitted]5(0 1 2)[1 0 0] grain boundary in Ni with Mo and C solutes

Ni and its alloys are susceptible to hydrogen embrittlement (HE). In this work, we perform a systematic density functional theory (DFT)-based investigation on the hydrogen-enhanced decohesion (HEDE) mechanism of HE for the case of the special Σ5(012) grain boundary (GB) in Ni containing C and Mo impurity atoms. Segregation and co-segregation energy profiles of H along with C and Mo solute elements are investigated in detail and used to analyze the effect of Mo and C solutes on HEDE in Ni within the framework of the Rice-Thomson-Wang theory. We show that H, C, and Mo segregate to the GB in Ni. H demonstrates the GB embrittling effect while C and Mo solutes strengthen the GB in Ni. The results also show that H–Mo and H–C interactions in the bulk and at the GB are very similar and can be neglected in most of cases of co-segregation.

Effect of misorientation angle of grain boundary on the interaction with Σ3 boundary at crystal/melt interface of multicrystalline silicon

Interactions between Σ3 grain boundaries (GBs), small-angle GBs (SAGBs), and general GBs at a silicon crystal/melt interface are studied by in situ observation during directional solidification. The interactions exhibit a dependence on the misorientation angle. SAGBs can propagate through Σ3 GBs, but this behavior transitions into coalescence with Σ3s when the misorientation approaches the limit of a SAGB, i.e. 15°. On the other hand, general GBs show the ability to terminate Σ3 GBs continuously. The present findings suggest that the presence of intrinsic dislocations in GBs plays a role in GB interactions.

A {112}Σ3 grain boundary generated from the decomposition of a Σ9 grain boundary in multicrystalline silicon during directional solidification

The generation of a {112}Σ3 grain boundary (GB) was observed in situ from the decomposition of a Σ9 GB during directional solidification of multicrystalline Si. A faceted groove formed at the junction of the solid/melt interface and the {112}Σ3 GB. This mechanism is different from that for the growth of {111}Σ3 GBs, for which no groove formed at the interface. If the growth rates for the adjacent facets of the groove are the same, the GB can grow in a straight manner along the {112} plane. The present results suggest that kinetics can give rise to high-energy GBs during solidification.

Molecular Dynamics Calculations of Grain Boundary Mobility in CdTe

Molecular dynamics (MD) simulations have been applied to study mobilities of Σ3, Σ7 and Σ11 grain boundaries in CdTe. First, an existing MD approach to drive the motion of grain boundaries in face-centered-cubic and body-centered-cubic crystals was generalized for arbitrary crystals. MD simulations were next performed to calculate grain boundary velocities in CdTe crystals at different temperatures, driving forces, and grain boundary terminations. Here a grain boundary is said to be Te-terminated if its migration encounters sequentially … planes, where “·” and “−” represent short and long spacing respectively. Likewise, a grain boundary is said to be Cd-terminated if its migration encounters sequentially … planes. Grain boundary mobility laws, suitable for engineering time and length scales, were then obtained by fitting the MD results to Arrhenius equation. These studies indicated that the Σ3 grain boundary has significantly lower mobility than the Σ7 and Σ11 grain boundaries. The Σ7 Te-terminated grain boundary has lower mobility than the Σ7 Cd-terminated grain boundary, and that the Σ11 Cd-terminated grain boundary has lower mobility than the Σ11 Te-terminated grain boundary.

Atomistic approaches to cleavage of interfaces

Four different models (corresponding to different loading conditions) of first principles tensile tests are employed to determine cohesion and strength of several interfaces, namely coherent interfaces of two fcc metals (Ni/Ag and Ni/Cu) and symmetrical tilted Σ5(210) grain boundary in fcc nickel (clean as well as sulfur-decorated). The purpose of this study is to compare the selected models of tensile tests and to critically discuss their advantages and limitations. Particular attention is paid to differences in their predictions, their ability to identify the weakest link in the studied system and the supercell-size convergence of the computed data. Selection of an appropriate model can be the crucial point in a computer assisted design of advanced materials with interfaces such as multilayered systems.

Phonon Transmission Across Silicon Grain Boundaries by Atomistic Green's Function Method

Nanostructured materials are of great interest for many applications because of their special properties. Understanding the effect of grain boundaries on phonon transport in polycrystals is important for engineering nanomaterials with desired thermal transport properties. The phonon transport properties of Σ3 grain boundaries in silicon are investigated by employing atomistic Green’s function method. Results show that similar to electron transport, the perfect grain boundary does not significantly reduce the thermal conductance, while defective grain boundaries can dramatically reduce the thermal conductance. This work may be helpful for the understanding of the underlying thermal transport mechanism with grain boundaries and the design of grain boundaries for energy applications.

Determination of minimal energy facet structures in Σ3 and Σ9 grain boundaries: Experiment and simulation

Grain boundary engineering (GBE) in FCC alloys relies on the presence of low-energy, coherent Σ3 boundaries to improve material performance. To make microstructures with a profuse network of Σ3 boundaries, a repetitive cycle of low-level deformation and followed by annealing is commonly employed. In this work, we use a combination of in situ SEM, in situ TEM, and a relaxation theory for grain boundaries to investigate the structural states of grain boundaries in Cu after a cycle or many cycles of deformation and annealing steps. It is revealed that during annealing the orientation relationships and boundary morphology of deformed Σ3 and higher order variants, Σ9 boundaries, change appreciably, from being curved to distinctly, crystallographically faceted. The theoretical analysis identifies the faceting process and the crystallography of the facets as corresponding to the optimal, low-energy structures for the observed orientation relationships. It is, therefore, shown that post-deformation heat treatments used in GBE are recovering the highly deviated and deformed Σ3s boundaries to a low-energy state.

Effect of the grain boundary character distribution on the self-organization of adiabatic shear bands in 1Cr18Ni9Ti austenitic stainless steel

The self-organization of adiabatic shear bands (ASBs) in the steel with a different grain boundary character distribution (GBCD) was investigated using the radial collapse of thick-walled cylinders. GBCD of 1Cr18Ni9Ti austenitic stainless steel was optimized by thermo-mechanical treatment. The results showed that the proportion of special grain boundaries, especially the Σ3 grain boundaries, were increased from 27.8, 18.9 to 72.5, 55.8%, respectively. And the high-angle grain boundaries were replaced or interrupted by the low-angle grain boundaries and special grain boundary clusters. The results of optical microscopic examination showed that the shear bands mainly propagated along the clockwise direction, and the multiple shear bands influenced each other along with bifurcation and merging. Also, the number and spacing of the shear bands of the solution treatment specimen (ST specimen) and thermo-mechanical treatment specimen (TMT specimen) were the same, which meant that GBCD optimization had no obvious effect on the nucleation of shear bands. However, the lengths of ASBs in TMT specimen were much shorter than those of the ST specimen under the same deformation conditions. The slower propagation rate of ASBs in TMT specimen suggested that by introducing a large number of special grain boundaries, the GBCD optimization hindered the propagation of ASBs and improved the damage resistance under high-strain-rate loading. Also, voids were nucleated preferentially in the ASBs and coalesced along ASBs, and cracks formed finally.

Three-dimensional in situ characterization of phase transformation induced austenite grain refinement in nickel-titanium

Near-field and far-field high-energy diffraction microscopy and microcomputed tomography X-ray techniques were used to study a bulk single crystal nickel‑titanium shape memory alloy sample subjected to thermal cycling under a constant applied load. Three-dimensional in situ reconstructions of the austenite microstructure are presented, including the structure and distribution of emergent grain boundaries. After 1 cycle, the subgrain structure is significantly refined, and heterogeneous Σ3 and Σ9 grain boundaries emerge. The low volume and uneven dispersion of the emergent Σ boundaries across the volume show why previous transmission electron microscopy investigations of Σ grain boundary formation were inconsistent.

Combined effects of nonmetallic impurities and planned metallic dopants on grain boundary energy and strength

Most research on nanocrystalline alloys has been focused on planned doping of metals with other metallic elements, but nonmetallic impurities are also prevalent in the real world. In this work, we report on the combined effects of metallic dopants and nonmetallic impurities on grain boundary energy and strength using first-principles calculations, with a Σ5 (310) grain boundary in Cu chosen as a model system. We find a clear correlation between the grain boundary energy and the change in excess free volume of doped grain boundaries. A combination of a larger substitutional dopant and an interstitial impurity can fill the excess free volume more efficiently and further reduce the grain boundary energy. We also find that the strengthening effects of dopants and impurities are dominated by the electronic interactions between the host Cu atoms and the two types of dopant elements. For example, the significant competing effects of metal dopants such as Zr, Nb, and Mo with impurities on the grain boundary strength are uncovered from the density of states of the d electrons. As a whole, this work deepens the field's understanding of the interaction between metallic dopants and nonmetallic impurities on grain boundary properties, providing a guide for improving the thermal stability of materials while avoiding embrittling effects.

An Ab Initio Study of Connections between Tensorial Elastic Properties and Chemical Bonds in Σ5(210) Grain Boundaries in Ni₃Si.

Using quantum-mechanical methods we calculate and analyze (tensorial) anisotropic elastic properties of the ground-state configurations of interface states associated with 5(210) grain boundaries (GBs) in cubic L1-structure NiSi. We assess the mechanical stability of interface states with two different chemical compositions at the studied GB by checking rigorous elasticity-based Born stability criteria. In particular, we show that a GB variant containing both Ni and Si atoms at the interface is unstable with respect to shear deformation (one of the elastic constants, , is negative). This instability is found for a rectangular-parallelepiped supercell obtained when applying standard coincidence-lattice construction. Our elastic-constant analysis allowed us to identify a shear-deformation mode reducing the energy and, eventually, to obtain mechanically stable ground-state characterized by a shear-deformed parallelepiped supercell. Alternatively, we tested a stabilization of this GB interface state by Al substituents replacing Si atoms at the GB. We further discuss an atomistic origin of this instability in terms of the crystal orbital Hamilton population (COHP) and phonon dispersion calculations. We find that the unstable GB variant shows a very strong interaction between the Si atoms in the GB plane and Ni atoms in the 3rd plane off the GB interface. However, such bond reinforcement results in weakening of interaction between the Ni atoms in the 3rd plane and the Si atoms in the 5th plane making this GB variant mechanically unstable.

Antithermal mobility in Σ7 and Σ9 grain boundaries caused by stick-slip stagnation of ordered atomic motions about Coincidence Site Lattice atoms

Antithermal grain boundary migration is an interesting phenomenon that has been recently discovered. These grain boundaries behave opposite to what is expected of thermally activated grain boundary migration; the antithermal grain boundaries exhibit mobility that decreases with increasing temperature. Two recent studies have provided insight into important behaviors correlated with antithermal migration. O'Brien and Foiles (J Mater. Sci. Vol. 51, p. 6607–6623, 2016) demonstrated that the high mobility exhibited by an antithermal Σ7 grain boundary is enabled by ordered atomic motions. Ulomek and Mohles (Acta Mater. Vol. 103, p. 424–432, 2016) demonstrated that the thermal migration of a different Σ7 grain boundary exhibited a two-step migration process. In this work, we demonstrate that the antithermal temperature dependence exhibited by these types of grain boundaries is caused by a combination of these two discoveries. Specifically, ordered atomic motions about Coincidence Site Lattice atoms (atoms common to the lattices on either side of the grain boundary), seen by O'Brien and Foiles, are interrupted by additional thermal energy at higher temperature. This is the source of the two-step process seen by Ulomek and Mohles. This two-step process is akin to stick-slip behaviors observed in shear coupled grain boundary migration. As temperature is increased, the duration of the stagnant portion increases and the mobility decreases. This behavior is demonstrated through molecular dynamics simulations in nickel bicrystals over temperatures ranging from 100 to 1400 K for Σ7 and Σ9 grain boundaries. For these Σ7 and Σ9 grain boundaries, those that have ordered atomic mechanisms are almost exclusively antithermal, while those that do not have ordered atomic mechanisms are thermally activated.

Effect of different annealing temperatures on microstructures and properties of Cu–Sn Alloy

Through an EBSD analysis on the change characteristics of the microstructure of a spinning formed thin-walled Cu–Sn alloy cylinder which is annealed at 300 °C–600 °C for 2 h, it indicates that the grain size increases with the rise of annealing temperature and the size falls back at 400 °C. At 300 °C, the microstructure is mainly composed of deformed grains. With the progress of recrystallization, the deformed grains disappear first, and the number of substructures gradually reduces but always exists. In terms of the grain boundary, the subgrain boundaries gradually disappear and the Σ9 grain boundary at the secondary peak gradually transforms into the Σ3 grain boundary. At 300 °C, a {100}//Z0 fiber texture appears, but the general orientation of the grain is random at other temperatures. The detection of mechanical properties found that the elongation of Cu–Sn alloy increasing from 14% to 65% gradually and the yield strength (YS) and tensile strength (TS)decreasing to 282 MPa and 352 MPa respectively.